diff --git a/OdieSolutions/NRPy+_OdieGM_Examples_Edited_E6.ipynb b/OdieSolutions/NRPy+_OdieGM_Examples_Edited_E6.ipynb new file mode 100644 index 00000000..91039134 --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Examples_Edited_E6.ipynb @@ -0,0 +1,6162 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Examples\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "## Introduction:\n", + "Welcome to the Ordinary Differential Equation Solver Tutorial Examples notebook, wherin we will showcase a program that solves Ordinary Differential Equations with the intent of helping users see different ways to use it. \n", + "\n", + "This Ordinary Differential Equation Solver, affectionately known as \"Odie,\" takes a system of Ordinary Differential Equations (ODEs) with initial boundary conditions and solves it numerically. There are many ways to implement the code, but the primary method shown here produces a text file with the previously unknown functions' values at various sequential points. More details can be found about the technicalities behind Odie's operation in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook (for new users) and [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook (for a deep dive). It is recommended that users look at the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook for context by which to understand this one. \n", + "\n", + "This notebook has two primary parts: the Simple Example, [Step 2](#S2), and the Complicated Example, [Step 3](#S3), which showcase two ways of using Odie to solve Systems of Differential Equations. \n", + "\n", + "### Citations:\n", + "\n", + "\n", + "[5] https://www.dataquest.io/blog/read-file-python/ (Opening and reading CSV files)\n", + "\n", + "\n", + "[6] https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib (Changing size of plot)\n", + "\n", + "\n", + "[7] https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine (how to move up out of a Python directory)\n" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "f70c4a52", + "metadata": {}, + "source": [ + "1. [Step 1:](#S1) Compiling Code\n", + "\n", + "3. [Step 2:](#S2) Simple Problem Example\n", + "\n", + " 1. [Step 2a:](#S2a) Simple Problem Customization\n", + "\n", + " 5. [Step 2b:](#S2b) Simple Problem Code Compilation\n", + "\n", + " 6. [Step 2c:](#S2c) Simple Problem Results\n", + " \n", + " 6. [Step 2d:](#S2d) Simple Problem Analysis\n", + " \n", + " 6. [Step 2e:](#S2e) Multiple Run Examination\n", + " \n", + "7. [Step 3:](#S3) Complicated Problem Example\n", + "\n", + " 1. [Step 3a:](#S3a) Complicated Problem Customization\n", + "\n", + " 4. [Step 3b:](#S3b) Complicated Problem Code Compliation\n", + "\n", + " 6. [Step 3c:](#S3c) Complicated Problem Results\n", + " \n", + " 6. [Step 3d:](#S3d) Complicated Problem Analysis\n", + " \n", + " 6. [Step 3e:](#S3e) Complicated Problem Extension: Adams Bashforth and Hybrid Methods\n", + "\n", + "8. [Step 4:](#S4) Conclusion\n", + "\n", + "8. [Step 5:](#S5) Questions/Exercies\n", + "\n", + "9. [Step 6:](#S6) Output this notebook to $\\LaTeX$-formatted PDF file" + ] + }, + { + "cell_type": "markdown", + "id": "d8d59df2", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Step 1: Compiling Code \\[Back to [top](#toc)\\]\n", + "$$\\label{S1}$$\n", + "\n", + "#### The program needs to exist to run\n", + "\n", + "This section, while visually long, has essentially nothing for the user to look at. The notebook just compiles all the files it needs in these next few cells. Make sure to run them all before running the rest of the notebook. \n", + "\n", + "Users that wish to know specifics of what the code is doing should invistigate the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) and [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebooks as required. " + ] + }, + { + "cell_type": "markdown", + "id": "a71319cc", + "metadata": {}, + "source": [ + "In order to run Odie, which is a C-code, from within this Python-based jupyter notebook, we will need to rely on NRPy+'s C-code generation libraries. This notebook, while it is a tutorial, is not concerned with explaining the ins and outs of how to do this; that can be found in the various [nrpytutorial notebooks](https://github.com/zachetienne/nrpytutorial). (NOTE: If this is in nrpytutorial this link is probably unecessary). " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d9b4753f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = 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+ "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a0f04fd5", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "92d5f951", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b3d7c41c", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "struct constant_parameters { \n", + " int dimension; // number that says how many constants we have. \n", + " double rho;\n", + " // double parameter;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to hard code some limitations \n", + " // on some varaibles.\n", + " // Good for avoding some divide by zero errors, or going negative in a square root. \n", + " if (y[0] < 0) {\n", + " y[0] = 0;\n", + " }\n", + " // In this case, the TOV Equations, we need to make sure the pressure doesn't go negative.\n", + " // Physically, it cannot, but approximation methods can cross the P=0 line\n", + " // We just need a hard wall to prevent that. \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to have \n", + " // a special termination condition.\n", + " // Today we do. We terminate once the pressure hits zero, or goes below it. \n", + " // Notably we also consider ridiculously small pressures to be \"zero\" since we might be asymptotic. \n", + " if (y[0] < 1e-16) {\n", + " return 1;\n", + " } else {\n", + " return 0;\n", + " }\n", + " // return 1; for termination.\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + " // Sometimes we want to evaluate constants in the equation that change, \n", + " // but do not have derivative forms.\n", + " // Today, we do that for the total energy density. \n", + " params->rho = sqrt(y[0]) + y[0];\n", + " // The total energy density only depends on pressure. \n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + " // GSL-adapted evaluation function. \n", + " // It is possible to do this with one array, but GSL expects two. \n", + "\n", + " // Always check for exceptions first, then perform evaluations. \n", + " exception_handler(x,y);\n", + " const_eval(x,y,params);\n", + "\n", + " // Dereference the struct\n", + " double rho = (*(struct constant_parameters*)params).rho;\n", + " // double parameter = (*(struct constant_parameters*)params).parameter;\n", + " // WHY oh WHY GSL do you demand we use a VOID POINTER to the struct...?\n", + " // https://stackoverflow.com/questions/51052314/access-variables-in-struct-from-void-pointer\n", + " // Make sure to dereference every parameter within the struct so it can be used below. \n", + "\n", + " // This if statement is an example of a special condition, \n", + " // in this case at x=0 we have a divide by zero problem. \n", + " // Fortunately, we manually know what the derivatives should be.\n", + " // Alternatively, we could define piecewise equations this way. \n", + " if(x == 0) {\n", + " dydx[0] = 0; \n", + " dydx[1] = 0;\n", + " dydx[2] = 0;\n", + " dydx[3] = 1;\n", + " }\n", + " else {\n", + " dydx[0] = -((rho+y[0])*( (2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0] ))/(x*2.0*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[1] = ((2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0])/(x*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[2] = 4*3.1415926535897931160*x*x*rho;\n", + " dydx[3] = (y[3])/(x*sqrt(1.0-(2.0*y[2])/x));\n", + " // Visual Studio likes to complain that M_PI is not defined, even though it is. \n", + " // So we used 3.1415926535897931160. which is just M_PI printed out to extra digits.\n", + " // There was no observed change in the final product. \n", + " }\n", + " // This funciton is not guaranteed to work in all cases. For instance, we have manually \n", + " // made an exception for x=0, since evaluating at 0 produces infinities and NaNs. \n", + " // Be sure to declare any exceptions before running, both here and in exception_handler, \n", + " // depending on the kind of exception desired. \n", + "\n", + " return 0;\n", + " // GSL_SUCCESS is 0. We do not support fancy error codes like GSL. \n", + "}\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) // This function is another one passed using GSL's formulation. \n", + "// Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + " // y[0] = ...\n", + " // y[1] = ...\n", + " // This function is only used if there are known solutions. \n", + " // Notably this is not the case for the TOV equations. \n", + " // If you do put anything here, make SURE it has the same order as the differential equations. \n", + " // In the case of TOV, that would be Pressure, nu, mass, and r-bar, in that order. \n", + "\n", + " return 1;\n", + " // report \"success,\" what would have been GSL_SUCCESS in the GSL formulation. \n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " // be sure to have these MATCH the equations in diffy_Q_eval\n", + " y[0] = 0.016714611225000002; // Pressure, can be calcualated from central baryon density. \n", + " y[1] = 0.0; // nu\n", + " y[2] = 0.0; // mass\n", + " y[3] = 0.0; // r-bar\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + " // Reading parameters from the constant_parameters struct is rather difficult, since it exists\n", + " // in the higher order \"objects\" as a void pointer. So the user should declare what constants\n", + " // are what for ease of use, usually for printing in an algorithmic way.\n", + " c[0] = params->rho; // Total energy density. \n", + " // Add more as required. \n", + "}\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "a44be45c", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.0001; // the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = true;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"ooData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " // AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b2102df1", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "8257daa8", + "metadata": {}, + "source": [ + "\n", + "# Step 2: Simple Problem Example \\[Back to [top](#toc)\\]\n", + "$$\\label{S2}$$\n", + "\n", + "#### Always begin with something easy to grok.\n", + "\n", + "Our Simple Problem that we will use as a demonstration of the code is stated below.\n", + "\n", + "$$ \\frac{\\partial^2 u}{\\partial x^2} = u + x; u(0) = 2, \\frac{\\partial u(0)}{\\partial x} = -1$$\n", + "\n", + "This is a second order differential equation. We can split it up into two first-order equations.\n", + "\n", + "$$ u' = z ; u(0) = 2$$\n", + "$$ z' = u + x ; z(0) = -1$$\n", + "\n", + "Now it is in a form that the program can solve.\n", + "\n", + "The solution can be attained analytically, and it is\n", + "\n", + "$$ u = e^x + e^{-x} -x .$$" + ] + }, + { + "cell_type": "markdown", + "id": "6db13cbb", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 2a: Simple Problem Customization \\[Back to [top](#toc)\\]\n", + "$$\\label{S2a}$$\n", + "\n", + "#### Even the simplest problems need some setup. \n", + "\n", + "Here is where users can adjust information in the notebook to change how the program runs. These changes only apply to the Simple Example, the Complicated Example has its own sections. \n", + "\n", + "First, `nrpy_odiegm_user_methods.c`" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "a0b0e98f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "\n", + "struct constant_parameters { \n", + " int dimension; // number that says how many we have. \n", + " // double rho;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " return 0;\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + "\n", + " dydx[0] = y[1];\n", + " dydx[1] = y[0] + x;\n", + "\n", + " return 1;\n", + "}\n", + "\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) //This function is the other one passed using GSL's formulation. \n", + "//Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + "\n", + " y[0] = exp(x) + exp(-x) - x;\n", + " y[1] = exp(x) - exp(-x) - 1;\n", + "\n", + " return 1;\n", + " //report \"success\"\n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " y[0] = 2.0;\n", + " y[1] = -1.0;\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "068321d3", + "metadata": {}, + "source": [ + "Naturally in this simple example most of the functions are empty, but we do have a `knownQEval` known solution. \n", + "\n", + "Next, we specify the part of `nrpy_odiegm_main.c` that we can alter. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "90ff0093", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.05; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 2; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 20; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = true;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oSData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_euler;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_euler;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " // AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF.\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "1bc04a29", + "metadata": {}, + "source": [ + "We have chosen the worst method, Euler's method, to make it easier to see differences in the program. We're also not taking many steps so it can be easy to see them. \n", + "\n", + "The user of this notebook can feel free to adjust parameters above, such as changing the method or step size, the results should still carry over to the following sections so long as the system of equations itself isn't altered. " + ] + }, + { + "cell_type": "markdown", + "id": "23e36456", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 2b: Simple Problem Code Compilation \\[Back to [top](#toc)\\]\n", + "$$\\label{S2b}$$\n", + "\n", + "#### The solver proper is finally within our grasp. \n", + "\n", + "Below is how NRPy+ actually generates the runnable C-code from all the strings we've made in the previous sections. NRPy+ takes several argumetns, each one with its own important role:\n", + "\n", + "`includes`: this is where all the .h files that the programs rely on are declared, and why `#includes` was always commented out above. \n", + "\n", + "`prefunc`: includes all the files and functions and declarations that are not part of the main function. \n", + "\n", + "`desc`: contains a description of the code. \n", + "\n", + "`c_type`: what does the main function return? Usually int. \n", + "\n", + "`name`: what is the name of the main function? Usually just main. \n", + "\n", + "`params`: a place to put special parameters. Usually blank, including here. \n", + "\n", + "`body`: the actual body of the main function. \n", + "\n", + "Once all this is passed to NRPy+ properly, it will run the code itself. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "796bd7b3", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverSimple1 `...\n", + "(BENCH): Finished executing in 0.20 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Simple Example: u''=u+x Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverSimple1\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverSimple1\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the terminal output into a text file. " + ] + }, + { + "cell_type": "markdown", + "id": "090498c1", + "metadata": {}, + "source": [ + "So, what do we get when we run this code? Well..." + ] + }, + { + "cell_type": "markdown", + "id": "f7dfc378", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 2c: Simple Problem Results \\[Back to [top](#toc)\\]\n", + "$$\\label{S2c}$$\n", + "\n", + "#### If it isn't the consequences of my own actions.\n", + "\n", + "First, let's see what the terminal printed. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7207ed74", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 1.\n", + "Printing to file 'oSData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t2.00000000000000e+00,\tEquation 1:,\t-1.00000000000000e+00,\t\n", + "FINAL: Position:,\t1.00000000000000e+00,\tEquation 0:,\t2.04829627827785e+00,\tEquation 1:,\t1.32183139850209e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "62f2b1bb", + "metadata": {}, + "source": [ + "The actual data produced by the program is below. Note: if the user chose a large `SIZE` it will be a very long result that might even be suppressed. " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "3b089a2b", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 0:,\t2.00000000000000e+00,\tEquation 1:,\t-1.00000000000000e+00,\t\n", + "Errors:,\tEquation 0:,\t0.0,\tTruth:,\t2.00000000000000e+00,\tEquation 1:,\t0.0,\tTruth:,\t-1.00000000000000e+00,\t\n", + "Position:,\t5.00000000000000e-02,\tEquation 0:,\t1.95125000000000e+00,\tEquation 1:,\t-9.00000000000000e-01,\t\n", + "Errors:,\tEquation 0:,\t1.25052087673794e-03,\tTruth:,\t1.95250052087674e+00,\tEquation 1:,\t4.16718753100120e-05,\tTruth:,\t-8.99958328124690e-01,\t\n", + "Position:,\t1.00000000000000e-01,\tEquation 0:,\t1.90750078125000e+00,\tEquation 1:,\t-7.99875000000000e-01,\t\n", + "Errors:,\tEquation 0:,\t2.50755486160670e-03,\tTruth:,\t1.91000833611161e+00,\tEquation 1:,\t2.08500039688087e-04,\tTruth:,\t-7.99666499960312e-01,\t\n", + "Position:,\t1.50000000000000e-01,\tEquation 0:,\t1.86876171923828e+00,\tEquation 1:,\t-6.99374882812500e-01,\t\n", + "Errors:,\tEquation 0:,\t3.78049991505947e-03,\tTruth:,\t1.87254221915334e+00,\tEquation 1:,\t5.01149115725186e-04,\tTruth:,\t-6.98873733696775e-01,\t\n", + "Position:,\t2.00000000000000e-01,\tEquation 0:,\t1.83505470117218e+00,\tEquation 1:,\t-5.98248906152344e-01,\t\n", + "Errors:,\tEquation 0:,\t5.07881006597133e-03,\tTruth:,\t1.84013351123815e+00,\tEquation 1:,\t9.20911234531752e-04,\tTruth:,\t-5.97327994917812e-01,\t\n", + "Position:,\t2.50000000000000e-01,\tEquation 0:,\t1.80641416505280e+00,\tEquation 1:,\t-4.96245076660080e-01,\t\n", + "Errors:,\tEquation 0:,\t6.41203470635054e-03,\tTruth:,\t1.81282619975915e+00,\tEquation 1:,\t1.46971027641646e-03,\tTruth:,\t-4.94775366383663e-01,\t\n", + "Position:,\t3.00000000000000e-01,\tEquation 0:,\t1.78288717007295e+00,\tEquation 1:,\t-3.93109521580353e-01,\t\n", + "Errors:,\tEquation 0:,\t7.78985818477085e-03,\tTruth:,\t1.79067702825772e+00,\tEquation 1:,\t2.15010847463804e-03,\tTruth:,\t-3.90959413105715e-01,\t\n", + "Position:,\t3.50000000000000e-01,\tEquation 0:,\t1.76453349847523e+00,\tEquation 1:,\t-2.88585856527693e-01,\t\n", + "Errors:,\tEquation 0:,\t9.22213983674292e-03,\tTruth:,\t1.77375563831197e+00,\tEquation 1:,\t2.96531540223688e-03,\tTruth:,\t-2.85620541125456e-01,\t\n", + "Position:,\t4.00000000000000e-01,\tEquation 0:,\t1.75142578908539e+00,\tEquation 1:,\t-1.82414547764261e-01,\t\n", + "Errors:,\tEquation 0:,\t1.07189545915198e-02,\tTruth:,\t1.76214474367691e+00,\tEquation 1:,\t3.91919936989238e-03,\tTruth:,\t-1.78495348394369e-01,\t\n", + "Position:,\t4.50000000000000e-01,\tEquation 0:,\t1.74364970281536e+00,\tEquation 1:,\t-7.43322674023445e-02,\t\n", + "Errors:,\tEquation 0:,\t1.22906342965869e-02,\tTruth:,\t1.75594033711194e+00,\tEquation 1:,\t5.01630127074010e-03,\tTruth:,\t-6.93159661316044e-02,\t\n", + "Position:,\t5.00000000000000e-01,\tEquation 0:,\t1.74130412050950e+00,\tEquation 1:,\t3.59287600712968e-02,\t\n", + "Errors:,\tEquation 0:,\t1.39478099032635e-02,\tTruth:,\t1.75525193041276e+00,\tEquation 1:,\t6.26185091619796e-03,\tTruth:,\t4.21906109874948e-02,\t\n", + "Position:,\t5.50000000000000e-01,\tEquation 0:,\t1.74450137358838e+00,\tEquation 1:,\t1.48641421571816e-01,\t\n", + "Errors:,\tEquation 0:,\t1.57014546595011e-02,\tTruth:,\t1.76020282824788e+00,\tEquation 1:,\t7.66178591509234e-03,\tTruth:,\t1.56303207486909e-01,\t\n", + "Position:,\t6.00000000000000e-01,\tEquation 0:,\t1.75336750802546e+00,\tEquation 1:,\t2.64084391139718e-01,\t\n", + "Errors:,\tEquation 0:,\t1.75629284590710e-02,\tTruth:,\t1.77093043648454e+00,\tEquation 1:,\t9.22277315676490e-03,\tTruth:,\t2.73307164296483e-01,\t\n", + "Position:,\t6.50000000000000e-01,\tEquation 0:,\t1.76804258227497e+00,\tEquation 1:,\t3.82542819285453e-01,\t\n", + "Errors:,\tEquation 0:,\t1.95440234999462e-02,\tTruth:,\t1.78758660577491e+00,\tEquation 1:,\t1.09522329674269e-02,\tTruth:,\t3.93495052252880e-01,\t\n", + "Position:,\t7.00000000000000e-01,\tEquation 0:,\t1.78868099985316e+00,\tEquation 1:,\t5.04309037661255e-01,\t\n", + "Errors:,\tEquation 0:,\t2.16570114087249e-02,\tTruth:,\t1.81033801126189e+00,\tEquation 1:,\t1.28583660178122e-02,\tTruth:,\t5.17167403679067e-01,\t\n", + "Position:,\t7.50000000000000e-01,\tEquation 0:,\t1.81545187736113e+00,\tEquation 1:,\t6.29683280802451e-01,\t\n", + "Errors:,\tEquation 0:,\t2.39146919925577e-02,\tTruth:,\t1.83936656935369e+00,\tEquation 1:,\t1.49501830692086e-02,\tTruth:,\t6.44633463871660e-01,\t\n", + "Position:,\t8.00000000000000e-01,\tEquation 0:,\t1.84853944882461e+00,\tEquation 1:,\t7.58974426721010e-01,\t\n", + "Errors:,\tEquation 0:,\t2.63304437850842e-02,\tTruth:,\t1.87486989260969e+00,\tEquation 1:,\t1.72375376542367e-02,\tTruth:,\t7.76211964375246e-01,\t\n", + "Position:,\t8.50000000000000e-01,\tEquation 0:,\t1.88814350731617e+00,\tEquation 1:,\t8.92500758178940e-01,\t\n", + "Errors:,\tEquation 0:,\t2.89182765585470e-02,\tTruth:,\t1.91706178387472e+00,\tEquation 1:,\t1.97311617983241e-02,\tTruth:,\t9.12231919977265e-01,\t\n", + "Position:,\t9.00000000000000e-01,\tEquation 0:,\t1.93447988491719e+00,\tEquation 1:,\t1.03059074651861e+00,\t\n", + "Errors:,\tEquation 0:,\t3.16928859803585e-02,\tTruth:,\t1.96617277089755e+00,\tEquation 1:,\t2.24427048977398e-02,\tTruth:,\t1.05303345141635e+00,\t\n", + "Position:,\t9.50000000000000e-01,\tEquation 0:,\t1.98778097217119e+00,\tEquation 1:,\t1.17358385998104e+00,\t\n", + "Errors:,\tEquation 0:,\t3.46697105991531e-02,\tTruth:,\t2.02245068277035e+00,\tEquation 1:,\t2.53847758803005e-02,\tTruth:,\t1.19896863586135e+00,\t\n", + "Position:,\t1.00000000000000e+00,\tEquation 0:,\t2.04829627827785e+00,\tEquation 1:,\t1.32183139850209e+00,\t\n", + "Errors:,\tEquation 0:,\t3.78649913526337e-02,\tTruth:,\t2.08616126963049e+00,\tEquation 1:,\t2.85709887855103e-02,\tTruth:,\t1.35040238728760e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oSData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "77a8ed2d", + "metadata": {}, + "source": [ + "Note that lines alternate between reporting the estimated values and errors. When reading these files to report data, that needs to be taken into account. Speaking of, it's time to do that. " + ] + }, + { + "cell_type": "markdown", + "id": "c9058edc", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 2d: Simple Problem Analysis \\[Back to [top](#toc)\\]\n", + "$$\\label{S2d}$$\n", + "\n", + "#### The wall of text tells us something, we just have to go digging for it. \n", + "\n", + "First, Let's examine how the true values of $u$ and $u'$ compare to the estimated ones by using Python's matplotlib to plot it out. " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "54333d8f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "# csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "\n", + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " else:\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " i = i+1\n", + "\n", + "# Next we plot it all using matplotlib. \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Exact and Calculated for Simple Problem')\n", + "ax.plot(positionList, truthList0, color='r', label=\"Exact\")\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"Calculated\")\n", + "ax.plot(positionList, truthList1, color='r', marker = 'o')\n", + "ax.plot(positionList, calculatedList1, color='b', marker = 'o')\n", + "\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "60ba8ace", + "metadata": {}, + "source": [ + "References: [1](#1) (reading files), [2](#2) (figure size), and [3](#3) (file access) \n", + "\n", + "The line with cirlces is $u'$, while the one without is $u$ itself. If the Euler method was used, as was set by default, we should see some clear divergence by the end of the procedure: the values start out nearly the same between calculated and exact but slowly diverge. Methods with orders that are much higher than Euler's will produce no discernable difference between the two graphs, everything will look blue. Which is not to say the result is perfect, merely that the difference is not discernable at this scale.\n", + "\n", + "Therefore we usually don't try to compare data to truth this way, we instead look at the errors directly. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "9e3ad2af", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " errorList0.append(float(row[2]))\n", + " errorList1.append(float(row[6]))\n", + " i = i+1\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Error')\n", + "ax.set_title('Error for Simple Problem')\n", + "ax.plot(positionList, errorList0, color='r', label = \"function\")\n", + "ax.plot(positionList, errorList1, color='r', marker = 'o', label = \"derivative\")\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying. \n", + "fig.set_size_inches(10,10)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "62e4326d", + "metadata": {}, + "source": [ + "Admittedly, the above graph isn't particuarly illumiating in most cases, it genreally just shows that errors rise with time. The program reports error in an exact sense: it can be positive or negative and indicates precisely how far off from the truth the result was. Often, however, we care less about that and care more about the relative error, since that can be plotted on a logarithmic scale to tell us to how many significant figures our program matches the truth. \n", + "\n", + "In this case, we define relative error as shown below.\n", + "\n", + "$$ \\left| \\frac{Truth - Calculated}{Truth} \\right| $$\n", + "\n", + "The errorr reported by the program is just $Truth - Calculated$. But no worries, this is very simple to resolve, for numpy can take the arrays we made and do operations on them. Like so..." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "d870165d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np # numpy, for doing math with our data. \n", + "\n", + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " errorList0.append(float(row[2]))\n", + " errorList1.append(float(row[6]))\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " i = i+1\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Relative Error')\n", + "ax.set_title ('Relative Error for Simple Problem')\n", + "ax.plot(positionList, abs(np.array(errorList0)/np.array(truthList0)), color='r', label=\"function\")\n", + "ax.plot(positionList, abs(np.array(errorList1)/np.array(truthList1)), color='r', marker = 'o',label = \"derivative\")\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying. \n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "0940b78c", + "metadata": {}, + "source": [ + "This tells us a lot more than the simple error plot! First of all, assuming the parameters have not been adjusted by the user, we can see clearly that the error starts at around 1e-3 and grows to 1e-2. Naturally this is not very good, less than 2 sig figs of agreement at the end, but this is Euler's method, we know it's not very good, we specifically chose it so we could visually see features on the full scale. \n", + "\n", + "One thing we do note is that the errors for the function $u$ are well behaved and don't do anything unusual, slowly growing as is to be expected. However, the errors for $u'$ spike in the middle! Why is this? Well, if we look at how $u'$ itself behaves in the first graph, that is where it crosses the axis—that is, $u'$=0 at some point. As the values get closer to zero, they get smaller and smaller, and thus the relative error between said values increases markedly. We could not see this feature in the direct error plot, but here it's on full display! Being aware of points where functions go to zero is an important part of analyzing them properly, and spikes like this in the error can be used to find them. \n", + "\n", + "These are generally the three graphs we make from one run of the program. However, there is more informaiton we can glean from running it multiple times. " + ] + }, + { + "cell_type": "markdown", + "id": "1045d7b4", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 2e: Multiple-Run Examination \\[Back to [top](#toc)\\]\n", + "$$\\label{S2e}$$\n", + "\n", + "#### Sometimes doing it once just won't cut it.\n", + "\n", + "Validation of the program can be done if it's run multiple times. In order to demonstrate this validation, we will run the program two times; both times using the RK4 method, but once at 0.01 step size, and another time at 0.02. Doing this is a simple as adjusting `nrpy_odiegm_main_c_modifiable` and calling NRPy+'s compiler again. \n", + "\n", + "Note: if running these cells independently, be sure to run the rest of this step first so it doesn't try to solve the system outlined in the latter sections of this notebook. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "5e9a6e14", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverSimple2 `...\n", + "(BENCH): Finished executing in 0.20 seconds.\n" + ] + } + ], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.01; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 2; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = true;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"RKData01.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " // AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF.\n", + "\n", + "\"\"\"\n", + "\n", + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # what \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # prefunctions are functions declared outside main.\n", + " # the specifics of what go here were declared above. \n", + " \n", + " desc = \"Simple Example: u''=u+x Solver\"\n", + " # just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # what does main return?\n", + " \n", + " name = \"main\"\n", + " # will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined in the customization section.\n", + " # Anything that isn't red indicates where we are inserting something, such as the butcherTable or step size. \n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "os.chdir(\"../\")\n", + "# return to parent directory\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverSimple2\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverSimple2\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "4c534cc0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverSimple3 `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.02; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 2; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 50; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = true;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"RKData02.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " // AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF.\n", + "\n", + "\"\"\"\n", + "\n", + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Simple Example: u''=u+x Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "os.chdir(\"../\")\n", + "# Return to parent directory\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverSimple3\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverSimple3\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "2108f41f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "\n", + "# \"a\" appended to the front of lists to be used for the second data set.\n", + "# Truth list is irrelevant, the value is the same for both. \n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('RKData01.txt') as f: # shenangians required to access the previous file. \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " else:\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " i = i+1\n", + "i = 0\n", + "with open('RKData02.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " i = i+1\n", + "\n", + "\n", + "# Next we plot it all using matplotlib. \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Exact and Calculated at Two Different Step Sizes')\n", + "ax.plot(positionList, truthList0, color='r', label=\"Exact\")\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"Calculated 0.01\")\n", + "ax.plot(apositionList, acalculatedList0, color='g', label=\"Calculated 0.02\")\n", + "ax.plot(positionList, truthList1, color='r', marker = 'o')\n", + "ax.plot(positionList, calculatedList1, color='b', marker = 'o')\n", + "ax.plot(apositionList, acalculatedList1, color='g', marker = 'o')\n", + "\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "7a1968d4", + "metadata": {}, + "source": [ + "Naturally, viewing it from the bird's eye view reveales absolutely nothing, as the exact, 0.01 step, and 0.02 step results are all essentially right on top of each other. We can tell that the resolution is different only because the dots use to mark $u'$ values are not in the same locations along the line. We have to examine the log plot to get anything useful out of this. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "0fa17036", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "\n", + "# \"a\" appended to the front of lists to be used for the second data set.\n", + "# Truth list matters now as we need to be calculating relative errors.\n", + "apositionList = []\n", + "atruthList0 = []\n", + "atruthList1 = []\n", + "aerrorList0 = []\n", + "aerrorList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('RKData01.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " errorList0.append(float(row[2]))\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " errorList1.append(float(row[6]))\n", + " i = i+1\n", + "i = 0\n", + "with open('RKData02.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " apositionList.append(float(row[1]))\n", + " else:\n", + " atruthList0.append(float(row[4]))\n", + " atruthList1.append(float(row[8]))\n", + " aerrorList0.append(float(row[2]))\n", + " aerrorList1.append(float(row[6]))\n", + " i = i+1\n", + "\n", + "# Next we plot it all using matplotlib. \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Relative Error')\n", + "ax.set_title('Relative Errors at Two Different Step Sizes')\n", + "ax.plot(positionList, abs(np.array(errorList0)/np.array(truthList0)), color='r', label = \"0.01 step\")\n", + "ax.plot(positionList, abs(np.array(errorList1)/np.array(truthList1)), color='r', marker = 'o')\n", + "ax.plot(apositionList, abs(np.array(aerrorList0)/np.array(atruthList0)), color='g', label = \"0.02 step\")\n", + "ax.plot(apositionList, abs(np.array(aerrorList1)/np.array(atruthList1)), color='g', marker = 'o')\n", + "\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "fig.title = 'Title'\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "3d861164", + "metadata": {}, + "source": [ + "We note the very curious result that while the errors are different in magnitude, their shape is virtually identical. The fact that 0.02 has more error than 0.01 is expected: smaller step size leads to higher resolution. But it almost looks as though there is a relaiton between the two errors. That is because there is a relation, that relation is based on the order of the error itself. Adjusting the step size by a factor of two should introduce an error difference of around $2^m$, where $m$ is the order of the error. in this case, $m$ is 4, so we should see error adjustments by a factor of 16. Do we? \n", + "\n", + "The best way to test is just to plot it again, but scale one of the values by 16." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "917e7f4f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "\n", + "# \"a\" appended to the front of lists to be used for the second data set.\n", + "# Truth list matters now as we need to be calculating relative errors.\n", + "apositionList = []\n", + "atruthList0 = []\n", + "atruthList1 = []\n", + "aerrorList0 = []\n", + "aerrorList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('RKData01.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " errorList0.append(float(row[2]))\n", + " errorList1.append(float(row[6]))\n", + " i = i+1\n", + "i = 0\n", + "with open('RKData02.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " apositionList.append(float(row[1]))\n", + " else:\n", + " atruthList0.append(float(row[4]))\n", + " atruthList1.append(float(row[8]))\n", + " aerrorList0.append(float(row[2]))\n", + " aerrorList1.append(float(row[6]))\n", + " i = i+1\n", + "\n", + "# Next we plot it all using matplotlib. \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Relative Error')\n", + "ax.set_title('Scaled Relative Errors at Two Different Step Sizes')\n", + "ax.plot(positionList, abs(np.array(errorList0)/np.array(truthList0)), color='r', label = \"0.01 step\")\n", + "ax.plot(positionList, abs(np.array(errorList1)/np.array(truthList1)), color='r', marker = 'o')\n", + "ax.plot(apositionList, abs(np.array(aerrorList0)/np.array(atruthList0)/16.0), color='g', label = \"0.02 step / 16\")\n", + "ax.plot(apositionList, abs(np.array(aerrorList1)/np.array(atruthList1)/16.0), color='g', marker = 'o')\n", + "\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "fig.title = 'Title'\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "e92782fe", + "metadata": {}, + "source": [ + "The scaling factor of 16 has made it so the two error plots are more or less right on top of each other. They agree remarkably, even near the spike as $u'$ approaches zero. \n", + "\n", + "This is effectively a validation check for the RK4 method itself—is it consistent with its supposed fourth-order accuracy? As we can see here, yes, absolutely. Everything matches. With that, we consider the Simple Example complete. We can now move on to a more complciated example, one where the truth is not known. \n", + "\n", + "This exact method was used to valudate accumulation error for the vast majority of available methods. This is admittedly only a visual validation of the data, but it is a pretty clear one. This validation fails at 8th order, for it becomes too difficult to get a smooth values that aren't interfered with by roundoff error. \n", + "\n", + "The user is enocuraged to edit the above code to test out different order methods, to see by what factor their relative errors differ. " + ] + }, + { + "cell_type": "markdown", + "id": "04ed9d70", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 3: Complicated Problem Example \\[Back to [top](#toc)\\]\n", + "$$\\label{S3}$$\n", + "\n", + "#### Don't hang up yet, I'm not done.\n", + "\n", + "The program is more than capable of handling questions that are far more complicated than a simple second-order differential equation. For instance, in General Relativity there are a sequence of equations called the TOV equations, the primary instance of which is described on wikipedia [here](https://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_equation) for those who want more information. In genreal, the TOV equations represent a relativistic picture of a spherically symmetric star with respect to the radius. \n", + "\n", + "The specifics of why we wish to solve the TOV equations are unimportant, what is important is the form they take. There are many ways to state and evaluate them, but the one we will implement here is given by the following.\n", + "\n", + "$$\n", + "\\boxed{\n", + "\\begin{matrix}\n", + "\\frac{dP}{dr} &=& - \\frac{1}{r} \\left( \\frac{\\rho + P}{2} \\right) \\left(\\frac{2 m}{r} + 8 \\pi r^2 P\\right) \\left(1 - \\frac{2 m}{r}\\right)^{-1} \\\\\n", + "\\frac{d \\nu}{d r} &=& \\frac{1}{r}\\left(1 - \\frac{2 m}{r}\\right)^{-1} \\left(\\frac{2 m}{r} + 8 \\pi r^2 P\\right) \\\\\n", + "\\frac{m(r)}{dr} &=& 4\\pi r^2 \\rho(r) \\\\\n", + "\\frac{d\\bar{r}(r)}{dr} &=& \\left(1 - \\frac{2m}{r} \\right)^{-1/2} \\frac{\\bar{r}(r)}{r}\n", + "\\end{matrix}\n", + "}\n", + "$$\n", + "\n", + "This is taken from the soon-to-be-depricated [NRPy+ TOV solver](http://localhost:8889/notebooks/Tutorial-ADM_Initial_Data-TOV.ipynb). (NOTE: link will either need to be changed or removed when this is added to nrpytutorial). $P$ is pressure, $\\nu$ is related to the curved nature of spacetime, $m$ is the total enclosed mass of the star, and $\\bar r$ is the isotropic radius (non-normalized). Though, really, as an example the physical meaning of the results are unimportant except for justifying some of the limitations we apply. \n", + "\n", + "In various implementations and models, the function $\\rho$ (energy density) can vary. In our implementation here, we treat it as\n", + "\n", + "$$ \\rho(r) = \\sqrt{P} + P, $$\n", + "\n", + "which we will report as a separate constant, making use of Odie's functionality in this regard. For completeness, a fuller definition of $\\rho(r)$ follows.\n", + "\n", + "$$ \\rho(r) = (P/K)^{1/\\Gamma} (1 + \\frac{P}{(P/K)^{1/\\Gamma} (\\Gamma - 1)})$$\n", + "\n", + "However, in our implementation $K$=1 and $\\Gamma = 2$ so it quickly reduces to our original declaration. (In actual implementations $K$ and $\\Gamma$ themselves could vary as well, generally turning this equation into a piecewise one). \n", + "\n", + "Another thing we need is initial conditions. The pressure has to be specified ahead of time, but all other values start at zero. In our case, Pressure is 0.016714611225000002. \n", + "\n", + "With all this, we have 4 differential equations and 1 constant we wish to report. We also need to consider our boundary conditions. Generally, we start from the center of the star at $r$=0. This, naturally, will provide some issues as the solver will run into divide by zero errors if it tries to evaluate any point there. However, in our declaration we will demonstrate how to avoid this issue, as well as avoiding problems that will arise if, say, the pressure goes negative due to an estimation error and makes the energy density `NaN`, which breaks everything. It can all be handled in the program so long as it is implemented properly. \n", + "\n", + "Note that unlike the Simple Problem, we do not know what the answer should be ahead of time, so there will be no relative error reporting this time around—but we will still have other forms of analysis. \n", + "\n", + "Furthermore, unlike last time, we will demonstrate the use of adaptive time stepping with this example. " + ] + }, + { + "cell_type": "markdown", + "id": "b0805b10", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 3a: Complicated Problem Customization \\[Back to [top](#toc)\\]\n", + "$$\\label{S3a}$$\n", + "\n", + "#### Curiously not much more complicated than the simple version of this section. \n", + "\n", + "Here is where users can adjust information in the notebook to adjust how the program runs. These changes only apply to the Complicated Example, the Simple Example has its own customization section. \n", + "\n", + "First, the `nrpy_odiegm_user_methods.c`." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "9e200082", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "\n", + "struct constant_parameters { \n", + " int dimension; // number that says how many we have. \n", + " double rho;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to hard code some limitations \n", + " // on some varaibles.\n", + " // Good for avoding some divide by zero errors, or going negative in a square root. \n", + " if (y[0] < 0) {\n", + " y[0] = 0;\n", + " }\n", + " // In this case, the TOV Equations, we need to make sure the pressure doesn't go negative.\n", + " // Physically, it cannot, but approximation methods can cross the P=0 line\n", + " // We just need a hard wall to prevent that. \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to have \n", + " // a special termination condition.\n", + " // Today we do. We terminate once the pressure hits zero, or goes below it. \n", + " // Notably we also consider ridiculously small pressures to be \"zero\" since we might be asymptotic. \n", + " if (y[0] < 1e-16) {\n", + " return 1;\n", + " } else {\n", + " return 0;\n", + " }\n", + " // return 1; for termination.\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + " // Sometimes we want to evaluate constants in the equation that change, \n", + " // but do not have derivative forms.\n", + " // Today, we do that for the total energy density. \n", + " params->rho = sqrt(y[0]) + y[0];\n", + " // The total energy density only depends on pressure. \n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + " // GSL-adapted evaluation function. \n", + " // It is possible to do this with one array, but GSL expects two. \n", + "\n", + " // Always check for exceptions first, then perform evaluations. \n", + " exception_handler(x,y);\n", + " const_eval(x,y,params);\n", + "\n", + " // Dereference the struct\n", + " double rho = (*(struct constant_parameters*)params).rho;\n", + " // double parameter = (*(struct constant_parameters*)params).parameter;\n", + " // WHY oh WHY GSL do you demand we use a VOID POINTER to the struct...?\n", + " // https://stackoverflow.com/questions/51052314/access-variables-in-struct-from-void-pointer\n", + " // Make sure to dereference every parameter within the struct so it can be used below. \n", + "\n", + " // This if statement is an example of a special condition, \n", + " // in this case at x=0 we have a divide by zero problem. \n", + " // Fortunately, we manually know what the derivatives should be.\n", + " // Alternatively, we could define piecewise equations this way. \n", + " if(x == 0) {\n", + " dydx[0] = 0; \n", + " dydx[1] = 0;\n", + " dydx[2] = 0;\n", + " dydx[3] = 1;\n", + " }\n", + " else {\n", + " dydx[0] = -((rho+y[0])*( (2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0] ))/(x*2.0*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[1] = ((2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0])/(x*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[2] = 4*3.1415926535897931160*x*x*rho;\n", + " dydx[3] = (y[3])/(x*sqrt(1.0-(2.0*y[2])/x));\n", + " // Visual Studio likes to complain that M_PI is not defined, even though it is. \n", + " // So we used 3.1415926535897931160. which is just M_PI printed out to extra digits.\n", + " // There was no observed change in the final product. \n", + " }\n", + " // This funciton is not guaranteed to work in all cases. For instance, we have manually \n", + " // made an exception for x=0, since evaluating at 0 produces infinities and NaNs. \n", + " // Be sure to declare any exceptions before running, both here and in exception_handler, \n", + " // depending on the kind of exception desired. \n", + "\n", + " return 0;\n", + " // GSL_SUCCESS is 0. We do not support fancy error codes like GSL. \n", + "}\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) // This function is another one passed using GSL's formulation. \n", + "// Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + " // y[0] = ...\n", + " // y[1] = ...\n", + " // This function is only used if there are known solutions. \n", + " // Notably this is not the case for the TOV equations. \n", + " // If you do put anything here, make SURE it has the same order as the differential equations. \n", + " // In the case of TOV, that would be Pressure, nu, mass, and r-bar, in that order. \n", + "\n", + " return 1;\n", + " // report \"success,\" what would have been GSL_SUCCESS in the GSL formulation. \n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " // be sure to have these MATCH the equations in diffy_Q_eval\n", + " y[0] = 0.016714611225000002; // Pressure, can be calcualated from central baryon density. \n", + " y[1] = 0.0; // nu\n", + " y[2] = 0.0; // mass\n", + " y[3] = 0.0; // r-bar\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + " // Reading parameters from the constant_parameters struct is rather difficult, since it exists\n", + " // in the higher order \"objects\" as a void pointer. So the user should declare what constants\n", + " // are what for ease of use, usually for printing in an algorithmic way.\n", + " c[0] = params->rho; // Total energy density. \n", + " // Add more as required. \n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "782087ad", + "metadata": {}, + "source": [ + "Note that we are now using *all* the functions in `nrpy_odiegm_user_methods.c` save for `known_q_eval`. \n", + "\n", + "Now the leading part of `nrpy_odiegm_main.c`..." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "ffce7883", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "ce825567", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 3b: Complicated Problem Code Compilation \\[Back to [top](#toc)\\]\n", + "$$\\label{S3b}$$\n", + "\n", + "#### The snakes complain that there's nothing different to do here. \n", + "\n", + "As with the simple example, we compile the C-code and run it via NRPy+'s methods. Very little is changed." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "555a60e1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated1 `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above.\n", + "\n", + "os.chdir(\"../\")\n", + "# Return to parent directory\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated1\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverComplicated1\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "markdown", + "id": "fff7a970", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 3c: Complicated Problem Results \\[Back to [top](#toc)\\]\n", + "$$\\label{S3c}$$\n", + "\n", + "#### If it isn't the consequences of my own actions. ...Again. \n", + "\n", + "First, let's see what the terminal printed. " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "ad9bf613", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 4.\n", + "Printing to file 'oCData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t1.67146112250000e-02,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\tEquation 3:,\t0.00000000000000e+00,\tConstant 0:,\t1.45999611225000e-01,\t\n", + "FINAL: Position:,\t9.56604504673252e-01,\tEquation 0:,\t0.00000000000000e+00,\tEquation 1:,\t4.59952331801525e-01,\tEquation 2:,\t1.40503033677089e-01,\tEquation 3:,\t1.15746784583246e+00,\tConstant 0:,\t0.00000000000000e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "931681d4", + "metadata": {}, + "source": [ + "Do note that we now report the constant as well! \n", + "\n", + "The actual data produced by the program is below. Note: if the user altered the code and chose a setup that resulted in a very long set of data, it will be cut off by the jupyter notebook. The file itself will still exist, though. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "1b3f1983", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 0:,\t1.67146112250000e-02,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\tEquation 3:,\t0.00000000000000e+00,\tConstant 0:,\t1.45999611225000e-01,\t\n", + "Position:,\t1.00000000000000e-05,\tEquation 0:,\t1.67146112179846e-02,\tEquation 1:,\t8.62303740841765e-11,\tEquation 2:,\t6.11561741308734e-16,\tEquation 3:,\t1.00000000003037e-05,\tConstant 0:,\t1.45999611190853e-01,\t\n", + "Position:,\t1.40613765222082e-05,\tEquation 0:,\t1.67146112114523e-02,\tEquation 1:,\t1.66521252757759e-10,\tEquation 2:,\t1.70029321224058e-15,\tEquation 3:,\t1.40613765230553e-05,\tConstant 0:,\t1.45999611159058e-01,\t\n", + "Position:,\t1.81227530444164e-05,\tEquation 0:,\t1.67146112027150e-02,\tEquation 1:,\t2.73915401060339e-10,\tEquation 2:,\t3.64009590207511e-15,\tEquation 3:,\t1.81227530462325e-05,\tConstant 0:,\t1.45999611116530e-01,\t\n", + "Position:,\t2.28342718558516e-05,\tEquation 0:,\t1.67146111898162e-02,\tEquation 1:,\t4.32460912130805e-10,\tEquation 2:,\t7.28118071572920e-15,\tEquation 3:,\t2.28342718594872e-05,\tConstant 0:,\t1.45999611053746e-01,\t\n", + "Position:,\t2.82621780878562e-05,\tEquation 0:,\t1.67146111712774e-02,\tEquation 1:,\t6.60330876826210e-10,\tEquation 2:,\t1.38056606556639e-14,\tEquation 3:,\t2.82621780947529e-05,\tConstant 0:,\t1.45999610963509e-01,\t\n", + "Position:,\t3.44452214047604e-05,\tEquation 0:,\t1.67146111453607e-02,\tEquation 1:,\t9.78886069517003e-10,\tEquation 2:,\t2.49935099209746e-14,\tEquation 3:,\t3.44452214172496e-05,\tConstant 0:,\t1.45999610837362e-01,\t\n", + "Position:,\t4.14215673965997e-05,\tEquation 0:,\t1.67146111099822e-02,\tEquation 1:,\t1.41373963201445e-09,\tEquation 2:,\t4.34630193771660e-14,\tEquation 3:,\t4.14215674183221e-05,\tConstant 0:,\t1.45999610665160e-01,\t\n", + "Position:,\t4.92279751252972e-05,\tEquation 0:,\t1.67146110626807e-02,\tEquation 1:,\t1.99514623223378e-09,\tEquation 2:,\t7.29585551308201e-14,\tEquation 3:,\t4.92279751617655e-05,\tConstant 0:,\t1.45999610434923e-01,\t\n", + "Position:,\t5.78999542358485e-05,\tEquation 0:,\t1.67146110005824e-02,\tEquation 1:,\t2.75842624634887e-09,\tEquation 2:,\t1.18706627873886e-13,\tEquation 3:,\t5.78999542951888e-05,\tConstant 0:,\t1.45999610132664e-01,\t\n", + "Position:,\t6.74718726692314e-05,\tEquation 0:,\t1.67146109203671e-02,\tEquation 1:,\t3.74439190006773e-09,\tEquation 2:,\t1.87848874893575e-13,\tEquation 3:,\t6.74718727631406e-05,\tConstant 0:,\t1.45999609742222e-01,\t\n", + "Position:,\t7.79770516309104e-05,\tEquation 0:,\t1.67146108182327e-02,\tEquation 1:,\t4.99977629326491e-09,\tEquation 2:,\t2.89961765644071e-13,\tEquation 3:,\t7.79770517758736e-05,\tConstant 0:,\t1.45999609245091e-01,\t\n", + 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1:,\t4.59590741387683e-01,\tEquation 2:,\t1.40502602537623e-01,\tEquation 3:,\t1.15627174252590e+00,\tConstant 0:,\t9.04089116987655e-05,\t\n", + "Position:,\t9.55827956126375e-01,\tEquation 0:,\t7.13969023182673e-09,\tEquation 1:,\t4.59614353465648e-01,\tEquation 2:,\t1.40502656949613e-01,\tEquation 3:,\t1.15634977293682e+00,\tConstant 0:,\t8.45038273876010e-05,\t\n", + "Position:,\t9.55882151118386e-01,\tEquation 0:,\t6.17694011778280e-09,\tEquation 1:,\t4.59637962319433e-01,\tEquation 2:,\t1.40502707693730e-01,\tEquation 3:,\t1.15642780327385e+00,\tConstant 0:,\t7.85996888719739e-05,\t\n", + "Position:,\t9.55936346110397e-01,\tEquation 0:,\t5.28401232065001e-09,\tEquation 1:,\t4.59661567948959e-01,\tEquation 2:,\t1.40502754769727e-01,\tEquation 3:,\t1.15650583353658e+00,\tConstant 0:,\t7.26964961404040e-05,\t\n", + "Position:,\t9.55981851022408e-01,\tEquation 0:,\t4.58816745367172e-09,\tEquation 1:,\t4.59681385963414e-01,\tEquation 2:,\t1.40502791463977e-01,\tEquation 3:,\t1.15657135171423e+00,\tConstant 0:,\t6.77406011418805e-05,\t\n", + "Position:,\t9.56027355934419e-01,\tEquation 0:,\t3.94150812567396e-09,\tEquation 1:,\t4.59701201704620e-01,\tEquation 2:,\t1.40502825571831e-01,\tEquation 3:,\t1.15663686983896e+00,\tConstant 0:,\t6.27853728845602e-05,\t\n", + "Position:,\t9.56072860846430e-01,\tEquation 0:,\t3.34401598143476e-09,\tEquation 1:,\t4.59721015172532e-01,\tEquation 2:,\t1.40502857093146e-01,\tEquation 3:,\t1.15670238791054e+00,\tConstant 0:,\t5.78308113773899e-05,\t\n", + "Position:,\t9.56112815656182e-01,\tEquation 0:,\t2.85992140685520e-09,\tEquation 1:,\t4.59738410174837e-01,\tEquation 2:,\t1.40502882637215e-01,\tEquation 3:,\t1.15675991488876e+00,\tConstant 0:,\t5.34810929406008e-05,\t\n", + "Position:,\t9.56152770465933e-01,\tEquation 0:,\t2.41370529559939e-09,\tEquation 1:,\t4.59755803424498e-01,\tEquation 2:,\t1.40502906187004e-01,\tEquation 3:,\t1.15681744182566e+00,\tConstant 0:,\t4.91318885203126e-05,\t\n", + "Position:,\t9.56192725275685e-01,\tEquation 0:,\t2.00535522879300e-09,\tEquation 1:,\t4.59773194921486e-01,\tEquation 2:,\t1.40502927742414e-01,\tEquation 3:,\t1.15687496872106e+00,\tConstant 0:,\t4.47831981574868e-05,\t\n", + "Position:,\t9.56226615963092e-01,\tEquation 0:,\t1.68865455831096e-09,\tEquation 1:,\t4.59787945458382e-01,\tEquation 2:,\t1.40502944462885e-01,\tEquation 3:,\t1.15692376446650e+00,\tConstant 0:,\t4.10949309008324e-05,\t\n", + "Position:,\t9.56260506650499e-01,\tEquation 0:,\t1.39918147958312e-09,\tEquation 1:,\t4.59802694734212e-01,\tEquation 2:,\t1.40502959748298e-01,\tEquation 3:,\t1.15697256018186e+00,\tConstant 0:,\t3.74070335108572e-05,\t\n", + "Position:,\t9.56294397337906e-01,\tEquation 0:,\t1.13692841751913e-09,\tEquation 1:,\t4.59817442748958e-01,\tEquation 2:,\t1.40502973598593e-01,\tEquation 3:,\t1.15702135586705e+00,\tConstant 0:,\t3.37195060692749e-05,\t\n", + "Position:,\t9.56322766934847e-01,\tEquation 0:,\t9.38322792930786e-10,\tEquation 1:,\t4.59829787212976e-01,\tEquation 2:,\t1.40502984089040e-01,\tEquation 3:,\t1.15706220228354e+00,\tConstant 0:,\t3.06329933131259e-05,\t\n", + "Position:,\t9.56351136531787e-01,\tEquation 0:,\t7.58781072031483e-10,\tEquation 1:,\t4.59842130793302e-01,\tEquation 2:,\t1.40502993573792e-01,\tEquation 3:,\t1.15710304867875e+00,\tConstant 0:,\t2.75467398315172e-05,\t\n", + "Position:,\t9.56379506128728e-01,\tEquation 0:,\t5.98298814863107e-10,\tEquation 1:,\t4.59854473489924e-01,\tEquation 2:,\t1.40503002052815e-01,\tEquation 3:,\t1.15714389505264e+00,\tConstant 0:,\t2.44607457812629e-05,\t\n", + "Position:,\t9.56402615975770e-01,\tEquation 0:,\t4.81653578696220e-10,\tEquation 1:,\t4.59864527185868e-01,\tEquation 2:,\t1.40503008216475e-01,\tEquation 3:,\t1.15717716845468e+00,\tConstant 0:,\t2.19470891065820e-05,\t\n", + "Position:,\t9.56425725822813e-01,\tEquation 0:,\t3.77650312499789e-10,\tEquation 1:,\t4.59874580295399e-01,\tEquation 2:,\t1.40503013712719e-01,\tEquation 3:,\t1.15721044184249e+00,\tConstant 0:,\t1.94336046726006e-05,\t\n", + "Position:,\t9.56448835669855e-01,\tEquation 0:,\t2.86286619863346e-10,\tEquation 1:,\t4.59884632818509e-01,\tEquation 2:,\t1.40503018541528e-01,\tEquation 3:,\t1.15724371521604e+00,\tConstant 0:,\t1.69202927837624e-05,\t\n", + "Position:,\t9.56467068976188e-01,\tEquation 0:,\t2.23120747987046e-10,\tEquation 1:,\t4.59892563687487e-01,\tEquation 2:,\t1.40503021880337e-01,\tEquation 3:,\t1.15726996737508e+00,\tConstant 0:,\t1.49374500383203e-05,\t\n", + "Position:,\t9.56486041087612e-01,\tEquation 0:,\t1.65745339002071e-10,\tEquation 1:,\t4.59900815524048e-01,\tEquation 2:,\t1.40503024913340e-01,\tEquation 3:,\t1.15729728324993e+00,\tConstant 0:,\t1.28743779154903e-05,\t\n", + "Position:,\t9.56501548362757e-01,\tEquation 0:,\t1.25172257435970e-10,\tEquation 1:,\t4.59907560051727e-01,\tEquation 2:,\t1.40503027058306e-01,\tEquation 3:,\t1.15731961047759e+00,\tConstant 0:,\t1.11881659943125e-05,\t\n", + "Position:,\t9.56517055637901e-01,\tEquation 0:,\t9.02869047440197e-11,\tEquation 1:,\t4.59914304315347e-01,\tEquation 2:,\t1.40503028902716e-01,\tEquation 3:,\t1.15734193769878e+00,\tConstant 0:,\t9.50203244332833e-06,\t\n", + "Position:,\t9.56529922559554e-01,\tEquation 0:,\t6.56583193606617e-11,\tEquation 1:,\t4.59919900063306e-01,\tEquation 2:,\t1.40503030204932e-01,\tEquation 3:,\t1.15736046336025e+00,\tConstant 0:,\t8.10304778594754e-06,\t\n", + "Position:,\t9.56542789481207e-01,\tEquation 0:,\t4.49445963456061e-11,\tEquation 1:,\t4.59925495629468e-01,\tEquation 2:,\t1.40503031300219e-01,\tEquation 3:,\t1.15737898901726e+00,\tConstant 0:,\t6.70411806066587e-06,\t\n", + "Position:,\t9.56552984539001e-01,\tEquation 0:,\t3.13117166889370e-11,\tEquation 1:,\t4.59929929126537e-01,\tEquation 2:,\t1.40503032021129e-01,\tEquation 3:,\t1.15739366774991e+00,\tConstant 0:,\t5.59571864116399e-06,\t\n", + "Position:,\t9.56562325146396e-01,\tEquation 0:,\t2.09784506015431e-11,\tEquation 1:,\t4.59933990950896e-01,\tEquation 2:,\t1.40503032567580e-01,\tEquation 3:,\t1.15740711625177e+00,\tConstant 0:,\t4.58024483777703e-06,\t\n", + "Position:,\t9.56571665753791e-01,\tEquation 0:,\t1.27077343739086e-11,\tEquation 1:,\t4.59938052679450e-01,\tEquation 2:,\t1.40503033004977e-01,\tEquation 3:,\t1.15742056475127e+00,\tConstant 0:,\t3.56480363763596e-06,\t\n", + "Position:,\t9.56578235891664e-01,\tEquation 0:,\t8.12565775125691e-12,\tEquation 1:,\t4.59940909622191e-01,\tEquation 2:,\t1.40503033247309e-01,\tEquation 3:,\t1.15743002435908e+00,\tConstant 0:,\t2.85056206327355e-06,\t\n", + "Position:,\t9.56584208118135e-01,\tEquation 0:,\t4.84585056694052e-12,\tEquation 1:,\t4.59943506529468e-01,\tEquation 2:,\t1.40503033420774e-01,\tEquation 3:,\t1.15743862310002e+00,\tConstant 0:,\t2.20133411857206e-06,\t\n", + "Position:,\t9.56589206735714e-01,\tEquation 0:,\t2.74880924458738e-12,\tEquation 1:,\t4.59945680051622e-01,\tEquation 2:,\t1.40503033531686e-01,\tEquation 3:,\t1.15744582004966e+00,\tConstant 0:,\t1.65795607884824e-06,\t\n", + "Position:,\t9.56593309352988e-01,\tEquation 0:,\t1.46890948340613e-12,\tEquation 1:,\t4.59947463950254e-01,\tEquation 2:,\t1.40503033599381e-01,\tEquation 3:,\t1.15745172694830e+00,\tConstant 0:,\t1.21198722930691e-06,\t\n", + "Position:,\t9.56596586508159e-01,\tEquation 0:,\t7.32318166292526e-13,\tEquation 1:,\t4.59948888908459e-01,\tEquation 2:,\t1.40503033638341e-01,\tEquation 3:,\t1.15745644535629e+00,\tConstant 0:,\t8.55756635769919e-07,\t\n", + "Position:,\t9.56599109833696e-01,\tEquation 0:,\t3.38112883347471e-13,\tEquation 1:,\t4.59949986081740e-01,\tEquation 2:,\t1.40503033659192e-01,\tEquation 3:,\t1.15746007840937e+00,\tConstant 0:,\t5.81475086788586e-07,\t\n", + "Position:,\t9.56600947796952e-01,\tEquation 0:,\t1.45692276646484e-13,\tEquation 1:,\t4.59950785246589e-01,\tEquation 2:,\t1.40503033669370e-01,\tEquation 3:,\t1.15746272468616e+00,\tConstant 0:,\t3.81696722368678e-07,\t\n", + "Position:,\t9.56602048232444e-01,\tEquation 0:,\t6.86868266620245e-14,\tEquation 1:,\t4.59951263725197e-01,\tEquation 2:,\t1.40503033673443e-01,\tEquation 3:,\t1.15746430907954e+00,\tConstant 0:,\t2.62081786214060e-07,\t\n", + "Position:,\t9.56603234589209e-01,\tEquation 0:,\t1.77407715979912e-14,\tEquation 1:,\t4.59951779561608e-01,\tEquation 2:,\t1.40503033676138e-01,\tEquation 3:,\t1.15746601718127e+00,\tConstant 0:,\t1.33194505607166e-07,\t\n", + "Position:,\t9.56604504673252e-01,\tEquation 0:,\t0.00000000000000e+00,\tEquation 1:,\t4.59952331801525e-01,\tEquation 2:,\t1.40503033677089e-01,\tEquation 3:,\t1.15746784583246e+00,\tConstant 0:,\t0.00000000000000e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oCData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "ac9530d9", + "metadata": {}, + "source": [ + "Note that there are no errors reported, just the positions, values of our functions, and the value of our constant. This should be the full solution to the system of differential equations. " + ] + }, + { + "cell_type": "markdown", + "id": "9b993645", + "metadata": {}, + "source": [ + "\n", + "\n", + "## Step 3d: Complicated Problem Analysis \\[Back to [top](#toc)\\]\n", + "$$\\label{S3d}$$\n", + "\n", + "#### Time to go mining again. \n", + "\n", + "Let's just print out our equations and constant, see how they behave. " + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "fa051a1d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "# Csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "# plt.ylim(0.0,0.15)\n", + "# plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "bcff3714", + "metadata": {}, + "source": [ + "Well, everything looks nice and smooth, but a lot of the information here is condensed at the bottom of the graph. Let's zoom in to examine the detail. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "cc265c0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution Detail')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "plt.ylim(0.0,0.15)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "6b7e76c5", + "metadata": {}, + "source": [ + "From this, we can confirm that our termination condition is working: we clearly stop as the pressure goes to zero. The density and pressure act as expected, starting high in the center of the star and going to zero, while the mass levels off to a certain value (since the mass would all be contained within the star, this makes sense). All we can say about $\\bar r$ is that it's increasing similarly but not exactly to $r$ itself, which is expected. Now, we happen to know that $\\bar r$ needs to be normalized, but the solver doesn't do that—we'll show how to do post-processing later. \n", + "\n", + "For now, we discuss validation. We don't have a closed form solution for the TOV equations, but we do have a solution printed out by a previous NPRy+ solver that solved TOV equations specifically. Let's compare our results shall we? " + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "4483d33e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution, Original NRPy+ TOV and Odie Comparison.')\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "ax.plot(positionList, calculatedList0, color='b') \n", + "ax.plot(positionList, calculatedList1, color='r') \n", + "ax.plot(positionList, calculatedList2, color='g') \n", + "ax.plot(positionList, calculatedList3, color='olive') \n", + "\n", + "ax.plot(apositionList, acalculatedList0, color='b', label = \"PRESSURE\") \n", + "ax.plot(apositionList, acalculatedList2, color='g', label = \"MASS\") \n", + "ax.plot(apositionList, acalculatedList3, color='olive', label = \"POLYTROPIC RADIUS\") \n", + "ax.plot(apositionList, acalculatedList4, color='purple', label = \"DENSITY\") \n", + "\n", + "plt.ylim(0.0,0.15)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "4ac2337b", + "metadata": {}, + "source": [ + "We can see rather clearly that pressure, mass, and total energy density visually match the values reported by the trusted solver, with the notable exception that the solver continued evolving past $P$=0 and so we have some trailling flat lines at the end. However, $\\bar r$ does not match. This is because, as previously mentioned, we have not normalized the data. Normalization of $\\bar r$ requires knowing what the estimate for values at the edge of the star are, which can't be done until the entire differential equation is already solved, so this is why we do it now. The below code demonstrates how to use numpy to do this post-processing. \n", + "\n", + "$\\nu$ is not reported in this graph since the NRPy+ solver did not report it. \n", + "\n", + "The normalization factor for $\\bar r$ is the following.\n", + "\n", + "$$\\frac{1}{2} \\frac{\\sqrt{R(R-2M) + R-M}}{\\bar R}$$\n", + "\n", + "Here, $R$ is the radius of the star, $M$ is the mass, and $\\bar R$ is the non-normalized isotropic radius of the star. These will be the *last* values in the lists of our data since we made sure to terminate at $P$=0. \n", + "\n", + "Also, it is often convenient to set the radius of the star to 1, so we also do that in the processing below. " + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "eddcf3c6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + " \n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalzied radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution, Original NRPy+ TOV and Odie Comparison, Normalized')\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "# POST PROCESSING!\n", + "# Now that we have all our data in lists, we can harvest the last values using Python's \"-1\" index trick.\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "# Calculate the normalization constant for r_bar\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + " \n", + " \n", + "# We multiply all positions by 1/R_Schw in order to normalize the radius to 1.\n", + "ax.plot(np.array(positionList)*(1.0/R_Schw), calculatedList0, color='b') \n", + "ax.plot(np.array(positionList)*(1.0/R_Schw), calculatedList1, color='purple') \n", + "ax.plot(np.array(positionList)*(1.0/R_Schw), calculatedList2, color='g') \n", + "ax.plot(np.array(positionList)*(1.0/R_Schw), calculatedList3, color='olive') \n", + "\n", + "\n", + "ax.plot(np.array(apositionList)*(1.0/R_Schw), acalculatedList0, color='b', label = \"PRESSURE\") \n", + "ax.plot(np.array(apositionList)*(1.0/R_Schw), acalculatedList2, color='g', label = \"MASS\") \n", + "# Make sure to actually normalize r-bar when plotting it. numpy can perform operations on the list if\n", + "# we convert it to a numpy array. \n", + "ax.plot(np.array(apositionList)*(1.0/R_Schw), np.array(acalculatedList3)*C, color='olive', label = \"POLYTROPIC RADIUS\") \n", + "ax.plot(np.array(apositionList)*(1.0/R_Schw), acalculatedList4, color='purple', label = \"DENSITY\") \n", + "\n", + "\n", + "plt.ylim(0.0,1.2)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "4fdcda59", + "metadata": {}, + "source": [ + "We zoomed out so we could focus on $\\bar r$ here. As we can see, now that it's normalized, both the trusted NRPy+ result and our program plot what is visually the same thing. This serves as a demonstration on how to do post-processing on Odie's data. Odie can only solve ODEs, it can't analyze the results or alter data that depends on the final result, such as the normalized radius or $\\bar r$ here. That is left to the user to do with whatever program is going to be plotting or analyzing the data. \n", + "\n", + "Anyway, while the graph above looks great, just because things are similar visually doesn't mean the errors are as small as we would like. Sadly, even though we have a trusted solution, it itself is just an approximation method and is not perfect, so we can't determine \"digits of agreement\" with the truth since the truth isn't known to absolute precision. Furthermore, both solvers plot distinct points, and those points genreally don't line up so we can't easily compare them. \n", + "\n", + "There is a solution, however. It is a little messy, but we can use scypy's advanced interpolation functions to draw lines that connect the data points together so they can be compared. This is, admittedly, a second level of approximation being added to the data, but with luck it will show us that the two answers agree extremely closely. To do that, we will cubically interpolate the NRPy+ data so it can be evaluated at the same points our solver has results at, then we can compare those. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "a41b0876", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "import scipy.interpolate as scy\n", + "import numpy as np\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "# Here is the interpolation. Admittedly not entirely sure how this all works, but here goes. \n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) # Collect x and y values for the \"truth\" values. \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") # Interpolate cubically between them. \n", + "xnew = apositionList # Make the step size equal to our solver's.\n", + "xnew.pop(0)\n", + "ynew = f0(xnew) # Use interpolation function returned by `interp1d` to get \"truth\" values\n", + "ynew2 = acalculatedList0 # Manually put our solver's values in, we wish to avoid double interpolating\n", + "ynew2.pop(0) # The first value, printed at r=0, is not reported in the Original NRPy+ solver, get rid of it. \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "0f857205", + "metadata": {}, + "source": [ + "Well that is certainly an absolute mess. Let's run it again but zoom in so we can actually talk about what's going on. " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "1dda92b5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth Detail.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") \n", + "xnew = apositionList \n", + "xnew.pop(0)\n", + "ynew = f0(xnew) \n", + "ynew2 = acalculatedList0 \n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) \n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) \n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0)\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) \n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0)\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.6,0.8)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()\n" + ] + }, + { + "cell_type": "markdown", + "id": "009e4416", + "metadata": {}, + "source": [ + "We see here a shape that regularly appears in error analysis: the COMB. \n", + "\n", + "The comb occurs when we have two sets of data that are reported at different resolutions but nonetheless represent the same quantity. As we can see, all four quantities we can compare demonstrate the comb effect. \n", + "\n", + "What's happening is that the original NRPy+ TOV solver and Odie don't sample the same points, but they sample points near each other, and the points that are nearest to each other have the lowest interpolation error. Every time the points line up, we get a downward spike in the comb, where we can get up to twelve digits of agreement, while the places that are furthest away from each other get around eight digits of agreement. These errors are largely due to the errors of the cupic interpolator itself, which is not able to perfectly smooth out all the data to make comparisons. However, even the worst parts of the interpolator only get errors of 7 digits, barring the spike that occurs at the edge of the star due to some values drifting near to zero. \n", + "\n", + "Keep in mind this does not necessarily mean Odie is \"less accurate\" than the original NRPy+ TOV solver. All we can say is that we are extremely close to what the NRPy+ TOV solver thinks the answer is near the points where the NRPy+ TOV solver was actually evaluating, which means the disagreement between them is minimal. It is impossible to reduce the disagreement to absolutely zero, since we use different stepping methods and have a slightly different (more general) implementaiton. \n", + "\n", + "One thing we can note is that this comb demonstrates how our method is using adaptive timestep: the lines are not smooth and are instead angled, with a conrner at every sampled point. This is primarly because we chose to interpolate the original NRPy+ TOV solver's data to match up with our own, so we see corners where Odie was evaluating and spikes where NRPy+ TOV was evaluating. Note that width between the spikes isn't consistent across the whole domain, since the original solver was changing its time step. We are also changing ours, which we can see from the distance between corners on the left of the comb being greater than on the right side of the comb. \n", + "\n", + "What happened is that Odie detected that the estimated error was growing above the desired bound during runtime, and thus shrunk the step size to increase accuracy. We can actually plot the step size based on the position, to get a better idea of what the program is doing. " + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "0fc9ed31", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionListMedium = []\n", + "positionListODE = []\n", + "positionListODE2 = np.arange(0,1,0.00001)\n", + " \n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionListMedium.append(float(row[0]))\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionListODE.append(float(row[1])) \n", + " \n", + "dpositionListMedium = []\n", + "dpositionListODE = []\n", + "dpositionListODE2 = []\n", + " \n", + "i = 0\n", + "while i < len(positionListMedium):\n", + " if (i == 0):\n", + " dpositionListMedium.append(0.0)\n", + " else :\n", + " dpositionListMedium.append(positionListMedium[i] - positionListMedium[i-1])\n", + " i = i + 1\n", + "\n", + "i = 0\n", + "while i < len(positionListODE):\n", + " if (i == 0):\n", + " dpositionListODE.append(0.0)\n", + " else :\n", + " dpositionListODE.append(positionListODE[i] - positionListODE[i-1])\n", + " i = i + 1\n", + "\n", + "i = 0\n", + "while i < len(positionListODE2):\n", + " if (i == 0):\n", + " dpositionListODE2.append(0.0)\n", + " else :\n", + " dpositionListODE2.append(positionListODE2[i] - positionListODE2[i-1])\n", + " i = i + 1\n", + " \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('Step Size')\n", + "ax.set_title('Step Size Comparison')\n", + "\n", + "ax.plot(np.array(positionListMedium)/R_Schw, dpositionListMedium, color='r', label=\"ORIGINAL NRPy+ TOV\") \n", + "ax.plot(np.array(positionListODE)/R_Schw, dpositionListODE, color='magenta', label=\"ODIE\") \n", + "ax.plot(np.array(positionListODE2)/R_Schw, dpositionListODE2, color='cyan', label=\"0.00001 step\") \n", + "\n", + "# plt.ylim(0.0,0.15)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "5a20555d", + "metadata": {}, + "source": [ + "The top line is for the original solver, Odie is below it, and below that is a straight line representing a non-adaptive stepsize. Odie takes smaller steps than the original solver for the RK4 method and the error limits we imposed on it, which implies that the results Odie produces should be more acurate than the original solver. However, the original solver was designed explicitly for the TOV equations and handles the core and edge of the star better, while Odie is entirely general it its application. We can also see that the original solver adjusted step size smothly, while Odie makes little staircase shapes as Odie has a \"happy zone\" where it will not adjust the step size, while the original solver would adjust the step virtually every time. \n", + "\n", + "Naturally, the non-adaptive timestep solution should be much more accurate than both of the above adaptive ones, since it takes smaller steps. And it is, it's just that taking larger steps when there are less errors about is far more computationally efficient. For a somewhat small number of evaluations like this, the difference in computaiton time is barely noticable, but for larger projects the time saved adds up quickly. \n", + "\n", + "In the interests of completeness we will run a non-adaptive version of the TOV equations, just to see the result. " + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "9b2c9cca", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData2.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "c06cfe4d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated2 `...\n", + "(BENCH): Finished executing in 0.41 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " \n", + " c_type = \"int\" \n", + " \n", + " name = \"main\"\n", + " \n", + " params = \"\"\n", + " \n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + "\n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "\n", + "os.chdir(\"../\")\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated2\", compiler_opt_option=\"fast\")\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "\n", + "cmd.Execute(\"ODESolverComplicated2\", \"\", \"terminalOutput.txt\")" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "bdf5b9fc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData2.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\")\n", + "xnew = apositionList \n", + "xnew.pop(0)\n", + "ynew = f0(xnew) \n", + "ynew2 = acalculatedList0 \n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) \n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) \n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) \n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0)\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "0b36ca69", + "metadata": {}, + "source": [ + "Note that while the general shape of the graph here is the same, the spikes go down much further, all the way to 15 digits of agreement in some cases! This is because the steps for the nonadaptive version of Odie are much finer and can get much closer to the actual values that the original code was evaluating. The humps, though, are still the same, and are presumably based in interpolation error. \n", + "\n", + "The other change is the edge of the star, which is unsurprising. The edge of the star is an extremely volatile region and slight changes in timestep result in wildly different results. Smaller is still better, but the different adaptive methods can do all sorts of things out here. \n", + "\n", + "One might consider doing a Hybrid method, but not the sort of one that `nrpy_odiegm_main.c` can do automatically, where instead of shifting from an RK method to an AB method, we shift from an adaptive RK to a non-adaptive RK. But that's beyond the scope of this tutorial. That said, we will still demonstrate the use of AB and Hybrid methods below. " + ] + }, + { + "cell_type": "markdown", + "id": "203aabef", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Step 3e: Complicated Problem Extension: Adams Bashforth and Hybrid Methods \\[Back to [top](#toc)\\]\n", + "$$\\label{S3e}$$\n", + "\n", + "#### Our code is mutating! " + ] + }, + { + "cell_type": "markdown", + "id": "14f68398", + "metadata": {}, + "source": [ + "Let's have ODIE solve the TOV equations with a pure Adams-Bashforth (AB) method." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "242890e2", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData3.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_AB;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_AB;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "421f4d3c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated3 `...\n", + "(BENCH): Finished executing in 0.40 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " \n", + " c_type = \"int\" \n", + " \n", + " name = \"main\"\n", + " \n", + " params = \"\"\n", + "\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + "\n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "\n", + "os.chdir(\"../\")\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated3\", compiler_opt_option=\"fast\")\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "\n", + "cmd.Execute(\"ODESolverComplicated3\", \"\", \"terminalOutput.txt\") " + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "be8cf7ed", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData3.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") \n", + "xnew = apositionList\n", + "xnew.pop(0)\n", + "ynew = f0(xnew) \n", + "ynew2 = acalculatedList0 \n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) \n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0)\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) \n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) \n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "d2b21180", + "metadata": {}, + "source": [ + "This is a 4th order AB method, which theoretically is comparable to the RK4 method used previously. Note that the errors now cluster at values at less than 10 digits of agreement, which is less accurate than what RK4 showed. Even though AB methods aren't adaptive, this is still worse than the adaptive methods!\n", + "\n", + "This is because AB methods take into account previously evaluated points, and in order to use a pure AB-method, lower order AB methods must be used to fill in the first few data points, and that error carries throughout the calculation. The solution is to use a hybrid method, where we \"seed\" the first few values with another method, then hand it off to AB. Since we only need to evaluate the first handful of points, we can go ahead and use a very intensive method to get those first points as accurate as possible. The best one we have is DP8, an RK method of 8th order. The first three points will be evaluated this way, and then we hand it off to AB of order 4 to continue the rest of the way. " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "fa5e7608", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData4.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_AB;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_DP8;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "dd896ce2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated4 `...\n", + "(BENCH): Finished executing in 0.41 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + "\n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " \n", + " c_type = \"int\" \n", + " \n", + " name = \"main\"\n", + " \n", + " params = \"\"\n", + "\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + "\n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + "\n", + "add_to_Cfunction_dict_ODESolver() \n", + "\n", + "os.chdir(\"../\")\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated4\", compiler_opt_option=\"fast\")\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "\n", + "cmd.Execute(\"ODESolverComplicated4\", \"\", \"terminalOutput.txt\")" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "ef7d034f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData4.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") \n", + "xnew = apositionList \n", + "xnew.pop(0)\n", + "ynew = f0(xnew) \n", + "ynew2 = acalculatedList0 \n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) \n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew)\n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew)\n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "327b9cac", + "metadata": {}, + "source": [ + "Note that at the core of the star this works *excellently*, the agreement is better than even our original results with adaptive RK4, and it continues far beyond the point at which DP8 is actually being used. This is the highest agreement we've seen so far. \n", + "\n", + "Choosing which methods to use and when is a bit of an art. Different problems behave differently for different types of methods, be they adaptive, nonadaptive, or rely on previously evaluated points. Learning when to choose certain things and when not to is best learned by experimenting. Users should feel free to change the methods used in the above code, adjust the order of the AB method, see what can be found. Of note, very high-order AB methods are unstable and are unlikely to give good results no matter what. Adaptive methods can often break as well if the error requirements are too stringent—or too weak! There are so many different variables to discover and tweak. The user can feel free to edit code in this section to see what happens, but there is also a playground specifically designed for user use in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook." + ] + }, + { + "cell_type": "markdown", + "id": "54ff26ba", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Step 4: Conclusion \\[Back to [top](#toc)\\]\n", + "$$\\label{S4}$$" + ] + }, + { + "cell_type": "markdown", + "id": "c33cdd06", + "metadata": {}, + "source": [ + "#### So, what have we learned today?\n", + "\n", + "In the previous sections we showcased two different examples of how Odie can be used to solve systems of Ordinary Differential Equations, making use of most of Odie's capabilities and showcasing how to turn the results into something useful. If users feel comfortable and have read at least the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, the next step should be to do the Exercises in the next section of this notebook. \n", + "\n", + "Beyond that, a user with a specific application in mind could use the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook's template to run whatever system of ODEs that needs to be solved. However, in the case of a more complex and invovled situation, it is recommended to run the code in C directly. If more advanced applications are needed, it is time to turn to the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook to find out exactly how many parts of Odie can be customized when a custom main function is created. \n", + "\n", + "For an extremely involved application of Odie, some of the program's structure will likely need to be fundamentally altered. Fortunately we also have an example of this, though not in jupyter notebook format. Odie's personal repository at https://github.com/GMBlackjack/ODESolver has a folder called TOVOdieGM. This contains a version of Odie specifically designed to solve the TOV Equations in complete generality in the Einstein Toolkit environment. Many fundamental things were changed to make this work seamlessly with the rest of the programs in the Toolkit, and it is not considered an example to follow as a template, but merely a proof of concept that the code can be adapted to even highly specific and restrictive situations and structures.\n", + "\n", + "Users are completely free to edit the code however desired. Even the header file and the functions usually kept from the user—there is nothing preventing adjustments. That said, the intent of Odie is to make it simple for users to solve ODEs of any sort; just because the option exists to edit everything doesn't mean it should be taken. Just put the differential equations into `nrpy_odiegm_user_methods.c` and run the main function with whatever settings are desired. This notebook gives a good idea of what parts of the code are expected to be altered in both `nrpy_odiegm_user_methods.c` and `nrpy_odiegm_main.c`\n", + "\n", + "It is important to know the limitations of the code, such as roundoff error, or the higher-order Adams-Bashforth methods breaking down. Alongside this, it is also important to experiment. It is often impossible to predict which method will be the best for any given problem, so users should try several options. Higher-order methods can crash easily, adaptive timestep might lower the accuracy too much, or a badly behaved function might fool the default settings on the error analysis and the error limits will need to be adjusted to compensate. The results can often be surprising, so it is best to fine-tune any algorithms used, and not just trust the first result Odie reports. \n", + "\n", + "With that, we wish any potential users good luck, hopefully these notebooks contain all needed resources to both use and adjust the code whenever and however it needs to be.\n", + "\n", + "-GM. " + ] + }, + { + "cell_type": "markdown", + "id": "da547397", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Step 5: Questions/Exercises \\[Back to [top](#toc)\\]\n", + "$$\\label{S5}$$\n", + "\n", + "#### POP QUIZ! \n", + "\n", + "It's always best to try a few things out to gain experience, and one way to do that is with exercises! Here's a few that are entirely solvable within the four Odie notebooks.\n", + "\n", + "1) Using the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the differential equation $y' = sin(y)$ with $y(0) = 0$. Evaluate at least from $x$=0 to $2\\pi$\n", + "\n", + "2) In [Step 2](#S2), we created a Simple Example. Redefine the problem so it solves the equation going backward from 0, rather than forward. (It is fine if the final plot is still shows positive $x$ values on the lower axis, as the code only knows how to step \"forward.\" To adjust this the Python code that plots the results would need to multiply every position point by -1).\n", + "\n", + "3) We can observe curious phenomena with the AB methods. For the TOV equations ([Step 3](#S3)), use all the AB orders 1 through 19, seeding them with the DP8 method. At which order is the result most accurate (compared to the old TOV solver)? At what order does the result start to break down? \n", + "\n", + "4) Using the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the differential equation $y''' = y' + y - 3x$. It will need to be split up into a system of three differential equations manually first. The initial conditions are $y(0) = 1$, $y'(0) = 0$, and $y''(0) = 0$. Evaluate at least to $x$=1.5. \n", + "\n", + "5) In [Step 3](#S3) we have an `exception_handler`. Disable the `exception_handler`, what does this do to the data at the outer edge for various different methods? \n", + "\n", + "6) Use the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the system of differential equations $z' = az+y^b+y^{1/c}; y' = bz+y^c$ with $z(0)$ = -1 and $y(0)$=1. Note the constants $a$, $b$, and $c$. They are defined as $a=2y$, $b=yz$, $c=z/5$. These values should be treated as constants and reported with the values of $y$ and $z$. Evaluate to at least $x$=0.443. This is a highly precise value for a reason—try evolving past it, see what happens!" + ] + }, + { + "cell_type": "markdown", + "id": "2d5604ad", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Step 6: Output this notebook to $\\LaTeX$-formatted PDF file \\[Back to [top](#toc)\\]\n", + "$$\\label{S6}$$\n", + "\n", + "((This is currently not functional due to file hierarchy, when in the actual nrpytutorial repo it should work)). \n", + "\n", + "The following code cell converts this Jupyter notebook into a proper, clickable $\\LaTeX$-formatted PDF file. After the cell is successfully run, the generated PDF may be found in the root NRPy+ tutorial directory, with filename\n", + "[NRPy+_OdieGM_Examples.pdf](NRPy+_OdieGM_Examples.pdf). (Note that clicking on this link may not work; you may need to open the PDF file through another means.)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "0cb86899", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[NbConvertApp] WARNING | pattern 'NRPy+_OdieGM_Examples.ipynb' matched no files\n", + "Created NRPy+_OdieGM_Examples.tex, and compiled LaTeX file to PDF file\n", + " NRPy+_OdieGM_Examples.pdf\n" + ] + } + ], + "source": [ + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "cmd.output_Jupyter_notebook_to_LaTeXed_PDF(\"NRPy+_OdieGM_Examples\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dd172247", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_1_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_1_Solution.ipynb new file mode 100644 index 00000000..e2134215 --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_1_Solution.ipynb @@ -0,0 +1,2522 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 1 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "[Examples](NRPy+_OdieGM_Examples.ipynb)\n", + "\n", + "[Quickstart](NRPy+_OdieGM_Quickstart.ipynb)\n", + "\n", + "[Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb)\n", + "\n", + "[Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb)\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e189a05f-54f3-46d0-a60a-f91fdbbde078", + "metadata": {}, + "source": [ + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "b3575c50-6ec6-4f4c-ac2f-564ca74c8dd0", + "metadata": {}, + "source": [ + "1. [Exercise 1](#E1)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "5f2c9b00-84ea-4de6-9bd6-0fec7f537f09", + "metadata": {}, + "source": [ + "\n", + "# Exercise 1 \\[Back to [top](#toc)\\]\n", + "\n", + "\"1. Using the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the differential equation $y' = sin(y)$ with $y(0) = 0$. Evaluate at least from $x$=0 to $2\\pi$\" (from [Examples](NRPy+_OdieGM_Examples.ipynb))\n", + "\n", + "To start, you can probably see what is going to happen when you plug in this ODE with an initial condition of $y(0) = 0$. If $y(0) = 0$, then $y'(0) = sin(0) = 0$. This means that the solution will remain zero for the next time step since the derivative is zero. At the next timestep, $y(x)$ remains zero, so the derivative stays zero as well. This continues on for as long as the program runs, meaning you will get a horizontal line at zero.\n", + "\n", + "Let's make sure the code agrees with this.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "d80ed50e-b1fc-48d3-815e-3dc13c2868c2", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "6dfcfc4a", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = 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+ "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c5d4ba59", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "b0fa46aa", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "245b247b", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "1f4e5331-1fd6-48de-94ab-2e9a249cef9b", + "metadata": {}, + "source": [ + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "8f9efac6-2fa3-4a58-9e53-74515c55b542", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "\n", + "Here is how we need to define our user methods and main function. There really isn't a huge change that needs to be made to the default [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) program. The only changes that need to be made are to the functions \"diffy_Q_eval\", \"know_q_eval\", and \"get_initial_conditions.\" Let's go through the changes one-by-one:\n", + "\n", + "#### diffy_Q_eval:\n", + "We're just changing the actual ODE that is here. Instead of the default from the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) program of `dydx[0] = y[0];`, we want to use `dydx[0] = sin(y[0]);`.\n", + "\n", + "#### known_Q_eval:\n", + "Just erase the known solution. Most of the time we don't have one, and although the ODE DOES have a known solution that you could put in, it does not impact the final results of our code. You don't have to do any extra work, so just leave this blank. (Note: You still need to return 1, however, so don't mess with the return statement).\n", + "\n", + "#### get_Initial_Condition:\n", + "Just change the initial condition, from `y[0] = 1.0;` to `y[0] = 0.0;`\n", + "\n", + "\n", + "Your `user_methods` function should look like this:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "86414d51", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "struct constant_parameters { \n", + " int dimension; // number that says how many constants we have. \n", + " // double rho;\n", + " // double parameter;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " return 0;\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + "\n", + " dydx[0] = sin(y[0]);\n", + "\n", + " return 1;\n", + "}\n", + "\n", + "\n", + "//This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) //This function is the other one passed using GSL's formulation. \n", + "//Allows the specific_methods file to be completely agnostic to whatever the user is doing. \n", + "{\n", + "\n", + " //y[0] = exp(x);\n", + "\n", + " return 1;\n", + " //report \"success\"\n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " y[0] = 0.0;\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "42c6a54d-bf42-4040-9e46-ee4bb7215056", + "metadata": {}, + "source": [ + "In the modifiable main function, there really shouldn't be much to change. I would suggest changing the `no_adaptive_step = true`, that we we can just step forward uniformly to 6.28 ($2\\pi$), but that is of personal preference and not required." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "a565cd03", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.01; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 1; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 628; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oUData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "927fe71c-79cc-414a-b449-94fd20f9aae8", + "metadata": {}, + "source": [ + "Now we just run the rest of the code and see what we plot" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "6ffc1243", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverCustom `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"User Custom System\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined in the customization section.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverCustom\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "# Note to change the name if you want to run more than once, otherwise it is ODESolverCustom.\n", + "# Will override the previous ODESolverCustom.\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverCustom\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "4cc9cc2d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 4.\n", + "Printing to file 'oUData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "FINAL: Position:,\t6.28000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "f220b31c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t1.00000000000000e-02,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t2.00000000000000e-02,\tEquation 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"Position:,\t6.15000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.16000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.17000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.18000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.19000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.20000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.21000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.22000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.23000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.24000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.25000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.26000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.27000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "Position:,\t6.28000000000000e+00,\tEquation 0:,\t0.00000000000000e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oUData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "c2c517cf", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "\n", + "# truthList0 = []\n", + "# Uncomment or add more if validation is desired.\n", + "\n", + "calculatedList0 = []\n", + "# calculatedList1 = []\n", + "# Uncomment for plotting more than one value. \n", + "\n", + "# errorList0 = []\n", + "# Uncomment for lists to store errors. \n", + "\n", + "# i = 0\n", + "# Use this i if a check has to be performed as to which row we're on. \n", + "\n", + "# csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oUData.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Here is where you would do any post-processing. Remember, use np.array() on the lists so operations\n", + "# can be performed properly. \n", + "\n", + "# Remember to change labels!\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Custom Graph')\n", + "ax.plot(positionList, calculatedList0, color='r', label=\"Insert Label Here\") # marker='o' (or whatever symbol) can be added here. \n", + "\n", + "fig.set_size_inches(9,9)\n", + "# plt.xlim(0.0,1.0)\n", + "# plt.ylim(0.0,1.0)\n", + "# The above two lines can control the region of the graph displayed. Comment out for auto scaling. \n", + "\n", + "# ax.set_yscale(\"log\") # Found in matplotlib's documentation. \n", + "# Uncommenting this sets the scale to logarithmic. \n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "55b94d15-5106-4047-bc47-1b9e33ed78fd", + "metadata": {}, + "source": [ + "And sure enough, we get the horizontal line we were predicting from the very beginning of the problem." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24336fc5-6471-4bfe-b7f3-96a70184dc25", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_2_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_2_Solution.ipynb new file mode 100644 index 00000000..d22b68ee --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_2_Solution.ipynb @@ -0,0 +1,2098 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 2 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "f49be4af-2592-4731-9216-d6f4e8ee4ebe", + "metadata": {}, + "source": [ + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "1842547f-f280-4813-9624-94b91b2ea051", + "metadata": {}, + "source": [ + "1. [Exercise 2](#E2)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "993da468-10a2-4e2b-aa7d-03e9c687db8b", + "metadata": {}, + "source": [ + "\n", + "# Exercise 2 \\[Back to [top](#toc)\\]\n", + "\n", + "\"2) In Step 2 (in the [Examples](NRPY+_OdieGM_Examples.ipynb) notebook), we created a Simple Example. Redefine the problem so it solves the equation going backward from 0, rather than forward. (It is fine if the final plot is still shows positive $x$ values on the lower axis, as the code only knows how to step \"forward.\" To adjust this the Python code that plots the results would need to multiply every position point by -1).\n", + "\n", + "In the simple example referred to in the 2nd exercise, we defined an ODE of:\n", + "$$ \\frac{\\partial^2 u}{\\partial x^2} = u + x; u(0) = 2, \\frac{\\partial u(0)}{\\partial x} = -1.$$\n", + "\n", + "This ODE also had a known solution of:\n", + "$$ u = e^x + e^{-x} -x .$$\n", + "\n", + "This problem is more a math problem than a coding problem, so let's discuss the math involved her.\n", + "\n", + "### The Setup:\n", + "The important thing to note about Odie is that it only solves ODE's forward in time. How can we solve the ODE BEFORE the initial conditions? Since our domain is all real numbers for the simple examples, that it wouldn't hurt to reason that we could reflect the function $u(x)$ across the y-axis. Going forward in time on this reflected function would be the same as going bacward in time for the original function. Lucky for us, we already have the known solution to this simple example:\n", + "$$ u(x) = e^x + e^{-x} -x .$$\n", + "\n", + "The reflected function would then be:\n", + "$$ u(x) = e^{-x} + e^{x} + x .$$\n", + "\n", + "Although it is quite easy to find the reflection of the solution, derivatives don't reflect quite the same way. We need to figure out what the 2nd-order ODE is that describes this new reflected function. We can do this by just taking the 2nd derivative of the reflected function:\n", + "\n", + "$$\\frac{\\partial^2 u}{\\partial x^2} = e^{-x} + e^{x}$$\n", + "\n", + "And according to the reflected function, **we know the ODE of this system should be**:\n", + "\n", + "$$ \\frac{\\partial^2 u}{\\partial x^2} = u - x$$\n", + "\n", + "This should be the ODE we need to put into the solver.\n", + "\n", + "### Breaking up the ODE\n", + "\n", + "Now that we know what ODE we are trying the solve for, we need to break it up into a system of 1st order ODE's that are compatible with Odie. We'll break it up just like we did the original simple example:\n", + "\n", + "$$ u' = z ; u(0) = 2$$\n", + "$$ z' = u - x ; z(0) = 1$$\n", + "\n", + "An important thing to note is why I changed the initial condition for $z(0)$ to $+1$ rather than the original $-1$. If you remember, this refers to the initial condition of the 1st derivative of the function. We are moving forward on the reflected function, which is BACKWARDS on the original function. If moving forward at that initial point gives a negative derivative, then moving BACKWARDS should yield the opposite derivative, a positive derivative.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "df44c2b0-5ec7-4583-8636-4627c942d27a", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d9b4753f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = {{333374427829017307697.0/51090942171709440000.0,-5148905233415267713.0/109168679854080000.0,395276943631267674287.0/1548210368839680000.0,-2129159630108649501931.0/2128789257154560000.0,841527158963865085639.0/283838567620608000.0,-189774312558599272277.0/27646613729280000.0,856822959645399341657.0/67580611338240000.0,-13440468702008745259589.0/709596419051520000.0,196513123964380075325537.0/8515157028618240000.0,-57429776853357830333.0/2494674910728000.0,53354279746900330600757.0/2838385676206080000.0,-26632588461762447833393.0/2128789257154560000.0,4091553114434184723167.0/608225502044160000.0,-291902259907317785203.0/101370917007360000.0,816476630884557765547.0/851515702861824000.0,-169944934591213283591.0/709596419051520000.0,239730549209090923561.0/5676771352412160000.0,-19963382447193730393.0/4257578514309120000.0,12600467236042756559.0/51090942171709440000.0},{0.0,57424625956493833.0/9146248151040000.0,-3947240465864473.0/92386344960000.0,497505713064683651.0/2286562037760000.0,-511501877919758129.0/640237370572800.0,65509525475265061.0/29640619008000.0,-38023516029116089751.0/8002967132160000.0,129650088885345917773.0/16005934264320000.0,-19726972891423175089.0/1778437140480000.0,3146403501110383511.0/256094948229120.0,-70617432699294428737.0/6402373705728000.0,14237182892280945743.0/1778437140480000.0,-74619315088494380723.0/16005934264320000.0,17195392832483362153.0/8002967132160000.0,-4543527303777247.0/5928123801600.0,653581961828485643.0/3201186852864000.0,-612172313896136299.0/16005934264320000.0,2460247368070567.0/547211427840000.0,-85455477715379.0/342372925440000.0},{0.0,0.0,14845854129333883.0/2462451425280000.0,-55994879072429317.0/1455084933120000.0,2612634723678583.0/14227497123840.0,-22133884200927593.0/35177877504000.0,5173388005728297701.0/3201186852864000.0,-5702855818380878219.0/1778437140480000.0,80207429499737366711.0/16005934264320000.0,-3993885936674091251.0/640237370572800.0,2879939505554213.0/463134672000.0,-324179886697104913.0/65330343936000.0,7205576917796031023.0/2286562037760000.0,-2797406189209536629.0/1778437140480000.0,386778238886497951.0/640237370572800.0,-551863998439384493.0/3201186852864000.0,942359269351333.0/27360571392000.0,-68846386581756617.0/16005934264320000.0,8092989203533249.0/32011868528640000.0},{0.0,0.0,0.0,362555126427073.0/62768369664000.0,-2161567671248849.0/62768369664000.0,740161300731949.0/4828336128000.0,-4372481980074367.0/8966909952000.0,72558117072259733.0/62768369664000.0,-131963191940828581.0/62768369664000.0,62487713370967631.0/20922789888000.0,-70006862970773983.0/20922789888000.0,62029181421198881.0/20922789888000.0,-129930094104237331.0/62768369664000.0,10103478797549069.0/8966909952000.0,-2674355537386529.0/5706215424000.0,9038571752734087.0/62768369664000.0,-1934443196892599.0/62768369664000.0,36807182273689.0/8966909952000.0,-25221445.0/98402304.0},{0.0,0.0,0.0,0.0,13325653738373.0/2414168064000.0,-60007679150257.0/1961511552000.0,3966421670215481.0/31384184832000.0,-25990262345039.0/70053984000.0,25298910337081429.0/31384184832000.0,-2614079370781733.0/1961511552000.0,17823675553313503.0/10461394944000.0,-2166615342637.0/1277025750.0,13760072112094753.0/10461394944000.0,-1544031478475483.0/1961511552000.0,1600835679073597.0/4483454976000.0,-58262613384023.0/490377888000.0,859236476684231.0/31384184832000.0,-696561442637.0/178319232000.0,1166309819657.0/4483454976000.0},{0.0,0.0,0.0,0.0,0.0,905730205.0/172204032.0,-140970750679621.0/5230697472000.0,89541175419277.0/871782912000.0,-34412222659093.0/124540416000.0,570885914358161.0/1046139494400.0,-31457535950413.0/38745907200.0,134046425652457.0/145297152000.0,-350379327127877.0/435891456000.0,310429955875453.0/581188608000.0,-10320787460413.0/38745907200.0,7222659159949.0/74724249600.0,-21029162113651.0/871782912000.0,6460951197929.0/1743565824000.0,-106364763817.0/402361344000.0},{0.0,0.0,0.0,0.0,0.0,0.0,13064406523627.0/2615348736000.0,-931781102989.0/39626496000.0,5963794194517.0/72648576000.0,-10498491598103.0/52306974720.0,20730767690131.0/58118860800.0,-34266367915049.0/72648576000.0,228133014533.0/486486000.0,-2826800577631.0/8072064000.0,2253957198793.0/11623772160.0,-20232291373837.0/261534873600.0,4588414555201.0/217945728000.0,-169639834921.0/48432384000.0,703604254357.0/2615348736000.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,4527766399.0/958003200.0,-6477936721.0/319334400.0,12326645437.0/191600640.0,-15064372973.0/106444800.0,35689892561.0/159667200.0,-41290273229.0/159667200.0,35183928883.0/159667200.0,-625551749.0/4561920.0,923636629.0/15206400.0,-17410248271.0/958003200.0,30082309.0/9123840.0,-4777223.0/17418240.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2132509567.0/479001600.0,-2067948781.0/119750400.0,1572737587.0/31933440.0,-1921376209.0/19958400.0,3539798831.0/26611200.0,-82260679.0/623700.0,2492064913.0/26611200.0,-186080291.0/3991680.0,2472634817.0/159667200.0,-52841941.0/17107200.0,26842253.0/95800320.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4325321.0/1036800.0,-104995189.0/7257600.0,6648317.0/181440.0,-28416361.0/453600.0,269181919.0/3628800.0,-222386081.0/3628800.0,15788639.0/453600.0,-2357683.0/181440.0,20884811.0/7257600.0,-25713.0/89600.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,14097247.0/3628800.0,-21562603.0/1814400.0,47738393.0/1814400.0,-69927631.0/1814400.0,862303.0/22680.0,-45586321.0/1814400.0,19416743.0/1814400.0,-4832053.0/1814400.0,1070017.0/3628800.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,16083.0/4480.0,-1152169.0/120960.0,242653.0/13440.0,-296053.0/13440.0,2102243.0/120960.0,-115747.0/13440.0,32863.0/13440.0,-5257.0/17280.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,198721.0/60480.0,-18637.0/2520.0,235183.0/20160.0,-10754.0/945.0,135713.0/20160.0,-5603.0/2520.0,19087.0/60480.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4277.0/1440.0,-2641.0/480.0,4991.0/720.0,-3649.0/720.0,959.0/480.0,-95.0/288.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1901.0/720.0,-1387.0/360.0,109.0/30.0,-637.0/360.0,251.0/720.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,55.0/24.0,-59.0/24.0,37.0/24.0,-3.0/8.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,23.0/12.0,-4.0/3.0,5.0/12.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0/2.0,-1.0/2.0},{0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a0f04fd5", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "92d5f951", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b2102df1", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "7fe79f91-5484-45b4-860c-970f22adf60e", + "metadata": {}, + "source": [ + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "2d3998a2-d525-48e2-84dc-b3dcc1cc191c", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "\n", + "Here is how we need to define our user methods and main function to solve this ODE backwards in time.\n", + "\n", + "#### diffy_Q_eval:\n", + "This time, we need to define two ODE's in an array as such:\n", + "\n", + "`dydx[0] = y[1]`\n", + "\n", + "`dydx[1] = y[0] - x`\n", + "\n", + "We'll also need to make sure `number_of_equations` variable in the main function reflects this amount of ODEs in the system\n", + "\n", + "#### known_Q_eval:\n", + "We're just changing the signs on all the x's in the equation to reflect the...well...reflection of the ODE. We also need an expression for the first derivative of that reflected solution:\n", + "\n", + "`y[0] = exp(-x) + exp(x) + x;`\n", + "\n", + "`y[1] = -exp(-x) + exp(x) + 1;`\n", + "\n", + "We do want the known solutions in exercise 2 so we can compare the known solution with Odie's solver.\n", + "\n", + "#### get_initial_condition:\n", + "Make sure to put in your initial conditions properly:\n", + "\n", + "`y[0] = 2.0`\n", + "\n", + "`y[1] = 1.0`" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "a0b0e98f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "\n", + "struct constant_parameters { \n", + " int dimension; // number that says how many we have. \n", + " // double rho;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " return 0;\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + "\n", + " dydx[0] = y[1];\n", + " dydx[1] = y[0] - x;\n", + "\n", + " return 1;\n", + "}\n", + "\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) //This function is the other one passed using GSL's formulation. \n", + "//Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + "\n", + " y[0] = exp(-x) + exp(x) + x;\n", + " y[1] = -exp(-x) + exp(x) + 1;\n", + "\n", + " return 1;\n", + " //report \"success\"\n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " y[0] = 2.0;\n", + " y[1] = 1.0;\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "feeeb6d7-2eec-4c0a-9475-dd3a362513cc", + "metadata": {}, + "source": [ + "The only thing that needs to change in the modifiable main function is the `number_of_equations` variable. We have 2 equations now, not 1." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "90ff0093", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.05; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 2; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 20; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = true;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oSData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_euler;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_euler;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " // AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF.\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "1aca01b3-742d-481e-a706-2acdb5eddec8", + "metadata": {}, + "source": [ + "Now time to plot and compare the solver to the known solutions." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "796bd7b3", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverSimple1 `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Simple Example: u''=u+x Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverSimple1\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverSimple1\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "7207ed74", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 1.\n", + "Printing to file 'oSData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t2.00000000000000e+00,\tEquation 1:,\t1.00000000000000e+00,\t\n", + "FINAL: Position:,\t1.00000000000000e+00,\tEquation 0:,\t4.04829627827785e+00,\tEquation 1:,\t3.32183139850209e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "3b089a2b", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 0:,\t2.00000000000000e+00,\tEquation 1:,\t1.00000000000000e+00,\t\n", + "Errors:,\tEquation 0:,\t0.0,\tTruth:,\t2.00000000000000e+00,\tEquation 1:,\t0.0,\tTruth:,\t1.00000000000000e+00,\t\n", + "Position:,\t5.00000000000000e-02,\tEquation 0:,\t2.05125000000000e+00,\tEquation 1:,\t1.10000000000000e+00,\t\n", + "Errors:,\tEquation 0:,\t1.25052087673794e-03,\tTruth:,\t2.05250052087674e+00,\tEquation 1:,\t4.16718753100120e-05,\tTruth:,\t1.10004167187531e+00,\t\n", + "Position:,\t1.00000000000000e-01,\tEquation 0:,\t2.10750078125000e+00,\tEquation 1:,\t1.20012500000000e+00,\t\n", + "Errors:,\tEquation 0:,\t2.50755486160736e-03,\tTruth:,\t2.11000833611161e+00,\tEquation 1:,\t2.08500039688087e-04,\tTruth:,\t1.20033350003969e+00,\t\n", + "Position:,\t1.50000000000000e-01,\tEquation 0:,\t2.16876171923828e+00,\tEquation 1:,\t1.30062511718750e+00,\t\n", + "Errors:,\tEquation 0:,\t3.78049991505991e-03,\tTruth:,\t2.17254221915334e+00,\tEquation 1:,\t5.01149115725186e-04,\tTruth:,\t1.30112626630323e+00,\t\n", + "Position:,\t2.00000000000000e-01,\tEquation 0:,\t2.23505470117218e+00,\tEquation 1:,\t1.40175109384766e+00,\t\n", + "Errors:,\tEquation 0:,\t5.07881006597222e-03,\tTruth:,\t2.24013351123815e+00,\tEquation 1:,\t9.20911234531641e-04,\tTruth:,\t1.40267200508219e+00,\t\n", + "Position:,\t2.50000000000000e-01,\tEquation 0:,\t2.30641416505280e+00,\tEquation 1:,\t1.50375492333992e+00,\t\n", + "Errors:,\tEquation 0:,\t6.41203470635121e-03,\tTruth:,\t2.31282619975915e+00,\tEquation 1:,\t1.46971027641629e-03,\tTruth:,\t1.50522463361634e+00,\t\n", + "Position:,\t3.00000000000000e-01,\tEquation 0:,\t2.38288717007295e+00,\tEquation 1:,\t1.60689047841965e+00,\t\n", + "Errors:,\tEquation 0:,\t7.78985818477151e-03,\tTruth:,\t2.39067702825772e+00,\tEquation 1:,\t2.15010847463826e-03,\tTruth:,\t1.60904058689429e+00,\t\n", + "Position:,\t3.50000000000000e-01,\tEquation 0:,\t2.46453349847523e+00,\tEquation 1:,\t1.71141414347231e+00,\t\n", + "Errors:,\tEquation 0:,\t9.22213983674380e-03,\tTruth:,\t2.47375563831197e+00,\tEquation 1:,\t2.96531540223688e-03,\tTruth:,\t1.71437945887454e+00,\t\n", + "Position:,\t4.00000000000000e-01,\tEquation 0:,\t2.55142578908539e+00,\tEquation 1:,\t1.81758545223574e+00,\t\n", + "Errors:,\tEquation 0:,\t1.07189545915203e-02,\tTruth:,\t2.56214474367691e+00,\tEquation 1:,\t3.91919936989238e-03,\tTruth:,\t1.82150465160563e+00,\t\n", + "Position:,\t4.50000000000000e-01,\tEquation 0:,\t2.64364970281535e+00,\tEquation 1:,\t1.92566773259766e+00,\t\n", + "Errors:,\tEquation 0:,\t1.22906342965878e-02,\tTruth:,\t2.65594033711194e+00,\tEquation 1:,\t5.01630127074004e-03,\tTruth:,\t1.93068403386840e+00,\t\n", + "Position:,\t5.00000000000000e-01,\tEquation 0:,\t2.74130412050950e+00,\tEquation 1:,\t2.03592876007130e+00,\t\n", + "Errors:,\tEquation 0:,\t1.39478099032644e-02,\tTruth:,\t2.75525193041276e+00,\tEquation 1:,\t6.26185091619824e-03,\tTruth:,\t2.04219061098749e+00,\t\n", + "Position:,\t5.50000000000000e-01,\tEquation 0:,\t2.84450137358838e+00,\tEquation 1:,\t2.14864142157182e+00,\t\n", + "Errors:,\tEquation 0:,\t1.57014546595016e-02,\tTruth:,\t2.86020282824788e+00,\tEquation 1:,\t7.66178591509270e-03,\tTruth:,\t2.15630320748691e+00,\t\n", + "Position:,\t6.00000000000000e-01,\tEquation 0:,\t2.95336750802546e+00,\tEquation 1:,\t2.26408439113972e+00,\t\n", + "Errors:,\tEquation 0:,\t1.75629284590717e-02,\tTruth:,\t2.97093043648454e+00,\tEquation 1:,\t9.22277315676467e-03,\tTruth:,\t2.27330716429648e+00,\t\n", + "Position:,\t6.50000000000000e-01,\tEquation 0:,\t3.06804258227497e+00,\tEquation 1:,\t2.38254281928545e+00,\t\n", + "Errors:,\tEquation 0:,\t1.95440234999467e-02,\tTruth:,\t3.08758660577491e+00,\tEquation 1:,\t1.09522329674268e-02,\tTruth:,\t2.39349505225288e+00,\t\n", + "Position:,\t7.00000000000000e-01,\tEquation 0:,\t3.18868099985316e+00,\tEquation 1:,\t2.50430903766125e+00,\t\n", + "Errors:,\tEquation 0:,\t2.16570114087258e-02,\tTruth:,\t3.21033801126189e+00,\tEquation 1:,\t1.28583660178125e-02,\tTruth:,\t2.51716740367907e+00,\t\n", + "Position:,\t7.50000000000000e-01,\tEquation 0:,\t3.31545187736113e+00,\tEquation 1:,\t2.62968328080245e+00,\t\n", + "Errors:,\tEquation 0:,\t2.39146919925584e-02,\tTruth:,\t3.33936656935369e+00,\tEquation 1:,\t1.49501830692089e-02,\tTruth:,\t2.64463346387166e+00,\t\n", + "Position:,\t8.00000000000000e-01,\tEquation 0:,\t3.44853944882460e+00,\tEquation 1:,\t2.75897442672101e+00,\t\n", + "Errors:,\tEquation 0:,\t2.63304437850849e-02,\tTruth:,\t3.47486989260969e+00,\tEquation 1:,\t1.72375376542369e-02,\tTruth:,\t2.77621196437525e+00,\t\n", + "Position:,\t8.50000000000000e-01,\tEquation 0:,\t3.58814350731617e+00,\tEquation 1:,\t2.89250075817894e+00,\t\n", + "Errors:,\tEquation 0:,\t2.89182765585481e-02,\tTruth:,\t3.61706178387472e+00,\tEquation 1:,\t1.97311617983242e-02,\tTruth:,\t2.91223191997726e+00,\t\n", + "Position:,\t9.00000000000000e-01,\tEquation 0:,\t3.73447988491719e+00,\tEquation 1:,\t3.03059074651861e+00,\t\n", + "Errors:,\tEquation 0:,\t3.16928859803594e-02,\tTruth:,\t3.76617277089755e+00,\tEquation 1:,\t2.24427048977400e-02,\tTruth:,\t3.05303345141635e+00,\t\n", + "Position:,\t9.50000000000000e-01,\tEquation 0:,\t3.88778097217119e+00,\tEquation 1:,\t3.17358385998104e+00,\t\n", + "Errors:,\tEquation 0:,\t3.46697105991542e-02,\tTruth:,\t3.92245068277035e+00,\tEquation 1:,\t2.53847758803007e-02,\tTruth:,\t3.19896863586135e+00,\t\n", + "Position:,\t1.00000000000000e+00,\tEquation 0:,\t4.04829627827785e+00,\tEquation 1:,\t3.32183139850209e+00,\t\n", + "Errors:,\tEquation 0:,\t3.78649913526345e-02,\tTruth:,\t4.08616126963049e+00,\tEquation 1:,\t2.85709887855106e-02,\tTruth:,\t3.35040238728760e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oSData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "54333d8f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "# csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "\n", + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " else:\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " i = i+1\n", + "\n", + "# Next we plot it all using matplotlib. \n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Exact and Calculated for Simple Problem')\n", + "ax.plot(positionList, truthList0, color='r', label=\"Exact\")\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"Calculated\")\n", + "ax.plot(positionList, truthList1, color='r', marker = 'o')\n", + "ax.plot(positionList, calculatedList1, color='b', marker = 'o')\n", + "\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "36a79a7c-1888-44ad-a3ef-575b8ecd7fb1", + "metadata": {}, + "source": [ + "Sure enough, this is the other side of our solutions, as if we went backwards in time.\n", + "\n", + "A very important note about his solution as mentioned in the question itself: The x-axis is still counting forward. This is because, technically, we are still moving forward in time, just on the reflected function. But you can be sure this is counting backwards in time." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "9e3ad2af", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " errorList0.append(float(row[2]))\n", + " errorList1.append(float(row[6]))\n", + " i = i+1\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Error')\n", + "ax.set_title('Error for Simple Problem')\n", + "ax.plot(positionList, errorList0, color='r', label = \"function\")\n", + "ax.plot(positionList, errorList1, color='r', marker = 'o', label = \"derivative\")\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying. \n", + "fig.set_size_inches(10,10)\n", + "ax.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "d870165d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np # numpy, for doing math with our data. \n", + "\n", + "# Make a bunch of lists to hold all our data. \n", + "positionList = []\n", + "errorList0 = []\n", + "errorList1 = []\n", + "truthList0 = []\n", + "truthList1 = []\n", + "# This counter here helps us keep track of where we are. \n", + "i = 0\n", + "\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oSData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " # Since we have alternating rows of data, we need to alternate our reading of it.\n", + " if (i % 2 == 0):\n", + " positionList.append(float(row[1]))\n", + " else:\n", + " errorList0.append(float(row[2]))\n", + " errorList1.append(float(row[6]))\n", + " truthList0.append(float(row[4]))\n", + " truthList1.append(float(row[8]))\n", + " i = i+1\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('Relative Error')\n", + "ax.set_title ('Relative Error for Simple Problem')\n", + "ax.plot(positionList, abs(np.array(errorList0)/np.array(truthList0)), color='r', label=\"function\")\n", + "ax.plot(positionList, abs(np.array(errorList1)/np.array(truthList1)), color='r', marker = 'o',label = \"derivative\")\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying. \n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "7a916225-09ed-4720-a721-a50436b55c84", + "metadata": {}, + "source": [ + "Finishing off, you can see the error of this reflected function." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_3_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_3_Solution.ipynb new file mode 100644 index 00000000..5e330ac6 --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_3_Solution.ipynb @@ -0,0 +1,2702 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 3 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "25ca112a-7b15-4664-9bef-366e62d52803", + "metadata": {}, + "source": [ + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "493a8fe7-f35b-41ea-abe8-d501da69f6f8", + "metadata": {}, + "source": [ + "1. [Exercise 3](#E3)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "c1a7966a-8405-47eb-9a7b-354ac989b206", + "metadata": {}, + "source": [ + "\n", + "# Exercise 3 \\[Back to [top](#toc)\\]\n", + "\n", + "\"3) We can observe curious phenomena with the AB methods. For the TOV equations (Step 3 in [Examples](NRPy+_OdieGM_Examples.ipynb)), use all the AB orders 1 through 19, seeding them with the DP8 method. At which order is the result most accurate (compared to the old TOV solver)? At what order does the result start to break down?\"\n", + "\n", + "This solution is more code than math. We're really just making a few updates to the modifiable main in what numerical method we are using to solve the ODE. That's all. \n", + "\n", + "To start, we need to use the template for the complicated example in Step 3 of the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. This is actually the default settings for the solver itself, and we won't make many changes to it at all." + ] + }, + { + "cell_type": "markdown", + "id": "a5bc196a-dc7c-4e1b-b72e-805a52827277", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "d9b4753f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = {{333374427829017307697.0/51090942171709440000.0,-5148905233415267713.0/109168679854080000.0,395276943631267674287.0/1548210368839680000.0,-2129159630108649501931.0/2128789257154560000.0,841527158963865085639.0/283838567620608000.0,-189774312558599272277.0/27646613729280000.0,856822959645399341657.0/67580611338240000.0,-13440468702008745259589.0/709596419051520000.0,196513123964380075325537.0/8515157028618240000.0,-57429776853357830333.0/2494674910728000.0,53354279746900330600757.0/2838385676206080000.0,-26632588461762447833393.0/2128789257154560000.0,4091553114434184723167.0/608225502044160000.0,-291902259907317785203.0/101370917007360000.0,816476630884557765547.0/851515702861824000.0,-169944934591213283591.0/709596419051520000.0,239730549209090923561.0/5676771352412160000.0,-19963382447193730393.0/4257578514309120000.0,12600467236042756559.0/51090942171709440000.0},{0.0,57424625956493833.0/9146248151040000.0,-3947240465864473.0/92386344960000.0,497505713064683651.0/2286562037760000.0,-511501877919758129.0/640237370572800.0,65509525475265061.0/29640619008000.0,-38023516029116089751.0/8002967132160000.0,129650088885345917773.0/16005934264320000.0,-19726972891423175089.0/1778437140480000.0,3146403501110383511.0/256094948229120.0,-70617432699294428737.0/6402373705728000.0,14237182892280945743.0/1778437140480000.0,-74619315088494380723.0/16005934264320000.0,17195392832483362153.0/8002967132160000.0,-4543527303777247.0/5928123801600.0,653581961828485643.0/3201186852864000.0,-612172313896136299.0/16005934264320000.0,2460247368070567.0/547211427840000.0,-85455477715379.0/342372925440000.0},{0.0,0.0,14845854129333883.0/2462451425280000.0,-55994879072429317.0/1455084933120000.0,2612634723678583.0/14227497123840.0,-22133884200927593.0/35177877504000.0,5173388005728297701.0/3201186852864000.0,-5702855818380878219.0/1778437140480000.0,80207429499737366711.0/16005934264320000.0,-3993885936674091251.0/640237370572800.0,2879939505554213.0/463134672000.0,-324179886697104913.0/65330343936000.0,7205576917796031023.0/2286562037760000.0,-2797406189209536629.0/1778437140480000.0,386778238886497951.0/640237370572800.0,-551863998439384493.0/3201186852864000.0,942359269351333.0/27360571392000.0,-68846386581756617.0/16005934264320000.0,8092989203533249.0/32011868528640000.0},{0.0,0.0,0.0,362555126427073.0/62768369664000.0,-2161567671248849.0/62768369664000.0,740161300731949.0/4828336128000.0,-4372481980074367.0/8966909952000.0,72558117072259733.0/62768369664000.0,-131963191940828581.0/62768369664000.0,62487713370967631.0/20922789888000.0,-70006862970773983.0/20922789888000.0,62029181421198881.0/20922789888000.0,-129930094104237331.0/62768369664000.0,10103478797549069.0/8966909952000.0,-2674355537386529.0/5706215424000.0,9038571752734087.0/62768369664000.0,-1934443196892599.0/62768369664000.0,36807182273689.0/8966909952000.0,-25221445.0/98402304.0},{0.0,0.0,0.0,0.0,13325653738373.0/2414168064000.0,-60007679150257.0/1961511552000.0,3966421670215481.0/31384184832000.0,-25990262345039.0/70053984000.0,25298910337081429.0/31384184832000.0,-2614079370781733.0/1961511552000.0,17823675553313503.0/10461394944000.0,-2166615342637.0/1277025750.0,13760072112094753.0/10461394944000.0,-1544031478475483.0/1961511552000.0,1600835679073597.0/4483454976000.0,-58262613384023.0/490377888000.0,859236476684231.0/31384184832000.0,-696561442637.0/178319232000.0,1166309819657.0/4483454976000.0},{0.0,0.0,0.0,0.0,0.0,905730205.0/172204032.0,-140970750679621.0/5230697472000.0,89541175419277.0/871782912000.0,-34412222659093.0/124540416000.0,570885914358161.0/1046139494400.0,-31457535950413.0/38745907200.0,134046425652457.0/145297152000.0,-350379327127877.0/435891456000.0,310429955875453.0/581188608000.0,-10320787460413.0/38745907200.0,7222659159949.0/74724249600.0,-21029162113651.0/871782912000.0,6460951197929.0/1743565824000.0,-106364763817.0/402361344000.0},{0.0,0.0,0.0,0.0,0.0,0.0,13064406523627.0/2615348736000.0,-931781102989.0/39626496000.0,5963794194517.0/72648576000.0,-10498491598103.0/52306974720.0,20730767690131.0/58118860800.0,-34266367915049.0/72648576000.0,228133014533.0/486486000.0,-2826800577631.0/8072064000.0,2253957198793.0/11623772160.0,-20232291373837.0/261534873600.0,4588414555201.0/217945728000.0,-169639834921.0/48432384000.0,703604254357.0/2615348736000.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,4527766399.0/958003200.0,-6477936721.0/319334400.0,12326645437.0/191600640.0,-15064372973.0/106444800.0,35689892561.0/159667200.0,-41290273229.0/159667200.0,35183928883.0/159667200.0,-625551749.0/4561920.0,923636629.0/15206400.0,-17410248271.0/958003200.0,30082309.0/9123840.0,-4777223.0/17418240.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2132509567.0/479001600.0,-2067948781.0/119750400.0,1572737587.0/31933440.0,-1921376209.0/19958400.0,3539798831.0/26611200.0,-82260679.0/623700.0,2492064913.0/26611200.0,-186080291.0/3991680.0,2472634817.0/159667200.0,-52841941.0/17107200.0,26842253.0/95800320.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4325321.0/1036800.0,-104995189.0/7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+ "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "a0f04fd5", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "92d5f951", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "b2102df1", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "e343e75d-b8d7-4b96-8484-321696b5e5d0", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "\n", + "For the solution to Exercise 3, we need to make no changes to the `user_methods` function, so we'll just just leave it in the complicated example's format." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "9e200082", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "\n", + "struct constant_parameters { \n", + " int dimension; // number that says how many we have. \n", + " double rho;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to hard code some limitations \n", + " // on some varaibles.\n", + " // Good for avoding some divide by zero errors, or going negative in a square root. \n", + " if (y[0] < 0) {\n", + " y[0] = 0;\n", + " }\n", + " // In this case, the TOV Equations, we need to make sure the pressure doesn't go negative.\n", + " // Physically, it cannot, but approximation methods can cross the P=0 line\n", + " // We just need a hard wall to prevent that. \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to have \n", + " // a special termination condition.\n", + " // Today we do. We terminate once the pressure hits zero, or goes below it. \n", + " // Notably we also consider ridiculously small pressures to be \"zero\" since we might be asymptotic. \n", + " if (y[0] < 1e-16) {\n", + " return 1;\n", + " } else {\n", + " return 0;\n", + " }\n", + " // return 1; for termination.\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + " // Sometimes we want to evaluate constants in the equation that change, \n", + " // but do not have derivative forms.\n", + " // Today, we do that for the total energy density. \n", + " params->rho = sqrt(y[0]) + y[0];\n", + " // The total energy density only depends on pressure. \n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + " // GSL-adapted evaluation function. \n", + " // It is possible to do this with one array, but GSL expects two. \n", + "\n", + " // Always check for exceptions first, then perform evaluations. \n", + " exception_handler(x,y);\n", + " const_eval(x,y,params);\n", + "\n", + " // Dereference the struct\n", + " double rho = (*(struct constant_parameters*)params).rho;\n", + " // double parameter = (*(struct constant_parameters*)params).parameter;\n", + " // WHY oh WHY GSL do you demand we use a VOID POINTER to the struct...?\n", + " // https://stackoverflow.com/questions/51052314/access-variables-in-struct-from-void-pointer\n", + " // Make sure to dereference every parameter within the struct so it can be used below. \n", + "\n", + " // This if statement is an example of a special condition, \n", + " // in this case at x=0 we have a divide by zero problem. \n", + " // Fortunately, we manually know what the derivatives should be.\n", + " // Alternatively, we could define piecewise equations this way. \n", + " if(x == 0) {\n", + " dydx[0] = 0; \n", + " dydx[1] = 0;\n", + " dydx[2] = 0;\n", + " dydx[3] = 1;\n", + " }\n", + " else {\n", + " dydx[0] = -((rho+y[0])*( (2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0] ))/(x*2.0*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[1] = ((2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0])/(x*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[2] = 4*3.1415926535897931160*x*x*rho;\n", + " dydx[3] = (y[3])/(x*sqrt(1.0-(2.0*y[2])/x));\n", + " // Visual Studio likes to complain that M_PI is not defined, even though it is. \n", + " // So we used 3.1415926535897931160. which is just M_PI printed out to extra digits.\n", + " // There was no observed change in the final product. \n", + " }\n", + " // This funciton is not guaranteed to work in all cases. For instance, we have manually \n", + " // made an exception for x=0, since evaluating at 0 produces infinities and NaNs. \n", + " // Be sure to declare any exceptions before running, both here and in exception_handler, \n", + " // depending on the kind of exception desired. \n", + "\n", + " return 0;\n", + " // GSL_SUCCESS is 0. We do not support fancy error codes like GSL. \n", + "}\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) // This function is another one passed using GSL's formulation. \n", + "// Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + " // y[0] = ...\n", + " // y[1] = ...\n", + " // This function is only used if there are known solutions. \n", + " // Notably this is not the case for the TOV equations. \n", + " // If you do put anything here, make SURE it has the same order as the differential equations. \n", + " // In the case of TOV, that would be Pressure, nu, mass, and r-bar, in that order. \n", + "\n", + " return 1;\n", + " // report \"success,\" what would have been GSL_SUCCESS in the GSL formulation. \n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " // be sure to have these MATCH the equations in diffy_Q_eval\n", + " y[0] = 0.016714611225000002; // Pressure, can be calcualated from central baryon density. \n", + " y[1] = 0.0; // nu\n", + " y[2] = 0.0; // mass\n", + " y[3] = 0.0; // r-bar\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + " // Reading parameters from the constant_parameters struct is rather difficult, since it exists\n", + " // in the higher order \"objects\" as a void pointer. So the user should declare what constants\n", + " // are what for ease of use, usually for printing in an algorithmic way.\n", + " c[0] = params->rho; // Total energy density. \n", + " // Add more as required. \n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "da9ada0c-befa-4959-ad71-634e06e27a6e", + "metadata": {}, + "source": [ + "The modifiable main is where the modifications need to be made. The two places I want to draw your attention to in the function is the variables `adams_bashforth_order` and `step_type` and the evaluation of the variable `step_type_2`.\n", + "\n", + "#### adams_bashforth_order\n", + "This is the variable you want to change and investigate. Just plug try out the numbers 1-19, and see what orders of AB work well, and which ones work terrible. It is a lesson that the highest order of a numerical method is not always the best. It depends on what you system of ODEs looks like. I noticed around order 5 and 6 had the best agreement.\n", + "\n", + "#### step_type\n", + "Set your numerical method to an AB method. You can do this by setting the variable from `nrpy_odiegm_step_RK4` to `nrpy_odiegm_step_AB`.\n", + "\n", + "#### step_type_2\n", + "This seeds your main numerical method with another method. We want specifically to seed it with DP8, so we want to set the variable from `nrpy_odiegm_step_RK4` to `nrpy_odiegm_step_DP8`." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "ffce7883", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 19; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_AB;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_DP8;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "411ef7c7-f080-4cbc-8df8-fbe8f2ec06bb", + "metadata": {}, + "source": [ + "For the purpose of this solution guide, I want to illustrate the errors at there worst, so I'm going to use a 19th order AB method (changing `adams_bashforth_order` to 19). You will see that the error starts to grow by a large amount. Let me plot these." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "555a60e1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated1 `...\n", + "(BENCH): Finished executing in 0.20 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above.\n", + "\n", + "os.chdir(\"../\")\n", + "# Return to parent directory\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated1\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverComplicated1\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "ad9bf613", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 19.\n", + "Printing to file 'oCData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t1.67146112250000e-02,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\tEquation 3:,\t0.00000000000000e+00,\tConstant 0:,\t1.45999611225000e-01,\t\n", + "FINAL: Position:,\t5.60000000000000e-03,\tEquation 0:,\t0.00000000000000e+00,\tEquation 1:,\t2.82652350329674e-01,\tEquation 2:,\t-7.07938784797796e-06,\tEquation 3:,\t-1.79251830198112e+143,\tConstant 0:,\t0.00000000000000e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "1b3f1983", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 0:,\t1.67146112250000e-02,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\tEquation 3:,\t0.00000000000000e+00,\tConstant 0:,\t1.45999611225000e-01,\t\n", + "Position:,\t1.00000000000000e-05,\tEquation 0:,\t1.67146112183157e-02,\tEquation 1:,\t8.21603740697393e-11,\tEquation 2:,\t6.11561741320131e-16,\tEquation 3:,\t1.00000000003048e-05,\tConstant 0:,\t1.45999611192465e-01,\t\n", + "Position:,\t2.00000000000000e-05,\tEquation 0:,\t1.67146111982627e-02,\tEquation 1:,\t3.28641496239836e-10,\tEquation 2:,\t4.89249392859855e-15,\tEquation 3:,\t2.00000000024442e-05,\tConstant 0:,\t1.45999611094858e-01,\t\n", + "Position:,\t3.00000000000000e-05,\tEquation 0:,\t1.67146111648410e-02,\tEquation 1:,\t7.39443366392778e-10,\tEquation 2:,\t1.65121669979811e-14,\tEquation 3:,\t3.00000000082530e-05,\tConstant 0:,\t1.45999610932181e-01,\t\n", + "Position:,\t4.00000000000000e-05,\tEquation 0:,\t1.67146111180507e-02,\tEquation 1:,\t1.31456598433274e-09,\tEquation 2:,\t3.91399513659886e-14,\tEquation 3:,\t4.00000000195659e-05,\tConstant 0:,\t1.45999610704432e-01,\t\n", + "Position:,\t5.00000000000000e-05,\tEquation 0:,\t1.67146110578917e-02,\tEquation 1:,\t2.05400934978556e-09,\tEquation 2:,\t7.64452174197046e-14,\tEquation 3:,\t5.00000000382175e-05,\tConstant 0:,\t1.45999610411613e-01,\t\n", + "Position:,\t6.00000000000000e-05,\tEquation 0:,\t1.67146109843641e-02,\tEquation 1:,\t2.95777346239874e-09,\tEquation 2:,\t1.32097335506963e-13,\tEquation 3:,\t6.00000000660426e-05,\tConstant 0:,\t1.45999610053723e-01,\t\n", + "Position:,\t7.00000000000000e-05,\tEquation 0:,\t1.67146108974678e-02,\tEquation 1:,\t4.02585832174147e-09,\tEquation 2:,\t2.09765675926534e-13,\tEquation 3:,\t7.00000001048757e-05,\tConstant 0:,\t1.45999609630762e-01,\t\n", + "Position:,\t8.00000000000000e-05,\tEquation 0:,\t1.67146107972028e-02,\tEquation 1:,\t5.25826392730459e-09,\tEquation 2:,\t3.13119608918315e-13,\tEquation 3:,\t8.00000001565517e-05,\tConstant 0:,\t1.45999609142730e-01,\t\n", + "Position:,\t9.00000000000000e-05,\tEquation 0:,\t1.67146106835692e-02,\tEquation 1:,\t6.65499027850062e-09,\tEquation 2:,\t4.45828504653516e-13,\tEquation 3:,\t9.00000002229052e-05,\tConstant 0:,\t1.45999608589626e-01,\t\n", + "Position:,\t1.00000000000000e-04,\tEquation 0:,\t1.67146105565670e-02,\tEquation 1:,\t8.21603737466374e-09,\tEquation 2:,\t6.11561733224844e-13,\tEquation 3:,\t1.00000000305771e-04,\tConstant 0:,\t1.45999607971452e-01,\t\n", + "Position:,\t1.10000000000000e-04,\tEquation 0:,\t1.67146104161960e-02,\tEquation 1:,\t9.94140521504981e-09,\tEquation 2:,\t8.13988664636699e-13,\tEquation 3:,\t1.10000000406983e-04,\tConstant 0:,\t1.45999607288207e-01,\t\n", + "Position:,\t1.20000000000000e-04,\tEquation 0:,\t1.67146102624564e-02,\tEquation 1:,\t1.18310937988363e-08,\tEquation 2:,\t1.05677866879535e-12,\tEquation 3:,\t1.20000000528377e-04,\tConstant 0:,\t1.45999606539892e-01,\t\n", + "Position:,\t1.30000000000000e-04,\tEquation 0:,\t1.67146100953481e-02,\tEquation 1:,\t1.38851031251225e-08,\tEquation 2:,\t1.34360111549914e-12,\tEquation 3:,\t1.30000000671787e-04,\tConstant 0:,\t1.45999605726505e-01,\t\n", + "Position:,\t1.40000000000000e-04,\tEquation 0:,\t1.67146099148712e-02,\tEquation 1:,\t1.61034331929292e-08,\tEquation 2:,\t1.67812537442864e-12,\tEquation 3:,\t1.40000000839049e-04,\tConstant 0:,\t1.45999604848047e-01,\t\n", + "Position:,\t1.50000000000000e-04,\tEquation 0:,\t1.67146097210257e-02,\tEquation 1:,\t1.84860840011990e-08,\tEquation 2:,\t2.06402081513689e-12,\tEquation 3:,\t1.50000001031995e-04,\tConstant 0:,\t1.45999603904518e-01,\t\n", + "Position:,\t1.60000000000000e-04,\tEquation 0:,\t1.67146095138114e-02,\tEquation 1:,\t2.10330555487960e-08,\tEquation 2:,\t2.50495680703953e-12,\tEquation 3:,\t1.60000001252462e-04,\tConstant 0:,\t1.45999602895918e-01,\t\n", + "Position:,\t1.70000000000000e-04,\tEquation 0:,\t1.67146092932285e-02,\tEquation 1:,\t2.37443478345061e-08,\tEquation 2:,\t3.00460271940503e-12,\tEquation 3:,\t1.70000001502284e-04,\tConstant 0:,\t1.45999601822248e-01,\t\n", + "Position:,\t1.80000000000000e-04,\tEquation 0:,\t1.67146090592770e-02,\tEquation 1:,\t2.66199608570368e-08,\tEquation 2:,\t3.56662792134484e-12,\tEquation 3:,\t1.80000001783296e-04,\tConstant 0:,\t1.45999600683506e-01,\t\n", + "Position:,\t1.90000000000000e-04,\tEquation 0:,\t1.67146088119568e-02,\tEquation 1:,\t2.96598946150174e-08,\tEquation 2:,\t4.19470178180362e-12,\tEquation 3:,\t1.90000002097332e-04,\tConstant 0:,\t1.45999599479693e-01,\t\n", + "Position:,\t2.00000000000000e-04,\tEquation 0:,\t1.67146085512679e-02,\tEquation 1:,\t3.28641491070003e-08,\tEquation 2:,\t4.89249366954752e-12,\tEquation 3:,\t2.00000002446262e-04,\tConstant 0:,\t1.45999598210810e-01,\t\n", + "Position:,\t2.10000000000000e-04,\tEquation 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2:,\t1.14830920408692e-06,\tEquation 3:,\t-5.84113927547098e+139,\tConstant 0:,\t1.81019850089872e-01,\t\n", + "Position:,\t5.45000000000000e-03,\tEquation 0:,\t8.10931225249104e-03,\tEquation 1:,\t1.05921839058530e-01,\tEquation 2:,\t-1.59424194290403e-07,\tEquation 3:,\t1.05115494952841e+140,\tConstant 0:,\t9.81610321277441e-02,\t\n", + "Position:,\t5.46000000000000e-03,\tEquation 0:,\t2.59062237742952e-02,\tEquation 1:,\t-1.13012626528102e-01,\tEquation 2:,\t-5.75159519613221e-07,\tEquation 3:,\t-1.46936473946773e+140,\tConstant 0:,\t1.86860328333002e-01,\t\n", + "Position:,\t5.47000000000000e-03,\tEquation 0:,\t7.21476736052882e-03,\tEquation 1:,\t1.16705896623390e-01,\tEquation 2:,\t1.83527793573080e-06,\tEquation 3:,\t1.34292667277912e+140,\tConstant 0:,\t9.21545540363195e-02,\t\n", + "Position:,\t5.48000000000000e-03,\tEquation 0:,\t2.61715257517616e-02,\tEquation 1:,\t-1.16114599480253e-01,\tEquation 2:,\t-2.80243081001627e-06,\tEquation 3:,\t3.13236692119283e+139,\tConstant 0:,\t1.87947685156544e-01,\t\n", + "Position:,\t5.49000000000000e-03,\tEquation 0:,\t7.68480230661429e-03,\tEquation 1:,\t1.10810174760830e-01,\tEquation 2:,\t4.25019803932208e-06,\tEquation 3:,\t-5.03209315711650e+140,\tConstant 0:,\t9.53478065137158e-02,\t\n", + "Position:,\t5.50000000000000e-03,\tEquation 0:,\t2.48778708807847e-02,\tEquation 1:,\t-1.00068203695803e-01,\tEquation 2:,\t-5.33539599337215e-06,\tEquation 3:,\t1.45540553318168e+141,\tConstant 0:,\t1.82605074878018e-01,\t\n", + "Position:,\t5.51000000000000e-03,\tEquation 0:,\t9.86817064989672e-03,\tEquation 1:,\t8.36942555475350e-02,\tEquation 2:,\t6.82227615572374e-06,\tEquation 3:,\t-2.96032518819080e+141,\tConstant 0:,\t1.09206837088986e-01,\t\n", + "Position:,\t5.52000000000000e-03,\tEquation 0:,\t2.17670392071399e-02,\tEquation 1:,\t-6.12618516133865e-02,\tEquation 2:,\t-7.83993985758245e-06,\tEquation 3:,\t4.71510337034237e+141,\tConstant 0:,\t1.69303608257460e-01,\t\n", + "Position:,\t5.53000000000000e-03,\tEquation 0:,\t1.39163295376528e-02,\tEquation 1:,\t3.29406815946420e-02,\tEquation 2:,\t9.14201565338029e-06,\tEquation 3:,\t-5.56987326485155e+141,\tConstant 0:,\t1.31883823101146e-01,\t\n", + "Position:,\t5.54000000000000e-03,\tEquation 0:,\t1.68016949306995e-02,\tEquation 1:,\t1.27656418184229e-03,\tEquation 2:,\t-9.83153652799884e-06,\tEquation 3:,\t2.90161454320736e+141,\tConstant 0:,\t1.46423047071076e-01,\t\n", + "Position:,\t5.55000000000000e-03,\tEquation 0:,\t1.97515254724371e-02,\tEquation 1:,\t-4.07437976792384e-02,\tEquation 2:,\t1.06590467557034e-05,\tEquation 3:,\t7.88610743101940e+141,\tConstant 0:,\t1.60291645980558e-01,\t\n", + "Position:,\t5.56000000000000e-03,\tEquation 0:,\t1.01727398929971e-02,\tEquation 1:,\t8.49448944925734e-02,\tEquation 2:,\t-1.07156360324889e-05,\tEquation 3:,\t-3.30192116479716e+142,\tConstant 0:,\t1.11032741345491e-01,\t\n", + "Position:,\t5.57000000000000e-03,\tEquation 0:,\t2.70638570191195e-02,\tEquation 1:,\t-1.32658571645197e-01,\tEquation 2:,\t1.07695906898733e-05,\tEquation 3:,\t7.77852314520845e+142,\tConstant 0:,\t1.91574820237744e-01,\t\n", + "Position:,\t5.58000000000000e-03,\tEquation 0:,\t2.33013177772568e-03,\tEquation 1:,\t1.82752666747050e-01,\tEquation 2:,\t-9.92389546483582e-06,\tEquation 3:,\t-1.39686441528227e+143,\tConstant 0:,\t5.06015703074160e-02,\t\n", + "Position:,\t5.59000000000000e-03,\tEquation 0:,\t3.52198286124601e-02,\tEquation 1:,\t-2.33350438369304e-01,\tEquation 2:,\t8.98508013654645e-06,\tEquation 3:,\t1.95147479297132e+143,\tConstant 0:,\t2.22889294995407e-01,\t\n", + "Position:,\t5.60000000000000e-03,\tEquation 0:,\t0.00000000000000e+00,\tEquation 1:,\t2.82652350329674e-01,\tEquation 2:,\t-7.07938784797796e-06,\tEquation 3:,\t-1.79251830198112e+143,\tConstant 0:,\t0.00000000000000e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oCData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "81d4cc5d-f21b-4fcf-92f9-f1a7ac2def85", + "metadata": {}, + "source": [ + "Don't worry if you get the error \"IOPub data rate exceeded,\" That just means jupyter can't print all the data in the file. You can still see the data in the `oCData.txt` file directly.\n", + "\n", + "Let's see what our function plots look like." + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "fa051a1d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "# Csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "# plt.ylim(0.0,0.15)\n", + "# plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "cc265c0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution Detail')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "plt.ylim(0.0,0.15)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "6158773a-0bbd-40e1-a874-3f60c70070cc", + "metadata": {}, + "source": [ + "Yikes, these look ugly! This just shows when you choose your numerical method you are using, try out multiple methods. Some might work better than others for different situations. It is clear in this case the 19th order AB seeded with DP8 is not a great method to use given our ODE system. Frankly though, you would probably never want to use the 19th order AB anyway.\n", + "\n", + "Let's look to see what is happening with the error." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "a41b0876", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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AMnPmTLP6ly5dUgDF1dVViY6ONtsXGhqq+Pj4KLGxsaZtR44cUbRarTJ48GDTtvfff18BlAEDBpjVv3XrlgIon332Wa634366dOmilCtXzmxbuXLlFEBZv3692fYPPvhAcXJyUs6ePWu2/Y033lB0Op1y+fJl07Z7H/e0tDSlRo0aStu2bc22Ozk5KUOGDLFol/H5eenSJYt27dixw7QtOjpa0ev1yvjx403bxowZo2g0GuXQoUOmbbGxsYqHh4fFMe915MgRBVDGjh2bY5mssnvOK8rdx37evHmmbUOGDFEAZcyYMaZtBoNB6dKli2JnZ6fExMSYtt/7nB88eLCi1WqVf/75x6INBoNBURRFSUlJUTIzMy3aodfrzV4X2bXN+DwziouLU+zt7ZXXX3/d7HgvvfSS4uTkpCQmJuZ8pyjqa6J69epm2wDFzs5OOX/+vGmb8f7++uuvTds+++yzbB+nsLAwRafTKR999JHZ9mPHjik2NjZm23N6TSrK3efRr7/+atoWHx+v+Pn5KXXq1DFtGzdunAIoO3fuNG27ffu2EhwcrAQFBZnu6+zuz+ze9xYtWmTx/C3sbU1LS1N8fHyU0NBQJTU11VTu+++/VwClVatWFu3Iyngbs75W7nXw4EEFUF555RXTNkDRarXKiRMnLMrf+9zt1q2b4ujoqFy7ds207dy5c4qNjY3Fe365cuXM3g+M7wPt27c3Pc8VRVFefvllRafTKXFxcaZt2d3nI0eOVBwdHc0+A4YMGWLxnpedrM/hSZMmKYBy4MABRVHuPuZZ33+N7wVz585VYmJilOvXryvr169XKlSooGg0GmXfvn1mxx8yZIji5OSkxMTEKDExMcr58+eVKVOmKBqNRqlVq5ap3IABAxR/f3+z17bxMcn6nMtOXsrkJrvPCCN3d3eldu3a963/0ksvKYBy9OhRRVEU5ebNm4per7f4THvjjTcUQDlz5kyubcruse7YsaNSvnx50/8rV65UgGzfM/Pj3s+o+32uZ/e5pSjZf07kdL8ay1atWtXsNT19+nQFUI4dO1ao2/Mwku5Vj5D27dvj7e1NQEAAvXv3xsnJiVWrVlG2bFlA7bKxZcsW+vbty+3bt7lx4wY3btwgNjaWjh07cu7cufumd7OOA0hKSuLGjRs0bdoURVGyTRnnRb9+/YiOjjbr0rJ8+XIMBgP9+vWzSruNnnjiCTZu3Gjx16ZNG7Nyer2eYcOGZXuMXr16mf2qFxERweHDhxk6dKjZryO1atWiQ4cOrF271uIY986W5eDggJ2dHdu2bePWrVu53o78Cg4OtuhCs2zZMlq0aEGpUqVM9+eNGzdo3749mZmZ7Nixw6x9Rrdu3SI+Pp4WLVoUuIuCUbVq1UzdFUD9Vbhy5cpcvHjRtG39+vU0adKE0NBQ0zYPD4889RNOSEgAyLZblbVk7cZi7KaSlpbGpk2bsi1vMBj47bff6Natm2n8VVbGLip6vd40CDczM5PY2FicnZ2pXLlyvu93Nzc3nnjiCVMfa+MxlyxZQo8ePQo0pgjU95us2axatWrh6upq9vjlZMWKFRgMBvr27Wv2/PP19aVixYps3brVrPz9XpP+/v5mmQpXV1cGDx7MoUOHiIyMBNTJLRo2bGjqzgjqr5HPPfccYWFhpm6S2cn6/DdmSxs3bgyQp8cir7d1//79REdHM2rUKLPM69ChQ3Fzc8v1PLdv3wbu/3w37jO+NoxatWpFtWrV7nv8zMxMNm3aRI8ePcwybRUqVKBz5865ts/oueeeM+uK1aJFCzIzMwkPDzdty3qfG9/zW7RoQXJyMqdPn87zubIzduxYSpUqxaRJk3ItO3z4cLy9vfH396dTp07Ex8fz008/0aBBA4uySUlJeHt74+3tTYUKFXjrrbdo0qQJK1euNJUZPHgw169fN3t+//LLLzg4ONCrVy/TtuTkZLPnijFDn5iYaLbNmp8Xt2/fzvW98t7nT6lSpXj88cdZtWoVSUlJgDpucPHixdSvXz9Pk7Rkfazj4+O5ceMGrVq14uLFi8THxwOYMoFr1qwpkhnY7v1ct7Zhw4aZvaaNn3t5ea981Ej3qkfIjBkzqFSpEvHx8cydO5cdO3aYdUM5f/48iqLw7rvv8u6772Z7jOjo6BxTvJcvX+a9995j1apVFm92xjeH/OrUqRNubm4sWbKEdu3aAWrXqtDQUNMbVmHbbVS2bFnat2+fa5vKlCmT4yCy4OBgs/+NH5SVK1e2KFu1alU2bNhgMVj83mPo9Xo++eQTxo8fT+nSpWncuDFdu3Zl8ODBFjOkFMS95wO1S8rRo0dzfKONjo42XV+zZg0ffvghhw8fNpv+sbBrQWTX5alUqVJmz63w8HCaNGliUa5ChQq5Ht/V1RW4+2XM2rRarcVAReNzNqexJjExMSQkJOQ6Ba3BYGD69Ol8++23XLp0yawvu6enZ77bOnjwYJYsWWKaaWbTpk1ERUUxaNCgfB/LKC+PX07OnTuHoihUrFgx2/22trZm/9/vNVmhQgWL52LWx8HX15fw8PBs+5ZXrVoVUJ9nOT0mN2/eZNKkSSxevNjsdQF5e9/L6201vpfcW87W1tbieZYd4xfC+z3fcwpMsnuPuFd0dDR37tzJ9rWXl9ej0b3PG2NXpazPmxMnTvDOO++wZcsWiwCpoJ81Rm5ubowbN47333+fQ4cO3ber1HvvvUeLFi1ITExk5cqVLF68OMcZuezt7Vm9ejWAaZyW8Qc/ow4dOuDn58cvv/xCu3btMBgMLFq0iCeeeMLsMfn000+zDYrGjBljmj0KoFy5clabEt3FxSXX98rsnj9PPfUUK1eu5Pfff2fgwIHs3r2bsLAwxo4dm6fz7tq1i/fff589e/aQnJxsti8+Ph43NzdatWpFr169mDRpElOnTqV169b06NGDgQMHWmXCgrw8/wsjL8/5/woJOh4hDRs2NP162qNHD5o3b87AgQM5c+YMzs7OpgHCr776ao6DR3P68MjMzKRDhw7cvHmT119/nSpVquDk5MS1a9cYOnSoxeDjvNLr9fTo0YOVK1fy7bffEhUVxa5du5gyZYqpTGHaXRD3m9nJGrM+ZXeMcePG0a1bN3777Tc2bNjAu+++y8cff8yWLVss+v9a43wGg4EOHTpYzMBiZPzStnPnTrp3707Lli359ttv8fPzw9bWlnnz5rFw4cJCtSunGa2Mv8YXVoUKFbCxseHYsWN5Kp9TEFUc63hMmTKFd999l+HDh/PBBx/g4eGBVqtl3LhxBXqtdezYkdKlS/Pzzz/TsmVLfv75Z3x9ffMUhOekMI+fwWBAo9Gwbt26bI9zb5/oBznb2r369u3L7t27mTBhAqGhoab30k6dOuXpscjvbS0oYwB19OhRs8xgVkePHgWwyGo86NnssmN83sTFxdGqVStcXV2ZPHkyISEh2Nvbc/DgQV5//fUCf9ZkZRzbMWnSpPuur1CzZk3Ta6RHjx4kJyczYsQImjdvbjHGRqfT5fp60ul0DBw4kB9++IFvv/2WXbt2cf36dYvZlAYPHmyWlQM1YJkwYQKPPfaYaZs1H7eqVaty6NAhUlNTc/wif/ToUWxtbc0C465du+Lm5sbChQsZOHAgCxcuRKfT0b9//1zPeeHCBdq1a0eVKlX48ssvCQgIwM7OjrVr1zJ16lTTY21cYG/v3r2sXr2aDRs2MHz4cL744gv27t1b6NdQdvejNT8Pivqz7mEiQccjSqfT8fHHH9OmTRu++eYb3njjDdOvZba2tvn+snHs2DHOnj3LggULzAYqbty40aJsfn8B79evHwsWLGDz5s2cOnUKRVFMXauAQrW7qJUrVw5QB2vf6/Tp03h5eeW5+0pISAjjx49n/PjxnDt3jtDQUL744gt+/vlnq7bZeK7ExMRc789ff/0Ve3t7NmzYYPZBNG/ePIuyRbEKdrly5bKd5SMvM384OjrStm1btmzZwpUrV3IdiGv89enexd2ydvvIymAwcPHiRbMuBGfPngXIcSCut7c3rq6uuU7Tu3z5ctq0acOcOXPMtsfFxZkGKeeH8cvO/Pnz+eSTT/jtt98YMWJEkU9lnNNzIiQkBEVRCA4OLvQ6OcZMaNZz3fs4lCtXLsfXqHF/dm7dusXmzZuZNGmS2aDYc+fOWZQt7G01tuHcuXO0bdvWtD09PZ1Lly7lOAOZUefOndHpdPz00085Dib/8ccfsbGxoVOnTvc9VnZ8fHywt7cv8Osxr7Zt20ZsbCwrVqwwm4r10qVLVjuHMdsxceJEhgwZkud6//vf/1i5ciUfffQRM2fOLNC5Bw8ezBdffMHq1atZt24d3t7eFj+mZTfdK6jBYlF9Bnbt2pU9e/awbNmybKeUDQsLY+fOnbRv397sS7per6d37978+OOPREVFsWzZMtq2bZunLP3q1atJTU1l1apVZtmAe7tXGjVu3JjGjRvz0UcfsXDhQp566ikWL15sNimCteTn86AoPvseVTKm4xHWunVrGjZsyLRp00hJScHHx4fWrVsza9YsIiIiLMrfO21hVsYvJ1kjc0VRmD59ukVZ45fsvK7M2759ezw8PFiyZAlLliyhYcOGZunOwrS7qPn5+REaGsqCBQvMbu/x48f5888/TQst3U9ycjIpKSlm20JCQnBxcSmy1Wz79u3Lnj172LBhg8W+uLg40wqyOp0OjUZj9utOWFhYtiuPOzk5WX015o4dO7Jnzx4OHz5s2nbz5k1++eWXPNV///33URSFQYMGkZiYaLH/wIEDLFiwAFC/9Ol0OrPxLADffvttjsf/5ptvTNcVReGbb77B1tbW1FXwXlqtlh49erB69Wr2799vsd/4+tLpdBa/gi1btqxQU2oOGjSIW7duMXLkSBITEwu0Zk1+5fRe0LNnT3Q6HZMmTbK4nYqimE1Hm5vr16+b9ZtPSEjgxx9/JDQ01PTF5/HHH2ffvn3s2bPHVC4pKYnvv/+eoKCgHMczZPe+B2T763hhb2v9+vXx9vZm5syZpqmTQZ3JKS+vq4CAAIYNG8amTZuynXJ05syZbNmyhWeeecai209eGH/J/+2337h+/bpp+/nz51m3bl2+j3e/84D5fZ6Wlnbf12FBjBs3Dnd39/vONHevkJAQevXqxfz5803jhfKrVq1a1KpVi9mzZ/Prr7/Sv3//ErF46MiRI/Hx8WHChAkWYw1SUlIYNmwYiqJkOyPVU089RXp6OiNHjiQmJibPa3Nk91jHx8db/Kh169Yti9eOMZtXVJ+RxvFqWT8PMjMz+f777y3KOjk5Fbrb340bNzh9+rRFF7NHTfE/00WRmjBhAn369GH+/PmMGjWKGTNm0Lx5c2rWrMmIESMoX748UVFR7Nmzh6tXr+a4DkCVKlUICQnh1Vdf5dq1a7i6uvLrr79m2yfRuNrrSy+9RMeOHXNNtdra2tKzZ08WL15MUlISn3/+uUWZgrY7q7Nnz2abNShdurRpas2C+Oyzz+jcuTNNmjThmWeeMU2Z6+bmlu2q7Nm1q127dvTt25dq1aphY2PDypUriYqKylOKuiAmTJjAqlWrTKsW16tXj6SkJI4dO8by5csJCwvDy8uLLl268OWXX9KpUycGDhxIdHQ0M2bMoEKFCqauGkb16tVj06ZNpoWwgoODc52jPTevvfYaP//8Mx06dGDMmDGmKXMDAwO5efNmrr8wNW3alBkzZvDCCy9QpUoVsxXJt23bxqpVq/jwww8B9dfPPn368PXXX6PRaAgJCWHNmjUW/fiN7O3tWb9+PUOGDKFRo0asW7eOP/74g7feeuu+gxKnTJnCn3/+SatWrXjuueeoWrUqERERLFu2jL/++gt3d3e6du3K5MmTGTZsGE2bNuXYsWP88ssveerbn5M6depQo0YNli1bRtWqValbt26Bj5VXxveCt99+m/79+2Nra0u3bt0ICQnhww8/5M033yQsLIwePXrg4uLCpUuXWLlyJc899xyvvvpqns5RqVIlnnnmGf755x9Kly7N3LlziYqKMvvi8sYbb7Bo0SI6d+7MSy+9hIeHBwsWLODSpUv8+uuvOfbTd3V1pWXLlnz66aekp6dTpkwZ/vzzz2x/dS/sbbW1teXDDz9k5MiRtG3bln79+nHp0iXmzZuX58d96tSpnD59mhdeeIH169ebMhobNmzg999/p1WrVnzxxRd5OlZ2Jk6cyJ9//kmzZs14/vnnyczM5JtvvqFGjRpmPwwURtOmTSlVqhRDhgzhpZdeQqPR8NNPP1m9K4qbmxtjx47N04DyrCZMmMDSpUuZNm0a//vf/wp07sGDB5ue3w8i+M8LT09Pli9fTpcuXahbt67FiuTnz59n+vTpNG3a1KJuq1atKFu2LL///jsODg707NkzT+d87LHHsLOzo1u3bqYfQ3744Qd8fHzMfmBcsGAB3377LU8++SQhISHcvn2bH374AVdX1zz9sFcQ1atXp3Hjxrz55pvcvHkTDw8PFi9ebPpBLqt69eqxZMkSXnnlFRo0aICzszPdunXL1/m++eYbJk2axNatW03ruzySHsAMWaKIGad2y246uczMTCUkJEQJCQkxTUt74cIFZfDgwYqvr69ia2urlClTRunatauyfPlyU73spoU7efKk0r59e8XZ2Vnx8vJSRowYYZomM+tUfhkZGcqYMWMUb29vRaPRmE2lyD1TMBpt3LhRARSNRmM2xW9WeWl3TrjPlLlZp6LMbnpQRcl+WsWsNm3apDRr1kxxcHBQXF1dlW7duiknT540K2OcyjTrdKqKoig3btxQRo8erVSpUkVxcnJS3NzclEaNGilLly7N9XZlldOUuV26dMm2/O3bt5U333xTqVChgmJnZ6d4eXkpTZs2VT7//HMlLS3NVG7OnDlKxYoVFb1er1SpUkWZN2+exbSsiqIop0+fVlq2bKk4ODgogGlqwpymzM2uXa1atbKYGvTQoUNKixYtFL1er5QtW1b5+OOPla+++koBlMjIyDzdNwcOHFAGDhyo+Pv7K7a2tkqpUqWUdu3aKQsWLDCbvjImJkbp1auX4ujoqJQqVUoZOXKkcvz48WynzHVyclIuXLigPPbYY4qjo6NSunRp5f3337eY6ja753x4eLgyePBg07TW5cuXV0aPHm2aVjElJUUZP3684ufnpzg4OCjNmjVT9uzZY3H/5GXK3Kw+/fRTBVCmTJmSp/tNUXKeMnf06NEWZe+dJlVR1OmZy5Qpo2i1Wovnwa+//qo0b95ccXJyUpycnJQqVaooo0ePNptqM6fXpPF8Xbp0UTZs2KDUqlXL9BxdtmyZRdkLFy4ovXv3Vtzd3RV7e3ulYcOGypo1a8zKZHd/Xr16VXnyyScVd3d3xc3NTenTp49y/fr1bB/Xwt5WRVGUb7/9VgkODlb0er1Sv359ZceOHdm+LnKSmpqqTJ06ValXr57i5OSkODo6KnXr1lWmTZtm9ro2yumxNO679zZu3rxZqVOnjmJnZ6eEhIQos2fPVsaPH6/Y29ublctpytx7P6ey+6zZtWuX0rhxY8XBwUHx9/dXXnvtNWXDhg0W5QoyZW5Wt27dUtzc3HKcMje755GiKErr1q0VV1dX0zS/xveDvIqIiFB0Op1SqVKlPNe593lZEPebMtfo0qVLyogRI5TAwEDF1tZW8fLyUrp372423XR2JkyYoABK375989WmVatWKbVq1VLs7e2VoKAg5ZNPPlHmzp1r9vo5ePCgMmDAACUwMFDR6/WKj4+P0rVrV2X//v35OldOU+bm9Ll+4cIFpX379oper1dKly6tvPXWW6bvKlmfh4mJicrAgQMVd3d3BTDdxzk9j+73vn3vlO2PGo2i/AdHsgghHmrjxo1j1qxZJCYmFvm4hEfJ9OnTefnllwkLCyuSBRMftKCgIGrUqMGaNWuKuyn/aT169ODEiRPZjnURlm7cuIGfnx/vvfdejjMyCvEokjEdQogS7c6dO2b/x8bG8tNPP9G8eXMJOPJBURTmzJlDq1atHomAQxSPe1+P586dY+3atY92lxArmz9/PpmZmYWaslqIh5GM6RBClGhNmjShdevWVK1alaioKObMmUNCQoL8QphHSUlJrFq1iq1bt3Ls2DF+//334m6SeIiVL1+eoUOHUr58ecLDw/nuu++ws7PLcfptcdeWLVs4efIkH330ET169MhxljshHlUSdAghSrTHH3+c5cuX8/3336PRaKhbty5z5swxm05T5CwmJoaBAwfi7u7OW2+9Rffu3Yu7SeIh1qlTJxYtWkRkZCR6vZ4mTZowZcqUHBc/FHdNnjyZ3bt306xZM77++uvibo4QD5yM6RBCCCGEEEIUKRnTIYQQQgghhChSEnQIIYQQQgghipSM6Sggg8HA9evXcXFxyXWBMiGEEEIIIR4GiqJw+/Zt/P39c1w8tSAk6Cig69evExAQUNzNEEIIIYQQwuquXLlC2bJlrXY8CToKyMXFBVAfEFdX12JujRBCCCGEEIWXkJBAQECA6buutUjQUUDGLlWurq4SdAghhBBCiEeKtYcPyEByIYQQQgghRJGSoEMIIYQQQghRpCToEEIIIYQQQhQpGdNRhBRFISMjg8zMzOJuihBFTqfTYWNjI1NICyGEEMKCBB1FJC0tjYiICJKTk4u7KUI8MI6Ojvj5+WFnZ1fcTRFCCCFECSJBRxEwGAxcunQJnU6Hv78/dnZ28uuveKQpikJaWhoxMTFcunSJihUrWnVBISGEEEI83CToKAJpaWkYDAYCAgJwdHQs7uYI8UA4ODhga2tLeHg4aWlp2NvbF3eThBBCCFFCyE+RRUh+6RX/NfKcF0IIIUR25BuCEEIIIYQQokhJ0CGEEEIIIYQoUhJ0CCGEEEIIIYqUBB3CzNChQ9FoNGg0Guzs7KhQoQKTJ08mIyODbdu2mfZpNBq8vb15/PHHOXbsWI7HyPrXqVMnU5kjR47QvXt3fHx8sLe3JygoiH79+hEdHW0qs3LlSho3boybmxsuLi5Ur16dcePGmfZPnDiR0NBQi9sQFhaGRqPh8OHDAFZttxBCCCGEyD+ZvUpY6NSpE/PmzSM1NZW1a9cyevRobG1tadKkCQBnzpzB1dWV69evM2HCBLp06cL58+fN1mYwHiMrvV4PQExMDO3ataNr165s2LABd3d3wsLCWLVqFUlJSQBs3ryZfv368dFHH9G9e3c0Gg0nT55k48aNBb5dhW23EEIIIYQoGAk6HgBFgeJaI9DREfK7RIher8fX1xeA559/npUrV7Jq1SpT0OHj44O7uzu+vr6MGzeO7t27c/r0aWrVqpXtMe61a9cu4uPjmT17NjY26lMwODiYNm3amMqsXr2aZs2aMWHCBNO2SpUq0aNHj/zdmCwK224hhBBCCFEwEnQ8AMnJ4OxcPOdOTAQnp8Idw8HBgdjYWIvt8fHxLF68GCBfK1D7+vqSkZHBypUr6d27d7YLJ/r6+rJw4UKOHz9OjRo1Ct74bBS03UIIIYQQomBkTIfIkaIobNq0iQ0bNtC2bVvT9rJly+Ls7Iy7uzsLFy6ke/fuVKlSxazumjVrcHZ2NvubMmUKAI0bN+att95i4MCBeHl50blzZz777DOioqJM9ceMGUODBg2oWbMmQUFB9O/fn7lz55Kamlrg21PYdgshhBBCiIKRTMcD4OioZhyK69z5ZfzinZ6ejsFgYODAgUycOJF//vkHgJ07d+Lo6MjevXuZMmUKM2fOtDhGmzZt+O6778y2eXh4mK5/9NFHvPLKK2zZsoW///6bmTNnMmXKFHbs2EHNmjVxcnLijz/+4MKFC2zdupW9e/cyfvx4pk+fzp49ewq00rs12i2EEEIIIfJPgo4HQKMpfBenB8n4xdvOzg5/f3/TuAuj4OBg3N3dqVy5MtHR0fTr148dO3aYlXFycqJChQr3PY+npyd9+vShT58+TJkyhTp16vD555+zYMECU5mQkBBCQkJ49tlnefvtt6lUqRJLlixh2LBhuLq6Eh8fb3HcuLg4ANzc3Iqk3UIIIYQQIn+ke5WwYPziHRgYaBFw3Gv06NEcP36clStXFuqcdnZ2hISEmGavyk5QUBCOjo6mMpUrV+bq1atm3bIADh48iL29PYGBgUXebiGEEEIIkTvJdIhCcXR0ZMSIEbz//vv06NHDNCg8NTWVyMhIs7I2NjZ4eXmxZs0aFi9eTP/+/alUqRKKorB69WrWrl1rmq524sSJJCcn8/jjj1OuXDni4uL46quvSE9Pp0OHDgB07NiRypUrM2DAAD788EN8fX05ePAg77zzDmPHjkWn01m13UIIIYQQomAk0yEK7cUXX+TUqVMsW7bMtG39+vX4+fmZ/TVv3hyAatWq4ejoyPjx4wkNDaVx48YsXbqU2bNnM2jQIABatWrFxYsXGTx4MFWqVKFz585ERkby559/UrlyZUANBv78808CAwMZMGAANWrU4P3332fs2LF88MEHVm+3EEIIIYQoGI2iKEpxN+JhlJCQgJubG/Hx8bi6uprtS0lJ4dKlSwQHB2Nvb19MLRTiwZPnvhBCCPFwu9933MKQTIcQQgghhBCiSEnQIYQQQgghhChSEnQIIYQQQgghipQEHUIIIYQQQogiJUGHEEIIIYQQokjJOh1CCCGEEEL8x/x1+S/mHprLqRunqOVTi+cbPE+ob2iRnU+CDiGEEEIIIf4jDIqB1ze+zud7Pjdt23t1LwuOLGB+j/k8Hvh4kZxXulcJIYQQQgjxH5E14BhSewg/P/kznSp0IjUzladXPM3x6ONFcl7JdAghhBBCCPEfsOjYIlPAMe+JeQwNHQpA/xr96bW0F7+f+Z2X1r1UJOeWTIcQQgghhBCPuJikGF5arwYU77Z81xRwAOi0Or7t8i2uelcOXD9QJOeXoEOYGTp0KBqNhlGjRlnsGz16NBqNhqFDh5pt37NnDzqdji5dumR7zJUrV9K4cWPc3NxwcXGhevXqjBs3zrQ/MzOT//3vf1SpUgUHBwc8PDxo1KgRs2fPtuZNE0IIIYT4z3p367vcSL5BrdK1eLfluxb7/V38ea7uc0V2fgk6hIWAgAAWL17MnTt3TNtSUlJYuHAhgYGBFuXnzJnDmDFj2LFjB9evXzfbt3nzZvr160evXr3Yt28fBw4c4KOPPiI9Pd1UZtKkSUydOpUPPviAkydPsnXrVp577jni4uKK7DYKIYQQQvxXhMeFM/fQXABmPD4DW51ttuWGhA4psjbImI4HQFEUktOTi+XcjraOaDSafNWpW7cuFy5cYMWKFTz11FMArFixgsDAQIKDg83KJiYmsmTJEvbv309kZCTz58/nrbfeMu1fvXo1zZo1Y8KECaZtlSpVokePHqb/V61axQsvvECfPn1M22rXrp2vNgshhBBCiOx9/NfHpBvSaV++Pc0Dm+dYroZPDWr71uYIR6zeBgk6HoDk9GScP3YulnMnvpmIk51TvusNHz6cefPmmYKOuXPnMmzYMLZt22ZWbunSpVSpUoXKlSvz9NNPM27cON58801ToOPr68vChQs5fvw4NWrUyPZcvr6+bNmyhRdeeAFvb+98t1UIIYQQQmQvPiWen47+BMA7Ld7JtfzAmgOLJOiQ7lUiW08//TR//fUX4eHhhIeHs2vXLp5++mmLcnPmzDFt79SpE/Hx8Wzfvt20f8yYMTRo0ICaNWsSFBRE//79mTt3LqmpqaYyX375JTExMfj6+lKrVi1GjRrFunXriv5GCiGEEEI84hYdX0RyejLVvKvRslzLXMsPrj24SNohmY4HwNHWkcQ3E4vt3AXh7e1Nly5dmD9/Poqi0KVLF7y8vMzKnDlzhn379rFy5UoAbGxs6NevH3PmzKF169YAODk58ccff3DhwgW2bt3K3r17GT9+PNOnT2fPnj04OjpSrVo1jh8/zoEDB9i1axc7duygW7duDB06VAaTCyGEEEIUwuyD6nepZ+s8m6cu9wX97pgbCToeAI1GU6AuTsVt+PDhvPjiiwDMmDHDYv+cOXPIyMjA39/ftE1RFPR6Pd988w1ubm6m7SEhIYSEhPDss8/y9ttvU6lSJZYsWcKwYcMA0Gq1NGjQgAYNGjBu3Dh+/vlnBg0axNtvv20xjkQIIYQQQuTubOxZDkQcwEZrw9O1LHusPEjSvUrkqFOnTqSlpZGenk7Hjh3N9mVkZPDjjz/yxRdfcPjwYdPfkSNH8Pf3Z9GiRTkeNygoCEdHR5KSknIsU61aNYD7lhFCCCGEEDlbfWY1AK2DWuPtVLzjZiXTIXKk0+k4deqU6XpWa9as4datWzzzzDNmGQ2AXr16MWfOHEaNGsXEiRNJTk7m8ccfp1y5csTFxfHVV1+Rnp5Ohw4dAOjduzfNmjWjadOm+Pr6cunSJd58800qVapElSpVHsyNFUIIIYR4xKw6uwqA7pW6F3NLJNMhcuHq6oqrq6vF9jlz5tC+fXuLgAPUoGP//v0cPXqUVq1acfHiRQYPHkyVKlXo3LkzkZGR/Pnnn1SuXBmAjh07snr1arp160alSpUYMmQIVapU4c8//8TGRuJiIYQQQoj8ik2OZdflXQB0q9ytmFsDGkVRlOJuxMMoISEBNzc34uPjLb6Up6SkcOnSJYKDg7G3ty+mFgrx4MlzXwghhCgZlp5YSr/l/ajhU4Njzx/Lc737fcctDMl0CCGEEEII8YgxZjlal2tdvA35lwQdQgghhBBCPGJ2XVGDjmaBzYq5JSoJOoQQQgghhHiEJKUlcTjyMADNAkpG0CGjdIUQQgghhCihFEVh5+Wd/HPtH3RaHX2r98Xfxf++dfZd20emkklZ17IEuAU8oJbenwQdQgghhBBClEARtyMYuGIg28K2mbZN2DiBqR2n8mLDF3Ost/vKbqDkZDlAgg4hhBBCCCFKnPC4cNosaMOluEvodXq6V+7OtdvX2H1lN2PWjcHR1pHhdYZnW/d4zHEA6vrVfZBNvi8Z0yGEEEIIIUQJkpqRSq+lvbgUd4mQUiEcf+E4S/ss5a9hf/Fa09cAGLt+LNFJ0dnWPxWjLu5c1avqA2tzbiToEEIIIYQQogR5a/NbHIg4gIeDB1uGbKGCRwUANBoN/2v/P+r51SMxLZEpO6dY1DUoBs7EngGgqrcEHUIIIYQQQoh7nL5xmul/Twdg/hPzCXQLNNtvDDwAvtv/HTfv3DTbHx4XTkpGCnY6O4Lcgx5Im/NCgg4hhBBCCCFKiNc2vkamkkm3St3oVrlbtmXal29PTZ+apGWm8cfZP8z2nbqhdq2q5FkJG23JGb4tQYcwGTp0KBqNBo1Gg52dHRUqVGDy5MlkZGSYymRmZjJ16lRq1qyJvb09pUqVonPnzuzatcvsWPPnz8fd3d1s2zPPPEPNmjVJS0sz27527Vrs7Ozo3r276fw5/d3bTltbW4KDg3nttddISUmxuE1r1qyhVatWuLi44OjoSIMGDZg/f75ZmbCwMLNzeHp68thjj3Ho0CFTmdatWzNu3DizeufPn2fYsGGULVsWvV5PcHAwAwYMYP/+/Xm6j3Nr+9WrV7Gzs6NGjRrZHitrm52cnKhYsSJDhw7lwIEDZuW2bduGRqMhLi4OyP6xyXrM3377zfT/ypUrady4MW5ubri4uFC9enWL+0EIIYQQ1nEs6hirz65Gq9HyaYdP71v2icpPAPD7md/Ntp++cRqAKl5ViqaRBSRBhzDTqVMnIiIiOHfuHOPHj2fixIl89tlngDpPdP/+/Zk8eTJjx47l1KlTbNu2jYCAAFq3bm32ZTU7U6dO5fbt27z//vumbXFxcYwYMYJ3332XhQsXEhERYforW7YskydPNtt2bzsvXrzI1KlTmTVrltlxAb7++mueeOIJmjVrxt9//83Ro0fp378/o0aN4tVXX7Vo36ZNm4iIiGDDhg0kJibSuXNn0xf1e+3fv5969epx9uxZZs2axcmTJ1m5ciVVqlRh/PjxebqP79d2UIODvn37kpCQwN9//53tsebNm0dERAQnTpxgxowZJCYm0qhRI3788cf7tiEvNm/eTL9+/ejVqxf79u3jwIEDfPTRR6Snpxf62EIIIYSwZOxW1bNqz1yDhieqqEHH+vPrScm4++NlSRxEDoAiCiQ+Pl4BlPj4eIt9d+7cUU6ePKncuXNHURRFMRgMSmpqYrH8GQyGPN+mIUOGKE888YTZtg4dOiiNGzdWFEVRFi9erADKqlWrLOr27NlT8fT0VBITExVFUZR58+Ypbm5uFuW2bNmi2NraKnv37jWds0GDBkp6erpF2XLlyilTp07NUzt79uyp1KlTx/T/5cuXFVtbW+WVV16xqP/VV18pgKkNly5dUgDl0KFDpjK7du1SAGX9+vWKoihKq1atlLFjxyqKoj6e1atXV+rVq6dkZmZaHP/WrVsW2/LTduM5ypcvr6xfv155/fXXlREjRlgcC1BWrlxpsX3w4MGKi4uLcvPmTUVRFGXr1q0KYGpXTo/NvcccO3as0rp16xxvS3bufe4LIYQQIm9ikmIU+w/tFSai/BX+V67lDQaDUuaLMgoTUTac32Da3mJuC4WJKL8c/aVA7bjfd9zCKDkdvR5h6enJfPyxc7Gc+803E7GzcypwfQcHB2JjYwFYuHAhlSpVols3y/6F48ePZ8WKFWzcuJEePXrkeLw2bdrwwgsvMGTIED744AOWLl3KwYMHsbEp+FPx+PHj7N69m3Llypm2LV++nPT09GwzGiNHjuStt95i0aJFNGrUKNtjOjg4AFh0BQM4fPgwJ06cYOHChWi1lsnCnLou5bXtAFu3biU5OZn27dtTpkwZmjZtytSpU3Fyyv2xfPnll/nxxx/ZuHEjffv2zXNb7uXr68vChQs5fvx4jl28hBBCCGEdy04sIyUjhVDfUJoGNM21vEajoXlgc5acWMKRyCM8FvIYABGJas+QANeSsRK5kXSvEtlSFIVNmzaxYcMG2rZtC8DZs2epWjX7VJ1x+9mzZ3M99scffwxA//79mTJlClWq5L/P4Zo1a3B2dsbe3p6aNWsSHR3NhAkTTPvPnj2Lm5sbfn5+FnXt7OwoX758jm2Ni4vjgw8+wNnZmYYNG1rsP3fuHECB2p2XtgPMmTOH/v37o9PpqFGjBuXLl2fZsmV5Or6xXWFhYQVqn9GYMWNo0KABNWvWJCgoiP79+zN37lxSU1MLdVwhhBBCWFpyYgkAA2sMNI1jzU117+oAnIg5YdoWkxQDgI+Tj5VbWDiS6XgAbG0defPNxGI7d34YvxCnp6djMBgYOHAgEydONO1XFKXQbXJwcODVV1/l5ZdfZuzYsQU6Rps2bfjuu+9ISkpi6tSp2NjY0KtXr0K1q2nTpmi1WpKSkihfvjxLliyhdOnSFuUKex/k1va4uDhWrFjBX3/9Zdr29NNPM2fOHIYOHZrr8Y3ty+sbVk6cnJz4448/uHDhAlu3bmXv3r2MHz+e6dOns2fPHhwd8/fcEkIIIUT2rt++zo7wHQD0rZ73XgrVfcyDjtSMVOJT4wEJOkqUJ598km3bttGuXTuWL19eZOdRZ4MqeBenB8n4hdjOzg5/f3+zbk+VKlXi1KlT2dYzbq9UqVKezmNjY4NOpyvwF2MnJycqVFAXypk7dy61a9dmzpw5PPPMM6Z2xMfHc/36dfz9/c3qpqWlceHCBdq0aWO2fcmSJVSrVg1PT8/7dpEy3sbTp09Tp04dq7d94cKFpKSkmHX9UhQFg8HA2bNnc72PjY9FcHBwtvtdXV1JSkrCYDCYdQ8zDpp3c3MzKx8SEkJISAjPPvssb7/9NpUqVWLJkiUMGzYsfzdcCCGEENlaeWolCgqNyzamnHu53Cv8q5p3NQBOxpzEoBiISVazHDZaG9zt3YuiqQX2n+5eNXbsWKvM8vMoMX4hDgwMtBhn0b9/f86dO8fq1ast6n3xxRd4enrSoUOHB9VUE61Wy1tvvcU777zDnTt3AOjVqxe2trZ88cUXFuVnzpxJUlISAwYMMNseEBBASEhIrmMyQkNDqVatGl988QUGg8Fif04zXuW17XPmzGH8+PEcPnzY9HfkyBFatGjB3Llzcz3mtGnTcHV1pX379tnur1y5MhkZGRw+fNhs+8GDB4H7B45BQUE4OjqSlJSUx1sohBBCiNxsurQJgO6VuuerXgWPCtjp7EhOTyY8LpzopGgAvB29C93jwdr+00FH69atcXFxKe5mPDT69+/Pk08+yZAhQ5gzZw5hYWEcPXqUkSNHsmrVKmbPnm020DkzM9Psi/Phw4dzzJQUVp8+fdDpdMyYMQOAwMBAPv30U6ZNm8bbb7/N6dOnuXDhAl9++SWvvfYa48ePz3EQeW40Gg3z5s3j7NmztGjRgrVr13Lx4kWOHj3KRx99xBNPPFHgth8+fJiDBw/y7LPPUqNGDbO/AQMGsGDBArN1U+Li4oiMjCQ8PJyNGzfSu3dvFi5cyHfffZdj8FS9enUee+wxhg8fzubNm7l06RLr16/nhRdeoF+/fpQpUwaAiRMn8tprr7Ft2zYuXbrEoUOHGD58OOnp6cUSXAohhBCPokxDJtvCtgHQrny7fNW10dpQ2bMyoGY7jEFHSetaBQ9x0LFjxw66deuGv7+/xYJmRjNmzCAoKAh7e3saNWrEvn37HnxDHyEajYalS5fy1ltvMXXqVCpXrkyLFi0IDw9n27ZtFrNWJSYmUqdOHbO/7Ga+sgYbGxtefPFFPv30U9Ov8OPGjWPlypXs3LmT+vXrU6NGDdMX8s8//7xQ52vYsCH79++nQoUKjBgxgqpVq9K9e3dOnDjBtGnTCtz2GTNmUK1atWwHqT/55JNER0ezdu1a07Zhw4bh5+dHlSpVeP7553F2dmbfvn0MHDjwvudcsmQJrVq1YuTIkVSvXp2XXnqJJ554gtmzZ5vKtGrViosXLzJ48GCqVKlC586diYyM5M8//6Ry5cr5uo1CCCGEyN7hyMPEpcThqnelrl/dfNfPOq6jJAcdGsUaI4OLwbp169i1axf16tWjZ8+erFy50uxL75IlSxg8eDAzZ86kUaNGTJs2jWXLlnHmzBl8fO4+ENu2beObb77JdUxHamqq2aw9CQkJBAQEEB8fj6urq1nZlJQULl26RHBwMPb29ta5wUI8BOS5L4QQQuTPZ7s+47VNr9GtUjdWDViV7/rvbnmXD3d+yPP1n6d8qfJM2DiBp2o+xc89fy5QexISEnBzc8v2O25hPLSZjs6dO/Phhx/y5JNPZrv/yy+/ZMSIEQwbNoxq1aoxc+ZMHB0d89QnPjsff/wxbm5upr+AgJI197EQQgghhHj4bA/fDkDb4LYFqm8cMB6fGl9ip8uFhzjouJ+0tDQOHDhgNpBWq9XSvn179uzZU6Bjvvnmm8THx5v+rly5Yq3mCiGEEEKIh5yiKGwL28YLf7zAsN+H8dXfX5GakfvaVociDwHQsIzl2mB54WavzjqZkJpAdPLdgeQlzSM5Ze6NGzfIzMy0WGOhdOnSnD592vR/+/btOXLkCElJSZQtW5Zly5bRpEmTbI+p1+vR6/VF2m4hhBBCCPHwSUxLZMTqESw+vti0bT7z+W7/d6wZsIYQj5Bs68UkxXD99nU0aKjpU7NA53bTq0FHfEo8BkWdVbMkZjoeyaAjrzZt2lTcTRBCCCGEEA+xtMw0ui7syvbw7dhobRhaeygBbgF8+8+3nL5xmt7LerN7+G4cbB0s6h6JOgJAiEcILvqCzaiaNdNxJ0Odfr8kBh2PZPcqLy8vdDodUVFRZtujoqLw9fUtplYJIYQQQohHzeg/RrM9fDsudi5sHbKVH7r/wHut3uPAcwfwdvTmcORh3t/2frZ1D0ceBiDUN7TA53fVq4O941PjS/TsVY9k0GFnZ0e9evXYvHmzaZvBYGDz5s05dp8SQgghhBAiP/688CezD81Gq9GytM9Smgc2N+0r41qGH7r9AMDM/TNJSE2wqG/MdNQuXbvAbcjavUqCjiKQmJhoWnAO4NKlSxw+fJjLly8D8Morr/DDDz+wYMECTp06xfPPP09SUhLDhg0rxlYLIYQQQohHQWpGKi/88QIAYxqOoVOFThZlulfuTlWvqtxOu828Q/Ms9lsj02HsXnUr5RYpGSmABB1WtX//ftOCc6AGGXXq1OG9994DoF+/fnz++ee89957hIaGcvjwYdavX28xuFwIIYQQQoj8mn94PhduXcDP2Y8P2nyQbRmNRsPYRmMB+G7/d2b7Mg2ZnLlxBoAaPjUK3A5j9yojBxsHnOycCny8ovLQDiRv3bo1ua1r+OKLL/Liiy8+oBYJIYQQQoj/ggxDBp/s+gSAN5q/cd9B4ANqDmD02tGciT3D5fjLBLoFAhCVFEW6IR2tRktZ17IFbouTrRM6jY5MJRMomVkOeIgzHUIIIYQQQhSHX0/+yqW4S3g7evNs3WfvW9ZV70o9/3oAbA/bbtp+JV5d883fxR8bbcHzABqNxizbIUGHeCgMHToUjUaDRqPB1taW0qVL06FDB+bOnYvBYDCVCwoKMpXL+ve///0PgLCwMDQaDT4+Pty+fdvsHKGhoUycONH0/6VLlxg4cCD+/v7Y29tTtmxZnnjiCbM1VTQaDb/99hvz58/P9rxZ/9q1a0fNmjVJS0szO+/atWuxs7Pj4MGDRXDPCSGEEOK/Yu7huQCMqj8KR1vHXMu3LtcagG1h20zbriSoQUeAa0Ch2yNBh3goderUiYiICMLCwli3bh1t2rRh7NixdO3alYyMDFO5yZMnExERYfY3ZswYs2Pdvn2bzz//PMdzpaen06FDB+Lj41mxYgVnzpxhyZIl1KxZk7i4OIvy/fr1MztfkyZNGDFihNm2FStWcPv2bd5//+70dHFxcYwYMYJ3332XunXrFv5OEkIIIcR/0tWEq2y8sBGAIbWH5KlO66DWAGwN22raZsx0BLgVPugwDiaHkht0PLRjOh4miqKQnpxeLOe2dbRFo9Hkq45erzetZ1KmTBnq1q1L48aNadeuHfPnz+fZZ9U0oouLS67rnowZM4Yvv/yS0aNH4+Nj+SI4ceIEFy5cYPPmzZQrVw6AcuXK0axZs2yP5+DggIPD3cV17OzscHR0tGjHvHnz6NixIz169KBRo0aMGzeOMmXK8Oabb+b9jhBCCCGEuMfPR39GQaFFYIscVxq/V/PA5ug0Oi7FXeJawjXKuJaxaqbDOG0uSNDxn5aenM7Hzh8Xy7nfTHwTOye7Qh+nbdu21K5dmxUrVpiCjrwYMGAAGzduZPLkyXzzzTcW+729vdFqtSxfvpxx48ah0+kK3VaANm3a8MILLzBkyBA++OADli5dysGDB7Gxkae8EEIIIQpu5emVADxd6+k813HRu1C+VHnO3TzH+ZvnrR50ZO1e5e3oXejjFQXpXiXyrEqVKoSFhZn+f/3113F2djb727lzp1kd4ziP77//ngsXLlgcs0yZMnz11Ve89957lCpVirZt2/LBBx9w8eLFQrf344/VQK9///5MmTKFKlWqFPqYQgghhPjvikmK4Z9r/wDQtVLXfNUNcg8CICwuDJDuVaII2Dra8mZi8XTrsXW0tdqxFEUx66o1YcIEhg4dalamTJkyFvU6duxI8+bNeffdd1m4cKHF/tGjRzN48GC2bdvG3r17WbZsGVOmTGHVqlV06NChwO11cHDg1Vdf5eWXX2bs2LEFPo4QQgghBMCGCxtQUAj1DcXfxT9fdS2CDuleJaxNo9FYpYtTcTt16hTBwcGm/728vKhQoUKe6v7vf/+jSZMmTJgwIdv9Li4udOvWjW7duvHhhx/SsWNHPvzww0IFHQA2NjbodLp8j2sRQgghhLjXuvPrAHi8wuP5rmsKOuLDSM9MJ+J2BGCdTIfMXiUeGVu2bOHYsWP06tWrQPUbNmxIz549eeONN3Itq9FoqFKlCklJSQU6lxBCCCGEtSmKwqaLmwDoVKFTvutnzXRcv30dBQVbra1VggTJdIiHUmpqKpGRkWRmZhIVFcX69ev5+OOP6dq1K4MHDzaVu337NpGRkWZ1HR0dcXV1vfeQAHz00UdUr17dbDD34cOHef/99xk0aBDVqlXDzs6O7du3M3fuXF5//fWiuYFCCCGEEPkUHh9OdFI0tlpbGpRpkO/6WYOO6KRoAEo7l0arKXwOIOuYDm+nkjmQXIIOYWH9+vX4+flhY2NDqVKlqF27Nl999RVDhgxBq737wnjvvfd47733zOqOHDmSmTNnZnvcSpUqMXz4cL7//nvTtrJlyxIUFMSkSZNMCwoa/3/55ZeL5gYKIYQQQuTTvmv7AKjtWxt7G/t81zcGHVfir5CYlgiQp4UF88LYvcpN74adrmR26ZegQ5iZP38+8+fPz7Vc1lmsshMUFISiKBbbZ82axaxZs0z/e3l5MX369FzPl92xALZt23bfekOHDrUY7C6EEEKI/7a159by1d9fcSLmBCGlQhheZziDag267xhQY9DR0L9hgc7p6+yLnc6OtMw0LtxSZ/TU6/QFOta9jN2rCtu16sCBHzhy5DcrtMiSBB1CCCGEEOI/IdOQycg1I5lzaI5p29WEq2wP384/1/5heufpOXZ3MgUdZQoWdGg1Wsq5lePczXOcuXEGoEAZk+w0DWhKNe9qDKgxoFDHWbPmOVJSrNIkCzKQXAghhBBCPPIURWHE6hHMOTQHnUbH+Cbj2TF0B2+3eBuAb/75hjkH52RbN8OQwYGIA0DBgw6Acu7lADgTqwYdehvrZDo8HT058cIJ3mn5jlWOVxQk0yGEEEIIIR55cw/NZd7heeg0Opb0XkKvauqMnC3KtcBN78Zrm17j9U2v06NKD4vB2Odiz5GcnoyTrROVvSoXuA3u9u4A3Ei+AVgv0/EwkEyHEEIIIYR4pIXHhTNuwzgAprSbYgo4jF5u8jK1S9fmVsotpu6dalH//M3zAFTyrFSo2aYcbBwAiEuJA6w3puNhIEFHEcpp8LMQjyp5zgshhCiJ3tv2HolpiTQPbM74JuMt9ttobUzdrBYeW4hBMZjtNwYdFTzytihyToyZDWPQIZkOUSi2trYAJCcnF3NLhHiwjM9542tACCGEKG4nok/w05GfAPjysS/RaXXZlutaqSsudi6Ex4ez6/Ius31FFXRYa0zHw0DGdBQBnU6Hu7s70dHqwi+Ojo73nYJNiIedoigkJycTHR2Nu7s7Ol32b+hCCCHEg/bJrk9QUOhZted9F/VzsHWgd7XezDs8j1+O/UKLci1M+87fsk7QYexedSfjDgD2uuLPdKSkxPHbb0OpVevpIj2PBB1FxNfXF8AUeAjxX+Du7m567gshhBDF7UbyDZaeWArA681ez7V8z6o9mXd4HtvDt5ttv3BTXVfDWpkOo5KQ6di8+S3OnPmdM2d+L9LzSNBRRDQaDX5+fvj4+JCenl7czRGiyNna2kqGQwghRIky//B8UjNTqetXlwb+OWc5jIxlztw4w+3U27joXUjPTCcsLgyAkFIhhWqPg62D2f8lYUxHTMzJB3IeCTqKmE6nky9iQgghhBDFYO6huQCMqjcqT13dSzuXpqxrWa4mXOVQ5CFalmtJeHw4mUomDjYO+Ln4Fao9FpmOEjB71Z07Nx/IeWQguRBCCCGEeOScvnGaUzdOYau1pW/1vnmuV9+/PgAHrquLARoHkYd4hBRqulywDDpKQqZDgg4hhBBCCCEKaOWplQC0DW6Lm71bnuvV86sHwP6I/QBcib8CQJB7UKHbZBxIbvRfCjqke5UQQgghhHjkrDytBh09q/bMVz1j0GHMdNxKuQWAh4NHodtUkgaS37lzk9TUBDL+nUmrqEnQUUhnzqzC2dmxuJuRBw/PlL0P1/TCD09bH5779WFp58N0n8LDcr/KfVo05H61PrlPi4a17te4lFvEXv+H8kBde3cuXtyU57qeKfGUBzJiz3Lu/AbiIw9RHvBKSchynIK1Mz32DMFZ/tfEhXHx4uYCHSsvFCWT2NhzODh4kJJyi4MHZ9O8+ZtERBzk77+nYzBkM9lRZGkgyupt0SiyhHCBJCQk4ObmxhtvgH3xZ8aEEEIIIYQotJTV7fnfgU3Ex8fj6upqteNKpqOQAgIa4+BQMu/Gkh9Pluz2lfz7D+Q+LKyS3T65/wpP7sPCkfuvcEr+/QeP6n14/fZ1Yu/E4unggb9LmXzXPxlzkkwlk0oeFYlKiiY+NR4/Zz+8HL3ubWG+jpuUlsTFuEum/wNcA3DPx3iTgnBzCyQq6iiJiZH4+9fn6tW92No64u1djevX91tWiHMvknaUzG/LD5Gnn95g1ShQCCGEEEIUTr3v63HwTiyLHp9B/xr9812/2oxqnLpxii1dZ/HJrk/YcGED89t9zJDQIYVq1z/X/mHC7Iam/3/tNC3fY04KwmDIIC0tETs7Z06cWIqfXz0SEyNZsKC1ZeH4ogmCJOgQQgghhBAllkExmGaQCnQLzHXcR0JqAocjDwPQIrBFgc7p4+TDqRuniE6KJi4lDoBSDqUKdKysimvKXK3WBnt7dwBq1hwIgKtrNhkghSILOmTKXCGEEEIIUSL9cvQXKn1diaDpQQRND6LBDw3YGb7zvnX+vvo3BsVAsHswZbL7Yp0HPk4+AEQnRZtmr3L/90t7YZSkxQHt7JwtN95xgHS7IjmfBB1CCCGEEKJEURSFCX9O4OmVT3Ph1gVstbbYaG04EHGAjj93ZM+VPTnWPRZ9DIB6/vUKfP6sQYcp02Ff+EyHg23JWqejbNkm5huKaDwHSNAhhBBCCCFKmE93fcrnez4H4N2W73Lr9Vtcf+U6nSt05k7GHbov7m4KBu51MuYkANW8qhX4/MagIyopilt3ijDTUYzrdAD07/8bjz02HYNBB9tbwtrHi+xcEnQIIYQQQogSY2f4Tt7a8hYAX3f+msltJuNk54S3kzfL+iyjqldVbiTfYNreadnWPxFzAoDqPtUL3AZj0BEWF0b6v2tZPMxjOnLi5OSDTvcSiREhsLUtXA0osnNJ0CGEEEIIIUqEDEMGz//xPAbFwODagxndYLTZfic7Jya1ngTA1L1TTVkII0VR7mY6vAue6fB29AbgbOxZAHQaHU62TgU+nlFRj+lIToZ582D0aHj7bTh7Nvc6+/eDcqvwq63nRoIOIYQQQghRIszcP5MTMSfwdPBkWsdp2c5U1ataL6p7VychNYFlJ5eZ7bt2+xoJqQnoNDoqeVYqcDuMmY7w+HBAzXJYY7V0G60NNtq7k8daM9Oxfz9UrgzDh8O338KUKVC9Onz55f3rHTsGSkLRrhUCEnQIIYQQQogSIC0zjY//+hiAyW0m59idSavRmtbe+OPcH2b7jFmOip4VsdMVfBYmY9BhZI3xHEZZAw1rjenYswdatICrVyEwECZMgE6dICMDxo+HlStzrnvsGJBQ9GvOSdAhhBBCCCGK3eLji7l++zp+zn48W/fZ+5btUrELAJsubiIlI8W0/UT0v+M5vAs+ngMsgw5rzFxl5GBzdwYra2Q6rl+Hnj0hJQUeewyOHoVPP4V162DcOLXM0KFw86ZlXUWB48dBe/vf6XN9I6DFjkK3KTsSdAghhBBCiGKlKApf7lH7AY1pOCbXLEWobyj+Lv4kpyezPWy7afuFWxcACtW1CtTMRtZuUEWW6bDCmI4XXoDISKhZE379Fdyy9JT67DN1e0ICzJxpWffKFYiPB22So7qh9hFotrvQbcqOBB1CCCGEEKJYHYk6wpGoI+h1ekbWH5lreY1Gw+MV1OldN13cZNoemRgJgL+Lf6Hao9FoKO1U2vS/NWauMsq6VkdhuoCBms34/XewsYFFi8D5nvX+bGzgtdfU6199pWZDsjqmLmmC7Z1/AyHXhEK1534k6BBCCCGEEMVq0bFFAHSp1AUPh7zNpFTfvz4Ap26cMm0zBh2+zr6FblP78u1N19317oU+npEx06HX6Qs1OF1R7gYUY8eqg8az068flC0LUVGwdq35vrtBx78ZF9cE7OwKP0tXdiToEEIIIYQQxcagGFh8YjEAA2oMyHO9Kl5VADh947RpW1RSFGCdoGNc43Gm67fTbhf6eEbGoKOw4znWrVPHY7i4wDvv3N2+d9peZjeaze0Itc22tvDkk+q+TZvMj3HuHGhQ0CbaqhtcE2jc+OVCtSsnEnQIIYQQQohi88+1f7gcfxlnO2fTAPG8MAYdl+IumQaTWzPTEeobarpe1atqoY9nZBxIXtig49NP1cuRI8HdHQwZBjLTM9k+eTvX9l1j2/vbmFFtBtsnb6f9v0mbjRvNj3HtGjiRBAYNaAzgnIhNEa2SbpN7ESGEEEIIIYrGxovqN+HHQh4zG++QGx8nH9zt3YlLieP8zfMEuQeRmJYIWCfoALj68lUWHFnAiw1ftMrxIEv3qkJ8uT99GrZvV8dsjBsHty7dYmbtmTh4OJBySw3ADv5wEIBt729j7M2W6HQazp+HsDAIClKPc+0auPLvOA7nRNAZ0BVynElOJNMhhBBCCCGKjXEgeIfyHfJVT6PRmHWxikpUu1Y52TrhbOd8v6p5Vsa1DG+1eAtXvfXWsbBG96qff1YvO3WCMmXg2MJjpN1OIz48PtvyKZejaNhQvZ61i9W1a+DBv3Pp/juIXGflVdKNJOgQQgghhBDFIjEtkd1X1Clasw7czqusQYexa1Vp59L3q1LsjNmcgk6XazDcDTqeflq9vPLXFbMyNvbmnZnCt4fTsqV6/dAh9fLOHbh1CypwXt0QoB5DMh1CCCGEEOKRsjN8J+mGdMq5lSOkVEi+61fxtAw6rNW1qqgUNtOxdy+Eh6sDyLt3h8y0TMJ3hpv22zra0u2Hbjj5OBHQNACAi5suUqG8AYAL6lImXLsGGgxU4qy6ofIZoOiCDhnTIYQQQgghisXOyzsBaBvctkDTxxoXATx389xDE3QYB5IXdEzHunXq5eOPw9Ef/mb92PUAOHo5MmjTIFDAN9SXWk/X4urfV5nTeA5nV5/FZvvnuDGSCxfU1QOvXYMAruLIHWxcICPwMoAMJBdCCCGEECVXbHIsa86uISopipo+NXks5DF0Wt196xyKVPv6NPBvUKBzGtf0SEhNuBt0OJXsoKOwmY4NG9TLxx5T+Ovtv0zbg9sG41vb/Lb71fXDq4oXN07fICPhDiFc4GhYXTIy1KDD2LXKu4kdETo1EyKZDiGEEEIIUeIoisLcQ3N5af1LJKcnm7a3LNeSX3r+QlnXsjnWOxihzrBUx69Ogc7toncB4Hbq7Ycm05F1ccD8unED9u9XrzepfIulkepsXSEdQ2j5bkuL8jpbHc8ff55Vz6ziyIIj+OmiOJgBV66oQYc7cQCUqmpPxL91tFoZ0yGEEEIIIUqYydsn8+zqZ0lOT6aGTw361+iPk60TO8J30H1Rd1IzUrOtF5EYQXRSNFqNllqlaxXo3MZZqhLTEq26MGBRKsw6HZs2qSuR16wJKWfVcRwBzQJ4ev3T+NTwybaOVqclqHUQAIH6aEAd13HtGjijBi323ncDoKLqXiVBhxBCCCGEKJCfj/7MxO0TAfigzQccGXWERb0WcXjUYTwdPDkUeYh3tryTbd1DEWrXqipeVXC0dSzQ+bMGHQ/L7FVOdk4ABbrNO9UhMLRvD5d3qGMwyrUsl2u90rXU+8QjPQpQTEGHE0lqm3zuro8iU+YKIYQQQogS41rCNUavHQ3Am83f5J2W76DVqF8tK3hUYO4TcwH4at9XRCdFW9Q3jueo41uwrlVwN+jIVDJNmY5S9qUKfLwHoVfVXvSs2pOR9Ubmu66xa1XDBgbCtoUBeQs6vKp6odFqsE2/gzOJFpkOp9J3AyCdzjbf7coLCTqEEEIIIUS+vbT+JRJSE2hYpiEftPnAYn/3yt1p4N+AtMw05h6aa7H/cORhoHBBh5Otk+l6xG11VII1F/IrCuXcy/Fr319p4NuMXbtg40Z1vYzcpKXBkSPqdbvd24kLi8PW0dY0Le792DrY4lFRHXRfmiguXICEOAOOqGNwnErfXUxRulcJIYQQQogSYf/1/aw4tQKtRsvsbrNznKXqhQYvADBz/0wyDZlm+y7cUheMMC7wVxA6rc40RiLdkA6U/KBDUWDxYnUl8ebN4bHHwNcXpk5V9+Xk+HFITYXyLtEc+2YHAF1ndUXvmrcgoXRNtYtVaaK5dg20d5LQAGg1OHm7mMrJQHIhhBBCCFEifLjjQwCeqvkUNUvXzLFcv+r9cNO7ER4fzoGIA2b7wuPUgdDl3HPvHnQ/xi5WRiU96Jg8GQYMUGei8vKC8uXVLMYrr8B77+Vcz9i1qpl/GADl25en1tN5H4DvXcNbvSSGtDSwSVXHc9i5O2KnvzumQzIdQgghhBCi2J2+cZrfz/yOBg1vt3j7vmUdbB1oUa4FoK4+bnQ79Ta3UtQ+RYFugYVqz8MUdPzwA0ycqF5/+224fh3On4cvv1S3TZkC//yTfV1j0BFkex1QZ63KD+9q9wYd/85c5emETZaZtIpqnQ4JOoQQQgghRJ7NOzQPgK6VulLZq3Ku5VsE/ht0XL4bdFyOV2decrd3L3SQkDXocLBxwLaIBkIX1rlzMHasen3iRPjwQ7C1BY0GXn5ZzX4YDDB6dPb1jx5VLx1uXQPAv4F/vs7vXVUNOry4QVqqgl2amumw93KWoEMIIYQQQpQc6ZnpLDiyAIDhdYbnqY4x6Pjr8l8YFHXV6/D4f7tWuRWuaxWYBx0lNcuhKDBiBNy5A23bZt+Nato0sLNTMx2HD1vuv3gR7Egl7foNAMo0KJOvNnhU9ACtBntS0d1JxC5dzXQ4+pgHHdK9SgghhBBCFKsNFzYQlRSFj5MPXSp2yVOdev71cLBxIPZOLKdvnAbuZjoKO54DHo6gY8MG2L4d7O1hzhw1u3EvHx/o3l29Pm+e+b7btyEmBvyJAAXcAt1w8nGyPMh92OhtcCqrTifsfCcG+wzjGh1O6PUugAadTi+ZDiGEEEIIUbx+O/0boA4Qz2s3JjudHQ3LNARg37V9wN1B5IGuhRvPAeZBh5u9W6GPZ22KcjezMXo0BAXlXHbYMPXyl1/UweVGly6plxUdC9a1ysgtRO1i5ZJyA4dMNdPh7OuEvb073br9QI8eC9BoiiY8kKBDCCGEEELkSlEU1p5bC6jjOfKjkmcl4G6wYepe9R/IdGzbpnaZcnSE1167f9nHHgNPT4iNNe9idfGielnBVs0QlW1StkBtca/kBYBLWoxpNXIXX/X+q1v3GWrU6Feg4+aFBB1CCCGEECJXhyIPEZEYgZOtE63KtcpX3QBXdaYlY7cqU/eq/8CYjh9+UC8HDVK7UBllpmeydsxalvZeyp2bdwCwsYFGjdT9f/99t+zFi6DBgFeyGqwFtQoqUFs8K6uZDveMWNPCgK5++eumVVA2D+QsQgghhBDiobbm7BoAOoR0QJ/PwcbGaXGvJFwB7mY6CjtdLoCL3d2F7Upa0HHjBvz6q3r9uefUy8TIRLa+t5XYM7GE71Dvh9izsYQ8FkKDFxrQqFEp1q6FffvuHufiRXUlcV16KnYudviG+haoPU7e6nocelKxIQMAe5cHM9uXBB1CCCGEECJX28K2AdAppFO+6wa4mWc6IhMjAfB3KdjYhKzMxnToS9aYjkWL1LEZdeuqfwDrXlrHyWUnAdDaaNG76ok+Fk30sWgiDkbQ6PUhgHmm48IFCOLfQK15IFqbgnVW0juoK8fryESHukK83jH71eStTbpXCSGEEEKI+8o0ZJoGgTcNaJrv+lkzHWmZaWQY1F/Z713YryBKcveq339XLwcOVC+v7LnCyWUn0Wg1NH+zOcN2DmPE/hG0ntwarY2WsK1hBOrUweLnzsHNm2q9ixchkH+7pLUqeJc0vZNl0GGjfzDhgAQdQgghhBDivk7EnCApPQlnO2eqeVfLd/2yrurA5+T0ZK4mXDVtd7R1LHTbSmrQERenTpML8MQTcP3AdZb2XApA6LBQ2k1pR9nGZSkVXIpW77ai5sCaABybuYuKFdV6//yjzn4VFqYu6gfgV8evwG0yZjWyBh06O8l0CCGEEEIIKzsadZSnVjxFre9q0e7Hdsw7NA9FUe5b5++ral+fhmUaotPm/0uqvY09Pk7qKGrjWh1ajRY7K6wJUVKDjnXrICMDqlWD4MBMFnVbRGJkIj41fWj3cTuL8k1fUzNIp1acom6gGmBcvAjJyZCWpuBOHADuQe4FblNxBh0ypkMIIYQQ4j/i892f8/qm100rgwNsubSF7eHbmd19Njba7L8a7r26F4DGZRoX+NyBboFEJ0Vz5sYZQM1yaLJbJS+fSuqYjjXquHu6d4fTv58mMSIRZz9nhv81HL2r5UB8n+o+VOpWibOrz1Lu+m6gOxEREB8PjiRjRzqgLgxYUDZ6yXQIIYQQQogi9Nmuz5iwcQIGxUCfan1YM2ANk1pPQqfRseDIAj7a8VGOdf++pmY6GpVtVODzG6fNNWY6nGytM1VrSc107NypXnboAAd/OAhAneF1sg04jJq/0RwAx7NHsCeFyEhISAB34gFw9nPGxr7gOQNjgCFBhxBCCCGEsLod4Tt4fdPrAHzU9iOW9llKl0pdeK/Ve8x9Yi4A/9v1P8LiwizqZhgyOBOrZidCfUML3AbjYHLjsawxngNKZtBx5Yr6p9NBJc9YLm5UV/er80yd+9YLaBpAqfKlINOAH9dNmQ5rdK2CuwGGDRnoMJhtK2oSdAghhBBCPMKS0pIYtHIQCgrDQofxVou3zPYPqjWINkFtSMlI4b2t71nUD4sLI8OQgb2NvWlAeEEYp8c9f/M88GgHHbt2qZehoXDgq78AqNilIqWCS+Va16+eOlDcjwgiI4sm6LD9d42OrNuKmgQdQgghhBCPsGl7p3E5/jLl3MoxvdN0i/0ajYYp7aYA8OupX0lKSzLbfy72HAAVPCqg1RT8q6MxIIhOigaKJuhwsy+6MR0GQ+5ljIxBR8tacRz98SgALd5ukae6vnXUhf/8iMzSvSoOALdyhbt92QUYEnQIIYQQQohCuZF8g092fQLAlHZTcNG7ZFuuUZlGBLsHk5yezB/n/jDbdzb2LACVPCsVqi3GlcPTDeqA6Ich05GaClOnQnAw2NpChQowfXruAYgx6KiQdARDhoGgNkEENAnI0zn96ppnOuLirJjpsJWgQwghhBBCWNnM/TO5nXabUN9Q+tfon2M5jUZDv+r9AFh8fLHZvnM31UxHRY+KhWrLvQGPtYIOd3t32gW3o21wW0rZ5959Ka/i49VB4K+8oq6TYTCoK4OPGwcvvqiun5Gd9HQ4dky9rrlwAYAa/Wvk+bzGdTi8iEWXkcqlS+D270Bya3WvMlLQoNXJ4oBCCCGEEKKAMgwZzDowC4DxTcbn2jWqXw016Fh3fp1pxXCwYtBhVzRBh0ajYeOgjWwevNkqU/ACpKXB44+rM1C5usIPP8Dly/Dll6DRwHffqX/ZuXhRXZ/DwzGFmMPqQoghHUPyfG4nHydcy6oZm9JEcuaM9cd0GBkKsOZKQUnQIYQQQgjxCFp1ZhVXE67i7ehNn2p9ci1fq3QtnO2cSclIMU1rC1bsXlVEmQ7AasGG0dtvw+7d4OYG27bBs89CQAC8/DJ8/rlaZtIkSEy0rHvqlHrZxPcSSqaCZ2VP3Mu55+v8PjXVhRS9iOXcqQz0pAHgXNr5ftVypdFpyJqgUSToEEIIIYQQhfHjkR8BGF5nOHqbnNeGMNJqtNQuXRuAQxGHAEjNSOVy/GUAKnqWzEyHte3bdzewmDcP6twzy+2YMerYjuhomDbNsr4x6KikU7tWhTyW9yyHkYu/el85c5vLZ1NM2+1cCreCu0ajwaC5G2gohZgYIL8k6BBCCCGEeMQkpiWy4cIGAAbWHJjnenV81W/YhyMPA3A5/jIGxYCjrSOlnUoXqk33ZjqstTigNSkKjB+vXn/6aXjyScsytrbw3r8zCy9YYDm2wxh0uN0KA6B8+/L5boezn5rRcCERbUYqABp7O6uMvzDLbugk0yGEEEIIIQpo7bm1pGSkUMGjAjV9aua5Xh0/Neg4FKlmOm4k3wDAx8mn0F2YHoZMx9q18NdfYG8PU6bkXK5HD7Czg/Pn7wYZRqdOqRkKbsSCBsq1LJfvdrj4GTMdidijBh1aR/t8Hyc7WYMO6V4lhBBCCCEK7NdTvwLQq2qvfAULxkzHochDKIrCzTs3AfBw8Ch0m5zszDMbJTHo+PJL9XL0aHUMR05cXKBdO/X677/f3a4ocPo0lCMcAN/avti75z9YuJvpuI0etXuVrVPuXeTyQjIdQgghhBCi0AyKgY0XNgLQo0qPfNWt7lMdW60tcSlxhMeHm4IOTwfPQrdLq9GaralR0oKOY8dgyxbQatVxG/dKvZ2KIfPuAh09eqiXv/12t8y1a+rg8mCNGnSUa5X/LAdkn+mwc7VO0GEWaDzAoMPmgZ1JCCGEEEIUuePRx7mVcgsnWyfq+9fPV107nR1B7kGcu3mO8Lhwq2Y6QO1ilZimTvlU0oIO4xS4Tz4J5f6NFVITUtk/az9nfjvDlT1XcPJxovPXnanepzqdOqllDhxQFxHU6+GqOkMuITbhkF7woMOY6XAm0ZTp0LtZp3tV1kBDYyOZDiGEEEIIUQDbw7YD0CywGTba/P++7O3kDUDsnVjrBx1ZBpOXpKAjIwOWL1evjxihXqYnp/NTh5/Y9Nomruy+AgokRSWxvO9y1r20jjJ+BtzcIDMTzqqzChMTAzoycE9Xx8KUbVS2QO1x9lWDDhsyTWt0OJayfqZDI92rhBBCCCFEQey4vAOAVuVaFai+l6MXoA4ij70TC1inexWYDyYvSUHHtm1qwODpCW3bgiHTwIqnVnBt3zUcPBzo/E1nxpwfQ4u3WwCw7+t97J22h2rV1PonTqiXMTHgwS00KOhd9aaMRX7Z6G1w8HQA1LU6AJw8iyDosJWgQwghhBDiPy/DkMGB6wf459o/JKcn51peURR2hKtBR8tyLQt0Ti+Hu0HHfyXTsXSpetmrlzol7p+v/snp306j0+vov6o/DUc3xCPEg7YftuXxGY8DsPuz3dSonA7AyZNq/eho8ELNcnhW9izUjF/GcR3G47l4Wad7VdYuVdK9SgghhBDiP27hsYVU+KoC9X+oT8PZDQmeHsycg3PuWyc8PpzopGhstbY08G9QoPNmzXRYO+hw1buarpeUoENRYNUq9XrfvnBlzxX+nvY3AD0W9CCwWaBZ+boj6uIe7E5yTDIhcQcA80yHMUjwquJVqHYZsyTG41mre5VGxnQIIYQQQgiAd7a8w1MrniI8PhxXvSueDp5EJ0Xz7Opn7xt4HI8+DkBV76p5WoU8O56OaleqIhnTkaV71b1T6BaXkychKgocHKB5c9j50U4AQoeFUqNfDYvyOlsdzV5rBoD2iLqeiTHoiI4Gz3+7Q3lWLlyXNGOmw4ZMAPRuVgo6snSp0kr3KiGEEEKI/6ZZ+2fx0c6PAHi7xdtEjo8kYnwEE5pOAGDUH6NMK4bfyxh01PCx/LKcV9llOoyBSGGVxDEdW7aol82bw82TEZz74xwarYYWb7XIsU71ftXR2mhJvhSNJ7GcP6/OYFUUmQ4jeyvNXqW1kaBDCCGEEOI/7UjkEcasUxeJmNJ2Ch+2/RAHWwdsdbZ80v4TulfuToYhgw92fJBtfVPQ4W2doMM4kPxRHtNhDDratr2b5agxoAYeFXK+zQ6lHAhuGwxAHf1JMjPhwgWIjlLuBh2VCxd0uAW6mf1fFJkOnQQdQgghhBD/LYqiMHrtaNIN6TxR+QneaP6G2X6NRsOUtlMAWHFqBSeiT1gcwxh0VPepXuB2GIOOqMQo4lLigKLpXlUSgo7MTHXmKoCGQdGc+vUUwH2zHEZVe1dVL1Hr3LwJiVFJ6mJ+Ws19g5a88Kxknl2yWqYja/cqOwk6hBBCCCH+U5acWMKuK7twtHXkm8e/yXbmo+o+1elZtScAsw7MMtuXYcjg1A31C7A1uleFx4ebtpWyL1Xg42VV0jIdZ85AXBw4OcHtTerg8aq9quJdzTvXuhUfrwiAR2okNmQQHw9pMfEAOPo4Y2NfuDW4PSqaBy16K61InjW7obN7cKHAfzbouHLlCq1bt6ZatWrUqlWLZcuWFXeThBBCCPEfpSgKU3aqWYw3mr1BWdecF5UbVGsQAOvPrzfbfv7medIy03C0dSTIPajAbTEGHUaueldsdbYFPl5WWTMd9jZWWmH7X7Gx8Nln0KkT9O4NCxeqM1Pdz+HD6mVoLQNnflMDtgYv5G3WLxd/F+xL2aNBwZNYrl4Fu4wkdZ9vwdbnyMotwA2d/m6AYK3uVVmzGzrJdBQ9Gxsbpk2bxsmTJ/nzzz8ZN24cSUlJxd0sIYQQQvwHbbiwgWPRx3C2c2ZMozH3Lds2uC02WhvO3TzHhZsXTNtP3zgNQFWvqmg1Bf+K527vblbfWl2r4G6mw8HGoVBtvNfu3VCzJrz2GmzYAL/+Ck89BV27QlpazvWOHFEv63mFcyf2Dg6eDpRrWS5P59RoNKaMiDcxnD8PTqhrqbj4Fn5mLo1Wg3uQu+l/a3WvyprdkKDjAfDz8yM0NBQAX19fvLy8uHnzZvE2SgghhBD/SdP2TgNgRN0RuNu737esq96VZgHqlK0bLmwwbb+WcA2Acu55+9KcE61GaxZoWDXo+DfTYc2uVfv2Qbt2EBEBVarA9OnwzjvqFLhr16qBSE6MQUfZBHV1vyo9qqC1yfvXY8ugQ/0B29HbOrfPufTdjIm1Mh02WQING70EHezYsYNu3brh7++PRqPht99+sygzY8YMgoKCsLe3p1GjRuzbt69A5zpw4ACZmZkEBAQUstVCCCGEEPkTmRjJxosbAXihwQt5qtOpQifAvIvV9dvXAfBz9it0m7J2sSqKTIe1go6oKHjiCUhJgY4d4Z9/4KWX4IMPYPFitcz06bBzZ/b11e5VCoZTZwGo2rNqvs5/b9Dh+G/Q4eRjnTVIsh7HWjNN6SToMJeUlETt2rWZMWNGtvuXLFnCK6+8wvvvv8/BgwepXbs2HTt2JDo62lQmNDSUGjVqWPxdv37dVObmzZsMHjyY77//vshvkxBCCCHEvRYfX4xBMdCoTCMqeFTIU53mgc0BOBp11LQtIjECsE7QkXXl8Ib+DQt9PKN6fvVoVa4VI+uNtMrxXnkFIiOhenVYuhScswyl6N4dnnlGvf7ll5Z1o6LUPy9iSYlOQKfXEdQmKF/nzxp0XLhwt3uVtTIdTqWtv4Bi1kDD9gEGHYUbVl+EOnfuTOfOnXPc/+WXXzJixAiGDRsGwMyZM/njjz+YO3cub7yhTjF32Dg6KAepqan06NGDN954g6ZNm+ZaNjU11fR/QkJCHm+JEEIIIUTOfjn2CwBP1Xwqz3UqeVYC4HL8ZVIyUrC3sb8bdLgUPui4mnDVdP21Zvfpn5RPDrYObBu6zSrH2rxZHSyu1cKCBeDqallm/HiYMwd+/x0uXoTy5e/uM3atauRzEaIhsFkgtg75GzBvDDo8uEnanUxT9yprZTqC2wbzz4x/rHIso6xBh429ZDruKy0tjQMHDtC+fXvTNq1WS/v27dmzZ0+ejqEoCkOHDqVt27YMGjQo1/Iff/wxbm5upj/piiWEEEKIwrqWcI391/ejQUPf6n3zXM/b0Rs3vRsKimkwecRtNejwd/EvdLtebfIqOo2ORb0W4WbvlnuFB0xR4N131evPPw/16mVfrmpVdTYrRYF588z3Xfh3DH5F7SUAgtsF57sdLmVc0NjbocNAKW7dDTq8rRN0VHmyCl2/78qIf0ZY5XhQfJmOhzLouHHjBpmZmZQuXdpse+nSpYmMjMzTMXbt2sWSJUv47bffCA0NJTQ0lGPHjuVY/s033yQ+Pt70d+XKlULdBiGEEEKITRc3AVDfvz6lnUvnUvoujUZjynacjVXHI1hzTMfLTV4m/o14+tfoX+hjFYUdO2DPHtDr4e2371+277+xnHHlcaMrV0CDAdebatBRvn158kuj0WDjpgYYDiRbPdOh0WioN6Ie/vULH0ga2WbJbtg6SPeqIte8eXMMBkOey+v1evR668waIIQQQggB8OfFPwHoUL5DvutW9KzIP9f/4WzsWdIz04lJjgGs070KwMnO+uMJrOWzz9TL4cPBL5eb26aNerlvHyQm3h33ceUKeHEDbVoqds52+NUr2P1m62xPehTYk4rjv2M6rBV0FAUZ05EPXl5e6HQ6oqKizLZHRUXh6+tbTK0SQgghhMg7g2Jg4wV11qrHQh7Ld/1KHnczHVFJ6nciG62NxeJ+j5rr12HdOvX6yy/f3Z4Uk8SxX45xZZfaG6XKk1WoMaAGQUEaypWD8HB1PY/H/r2rr1wBX9T7rXSt0mh1BesApHfVkwy4cBtbMgDrDSQvCmaZDhnTcX92dnbUq1ePzZs3m7YZDAY2b95MkyZNirFlQgghhBB5cyzqGDHJMTjZOtEkIP/fX4zdq87dPGcaz+Hr7GvVRfdKol9+AYMBmjaFihXVbdf3X2dm7ZlseHkDJ5ef5OTyk6x4agW/9v8VQ4bBlO3YuvXuca5cgdKo3fJL185717Z72burPWE8UNd709nbYudkV+DjFTW7LF2q7KR7FSQmJnL+/HnT/5cuXeLw4cN4eHgQGBjIK6+8wpAhQ6hfvz4NGzZk2rRpJCUlmWazEkIIIYQoyfZdU9cXa1y2MXa6/H9JzTqmw5rT5ZZ0P/6oXg4Zol5GHIpgQZsFpCWm4VnZkzrD63Dn1h32fLGHE0tP4BrgSqtWjzF/vprpADVouXIFmhozHYUIOhw91JXCjUGHg1fJzXKAeXZD7yhBB/v376eNMSwFXnnlFQCGDBnC/Pnz6devHzExMbz33ntERkYSGhrK+vXrLQaXCyGEEEIUtf3X9/PL0V84e/MsVb2qMqr+qFzX3DgYcRBQ164oiPKl1IHPUUlRXLx1EbDeeI6S6tw5OH4cbG3VAeKJkYks7LKQtMQ0yrUqR//f+2PvpgYBfnX9WN53OXu+2EPD7yoD5bio3k1ER0N6OpTO0r2qoJw91IDRGHS4FMHaGtYkmY57tG7dGkVR7lvmxRdf5MUXX3xALRJCCCGEMGdQDLy9+W0+2fUJCur3lrXn1jLrwCzmPzGfXtV65Vj3YKQadNT1q1ugczvb3V0Jzzht7qOe6Vi7Vr1s0QLc3WHF03+SGJGId3Vvs4ADoHqf6lx45gKH5hwiZvVeoBzXrkFamprlcCIJFxJBA6VrFiLo8DLPdDiX8KAja3bjQWY6Hu1Of0IIIYQQRURRFF5e/zL/2/U/FBT6VOvDN52/oUVgCxLTEnlqxVOciD6Rbd30zHSORKqr09XzL1imw1Zni61WXczuSoI6eNrb0btAx3pYGAeQP/44hO8M59gvx0ADPeb3MAs4jBq/3BiAsPVn8NHHoShw9apxPIea5fAI8cDOueBjMBz+HdNhRzpQsmeuAvPshgQdQgghhBAl3A8Hf+CrfV8BMO+JeSzts5TRDUezdchWOlfoTGpmKoNWDiLTkGlR99SNU6RmpuKqdzV1kyoIR1t1/IBxutySPM1tYSUnw7Zt6vXOnWHrO+qo8LrP1s1xHQuf6j4EtwtGMSi0dD4MQFiYGnQYMxNeVQo325fezXxJhZI8cxWAk+vdQMNegg4hhBBCiJLrcvxlXv3zVQD+1+5/DA0datqn0+qY030O7vbuHIo8xLrz6yzqG8dz1PGtU6jZpoxBx43kGwA42T66Qcdff0FqKgQGgmNMOOE7wtHZ6Wj1Xqv71qvRvwYAgQZ1EUBj0OFKPACuga6Fapfe1TzoKOmZjqxBh50EHUIIIYQQJdcrG17hdtptmgY05dWmr1rs93PxY3jocAC+P/C9xf6TMScBqFW6VqHacW/QYfz/UfT33+plixaw+7NdAIQOC8W17P2DhqA2QQC4xF/FlnTCwiA+HtxIAMAtwK1Q7bq3W1dJDzp0drpsrxc1CTqEEEIIIfLhSOQRfj31Kxo0zOwyE502+y9uz9V7DoA/zv3B1YSrZvvC4sIACtW1CsDB1gGAW3duAY9296p96gzD1K98m/Pr1GUVmryS+/ompcqXwjXAFY3BQACXCQtTMyauxqAjsHBBx72ZjpLevUqCDiGEEEKIh8AHOz4AoG/1vtQsXTPHcpW9KtMisAUGxcBvp38z22cMOoLcgwrVFmNmwzhz1sOS6bhyBWbPhg8/hC1b1HUz7kdR7gYdvjHHUAwKZZuUxbOSZ67n0mg0BLcJBiCYMMLCICUF3IzdqwIK2b3K7eHqXiVBhxBCCCFECXcl/gorTq0A4N2W7+ZavkP5DgDsvrLbbLu1g46c/i9pFAU++QQqVYIRI+Ddd6FdO3VgeFxczvUuX1bX1rCxgZvbjgJQe3DtPJ/X2MUqgCtq0HFHuZvpKGT3KosxHd4SdGRHgg4hhBBCiDyaf3g+Cgqtg1pT3ad6ruWbBjQFYNeVXaZtSWlJptmmrB10lOSB5IoCL78Mb7yhZhoaNIABA8DREf78Uw08Mi0n+gLuZjmaVL5JzLEotDZaqvfN/f438qqqzlBViltcvQppcUnYkAkacCnjUqjbde+YjpLevUprq832epGf94GdSQghhBDiIWZQDMw9PBeAZ+o8k6c6jco2QqvRcjn+smlcR3h8OABuejfc7d0L1aaHKdPx9dcwfbp6/Ztv1IHhCxeqs1K5usLevfDdd9nXPXRIvazvfg6AwOaBOHg45Pnc7kHuALhwG62SSfoNNcth4+6CzrZwv/bbudxd48PO2Q5bB9tCHa+oSaZDCCGEEKIE231lN2FxYbjqXelVNeeVxrNytnOmdunapvpgva5VkE2mo4QOJD99Gl5/Xb3+xRcwejRoNOr/derAxx+r1996S51Z6l7n1FgDz1h1AHmFxyvk6/xOPk7Y2NugRe1WZbilnsTOu3DjOQC0Oq1pccGSPp4DJOgQQgghhCjRVp9ZDUDXSl1Ns0blRbOAZgDsubIHsG7Q4WBj3o6SmOlQFHjhBbVLVceOahere40cCVWqwO3b8OuvlvvPnwdb0sm8GAZAxccr5qsNGo0Gt3Lq2A134tDcVjMdDqULN57DyDiu42EIOuyc7dDaaLGxt8FGb/PAzitBhxBCCCFEHqw+qwYd3Sp1y1e9at7VALgYdxEo2kxHSQw6Nm+GrVvBzg5mzbqb4chKp4MhQ9TrP/1kvk9R4MIFCOQySloGrgGueFfzznc7jF2s3InD9o6a6XD0K3ymA+7OYFXSx3MA2DnZ0XtJb/os64PWRsZ0CCGEEEKUGBduXuDUjVPoNDo6hnTMV92yrmUBuJZwDSji7lUlbCC5oqgzVAGMGgXlyuVcduBA9XLbNnW2KqOYGDUDUgb1/ivXohya7CKXXGQNOvRKCkC+xoXcj3Ew+cOQ6QCo2rMqlbpWeqDnlKBDCCGEECIX68+vB6BFuRaUciiVr7rGoMM4kDwyMRIAfxf/Qrcra9Bho7XBVleyBjHv368OENfr1fEa9xMYCM2bq9fXr7+7/bw6jIMKDmrQ4d+wYPebMehwI16duQqwc7RO9yJj96qHIdNRXB5cRy4hhBBCiIfU7qvqIPA2QW3yXdcYdEQlRZGWmUZSehIALnaFm6oVzIOOkti1auZM9bJPHyhd+u72hGsJXNp8iaToJMo0LENg80A0Wg3Nm6uzWR04cLesGnQo+GaqQUeZhmUK1JasmY4k1IyE3tk6X4UdvdT73sW/8I/po0qCDiGEEEKIXBhnnmpStkm+63o5emGnsyMtM42I2xEkpiUC6sxWhZU10ChpXavi42HRIvX6qFHqpaIo/P3V32x+czMZdzJMZSt0rkDvJb2pV0/NGNwbdLiSgF1aElobLb6hvgVqT9aB5Kmo57G3Uqaj6WtNcfR2pObAnFeo/6+T7lVCCCGE+E9JTk/mSOQRTsWcQlGUXMtHJkYSFheGBg2NyjbK9/k0Gg1lXNRf568mXLVq0JF19qqSlulYvRru3FFnpWraVA04Nr2+iQ3jNpBxJwPfOr5U7VkVGwcbzq87z8IuC6lXV308jh6F1FT1OBcu3B3P4VPTp8DrYLgFqkGHKwnYkg5YL9PhW9uXTtM64ehZsh6DkkSCDiGEEEL8J6RnpjNl5xR8P/cldFYo1b6tRu2Ztdl/ff996xmnuq3uUx1XfcFmOzINJr99regyHSVsjY6VK9XL3r3VGav++fYfdn+mZowe++IxnjvwHH1/7cvQ7UOxc7bj8s7L3NhwAA8PSE+H48fV+uHh4EcEAP4NCj4OxjjuQouCHjWicXCRTj8PigQdQgghhHjkpWSk0HtZb97e8ja3027j4eCBXqfnWPQx2v3Yjr+v/p1j3T1X1aCjIF2rjMq4qpmOK/FXTEGHNYKEkjqm486du4PBe/SA2LOxbJywEYD2n7anyStNTDNQlWlQhrZT2gKw+c1NNApVA4L9/8aCN2+CB7cA8K6a/6lyjbJmSBy4A4C984NbHO+/ToIOIYQQQjzSFEXh2VXPsurMKvQ6PQt6LCBmQgzXx1+nVblWJKQm8PTKp0nLTMu2/pGoIwA08G9Q4DaUdVEzHRduXcCgGADrZzpKUtCxcSMkJ6szUtWtC2tfXEvGnQyC2wXTdHxTi/INXmiAZ2VPUuNTqWt/ClC7WAHExYEHNwEoFZK/mcOy0tpoUTTqV1971Clz7a3UvUrkToIOIYQQQjzSfjzyI78c+wWdRsfqAasZXHswWo0WDwcPVg9YTWmn0py/eZ4Z+2ZkW//MjTMAVPWuWuA2GLtXnYk9Y9pmjYHfJXUg+aZN6mWXLhC29RIXN15Ea6ul2/fd0Ggt19jQ6rTUHlwbAMcLarQRqc4szK2biino8KjgUah2KTo1yDAGHbYOEnQ8KBJ0CCGEEOKRdfPOTcZtGAfApNaT6BDSwWy/i96FD9t+CMBHOz+yyHbcSb/D5Xh1pbpKngVfTM3Yver0jdOAOgBcpy18156Smun46y/1slUr2PLOFgDqjaxHqfI5ZyqMMz+ln72ECwlER0NKCmhTk7EnFTRQKrjgmQ4AxUYNMrSoA9Zt9BJ0PCgSdAghhBDikfXRjo+IS4mjpk9N3mj+RrZlhoUOw8fJh9g7sWy9tNVs3/mb51FQcLd3x9ux4OMJjLNXXb99HbBO1yoAB9u7s1eVlExHQgIcUXukUcX1Olf3XEVnp6PFWy3uW889yJ2ApgGgQEXOER1t3rXKLcANG/tCBgm25jNfFfp4Is8k6BBCCCHEIynidgTf/PMNAJ92+DTHzIJOq6NnlZ4ALD+53Gzf2dizgJrlMA58LggPB/NuQdaaaaokZjp27waDAcqXh/AV6mjwqr2q4uKX+8J5Ac0DAPAnguhouHULq3WtAtDYmgcZEnQ8OBJ0CCGEEOKRNOvALNIy02ga0JSOIR3vW7Z3td4ArDy9kvTMdNN2Y9BR2bNyodpyb9BhrUzHgwg6rl6FnTvh5Mm8lTd2rWrZKJXji9R5b+uPqp+nuv711Slx/YggLg6io60ziNxIgo7iI0GHEEIIIR45aZlpzDowC4CXGr6Ua5aiVVArPB08ib0Ty4GIu8thGwd+F2Y8B0ApB/MvzFbrXpVlcUBrr9MREwNPPQXlykHLllC9OrRuDWFh96/397+zD4c6nCE9KR3PSp4EtgjM0zmNQUdpotCRyblzd6fLtUamQ2tn3r1Kp5cpcx8UCTqEEEII8cj5/fTvRCZG4u/iT8+qPXMtb6O1ob6/+mv8kcgjpu3WynTYaG3MFha0VtBhq7PFVqt+kbZmpiMsDJo1g4UL1a5SFSqowyG2b4f27SEqKue6xoyI/tK/s371qprnrmnuQe7Yl7LHhkx8iObsWXAnTt0X7F7wG/QvrV4yHcVFgg4hhBBCPHKWnlwKwKBag7DV2eZSWlW7tDplq3FdDlDX1QCo4FGh0G3K2sXKWkEH3A02rDWQPCkJunaFc+fULMf+/er1s2chOBguXIBnn82+blwcXL8ONqRzc985AKo8WSXP59ZoNKZshz/XOXPm7kJ+jl6FD6p0EnQUGwk6hBBCCPFISUpLYu25tQD0qdYnz/Vqla4FwNEodZ0Ig2LgRvINAHydfQvdrqxBhzVnmjLOYGWtTMdLL8GJE+Drq47PqFdP3R4UBGvWgE6nXv6dzSLuxixHQ8+LpCel41rW1RRE5JVfXT8AShPJmTNZFvJzty/oTTKxcbine5WddK96UCToEEIIIcQjZd35dSSnJxPkHkRdv7p5rlfbV810HI06ikExEJ8Sb1o93NPRs9DtKupMhzWCjt27Ye5c0Ghg0SIoW9Z8f7VqMHiwen3iRMv6xqCjhtNFACp2rZjvWb9cA9RuaM4kcfbs3aDDoZTD/arlSdbMhkGrK9SMZCJ/JOgQQgghxCNl9dnVAPSu2jtfXyore1bGTmfH7bTbhMWFmbIcLnYu2OnsCt2ukh50GAzw8svq9eHD1UHj2Xn7bfVywwZ1sHlWxqDDJ+UKAEGtgvLdDicfNQvkRBI6JQNbMgDrZDqyrkBuXJ1cPBgSdAghhBDikaEoCtvCtgHwWMhj+aprq7Olund1QM12xN6JBayT5QAoZX93BitrBh1P13yaWqVr0SSgSaGOs2ED7NsHzs7w4Yc5lwsJgTp1QFFg3TrzfSdOgJ5UbGIiAQhsnrdZq7LKGnQYsxxoQO+qz/ex7mXnKEFHcZGgQwghhBCPjLC4MC7HX8ZGa0PTgKb5rl/VuyoA52LPmTIdXo5eVmlbUWU6Xm/+OkdGHbFYCyS/pk5VL597Th3PcT9duqiXf/xhvv3kSSjLVVAU3IPccS3ralk5F9kFHVoHezTawneFsnXMMqZDgo4HSoIOIYQQQjwyjFmOhmUaFmjdCm9HbwBu3rlJbPK/mQ4H62Q6imoguTUcPw4bN4JWC2PGmO9LjEzk6t6rxJ6LNW3r2lW9XL8e0v9dSzEzU525KpBwgDyvzXEvY9DhQApOJAFg61r4rlUAeucsgYatBB0PktzbQgghhHhkbA/fDkCrcq0KVN8YGNy8c9OU6bBW96qiynRYw4IF6mWPHuosVQB3bt7hz/F/cuSnIyiZCgDlO5Sn++zuNGjghqcnxMbCkSNQvz7cuKGOCynLNQACmgUUqC0OpRzQ6DQomQqeqIGO3q3wg8gB9E53v/pqbGTmqgdJMh1CCCGEKHHSMtOYe2guHX7qQPO5zXlp3UtEJkbmWm/XlV2AFYKOlJumMR1eDiW7e1VhGQyweLF6fdAg9TL+cjxzm83l8PzDKJkKboFuaHQaLm68yE8dfuJObBI1aqhlT59WLyP/fXhKa9XR5aVrlS5QezRaDU7earbDGHTYl7JOpsPe+W73Ko1kOh4oubeFEEIIUaJEJkbSc0lP9lzdY9q268ouFhxZwObBm00rh98rKS2JCzfVxfzyM1VuVv/FTMfu3XD1Kri6QqdOkH4nnUXdFnHj9A1cyrjQZ1kfApoEcPP8TX5s9yOxZ2NZ89waqlTpx/bt5kGHnhScDbcB8K7qXeA2OXo7khiZaAo6XLytFHS43P3qq7WTr8EPkmQ6hBBCCFFixKfE03ZBW/Zc3YOb3o2P233Mwp4LqetXl4TUBHos7kHE7Yhs656IOYGCQmmn0ng7FewLb9agw5TpKOEDyQtrqbp4O08+Cfb2sH7ceqKORuHk48Qzu58hoInaTcqjggcD1gxAo9Vw+rfTVHC8DpgHHd6oWQ6XMi6FmuLWOK6jpp/6GLj6WCfocJCgo9hI0CGEEEKIEkFRFAatHMSpG6co41KGfSP28UbzNxhQcwBbh2ylqldVrt2+9n/27js8yirt4/h3eibJpJPeIPTemzQFQcEG9raIbe3rouuua9tdu7uia1k7a1l5bSj2BoIoXXpNKAmQQkJ6bzPz/nEykwwpZEoghPtzXVzP5JnnPHOS7Mb5zX0Kf/3pry223567HYBBUYM87oNj0nhBZUFjpaMDJpL7avdwX/jhB3W86CLIXJfJptc3ATBn0RyCE4Ndro0aFMXga9TO7YZfVwCNoSM3tzF0dOvveZUDGkNHfa5vh1f5BzUOr9JJ6DihJHQIIYQQolP4YMcHfJn2JSadiSVXLKF3eG/nc0GmIP574X8BeH/b+xwuOdys/fa8htAR6XnoaGl4la8qHU336bBj98k9vZWZCampatWqyZPtfH/39wAMvW4oPab2aLHNxAcnAlCycR/+VLJ3L9TXq0pHpI9Dh92mfk6+2BgQXIdX6UwSOk4kCR1CCCGEOOlKa0q554d7AHho0kMtztsYEz+GKclTqLPV8fza55s978vQUVFXQXaZGj7kqzkdZoOZEL8QAHqF9fLJPb21bJk6jhoFBev3k7k2E0OAgbMeP6vVNuG9wokaEoXdZqefYR+1tZCR4Tq8ylehw8Ec6pvVq5ruSK7zk9BxIknoEEIIIcRJ958N/yGnPIeeYT25d/y9rV53zzgVTD7c+SF2u2u1wBfDq4L9gtGgNqErri4GfFfpAMian0XRn4s82kOkIyxdqo5Tp8La59YCMPzG4VhiLW22632eqkINC0gD1BArl9AxwLehw1fDqwzmxuFVepMsmXsiSegQQgghxElVXV/trFw8OPFBTHpTq9dO7T4VP70fWWVZ7M7f7TxfUFnA0cqjaNDQv1t/j/ui1WgJNYe6nPPVnA5Qczkc1Y7OYOVKdRybcpT93+9Ho9Uw5q4xx23Xa5aq1MRU7EeLlYwMyM2xYUGtXBXaPbSN1sfXLHT4aHiVvkmlo2nVQ3Q8CR1CCCGEOKne3/Y+uRW5xAfFc+WgK9u81mwwMylpEgA/7v/Ref5wqZrjERkQ6fUk7aYhw6w3Yzb4ZmjPiVBeDrW17bu2oAAOHVKPtdu2ANDngj6E9jh+YIgbHYdfqB+6umqiyKW8HEqOVKLFDhq15K03jq2U+G54laHJYwkdJ5KEDiGEEEKcVAu3LATgztF3YtQZj3v92T3OBuCHAz84zznmX8RaYr3uT9NVpnqFd465F8ezejWceabaa8PPDyZNgp07226zebM69kyxs/czdfHgawe36/W0Oi1Rg9TmfxHkU1AA9cXlAJjD/dEZvBu6FJYSRt/ZfZ1f+6zS0WQeR2iEDK86kSR0CCGEEOKkOVB0gNWHV6PVaLlm8DXtajM9ZToAKzJWUG+rBzoudIyOHe31/TraK6+okLFiBdjt6t8vv8DIkbBuXevtHKFjXEImJYdKMFqM9Dy3Z7tfN7yvqghFkM+BAxBIBQCWGN/sQTLpwUnOx/4RvlliuOnwqsg4qXScSBI6hBBCCHHSvL/tfUDN1WhvYBgYORCTzkRlXaVz6dys0iwA4ixxXvfJJXTEde7Q8fHHcNttYLXCVVdBejrs2wdnnQXV1XDFFVBS0nJbR+joVauqHP1m93MZfnQ8EX3VBPsICkhPh0BUpSMw2jehI2Z4DOe/cT7nvnSuz0KHy0RyWb3qhJLQIYQQQoiT5uNdHwNw9aCr291Gq9HSI1TtIbGvcB/g20pH04nenTl07N8Pc+eqx3feCf/7HyQnQ0oKfPqpepyRAU880XL7LVvU0Xh4PwB9Luzj1us3ho58srJ8HzpAraQ1+nbf/Q6aBg297NNxQknoEEIIIcRJkV2Wzfa87WjQMKv3LLfa9gxTw4CcoaPcd6GjoKrA+XhA5ACv79cR7Ha49VaoqoIpU+C550CjaXw+OBief149fvNNdV1TlZVqU0ALpVQfzkej1ZB8ZrJbfejWT032DqeA/DybM3QERHWO5YBbojPpaFgRWSodJ5iEDiGEEEKcFI7Vp0bEjnB7L4xjQ4djeJUvQoe/vnEoj17bOd+Yfv45/PgjmEzw+uuga2FO9HnnQVISFBbChx+6PnfgANhsMNA/HYCYETFurxAVnBiMxqBHj5VgiglomNPhy0qHr2k0GmfYkNBxYknoEEIIIcRJ8f3+7wGYkTLD7bbO0FHkOrwqLsj7OR2PTHmEaT2m8fkVn3t9r45gt8Ojj6rH8+dDr1YW2NLpVDUE4O23XZ87eFAd+5lU6OgxrYfb/dBoNZgTGieTd8Twqo4goePkkNAhhBBCiBPObrfz4wFV6fAmdOwt2EudtY68ijzAN5WOxOBEfrz2Ry7oc4HX9+oI330HmzaBvz/88Y9tXzt7tjquXQs1NY3nHftzRFVnAND9rO4e9SUgXk26D6X4lAkdjsnkOtmR/ISS0CGEEEKIE25/0X7yK/Mx6UyMiT/+DtjHcoSO/UX7ySrLwo4dvVbv9jCtU9HLL6vjzTdDN9c99KirqsNmtTm/7tULIiNV4NiwofG6gwfBTCWmKrW0VdxozypEfiFq93gjtadM6HAsmyuVjhNLftpCCCGE8EqdtY5fD/3KliNb6BHag6k9phJobPuN52/ZvwEwJHpIuzYEPFZicCJ6rZ5aay0bstS76ZjAGLSarv15ak6OqnQA3HJL4/ms9Vn89OBPpP+UjkajIWlyEjNfnklEnwgmTYJPPlF7d0yYoK4/dAiiOQJAaEoopiCTR/0xB6vfnZkq/FGz1Tt76AhJDqFofxHBicEnuyunFQkdQgghhPDY5pzNzF0yl+15253nEoIS+OSyT9pcbnZj9kYARsaM9Oh19Vo9ySHJ7Cvcx+rDqwHfDK3q7P73P7Unx7hx0KdhhduNb2zkm9u/wVanKhx27KQvS+e1Ya8xb+U8Jk6M5ZNPYOVKuP9+1ebgQYhpCB3RQ6M97o9/iAodoRSpE1qt2xPST7RLPriEovQi5+pb4sTo2h8HCCGEEKLDrM1cy8T/TmR73nZC/UK5sM+FxAfFc7j0MFPensKe/D2ttv0tR1U6RsSO8Pj1g03qk+q8SjWfw2KyeHyvU8WiRep43XXquPuz3Xz1+6+w1dnof0l/7ki7g9t3307SpCTqq+r55IpPGDdcTeZYtUpNQgcVOhyVjuhhnoeOgFAVOkIoBkBr8Uej1bTR4uTzj/AnbpT3Cw4I90joEEIIIYTbDhYfZOb7M6moq+Cs7meRekcqS65Ywo5bdzApaRJV9VVc//n1WG3WZm1tdhubcjYBMCLG89Dhp/cDoLi62OXrriozU23op9GoCeLFGcV8ds1nYIeRt47kko8uIbxXOBF9I7h8yeUEJwZTtL+Ioi9+QaOBsjI4ehTq6iA7uzF0xAyL8bhPjtBhoQwAfUDX/h0Iz0noEEIIIYRb7HY7N3xxA0XVRYyKHcUXV3xBtwA1VCXYL5j3Zr+HxWhhTeYaPtjxQbP2+wr3UVpTip/ej/7d+nvcj9MtdHzzjTqOGQMREXa+vvVr6irrSJqUxLkvnIumye6A5lAzM55Xq4JtWbiJuKh6AA4fVuFFZ68jgnzAu0qHX5AKHY5J5IZAz+aGiK5PQocQQggh3PLu1ndZlr4Ms97M+3PeJ8DougN1YnAi946/F4A3Nr3RrP2uo7sAGNBtAAadweN+mPTqDe7pFjpmzYK0r9LY990+dEYd571+Hlp987d0fc7vQ1BCEFUFVYzy3wmoCeSHDkEYRWix4xfqhyXG82FpRosKHY64YwqW0CFaJqFDCCGEEO1WZ63jbz//DYBHJj9Cr/CWd6abN3QeGjT8fPBn567hDulFDRvShbq/IV1TzSoduq4bOmprYelS9XjmTDsrH10JwJi7xxDRp+VlgrV6LSNvVRP1U8q2ACpwZGVBMGqp3JCkEK/6ZQx0XXnMHCKhQ7RMQocQQggh2u3tLW+TUZxBVEAUd465s9XrEoITmNFTDe95Z8s7Ls+lF6vQ0T3Esw3pHByho6S6xOXrrmjbNqiogNBQCDp6gOwN2ejNesbfM77Ndv3m9AMgoDATHfUcPqzuE9ww8dvbZWOPDR3+EjpEKyR0CCGEEKJd7HY7C9YuAOAvE/6Cv8G/zesv638ZACsOrnA57wwdoV6GjobKRkVdhfq6C4eOtWvVccwY+O0/al+S4TcNJyAyoI1WEN47nIDIADTWemLJ5tAhqKxsrHQEJ/k2dASES+gQLZPQIYQQQoh2WXV4FXvy9+Bv8Of6Ydcf9/pxCeMAtRFgnbXOed4xvMpXlY7Wvu5K1q1Tx7EDy0n7Og2Akb8//h4nGo2GxImJACRxyBk6Qhyhw8eVjkAJHaIVEjqEEEII0S6OSeFXDLiCIFPQca/vHd6bUL9Qquur2Zq7FVDVEp9VOo4JGY6J5Z2Z1Qqvvgrjx0NMDJx/Pixbdvx2jtCRWLwNu9VO3Og4uvVv3+Z2jaHjIIcPd2ylQ+Z0iNZI6BBCCCHEcVXVVfHJrk8AuHH4je1qo9VoGRM/BlAbCQIcrTxKZV0lAEnBSV716VSrdJSUwJQpcOutsGYNHDkCX30F06fDG80X+XIqKIC9e9XjqvVq5/eh84a2+3WTJqqfcwKHycm2U1zcJHT4uNIhq1eJ1kjoEEIIIcRx/ZT+E5V1lSQEJTA2fmy7242LV0Os1mSuASCjOAOAWEus15WJUyl0VFbCOefAr79CUBAsWAC//ALXXgs2G/z+97B+fcttN25Ux8HdSzm67QhoGieIt0e3Ad1AA37UYKaSvXuszs38vF29yuDvuuSxKUhCh2iZ/mR3QAghhBCd3xepXwBwQZ8LXDahO54xcarS4diB3FfzOaD5cKrOHDruu09NBg8LU8Ophg5V5884Qw25WrQI7rhDXaM95iPh1FR1HBmslh6OGxV33AnkTelNegKjAik/Uk4wJWTtrkOLHXQ6t+7TEq1Oi91gQFOn5uxI6BCtkUqHEEIIIdpks9v4Mu1LQIUOdzjmbWSWZgKNlQ5v53PAqVPpWLoUXn5ZPV60qDFwAGg08OyzqvqxYQMsWdK8vWNoVWyFetBrVst7o7TFMYwqmFJqjqqhVbqwYDTa9gfI1miMjUOsJHSI1kjoEEIIIUSbtuVuI6c8h0BjIJOTJrvVNtYSC0B5bTllNWXkV+YDEOkf6XW/ToXQYbPBvWpzdm67DWbMaH5NdDTccot6/P77zZ/fuxe0WDEcOgB4GzpKMNWWAqAPP/5iAO2h9ZPQIY5PQocQQggh2rTq0CoAJiROcHseRqAx0LnSVXZZNuW15QBYTBav+3UqhI4PP4StW1Ul4x//aP26K69Ux6+/htJS1+f27oUocrHX1OIX6kfMsBi3+xGUoH4HwZRgpBYAQ6BvAkJwpIQOcXwSOoQQQgjRptWZqwEYH9/27tetcVQ7ssqyKKtVE5gtxq4fOux2ePJJ9fhPf4Lw8NavHTIE+vaFmhrXIVZ1dZCRAfFkARA3Os6jIVGOSkcQpRhQ8y+OnQTuqcDQxtDhF9y5fgei85DQIYQQQpxG7HY72WXZZBRnYLfb29Vm9eGG0JHgWeiIs8QBqtLhDB2nQaVj1SrYvh3MZjVJvC0aDVxyiXr844+N59PT1UTzZL2aExM/Nt6jvjQdXuUIHUZ/36wn1HTZXKPF2MaV4nQmq1cJIYQQp4lPd3/KX5f9ldQCtRzS0OihLJi+gDO7n9lqG0dA0Wq0jI4b7dHrOiod2WXZlNV0XKXDpOtcQ3v+8x91vOoqCAlRj+02O5v/u5lt722jOL2YmBExjL17LEmTkhijFvpi8+bGezgmkSfqsqAe4sbEedSXpsOrHKHDFOibSocjdBgCDGh18nm2aJmEDiGEEKKLs9vtPLryUR5Z8QigNu3TarRsObKFc98/l8+v+JwZPVuY4QysOaz21xgcNdjj6oSj0pFVmnXaVDpKS2HxYvX41lvVsaashg8u/ICM5RnO60oOlZD6RSoXvHkBw84eCsCePVBVpSokaWlgpgpLTQGghld5wlHpsFCGHzWA70OHzOcQbZE4KoQQQnRxL61/yRk47hl3D0V/LiL33lwu6nsRNdYaLv/kcueqUsfamrsVgJExIz1+fWelo9y3lY5jKxudKXR8/TXU1kKfPjB8ONRV1bFo5iIylmdgDDQy9amp/O6n3zHg8gHYrXY+v/5zyMmmWzc1nGq72niczEyIIRuAsJ5h+If7e9SfgG4BoNehAcIoBMAvyDehw9AQXiR0iLZI6BBCCCG6sI3ZG7nnh3sAeGrqU/xr+r8IMgURZg7jw0s+ZEjUEEpqSnhs5WMttt+TvweAft3avwP2sVyGV50mlY5PP1XHOXPUfI1l9y/j0K+H8AvxY+6KuUz48wS6n9mdi//vYgZcNgDs8O0d3zB8mJpn4xhiVVgIEagqR+RAz5cZ1mg16ELUEKvwhvuZfRQ6pNIh2kNChxBCCNFF2ew2bv7qZupsdczuO5v7zrjP5XmjzsgzZz8DwH82/Ies0qxm93DM/+gT3sfjfsQFNRle1YFzOjpL6Kiqgm++UY/nzIGMFRms+/c69fX7c4gdEeu8VqPRMOO5GRgDjWSty2JEoPp5Nw0dYQ0hIaxXmFf90lvUz8eC+h34+zh0yMpVoi0SOoQQQoguatH2RWzK2YTFaOHV815Fo2m+1Or0lOmMjR9Lna2OT3d/6vKczW4jrSANgL4RfT3uR4tL5nbhSscvv0BlJcTHw/Bhdn645wcAht88nF4zm2/sZ4m1MOKWEQCEZ6lxVVu2qOcKCiC8YTiUt6HDENAw4Zt6AAJCfBM6HBUOU7BUOkTrJHQIIYQQXZDVZuXh5Q8DcP+E+4kMaH1ozqX9LwVg8e7FLucPlRyiur4ao85Ickiyx32JCVSb2dXb6p3nunKlY+VKdZw6FXYv3kXOphyMFiNnPXZWq20GXTkIgIotaZioISdHnVeVDhU6wnu1sdFHO5gsx8yBCfLN8rZ9L+pLz3N6MuL3I3xyP9E1SegQQgghuqAv074kvTidMHMYfxj7hzavndNvDgC/HPqFvIo85/nUfDXUp2dYT3Rancd9MegMhJsb3zBrNVr8DZ5NiG6qacjQarTotZ1jUc6ff1bHCRPs/PLELwCMu2ecmszdiuhh0YT3DsdWU08f9pDfMK+/uMBKKEWA95WOY0OGMcA3lY6QpBCu/vZqUs5O8cn9RNckoUMIIYTogl5Y9wIANw+/+bhv8JNDkhkeMxyb3cY3e79xnndMIvdmaJVDVGCU83GgMbDFoV7uaho6/PR+Prmnt6qqYP169bi/JZPcrbno/fSMuXNMm+00Gg39LlGT9VM4QGWlGqJlKyxGix292YAl1rvqkDnENXT4akdyIdpDQocQQgjRxewt2MvyjOXoNDpuHXVru9pMSZoCwKacTc5zvphE7hAV0Bg6fDG0CtREeIfOsjHg+vVqqdzoaDjy5QYABl45EHOY+bhtHbuNx3AEgIMHIaheTSIPTQnzOlT5h7r+jCR0iBNJQocQQgjRxXy08yMApvWYRmJwYrvaDIpScwq25213njtYchCAHqE9vO5T00qHLyaRg6oOOMJGR8znyMqCv/wFpk+HCy+EL78Eu73tNmvUXopMHlvDrk92ATDy1vbtcRIzTM19ieAoeupIS2ucRB7Rx7uhVQCBYVLpECdP5xj8KIQQQgif+XjXxwBcNuCydrcZHDUYgO2527Hb7Wg0Go5WHAVocxJ6e3VEpQNU2Kix1vg8dHzxBVx5pRri1PTcddfBwoVq742W7NihjgP99mKtsRLWK4zYkbEtX3wMS5wF/wh/KvMriSSPtLQ4gigBIKR7iOffTIOAMKl0iJNHKh1CCCFEF5JWkMbW3K3otXou6ntRu9v1i+iHVqOloKqAI+VqeI9jl/Ju/t287pdL6PBRpQMaKxy+DB2ffQYXXaQCx5gx8OabcN99oNPB22/D3/7WeltH6LAcbthUcU6/dg+L0mg0RA+LBtQQq7Q0MFMNgH+E9xPvTUFS6RAnj4QOIYQQogv5Ku0rAM7qfhZh5vYPyTEbzPQKU3tIbMvdBjSGjgj/CK/75TK8yseVjqZHb+3ZA7/7nRpGNW+e2nPjhhvg6afhtdfUNU88ARkZzdvW18Pu3aCnnvLNan+TfnPc28k9ZrgaYhVNTkPoqAJo15yQ43Fs4ucgoUOcSBI6hBBCiC5kRcYKAM7ucbbbbZvO66ipr3Fu5OeT0HEKVDrsdrj+eigvhylT4PXXwdDkffkNN8C0aSpcPPVU8/b796tJ5L1MB6mvrMMSZyF2VPuGVjk4Kh3R5JKa6tvQcew+HRI6xIkkoUMIIYToIqw2KysPqp3ppiRPcbv94Eg1r2NH3g5nlUOn0RHiF+J1306FSsf776uJ4AEB6rG+hZmvD6v9Flm4EHJzXZ9zDK0aFqYm4Hc/q7vbK06Fdg8FwEIZubk+rnRYGisddo0GrUHeBooTR/7XJoQQQnQRW45soaSmhGBTMMOih7ndPiE4AYAj5Udchlb5Yv+L6MBo5+NAY6DX93PwVeioq4O//lU9fvBBiG2lQDFxIgwbpq7/7jvX53buVMdE2yEAkiYlud0Px9wNf9QM9o6qdNj1hk6xr4k4fUjoEEIIIbqI5RnLAZiUNMmjHcRD/dSn7EXVRRytVCtXdQvwfhI5uK6AVW+r98k9wXeh46OP4PBhiIqCu+9u+9pZs9Tx229dz+/cqeZz+BVkAt6FDiN16KlrDB8+rnS4jBsT4gSQ0CGEEEJ0MjX1NTz969MM+M8AIp6JYOybY/l+3/fHbbcuax0AExMnevS6oeaG0FFV5NNJ5OC6kV9lXWUbV7rHETZMes83B7Tb4dln1eM77wS/4+SXc89Vxx9+UPM7HA4dgliyoN5KQFQAYb3c31vDaDGi0au3ZyGUoMMG+L7SoTFK6BAnluzTIYQQQnQiOWU5XPThRazPWu88V5BVwDnvn8M/z/4n946/t9W2jlWnhkYP9ei1XSodDXt0+Cp0NOXL0OEIG95UOjZsgM2bwWyGW25pPF9+pJwN/9lAzqYcDGYDw24cRsr0FEaP1hAaCkVFagfy8ePV9Tk5kMBhAJImJnk0fEmj0WAM9qemoJxw1G7kGr3OJ5O+m1Y6TIESOsSJJZUOIYQQopOoqK1g5qKZrM9aT6hfKG+c/wbbbtnGHaPuAODPS//Mj/t/bLFtZV0lewv2Ao0b/bmraaXDObzKB3t0ODiCwZnJZ/r8nn46z0PHokXqOGcOhIerx3u/2cuLvV5k5aMr2fv1XnZ9sov3z3mfr37/FTqdnTMbvgXHDuR2uwodkaifm2MVKk+YG4ZYOUKHOczsk/kXBn8DGq26T0SMhA5xYp3WlY7k5GSCgoLQarWEhoayfPnyk90lIYQQp7GbvryJLUe2EBkQyarrV9EzrCcAL5z7AlX1Vby1+S1u/fpWUu9IbTZnY2feTuzYiQyIdFkpyh2OSofVbiWjOAPwbaVjz+17WJO5hkv7X+qze3o7p8NqhQ8+UI+vukodU79I5cPZH2K32YkZEcOwG4ZRkFbA+hfWs+mNTQQnBtO//yQ+/RT2qpxHUZFaLjeSPAC6DfA8rFki/SlObQwdAd28H1oFDVWUQCM1pTUYA4zHbyCED53WoQNg9erVBAb6bhUNIYQQwhPf7fuO/9vxf+g0Oj67/DNn4AD1ZvHf5/ybT3d/yv6i/Xye+jlz+s1xab89bzsAgyIHedwHf4M/Bq2BOlsdewvVu2lfho6kkCSSQtyfXN0WR4XD09CxYoVa+jY8HM4+Gwr2FvDZtZ9ht9kZfM1gLnjrAnRGFfAi+kTw9a1f8/M/fqb704OBEFJT1X1yckCDjW4NlY7IgZEtv2A7WKJUpWNoQgEc9s18DgejRYUO2aNDnGgyvEoIIYQ4yeqsddzxjRpC9Ycxf2B8wvhm1wQYA7ht1G0A/HP1P5s975jP4enQKlDhxjHEKq1A7ajty+FVHcHx/To2NnTX11+r40UXgV5v54vrv6CmtIbECYlcsLAxcACMvGUk3c/qjq3OBr+uAiBN/ZjIyYEwitBjRW/WO/fb8IQ5QoWM4PrG4VW+4phMLqFDnGidNnSsXLmS888/n9jYWDQaDUuWLGl2zcsvv0xycjJ+fn6MGTOG9evXN79RGzQaDZMnT2bUqFG8//77Puq5EEII4Z5F2xexv2g/UQFR/G3K31q97s7Rd6LVaFmbuZZDJYdcnvNF6IDGIVaFVYVAx0wk96XbR9/OkXuOcNWgqzxq/2PDFJnp02HHBzs49OshDP4G5iyag87QfNnhSQ9NAiDrq834U0F2ttrBXM3naBha1b+bc+6EJxzL5pbnlAM+rnQEqmFVEjrEidZpQ0dFRQVDhgzh5ZdfbvH5Dz/8kPnz5/PII4+wadMmhgwZwowZM8jLy3NeM3ToUAYOHNjsX3Z2NgC//vorGzdu5IsvvuCJJ55g27ZtrfanpqaG0tJSl39CCCGEt2x2G0+vehqA+ePmYzG1vlt3VGAUo+NGA7DswDKX5xyViX4R/bzqj6PS4dDZQwfg8RyWnBy1i7hGA1MmWVl2v/qZTrh/AsEJwS22SZqcRNSQKGy1VoYF7gPUvI6cHOjWEDq8GVoFjaHDwdfDqwD0/qf9CHtxgnXa0HHuuefy2GOPMXv27BafX7BgATfddBPz5s2jf//+vPrqq/j7+7Nw4ULnNVu2bGHHjh3N/sU2bDMaFxcHQExMDDNnzmTTpk2t9ufJJ58kODjY+S8hIcGH360QQojT1ff7vmd3/m6CTcHcMvKW414/rfs0AJamL3Weq7fVc6T8CNC4q7inHJUOB2/v15ktbfgRDh8Ouct3UXKwBP9u/oy7Z1yrbTQaDb1m9QJgoJ8KHWlpkJ3duHKVN5PIoWNDhwyvEidLpw0dbamtrWXjxo1MmzbNeU6r1TJt2jTWONauO46KigrKysoAKC8v56effmLAgAGtXn///fdTUlLi/Hf48GHvvgkhhBACeHfbuwDMHTKXIFPQca+f1qMhdBxYit1uByC3PBer3YpOoyMqwLNP/R2aVjpC/EIIN4d7db/OzLFo5bSpdtY8q94/jL5jNAZz22/Ie52rQkdk2X402EhLU5WOYEoACO3h+XwOODGVDgkd4kQ7JWtr+fn5WK1WoqJc/7BGRUWxZ8+edt0jNzfXWUWxWq3cdNNNjBo1qtXrTSYTJpPnu50KIYQQxyqpLmHJniUAXDvk2na1GRs/Fn+DP3kVeew8upOBkQPJKssCIDowutlSuu5qWunoFdbLJ/tDdFYbN6rj0MgcUjfmoPfTM+q21t8LOMSPjccvxI/q4iriyGbfvnhyciAGNQfDEtP6ELn26MjQ0a2/qsJE9On8w+ZE13JKhg5f6NGjB1u3bj3Z3RBCCHEaW7x7MdX11fSL6MeImBHtamPSmxgWPYxVh1exM68hdJSq0BEXFOd1n1xCR3gvr+93ItjtaqjU559DdTWMHg3z5oGhjQ/zq6th5071WL9HLTfcd3bfZm/4W6LVa0k+M5k9n+0hgcOUlcWTk23HghpBERjj3VL8TftgCDCQOCHRq/s1NeEvE+h3cT/Ce3fdCpbonE7J4VURERHodDpyc3Ndzufm5hId7fkOoEIIIcSJ9EXqFwBcOfBKtyoKKWEpAOwv2g/grHTEWXwQOpoMr+oZ2rONKzuH4mK49FK1+tTLL8Nbb8Hvfw9nnAFZWa23275dbQwYGWHj4Nc7ABh0VfuX3XVUDMIpoLISinOr0WMFfFvpmPL3KVhivbtfUxqthog+EV26giU6p1MydBiNRkaMGMGyZY0rd9hsNpYtW8a4ca1P/hJCCCE6i1prLcvS1X/HZvaa6VbblNCG0FHYEDpKfRg6TqFKR1UVzJoFixerqsbvfw8PPgghIbBhA1xxhQoWLXEMrZqcfJDynHLMYWZSpqe0+7UdlYJwCqioAE25GlplDPZD7+fdQBJjgJHJf5vMmD+MYezdY726lxCdRacdXlVeXs6+ffucX6enp7NlyxbCwsJITExk/vz5zJ07l5EjRzJ69Gief/55KioqmDdv3knstRBCCNE+aw6voby2nG7+3RgWM8ytts7QcWylwxfDq8yuczo6sxtvhNWrVcj44QdwTM383e9gxAj49Vf417/gz39u3taxYGUfrdp5vc+FfVw2AjyepqHjtyIah1ZFeze0ymHKI1N8ch8hOotOW+n47bffGDZsGMOGqT/E8+fPZ9iwYTz88MMAXH755fzrX//i4YcfZujQoWzZsoXvvvuu2eRyIYQQojP6bt93AMzoOQOtxr3/HHfk8CqTrnHRlM5c6ViyBBYtAp1OPW66FkyvXvDcc+rxs89CTU3z9o7QEZB7AICUGe2vckBj6AiijKLcWgIbQkdQnO+GQgnRlXTaSseUKVOcSwG25o477uCOO+44QT0SQgghfMcxtGp6j+lut3VUOrJKs6iur3YOr4oPive6X5EBjRvbhZnDvL5fR6ishNtvV4//9CeYPLn5NXPnwsMPq/0zPvtMDbVysNvV3hoBlFNzUM0P7X5Wd7f6YA4zYwg2U1dSBYWFWBpWrgry4fwLIbqSTlvpEEIIIbqqmvoathzZAsAZiWe43T7CPwKL0YIdO+lF6T4dXjUidgT/mfkffrz2R6/v1VFee02FieRkFSxaotfDTTepx6+84vpcURGUlUEPVJUjelg0Ad0C3O6HJVlVO0JtBc5Kh7crVwnRVUnoEEIIIbyQVpDG77/8PcNeG8a0d6fxyoZXsNltbbbZkbeDOlsdYeYwuoe49wk7qF2xHUOsthzZQnmt+pTdF8OrAG4ddatzE8LOpqoKnnlGPX7gATC3sYXFjTeq48qVUFjYeP7gQXXs75cOQI9pPTzqS2hPtddFOAXOSoeEDiFaJqFDCCGE8NCbm95k8CuDeX3T62w5soVl6cu47ZvbmPPhHKrqqlpt91v2bwCMjB3p8dKljiFWG3PUMkwGrYEAo/uf1p9qPvgAjhyBxEQ1Ybwt8fHQu7d6vGZN4/mMDHWM0+YAkHBGgkd9Ceulhp+FUUigjzYGFKKrktAhhBBCeOCdLe9w05c3UWOtYXrKdBZftpgnpz6JSWfi89TPeWj5Q622dYaOmJEev350oNqXKqdcvXE26U1tXd5lvPWWOt52GxiN6rHdbidjRQbfz/+er279ii1vb8FWr6pNZzSMXlu1qvEeGRmgpx5L1VEAYobHeNQXS6Qqsxip9dnGgEJ0VZ12IrkQQgjRWW09spWbvlQTBv4w5g88N+M5Z8ViYORAzv+/83lu7XNcNuAyRseNbtb+t5zGSoenjDr1jtsxtMrxdVeWmqrCg07XWOWoKa3hq99/xY4Pdjiv2/jqRja+vpHLFl/GGWdY+O9/XUPHwYMQSS4auw3/CH+C4oM86k9AsNry3EgtAVQAvlsyV4iuRiodQgghhBtqrbXMXTKXOlsdF/S5wCVwAJzX+zyuHnQ1NruNx1Y+1mL7HXnqDfKI2BEe9+N0DB3vvquO554LMTFQX13PovMWseODHWh0GobOG8r4+8ZjCjKRuSaTxVcuZvw4VfFYvx5qa1X7jAyIQVWIYobHeDzEzS9IhQ4DdZhQ6/Kagk6PipMQ7pLQIYQQQrhh4eaFbM3dSrg5nNfPe73FN6wPTnoQgG/2fsOR8iMuzx0sPki9rR5/gz8JQZ7NJYDG/TQcoaPp/hpd1ZdfqqNj+duvfv8Vh345hCnIxLyV87hw4YWc/fTZ3LjuRgwBBg7+fJCib9YSHg7V1bBtm2rXNHRED4/2uD8GfxU6zFShOeacEMKVhA4hhBCinarrq53Vi79N+RtRgS1vSNs3oi9j48ditVv537b/uTx3oEgt09o9pLvHn7BDY2WjrKbM5euu6uBB2L4dtFpV6Uj9MpWt725Fo9Vw+WeXkzC+McBF9I1gxoIZAKz+52r69LQ67wGO0KHCoKfzOaAxYPhT6TxnDOjavwchPCWhQwghhGinhZsXklWWRUJQAjcNv6nNa+cNnQfAou2LXM6nFzcs0xrq2TKtDqfb8Kqvv1bHM84Ai7mOb277BoBx94xrcWO/ofOGEhgTSEVeBf00ewDIzISSEigpsRNOAQCRAyObtW2vY0OHXatDq5e3VkK0RP6fIYQQQrSD3W7n1d9eBeDe8fced7Wo83qfB8DW3K3OYACulQ5vOCsdtadHpcMROs47Dza9sYnSzFKCE4OZ8rcpLV6vM+gYfuNwAGIy1cT9zEzIywM/qvFrmIMRkhTicZ8coUOLHQC7QYZWCdEaCR1CCCFEO6zLWsf2vO346f343ZDjbBABxFpiiQ+Kx2a3sTF7o/O8VDrcZ7PBr7+qx1Mn17PqabUU1cQHJrY5h8IROvRZGfhRTWYmVFRACMUABEQGeDUH49i2GqOEDiFaI6FDCCGEaIc3Nr4BwOUDLifEL6RdbcbGjwVgbeZa5zlnpSPUu0qHo9JSb6sHunbo2L0bSkshIAA0O3dQll1GUHwQQ+YOabNdcGKw2sDPDvEcJjMTysshhBIAQpJDvOpXs9Bh6rq/AyG8JaFDCCGEOI56Wz2fp34OwNwhc9vdbmycCh3rstY5zzlCh68qHa193ZWsbchso0bB1rc3AzDytpHoTcffbizxjER15FCzSkdwUrBX/To2dOhMUukQojVuhY66ujqmTp3K3r17O6o/QgghRKez+vBqCqoKCDOHMTFpYrvbjYkfA8CazDXY7XaKqooori4GIDkk2as+naqho6gI/vMfuPtueOklNcfieNasUcfxvQs49MshNFoNQ37XdpXDIeEMtapVIofJylIVE0fo8LbSoTe7hh6dWUKHEK1xa0dyg8HANsci10IIIcRp4ovULwCY1WsWem37/9M5ImYEGjQcKT/C0cqjZJZmAhAZEEmg0budq48NGceb2N4ZfPIJ3HILFBQ0nnvwQbX/xsQ2spyj0pFQvJVcIGVGCkFx7dtF3BE64sjCVmclPV1HsI+GV+kMOuxaLRqb2oBQbz41gp8QJ4Pbw6uuueYa3nrrrY7oixBCCNEpOULHBX0ucKud2WB27uWRVZpFTpnakC4+KN7rPh27GWBnr3S89x5cdpkKHP37wx//CAMHqiVsp0+HrVtbbldeDrt2qcf1O9IAGHjlwHa/bkTfCMxhZgzUE0kuqam+G14FYNc3VjdkY0AhWudWpQOgvr6ehQsXsnTpUkaMGEFAQIDL8wsWLPBZ54QQQoiTLbssm72Fe9FqtExPme52+1hLLEfKj5BVluXcyC/Y5P2b3VNpeNWGDXD99WC3w803w8svg14PVVVwwQWwdCncdResWAHH7peYlqbadQ8roWBXLhqthl7n9mr3a2s0GsL7hJO5JpMQitmzJ5aJPhpeBYDBALVq+V1joIQOIVrjdujYsWMHw4erJejS0tJcnvNmZ1UhhBCiM1p1SC3POjhqMEGm9g3paSrOEsemnE1kl2U7z3lyn2M1Cx3azhk6Kirg6quhvh4uvhheeUXtKg5gNsNbb0HfvrByJXz6qbqmKcdbjdEhaVAI8ePi8Y/wd6sPQfHq5x1EKQd2VTOdasC7PTocNEYDVKjHJgkdQrTK7dCxfPnyjuiHEEII0SmtPrwagDMSzvCofawlFlDDqywmC4Dz6I1TpdLx3HOwdy/Ex8MbbzQGDofERJg/Hx5/HF57rfXQkVSrFrHpfV5vt/vQNHTUFjfsHm4wYgz0/memNRkatgaU0CFEW7xaMjczM5PMzExf9UUIIYToMDX1Nbyy4RXOfu9sxr45lr8s/YtL9aE1qw6rSsf4hPEevW6cJQ6ArLIsSmtKAQgyel/pOHbieGcMHfn58Mwz6vEzz0BoaMvXXXedOv70Exw96vpcWhposOOffwiAlOkpbvejMXSUYaQWAI2fb35e2ibL5PoFdb7fgRCdhduhw2az8Y9//IPg4GCSkpJISkoiJCSERx99FFvD6g1CCCFEZ5JZmsnIN0Zy2ze3sfTAUtZlrePpVU8z7LVh7Mnf02q7yrpKNh9R+0J4W+nILst2zunokOFVnTB0PPcclJXBsGFw+eWtX9ezJwwfDlYrfPaZ63NpaRBBPlTXYPA3EDU4yu1+NK10OEOHjzby0/k1hg7/EKl0CNEat0PHAw88wEsvvcRTTz3F5s2b2bx5M0888QQvvvgiDz30UEf0UQghhPBYbnkuExZOYEfeDiIDInl2+rO8e9G7DOg2gLyKPKa+O5XCqsIW2245soV6Wz0xgTEkBid69PpxQc0rHafD8KqaGjWcCuCBB5oPqzrWZZep4yefNJ6z2yE1FeJRoypiR8Wi1bs/SKNp6DA0hA6dj5a31TfZm8M/SEKHEK1xe07HO++8w5tvvskFFzQuGzh48GDi4uK47bbbePzxx33aQSGEEMJTVpuVqz+9moMlB+kZ1pOl1y4lKSQJgHN7ncsZC88grSCNJ395kn9O/2ez9o4qyMDIgR4vluJS6QjvuEpHZ9un4+OP1VCp+Hi48MLG8zWlNez8aCcFaQWEpoTS/5L++If7c8458Je/wPr1KmxoNGrjwNJSSOAwAPFjPVtquGnoMDWEDr2PNvJrukxuQGjnCn5CdCZuf1xQWFhI3759m53v27cvhYUtf1IkhBBCnAwvb3iZZenL8Df48/kVnzsDB0CEfwTPz3gegBfXv8ihkkPN2jtCR9+I5v/day/HnI78ynyOVqoJC6fD8Ko331THm29Wy+MC7Fmyhxd7vciXN33J6n+u5utbvubFXi9yeM1h+vVTq8+WlMChhl+FYxJ5d0MWoFau8kRgTCBoQIfNuUeHIcA3Py9jQNM5HVLpEKI1boeOIUOG8NJLLzU7/9JLLzFkyBCfdEoIIYTwVmFVIX9b8TcA/nX2v+jfrX+za87peQ6TkyZTY61h4eaFzZ73RegIM4c5N/JLzU8FwGL0fnhVZ94cMDdXLYEL8LvfqeOOD3bw0cUfUZFXQVivMEbdPoqIvhFUF1Xz3rT3KErNpX/Dr2jLFnXMzgYjtYTU5QEQP8az0KEz6PCLUDvAR5APgNFHocMUIJsDCtEeboeOZ555hoULF9K/f39uuOEGbrjhBvr378/bb7/NP//ZvDQthBBCnAxP/foURdVFDIwcyE0jbmrxGo1Gw7yh8wD4bM9nzZ5PLVAhoU94H4/7odFonEOscsrVjuRdvdKxZIkaIjVqFCQlQc6mHD773WfYbXaGzhvKbTtuY+ZLM7npt5tIPjOZuso6vvvDdwwZrBafdexOXlAAYRSgAfwj/AmMDvS4T4Gx6mfuDB0W3/y8LOGNQcNXQUaIrsjt0DF58mTS0tKYPXs2xcXFFBcXM2fOHFJTU5k4cWJH9FEIIYRwS1lNGa9tfA2AJ6c+iV7b+hTG8/ucj06jY1vuNg4UHXCer7XWsr9wP+BdpQMa53U4dPXQ4ZgMfvHFUFdVx+KrFmOrs9H3or5c8OYF6Iw6QL1Jv3Dhhej99GQsz6C/TlWWHKEjPx/CKQAgvHe4V30KSXQNHWYfDYXqFtuk0hEglQ4hWuNW6Kirq2Pq1KlUVFTw+OOPs3jxYhYvXsxjjz1GbGzs8W8ghBBCnABvb3mb0ppSeof3ZmavmW1eG2YOY3LyZAA+291Y7dhfuB+r3UqgMbBZaHCXYwUrB1+sXnVskOosoaO8HFasUI/nzIG1z6+lILUAS6yF8988H43WdUJ+SHIIY+4eA4B550agcXhVQYEPQ0ecqpL4UwX4bk+NpkOqZHiVEK1zK3QYDAa2bdvWUX0RQgghvGa323l5w8sA3DX6LrSa4/+n7vze5wPwU8ZPznNN53N4unKVQ2yg7ysdGo3GZV5HZwkdq1dDfb0aVhUXVsmqp9XmitOenoZ/uH+LbYZdPwyA4k0HMFPJgQNQWekIHWqRmvA+3oUOvzA/l699tdJU06Ahw6uEaJ3bw6uuueYa3nrrrY7oixBCCOG1rblbSS1IxaQzce2Qa9vVZnjMcAB25O1wnttfpIZW9Qrr5XWfjq10+CJ0gGvQOHZi+cny88/qOHkyrPv3OmpKaogaEsWgqwa12ia8VzjRQ6OxW+0MbBhilZ/v20qHOdTs8nWAjzbyc6l0yPAqIVrl9j4d9fX1LFy4kKVLlzJixAgCAgJcnl+wYIHPOieEEEK466OdHwEws9fMdr+5HxSp3hAfKjlEaU0pQaYg8irUiknRgdFe96np8CwNGgIMAW1c3X5NQ0dnqXQ4Qsek8fVsfFgNl5r4wMRmw6qO1f+y/hzZcoTB+l1ssA6noAAK8u0MbZiD4W3o8Avt+EqHDK8SonVuh44dO3YwfLj6RCjNsYB2A2/Lz0IIIYQ37Ha7M3RcPuDydrcLNYcSZ4kjqyyLHXk7GJ8w3rmnRjf/bl73y7FXB6j5HL7672VnCx2VlWpzP4Ckyt1k5lVgibXQ96LjT8TveU5PfvrrT0TVZQF2Cgs1lOdV4kcNaCA0JdSrvpnDXCsdxkAZXiXEieRW6LBarfz9739n0KBBhIZ6939+IYQQwtd2Hd3F/qL9+On9mNV7llttB0YOdA0dFQ2hI8D70NG00uGroVXgugu5r0OH3a7mZyxdqjb3u+giGDCg7TYbN0JdHcTGQtaXmwAYfvNwdAbdcV+vW/9uaPVajPXVBFNKQUEw9nw1tMo/JhiDlzuIHzu8ytehQ2fUodW7PWpdiNOGW//v0Ol0TJ8+neLi4g7qjhBCCOG5n9LVRPAJiRMINLq3p4NjiNX23O0APq10dFTo6KhKR0EBTJ8OEybA3/4GDz4IgwbBvfeqMNKa7epHx6j+FRz8+SAAQ37Xvo2D9SY93fqrn3U0R8jNBV1lKQDBicEefy8Oxw6v8tX8C0fokKFVQrTN7Ug+cOBADhw4cPwLhRBCiBNsecZyAM5KPsvttgMjBwKw46iaTO7LSkeAMYBgk3rj7IvdyB06InTk5cG4carC4ecHV14Js2apsPHss/DMM623dYSOgfo92G12YkbEENq9/SMjooZEqSNH2Lu3cXnboOiWV71yR0dVOgIi1fycgCjfzNMRoqtyO3Q89thj3HvvvXz11Vfk5ORQWlrq8k8IIYQ4GWx2GysyVgBwZvcz3W4/IFKNHUrNV7uQOyodEf4RPumfYwWrzlzpqKuDyy6DvXshMRF++w0WLYKvvoKXXlLX3H9/Y7g41o6Gxb+CsnYD0O/ifm69viN0RJNLWhqYqQTAP8LcVrN2ObbS4avQEd47nNnvzWb2u7N9cj8huiq3J5LPnKk2WbrgggtcJsLZ7XY0Gg1Wq9V3vRNCCCHaaeuRrRRVFxFoDGREzAi32zuGURVVF1FdX015bbnLeW/FWmLZdXRXpw4d//qXWn0qMBC++w76NckMt98Oy5fD4sXw1FPw/vuube12FUYM1FK9Ox2AfnPcCx3RQ9VKYdEcYUMa9GmodLS2v4c7jIFG0GrApsaH+XLS9+BrBvvsXkJ0VW6HjuXLl3dEP4QQQginz3Z/xuubXic1P5X4oHjuHns3s/vObnPVp9WHVwNwRsIZGHTuj68P8QsBoLq+mszSTEDt+u047y3HCla+2I3coeneHE0nlXvi8GF47DH1+OWXXQOHw4MPqtDxwQfwj39ASkrjc5mZUFICPbWZ2OttBCUEub3MbfQQFTrCKCIzvY5hzkqH96FDo9FgDjNTla/u6atKhxCifdwOHZMnT+6IfgghhBDUWmu59atbWbhlofNcenE6vxz6hTtG3cGLM19ste223G1A40Z/7rKYLGg1Wmx2G3sL9gJqaJWvlrdNCVXv0GMCY3xyP/BtpeOhh9SStxMmwLWt7Kk4dCjMmAHff6+GXT30UONzjqFVw8MyIB+SJye7/bMzh5vR6HXY6634U4m5odJhDvd+eBWAf5PQIRv5CXFiebS22y+//MI111zD+PHjycrKAuC9997j119/9WnnhBBCnD7sdjs3f3kzC7csRKvR8qfxf+Ln637m/gn3o0HDSxte4q1Nb7XaflueCh1Dotq3WtKxtBqtc7L33kIVOnw1tArgzjF38vLMl5k/br7P7umr0HH4cONwqWefhbaywuyGqQs//OB6fudOdUxCrVqVNDnJ7X5oNBoMQSpgmKnE31Hp8MHwKmgyr0OD10vwCiHc43boWLx4MTNmzMBsNrNp0yZqamoAKCkp4YknnvB5B4UQQpweXlz/Iu9sfQedRsfnV3zOM2c/w6SkSTwx9QkePfNRAO767i4KqwqbtbXZbc6lbgdHeT6+3jGUylHp8MXKVU3vfduo23w2MR18Fzr+/W+or4cpU2D06LavnTFDHdesUcOpHDIzQU8d/kXqw0hPQgeAX6gjdFT5vNLhWMHK4G847g7pQgjf8mj1qldffZU33ngDg6HxU4IzzjiDTZs2+bRzQgghTg+HSg5x/7L7AVgwYwHn9T7P5fn7J97P0OihVNZV8upvrzZrn16UTkVdBSadiV7hvTzuR6hZLe+aVpgG+LbS0RF8sTlgdTW8+aZ6fO+9rs9lrc/ilyd/YdU/V5Gfmg9AcjL07g1Wq5pY7pCdDbHkoLFaCYwOJKxnmEf9caxU5U9VY6XDB3M6oLHSIfM5hDjx3A4dqampTJo0qdn54OBg2TRQCCGER+Z/P5/KukomJE7gjtF3NHteq9Fyz7h7AFURqamvcXl+a+5WQC17q9e6PV3RqVmlo5OHDl9UOr75RlUs4uPh3HPVuaqiKt6f+T5vjnmTn/76E0vvW8p/BvyHpfcvxW63M326um7p0sb7ZGdDJLkAxAyP8XgujCVSBYwAyvFD/Z59PbxKQocQJ57boSM6Opp9+/Y1O//rr7/So0cPn3RKCCHE6WNH3g4W716MBg2vzHoFrabl/zRdPuByYi2xHCk/wo8HfnR5zjGJ3NP5HA6O0JFerJZ89eXwqo5g1Ko3zxo06DQ6j+7hmMtx5ZWg1UJlfiULxy9k37f70Bl19Lu4HynTU7Bb7ax6ahVrFqxxDsHatavxPtnZEEUeAJGDIj3+ngK6qWAQRsMwOk3zPTY85Rhe5cvlcoUQ7eN26Ljpppv4wx/+wLp169BoNGRnZ/P+++9z7733cuutt3ZEH4UQQnRhT/36FAAX97/YuSt4Sww6A7N6zQJg2YFlLs+lFqgN/fp36+9VX0L9XHfPPlUqHUad0aPKQkmJ2vgP4OqrwVZv45MrPiF/Tz5B8UHcuP5GLvvkMq75/hpmPKcmc/z4px+J0auNE/eqghB2u6PS0RA6BnoeOhxVjfCG0OEX4odW59G6N82YwxpCh1Q6hDjh3K5B/+Uvf8FmszF16lQqKyuZNGkSJpOJe++9lzvvvLMj+iiEEKKLyinL4YMdHwBw/4T7j3v91O5TeWPTGyxLdw0djn01EoMTverPsXtyOHYR76wcczo83aNj2TKorVVzNAYPhtX/XEP6snQMAQau/vZql/Aw5g9jyFiRQernqeQv+RWYTWYmVFWpfzU19sbQ4UWlwxEMwikAfDefAyAgMgDwXeVECNF+bn90oNFoeOCBBygsLGTHjh2sXbuWo0eP8uijj3ZE/4QQQnRh729/H6vdyviE8e3aX+Os7mcBsD1vO3kVec7zWaVqxSTHBnyeOjZ0JAV7tgLTidK00uEJx7K3M2ZAWXYpP//jZwDOffHcZtUKjUbDpIfUnM60xdtJtBQBsH+/qnIEUYaZajQ6DRF9PV+hy7FSVRjq/r6azwHQ58I+jP3jWOf3IYQ4cTyuVxqNRvr378/o0aMJDAz0ZZ+EEEKcBux2O+9sfQeAuUPmtqtNt4BuziVxf0r/yXmfrDIVOuKD4r3q07HDq5JCum7osNvVJn8A06fD8oeWU1dRR/y4eIbOHdpim9gRsfSY1gO71c4ZQWqJ4r17XYdWhfcOR2/yfDK/o9Lh/NpHy+UCmCwmZiyYQfwY7/53IoRwn28GSQohhBBu2pq7lR15OzDpTFza/9J2t5uYOBGATTlqmfb8ynxqrbUAxFi82+27aaUjyBTUrPLR2XgTOvbvh4wMMBhgRO9Stv1PTcafsWBGm3tY9J3TF4CE2v0A7NsHOTnQzQfzOaB5ZcOXlQ4hxMnj+UcRQgghhBe+TP0SgHN6nuPcH6M9eob1BBpXmHJUOSIDIr3aIA9cQ0dnH1oF3oWOn1ShiHHjYMdb67DV2UialET82LarAD1nqJ+/uSATEzXs3Wuivh6CKAUgpHuI231p6tjKhjnCd5UOIcTJI5UOIYQQJ8V3+78DYGavmW61SwlNAWB/ofqk3TGJ3NuhVYBL+OnsQ6sATDo1gdyT0PHbb+o4fnQ9m95QVaNx9447brvQHqGE9QxDY7ORTLpzeJWFcgAssRa3+9LUscOrYoZ5V70SQnQOEjqEEEKccEVVRazNXAvAjJQZbrXtEar2hNpftF/N5/DRJHI4dSsdWI28/DI8+CB8/LFakep4NqmcQS/NPqqLqrHEWug1s327uafMUMGvBwfIyHCEjjLA96EjcaJ3K5IJIToHj0LHe++9xxlnnEFsbCwHDx4E4Pnnn+fzzz/3aeeEEEJ0TUsPLMVmt9Evop/bFYXuod0BKK0ppbCq0KeVjqahw9vld08EQ0Po2LnVyB13wOOPw2WXwRlnqPkaramthe1qHjiaHerBwCsHtns/jLjRKuB1I5/KSrXfh69Ch8FscPk6JCnEq/sJIToHt0PHK6+8wvz585k5cybFxcVYrVYAQkJCeP75533dPyGEEF3Q8ozlAExPme52W3+DPzGBasjNgaIDzjkdvqh0NF29Ktwc7vX9Otrni1XosNebGDMGbroJQkPV0KmZM9X+GS3ZsUMFj6iQGrJ+UhsrDrp6ULtfN6xXGKD20qiqgqpKu89CR1PhvTv/70AI0T5uh44XX3yRN954gwceeACdTuc8P3LkSLY7PjYRQghxWimrKaOspqzd12/I3gDA+ITxHr2eY4jVgaIDPq10+OkbN41zZ3L7yfDWW/DVW4PBqmdS72GsWQOvvw5btkB0NOzerYZbtWTjRnWcnHAAa42VsJ5hRA+Nbvdrh/dSYSCYUuqr6rBWVGOgHgBLjO9CR8KEBJ/dSwhxcrkdOtLT0xk2bFiz8yaTiYqKCp90SgghxKnhx/0/Mvy14QQ9FUTI0yFMeXsKu4/ubrNNTX0NW49sBWBk7EiPXjclrGEyedH+xkqHD3YP12g0XNzvYnqH9+acnud4fb+OcvAg3H03kDuE+/VHWfGXBWgaVrlNTIQ331SPX3gBjhxp3t45n0OnJuOnnJOCRtP6MrnHMoebMQapSeyB9UXYSlTg1AeZ0ft5vzDmuS+eS9zoOKY9Nc3rewkhOge3Q0f37t3ZsmVLs/Pfffcd/fr180WfhBBCnAKe+OUJpv9vOpuPbAbAZrfx88GfGfvWWFYdWtVqu+1526mz1RFmDqN7SHePXrtHSGOlo7xWrZoUbAr26F7H+vjSj9lz+x78DZ13f4g774TycjV347EHQ5oFhlmz1FK49fXw9tvN2+/bp47m7AMApExPcev1NRoNoT1VtSOcQqwNocMvwjdVjtF3jObGdTcS0C3AJ/cTQpx8boeO+fPnc/vtt/Phhx9it9tZv349jz/+OPfffz/33XdfR/RRCCFEJ/Piuhd54KcHALht5G3k3JPD/rv2MzFxIqU1pVz72bVU1LZc/d6QpYZWjYwd6dan6005Jp8fLj1MnbUOAIPO0FaTdtNoNB7360RYvx6+/BJ0OlXR0LbyX/KbblLHN94Am831ufR0CKWQ+rwitHotyVOS3e5HeMO8jjAKoEyFDv8o3w2tEkJ0LW6HjhtvvJGnn36aBx98kMrKSq666ipeeeUV/v3vf3PFFVd0RB+FEEJ0IluPbOWeH+4B4NEzH+XlWS8THRhNj9AefH3V1yQEJZBenM7ff/57i+1/y1YbRIyKHeVxH8x6taxqrbWWOltD6ND6JnR0dn9v+LFeey307dv6dZddBkFBcOCACioOViscOgTdUZsrxo+Nx2Qxud2PiN6O0FGIv1WFjoBoCR1CiJZ5tGTu1Vdfzd69eykvL+fIkSNkZmZyww03+LpvQgghOhmrzcrcJXOps9VxUd+LeGDiAy7PW0wWXpr5EgCv/PZKi9UOx3CsETEjPO6Ho6pRa631eaWjM9u9G775RlU5Hnig7WsDAmDKFPV49erG89nZUFcH8ZpsABLO8GyyduMKVoVNVq4K9OheQoiuz+3Q8dhjj5Gerj4d8ff3JzIy0uedEkII0Tkt2r6IrblbCfUL5bXzXmtxGNL5vc+nR2gPymvL+XT3py7P2e129hepyct9Ivp43A9HVaPOWndaVTreeksdzzsPevZsPF+WU8bGNzay4u8r2LNkD9Y6tZz9+IbFwZqGDsf+HYlGNcM8ZrhnO36H9lCre4VQ7NyNPDheKh1CiJa5HTo+/vhjevbsyfjx4/nPf/5Dfn5+R/RLCCFEJ1NnreNvP/8NgD+f8WciA1r+0Emj0XDdkOsA+O+W/7o8V1RdRGlNKQDJIcke98VR1aiz1Z02lY7aWnj3XfXYMbjAbrez/uX1vNDjBb66+St+/tvPfDj7Q96e/DYlh0sYN05dt2oV2O3qcXo66LASVpsLQMwIz0KHqWH1KgN1+FENQGA3c1tNhBCnMbdDx9atW9m2bRtTpkzhX//6F7GxscyaNYtFixZRWVnZEX0UQgjRCSzevZgDRQeICojijtF3tHnt3KFzAbUJYH5l44dTB4rUaknRgdFerQ5lbNiJ+3SqdHz3HRw9CjExcO656tyKR1bw7R3fUl9dT8zwGIbMHYIp2ETmmkwWzVzE0EH16PVq2dyDB1WbjAzoRh5auxW/ED9nxcJdjqVxDdShb9ijwz/I++VyhRBdk0dzOgYMGMATTzzBgQMHWL58OcnJydx9991ER7d/YyEhhBCnltc2vgbALSNvIcDY9lKmicGJ9AlXw6fWZa5znneEDsfmfp5yBIzq+urGc1280vH55+p46aWg18OWd7aw8tGVAEx7eho3bbiJi96+iN9v/j0BkQHk7chj3VPLcWyt5RhilZ4OseQAamiVpyt1Gczq562n3hk6TIESOoQQLfModDQVEBCA2WzGaDRSV1fniz4JIYToZFLzU1mRsQKtRssNw9q3cMiY+DEArM9qXDopvUjNCfQ6dDQEjMq6xgp7V6502Gzw9dfq8fnnQ2lmKd/e+S0Akx6exBn3nYFGq8JDaPdQznv9PADWLljLiD5qvsWePap9RgbEOEKHh0OroLHSocOGkVqgMYgIIcSxPAod6enpPP744wwYMICRI0eyefNm/v73v3OkpW1PhRBCnPLe3aomE8zsNZOE4PatdjQmToWOdVktVDpCfFPpcAkdXbjSsWED5OaCxQKTJsG3d35LbVkt8WPjmfzw5GbX972wL3Fj4rDV24jJVbu/Z6vFqjh4UC1zC9CtfzeP+9R053HHnA5f7EYuhOia3P7rMHbsWDZs2MDgwYOZN28eV155JXFxcR3RNyGEEJ3EktQlAFw58Mp2t3GEjvVZ67Hb7Wg0Gg4U+2h41WlW6XBUOWbMgKNbs9izZA8arYbz3zwfra7lzw+H3zScrHVZ6LZuAsaTlaUqIcXFasUpgJDuIR73qWnAMFOlzpkldAghWuZ2pWPq1Kls376dzZs3c++990rgEEKILm5f4T52Hd2FXqtnZq+Z7W43OGowJp2Jouoi9hbuBXw/p8MxiVyDBp1W59U9O7NfflHHs8+Glf9Q8zgGXT2IyAGtL1s/8PKBGC1G6vMKiSObrCy1glV5qc0ZOkK7ezaJHECr12LXqLcROtSW51LpEEK0xu3Q8fjjj9O/f/+O6IsQQohO6PM9agbz5KTJhPiFtLudQWdgSPQQALbnbqfeVs/BYrWEkq8qHa193ZXU1zfuKD4oJp+0r9LQaDVMenBSm+2MgUaSpyQDkMAhsrLUsrtmazk6bGj1Wixx3u2rYdO5hgyZ0yGEaE27PpKYP38+jz76KAEBAcyfP7/NaxcsWOCTjgkhhOgcvtn3DQAX9rnQ7bYJQQmsz1pPTnkOJdUlWO1q07qowCiv+nTsUKquPLRq+3aorISgIChbqXZz7zWzF+G9w4/bNmF8AmlfppFAJmsL1ZK7IRQBEJQY3OrQrHbT66G+tvFLqXQIIVrRrr8Omzdvdq5MtXnz5g7tkBBCiM6jzlrH2sy1AJzV/Sy328cEqtWRssuynZsC+hv80Wu9e3N6qlY6amrggw9g2zYIC4Mrr4Qexyn6rFmjjmNHWdn2rpoUPuyGYe16vfhx8QAkchiwk5qqaRxalRziwXdwDL3r71HmdAghWtOuvw7Lly9v8bEQQoiubWvuVirrKgnxC6Fft35ut4+xqNCRU57jDB1BpiCv++XYHNDhVKh0rFsHV10FBw40nnvkEXjjDZg3r/V2jtAxLnI/FXkVBEQF0GtWr3a9ZtyoODQ6DRZrGcGUkpoaTKgPJpE7GVx/7lLpEEK0xu266vXXX09ZWVmz8xUVFVx//fU+6ZQQQgjfq6yr5JNdn/Dqb6+y6tAq7Hb7cdusOrQKgPEJ49Fq3B+K46h05JT5NnQ0G17VySsdv/4K06apwBETA3ffDWeeCVYrXH89fPRR621/+00dIwvVRhv9L+2PztC+SfMGfwMxw9TvIIHDpKY2WbnKB5UOjaExZNg1mnb3Swhx+nH7vyDvvPMOVVVVzc5XVVXx7rvv+qRTQgghfOuDHR+Q/Hwyl358Kbd+fSsT/juByW9PJr8yv812qw6r0HFGwhkevW5HVTqaDa/qxJWOnByYPRvKy2HqVEhNheeeg2XL4Pbb1TV33w0VFc3b1tfDvn2gwU75JrUCWJ/z+7j1+tHDogGI4Ch79vhmuVwHrbFJ6NBJlUMI0bp2h47S0lJKSkqw2+2UlZVRWlrq/FdUVMQ333xDZGTrS/cJIYQ4OZ5b8xxXLr6So5VHSQpOYmavmZh0Jn459Avn/O8cymqaV68dVh9eDahKhydO90qH3Q7XXQf5+TBkCHz5pdrgD0CjgWefhe7dVTD55z+bt09PV8Ej2ZRN1dFyjIFGkiYnudWHoHj18w6ijNRUCKYEgJCkEC++M8U1dHTO34EQonNod+gICQkhLCwMjUZD7969CQ0Ndf6LiIjg+uuv53bHRzZCCCE6ha/Tvmb+D2rVwflj57Pvrn18fdXXbP79ZiL8I9iYs5FHVz7aYtvCqkKyyrIAGBEzwqPXj7XEAnC08igFVQWAb0LHsRPRO2ul44sv4IcfwM8P/u//wGx2fd5kgiefVI9feUUNt2oqNVUdRwerKkfK9BT0JvcqCo5lcS2UcfBg40Z+/hH+7n0zLdCZmvzc9VLpEEK0rt1/IZYvX47dbuess85i8eLFhIWFOZ8zGo0kJSURGxvbIZ0UQgjhvtzyXK797FoAbht5G8/OeNb5XL9u/Xj7wrc57//O48X1L/KHMX8gLsh1s9fUfPWONz4oHovJs/0cwv3D0Wv11Nvq2Vug3jj7InRoNBrnfaFzVjrq6+Evf1GP//hH6NfKPPw5cyA0FPLy1NyPyZMbn3OEjgQOAdBjuvv7mwTFqZ+3hTLAjhG1xK3RYmyjVfvo/PTUOb4wSOgQQrSu3X8hJjf8FUxPTychIQGt1su1vYUQQnSoB396kKLqIoZFD2PBjOZ7KM3sNZOJiRP55dAvPLPqGf597r9dnt+TryYu943o63EftBot0YHRZJZmklqg3kEHGb0PHaCqG87Q0QkrHYsXw549EB4Of/5z69cZDHDhhfD22/DJJ66hIy0NtNgIKFYVp4RxCW73w1HpCKIUHVbn7uHGQO9DR9Oqi0ZChxCiDW4nh6SkJLRaLZWVlezZs4dt27a5/BNCCHHybcvdxlub3wLgpZkvYdKbml2j0Wj4ywT1Ufwnuz/BZre5PO8MHeGehw5onNfhDB0+qHSAa3WjM1Y6XnpJHe+4A4KD2772kkvUcfFisDX5NaSmQiR5aGprMVqMdBvQze1+OCod/lThT6XzvC9Ch8G/MWg0nd8hhBDHcvsvxNGjR5k3bx7ffvtti89bjx2QKoQQ4oR7ZtUz2LFzaf9L25wEPrX7VCxGC9ll2WzI2sCY+DHO53bn7wbwaH+OphwrWGUUZwA+DB1NqhudrdKxZYsaKqXXw803N5631lnZ9fEucrfnYg4zM/DygQQnBjNtGhiNakJ5RkbjhoGpqRDPYQDix8R7tIO4X6gfOj891up6IlDzaux6vfe7keO6L4fW2Ll+B0KIzsXtvzh33303xcXFrFu3DrPZzHfffcc777xDr169+OKLLzqij0IIIdyQVZrFhzs/BHBWMlpj0puY2WsmAEv2LHF5zhfDq6Cx0uHgq9DRdINAb3c497WFC9VxzhxwTHfM3pjNKwNf4dOrP2XVU6tYet9SXkh5gW3/24bJBP37q+scgwbKy+HIEUggE2jcXdxdGo2GoIYhVuGoJZI1fs0rX54wNql06Nyc4C6EOL24HTp++uknFixYwMiRI9FqtSQlJXHNNdfwzDPP8KRjCQ4hhBAnzSu/vUK9rZ5JSZMYHjP8uNdf1PciAL5M+9J5rqa+hgNFautsb0NHnMV1gnpXH15ls6lhUgDXqnn8HF5zmHfPepeCtAICIgMYedtIEs5IwFZv47PffcbuT3czeLC61hE68vLUMU6TDUD8WM9CB4AlVoWOiIbQofXzfmgVHBM6ZDdyIUQb3A4dFRUVzv04QkNDOXr0KACDBg1i06ZNvu2dEEIIt9jtdt7f/j4At49q3zLmU5KnAGo4VVWdWk51f9F+rHYrFqOlWaXCXYnBiS5fd/XhVWvXQna22o/j7LOhPLecDy/6kJrSGpImJ3FH2h3MenkW81bOY8TvR4Advr3rWwb3U+tAOUJHfr6aRB5qLwTwaD6Hg2Neh2N4lc7so9AR0Bg09BI6hBBtcDt09OnTh9SGNfyGDBnCa6+9RlZWFq+++ioxMd79h0kIIYR31metJ6M4gwBDAOf1Pq9dbaICogg3h2Oz25xDqrJK1WpJSSFJaDQar/rUYaGjk1Y6HFWOCy4Ao9HOF9d/QUVeBZEDI7nq66vwC/YDQKPVcM7z5xCcFExZVhmhu9VGjE1DRwjF6LChN+sJTjjObPQ2WJzDq1ToMAT6ZniVX2Djz11v7jy/AyFE5+N26PjDH/5ATk4OAI888gjffvstiYmJvPDCCzzxxBM+76AQQoj2c8zluKDPBfgb2rf5m0ajYWDkQAB25O0A1GZ+AN38Pf903eF0q3R88406zpkDe7/ey95v9qIz6bj4/y7GGOBaYdD76Zn65FQACr77DQ029u2DigoVOhxzMMJ7haPReh7+HKEjlGKAZv3wlKlJpcNg1vnknkKIrsntWug111zjfDxixAgOHjzInj17SExMJCIiwqedE0II0X52u53Fu9XH7JcNuMyttgMjB/LzwZ8bQ0dFQ+gI8D50xAe5zkXoypWOI0fU3hwaDUyeaOPDKUsBGPOHMUQOjGyxTf+L+/N18NdU5pUzJPQwW4qS2LFDhQ7HcKjw3uFe9csS47q5oynIN6HDHNT4NsIolQ4hRBu8Xi/P39+f4cOHS+AQQoiTbH/Rfg6VHMKgNTA9ZbpbbZ2VjqO+r3SY9CaX+3TlSsfKleo4ZAgcWbGbo7uO4hfqx4S/TGi1jc6oo++FarL+ML9dAGRlQUFB43Co8D7ehQ7/bq5VLz9fhY7AJqEjQOZ0CCFa166/EPPnz2/3DRcsaL7rrRBCiI63PH05AGPjx7Z7aJVDs+FVFb4LHQBh5jBnkOmQSkcnCR0rVqjjlCmw4aUNAIy+YzTmUHOb7fpf2p+t724lpnA3cA6FhZqG4VW+CR0B3QJcvvYP8U3o8LNI6BBCtE+7/kJs3ry5XTfzdrKhEEIIz/2U8RMAZ3U/y+22A7oNAOBQySFKqksaKx0+GF4FEOIX4nzc0u7onnCpdHSS4VWO0DE6KZe05w+i0WnUClXH0ePsHuiMOow1ZYRQTFFRKPn50L1hTkdEH+9GExxb6fAP9VGlw9L4c/eT0CGEaEO7/kIsX768o/shhBDCC3a73VnpODP5TLfbh5pDCfULpai6iKyyLJ8OrwLX0OErTTcH9HWlw2aD776DTz4BqxUmToTrrlM7jLempAR2q03c8dutPqzrN7ufc7natuhNeiL6RZC7NZcociksDKUwt5bBlAPez+nwj3ANHYFhPgp+5sYfiCWscwQ/IUTn5PGcjn379vH9999TVaXWdLfb7T7rlBBCnM6WHVjGhR9cSNS/ohj4n4E8+cuT1Fnr2myzr3AfuRW5+On9GBs/1qPXDTWHAlBcXezTieTQMaGjoyaSFxbCjBkwaxb897/w7rtw000wcqSaZ9GaHWpkGnGxdjK+Uelj8LWD2/260UOiAYgil6IiqMitAEDrZ8AvxM+zb6aBzqBDF9h4D18Nr9I3CR2h3aTSIYRonduho6CggKlTp9K7d29mzpzpXD73hhtu4J577vF5B4UQ4nRht9t58KcHmfbeNL5I/YK8ijx2Ht3JX3/6K1PemUJ1fXWrbbcc2QLA4KjBHg9fcgSD4upin1c6HHNGfKkjJpKXlsKkSbB0KQQEwB/+AA89BOHhsHUrXHIJ1LWS/7ZvV8dxiVmUZpZitBhJmZ7S7teOHKxWt4oij8JCqCqoBMAU0vZ8kPYKimmc12G0+Ch0NNkQsGkAEUKIY7kdOv74xz9iMBg4dOgQ/v6N5drLL7+c7777zqed62jPPfccAwYMoH///tx1111SrRFCnFRP/PIEj//yOAA3Db+J1dev5s3z3yTEL4TVh1dz17d3tdp2W67aUW5wZPs/WT+WI3TkV+ZTWNWwC7aPKh33jLuHuUPm8ulln/rkfuD7SofNBtdeCzt3QkwMrF4Nzz8P//iHmqsRGKiOr7zScntH6OhTr1ag6nN+H7d26Y4aHKWO5FJQALUlKnQcOzTKU4GRjfcxWXw1vKrJ5oCyI7kQog1uh44ffviBp59+mvh413XXe/XqxcGDB33WsY529OhRXnrpJTZu3Mj27dvZuHEja9euPdndEkKcpr7Z+w0PLn8QgBfOeYHXz3+dcQnjuGH4DXx0yUdo0PDGpjf4OePnFttvzd0KqEqHp0L91PCq/YX7AdCgIdzs3VwCB7PBzNsXvc3sfrN9cj/wfaXjvffgiy/AZIIlS2Bwkx/lwIHwzDPq8bPPtlztcIQO/5x9APSd3det13eEjnAKOLS/Dj+bCh2WKN+EjqYrWBkDfV/pMMg+HUKINrgdOioqKlwqHA6FhYWYTL755OREqa+vp7q6mrq6Ourq6oiMbHnjJiGE6EgVtRXc+vWtANwx6g7uHHOny/Nnp5zNzSNuBmDB2paXJXdWOrwIHY5KR1phGqCWudVpO+8u076sdBQXw333qcf/+AeMHt38mnnzICoKDh2CDz5wfc5uV6EjgArqso6CBrqf1d2tPgRGBWIMDUADVB3Mwx8VOppWKLzRdAWrDhleJZUOIUQb3A4dEydO5N1333V+rdFosNlsPPPMM5x5pvsrprRm5cqVnH/++cTGxqLRaFiyZEmza15++WWSk5Px8/NjzJgxrF+/vt3379atG/feey+JiYnExsYybdo0UlLaP/ZWCCF85alfn+JQySGSgpN4atpTLV7zx7F/BODL1C9JK0hzea6kuoSDJarS7IvQsbdgL+C7oVUdxZeVjgULIC8P+vaFu+9u+Ro/P7izIQ++/77rc1lZKrh012YAqmphDnN/LoYlSVWbgih1hg5fDa8KiOyASodZ5nQIIdrH7dDxzDPP8Prrr3PuuedSW1vLfffdx8CBA1m5ciVPP/20zzpWUVHBkCFDePnll1t8/sMPP2T+/Pk88sgjbNq0iSFDhjBjxgzy8vKc1wwdOpSBAwc2+5ednU1RURFfffUVGRkZZGVlsXr1alY6tpIVQogTpLi6mBfWvwDAghkLCDAGtHhdn4g+zOo1Czt23tv6nstzjipHQlCCcwUqTzhDR2FD6PDRJPKO4qt9OsrL4aWX1ONHHwVjG+/HL7xQHVeuhOom8/pTU9VxsCUDgKTJSR71JbCbCip+VPk8dDStdPhqTodUOoQQ7eV26Bg4cCBpaWlMmDCBCy+8kIqKCubMmcPmzZt9Wik499xzeeyxx5g9u+XxvwsWLOCmm25i3rx59O/fn1dffRV/f38WLlzovGbLli3s2LGj2b/Y2FiWLl1Kz549CQsLw2w2M2vWrDbndNTU1FBaWuryTwghvPXS+pcorSllYORALup7UZvXzuk3B4Bl6ctczu86qiYue7tClCN0lNaov2+dvdLhq306Fi6EoiLo2RNa+U+O04ABapJ5VRWsWtV4PjtbHePqVcUpeUqyR32xRKrQYaYKf9SS9L4KHU0rL76qdOiMOmjYF1hChxCiLW6Fjrq6OqZOnUpeXh4PPPAAH330Ed988w2PPfYYMTExHdXHZmpra9m4cSPTpk1zntNqtUybNo01a9a06x4JCQmsXr2a6upqrFYrK1asoE+fPq1e/+STTxIcHOz8l5CQ4PX3IYQ4vdXb6nl5g6rm/nXCX9Fq2v6TPLX7VADWZ613BgOAzNJMAJKCPft03eHYvTSiA6K9ul9H88WcDrsdXn9dPZ4/H3Q6x3k7B5Ye4KtbvuKLm75g67tbsVltaDRw9tnqmh9/bLxPVhaYqCGgYX+TxAmJHvXHP1ztpWGm2ueVjqYTvX01p0Oj0eAfrvrnyXAyIcTpw63QYTAY2LZtW0f1pd3y8/OxWq1ERUW5nI+KiuLIkSPtusfYsWOZOXMmw4YNY/DgwaSkpHDBBRe0ev39999PSUmJ89/hw4e9+h6EEOLH/T9ypPwIEf4RXNz/4uNenxSSREpoCla7lV8O/uI8n1WWBUB8UHxrTdvFsXqVQ2KwZ2+cTxRfzOnYtk0tkWs0wpVXqnPVJdUsmrWI985+j42vbWTzm5tZMncJb455k6qiKqZPV9ctXdp4n6wsiEQN77XEWlxWinKH4427uQOGV7kMhTL5ripxyYeXMGfRHAKjAn12TyFE1+P28KprrrmGt956qyP6csI9/vjj7N69m507d/LCCy+g0WhavdZkMhEUFOTyTwghvPHuNrUox1UDr3IZKtSWs7qfBbgOsXJUOrwNHcdWOjp96PBBpeN//1PH88+HkBCoLa/l7clvs+/bfejNekbeNpIz/nwGfiF+5GzM4ZPLPmHUCBsAu3apvT1ADa+KJBeAyEGer4TYkaGj+1ndCUoIovtU91bVas99B105yKf3FEJ0PW5/1FFfX8/ChQtZunQpI0aMICDA9dOcBQtaXs7RlyIiItDpdOTm5rqcz83NJTq6cw8HEEIIgPLacpbsWQLA74b8rt3tJiVN4o1Nb/Bb9m/Oc47QERcU51WfTrnQ4WWlw26HDz9Uj6++Wg2pWjJ3CblbcwmICuDqb68mZpgaOjzwyoEsHL+QA0sP0POH39DpRlNVBTk5EBenKh1RDZUOr0JHaMeFDoO/gbv234VW5/bnjUII4TW3//Ls2LGD4cOHY7FYSEtLY/Pmzc5/W7Zs6YAuNmc0GhkxYgTLljV+0mez2Vi2bBnjxo07IX0QQghvLDuwjOr6alJCUxgeM7zd7XqH9wbgQNEB5zlfDa865UKHl5WOXbvg8GG1FO4558D297ez+9Pd6Iw6Lv/scmfgAIgeEs20p9U8wnULVtM9yQrAfrWPYkOlQ4WOqEGuQ3/d4ah0hFKEFrs6F+67uRI6gw6NtvWqvhBCdBS3Kx3Lly/viH40U15ezr59+5xfp6ens2XLFsLCwkhMTGT+/PnMnTuXkSNHMnr0aJ5//nkqKiqYN2/eCemfEEJ449t93wJwbs9z2xzaeaweoT0AFTSq66ups9Y5J5XHWXxb6YixnLgFQjzhbaXjhx/UcfJk0NbV8OOf1MzwyX+bTMK45ouFDLthGD//42dKDpYwetBO9jGYfftgwgTIybYT5YPhVX6haiJ5KMWAmvDty/kXQghxsnTav2S//faby2aD8+fPB2Du3Lm8/fbbXH755Rw9epSHH36YI0eOMHToUL777rtmk8uFEKKzsdvtfLfvOwDO6XmOW23DzeFYjBbKasvIKM5wng8yBWExWbzql7+hcRiPBg16baf9TwTgfaXj++/Vcfp0WPPcGsqPlBPWK4xx81uumBvMBkbfOZoVD68gqWQ7NISOvDwwW8swU41Gp6FbP8+XGj52BSjHylBCCHGq67T/RZkyZQp2u73Na+644w7uuOOOE9QjIYTwjT35ezhYchCTzsSU5ClutdVoNKSEpbDlyBYOFB1wTkD3dmiV494OQabOv1iGN5WO6mr4+Wf1eOqkOr4/Zz0AZz56ZpuVhb4X9WXFwysw5WSgo559+/RkZ0MEBQCE9gj1ar+KZqHDR/M5hBDiZJPZZEIIcYKtPLgSgDMSz2h1B/K2OIZY7S/cT1apms/h7dCqY50KocNlc0A3Kx2//aaCR3Q01KzdTFVBFaE9Qul/cf8220UOjCQwOhDq6kngMPv3q0nkFtQQt+DEYPe/kSb8Qvxcvg7rGebV/YQQorPotJUOIYQ4Ffyc8TM/7P+B0ppSpiRP4YI+Fxz3DbBj5akxcWM8es0eISp0HCg6QIR/BOCbSkdTp0LocBle5WalY+NGdRw9Gja9sQmAsX8ci1bf9mdxGo2GHmf3YNt720hhPxv2dScrC4IoA9QeHd7QGXQYLUZqy2oB6Dagc+8KL4QQ7SWhQwghPFBWU8aNX97IRzs/cp57acNLTE6azKeXf0qYufVPqDdkbwBgZOxIj17bUek4UHyA6vpqwPehY2DkQJ/eryM0DRoPP2jgyGbo0wduv11NDm/Lbw0rDg+PyyX3i1x0Rh2Drm7fXhOO0NGDdJaVwp49YHGEjjjvQgeoZXOdoaO/hA4hRNcgw6uEEMJNZTVlnPv+uXy08yN0Gh3XDr6Wu0bfhcVo4eeDP3PeovOw2qwttq2qq2JH3g4ARsWO8uj1U8JSAFXpKKkpAZrvJu6pr678ilm9ZvH8Oc/75H4dSadpDB0/fGtg2zb4+GM46yz417/abuuodETnbQOg16xezj0yjid+rAp4aolcO3l5TUKHl5UOcB1iJZUOIURXIaFDCCHcdMvXt7Dq8CpC/EJYdf0q3p39Lv8+99+sun4VQaYg1mSu4eUNL7fYdmvuVqx2K5EBkR5XJ5JDkgE4WHyQOlsd4PmO3Mea1XsWX131FdGBnXujVbsd3nit8Xu+/FIDn30Gc+eqXcL/9CdospWTi/JyVZ0AO+VrdwK0u8oBEJIUgkanwUA9FsopLW0MHUFx3g9LqymrcT4OS5E5HUKIrkFChxBCuOHjnR+zaPsidBodX1/1NWPiG+dlDIoaxNPTngbggZ8eoKS6pFn7DVlqaNWo2FFu7c/RlGNpW8c+HeDZPhWnstdeU9UNh8f/YeCii+Dtt+GWW9S566+HiormbTdvVqFlQGQ+5Vkl6Ew6es3s1e7X1hl1hCSFABBGIaWlENQwkdwXw6vKssucj483x0QIIU4V8tdMCCHaqaquiru/vxuAv078K+MTxje75uYRN9Mvoh/lteV8suuTZs9vz9sOwLDoYR73w7FqU52tzueVjlPBwYOqkoG15X06/vlPSEyEQ4fggw+at9+6VR3HdlPbiSdNSsJgdu/n51hVKpRCSortBFIO+GZ4lbWm5aF5QghxKpPQIYQQ7fTS+pfILssmKTiJByY+0OI1Wo2WuUPmAvDO1neaPX+g6AAAvcLb/8n6sZpWNRwTyU+nSsef/qSGSA3s3/LqVYGBajI5wFtvNW9/QP0KiK5QoSNlRorbfQhNUXNowiikpqgCHTbQoJbT9dKsV2YBcM4L7m0cKYQQnZmEDiGEaIfKukqeWvUUAH+f8ndMelOr1149+Go0aPjl0C/OkOHg+NqxApUnmn6qX1lX2excV7Z9u5osDnDfPa3vSP6734FeD2vWwM6drvdITwc99RiyMgBIme5+6HBUOsIowl6ihkNpAgPQGXRu3+tYI28Zyfys+Yy+Y7TX9xJCiM5CQocQQrTDxzs/prCqkOSQZK4ZfE2b18YHxTMpaRIAyw40zmaus9ZxqOQQAN1Dunvcl6af6lfUVjQ715U9+qg6XnIJ9O/TZHPAY77/6GiYpQoGLF7seo/0dIghG+rqCYgKIHJgpNv9aAwdhWgrVOjQhfpubxNLrMXjOT9CCNEZSegQQoh2eG3jawDcPPxmdNrjf5rtmO+xLmud89zh0sNY7VZMOhMxlhiP+3K6VjpycuDTT9Xjhx46ZnPAFr7/adPUcc0a1/MZGRBLDgBxo+M8enPfNHQE2NQkckOo9/M5hBCiq5LNAYUQ4jh2Hd3Fmsw16LV65g2b1642Y+PHArA2c63znGNoVffQ7mg1nn/mo9Vo0Wq02Oy2xtBxGlQ63nkHrFYYPx4GD4bdR9X3nJyezHc3fEf+rnwi+kYw6rZRJIxPYNw41W7tWrWMrlYLRUVQUgIxDaEjZoRn4S+0h5rT4UcNEeQDYAwL8PI7FEKIrktChxBCHMfiXWp8zrk9z233/hVj4tRSuruO7qK0ppQgU5BP5nM4GLQGaqw1p02lw25vnBR+443qqEPHOd+ew9h1Y9mOWhUsZ2MOOz7YwfRnpzPitrGYzVBcDGlp0LevGloFkKjLBivEjoj1qD96Pz1WnQGdtY4A1O9A7+YKWEIIcTqR4VVCCHEcS1KXADC77+x2t4kKjCIpOAk7dn7L/g1oMok8xAehoyFknC6Vjo0bYd8+CAiASy8Fu93O5r9uZuw6VVEadsMwLvnoEgZeORC71c73d39P1qoMRo5U7R1DrNLTwUAtoVZVnfC00gFg16nP7fxoWEHMz/tJ5EII0VVJ6BBCiDYcKjnEppxNaDVazut9nlttHUOs1mWqeR3pxepjdl9UOpru1QFdv9Lx5ZfqOGOGWhJ381ub2fPmHuwaO6V/KuWCNy9gwKUDmPP+HIbdqPZA+Xze54wbqX4+TUNHNEfQYMcSa8ES48U8DJ0KGSbUDuIGPxk8IIQQrZHQIYQQbfgi9QsAJiROoFtAN7fa9u/WH2gMG+lF6tg91POVqxyOrWx09UqHI3RccAGUZpbywz0/ADDtyWk8+8yzzus0Gg0zFswgKD6I4oxiuleo9XL37lXPO0IHQMxwz6scADRUOpyhwyyVDiGEaI2EDiGEaMPKgysBmJEyw+22MYHqTW1OuZq0XFRdBECEf4TX/Tq2stGVKx2ZmbB5M2g0MHMm/Hjfj9SU1hA/Np7x9zbfFd5kMTHq9lEAVK3eBEB2tnruyBEIRf0ewnqFedcxvWvoMAZIpUMIIVojoUMIIVpht9tZdXgVAGcknOF2e8eyuDllKnSU1qilVYNM3u/ncDpVOn5QRQ3GjgV7Xh47PtgBwMz/zESra/k/Y0PmDkGj01C64zARHHWGjtJSCKUYgJDuIV71S6NXlQ3HnA6jWUKHEEK0RkKHEOK0UF1fzXtb3+Ofq/7JRzs/orq++rhtDpYcJLssG71Wz6i4UW6/5rGVDp+GjtOo0rF6tTpOngy/PPYL2KHv7L7EDGt9eJQlxkKvmb0A6M8uystV4Cgrg5CG0BHaPdSrfmkMrpUOk78MrxJCiNbIxzJCiC5v6YGlzF0yl+yybOe5qIAoPrv8M8YljGu13apDqsoxPGY4/gZ/t1/XUenILc+lpr7GGXSk0uEexyTwkf3K2fWvXQBMemjScdv1OLsHaV+mkazPYmW9GmJVVtY4vMrrSodBhQwtdgCM/vKfVCGEaI1UOoQQXdr/tv2Pc/53Dtll2cQHxXPN4GtICEogtyKX8/7vPNIK0lptu/qw+oh9fHzzeQPtERkQiQYNVrvVuVwugMXo/c7Vp3Klw2aD+vr2XVtUBLtUzsCyfyu2ehvxY+PbrHI4xI+NByDOngnYyc6GmpIq/BoqEyHJIR70vpHW6Boy/AKl0iGEEK2R0CGE6LI252zmxi9uxGq3cu3ga9l7517em/0eu2/fzajYURRWFXLDFzdgt9tbbP9bjtpfo61qSFv0Wj2RAZEApBakAmDWm30SEE7FSsevv6ohUmazWvb2yivh4MG226xTqw3Tq6edtA82AziXxD2e6CHR6P30mKxVhFNAdjZoS4oBMIX5YwwwevqtAC2FDql0CCFEayR0CCG6pJr6Gq5cfCU11hpm9ZrF2xe9jZ/eD4AAYwCfXv4pfno/fj30K1+lfdWsvd1uZ0/+HgAGdBvgcT8cQ6xS81Xo8MXQKmjcp8Ohs1c6/v1vmDgRVq6E2lqoqYEPPoAJExqXs22Jcz5HnyMUpBVg8Dcw4LL2/T50Rh2xI9WO4wlkkpUFxspiAIISvZvP4bh/U36yepUQQrRKQocQokt6ds2zpBakEh0YzTsXvYNW4/rnLj4onj+M+QMAj6x4pFn7nPIcSmtK0Wq09Azr6XE/HJPJHZUOi8n7oVXQwvCqTlzpeP11uPtu9fi66yA1Fdavh7591XK4F18MVmvLbXeoharoaVU/v5QZKZgspna/dvw4NcQqnsMcOABBNjWfI7RHiAffiSudyTVkmGV4lRBCtEpChxCiyzlSfoTHVj4GwD/P/ifh/uEtXven8X9Cp9Gx+chmlzkXgLPKkRKagknf/je5xzo2dPiq0tFseFUnrXRs2wZ33aUeP/ggLFwIvXvDqFGwfDmEhsL27fDf/7bcfo/6NaDbr+be9D6/t1uvHzUkCoBwCtmzp3G53IheIe5+K83oTa4hwyBL5gohRKskdAghupxXf3uVqvoqRseN5upBV7d6Xbh/OJOS1CpIn+/53OW53Ud3A9A3oq9XfXEMr3JMWPdZ6DgFKh02G8ybp4ZSzZoF//iH2uDPIToaHnpIPX7oIairc21fXw/79oGFUir25oAGes9yL3QExamft4UyUlMhkHIAghO8/z3o/fRtfi2EEKKRhA4hRJdSa63l1d9eBWD+2Plomr7LbcGFfS4E4PNU19DhqHT0i+jnVX8clY78ynygYyodGjTotJ1vaM+iRbBpEwQFwVtvuQYOh9tug27d1E7hy5e7PpeRoYJIX4OqQsWNjiMgMsCtPlhi1XA2C2Xk5jbZUyPI8+qVg8HP9WeuM3W+34EQQnQWEjqEEF3Kp7s/Jbcil1hLLHP6zTnu9Rf2VaHjl0O/UFRV5Dy/O9+3lQ6Hjqh0dMahVXV1ajgVwF/+AlFRLV9nMsHs2erx4sWuz6WqEWn0txwGIHlKstv9cIQOE7UYqcFIrfrajXkhrWlW6TBJpUMIIVojoUMI0aX8b9v/ALhh2A3tejOeHJJMckgyNruNrblbneedlY5u3lU64oPiXb4OMvq+0tEZh1YtWaKWw42KapxE3pqLL25s03RCuSN0xNSr0OGYFO4OY6ARY0NVw0KZs9JhtHi3XC40n8MhlQ4hhGidhA4hRJeRX5nP9/u/B+CqQVe1u92gyEEA7MhTSyXVWevIKssC1ERybzQLHadJpePFF9Xx979X+3I0Zbfbsdsa90Y580w1oTwvr3FfDlChw49q/EqPApAwLsGjvgQ1GWLlHF7lg0qH0ewaMqTSIYQQrZPQIYToMj7Z9Qn1tnqGxwx3a1iUI3Rsz90OQEFVAQBajZYwc5hXfYoKiEKvbXwz2hFzOjpbpWP7dvjlF9DrVehwyFyXyXtnv8eTlid5MuhJlsxdQmlmKQaD2q8D1BwQhz17II5MAMJ6hrk9n8PBMcQqiDLn8CpfVDqM/jKRXAgh2ktChxCiy1iyZwkAVwy4wq12AyMHArA9T4WOoxXqk/Uwc5jXE7R1Wh1xljjn177ap6Pp5oCdrdLx4YfqeN55EKv25mPDfzbw1ri3OLD0AHUVddRV1LH13a0snLCQogNFDB6srtu+vfE+hw9DAp4PrXJonExe6tOJ5KYAGV4lhBDtJaFDCNEl1Fnr+PXQrwDM6DnDrbaDohqHV9ntdo5WqtDRzb+bT/qWENw4LKirVzrsdvj4Y/X4ssvUcfPCzXxz+zdgh0FXDeLW7bdy/arrCesVRsnBEj66+CMGDrABal8Ph/x8iCIPgJgRrhPy3WGJU6EjlCK0qGFdPhle5S/Dq4QQor0kdAghuoTfsn+joq6CcHO4s3LRXn3C+2DQGiirLeNQySHn8rYR/hE+6VtCUAeEjk46p2P7dkhLU6tSnXce5O3MU4EDGH/feGb/bzaRAyNJGJ/AdSuuwxRs4siWIwQdUJP4d+xQ+3vU1EBZGYSjhrpF9PX8d+GodEQ03AvUBHNv+TWpdNg0WjTatpdnFkKI05mEDiFEl7AiYwUAk5Mno9W496fNoDM454Bsz9vuHF7VLcA3lY6mk8m7eqXjs8/UccYMCAyw8/m8z6mvridlRgrTnpzmsm+KJdbCpAfV5oy7/7Mcs9FKebnanyM/HzTYCKMQgIg+3ocOR4DBaPBJQPALaKx02DvhPilCCNGZSOgQQnQq9bZ6Ptr5EZd/cjnzv5/P2sy17Wq3PEPtLHdm8pkevW730O4AZJdlN1Y6zFLpcJdjg79Zs2DHhzvI3pCNMdDIhf+9sMU3+qPvHI1/hD/l2WVMTDgIqCFW+fkQQjF6rOj99AQnBnvcp8Y5HWo3co3J+6FVAH6BjZUOu06GVgkhRFvkr6QQotPYlruN65Zcx+Yjm53nnlv7HBf1vYj357yPv8G/xXY2u401mWsAmJQ0yaPXDvULBaC4urhxToePKh2ny5yO6mpY25ARJ02w8f15PwFwxp/PwBLT8gR6vUlPn4v6sPnNzQzU7eIHerBjB1gsjcOhwnqFeVWZcIQOB52/90OrwDV0IKFDCCHaJJUOIUSnsL9wP1PensLmI5sJ9Qvlz2f8mWsGX4NOo2PJniX8+cc/t9r2QNEBymvLMelM9O/W36PXD/ELAVTo8PWcjg4ZXtUJKx1r16q5GDExYNu1h+L0Yvy7+TP2dUJqSAAAlcJJREFUj2PbbNf/EvU7s2TtQYONvDw4ehTCafg9eDG0CiAgynWpXb2/byodLhPJdTK8Sggh2iKhQwhx0lXWVXLRhxdRVF3EqNhR7L59N09Ne4r3Zr/HV1d9BcBLG17ip/SfWmy/9YiahDwwcqDLnhjuaBo6fL16VUxg48pLFqNvlsztjJWOFSvUccoUWP/SegBG3DwCY0DblYXuZ3bHL8QPTUUFcWRRVKSGV0U0hI7wPuFe9ctgNjh3JQfQB/omdBia7suhl0qHEEK0RUKHEOKku+/H+9iRt4PowGiWXLGEqMAo53Pn9DyHW0bcAsDff/57i+235qrQMSRqiMd9cISOouoiZ6XDV8Or4oLieHDig/xt8t8IMHq2wd2xmu7T0fSxr9jtsH49/PCDmtjdHr/8oo7je+Vx8OeDaHQaRt4y8rjtdEYdiRMSAYghp0no8H7lKgdLTKDzscbkm59X080ANXqpdAghRFskdAghTqpfD/3KyxteBuCdi94h1hLb7JoHJj2AQWtg5cGVLU4sd4aOaM9Dh8ucjobVq3w1vArg0bMe5ZEpj/jsfh05vGrlSujfH8aMUatQpaTArbdCZWXrbex22LJFPQ7L2gFA71m9CYpv33CyyMGRgNqXo7BQhY4gSgEI6R7i6bfiFBjdGDoCw31T6Wi6GaDGKJUOIYRoi4QOIcRJtWDNAgCuH3o901Omt3hNfFA8Vw++GoAX17/Y7HnH8CqfVDqqmlQ6fDS8qiN01PCqRYtg6lTYswcCA1X4sNng1Vdh3jwVLlqSkwOFhaDV2Cn4ZRcA/S9r//yaqEGquhVFLkVFak5HABUABER6Xx0KjGoMHbHJPqp0NNkMUGOQ0CGEEG2R0CGEOGkOFh/k89TPAbhn/D1tXnv90OsBWHpgKfYm73yLq4s5WKKWWh0cNdjjvjhCx6GSQ9TZ6gDfVjp8rSMqHatWwXXXQX09XH45ZGXBzp3w7bdgMMBHH8GLzTMfoDYFBBiVfJTCtAJ0Rh19zu/T7teOGqxCRyR5FBXaKcirx0QtAP4RLa9a5o6A6MbgYrT4JnQ0rXRoDTK8Sggh2iKhQwhx0rzy2yvY7Damdp963FWnRseNxqw3k1eRx+783c7z+wr3AWqydqg51OO+OEJHTnkOAAGGAMwGs8f362i+rnSUlsJll0FdHVxyiap4BDWMjDrnHHj2WfX4iSfU0rjH2rZNHUf4q99NyowUTEHtH8YU3jscrVGHiVpsRcWUHqlST2g1+AX7efptOTUdXmWy+GZ4VdM5HVoZXiWEEG2S0CGEOCmq6qp4c9ObANwx+o7jXm/SmxifMB5o3H0c1GZ+4LosrSccocOhM1c5wPeVjr//HbKzoWdPePtt0B7zX4dbboGEBMjNhffea97eUemIrMgAoNfMXm69vlavJbyPGs4WVpdLUZYaWmUM8ffJ7uFNQ4evKh1Nh1fpjFLpEEKItkjoEEKcFB/s+ICCqgISgxM5r/d57WozJXkK4Bo6skqzAFqcgO6OY0NH0w39OiNfVjr27oV//1s9fvFFCGhhCoXBAPPnN15zrG3bQE89mqzDACRPSXa7HzFD1WTySPKwlqlZ6/7h3g+tgo6pdDQdXtU0gAghhGhOQocQ4qR4beNrANw28rZ2763hCB0rD650nnNUOuIscV71x2KyoNU0/klMDkn26n4dzaXS4WXo+Ne/wGqFc89VQ6la87vfgUajqhpZWY3nrVbYvRviyMJeZyUgKsCjvTWCEtR4rkAq8EeFjsCoDggdbgz7aotWr8Uxu8hglkqHEEK0RUKHEOKEK6gsYH2W2jzu2iHXtrvd0OihAORW5FJcXQxAVpl69xsX5F3o0Gq0BJuCnV8nByd7db+O1nRvDm+GVx05Au+8ox7ff3/b14aFwciGbTeWLm08n5cHtbXQXZMBqCqHRuP+kChzqJpD40e1M3RYOiB0GAJ8M/Feo9Gga6hwJKdIpUMIIdoioUMIccL9lP4TduwM6DbArWFRgcZAogOjgcYJ5I5Kh7fDq8B1iFVSSJLX9+tIvhpe9cYbUFMD48bBhAmN5+12O0e2HCFjRQalWaXO82efrY4//NB4raPq0dOgVhFLmuzZz84vVE0YN1NFQEPo8MXKVQAB3RrHjFlrrD65J4DRrMKGn0UqHUII0Rb5aEYIccL9eOBHAM7ucbbbbXuG9eRI+RH2Fe5jZOzIxkqHl8OrwDV0nFLDqzysdNjt8L//qce33KKGTgEcXnOYr37/FXnb8wA1jGjkbSM5++mzOftsPU88oSodNpuacJ6dDWAn0nYEgLjRnv0uWqp0+Cp0aPWNn7FZ4iw+uSc0zuuQOR1CCNE2+SsphDjhlh5QY3POTvEsdPx66FdnpcNXE8kBgv2aDK/q7KHDB5WODRsgLQ3MZpg9W53b+dFOPrv2M6y1VvRmPUFxQRTuK2T9C+upyq9i5luzMRo15OXBwYPQvbuqdARSjrG+Co1WQ7f+nm2q2LTS4evQATB3+Vzy9+QTP8a7lc6acoSNpsvnCiGEaE6GVwkhvFJZV8m23G3UWevadf2hkkOkF6ej1+qZlDTJ7dfrFaaWYt1XuI+quiqKqosA7+d0ANTb6p2PE4I6+epVPqh0vP++Os6eDRYLZK7LdAaOfnP6MT9rPnfuvZMrPr8CrV7L9kXb2b7wN3r0UO3271fHrCyIQlVFwnqFYTB71p8WKx3dfBc6kqckM/KWkT67HzSGjaYrWQkhhGhOQocQwiObczZz/efXE/WvKIa8OoRhrw3jp/SfjttubeZaQE0KDzQGHufq5nqG9QRU6HDM5/A3+LtMAvdUSXWJ87FJ75sVjjqKLyodX32ljpdfDjVlNXx8ycdYa630vagvl358qTME9LmgD9OemQbAysdW0qu7Cmf7VLGJ7GyIIheAqEFRHvUFOr7S0RFkeJUQQrSPhA4hhNs25Wxi7Ftj+e+W/1JeW45Oo2Pn0Z1MfXcqcz6cg81ua7WtI3SMiRvj0Ws7Qsfewr0uk8g9WS3pWI4VsU4F3lY69u2DAwfU/htnnQUrH11JaWYpoT1Cuejdi5ptyDf69tFY4iyU55TTt1ZtP9600hHZUOmIHBTp4XfUWOnQYyUYFQA7e+hwhA2pdAghRNskdAgh3JJfmc+lH19KrbWWKclT+GXeLxy59wi3j7odg9bAZ3s+Y/Guxa22X5e1DoCx8WM9en1H6MiryGNP/h7AN5PIAXqH9/bJfU4Ebysd33+vjuPHQ21uIWufU2HwnBfOaXHzPJ1Rx9g/qt9Z0G613LGj0qGGVzVUOgZ7XukwWozYG8KjmWqg84cOZ6VD5nQIIUSbJHQIIdqtoLKAae9O40DRAZKCk/j0sk+ZkDiBCP8IXpr5Eg9MfACAv/38N6y25suS1lpr2Zi9EfC80hFkCiLcrDae23xkMwDh/u5vRNeSN85/g8sGXMb6G9f75H4dydtKh2PJ2xkzYM2za7DV20iZnkLvWa0Hr6HXDQUNWLNzsVDmrHTkZNnoxlHAu0qHRqNBH+jncq6zhw5HQDMGGo9zpRBCnN4kdAgh2u2h5Q+xNXcrUQFRfHv1t4SaQ12ev3vs3YT4hbDr6C4+T/28WfttuduosdYQZg5zViw8EWBUey6U1ZYB3u/I7dA9tDsfXvIho+JG+eR+Hcllc0A3v3+bDVasUI8njahgy3+3ADDhrxNabQPgH+5PzPAYAHpwgP37obISaosr0WNFo9UQkhTiVl+OFRxldj72C/XDGNC538xP+OsERtwygl7n9jrZXRFCiE5NQocQol2Kqop4Z6vauvr9Oe/Tr1u/ZtcE+wVz28jbAHhx/YvNnt+RtwOA4THDvZqD4XiTXVVXpb72YkfuU5XL8Co3v/+9e6G0FPz8oG7dRuqr64kbHUfSpONv6tfjbLV0VQoHqKyEjRvBgto8MCAqwGU/DE84JpMDhPf2TQWrIyVNTOK8V87DFNS5Fx4QQoiTTUKHEKJd3tr8FpV1lQyOGsxZ3c9q9bpbR92KTqNjRcYKtudud3kuozgDgB4hPbzqi+NNdmWdWuHIV5WOU0nToLHsBwNXXgn33gtr1x6/7UY1wo2hQ+zsXKR+RyNvHdmuIJhydgoAPXUHADu//gpBqIqTJdb7TffMYY2VjlMhdAghhGgfCR1CiOOqqa/h3+v+DcBdo+9q881pfFA8F/W9CID3t7/v8tzBkoMAJIUc/xP1tjgrHfWq0qHXnn6TeJsGrUX/M/DBB/Dss2pi+BNPqN3GW/Pbb+o4NjGH/D356P309JvTvHLVkoQzEtAZdfhbywmhmLQ0sDSEjqC4II+/HwfHClag9vwQQgjRNUjoEEIc19tb3iazNJNYSyxXD776uNef0/McADbmbHQ576h0JAV7FzocIeN0rnT8tLTxe46LMfDYY3DJJSpsPPBA48Z/LXFUOhJL1NK3fS/q2+7hQXqTntAeai5PGEWUlTUOr7LEeV/pONWGVwkhhGgfCR1CiDbZ7DaeXvU0APeNvw8/vd9xWqg5GwAbszdib/KR+8FiVelIDkn2qk+OoUWn65yOffvg0ku0YFN/wv+9wMADD8DHH8NDD6lr7roLcnKat7XZYNMm9di6Ow2AAZcPcOv1Q1NU6AilkNLSJsOrJHQIIYRohYQOIUSbthzZQnpxOoHGQG4acVO72gzoNgCD1kBRdZFzSJXVZuVw6WHAd8OrTsdKh80GN9wAFRWgsavv29/U+P0//DCMGAFFRfDcc83b79sH5eUQYyqk4nARWr2W7md1d6sPYT3VsKcwiigt9e3wqqabEjpeRwghxKlPQocQok3f71O7yJ3V/Sz8De3bM8GkNzEwciCgdi8HyC7Lpt5Wj16rJyYwxqs+OSsdp+GcjnffhZUrISCgMWw0rfTo9Y3Vjnfegbo61/aODf3GRKhNNhLGJ7i98pKj0hHWUOmw+HAieWV+pfNxS5sUCiGEODVJ6BBCtOm7/d8BcE7KOW61cwyxcoQOR8UjMTgRnVbnVZ8cIeN0G15VVwf/+Id6/PDDYDKoPSyOrfTMnAlRUZCXB1995XqP9HR1TLYdAKDHdPdXEnNUIEIb5nQE+XBOR49pqj/mcPNxrhRCCHEqkdAhhGhVaU0pqw+vBmBGzxlutT02dPhqEjmcvsOr3ntPhYbISLj99sbv+9jQZTDA3Lnq8f/9n+s90tNBg53gQpU+UqanuN2PsBTH8KpCqkrrMFMN+GZ4Vb85/bjyyyu5ddutXt9LCCFE5yGhQwjRqp/Sf6LeVk+vsF70CHXvE/G+EX0BOFCkPlH31SRyaHyTXWOtAU6P4VV2O7zwgnr8pz+p4VWOSf0tTe6fNUsdV61yXT43PV2FBU1NDXo/PdFDo93uS0hyCHaNBiN1BJSq2eo2vQFTsPfDoTQaDb3P6+2ToVpCCCE6DwkdQpxGiqqK+PXQry4rSrXlu31qaNWMFPeqHAAJQQkAHC49jN1uJ6ssC1D7eHjr2MrG6TC8atMm2LoVTCa4/np17uHJD3NjrxupW1zHkrlLWHr/UrI3ZgMwcqSa35GdDYcPN97nwAGIQV0TNSQKncH9oW46ow57UDAACRwCwOYf6NUu80IIIbq2rv/xoBCnuZLqEm744gbMBjMrMlaQWZrJfePv4+mzn26znd1u5/v9ahK5Y98NdzjCRWVdJUXVRRRXFwMQ6hfq9r2OdWxl43QYXvXGG+p48cUQ1rCo05SCKRTdW8R3Od85r1v9z9VMe2oa4+4Zx5AhGjZuVLuUJyaq59PTYUxD6IgdGetxfzQhwVBSTAQF6oTR6PG9hBBCdH0SOoTo4v689M8s3r3Y5dwzq5+htKaUR6Y8QnRgy8Nr0grSyCjOwKgzMiV5ituvazaYifCPIL8yn8zSTEpqSgAI8Qtx+17HajaHoYtXOurr4aOP1OMbblDHA8sOsGjWIqy1VsJ7hzPgigHkbskl9YtUfvzTj1jiLIwdO4iNG2HNGrjsMrWMbkkJxKKGRHkTOrQmA3bAhBriptHLf06EEEK0Tv4rIUQXVW+r58V1L/LaxtcA6B3emwkJE+gW0I2nVz3NqxtfZV3WOjbevLHFYTE/7P8BgImJEwkwBnjUh4SgBPIr8zlccthZ6Qj2C/bsG2ri2MpGV5/TsWqVCgzh4TB5MhQdKOLDiz7EWmul35x+zP7fbAxmA3a7nZ8e+Ilfn/yVb+/4llH/6A4EsmaNuo9jEnmsJgfsEDPC86WLdQYd9TQJHR4M0xJCCHH6kDkdQnRR87+fz/wf5gNw28jbSL0jlbcufIunpj3Fj9f+iJ/ej81HNrP5yOYW2+86ugv+v737DpOqPPs4/p0+s70XylKlNwFFsKAGgw0sUbF3YxK7MdGY2JOY5LXGEhOjYq+xiwpiRREVRWku0pe27LK9TznvH8+eaTszO7Mzww5wf66La9o5Z86wo5zf3vfzPMBB/Q7q8TnoLVYVDRXUt6lKR7Yt8aFjb2+vevNNdXv88WA0aLx58Zt0NHXQ/+D+nPzcyVgc6vMbDAYOv+1wSiaU0FrTin3ZlwCsWKH237BBrSJu1TowO8wUjizs8TkZbSro6aHDaNm7g58QQoj4SOgQYi/U2N7IY989BsC9M+/ln8f8M+D1GYNncPyw4wF4fvnzXfYH2Fi/EYBBObGtVu3PO5jcr9KRiPaqLmM69uL2Kk3zhY5Zs2D5c8vZ+NFGLGkWTnzyRMy2wL8Lk8XEYTcdBkDFW99jxENzMzQ2wpYtauYqgPz98jGae/5PgMmqKhtWOgAwSqVDCCFEBBI6hNgLvbLqFVqcLQzPH85VU64KuRjfGWPOAOCFlS/g0TxdXt9Qq9ZxiGeK2/7ZKnRsafSN6UhIe5Vp32mvWr9erSJuscCMIz18ctsnABz6p0O962UEG3b8MNKL0mmubGKs/ScAtm+HhgbIpQ6AnEE5cZ2Xyaa+U95Kh1VChxBCiPAkdAixl3G6nTyy9BEAzp9wfthpTI/d71hy7DlsadjCCyteCHhN0zTvCuKDcuOvdGys20hTRxMg7VWx+kKtzcikSbDhzR+oWVtDWkEaU66YEnYfk9XEuHPHATDRvBxQoaOxUa0iDvGHDnNQe5XJuvcGPyGEEPGT0CHEXkTTNM569Sy+2voVNpONc8adE3Zbu9nO76b9DoCbPrqJDneH97XK5kraXG0YDUZvcOgJfUzHyp0rvc8lo9KxN7dX6YPAp02Dr/75FQBTr5uKNSPyFLXDjh8GQHGHWkdDDx05nZWO3EHxTV1stgW2V5mk0iGEECICCR1C7EUWb1nMy6texmK08Mppr9A3q2/E7a+achXF6cWsr13P22ve9j6vt1b1y+oX1wW93l61q1Wt5eAwO7Ca4l/PYU9ep6O1FXbujH57vdIxoXg727/djslqYuJFE7vdr8/kPhhMBuwdjWTRwLZtia10WOwqZBhRC03q7VZCCCFEKBI6hNiLfLJR9fvPHj7bO1A8knRrOjOHqtXGy6vLvc9vrNsIxDeeA6BvZmDoScQgctgzp8xduhSOPBLS0qC4GCZMgHnzIu/T2AjLVXcU9lXfAjDipBGkFaR1+37WdCvF44oB6EdFwisdFkfg37lZQocQQogIJHQIsRdZVLEIgEPKDol6n8E5gwFYX7ve+9yGuvgHkQPYzDaK04u9jxPRWgV7XnvVyy/D1Knw0Ue+577/HmbP9i36F8pXX4HHAwP6e9jwlmpRm3hx91UOXb+pqr2tP1vYvh1adrXhoA2AnIE5MX8OfxZHYMgw21M/+AkhhOg9EjqE2Eu4PW4+3/w5oBb0i5Y+UHx9nS906JWOeKbL1ektVpCYQeSwZw0kX7AATj8dnE444QQ1G1V1NZx9NrjdcO65sHFj6H1/+EHdHjaogtaaVhx5DgYePjDq9+4/Vf3d9+sMHe4a1Vplzk7rdkxIdyxBIcNsl0qHEEKI8CR0CLGXWFm1kvr2ejKsGYwvGR/1foNzu1Y6EtVeBb7B5JC49qrgdqpUba+qrIRzzlHVinPOgf/9DwYNUiuLz50LRxwB7e1w442h9y/v7Hgb2K7u7HfcfjGtraGvOF7ETrZvB0NdHQCOPvG1VgHY0gJDhkVChxBCiAgkdAixl1iwbgEAU/tNjekiXA8dFfUVON1OALY0bAGIa+Yqnf8x9rX2qmuvVcFjzBj497/B5HddbjLBPfeAwQDPP+8bu+FPDx32TWsAGDZrWEzvn9UvCwAbHVRv68DU3ABARt/4fw7WoPYqq7RXCSGEiEBChxApStO0mLZ99NtHAThpxEkxvU9JRgl2sx235qaioQKAbY3bALqd/SoaAaFjH2qv+uYbeO45dX/uXHA4um4zYYJquQJ48cWur5eXQw61OHfswmgxMnTm0JjOwZZpw9LZRuWub8TVrMZzpOXZYjpOyGOnBc0g5pBKhxBCiPAkdAiRQsqryxn3r3E89NVDzH5hNmX3lrG9cXu3+3208SPKd5WTYc3g7HFnx/SeRoPRO3Zjfe16mjuavauH98nsE/uHCOI/piNhs1ftAZWOP/5R3Z59tlrYL5xTT1W3//tf4PMNDWptjf6oIFg6sRRbVuxhIbM0Q93SiLlzLZb03ASEjvSgSoeEDiGEEBFI6BAihdz00U0s37mcy9+9nLfXvE1FQwX3L7m/2/2e+v4pAM4Zdw6ZtsyY39d/XMfWxq0AZFgzyLJlxXysYP5jOhJV6Uj1MR2rVsH8+WA0wu23R972+OPBaoUff1T76daojiqGO1To6D+tZ61umaXq+5BJE9bO1cMz8hMROgL/zq1pqfUzEEIIkVokdAiRAt4qf4vjnzuel1e93OW1v3/+d8743xl8s+2bsPv/WP0jADMGz+jR+/uHDr21KhFVDkjSmI4Ub6968EF1O3u2Gjjuz+1001bX5n2clQVHHaXuv/mmbzt9PMcAoxpfo09/G6uMzkpHBo3Y0Csd8S/QaA+qdAQPLBdCCCH8ya+mhOhlLo+Lc18/l7q2OkCtsbG9cTtl2WVsb9rOj9U/8sKKF6hqruKDcz8IeYx4p7jVg8HWxq1sbVCVjuCF/XqqT2YfDBjQ0PaJ9qrmZnhKFZ644grf8zu+38EH13/AuvnrQIM+B/ThyD8fyZCfD2H6dHjnHfjuO9/25eVgpYOMlkrAN/1trDL7+Fc6VOjoSZtWMHuGVDqEEEJET/6VEKKXLd221Bs4pvabyiPHPcLootEALNq8iHNfO5cNdRv4Zts3aJqGwWAI2L/V2Upls7ow7ekUt0XpRQDsbN6Z0EHkoAJBaWYp2xq3JW0geSq1V82bp4LH4MFqSlyAH1//kVfmvIK7w+3dbtvX23juuOc45aVTGDduJOBblwNg0yboy1YMmkZW/yzvTFSx8lU6mrB1tldZM+OvdASP4QiufAghhBD+pL1KiF62YL2a6vbkkSfzxUVfeAMHqKpH+eXl2Ew26tvrWVe7rsv+m+o3AZBly+pxJUEPHVXNVd4xHX0yEtNeBXDkoCNxmB0xrR8SSZdKRwq1V73c2SF36qlqOtwNH23gpVNewt3hZr9j9+OyHy/jtzt+y5jTx+BxeXj1zFcZlKcG7q9ZA62tav/qaihGhck+k3v+s/CN6Wj0VToy4690BC8GKKFDCCFEJBI6hOglLo+L+768j5s+ugmAowYfFXI7i8nivVhfum1pl9f9F/ILroJEy7/SoYeORFU6AJ468SmqfldFWXZZQo4XXNlIlfaqlhbVJgUqdDRXNfPqWa+iuTXGnD6G0984nYLhBWQUZ3DSMycx4LABuNpcrPjnh+Tnq0UEV69W+1dXQz7VABSMKOjxOWX4zV6VyEqH2Rb4MwhutxJCCCH8SegQopc8t/w5rnn/Gu/jSIPAJ5dOBgg5mDwRq4cHhI7OMR2JGkgOYDAYSLemJ+x4qTqQ/IMPVPAYNAgmToQF1y2gaXsTBSMLmP3Y7IDVxI0mIz+/5+cALH/mBw4ashPwtVhVV0MBuwDIH57f43PSKx3+7VWJGNNhsgVNmSsDyYUQQkQgoUOIXvLlli+9948fdjxDcoeE3XZSH7XQw1fbvury2obaDQAMzB7Y43MpTC8EwOlxsqpKzduaqIHkyRBc2UiVMR0ff6xuZ86EHcu28/3T3wNw4twTsaR1DUZ9JvVh+OzhAIzRVgCBoSO/M3QUDO95pUMfSO6gDQeqdysh7VVBlQ6zTUKHEEKI8CR0CNFLvt3+LQDP/+J53jrjrYitUQf1OwiATzd9ynmvnxewWvnG+o1AfJUOu9lOplVdnCZyYcBk8a9sGDBgMqbGBa8eOqZPhw//+CFoMOaMMfQ9MHyAG3XqKAAyt6i+qpUrob0d2hrayaIRiK/SYcu2YbKrgGBGDWRPRHtVcKUjOIQIIYQQ/vaJ0HHSSSeRm5vLKaecEtNrQiSLy+Pi+0r1W/BJpRGWq+40qnAUfz7iz5gMJp76/il+qPRNc5SI9irwtVgBWE3WgEX9Uo1/ZSNVxnPU1sKyZer++L7VrH13LRjgiDuOiLjfsOOHYbQYcW2vpoAqqqpg1y5flSO9KB1HrqPH52UwGLyrkusSUekwWQNDR3AIEUIIIfztE6Hjqquu4il94vwYXhMiWVZXrabN1UamNZMheeHbqvz98bA/eme22tG0AwBN01hXo2a0GpAzIK5z8g8dw/KHpUz1IBT/oJEqrVWffQaaBsOHw4aXVBvc8FnDyRuSF3E/e46dwTPU4ozDKae2NnHjOXT6uA4AzWDA7Ij/7yy4shEcQoQQQgh/+0ToOPzww8nMzIz5NSGS5ettXwMwsXQiRkP0/xkWpqmxF1UtVQCsq13HrtZdWE1WRhWOiuuc/EPHiIIRcR0r2fzbq5IxiHzTJrjlFjj3XLjxRtiypft9Fi1St9OnOfn+SVXFOvCKA6N6v4GHDwSglB3e0KHPXJWI0JHhV+kw2Kw9nuXMn7RXCSGEiEWvh45PP/2UWbNm0adPHwwGA6+//nqXbR566CEGDhyI3W5nypQpfPVV18G0Quxu2xq38YcP/sDO5p3UtNZQ31Yf1X6/X/B7LnrzIkCFjljoA76rmlXoWLRZXeke0OcA7GZ7TMcK5h86RhaMjOtYyeZf6Uh0e9V//gPDhsHtt8PTT8Odd6rH+vob4egDwEdZfqKjsYOcgTkM+ll0K8QXjytWt1RSXw+VlZCD+j7lDs7t8WfR+YcOU1r8rVUARrMRze+xtFcJIYSIpNd/NdXc3Mz48eO58MILOfnkk7u8/uKLL3LttdfyyCOPMGXKFO677z5mzpxJeXk5RUXqImnChAm4XK4u+86fP58+fVJ3MKzYs/3l07/w8DcPU9FQwccbP8ZmtlF+eXm37T7P/PAMoC7sL9z/wpjeU6907GxW06vqoeOQskNiPf0u9qRKR8CYjgRWOv7v/+D3v1f3DzsMjj0W3n5bVTHOPVdNhTt5cuh9ly9Xt/Z1avavUaeOirqiUDRW/d3nswszLtauNZNGC6DGdMRLn8EKILsoMaHDYDDgMZoxedT/e6XSIYQQIpJe/1fimGOO4Zhjjgn7+j333MMll1zCBRdcAMAjjzzCO++8w+OPP84NN9wAwDJ99GYStbe3097e7n3c0NCQ9PcUqanN1YZH83inr312+bPe19bWrI14we7RPN7AsOCcBTEvwBfcXqWHjkPLDo3pOJGODakfOvyDRqLGdMybB9dfr+7fdhvcdJNaUfx3v4MTTlDh4+yz1exSpqBf6tfUwLZtYMbJri/XAL5ZqaKR2ScTR56D1ppWCqhizZpSX+goTEDo8BvT4ciOf+YqnWY0QWfokDEdQgghIun19qpIOjo6WLp0KTNm+BZNMxqNzJgxg8WLF+/Wc7nzzjvJzs72/unfv/9ufX+RGpxuJ2P/NZbRD48OuVDf8srlbGnYEjClrb9dLbtwa2raUv/KQrT0fapaqqhqrqJ8VzkA0/pPi/lYwfwHjg/PHx738ZIp0e1VDQ1w8cVqIPill8LNN6vAAWA0qjarnBwoL4c33ui6v17lOKhoA85mJ9ll2fSZHH2V1WAwBLRY/fQT3tCRVpAWz0cDAturEjFzlZdf+jJaUvqfEyGEEL0spf+VqK6uxu12U1xcHPB8cXExO3bsiPo4M2bM4NRTT2XevHn069cvILBEes3fH/7wB+rr671/KioqevahxB6tfFc5a2vWeqepDXb+G+fT/97+PL/i+ZCv67NOFaQV9Ohi2X9Mx+b6zYBaxC/XEX/ff0GabwG6RK4engyJHkh+662wfTsMHQr33df19ZwcuOwydf9vf1PhxJ8+nmNs5kYAhhw9JObB2nqLVTJCh3+lIxFrdOg0k6oyeYymhAxOF0IIsffq9faq3eGDDz7o0Wv+bDYbNlsCf0Mo9iiN7Y28sOKFbi+sWpzqQvHa96/lzLFndnldDx3F6cVdXouGf3tVQ7tq8cuyZfXoWMFOGXUKS7Ys4fCBhyfkeMnk31IVb3vVli3wwAPq/gMPgD3MePwrr1RjPr7+WlU8Rvh1oOmVjsLmjYBvNqpY6KGjiCrqa9zYUe2cCa90ZCW+0uFJkWmLhRBCpK6U/peioKAAk8lEZWVlwPOVlZWUlJT00lmJfdH1H1zPv775V5fnL9r/IjrcHWRaM3n4m4e9z5dll4U8TmWz+i6XZPTs++tf6WjsUKtVJyp0mI1m7j363oQcK9kS2V51773gcqlVxI8+Ovx2RUVwyCHw4YewYEFg6Fi1Cuy0YaxUoXLg9IExn0dWX/VzTKcZR2eVA6MBe058s5IBpOWnYbQY8Tg9Ca10YO78JySF13QRQgiRGlK6vcpqtTJp0iQWLlzofc7j8bBw4UKmTp3ai2cm9jVzl80N+fyEkgk8ddJT3Dz95oDn9SpEML3S0ePQ0VnpqG+vZ1eLWjwu07bvrTOTqPaqujo1RS74BpFHctRR6nbBgsDnt2yBMjaDppE/LD9gtqhoOfLUquN22kjvDB22nDQMxvjblgxGAxklqtqRyDEdBrMKG1rwyHohhBAiSK9XOpqamli7dq338YYNG1i2bBl5eXmUlZVx7bXXct555zF58mQOPPBA7rvvPpqbm72zWQmxOwzNG8ryncu9jy8/4HKanE1ctL9ab6M4I7BdalP9JjRN69KOFW/oyHXkYjKYcGtu1teuBxJX6diTGAwG799DPJWOF1+EpiYYPTqwytG4rZFlc5dRu6GWrH5ZTL50MhklGRx1FPzhD/Dxx+B0gsUCHo+auWo6aoxN2WGhq1zdseeqioaDVu94jozi+FurdJmlmTRUNCS00mHQKx2mXv+nRAghRIrr9X8pvvnmG4444gjv42uvvRaA8847j7lz5zJnzhyqqqq4+eab2bFjBxMmTOC9997rMrhciGSqa6sLeHz7Ebd3Gbx902E38eLKF1mzaw1trjZ2Nu/sEkbiDR1Gg5H8tHx2Nu9kXe06ADKt+16lA1Q7mNvtjmtMx9NPq9vzz/fNVrVs7jLe/tXbuNvd3u0W37WYk54+if1njyA/H3btgq++goMPVquHO51qADhAn0k9WxvIkatXOtpJpwmAjMLEhY7ssmy2frWVtPzEHdNo6axwmKXSIYQQIrJeb686/PDD0TSty5+5c+d6t7n88svZtGkT7e3tLFmyhClTpvTeCYt9jtvjZlvjtoDnQs0WdfsRt1N+eTl9M9XaG19v+7pLWNHHdPR0IDn4Wqz25UoH+MZy9LS9av16+PxzFTbOOEM99+V9X/LGBW/gbnfT76B+HH7b4fQ5oA8dTR28etar7PxhB3pnpz5j1bbOr0apsfNnO65nP1u90gGQRy2QmEHkuum3TOfgGw5m9GmjE3bMghIVNrLzJHQIIYSIrNdDhxC7g0fzUNlU2f2GQZ5f/jx3L77bu7bGoJxB3HzYzRH3GZAzAIBZz89iyn+nBKzZEW+lA3yDyff1SoceNnraXvXyy+r2yCOhb19YN38d8387H4BD/3goF35+IdNvns5Fiy9iyMwhOFucvHrWq+w3VP089a7QrVtVS1SGRw3sLxoT+/orACaLCYNNfZZ81HidtARWOorGFDHjzhkJGZiuyy9SVabcgl4vmgshhEhxEjrEXm1Xyy6cbidXzLuCkrtLWLJlCa7OFZS70+5q58xXz+T6D9QI47LsMtZftZ7bjrgt4n4Dsgd476/ZtQaP5sHtcfPSypdYsXMFEGfo6Kx0VLdUA1Lp6Gl71fvvq9uTToL2xnbeuPANNI/GhAsncMQdR3gHcBtNRn7x3C+wZduoWlVFvxa1IOM6lfnYtg2KOlurcgbmxDUlrSVLtVh5Q0cCKx3JYLKZAm6FEEKIcCR0iL3WtsZt9L2nL7NfmM2XW78E4N2171J6dykXv3lxt/vXt9cHPO6fFd0q9P6hA8DpcTJ/3XzmvDLH+1wiQoduX5y9CnxhoyftVU1NsGiRuv/zn8Mnt39C49ZGcgfncuyDx3aZAMCR52DyrycDoH36OaAFVDqK2Qn41troKVu2Ch151ACpHzrMNvUzMFkldAghhIhMQofYa63YuYJ2dztfVHzhHZPxZvmbVLdU897a97rdv7G9MeBxuLU3gtnNge0rLo/LO5YDIM2SRn5aflTHCqUoPfDCdp+tdMTRXvXJJ2rw98CBUORoYMn9SwA45oFjsDhCH++gqw7CaDHS9OMW8qlh3To1c9XWrb5KR7yhQx/XkUaruk3x0KFXOPTwIYQQQoQjoUPstfT2o4b2Bu9YipVVK72v3fflfez3wH5srt8ccn998T1dtJWOM8eeicng+82vy+Oi1dnqffz8L57HaOj5f3r6mA7dPjumI472qvlq6AYzZ8KS+7/E4/RQdmgZ+x27X9h9MkoyKDtEBc+hhnW0tanWqm3boBD1XevpeA5ddrEj4HHKhw6rtFcJIYSIjoQOsdd57NvHGPHgCL7c8mWX1zrcHQC0u9u55v1rWFuzlts/uT3kcYIrHVZTdOsb7Je/H21/avM+dnlctLnU4zPHnsns4bOjOk44we1V+3ylowftVZ9/rm6nH9TG0n8vBeDg6w/udr/BRw0GYIxDzRy2bp2qdGSjWvFyB3Wd1SwWGYWBVbLMvqkdKKXSIYQQIloSOsRe5+K3LqZ8VzkPfPVAVNv7zy7lL3hV8fEl46M+B7PR7K1m+IcOuyn+mYO6VDr28TEdmsvCW2+pVcKbm7vfr73dN91t3vaVdDR2UDCygP2OCV/l0A05aggApR0bMeJh7VrYtlUjExVQe7ISuT99VXIADJA3NC+u4yWbjOkQQggRLQkdYp+Xbk0P+bzeXtU3sy9PnPAEvxj5i5iOq18UuzwuWl2qvcphcUTaJSpS6VDMBlXheOYpC7NnqwHh/frB//4Xeb8VK9R4jrw82PaeWmV+wvkTvLNVRVKyfwn2XDtmVzt92Ep5OTRXt2DCA6gWrHj4r9WRMyAn7PiSVCGzVwkhhIiWhA6xz0u3BIaOyqZKbv/kdlZXrQZgUp9JnD/h/C4zGnXHP3R4Kx3mJFQ69sExHR0dsH6tuiD3uMwMG6bW2qirg1NOgWeeCb/vN9+o22mj6tj86SYwwJgzxkT1vkaTkf7T1NieEirZsQNvlSOtMD3u3/jrq5ID5A/r+WQDu8uQnw8hq38W+x3XfZVICCHEvk0accU+z6N5Ah6f89o5LFi/wPu4p5WEZIWOfEc+BgxoaHGd357s17+Ges0CmXD8sRbevAxcLrjmGnjoIbjySpgxA0pCzEy8VA3hYLxFTSowcPpAsvtnR/3eefuplqdcaqivh6wEtVZBYKUjf3jqh44Bhw7gms3X9PZpCCGE2ANIpUOknIr6Cr7e+nVM+3g0D1fMu4Jnf3g25vdr6mgKeOwfOKDnlYRQocNhjr+9ymQ0kedQF75Gg5E0S2rPcJRoL70Ejz8OaOrvd/QICwYDWCxw330wcSLU1sKNN4beXw8dOdVqdb8RJ42I6f3zhqi/+zxqqa+HTNTYn6x+8YcO/zEde0KlQwghhIiWhA6REjRNY3nlctpd7Rz//PEc9NhBLK9czlXvXsW327/tdv+317zNg18/yNmvnR3ze1c0VDD8weHcuFBdpQZPZ5uI0KGP6UhEpQN8LVaZ1syY2772ZDU1qsoBMKis65S5ZjP885/q/gsvqHYrfx6PGtNhwUnrj2qq5CEzh8R0Dvrg7jxqaGggYYPIIai9ag+odAghhBDRktAhUsL7695n3CPj+O3837K+dj0ezcOJL57IP7/6J5P+M6nb/eva6nr83m+teYs1u9Zw56I7AbCZbAGv93R2qGS1V4FvMPm+NnPVffep4DF6NAzfL/SUudOmwZgx0NoKzwYVvrZvV+NBBhk34XG6yS7LjrmiEBA66jVfe1UCpre1ZvqmZZZKhxBCiL2JhA6REtbsWgPAqqpV3nan9bXro94/mov5QTmDut3G6XZiMweGjlQb0wG+Sse+NJ6jthbuv1/dv+02sJlDr0huMMAll6j7jz0WeIwNG9Tt+Iy1AAz++eCYK0XZA7LBaMCCC3ddY0IrHf5jS2IZZyKEEEKkOgkdolc9v/x5rnnvGu+aGNsat4Xcrqa1JmIICa5O+D8/omAEufZcpvWf1u35bG3c2rXSkYj2KmfipswFX6VjXwodjz4KDQ2qinHSSb6wEWpxwNNPV7fffafCim7jRnXbX6sAYPDPBsd8HiaLCWthDgDmhhpv6MjqG//Pwpph5cr1V3Lt1mujmsJXCCGE2FPI7FWiV5356pkADMsfBsCWhi0htyu5qwSnx8mmqzdRll3mfb6yqZJPN33aZRyGrjC9kK8v+Zp2VzsPff0QAAOyB7CpflPI7TfVbepS6UjF9qqi9CJ1bvvIdLkejwodoGaoMhrxDqC3O+2sfW8tJquJvlP6Yk23UlQEQ4aoFcOXLIGjj1b7btgAJtxkNlcC0PfAvj06H3ufPDoqa8l01SS00gHxr2ouhBBCpCIJHSIl6O1Vzc7QS0o7PU4APtv0GWeNO8v7/IH/PZDN9Zs5qN9BIfcrSCsgw5pBhjWD8yecz8a6jRw56EjOee2ckNtvrt/c5blUbK/qm6kulgvSChJyvFT38cewdi1kZsKcOeq5KyZdQcFrBTT8vYFnW9XgDXuOnVmPzmLUKaOYOlWFji+/DAwdRezE4HFjz7WTMyinR+fj6JdLw3dQwC4yUN/ZjNL4FgYUQggh9mYSOsQepcXZEvBYDwlfbvky5Pb+F+Vl2WU8fsLjYVu49OMFT6GbalPmApw+5nS2NGzhjLFnJOR4qW7uXHV71lmQng4el4e1V6wl640sXLjIGZSDu8NN49ZGXj71ZU56+iQOOmgczzyjQodu40bog/r595ncp8czfzkK1IKSGfi+K9YMa7jNhRBCiH2ejOkQu53T7eSp758K20oVSXDo6E6+o+sMQKGe022q30Rje2PAc4lor0r0lLnZ9mzuOPIORhWOSsjxUpnbDe+8o+6f0Zmx5l0xj/I3yjHZTJz45Ilcue5KrtpwFQdcdgAA7175LhOGqkDw5ZeqPQtUpUMPHaWTSnt8TlaH+tnaaPc+Z7bJ73CEEEKIcCR0iJjtaNrBXV/cxa6WXbxZ/iYL1i3ofic///fF/3He6+dxwKMHxPze+sV7d2wmG0Nyh3DqqFO7vma2cemkSzmw74FdXvup5idvK5cu3vYqp9uZ8PaqfcnixWqa3NxcNR3u6tdWs/SRpWCAXzz/C8afOx6DwYDJYuLo+46mdGIpbbVtVL2wELsd6uth/Xq1YnlFRWClo6esDhPgCx0aBoxm+d+pEEIIEY78ak5E7YuKLzAZTLxR/gZ3LrqTHU07uHvx3QC4bnJhMpqiOs4rq14BVHiJVbSVjiMGHcG7Z70b9vVHjn+E+rZ6cv6eE/D8yp0ru2yb0PaqBM1etS95+211e8wx4Gpq4+1fqicO/v3BjDxpZMC2RrORo+8/micOfYKVL65gaL+ZrFhrp6JCLRzocWsUUgVA6f5xVDrS1M/Wjvq5eqL87gshhBD7KvnVnIhKm6uNGU/N4Kinj6KqWV20bazb6H198ZbFnPm/M1lXs67bYzV2NHa7TThNHU18sP4DGtobaHe1h90uw9r9oN50a3qX56paqro8l5D2Kmdi26v2JfPmqdvjj4cl/1xCS3ULBSMLOPy2w0Nu3//g/hSOKsTV6mK8cTkAW7dCZaVaPdyMG4PJQHZZz9fBsKUFVTpM8vsbIYQQIhIJHSIqje2NtLpaaexopMmpeuXdmtv7+qFPHMrzK57nxBdPDHsMt8dNQ3tDlzETsXjq+6c46umjGPbAMFbsXBF2u3RL10ARzGw0h13fI3i7nvC2V3mkvaqnamthucoNHDalnS/vU6PCp98yPewYCoPBwMRLJgLQv/o7QIWOxkbIQS3akV2WHVc7lD0jaEyHhA4hhBAiIgkdIir+4xz0FqdQrU4rdq7g/NfP5/cLft/ltdkvzKb07lIqO9dI6IldrbsAqGyuZOYzM8NuF02lA0JXOxJFDx2tzlY0NEBCR6wWL1a3w4ZBxZvf0VbbRv6wfEadEnkA/ZgzxgBgr9mOnTa2bdNDRx0Q/1oYtvTg0CHtVUIIIUQkEjpEVJxuX+jQW4WaO0KvqfHk90/yf1/8H3VtdQH7z/tpXsyzT0WiB5BQog4dfhWR0oye9/iHoocO/yl4EzVl7p6quVmtEt4YZbHriy/U7bSpGkv/sxSAKVdPwWiK/L+ujOIMcgerYNGXrd5KR25n6Mge2PPWKgB7ugoZZjqrfWapdAghhBCRSOgQEX2++XMOePQAPtv8mfc5fQap7gLEqqpV3vvlu8qTc4JhRNNeBYHhZHTR6ISegx46/MewWE375loOS5fC7NmQnQ0TJ0K/fvDXv/qmsg1HDx2TiiuoXl2NJc3C2DPHRvWe/Q7qp27Z4tdeVQfEX+nQ26u8zFLpEEIIISKRX8+JiA554hCAgBW89bARbvVw3Zvlb/LyypfJsedEPbNVosTaXqVPsfsBHwBwzNBjOG/8eUwsndjjcwiudNjN9h4vRrcnW7ECjjjCV93IyICGBvjjH2HNGnj8cTCG+PWHywVLlqj7WeuWsQsYPWc09uzoWtT6HtSX5c8tpx9b+DQodPR0JXKdNS3w+2ywyP9KhRBCiEjkX0oRM2/oCNNepfv753/fHacTUrShQ98u255N38y+3uczbZnMGTMnrnMIDh37YmvVzp1q1qnGRjjkEHj0UTU+47HH4Ne/hiefVIHkvPO67lteDi0tkJmhsfOzNQBRVzkA+k/tD6hKx/ZtGvX1BnI7B5LnDMyJ63NZ7IH/6zRKpUMIIYSISNqrRMyirXQkU3crccc6piPHnkO/rH7e53u6Noe/UJWOfUl7O5x4ImzaBEOHwuuvw4gRqqpxySXw5z+r7W67DZzOrvuvUTmDg/pvpXlnM7YsGwMOGxD1+xePK8ZkM+GgjUx3LRvWucmiAYi/vcocHDqs8vsbIYQQIhIJHSJm0VY6APpk9mHWsFkJP4dJpZMivh7trFTeSoctm75ZfpWOBIQOi9EC+MZ07Guh48EH1exTOTlqgb/8/MDXr7gCiopgwwZ45pmu++uhY6RRjQcaesxQTNboKwomq4mcATkAZNPA5uUNGNHAbCKjJLpQGvbYtsDzkNAhhBBCRCahQ4R01btXceW7V4Z8TZ+9yn8a3XCm9pvKOePO6Xa7WJiNZsYWRW6zibXSEaq9Kl77cqWjoQHuvFPdv+ceGD686zbp6XDNNer+k092fb28c+6BvOqfABg2a1jM55HZV/0cM2lkxzoVko1ZGRiM8Y2tCV4jxBhDGBJCCCH2RRI6hFd5dTlnvXoWX1R8wT+/+icPfPVAyO1imfZ2zug5nDTyJC6ccGHCKh6FaYWUZZdF3CbWgeTZtuyA9iqTIf6LyC5jOiz7zpiO+++HXbtUO9U5ETLnmWeq208/VQv4+VuzBhy0qqXEgSFHDYn5PDL76KGjAYNTralhSut+QcjuBFc6TGEWKhRCCCGEIqFjL/fc8uc4fO7hVDZ1vyDfo98+ynPLn+PPn/454nb6QneR/PmIP/P0SU9zyqhTMBvNPHbCY/zruH9Ffd6RFKUXBQSEUGIeSG7LJsuW5X2+ob2h5yfYyTtlbvu+1V7V0gL//Ke6f8stkZewKCtTA8w1DV58MfC18nLoRwUA+cPySS+KfSFH/0qHjQ4ALOnxT1scXOmIpe1LCCGE2BdJ6NjLPfLNI3yy6RM+WP9Bt9tua9wGwMqqlXG/78yhMzl73NkBU8QWpRdF3Md/HEVhWmHY7YrSi+if3T/s6zaTLeqF/o7d71gG5QzixBEnBpxrfXt9VPtHsq+2Vz35JFRXw6BBcMopga9pmkZzVTMet2+BjtNPV7dvv+3brqZGHaOsM3T0Pzj8zzsSvdKRRSPWztXDrRnxVzqCB5Kb7RI6hBBCiEikJ2Av9faatxmeP9w7iNl/VexwdjTtAGBz/ea43z9UwLCYLOQ58qhprQm5T5/MPpTvKsdhdpBjz6GqpSrsscOFigePeZAjBh1BriO62YkOKTuE9Vet9z4+eujRvLf2PX456ZdR7R/Jvjpl7sMPq9trr/VVOXau3MniuxdT/mY5rbtayR2cyxF3HMHYM8cybZra5ocfVMXDYICf1DAOhloroAPKDoncThdOVl9VvfKvdNiy4q90BLdXBVc+hBBCCBFI/qXcC63cuZJZz8/igD4HeFt7mjqa0DQt4uJ0euhIhHCViuL04rChY//S/XF6nIwrHsemuk1hj12UXoTFZGHG4BldKjiDcwd3O51uJG+e/iaVzZXdtm9FI3hF8n2h0rFunVoM0GSCs85Sz23/djtPHvEk7Q3t3u1q19fy6lmvsvXrrRz2l5kYjQZ27VLDN0pKYO1aMOGmyKUGevS40uHXXmXtDB2O7PgrHUazEQ3Q/2uyOKTSIYQQQkQi7VV7oS0NWwCoaKjwXvBurt/MwPsHcu3714bdr7K5+3Ef0ciwZoQdNB2pxaowrZA1l6/h1dNejTgmQz/G+2e/z/JfLw94zWqK77fYFpMlIYEDfKGjzdUG7Buh46231O1hh0FuLtRX1PPM0c/Q3tBOv6n9OO/j8/j9rt9z6J8OBWDJfUtY/+ZKhg5V+61YoW537oR8qjF5XNhz7OQPyw/xbt3zDSRvxNbZXpWWE3+lw2AwoBl9v7MJXixQCCGEEIEkdOyF9HaehvYG7/2Hvn6IzfWbuffLe0Pu0+5qD1uBiFWkYFGcURz2tQxrBiajCYPBEDF06Gt0GA3GLutp2Mzx/xY7UczGwAvRfSF0vPmmuj3hBHC1u3j5lJdpqWqheHwxZ793NgOnD8SR5+DIO47ksJsOA+DTOz5lzGg1OYEeOqqrIZ9dAOQPz49YoYsks1R9P8y4yUaN00nPiz90AGgmX3XD4pDQIYQQQkQioWMvpAeNFmeLd3pbt+b2vu72uLvss7N5Z8LeP9Ig8AsmXMCw/NDrLfgHjVBjMmYPn83Wa7dy1JCjvM8Fh4x4Kx2JFBw69vYxHfX1aupbgFmzYOl/lrL1q63Yc+3MeW0OtqzAn9XU307FnmOnalUVY02rgDCho4dVDlCzSjkK0gAooBqAjPzEBFP/Soc1TdqrhBBCiEgkdOyFuhs0rrdRaZrGc8ufY8XOFQkZzzG6cDQH9TuISyddGnabo4cezdJfLg352vji8d771x98PVdPuTogiNhMNvpk9gnYx2bac0LH3l7pWLgQ3G61NseAfm6++L8vADjyL0eSO6hriLRn2zng8gMAyFy3DAgOHaryFk/oAMjqpwaT66HDnp2g74jfXMBWqXQIIYQQEUnoSFEuj4sTXziRv37215j37S50bG1Qg3Pnr5vPWa+exbh/jePRbx/t0Xn6G5I3hMUXLeaC/S+IuF3wxfiEkgns+O0Ojht2nPe5ccXjuPfoeynJKPE+ZzFZuhwruNIRHEJ6074WOt5/X93+/Ofww7M/0FDRQEZJBvtfsH/Yfcafo4Jm8w/rSKOZlSvVDFaJqnQAZHUOJrfiBMCWmaDviNlX3bBJpUMIIYSISEJHipq/bj5vlL/BHz/8Y8z7dhc6Hv/ucS558xLmfj8XUIv9JSJ0RLsgX/DFuMVoCTvWw2L0BY1QVYw9qdKxN69Irml+oWOGh0V3LgJUC1Xwmhb+8oflUzqpFM2tMYpVNDVBa2tiQ0d6ceCigtbMxFc6bOlS6RBCCCEikX8pU5TR4MuDHe6OmC6mm53NEV9/ZOkjPT6vSNIt0a0YbTIErXFgDP819K9u+AcQ77GMJkwGk3fMSiqHjj2p0uHxQEMDbNkCI0eqKXAjWbMGNm0CqxVKalfzzU81OPIcTP7V5G7fa8wZY9i+dDsjDeV8ox1ATQ007mwlHTUeKW9oXlyfJaM4MAwnqtJh8K90pEulQwghhIhEKh0pyn9Wpqrm0IvkhRPNQoD+fjv1tzFtH060lQ6DwRBwQR4xdBgjhw4IvJiX0BGf+no44ggVMnJzYexYOPxwNYVtJF99pW4PPBC+e3gxAFOumoI1o/ufx4BDBwBQalDjiqqrgRpV5UgvzYzqGJGkFyWn0mG0+H6+dql0CCGEEBFJ6EhRLo/Lez/cytxbG7ZywRsX8O32bwOejyV0TCiZwJzRc7yP45lhKdpKBxB16PAPEeEChf+4Dpkyt+fa2uAXv4CPP/Y9ZzbDokVwwAHw/ffh912lJp9i/MA6ti7ZisFoYNKlk6J638LRhWCANE8zaTSzfj3keGoByN8vvioHdG2vSlSlw2j1Dx1S6RBCCCEikdCRopwep/d+uOlsn1v+HHOXzeWBrx4IeD6a0FGaUcrxw47nv7P+y6Q+vovDsuwyAHLtuTEPyo620gHRh46A9qoQA8khcFxHKlc6UnnK3MZGOOYYNQNVRoYKGjU18MMPMHQobN4MRx6pWq5CWb1a3Q5oVncGHDagS1tTONZ0K7mD1exWxeykvBzSUd9hfRB4PILPI2GVDqsvaDgypdIhhBBCRCKhI0U53d2HDn0xv+BF/aIJHWePO5u3zniLSX0mYTQY+d9p/+OssWdx/cHXA1CYXkh+WmwDeNOtia90dDeQHAKrG6kcOlK50nHbbarCkZmpVhU/+GDVXjVypGqdGjxYhZA33gi9vx46TOXqzshfjIzp/YvHqokEiryhQ43nSOtcYyMewe1Vyah0yOKAQgghRGQSOlJUNJWOhvaGgFtdNKFj/5LAaUxPHnkyz5z8DIcNOAybyca0/tMiLvIXSiztVf5hIp6B5OCrdBgNxojH2t32lNBRVwf//re6/+yzagyHv9xcOPdcdf/557vu394Oa9dCOs00rqoAYOTJsYWOorFqFfsiKlmzBtL00FGYgNARPHtVnGNEdCa/SofJJu1VQgghRCQSOlKUf6Uj3EDyxo5GAOrb6gOejyZ0jCocFfL5IXlDqPpdFY/PfpzrD76enw/5ebSnnJz2KmMU7VWdlY5UqnLAnjNl7iOPQFMTjBkDxx8fepszzlC3CxZ0DvT289NPararkY6NABSPKyazT2xtUUVjVOgoZmdg6EhApSMtP/AYRnNi/rdntplD3hdCCCFEVxI6UpR/pePtn97m8nmXd2mj6kml42eDfsaFEy5kXPG4sNtk2jIxGAycMfYM3jg9TD9NCElprzJF0V5l2jNCRypWOn76Cf78Z3X/uuvAYAi93bBhMHEiuFzwyiuBr+mDyMdlbgBg4BEDYz4PvdJRSBW7dmne0JFeGP13KhyDMcyHipN/dUMqHUIIIURkEjpSlH+lY8XOFTz09UPc9cVdAdv0JHQ8OutRHjvhMQzhri6DhGtpCmVo3tCot03klLl6pSOVViOHPSN0XHghNDeraXLPOSfytqefrm6DW6z08RylbRsBGHTkoJjPI6tfFgA2OrDgIh211kwiKh3J4j+OQyodQgghRGQSOlKUf6VDFzy2Qw8b9e3Rt1dl2bJiOg998b1I/n38v/nxsh8Zlj8s6uNGMytVtNvtKZWOVJu9at06NUuV2Qxz54IxxP8NPG6P9/6czpmVP/tMLRqo27gRMmnE0rALg9HAgMMGxHwu1gwrmNQJOGhN6JiOZDHbpdIhhBBCREtCR4ryr3To+mf1D3ish44Odwftrnbv/VCBRZdpi30K0kihACDfkc/wguExHTOg0mFIzOxVqRY6giszqVbpeP99dXvwwVBW5nt+6aNLefqop7m7z938xfEX3rzkTTqaOigrg0MOAU2Dl1/2bV9RAf3ZDEDx+GLsObF/ToPBgCVThbI0mnHQqu4nqNJhtie+ElFYIpUOIYQQIloSOlJUqODQ4mwJeOzfVqVXOyJVOWwmW48uzLvbp7tQEkpC26s6Kx2ptDAgpH57lR46Zs70Pff1v77m7V++zfoP1tO0vQmP08N3//2O/x70Xxq2NHDMMWq7b/3Wo6yoUFPdApTsX9Lj87HlqtCRRw1681/wIPCesqTF/h3tTn6xr7qRjFAjhBBC7E0kdKSoUJWO4EChz14FvgASKXT0pMoB3YeOngSZhA4kT9FKRyqHjo4OtRAgwNFHg8fl4cM/fci7l78LwJSrp3DRlxdx9vtnk1GaQdXKKuZOn8ug/i4ANqgx42iaCh3FnaFDX2+jJ9LyVegoYBcA9lx7wmaa6ntg34Qcx59/dUPaq4QQQojIJHSkqFCVjmZns/e+y+MKqHzo0+aGCh16JSDT2rPQ0d1g8lgGm4faJ+4pc/eUMR0pNGXuhx+qAeRFRTB+PCz62yI++8tnaB6Nyb+ZzMx7ZtJvSj+G/HwIFy2+iIzSDGrX1+LYqEaNr1+vjlNTA62tvkqHPvVtT2QUqr+f/M7QkYiZq3SzH5/N+HPHc/GSixN2TL26YTAZMJrkf6VCCCFEJPIvZYoKVenQQ8edn93JhW9cGPBacKXD/7fqJRmq5SXWQeS63qx0+B+72/aqFJ69yoChR+EsWZ58Ut2edhq425x8ed+XABzzwDEc99BxAbOb5QzIYdKlkwCofl/1VW3frsJGRQWYcZKHms45ntCRWaRXOtRCIImcuSqzNJMTnzwxoRUPvboh4zmEEEKI7knoSFF6peNXk37FEyc8AahAsXD9Qm788Eae/uHpgO3r2+u5/8v7mfLfKQD0zfRdXOmhI1ntVUkd07GXtFfZzfaopylOtvp6eP11df+88+C7x7+jdVcruYNzmfyrySH32f/C/TEYDWz9fCNl6aoSsXEjbN6s1tYwoEJC8OrfsXDkBVY6Unm6XPCFDWmtEkIIIbonoSNF6ZUOi8lCukVdyDW0N3D1+1eH3P7hrx8OeC0/LZ+y7DIyrZkMyRsC7JmVjr2lvSqVWqtefRXa2mD0aChLq2LhjWpwx0HXHhR2DEV2/2yGHq3WYZmW8QOgxnX4DyIvGlMUV7DSQ4cdNRNbKk+XC1LpEEIIIWIhoSNF6ZUOi9FChjUDgK+2fsWKnStCbr9g/YKAxxnWDJZcvIQffv0DxelqcG+Px3R0U8noSdtQTyod3S0OmMqhI5UGkS9Zom5nHa/xymkv09HYwYDpA5j0y0kR9xt71lgABjUtBzRv6CikCoDC0YVxnZceOnRS6RBCCCH2HvIruhQVUOmwqkqHy+OKev/6tnpfW1Vn2EilSod/mIi20hG2vWoPmDI3WaHjyy+hoUGNr9i8GS65BOzdvNXy5ep2WHYlm1dWYUmzcOrLp2KyRL54Hj57uJp6trmWvmxj/fq+7NgB2ajxRDmDcuL6LI78wNCR2adnIXl3kUqHEEIIET351zJF+Vc69Paq7owpGuOthCzdvtT7/GmjT+OLLV9w/oTze3QuqTKmI9z76K1LqTyQPNGhQ9Pgvffg2GMDn9+0Ce66K/J+KzqLZZnb1wAweMbgqGaKsmZYGT57OCteWMEIVrNhQ1927YIhnaEju392jz6LLrjSEc+g9N0hs1SFooySjF4+EyGEECL1SXtVivKvdOjtVd0ZWTCSKw+8EoArDrzC+/zootEsOGcB0/pP69G5dNc+tbvGdIR7n1nDZnFI2SGcM+6cmM8jmQLGdJgTN6bjrrvAYoFTTlGPi/2WxvjnP+Gxx1T4CGXzZlUZsVig9qufANjvuP2ifu9+0/oBai2NzZvVoPSsztCR1a9nlTRdl9AxNrVDR8n+JZz+xumcMPeE3j4VIYQQIuVJpSNFBVQ6rIG/hS7LLmNz/eYu+4wsGMmfDvsTPx/ycw4feHjCzqXbSkcvj+kYXjCczy74LOZzSLZkVDo6OuDvfwe3G1pa1GDwr78GhwOOOUZVPy6+GIYNgx9/hOBx3Xpr1dghzWz7agsQW+jIHZyrbqmlqQk8bi0poSO9OD2h63Qkg8FgYPjs4b19GkIIIcQeQSodKcobOkJUOsYWjfXe928pGlk4EovJwnHDjusSVOKRlDEdCVwcMFUlI3S8/TZUq2UseOABmD9fBQ6Ahx+GI49U99esCV3t0EPHATlrQYOSCSVk9Y0+LOihI4c6Wpo1tKZmTHjAaCCjNL42I//Qkb9fflzHEkIIIURqkdCRorztVSHGdPiHDv9wMbJgZFLOpdvZq3p5nY5UlegpczUN/v1vdf+GG+Dyy6FPH9/rgwbBwoVw0EHq8aefdj2GPp6jb3PsrVUAOQNzADWtrae5FXOLqnI4CjK6HYjeHVuWL0DHWzURQgghRGqR0JGi/CsdFpMl4Df+fTJ9V5o1rTXe+8PyhyXlXHq1vcrYfXtVqkp0peO//1WVDaMRLrww/HaHHaZuQ4WO5cvBiBvD+rUADDs+tu+MxWHBUaQqGtaWWqyt9QCk94k/JPiv8ZHZN7VnrhJCCCFEbCR0pCj/SgcQ0GKV68j13i9M862NkKwF6Hpz9ir/996TKx3xho6dO+GKzrkB/vpX2C9CgUIPHZ8FDXNxOtU4jzIqcDe3k1aQRp8D+nQ9QDeyB6rvX1p7HXZnYsZz6ApHqe/zuHPGJeR4QgghhEgNMpA8RflXOkC1UdW21QKQa89lRMEIfqz+kb/+7K+UZJQwNG9o0s4lUoXBZDBhNMSeXaMe0xHFlLmpKiB0mOILHR99BO3tMGYM/O53kbc9+GA1gHzNGrVq+KBB6vnychU8hls3QAcMPXooRlPsP7u8Ibns+KqCXGqx0wpATlliQscFiy6gaXuTN3wIIYQQYu8goSNFBVc6/Md15DpyWXTBIr7e9jVHDT4KkzG5KyJHqjD0tPqwL7RX+YexeKtQetXiZz9T7VUAmqZR/mY5ZpuZLUu2sPbdtZz45IkUDC9gxgxYsADuuUcNOAffIPIhaduhA/oe1LdH55I/1DeDlZUOAPIGJSZ0OHIdOHKTU7ETQgghRO+R9qoUFVzp8G+vyrHnkJ+Wz9FDj0564IDIwaKn1Yd9YSC5wWDwfrZ426v08RmHHup7bvlzy3nxxBd59phn+eTWT9i6ZCuf3PoJAH/4g9rmv/+FysrO7TtDR37HdgBKJ5b26Fz8Q4c+XW62DPwWQgghRAQSOlJUl0qH3yxVufbckPskSypUOgwYdkvASrREhI7aWt+sU4ccom53/bSLeb+ZB4DR4vvPeMULK/jvQf/F+vXnTJoEbW3wzjudr62ADJowtTRhMBooHldMT2T2UYO802nGRjvQdWE/IYQQQgh/EjpSVKRKh/9A8t0hVFuT3jrU05Yn/wpGNJWOPW08h07/bPGsSP7aa2q63OHD1erjlcsreeLQJ2hvaKffQf34/a7fc33t9fSf1h+ArUu28uGfPmT0cBcAu3ap4yxfDiWoKkfBiAKs6T0MjA71mcy4MOMKeE4IIYQQIhQJHSkq3JgOu9mesIXmohWqmqGfz+6qdOxprVW6eCsdH30Ev/qVuv+LX0BrTSvPz3qe5spmiscXM+e1Odgybdhz7Bx282HeqofH6aGgtQJQlRKAbduglPhaqwAsaZ1BECcWnAHPCSGEEEKEIqEjRYWavQp2f2sV+C74/Vc/189nd43p2NMGkeviDR0PPqhmnDrpJLjtNnjrl29Rv6me3CG5nPfReWSU+CpgQ2cO5camGxl3tppuNrN6AwB1deB2Q0cHlLIDgJL9S3r8mSyOEKHDsWf+fIQQQgixe0joSFFd1umwqIvLHHvObj8X/cLffwamNEsakPxKx5DcIfTP6s8Rg47o0fv0Nv3n5/9353KpIBGNn9TC4VxyCexaXcnq/63GYDRw6sunhpzlyWQ1MfDIgQCYKzYCqtLR1qZeL2InQI/Hc0DoSoe0VwkhhBAiErlSSFFhKx27eTwH+IKFw+ygjjp1Pp3tVT2tQEQbOtKt6ay/aj0mw543iBx8n622yk5BAfzmN2psxYcfwqpV0DfCrLWaBuvXq/tDhsCXf/8SgJG/GEnp/uHbowYdqRbmcFdsxUo7dXU22trAhIs81Ar2haN7vg6Gb0yH2/uctFcJIYQQIhKpdKSocGM6erO9ymqyei+i4610RLs4oP66wWDo0fv0Nv2zfbjAzq5dcMcd8Prr0NAAb7wRed/KSmhuVutyFKU3s/xZNeftQVcfFHG/nAE55AzKAbeHMjZTWwutrZDPLoxo2HPsAW1ZsQoVMKS9SgghhBCRSOhIUcGVjn5Z/QAYmDNwt5+LHhAsJov3vh46kj2mY09nMqjPVlPZdUzH999H3nfdOnXbvz/8+PJy3O1uSieW0m9qv27fV692DGIDdXWqvaqIKgAKRxXGFeJCBQxprxJCCCFEJHKlkKKCKx1njj2TdGs6Pxv0s91+Lno1w2K0YDFZaHW1cuSgI2lob+Dccef26Jj7Suio2VIA6T/xxfyuA7cXLYJnnoHDDoOysq776qFjyGCN7x7/DoD9L9o/qsAw6MhBfPfYdwxiI993VjoK9dARR2sVgMFoQDOZMLhVe5VmMGKy7Jntb0IIIYTYPfbeq709XHClw2a2cdro03rlXLyhw6/S0S+rH9/88pseH3NfCB0uF9Q8/gQU/wA7xgMwfjxYLPDNN2pMxznnwOzZoVut9NAxIns7Oz/aiclmYswZY6J674FHDATUFLltta20tjp8oWNUfKEDQDNbfKHDvHf+/IQQQgiROHK1kKKCKx29yX9MR6KmsI12ccA92Zo1wK7h6g8waBAsW6Ze8y9WvPlm6P3XrlW3pTUrcAMjThwRcsaqUDJLM8kbXkBNeTWlzk3U1o5IaOjAYoH2Nt99IYQQQogIZExHigqudPSmkYUjMRlMjCkaEzC+Ix57c6Vj0ybo0wdOOCHw+aws3/0ZMwJf0xfw86cqHRrG8h8BGHXqqJjOo3SCmhY3lzq2b4eczpnH8obmxXScUAwW38/MYO3976gQQgghUpuEjhTk0Tx4NA+QGpWOEQUj2HHdDh6b/VjCKh17c+h4/HHYvt1XqcjMhIwMuPtu3zb33w+//rWv4rFyZeAxnE7VflVMJc7KWsx2M0OPHhrTeaQVqsH+abSwbRuYOqe4Ndvj//s22nw/f6OEDiGEEEJ0Q0JHCtJbqyA1Kh0ABWkFGA1GqXREQV+IT3f33dDYCD/zmwNg1Ch4+GGYOVM9Dg4dS5aofSY5VgMw9OihWNNjm544vVBNs5xGM9u3aRjRADBa4v/P3uQfOmx7189PCCGEEIknoSMF6a1VkBqVDn8JG9MRwzode5oNGwIfT5gQftvRo9VtcOiYP1/djk1To8mHzR4W83mkFahKRzotbN/m8T6fiJmmTH7VEv8AIoQQQggRioSOFJSKlQ7daaNOY3j+cCb3mRzXcfbmSod/6BjLcrY8/CbOFmeX7VxtLvqt/4RidvD004H7zZ8PNtpx1G4DfOtuxMK/varSL3QkotJh9lurwyQLAwohhBCiG3vX1d5eIpUrHTdNv4mbpt8U93H25tCxfr26vf12Dc/Nr/LDXDAaNXb9uIsxZ4xh86LNbFm8hdwhudR/tJE5fM8/665k2DDYuBHS0+Hrr2EIm8CjkTskl5wBOTGfh6+9qoWdO9ze543mxIYOiywMKIQQQohuyNVCCtIrHSaDKa6Vo1PZ3hg6qqpUm1RNjXp83qxanrhZ3V/2+DIAKr6o8G5fv7kegDzU1FUulxp8XlgIHg+MtG2Adt+aG7HS26vSaKFqR2Lbq6xpfqEjLbWCsRBCCCFSj7RXpaBUmi43WVJ5nY4PP1QrhL/1Vmz7nXsuHHGEGrh9qflxPrjs9aj2s6RZmDRJ3W9uVn9MuBns/gnoWWsVBLZXudpdAGgGAwZj/EHWmu77mVnTUuvnJ4QQQojUI1cLKSiVFgZMllSrdGiaWhm8vh5GjoSKCnjpJXjoIWhvh4ULwdhNRH/vPXU7ge8pdVVQ8UXg66NPG43RbMSea6f6x2o2LFSDOJwtTjIcLsBMczOkpcEMFpDj2oU9x86Qnw/p0Wdy5KmFBA1ABs3qye4+RJRsGb7vpjV97/2eCiGEECIxev9qT3SxL1Q6/IOGyRh/u09PbdgAt92m1sx4+2313E+qwMBnn6mF/gB27FAL/kUjg8aAx8c+fCzOFieTLpmELcsGQNOOJr5/+ns++P0HAOSYm4FsmpvB3NbEVJYAcOKTJ5KWn9ajz2aymDCk2dFa2nznZErM37Utw/fzs2fsvd9TIYQQQiTGPtFeddJJJ5Gbm8spp5wS8vWWlhYGDBjAddddt5vPzGf+uvl8v+N7YN+qdBgNRoyG3vsann46PPkkHHSQ77kdO9StHjgg9Irh/jQNzJ3X4QXsCnhtxAkjmPbbad7AAZBRksHBvzuYrP5qmfJsUxMATU3QsENVJTos6QyfPbwHn8rHnKUCSybq+AZTYv6uHZm+76Y9U353IYQQQojI9onQcdVVV/HUU0+Fff0vf/kLB/lfde5mK3eu5OhnjmbCvyewsW7jPlXp6O3WqlWrottu167Ir7e2qoHgAENz1cY5A3OY+tupZPbJDLtfRkkGAOmaCgXNzdBS2wGAxxz/z9+Wp2awyuysdCQsdGRZQt4XQgghhAhlnwgdhx9+OJmZoS/8fvrpJ3788UeOOeaY3XxWPm+Uv4HWuVr0L9/65T5R6dA/W2+HjoyM6LZbsAB+/nNYujT06w0N6taMC1ODKotc+PmF/Pyun0c8bmap+l6muVUoaG6GlvrOKZOtsa1AHoo+g5UvdCSmvSo92/dzS8/Ze7+nQgghhEiMXg8dn376KbNmzaJPnz4YDAZef/31Lts89NBDDBw4ELvdzpQpU/jqq68S9v7XXXcdd955Z8KOF4v31r7H4XMP58+f/tn73IL1C1hZpZan3psrHYNyB3HM0GO4ZOIlvXoe0YaOP/9ZBY/jjw/9er2a/Zb+GbVobg1rhpWM0u4Pnl6iKhE2l6/S0dagKh2GBISOjCIVOjL09qoErNEBYA+odEh7lRBCCCEi6/WrhebmZsaPH8+FF17IySef3OX1F198kWuvvZZHHnmEKVOmcN999zFz5kzKy8spKioCYMKECbj03hY/8+fPp0+E0b9vvPEGw4YNY9iwYXzxxRdht0uWv3z2FxZtXuR9nGHNoKmjiU11ajDB3lzpMBqMzDtrXm+fBmEKYGHt2KEGnBsMcNxxUFenxoUMG6Ze72urhiYoGFEQ1RoreqXD2uEb05HW2IEZMNjjDx3ZpYGVDmMC1ugAsPgvDijrdAghhBCiG70eOo455piIrU333HMPl1xyCRdccAEAjzzyCO+88w6PP/44N9xwAwDLli3r0Xt/+eWXvPDCC7z88ss0NTXhdDrJysri5ptv7rJte3s77e3t3scNej9NghSnFzMsfxifbf6MbY3bgL270pFomqamtx07FqZPj36/WEMHwKxZ6raxET74AN5/X/0BKDar8Rz5w/OjOpY+psPc4qt0tDc6MQMme/w//5xSNW2uXukwJajS4R80/AOIEEIIIUQovd5eFUlHRwdLly5lxowZ3ueMRiMzZsxg8eLFcR//zjvvpKKigo0bN3LXXXdxySWXhAwc+rbZ2dneP/3794/7/f0rGQ8f9zCF6YUAbGva1uV1oVbp3ro19GsrVsAVV8DFF8d2TP/2qmN4lxN4A9DoLKJ1YfH7kdTWBg4wN+JmcMMyAEr2L4nu/TtDh8EvdDibVXuV2RF/pUOf2taCGiditCTmP3mzw/f7Cql0CCGEEKI7KR06qqurcbvdFBcXBzxfXFzMDn1e0yjMmDGDU089lXnz5tGvX78eBZY//OEP1NfXe/9UVFTEfIxgra5WAF6b8xonjzyZwrTO0CGVjpBuvBH69VPVhWDb1F8Z3X0tOjoCH6enq9YjAx6m8BX7s4xCqpk1vQE6B/f7s9t99xsaoKbG93gSS0lv3UVaQRoTL54Y1WfSx31ojb72KleLOklLAhbdM1lVO5UVdUxTotqr/IKGfwARQgghhAhln7ha+CDUVWqQ888/P+LrNpsNm80WcZtYtTpV6HCYVQtMl9AhlY4A336rbpctA7/iF+C7+G9qUlPXmkN8s+fNgxNPhEcegQsvVM/l//Qlv+V9PuNg73an5n1I0cs/cvfJM2gYezC33eY7hv/Y7rq6wNAxke8AOOzmw7Bn+6WTCLL6qXU6XDUNZFFPc3M2rtbO2cvS46906KHDjLvzcYLaqxzSXiWEEEKI6KV0paOgoACTyURlZWXA85WVlZSURNe+ksr0SkeaRQ321durqluqAal0BNNbmerqur7mf/GvzyQV7PjjwemEiy6CJUtg4UIoWaYGYxzK597timp+BKDx1Q844ojAYzT6LTZeVxe4aKA+bqLskLJoPg4AWX2zGDB9AHg0prGY5mZwt6qqhC0BK32bbYHpSw8h8QoY0yHtVUIIIYToRkqHDqvVyqRJk1i4cKH3OY/Hw8KFC5k6dWovnllieCsdlsBKh25PrnRomlowL5H0YFFXBw8/DB9+CKtXw1/+Av7dbqFCiX5OumOPhWiWZsnvHA/uoIUpfIm5ozngfXxhRyONFsC3Nka0Dv3joYBqz3I2tKK1q0qHPStxlQ6dOUGVDv+WKmmvEkIIIUR3ev1qoampibVr13ofb9iwgWXLlpGXl0dZWRnXXnst5513HpMnT+bAAw/kvvvuo7m52Tub1Z6sxakuUr3tVelBoWMPrnScdRa89BJs2KBmiMrOVtPMxkO/wH/jDXjyoSbasWGyW2hrC9wuXOgIdazuFBSo29N4mUFsZCjreJazAFXl0I9jowMTHgDS8mMLHYNnDMZelAk7G7HUV6O5VaUjlUOHTJkrhBBCiFj0eqXjm2++Yf/992f//fcH4Nprr2X//ff3ziI1Z84c7rrrLm6++WYmTJjAsmXLeO+997oMLt8T6e1Ve2Ol4/nnwe1W4SM3F665Jr7jOZ2+Vb9rtjRzNfdxDk93CRygBppfd52vFerZZ+HeeyGXWk7lZfqwLer3zctTt4PYCMB++AKyf6VDr3JgtcR8EW4wGLBmqvFCHW1uDE4VOtKyEzeQXGe2Jai9Kl1ChxBCCCGi1+uVjsMPPxxN6zpLkL/LL7+cyy+/fDed0e6haVrXgeRBlY7gELIn+uwzdXv//XDffbHtq2m+6oj/2Ik8ajDjppCqkPt1Lt/C+PFw9tlwySWq1etXvEgJlQxjDX/hj92+v9lh5tNbPuB4i5vOGWdx+v0nEyp0mDJjq3J436szDHS0ejCY1Zul5yag0hEUMiy2xPyewZpu5YDLDsDtdEc9aF4IIYQQ+65er3TsqzrcHWidU7LqA8kL0goCtjmo30G7/bx6Q3W1qoz4Vy0efli1Nn31lXrsvx6GHbVIoz4NbDg7d6rZrPSxJSWoCQksdF29PhTNrfH53z5nsvNL73Nt+C6w/QeS66HDmt2z0KGHARNuDC71uRISOqzBoSMxlQ6AYx88lln/npWw4wkhhBBi7yWhI8m2NGyhprXrAAK9tQp87VVWk9Vb9QCY2n/PHywfjeuugzPPVG1Qutsv28GBNe9y503qYt5/DIatM3SY8GDqnAo2lNrawApJrNwdXY/diu/ns2MHtHR2Vemhw5bX09ChwoAJtzdMZeYnPnQkaspcIYQQQohY9Hp71d5sR9MO+t/bnzxHHrt+vyvgNX0QudFgDBi74R9G9svbb/ecaC/SNHj3XUijma1vr6Hx2KEYMjP5Nf8GoHldG3BSyNABqtrhHwQAsqlnIBuoqRpLTU10v9l3Y/QOBI+kFQcD2QDA+vWDvM/3dOYqnd4GZcTtXT08qyDxYzqMZgkdQgghhNj9JHQk0byf5gGErnT4jecwhJnWKdzzqeb+++Gtt+D11yEjI/x2zlYXHU3tpBeme59buRJyd5ZzCa+gve7ijZYh9Ln+bO/r9oadQGB7VXeh41L+TRqtVC1uoPb0w0Key1HMJ10f/A24MUUVOlyYOYvnALhn3Q2AuqjXQ0dGkSPcrhHpK4UHVDry4q90BK/TYbRI6BBCCCHE7idXIEn0Y/WPYV8LnrlKZzOpWYyOGRrFIhIp4uqr1UJ7zzwTebtnjn6We/vdy9r3fDNALVwI+/Odd5zFuvnr+PzdBu/r7s5pgwMrHb7BH6HGdaTR+Xe7qTxke5UTMwezmAl873sfoquIWOnAgkudb4fvvfXQkV3aw0qHtWvosGUmob3KkrgxHUIIIYQQ0ZLQkUSrq1eHfU2vdOiDyHULz13IWWPP4okTnkjquUVryxa46SbYFmaW2Z07fffdfkMgcnICt8ujhs2fbsTd4ebZY5+l+ke16vrChWoqW38b3lruve80qAvvSJWOsDravaHD7Dd4XKNrBckVZdHP//30Y5aV+UJHbp/4QocVp7fi4j8tbU91aa+SSocQQggheoFcgSRRuEpH044mGnap3+b7DxwHOLjsYJ45+RmKM9Q6JO0N7TRua0zuiUYwezb8+c9w/vmhX1/uywfedTHAt6iebhSrfA80WPHiClwu+ORjzRs6qoergfNpa/1CB6EqHdGFDqOrw292Kd9K4qEGnxeVRl/p0OmhY/RoGDNYhY6sHlY69DBgxzemx5oulQ4hhBBC7B0kdMTpm0e+oXF76FCwtsbXRjRvHkyZAt9+2sSDIx5k6S+WYvAYurRXBbur5C7u6XsPTZVNEbe7/no4+WTf9LDR0jS48EK1iF+o5VK++07dLlgQev8ffvDdr6z03Q8ejqKHjqx+WQA0bGlg6VJwN7ZgxYkGbCudDEC+21c+afd0DR32KEOHye0LHekBoaPr2A1jlBfjoUJHXh7k2uIcSN4ZDhydrWMeg7FLYOjRcW1S6RBCCCFE75MrkDgtuH4BNWu7DhRvaFeVjBGrRzBg4wCOOw6++sbFny9YR3t9O61rWynbXNal0hHM1aoubLcs3hLw/H/+AyNGwE8/qcf/+Ae89hpceqlvm/Z2uOIKGDkSNm8OffzycnjiCXjuOaivD38eWVmhnw8XOvyl00wftoMBDrj8AAAatzaycCHkdFY5Gsii1pMNgBFf+tFDR7j2qmIqOZAlmHF2GcRu1dq9+/mHjlD8B1z3mdyHPpP7hNwuXOhoqU5M6LB3hg63Mf4qh/9xdTJ7lRBCCCF6g1yBJIAeDPyVV5eTU5vD6S+ezgVzL8Ax/l9wYwbpzV94txm9cnS3lQ6dxxX42/lLL1WB4c47A7d7+mlY3TmU5PTT4cEH4ccf4eOPQx930aKuz2kazJoFRx3ley43N/T+0YSOTFQAM+dkULp/KaAqHf7jOWrJpanVBI7A1a2dnSuB65UOmy0wdBzJRxzLe4xkNUOGBL6vAaioUPe7Cx3+FYGz3z+bnIE5IbfzX1jQ2141ykPrrs4xOj0MHXoFwtHZXuUxJyd0SHuVEEIIIXqDhI4EcLY6uzy3Ztca+mzz/bZ8/6JnwNROUYuv5WrUqlGkGbtepLbVt/HxbR9TtarK+5x/6PjxjXL251vAN0XtKHM5E/kW0FiyRAWH11/3HTNcFePzz333m3c08tHNH7HtxwY2v/0DlR/4EoUx6JuyYwdMnAjffut7bud2N5/d+Rk7lu0I2FafmtaYmU5m30xAhY7PPw8MHc3N0GFJD9hXX6BPr1gMHhwYOnTZhkaOO67r51u/Xt1mdBc6gi7Obdm2iNsDmHFixEPm2y+ieTSsGVbS8hNT6bBmxD+IHMBoMmIw+nrdpL1KCCGEEL1B1ulIAGdL19BR01pDcWWx9/HkbyazduhashqzcJlcOC1OMpozyK3oWkJY+dJKPrn1E6pWdA0dVaurePHEFzgB2MRA+vXLw+10c5rrBQDasNPePor2dhjMOuy0sYrRUYWON898gZ3fbWP1mz9xMtsBWMtQWkmjujpwv9de84330BVt/oYPb/yQ5c8sB+3XgIH33oOX/tQM38COhnT++mAWuUBbbRseOuiXXgvNUEsOzc3Q4E6nAF8vleZ0s3Wrrz1s/Hiwre4aOm68tpWjboO//jXweT10xNJeBYGhI60gzds+5S/N4uKlO9az4oY1mO1mZv13Vo/HYej7TRzZSs1q6DMgMZUOUFUcvRonlQ4hhBBC9Ab5tWcChGqvqm+vDwgdebV5XPj4hQBsHLiRHSWqGpC+LZOHH4ZNm6BmbQ2bF22msUr9tnvXZt/gcT10LLjON6K7iJ24XFC73jfl7M9YSFuzm9ZmD+fyDKfxCtnU0fTtGtobAy/Wa2p8Y0IAdn6n5sWt+n6797kc6gA1M1W73+7LlsEANnL8Ec3eC/shzaoyUrWqitz2zs+XDhkGdcG/pS6d+x+xgU1dUGfRyOBcdfw6cqmvh6qWwIEZHpeb//1P3Z9+YCsjDOXeFiR/7uY2zJ25we33tdaX0ug2dNgDL8bt2b42r1NfOZUDrzywyz6P/cfFkGL1Mxp4xEDGzBkT8T0i0cOAq1GvdCQwdPgFIal0CCGEEKI3yBVIAujtVR3NHbidqh2ovs0XOr6e9jUukwt7u53mtGYWHLWA6gJVOtj6aRqXXQY/P0rjgf0e4IlDn+Ddp9Vv+tcs913lu9pdVP9YzU/zfCmhgGra2vCueQGQTw0t35VTs8k3o9ZRfIDjted59cxXA8572bLuP1s2vhJJla/wQuUHy7mAJzms6n+UlUGhoZq++BbzGNToW3jP4VEX/M2kAQZaTGpUehYNZHnqAFXpqKuDRi2wPcmoub2LDs40zIfnXwgYV6Frq1UX65s3gyNEa1T3lY6g9qos3zH6TenHxIsmdtnHYXHRVqfe1z+k9IQeDFprVaBKxBodwccGGUguhBBCiN4hVyAJ4Gxxsm3pNu4ru4/HDnoMgPpd9eTWqdapz4/4nKfOfYqvJ3/NYxc9RmVJpTd0pO1Qv9He+VOd93iVP6rKhafVFzqczU5q1gXOklVANe3tUL06sPepY1s1uzb4wsIYVgKw5u01AdvVdJ10q4tcfOelt1i5XDBgw8cAtKzYgMkEB6atAMCaq0LDwMaV3v1sLj10qPEa21tU6BiQ24DWoi7aW0jr3Caw0mHCzddfq/tZrWFGquMLHf37gyOna5UgxxZ5LmGLPXR7lTXDitluDtk25WrzhQ5bTvdjQCLRj+9sVgHW4khO6JD2KiGEEEL0BhnTkQB1G+t4dPKjALTWtHLt1R7a81RfT31WPc2WduoGbGbzAN+8tXroKGhSF5f98E2Jq8+K5D9gumZHBy+93kiO3/sGVzrcGDHhwb2rjvrNDd2ed+A4D980tUabGU9758xMfWqpMKqVyfVKx6oVHvI0X2Jxd7gptqjHhcdMZutzn+JwN2HBCVgwtzfjwRc6GlCh46gp9bTPV5+xHXXRrm+j0xfyGzwYmrfUhf0seoUAwJbZNQAUZ7XirurytJclTHuVPhtVqLYkV6uLtvrOSkdOfJWO4OOb7Yn7T9N/vIq0VwkhhBCiN8gVSAKUv1Ee8Pih+520rlAX8ZXFlWraV0/gX3VVoboCzms1YMRNf7/Qoc9gpN8CzHvdybLPVJCoMJQBUEgV7W2at9LxE/sBoNXUUb/Zlyha8V0Q+w+I9g8d/uMkTHbfb9mP2L+O/fbrPOfOi/YvXwpc9KN+cz1ZRjW2oT0j39vCk0UDNUs3YGxSrV6+0KFmsBpZVIPmUX9PeuhoChM6yorbaK0JX63QKx0A1kxfpcOEG7sdrO7ORfcwdNkXuo7pKBipllQvGlukjhOm0tFep0JTotqrvI/tiatISKVDCCGEEL1NQkcCNFUGjhew4sS6Wf12WR8wjjPwYrohq4EOSwcmDfKopczoCx16hcN/kbzanR1koi7eN2gD8GDARgfOmkZvpeMnhgJgqKulcYsvUaiKg+I/Da9/6MjCVxlxt/vGTNRtqKOwUN3X26s2LlwX8Flq19eS5laho0HLwJGv1h6ZzZt8d/VTuLaov4Nm0vnlL+G8y1Slo7rzXAxGg7edKLjSoVd9BmTVEYl/pcN/ELaVdnJzNO/repUlmCmoAlA4spArfrqCU144Rb3eTXtVvJWO4OMnstIhA8mFEEII0dvkCiQBtKCF+6x0kLVVteVUFneOQ+gIvJjG4GuxKmE7RR7f2hb+FQ6dzegkqzN01JJDLWq8iLliA+0N7XgwsA61Op6xqZ7mCt+MVubOagHAzpU7aW9Xs1YFhg7fwHNPmy+k1G2soyBfhR+90rGrInD62NoNtZjbVeho9GR416oYQGBFpJl0xo2DAw5P8x4b1KDt9AxD5zZdx3QAFFtriaStrg1NU+fpP1j6RN7grBFLvd1jTYbM0AcIUQDJG5qHJU2FoVAVAlebr70qmnU9Igk+ftJChwwkF0IIIUQvkCuQJLDSTl5lNuAXOoIqHQA1eWocxGA2YMLjt3/XdT+s+CodjWSxHbWyd/HSdwGoNhRSTw4uTBg0jbrlFSHPrWpVFRddBMOGwcKFvuczCT0GxNnipDBdhYyqKrXoYH114OxRu8p3YWzrrCR4fJWOYM2kM2gQOPLU63qrly3LRnq6bxt/eujI0SKHDs2t0dHU0eX54awha5H6O7KkWegw9qwisbdUOqS9SgghhBC9QUJHEhRTicVpwWl2eoMFHRldtmuzqwvWrDAX/P6sOP1CRyYfMx0nZkwu1Yr1oWkGGgZvBcTd0nUBPYCqlVWsWqXur1jhe96/0hEsp3PV8KoqtZ6Ix6lCR+6QPAC2Ltmq3hMj9R2OsKtyO7EyeDDYcwMv0G3ZvtDRjhUsvgtuPXQ42uvCnp/Of1yHP32NE0eeA4+xZ7NChQodzlbnnhE6bNJeJYQQQojeJVcgSdCfTQDsLNqJx9RZwQhurwLabSoYRBM6TB2tpKMqAw1kUk0h8/k5AAdcfgDrjWq0d13A/FZdNVQ0hFydPFylAyDTpKoYVVVqFXJ9jEjRaDXYo2Kxqqo0k05jkwF7XvgL8AEDwJEbWAnxr3SAAcfQft7X9NBhaqwDYL9j1eccf+74Lsf2H9cRij3XjtvUs9ARcvaqNhft9YkZSJ7M2auk0iGEEEKI3iahIwn6G9RYBm9rFYRsr4oldDhaVcXEhYlW1EX71xzAJ5Ou4Zh/HuPdrrab0NFW3xYydESqdGR2DoOorVULCuqDuws7Q4d3vAQZNDQQttJx9dXgcISodASEDhj7j7O5YNEFgC90uHaqastB1x7EdZXXcdT/HdX1s4WpdOgceQ40c89Ch8FgAFPgfy6u1uS1VyVrnQ6pdAghhBCiN8gVSBIUdo4/0AeKAxErHXZCt0L5s3v0KkcWYCCrcxKmBrLUBXGnLfSPeJyW2vaQoSPSit0ZnZ1hdXVBlY4xRRiMvvduJp2GBkKO6dj/4v25915135ZpC9gvOHQUFJvIKFZvqocOZ506v4ziDNKL0gNmqNJ1V+lw5DrQTD2vIBjMgcGgpbrFO+VvSrdXyUByIYQQQvQyuQJJAn2q21aH30Wws+tv//XQEYvGzjUuSkrU47agX+7/wFg+HX0p2Vefz2cc3PUALrdaUrzTMMrJpSbkjFk6PXTU1sLatb5KhyPfQcn+Jd7tQlU6bEVZXPHTFRz38HHe5wxGQ8BFenDoyM/3XSjr76XPLqWHFbOj60V5d5UOe569x5UOAHNQMGjunCrZaDaGPJ9YJHP2Kv/FAaW9SgghhBC9QUJHArUQ+Bt+p91vKl0t6K+6fBaWpikxv4ceOkrV5FW0d8ktBqqMJbj7DaCF0G1Ots6AMZmvOZMXOJVXAhYHDOadWaoZduzwVTosDgsDDhvg3a6JDBobAysd1tx08obmdbnY1WewAhU6jH5/Pf6hQ1U6NIL5V3fyh+cDUVY64ggdFnvgz7Bph5om2J5jDzifnpB1OoQQQgixN5MrkARqClpjwu2I8FvlRTdQsuN3Mb9HPWoq3nCVDlBBpL0dnAReYLs7f9x6O9cxvAdAH7Z7FyQMxb8KUVvrqz6YHWbKDi3zvtakt1fl+YeOrrN2QeC4DluWLSA8ZWX5ZlwyELhIor85r8/h6PuPZvCMwQDe8RXhOPIcYOl56AgOBs07VaUj3taqUMdOZOgwWn3/mUulQwghhBC9QUJHAgWHDo+167gDr44MTI7ABeWcdH+hWd+5onb4SocKIm1taopaneZ3fjba6MeWgLVBwl3YA5hMvsHkEFjpKDvEFzo8mGhpAWu2r8Jize06lgUCZ7AKDh0GQ+BF+N//6iaUESeMYMqVU7wBptv2qlw7BmviQocu3oUBYffNXiWVDiGEEEL0BrkCSaDg0NFhinAx2pGOOT3w9eCF8ULRKx166AhV6dBDR4dfpaMDK+2o97PTzjDKu+wXPnZAbq7vvn+lI73Qd847KAbAY/OrdOSF/kyRKh0QeKF82a8CFyMMpldWWnd1016V4EqHLtUrHTKmQwghhBC9TUJHAgWHhla6zuLk5ewaOsKNwfAX3F4VqtIRqr3KiYU21MWxjTYyaeq6nzl86MnJ8d33r3QAXLH2Ck5/83R2WtXMWU6LX6UjJ7rQERye/GdZcneErnTo0ovUe+jtTrr9jtuPs949y/vYkevAaIsjdIS5YI93jQ6Q2auEEEIIsXeTK5AE8q90aGg0t4cezwBARwaWjPgrHR0d4PEEbhOqvcq/0mGjPeQUuS6LI2yLl17pMOL2tmLpF8Z5Q/IYPms4mVlqMHVzmwmnQb13uEpH8EDyn/1M3denAjYYDN5xHd2FDn163eDQMerUUb61RDrfMyntVTnxt1clc/Yqaa8SQgghRG9L3JWNCAgNbfY22upzADUmostlszMNe1bgjEfRhA69elLim6mWjo7Abdrbu7ZXFfax0NJihzrVXhUqdHisdtytJix0bWfSKx3+rwVPE5uVBdXV0NAA7SYHFlcH1rzQwSt4TMcNN0BxMRzjW+cQk9WEu90ddaWjqbJr9SajJEONRtdUdcVkU39ZLkyYu/5UIgrbXrUHVTqkvUoIIYQQvUF+7Rknt7FzxWwTtOH7jXebvQ3njzMBFToGDfbtY9YcoBmxOwwBi9xFEzr0BSv0SgeEHtfR0BDYXlVaZiWjQK90tJHR2V7lMfi+AprNjqubSoe5s7UKul4YexcsbIDynANZzyCyx4RerDCgvSrbht0Ov/41DBzo20a/WHa3dxM6itXfW0t1Cx53YNnHZDFx0DUHMerUUeQOysVZ3Jd1DOYLpkU8ZijhQkdGaYSKVg+PndDQYZNKhxBCCCF6l1Q64uS0OKEdXBbocPsCRBsO2DY55D4WLQMXYLer3/J3NKnfvjdHMaYDVIjJy/M9DjWuo74+sL3Kkm7B2uEbSK5XOtqzCnHUVwJgcDjCho7gSofZbu6yNoUeOhob4cfcafxUPY1LwhQBgisdoegDoLurdKQVpHmrGS3VLV1en3n3TN8xHRae5hwsdHAYn0U8brBwF+zZ/bNjOk40x5ZKhxBCCCH2JvJrzzi5zOoi3G0Dp9nXetTaXBZuF8ya+s28wxF4wd1dpaO1cyB4bi4YjWDr3DV86PBVOqzpVhydU7tm0eBtLXLn+cY8GNNsUVc6Qq3ArU+r29AQ8WMAXQeSh+KtdHQTOowmowoe+FYJD0efxTjc54wkXKUjuyz+0CEDyYUQQgixN5MrkDg5Leoi3GODjtIV3ufbnPne+8GLVZvcKlzolQ5dd6GjhTQmTYLzzlOP9dARqr2qri5wTIcl3UJ6vrrQz2cXAB0GK4PG+Rbg0OyhKx3tje2Y3/gfI1nlrXToM1f582+v6o53ILlBBaJQ9ItlV3vkKXMh/GDyYPqMuVrnkPhY7BWhQ9qrhBBCCNEL5AokTpmdv97X7NAx4Evv8/r0tKGY3OoCOTh0dDdl7reOg/nmG7jrLrz7Q/hKhwuzPgQES7qFzM4xHXroKB6czqjJvjYnzWbHTdcL6x+e+gHntyuYw8sRKx2xhI7ssmzMdjN5Q/IwGA0ht4m20gGRB5P781+vMdZqR7jWpESM6fCvQBhMhoRWJLzrdBhUVUgIIYQQYneTMR1x0qydS+o5oGPQIlh0NBA5dBhdvvYqa6a6Cm7HGtAO5e91TqCKQjzZfQKej1TpqK8HMGC0WfC0ObGmW8nOsVOJb1xGRnEGjjxf0PGEGUju/1t3fSxIpEpHY2PIjxHAkevg0mWXhm2tAqKeMhd8g8m7q3QEhw4bHeE3Dj6fMJWORFzIGwwGjBYjHqcnoVUO8J23jOcQQgghRG+RX3vGSQ8dHocLZ79vvc+3+oWO4PYqS7sKD/6VjnZsuMKEjjbsbKUvjrTAA4WqdOjv5ersSDI51FW2Jd1CbmngBX56UTqOfL9KhzV0e1VaoS+Y9KcCiH9MB0DB8AIySzPDvt6TSkd3Yzr8FyQPF/K6Ox9//n838dKPHyrQJeK40lolhBBCiN4iVyFx0kOH29HhHd8B4SsdfY0TGfjT34FQoSP0b7hdnS1PjqAFzkNVOuxBb2vuvIC1plsp6Bv4YnpxelSVDn9lnaEj3jEd0Yh2ylzoeaUjFkZr1/9c0gujmeY4OnolIlmVDhlELoQQQojeIlchcdJDhyFNQzNqdFhUu04bjpDb728+E61BVTr8Z6+KFDrcnc8Hh45QlQ5bULeSHjos6RaK+oeodPitDB4cOowhfrPfny2dx41vTEc0kl3pSMSYDv19E0H/vAkPHTZprxJCCCFE75LQESc9dJiz1G2HVQ8d4durWlvVrd3uG9PRgZXC0nCVjtChI5pKhyVNHd+abqWgX6hKh397VWDoiHTxG6rSoZ+f/vniFe06HeCbvSqpA8lDhLA9InRIe5UQQggheplchcTJk9m5AnaOum1JV4vTNRJ+RiM9JNjtvovlmSdnsGpN6N9Ed9de5V/pCA4djnzVPpVWkIY924bJ74I2u382joI0XJjwYMBjTwuYvcpkC3/xG6rSERyu4hVLpUMfWxFqcUB//qGjNUw1qrvz8TfwyIExHSMSPRQkOnTYc+wBt0IIIYQQu5vMXhWn5uOb+c75HWOOGgNr4N1Z7/LChBf4++9KgE0h99FDh8MBo04ZRVNlEyNPHkl6htE7g5G/7tqr/Csdwe1VB900g/pjBzD0mKEYzUZOffEU1n+wnozSDIYeMxS3ZuIVfoEJN4dYbVFXOkKFjkSLZZ0OfbyC5tEibuffXvWx+SgGuDZhxRl+hxDnA3D+p+ez7ettTLpkUlT7xnL8RIeOwlGFHPvQsRSPK07ocYUQQgghoiWhI06eAg+LDl3E6MzRAGwZsIUDLz+QvL/B1jDDCwLaqzKsHHL9Id7XzHYzHc7AaVzjqXT0mVDEmCOLvI+Hzx7O8NnDvY/dHfAjIwE4xO+9ACz28GMAEj3DUiixTJkbrYBKR1YRX9RM43A+iWpf//ak/tP6M+DQAQk7L0he6DAYDBzwmwMSekwhhBBCiFhIe1WS5OWFf82/vSpYqAvOeAaSh3qPSFKx0pHI0KFXOozGrn+f0Z6PwWhIyiJ7yZq9SgghhBCit0noSJJoQkeoi17vBaff+Ai9+hAcIKIZSB4cQrrjHzrCLYYHu6nSEcOUudHSKx0WS2CrVSzno1dgEi1ZlQ4hhBBCiN4moSNJIoUOvTIRqdJhTPO9aHVEX+nwP6bZDKYYr4/1qooLE4YII8P31EqHHjqs1sBWq6jOp7MSESmMxUNChxBCCCH2VhI6kiRc6HD5jVmOFDrM6b4SRW5B9IsD+lc2Yq1ygK/S4TZEvvDdU8d06NWNHoUOPRREmNUrHvqYEVOEsTRCCCGEEHsiCR1JEi50OP0mYorUXmXJ8CWS3MLI63SEq3TEOp4DfKHDY4x8Yb1PVjqsUukQQgghhOgJCR1J0l2lw2RS7U/BvKEjUyUKN0YyMlWbUzRT5sYfOtSFrydEpUNfCwN275iOaKbMjVZCxnRI6BBCCCGEiImEjiQJW+noDB3hWp/0C05btkoMbkykdy56HeuK5PG0V3lMXS98s/plee93NHd0eT3R9ItwT4enmy2jF0+lw9v+lKyB5DJ7lRBCCCH2UnJ1kyQzZ8KYp2FF0PP62nWhqhzgu+As7G+nErA4zJx7LlRWqmMGbNt5DI/fNfmsWfDpp1BfD5dcEvt566EjJ7/rCfqPZehu5e9E0N8vke1VkybBIYfA8cdDQQF8uA7YFt2+UukQQgghhOgZubpJkgED4K23YND9se2XPywfgCFHDWL1yyspGZvHnDkwZ050+0+YAD/+GNt7+qtBlWiGHZRH/eb6Lq8XjCygenV1wAKDyaKvMu52Ji50pKfDZ5/5Hg+pgE9ui27fvCHq7yZvaISpyeKQOzQXgPz98pNyfCGEEEKI3iKhI8XM+NsMJl48kfzh+Qw8fCCO3BhXsItTFUU0XnAFJz2UydzD5nZ5/ZKvL6FpR5P3Ajypws/Y2yuKxhRxxU9XkNk3MynHn37zdMbMGUPByIKkHF8IIYQQordI6EgxRrORghHqojNnQE6vnIOWm4clTNaxplt3T+BIUcmqcgAYTUYKRxUm7fhCCCGEEL1FBpILIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpJHQIIYQQQgghkkpChxBCCCGEECKpzL19AnsqTdMA6GjpgDZob26HNtCMGg0NDQA0NjSq58wanvYOsICrrQ1oQNOgc7Mea2tTtx0d0Hk6NDbGdtyOjq7329vVMVrdrbTRRnN7M2200epq9X62UFpa1K3LBW63ut/c3PPP2dTaRBtttHS00OZpo402GpsasTXYumzb2NRIG21YPVZanC200UZTa1PE8wW8n62lQ+0D0NDQgNPs7NlJCyGEEELswfRrJ/1aN1EMWqKPuI9Yv349Q4YM6e3TEEIIIYQQIuHWrVvH4MGDE3Y8qXT0UF5eHgCbN28mOzu7l89GpLKGhgb69+9PRUUFWVlZvX06IsXJ90VES74rIhbyfRHRqq+vp6yszHutmygSOnrIaFTDYbKzs+U/XhGVrKws+a6IqMn3RURLvisiFvJ9EdHSr3UTdryEHk0IIYQQQgghgkjoEEIIIYQQQiSVhI4estls3HLLLdhsXWdSEsKffFdELOT7IqIl3xURC/m+iGgl67sis1cJIYQQQgghkkoqHUIIIYQQQoikktAhhBBCCCGESCoJHUIIIYQQQoikktAhhBBCCCGESCoJHRE89NBDDBw4ELvdzpQpU/jqq68ibv/yyy8zYsQI7HY7Y8eOZd68ebvpTEVvi+W78uijj3LooYeSm5tLbm4uM2bM6Pa7JfYusf6/RffCCy9gMBg48cQTk3uCImXE+l2pq6vjsssuo7S0FJvNxrBhw+Tfon1IrN+X++67j+HDh+NwOOjfvz/XXHMNbW1tu+lsRW/59NNPmTVrFn369MFgMPD66693u8/HH3/MxIkTsdlsDB06lLlz58b+xpoI6YUXXtCsVqv2+OOPaytXrtQuueQSLScnR6usrAy5/eeff66ZTCbtH//4h7Zq1SrtT3/6k2axWLTly5fv5jMXu1us35UzzzxTe+ihh7TvvvtOW716tXb++edr2dnZ2pYtW3bzmYveEOv3Rbdhwwatb9++2qGHHqqdcMIJu+dkRa+K9bvS3t6uTZ48WTv22GO1RYsWaRs2bNA+/vhjbdmyZbv5zEVviPX78uyzz2o2m0179tlntQ0bNmjvv/++Vlpaql1zzTW7+czF7jZv3jztj3/8o/bqq69qgPbaa69F3H79+vVaWlqadu2112qrVq3SHnjgAc1kMmnvvfdeTO8roSOMAw88ULvsssu8j91ut9anTx/tzjvvDLn9aaedph133HEBz02ZMkW79NJLk3qeovfF+l0J5nK5tMzMTO3JJ59M1imKFNKT74vL5dKmTZum/fe//9XOO+88CR37iFi/K//617+0wYMHax0dHbvrFEUKifX7ctlll2lHHnlkwHPXXnutdvDBByf1PEVqiSZ0/P73v9dGjx4d8NycOXO0mTNnxvRe0l4VQkdHB0uXLmXGjBne54xGIzNmzGDx4sUh91m8eHHA9gAzZ84Mu73YO/TkuxKspaUFp9NJXl5esk5TpIiefl9uv/12ioqKuOiii3bHaYoU0JPvyptvvsnUqVO57LLLKC4uZsyYMfz1r3/F7XbvrtMWvaQn35dp06axdOlSbwvW+vXrmTdvHscee+xuOWex50jUNa45kSe1t6iursbtdlNcXBzwfHFxMT/++GPIfXbs2BFy+x07diTtPEXv68l3Jdj1119Pnz59uvwHLfY+Pfm+LFq0iMcee4xly5bthjMUqaIn35X169fz4YcfctZZZzFv3jzWrl3Lb37zG5xOJ7fccsvuOG3RS3ryfTnzzDOprq7mkEMOQdM0XC4Xv/rVr7jxxht3xymLPUi4a9yGhgZaW1txOBxRHUcqHUL0or/97W+88MILvPbaa9jt9t4+HZFiGhsbOeecc3j00UcpKCjo7dMRKc7j8VBUVMR//vMfJk2axJw5c/jjH//II4880tunJlLQxx9/zF//+lcefvhhvv32W1599VXeeecd7rjjjt4+NbGXkkpHCAUFBZhMJiorKwOer6yspKSkJOQ+JSUlMW0v9g49+a7o7rrrLv72t7/xwQcfMG7cuGSepkgRsX5f1q1bx8aNG5k1a5b3OY/HA4DZbKa8vJwhQ4Yk96RFr+jJ/1tKS0uxWCyYTCbvcyNHjmTHjh10dHRgtVqTes6i9/Tk+3LTTTdxzjnncPHFFwMwduxYmpub+eUvf8kf//hHjEb5vbRQwl3jZmVlRV3lAKl0hGS1Wpk0aRILFy70PufxeFi4cCFTp04Nuc/UqVMDtgdYsGBB2O3F3qEn3xWAf/zjH9xxxx289957TJ48eXecqkgBsX5fRowYwfLly1m2bJn3z+zZszniiCNYtmwZ/fv3352nL3ajnvy/5eCDD2bt2rXeYAqwZs0aSktLJXDs5XryfWlpaekSLPTAqsYXC6Ek7Bo3tjHu+44XXnhBs9ls2ty5c7VVq1Zpv/zlL7WcnBxtx44dmqZp2jnnnKPdcMMN3u0///xzzWw2a3fddZe2evVq7ZZbbpEpc/cRsX5X/va3v2lWq1V75ZVXtO3bt3v/NDY29tZHELtRrN+XYDJ71b4j1u/K5s2btczMTO3yyy/XysvLtbffflsrKirS/vznP/fWRxC7Uazfl1tuuUXLzMzUnn/+eW39+vXa/PnztSFDhminnXZab30EsZs0NjZq3333nfbdd99pgHbPPfdo3333nbZp0yZN0zTthhtu0M455xzv9vqUub/73e+01atXaw899JBMmZtoDzzwgFZWVqZZrVbtwAMP1L788kvva9OnT9fOO++8gO1feuklbdiwYZrVatVGjx6tvfPOO7v5jEVvieW7MmDAAA3o8ueWW27Z/ScuekWs/2/xJ6Fj3xLrd+WLL77QpkyZotlsNm3w4MHaX/7yF83lcu3msxa9JZbvi9Pp1G699VZtyJAhmt1u1/r376/95je/0Wpra3f/iYvd6qOPPgp5HaJ/P8477zxt+vTpXfaZMGGCZrVatcGDB2tPPPFEzO9r0DSpoQkhhBBCCCGSR8Z0CCGEEEIIIZJKQocQQgghhBAiqSR0CCGEEEIIIZJKQocQQgghhBAiqSR0CCGEEEIIIZJKQocQQgghhBAiqSR0CCGEEEIIIZJKQocQQgghhBAiqSR0CCGESLqBAwdy3333eR8bDAZef/31pL3fxx9/jMFgoK6uLmnv4e/888/nxBNP9D4+/PDDufrqq3fLewshxJ7A3NsnIIQQYt+zfft2cnNze/s0kubVV1/FYrH09mkIIUTKkNAhhBCCjo4OrFbrbnu/kpKS3fZe0XI6nQkLCnl5eQk5jhBC7C2kvUoIIfYwhx9+OFdeeSW///3vycvLo6SkhFtvvTVgm82bN3PCCSeQkZFBVlYWp512GpWVld7Xb731ViZMmMB///tfBg0ahN1uB1Tb07///W+OP/540tLSGDlyJIsXL2bt2rUcfvjhpKenM23aNNatW+c91rp16zjhhBMoLi4mIyODAw44gA8++CDiZ/Bvr7r11lsxGAxd/sydOxcAj8fDnXfeyaBBg3A4HIwfP55XXnkl4Hjz5s1j2LBhOBwOjjjiCDZu3Njt36PBYOBf//oXs2fPJj09nb/85S+43W4uuugi73sNHz6c+++/P2A/t9vNtddeS05ODvn5+fz+979H07SAbYLbq0K1k+Xk5Hg/Y0dHB5dffjmlpaXY7XYGDBjAnXfe2e1nEEKIPYWEDiGE2AM9+eSTpKens2TJEv7xj39w++23s2DBAkBdpJ9wwgnU1NTwySefsGDBAtavX8+cOXMCjrF27Vr+97//8eqrr7Js2TLv83fccQfnnnsuy5YtY8SIEZx55plceuml/OEPf+Cbb75B0zQuv/xy7/ZNTU0ce+yxLFy4kO+++46jjz6aWbNmsXnz5qg+y3XXXcf27du9f+666y7S0tKYPHkyAHfeeSdPPfUUjzzyCCtXruSaa67h7LPP5pNPPgGgoqKCk08+mVmzZrFs2TIuvvhibrjhhqje+9Zbb+Wkk05i+fLlXHjhhXg8Hvr168fLL7/MqlWruPnmm7nxxht56aWXvPvcfffdzJ07l8cff5xFixZRU1PDa6+9FtX7hfPPf/6TN998k5deeony8nKeffZZBg4cGNcxhRAipWhCCCH2KNOnT9cOOeSQgOcOOOAA7frrr9c0TdPmz5+vmUwmbfPmzd7XV65cqQHaV199pWmapt1yyy2axWLRdu7cGXAcQPvTn/7kfbx48WIN0B577DHvc88//7xmt9sjnuPo0aO1Bx54wPt4wIAB2r333hvwPq+99lqX/RYvXqzZ7XbtxRdf1DRN09ra2rS0tDTtiy++CNjuoosu0s444wxN0zTtD3/4gzZq1KiA16+//noN0Gpra8OeI6BdffXVET+HpmnaZZddpv3iF7/wPi4tLdX+8Y9/eB87nU6tX79+2gknnOB9bvr06dpVV10V8F7Bnzc7O1t74oknNE3TtCuuuEI78sgjNY/H0+35CCHEnkgqHUIIsQcaN25cwOPS0lJ27twJwOrVq+nfvz/9+/f3vj5q1ChycnJYvXq197kBAwZQWFgY8djFxcUAjB07NuC5trY2GhoaAFXpuO666xg5ciQ5OTlkZGSwevXqqCsdus2bN3PiiSdy3XXXcdpppwGqGtPS0sJRRx1FRkaG989TTz3lbfFavXo1U6ZMCTjW1KlTo3pPvZri76GHHmLSpEkUFhaSkZHBf/7zH+9nqa+vZ/v27QHvZzabQx4nFueffz7Lli1j+PDhXHnllcyfPz+u4wkhRKqRgeRCCLEHCh7wbDAY8Hg8MR0jPT2922MbDIawz+nvd91117FgwQLuuusuhg4disPh4JRTTqGjoyPqc2lubmb27NlMnTqV22+/3ft8U1MTAO+88w59+/YN2Mdms0V9/HCC/w5eeOEFrrvuOu6++26mTp1KZmYm//d//8eSJUvieh+DwdBl3IfT6fTenzhxIhs2bODdd9/lgw8+4LTTTmPGjBldxq4IIcSeSkKHEELsZUaOHElFRQUVFRXeaseqVauoq6tj1KhRCX+/zz//nPPPP5+TTjoJUEEhmoHcOk3TOPvss/F4PDz99NPeUAOqQmOz2di8eTPTp08Puf/IkSN58803A5778ssvY/8gqM8ybdo0fvOb33if8x80n52dTWlpKUuWLOGwww4DwOVysXTpUiZOnBj2uIWFhWzfvt37+KeffqKlpSVgm6ysLObMmcOcOXM45ZRTOProo6mpqZGZsIQQewUJHUIIsZeZMWMGY8eO5ayzzuK+++7D5XLxm9/8hunTp8fdBhTKfvvtx6uvvsqsWbMwGAzcdNNNMVVdbr31Vj744APmz59PU1OTt7qRnZ1NZmYm1113Hddccw0ej4dDDjmE+vp6Pv/8c7KysjjvvPP41a9+xd13383vfvc7Lr74YpYuXeqdFaonn+Wpp57i/fffZ9CgQTz99NN8/fXXDBo0yLvNVVddxd/+9jf2228/RowYwT333NPtIoRHHnkkDz74IFOnTsXtdnP99dcHVI/uueceSktL2X///TEajbz88suUlJSQk5PTo88hhBCpRsZ0CCHEXsZgMPDGG2+Qm5vLYYcdxowZMxg8eDAvvvhiUt7vnnvuITc3l2nTpjFr1ixmzpwZ8bf+wT755BOampqYNm0apaWl3j/6+d5xxx3cdNNN3HnnnYwcOZKjjz6ad955xxsEysrK+N///sfrr7/O+PHjeeSRR/jrX//ao89y6aWXcvLJJzNnzhymTJnCrl27AqoeAL/97W8555xzOO+887wtWHqVJ5y7776b/v37c+ihh3LmmWdy3XXXkZaW5n09MzOTf/zjH0yePJkDDjiAjRs3Mm/ePIxG+WdaCLF3MGjBTaZCCCGEEEIIkUDyKxQhhBBCCCFEUknoEEIIIYQQQiSVhA4hhBBCCCFEUknoEEIIIYQQQiSVhA4hhBBCCCFEUknoEEIIIYQQQiSVhA4hhBBCCCFEUknoEEIIIYQQQiSVhA4hhBBCCCFEUknoEEIIIYQQQiSVhA4hhBBCCCFEUv0/FYdm5LlVg6AAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "import scipy.interpolate as scy\n", + "import numpy as np\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "# Here is the interpolation. Admittedly not entirely sure how this all works, but here goes. \n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) # Collect x and y values for the \"truth\" values. \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") # Interpolate cubically between them. \n", + "xnew = apositionList # Make the step size equal to our solver's.\n", + "xnew.pop(0)\n", + "ynew = f0(xnew) # Use interpolation function returned by `interp1d` to get \"truth\" values\n", + "ynew2 = acalculatedList0 # Manually put our solver's values in, we wish to avoid double interpolating\n", + "ynew2.pop(0) # The first value, printed at r=0, is not reported in the Original NRPy+ solver, get rid of it. \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "300b2e55-b5c3-48ba-9fa3-ba404d51eec6", + "metadata": {}, + "source": [ + "Although the method starts off well (as would practically any method), the 19th order AB method error starts to explode, and keeps going the longer the program runs. This is not the case for a 5th or 6th AB method, the errors are much better. For the complete solution to this exercise, you need to test this seeding with all orders of the AB method that are compatible with Odie. All you have to do is change the value of `adams_bashforth_order` in the modifiable main function from 1-19 and see what happens to this error plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3537b75e-6852-4399-a6fa-efefde26e59a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_4_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_4_Solution.ipynb new file mode 100644 index 00000000..09848249 --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_4_Solution.ipynb @@ -0,0 +1,2405 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 4 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "[Examples](NRPy+_OdieGM_Examples.ipynb)\n", + "\n", + "[Quickstart](NRPy+_OdieGM_Quickstart.ipynb)\n", + "\n", + "[Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb)\n", + "\n", + "[Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb)\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "5f0b24ed-bd69-4cab-acdc-27dadd97ee29", + "metadata": {}, + "source": [ + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "f6f74367-f351-4f58-825d-4a58747d4054", + "metadata": {}, + "source": [ + "1. [Exercise 4](#E4)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "3ff13d42-0a08-4544-8d34-075770cf161f", + "metadata": {}, + "source": [ + "\n", + "# Exercise 4 \\[Back to [top](#toc)\\]\n", + "\n", + "\"4) Using the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the differential equation $y''' = y' + y - 3x$. It will need to be split up into a system of three differential equations manually first. The initial conditions are $y(0) = 1$, $y'(0) = 0$, and $y''(0) = 0$. Evaluate at least to $x$=1.5.\"\n", + "\n", + "This exercise is a more advanced version of the first problem, but it is only applying what you have learned from working through the previous problems. Just like all other multiple-ordered ODEs, we need to break this apart into a system of 1st-ordered ODEs. Since we have a 3rd-ordered ODE, we need 3 ODEs in our system:\n", + "\n", + "$$y'(x) = u; y(0) = 1$$\n", + "$$u'(x) = v; u(0) = 0$$\n", + "$$v'(x) = u + y - 3x; v(0) = 0$$\n", + "These are the ODEs we want to plug into the solver, so we'll need to make sure to update the value of `number_of_equations` to 3." + ] + }, + { + "cell_type": "markdown", + "id": "26cbb586-48f6-4195-832a-58a87f1233dc", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "6dfcfc4a", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = {{333374427829017307697.0/51090942171709440000.0,-5148905233415267713.0/109168679854080000.0,395276943631267674287.0/1548210368839680000.0,-2129159630108649501931.0/2128789257154560000.0,841527158963865085639.0/283838567620608000.0,-189774312558599272277.0/27646613729280000.0,856822959645399341657.0/67580611338240000.0,-13440468702008745259589.0/709596419051520000.0,196513123964380075325537.0/8515157028618240000.0,-57429776853357830333.0/2494674910728000.0,53354279746900330600757.0/2838385676206080000.0,-26632588461762447833393.0/2128789257154560000.0,4091553114434184723167.0/608225502044160000.0,-291902259907317785203.0/101370917007360000.0,816476630884557765547.0/851515702861824000.0,-169944934591213283591.0/709596419051520000.0,239730549209090923561.0/5676771352412160000.0,-19963382447193730393.0/4257578514309120000.0,12600467236042756559.0/51090942171709440000.0},{0.0,57424625956493833.0/9146248151040000.0,-3947240465864473.0/92386344960000.0,497505713064683651.0/2286562037760000.0,-511501877919758129.0/640237370572800.0,65509525475265061.0/29640619008000.0,-38023516029116089751.0/8002967132160000.0,129650088885345917773.0/16005934264320000.0,-19726972891423175089.0/1778437140480000.0,3146403501110383511.0/256094948229120.0,-70617432699294428737.0/6402373705728000.0,14237182892280945743.0/1778437140480000.0,-74619315088494380723.0/16005934264320000.0,17195392832483362153.0/8002967132160000.0,-4543527303777247.0/5928123801600.0,653581961828485643.0/3201186852864000.0,-612172313896136299.0/16005934264320000.0,2460247368070567.0/547211427840000.0,-85455477715379.0/342372925440000.0},{0.0,0.0,14845854129333883.0/2462451425280000.0,-55994879072429317.0/1455084933120000.0,2612634723678583.0/14227497123840.0,-22133884200927593.0/35177877504000.0,5173388005728297701.0/3201186852864000.0,-5702855818380878219.0/1778437140480000.0,80207429499737366711.0/16005934264320000.0,-3993885936674091251.0/640237370572800.0,2879939505554213.0/463134672000.0,-324179886697104913.0/65330343936000.0,7205576917796031023.0/2286562037760000.0,-2797406189209536629.0/1778437140480000.0,386778238886497951.0/640237370572800.0,-551863998439384493.0/3201186852864000.0,942359269351333.0/27360571392000.0,-68846386581756617.0/16005934264320000.0,8092989203533249.0/32011868528640000.0},{0.0,0.0,0.0,362555126427073.0/62768369664000.0,-2161567671248849.0/62768369664000.0,740161300731949.0/4828336128000.0,-4372481980074367.0/8966909952000.0,72558117072259733.0/62768369664000.0,-131963191940828581.0/62768369664000.0,62487713370967631.0/20922789888000.0,-70006862970773983.0/20922789888000.0,62029181421198881.0/20922789888000.0,-129930094104237331.0/62768369664000.0,10103478797549069.0/8966909952000.0,-2674355537386529.0/5706215424000.0,9038571752734087.0/62768369664000.0,-1934443196892599.0/62768369664000.0,36807182273689.0/8966909952000.0,-25221445.0/98402304.0},{0.0,0.0,0.0,0.0,13325653738373.0/2414168064000.0,-60007679150257.0/1961511552000.0,3966421670215481.0/31384184832000.0,-25990262345039.0/70053984000.0,25298910337081429.0/31384184832000.0,-2614079370781733.0/1961511552000.0,17823675553313503.0/10461394944000.0,-2166615342637.0/1277025750.0,13760072112094753.0/10461394944000.0,-1544031478475483.0/1961511552000.0,1600835679073597.0/4483454976000.0,-58262613384023.0/490377888000.0,859236476684231.0/31384184832000.0,-696561442637.0/178319232000.0,1166309819657.0/4483454976000.0},{0.0,0.0,0.0,0.0,0.0,905730205.0/172204032.0,-140970750679621.0/5230697472000.0,89541175419277.0/871782912000.0,-34412222659093.0/124540416000.0,570885914358161.0/1046139494400.0,-31457535950413.0/38745907200.0,134046425652457.0/145297152000.0,-350379327127877.0/435891456000.0,310429955875453.0/581188608000.0,-10320787460413.0/38745907200.0,7222659159949.0/74724249600.0,-21029162113651.0/871782912000.0,6460951197929.0/1743565824000.0,-106364763817.0/402361344000.0},{0.0,0.0,0.0,0.0,0.0,0.0,13064406523627.0/2615348736000.0,-931781102989.0/39626496000.0,5963794194517.0/72648576000.0,-10498491598103.0/52306974720.0,20730767690131.0/58118860800.0,-34266367915049.0/72648576000.0,228133014533.0/486486000.0,-2826800577631.0/8072064000.0,2253957198793.0/11623772160.0,-20232291373837.0/261534873600.0,4588414555201.0/217945728000.0,-169639834921.0/48432384000.0,703604254357.0/2615348736000.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,4527766399.0/958003200.0,-6477936721.0/319334400.0,12326645437.0/191600640.0,-15064372973.0/106444800.0,35689892561.0/159667200.0,-41290273229.0/159667200.0,35183928883.0/159667200.0,-625551749.0/4561920.0,923636629.0/15206400.0,-17410248271.0/958003200.0,30082309.0/9123840.0,-4777223.0/17418240.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2132509567.0/479001600.0,-2067948781.0/119750400.0,1572737587.0/31933440.0,-1921376209.0/19958400.0,3539798831.0/26611200.0,-82260679.0/623700.0,2492064913.0/26611200.0,-186080291.0/3991680.0,2472634817.0/159667200.0,-52841941.0/17107200.0,26842253.0/95800320.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4325321.0/1036800.0,-104995189.0/7257600.0,6648317.0/181440.0,-28416361.0/453600.0,269181919.0/3628800.0,-222386081.0/3628800.0,15788639.0/453600.0,-2357683.0/181440.0,20884811.0/7257600.0,-25713.0/89600.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,14097247.0/3628800.0,-21562603.0/1814400.0,47738393.0/1814400.0,-69927631.0/1814400.0,862303.0/22680.0,-45586321.0/1814400.0,19416743.0/1814400.0,-4832053.0/1814400.0,1070017.0/3628800.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,16083.0/4480.0,-1152169.0/120960.0,242653.0/13440.0,-296053.0/13440.0,2102243.0/120960.0,-115747.0/13440.0,32863.0/13440.0,-5257.0/17280.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,198721.0/60480.0,-18637.0/2520.0,235183.0/20160.0,-10754.0/945.0,135713.0/20160.0,-5603.0/2520.0,19087.0/60480.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4277.0/1440.0,-2641.0/480.0,4991.0/720.0,-3649.0/720.0,959.0/480.0,-95.0/288.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1901.0/720.0,-1387.0/360.0,109.0/30.0,-637.0/360.0,251.0/720.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,55.0/24.0,-59.0/24.0,37.0/24.0,-3.0/8.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,23.0/12.0,-4.0/3.0,5.0/12.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0/2.0,-1.0/2.0},{0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c5d4ba59", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "b0fa46aa", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "245b247b", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "346fb2f1-6321-44d6-9689-edb6ac43d0e6", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "\n", + "Round up the usual suspects: We're going to making updates to the functions `diffy_Q_eval`, `known_Q_eval`, and `get_initial_condition`. This time, we have three equations instead of 1 or 2.\n", + "\n", + "#### diffy_Q_eval:\n", + "\n", + "Let's plug in our system of ODEs:\n", + "\n", + "`dydx[0] = y[1];`\n", + "\n", + "`dydx[1] = y[2];`\n", + "\n", + "`dydx[2] = y[1]+y[0]-3*x;`\n", + "\n", + "#### known_Q_eval:\n", + "\n", + "Just erase the inside of the function, we don't need to compare to it. Just keep `return 1` so it runs properly\n", + "\n", + "#### get_initial_condition:\n", + "\n", + "Plug in your three initial conditions to these equations as well:\n", + "\n", + "`y[0] = 1.0;`\n", + "\n", + "`y[1] = 0.0;`\n", + "\n", + "`y[2] = 0.0;`" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "86414d51", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "struct constant_parameters { \n", + " int dimension; // number that says how many constants we have. \n", + " // double rho;\n", + " // double parameter;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " return 0;\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + "\n", + " dydx[0] = y[1];\n", + " dydx[1] = y[2];\n", + " dydx[2] = y[1]+y[0]-3*x;\n", + "\n", + " return 1;\n", + "}\n", + "\n", + "\n", + "//This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) //This function is the other one passed using GSL's formulation. \n", + "//Allows the specific_methods file to be completely agnostic to whatever the user is doing. \n", + "{\n", + "\n", + " //y[0] = exp(x);\n", + "\n", + " return 1;\n", + " //report \"success\"\n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " y[0] = 1.0;\n", + " y[1] = 0.0;\n", + " y[2] = 0.0;\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + "\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "441a1b08-ba7b-4346-baa7-3bc67b54e280", + "metadata": {}, + "source": [ + "The only last update we need to make is to the modifiable main function. Make sure to set `number_of_equations` to 3." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a565cd03", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.01; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 3; // How many equations are in our system?\n", + " int number_of_constants = 0; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 500; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oUData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "f9303319-4934-42d1-90f6-dde14576ba53", + "metadata": {}, + "source": [ + "Now the rest you should be used to now. We'll run the plot code and see the solution we get." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "6ffc1243", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.40 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverCustom `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"User Custom System\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined in the customization section.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverCustom\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "# Note to change the name if you want to run more than once, otherwise it is ODESolverCustom.\n", + "# Will override the previous ODESolverCustom.\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverCustom\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "4cc9cc2d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 4.\n", + "Printing to file 'oUData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t1.00000000000000e+00,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\t\n", + "FINAL: Position:,\t1.95292668148831e+00,\tEquation 0:,\t4.52043132601397e-01,\tEquation 1:,\t-1.88602634411037e+00,\tEquation 2:,\t-4.39863630712765e+00,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "f220b31c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position:,\t0.00000000000000e+00,\tEquation 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1:,\t-1.56915996171240e+00,\tEquation 2:,\t-3.86529021393279e+00,\t\n", + "Position:,\t1.87990173531199e+00,\tEquation 0:,\t5.78504444232690e-01,\tEquation 1:,\t-1.58367198621506e+00,\tEquation 2:,\t-3.89009903963338e+00,\t\n", + "Position:,\t1.88364418097290e+00,\tEquation 0:,\t5.72550337592141e-01,\tEquation 1:,\t-1.59827707831000e+00,\tEquation 2:,\t-3.91502654836670e+00,\t\n", + "Position:,\t1.88738662663381e+00,\tEquation 0:,\t5.66541397343950e-01,\tEquation 1:,\t-1.61297568319718e+00,\tEquation 2:,\t-3.94007329382356e+00,\t\n", + "Position:,\t1.89112907229473e+00,\tEquation 0:,\t5.60477272685267e-01,\tEquation 1:,\t-1.62776824815426e+00,\tEquation 2:,\t-3.96523983267450e+00,\t\n", + "Position:,\t1.89487151795564e+00,\tEquation 0:,\t5.54357611135425e-01,\tEquation 1:,\t-1.64265522254786e+00,\tEquation 2:,\t-3.99052672458389e+00,\t\n", + "Position:,\t1.89861396361656e+00,\tEquation 0:,\t5.48182058528100e-01,\tEquation 1:,\t-1.65763705784467e+00,\tEquation 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"Position:,\t1.92341948006724e+00,\tEquation 0:,\t5.05810536141659e-01,\tEquation 1:,\t-1.75937032026860e+00,\tEquation 2:,\t-4.18743969310722e+00,\t\n", + "Position:,\t1.92669805800291e+00,\tEquation 0:,\t5.00019756582595e-01,\tEquation 1:,\t-1.77313697002590e+00,\tEquation 2:,\t-4.21051597944745e+00,\t\n", + "Position:,\t1.92997663593859e+00,\tEquation 0:,\t4.94183717792220e-01,\tEquation 1:,\t-1.78697943537773e+00,\tEquation 2:,\t-4.23368883188598e+00,\t\n", + "Position:,\t1.93325521387426e+00,\tEquation 0:,\t4.88302170683489e-01,\tEquation 1:,\t-1.80089803357529e+00,\tEquation 2:,\t-4.25695864830380e+00,\t\n", + "Position:,\t1.93653379180994e+00,\tEquation 0:,\t4.82374865127082e-01,\tEquation 1:,\t-1.81489308317732e+00,\tEquation 2:,\t-4.28032582844255e+00,\t\n", + "Position:,\t1.93981236974561e+00,\tEquation 0:,\t4.76401549947108e-01,\tEquation 1:,\t-1.82896490405623e+00,\tEquation 2:,\t-4.30379077391222e+00,\t\n", + "Position:,\t1.94309094768129e+00,\tEquation 0:,\t4.70381972916787e-01,\tEquation 1:,\t-1.84311381740418e+00,\tEquation 2:,\t-4.32735388819892e+00,\t\n", + "Position:,\t1.94636952561696e+00,\tEquation 0:,\t4.64315880754113e-01,\tEquation 1:,\t-1.85734014573928e+00,\tEquation 2:,\t-4.35101557667265e+00,\t\n", + "Position:,\t1.94964810355264e+00,\tEquation 0:,\t4.58203019117500e-01,\tEquation 1:,\t-1.87164421291181e+00,\tEquation 2:,\t-4.37477624659512e+00,\t\n", + "Position:,\t1.95292668148831e+00,\tEquation 0:,\t4.52043132601397e-01,\tEquation 1:,\t-1.88602634411037e+00,\tEquation 2:,\t-4.39863630712765e+00,\t\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oUData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "c2c517cf", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "\n", + "# truthList0 = []\n", + "# Uncomment or add more if validation is desired.\n", + "\n", + "calculatedList0 = []\n", + "# calculatedList1 = []\n", + "# Uncomment for plotting more than one value. \n", + "\n", + "# errorList0 = []\n", + "# Uncomment for lists to store errors. \n", + "\n", + "# i = 0\n", + "# Use this i if a check has to be performed as to which row we're on. \n", + "\n", + "# csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oUData.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Here is where you would do any post-processing. Remember, use np.array() on the lists so operations\n", + "# can be performed properly. \n", + "\n", + "# Remember to change labels!\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Custom Graph')\n", + "ax.plot(positionList, calculatedList0, color='r', label=\"Insert Label Here\") # marker='o' (or whatever symbol) can be added here. \n", + "\n", + "fig.set_size_inches(9,9)\n", + "# plt.xlim(0.0,1.0)\n", + "# plt.ylim(0.0,1.0)\n", + "# The above two lines can control the region of the graph displayed. Comment out for auto scaling. \n", + "\n", + "# ax.set_yscale(\"log\") # Found in matplotlib's documentation. \n", + "# Uncommenting this sets the scale to logarithmic. \n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "5b726157-8834-4ca5-bbb1-3acaa756fe33", + "metadata": {}, + "source": [ + "And that's really all there is to it for this one. Nothing you should be unfamiliar with if you have already done the first 3 problems, just 1 more equation in your system." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3deaff07-2e9e-4614-8a8f-f4b61f8d5f48", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_5_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_5_Solution.ipynb new file mode 100644 index 00000000..d7d7fd00 --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_5_Solution.ipynb @@ -0,0 +1,2368 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 5 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "74e0d50c-40d1-46c3-b0b7-dfcd9fe2913f", + "metadata": {}, + "source": [ + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "d03a4281-a7c6-4b17-bbff-84d9825e9761", + "metadata": {}, + "source": [ + "1. [Exercise 5](#E5)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "51f95be3-5cd5-4306-825a-f146c21a521e", + "metadata": {}, + "source": [ + "\n", + "# Exercise 5 \\[Back to [top](#toc)\\]\n", + "\n", + "\"5) In [Step 3](#S3) we have an `exception_handler`. Disable the `exception_handler`, what does this do to the data at the outer edge for various different methods?\"\n", + "\n", + "This is the easiest of the 6 exercises. All we want to do is comment out the exception handler used within `diffy_Q_Eval` to stop exceptions from being handled in the TOV equations." + ] + }, + { + "cell_type": "markdown", + "id": "d1e5538c-db6d-43a7-84b2-9ab2aaca0e0d", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d9b4753f", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = {{333374427829017307697.0/51090942171709440000.0,-5148905233415267713.0/109168679854080000.0,395276943631267674287.0/1548210368839680000.0,-2129159630108649501931.0/2128789257154560000.0,841527158963865085639.0/283838567620608000.0,-189774312558599272277.0/27646613729280000.0,856822959645399341657.0/67580611338240000.0,-13440468702008745259589.0/709596419051520000.0,196513123964380075325537.0/8515157028618240000.0,-57429776853357830333.0/2494674910728000.0,53354279746900330600757.0/2838385676206080000.0,-26632588461762447833393.0/2128789257154560000.0,4091553114434184723167.0/608225502044160000.0,-291902259907317785203.0/101370917007360000.0,816476630884557765547.0/851515702861824000.0,-169944934591213283591.0/709596419051520000.0,239730549209090923561.0/5676771352412160000.0,-19963382447193730393.0/4257578514309120000.0,12600467236042756559.0/51090942171709440000.0},{0.0,57424625956493833.0/9146248151040000.0,-3947240465864473.0/92386344960000.0,497505713064683651.0/2286562037760000.0,-511501877919758129.0/640237370572800.0,65509525475265061.0/29640619008000.0,-38023516029116089751.0/8002967132160000.0,129650088885345917773.0/16005934264320000.0,-19726972891423175089.0/1778437140480000.0,3146403501110383511.0/256094948229120.0,-70617432699294428737.0/6402373705728000.0,14237182892280945743.0/1778437140480000.0,-74619315088494380723.0/16005934264320000.0,17195392832483362153.0/8002967132160000.0,-4543527303777247.0/5928123801600.0,653581961828485643.0/3201186852864000.0,-612172313896136299.0/16005934264320000.0,2460247368070567.0/547211427840000.0,-85455477715379.0/342372925440000.0},{0.0,0.0,14845854129333883.0/2462451425280000.0,-55994879072429317.0/1455084933120000.0,2612634723678583.0/14227497123840.0,-22133884200927593.0/35177877504000.0,5173388005728297701.0/3201186852864000.0,-5702855818380878219.0/1778437140480000.0,80207429499737366711.0/16005934264320000.0,-3993885936674091251.0/640237370572800.0,2879939505554213.0/463134672000.0,-324179886697104913.0/65330343936000.0,7205576917796031023.0/2286562037760000.0,-2797406189209536629.0/1778437140480000.0,386778238886497951.0/640237370572800.0,-551863998439384493.0/3201186852864000.0,942359269351333.0/27360571392000.0,-68846386581756617.0/16005934264320000.0,8092989203533249.0/32011868528640000.0},{0.0,0.0,0.0,362555126427073.0/62768369664000.0,-2161567671248849.0/62768369664000.0,740161300731949.0/4828336128000.0,-4372481980074367.0/8966909952000.0,72558117072259733.0/62768369664000.0,-131963191940828581.0/62768369664000.0,62487713370967631.0/20922789888000.0,-70006862970773983.0/20922789888000.0,62029181421198881.0/20922789888000.0,-129930094104237331.0/62768369664000.0,10103478797549069.0/8966909952000.0,-2674355537386529.0/5706215424000.0,9038571752734087.0/62768369664000.0,-1934443196892599.0/62768369664000.0,36807182273689.0/8966909952000.0,-25221445.0/98402304.0},{0.0,0.0,0.0,0.0,13325653738373.0/2414168064000.0,-60007679150257.0/1961511552000.0,3966421670215481.0/31384184832000.0,-25990262345039.0/70053984000.0,25298910337081429.0/31384184832000.0,-2614079370781733.0/1961511552000.0,17823675553313503.0/10461394944000.0,-2166615342637.0/1277025750.0,13760072112094753.0/10461394944000.0,-1544031478475483.0/1961511552000.0,1600835679073597.0/4483454976000.0,-58262613384023.0/490377888000.0,859236476684231.0/31384184832000.0,-696561442637.0/178319232000.0,1166309819657.0/4483454976000.0},{0.0,0.0,0.0,0.0,0.0,905730205.0/172204032.0,-140970750679621.0/5230697472000.0,89541175419277.0/871782912000.0,-34412222659093.0/124540416000.0,570885914358161.0/1046139494400.0,-31457535950413.0/38745907200.0,134046425652457.0/145297152000.0,-350379327127877.0/435891456000.0,310429955875453.0/581188608000.0,-10320787460413.0/38745907200.0,7222659159949.0/74724249600.0,-21029162113651.0/871782912000.0,6460951197929.0/1743565824000.0,-106364763817.0/402361344000.0},{0.0,0.0,0.0,0.0,0.0,0.0,13064406523627.0/2615348736000.0,-931781102989.0/39626496000.0,5963794194517.0/72648576000.0,-10498491598103.0/52306974720.0,20730767690131.0/58118860800.0,-34266367915049.0/72648576000.0,228133014533.0/486486000.0,-2826800577631.0/8072064000.0,2253957198793.0/11623772160.0,-20232291373837.0/261534873600.0,4588414555201.0/217945728000.0,-169639834921.0/48432384000.0,703604254357.0/2615348736000.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,4527766399.0/958003200.0,-6477936721.0/319334400.0,12326645437.0/191600640.0,-15064372973.0/106444800.0,35689892561.0/159667200.0,-41290273229.0/159667200.0,35183928883.0/159667200.0,-625551749.0/4561920.0,923636629.0/15206400.0,-17410248271.0/958003200.0,30082309.0/9123840.0,-4777223.0/17418240.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2132509567.0/479001600.0,-2067948781.0/119750400.0,1572737587.0/31933440.0,-1921376209.0/19958400.0,3539798831.0/26611200.0,-82260679.0/623700.0,2492064913.0/26611200.0,-186080291.0/3991680.0,2472634817.0/159667200.0,-52841941.0/17107200.0,26842253.0/95800320.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4325321.0/1036800.0,-104995189.0/7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+ "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a0f04fd5", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "92d5f951", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b2102df1", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "1131dc97-a5ee-4fa2-92b2-c8bec76cee2e", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "There is only ONE CHANGE to be made to the code for the TOV example. In `diffy_Q_Eval` on the fourth line, there is a call to the exception handler. Just comment it out, and see what happens to the resulting plots of error." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "9e200082", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "\n", + "struct constant_parameters { \n", + " int dimension; // number that says how many we have. \n", + " double rho;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to hard code some limitations \n", + " // on some varaibles.\n", + " // Good for avoding some divide by zero errors, or going negative in a square root. \n", + " if (y[0] < 0) {\n", + " y[0] = 0;\n", + " }\n", + " // In this case, the TOV Equations, we need to make sure the pressure doesn't go negative.\n", + " // Physically, it cannot, but approximation methods can cross the P=0 line\n", + " // We just need a hard wall to prevent that. \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " // This funciton might be empty. It's only used if the user wants to have \n", + " // a special termination condition.\n", + " // Today we do. We terminate once the pressure hits zero, or goes below it. \n", + " // Notably we also consider ridiculously small pressures to be \"zero\" since we might be asymptotic. \n", + " if (y[0] < 1e-16) {\n", + " return 1;\n", + " } else {\n", + " return 0;\n", + " }\n", + " // return 1; for termination.\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + " // Sometimes we want to evaluate constants in the equation that change, \n", + " // but do not have derivative forms.\n", + " // Today, we do that for the total energy density. \n", + " params->rho = sqrt(y[0]) + y[0];\n", + " // The total energy density only depends on pressure. \n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + " // GSL-adapted evaluation function. \n", + " // It is possible to do this with one array, but GSL expects two. \n", + "\n", + " // Always check for exceptions first, then perform evaluations. \n", + " //exception_handler(x,y);\n", + " const_eval(x,y,params);\n", + "\n", + " // Dereference the struct\n", + " double rho = (*(struct constant_parameters*)params).rho;\n", + " // double parameter = (*(struct constant_parameters*)params).parameter;\n", + " // WHY oh WHY GSL do you demand we use a VOID POINTER to the struct...?\n", + " // https://stackoverflow.com/questions/51052314/access-variables-in-struct-from-void-pointer\n", + " // Make sure to dereference every parameter within the struct so it can be used below. \n", + "\n", + " // This if statement is an example of a special condition, \n", + " // in this case at x=0 we have a divide by zero problem. \n", + " // Fortunately, we manually know what the derivatives should be.\n", + " // Alternatively, we could define piecewise equations this way. \n", + " if(x == 0) {\n", + " dydx[0] = 0; \n", + " dydx[1] = 0;\n", + " dydx[2] = 0;\n", + " dydx[3] = 1;\n", + " }\n", + " else {\n", + " dydx[0] = -((rho+y[0])*( (2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0] ))/(x*2.0*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[1] = ((2.0*y[2])/(x) + 8.0*3.1415926535897931160*x*x*y[0])/(x*(1.0 - (2.0*y[2])/(x)));\n", + " dydx[2] = 4*3.1415926535897931160*x*x*rho;\n", + " dydx[3] = (y[3])/(x*sqrt(1.0-(2.0*y[2])/x));\n", + " // Visual Studio likes to complain that M_PI is not defined, even though it is. \n", + " // So we used 3.1415926535897931160. which is just M_PI printed out to extra digits.\n", + " // There was no observed change in the final product. \n", + " }\n", + " // This funciton is not guaranteed to work in all cases. For instance, we have manually \n", + " // made an exception for x=0, since evaluating at 0 produces infinities and NaNs. \n", + " // Be sure to declare any exceptions before running, both here and in exception_handler, \n", + " // depending on the kind of exception desired. \n", + "\n", + " return 0;\n", + " // GSL_SUCCESS is 0. We do not support fancy error codes like GSL. \n", + "}\n", + "\n", + "// This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) // This function is another one passed using GSL's formulation. \n", + "// Allows the nrpy_odiegm_user_methods.c file to be completely agnostic to whatever the user is doing. \n", + "{\n", + " // y[0] = ...\n", + " // y[1] = ...\n", + " // This function is only used if there are known solutions. \n", + " // Notably this is not the case for the TOV equations. \n", + " // If you do put anything here, make SURE it has the same order as the differential equations. \n", + " // In the case of TOV, that would be Pressure, nu, mass, and r-bar, in that order. \n", + "\n", + " return 1;\n", + " // report \"success,\" what would have been GSL_SUCCESS in the GSL formulation. \n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " // be sure to have these MATCH the equations in diffy_Q_eval\n", + " y[0] = 0.016714611225000002; // Pressure, can be calcualated from central baryon density. \n", + " y[1] = 0.0; // nu\n", + " y[2] = 0.0; // mass\n", + " y[3] = 0.0; // r-bar\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + " // Reading parameters from the constant_parameters struct is rather difficult, since it exists\n", + " // in the higher order \"objects\" as a void pointer. So the user should declare what constants\n", + " // are what for ease of use, usually for printing in an algorithmic way.\n", + " c[0] = params->rho; // Total energy density. \n", + " // Add more as required. \n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "ffce7883", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "555a60e1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated1 `...\n", + "(BENCH): Finished executing in 0.41 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined above.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above.\n", + "\n", + "os.chdir(\"../\")\n", + "# Return to parent directory\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated1\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverComplicated1\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "ad9bf613", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 4.\n", + "Printing to file 'oCData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t1.67146112250000e-02,\tEquation 1:,\t0.00000000000000e+00,\tEquation 2:,\t0.00000000000000e+00,\tEquation 3:,\t0.00000000000000e+00,\tConstant 0:,\t1.45999611225000e-01,\t\n", + "FINAL: Position:,\t9.89258236509741e+03,\tEquation 0:,\t nan,\tEquation 1:,\t -nan,\tEquation 2:,\t -nan,\tEquation 3:,\t -nan,\tConstant 0:,\t nan,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "1b3f1983", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "IOPub data rate exceeded.\n", + "The Jupyter server will temporarily stop sending output\n", + "to the client in order to avoid crashing it.\n", + "To change this limit, set the config variable\n", + "`--ServerApp.iopub_data_rate_limit`.\n", + "\n", + "Current values:\n", + "ServerApp.iopub_data_rate_limit=1000000.0 (bytes/sec)\n", + "ServerApp.rate_limit_window=3.0 (secs)\n", + "\n" + ] + } + ], + "source": [ + "with open(\"oCData.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "0c7d74ca-5070-4520-9737-3c0207eebd12", + "metadata": {}, + "source": [ + "Once again, don't panic if you see an error of \"IOPub data rate exceeded.\" It just means there is to much data for jupyter notebook to print. You can still see the raw file of `oCData.txt` by opening it up in its file location." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "fa051a1d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 47, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "# Csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "# plt.ylim(0.0,0.15)\n", + "# plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "cc265c0a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "calculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('radius')\n", + "ax.set_ylabel('result')\n", + "ax.set_title('TOV Solution Detail')\n", + "ax.plot(positionList, calculatedList0, color='b', label=\"PRESSURE\") \n", + "ax.plot(positionList, calculatedList1, color='r', label=\"ν\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"MASS\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"POLYTROPIC RADIUS\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"DENSITY\") \n", + "\n", + "plt.ylim(0.0,0.15)\n", + "plt.xlim(0.0,1)\n", + "fig.set_size_inches(9,9)\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "cd749afd-c53f-41e9-839a-2e43c7180d19", + "metadata": {}, + "source": [ + "Well that's quite interesting. At a glance, this plot looks identical to the plot that comes out of the TOV example without any modifications. Does the exception handler do anything?\n", + "\n", + "Well, notice what happens when we look at the data. Some nans have occured. How bad could this affect the error of the plots?" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "id": "a41b0876", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "import scipy.interpolate as scy\n", + "import numpy as np\n", + "\n", + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "# Here is the interpolation. Admittedly not entirely sure how this all works, but here goes. \n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) # Collect x and y values for the \"truth\" values. \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\") # Interpolate cubically between them. \n", + "xnew = apositionList # Make the step size equal to our solver's.\n", + "xnew.pop(0)\n", + "ynew = f0(xnew) # Use interpolation function returned by `interp1d` to get \"truth\" values\n", + "ynew2 = acalculatedList0 # Manually put our solver's values in, we wish to avoid double interpolating\n", + "ynew2.pop(0) # The first value, printed at r=0, is not reported in the Original NRPy+ solver, get rid of it. \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it.\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) # Use interpolation function returned by `interp1d`\n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0) # The first value, printd at zero, is not reported in the NRPy+ solver, get rid of it\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "b153597b-3bca-4936-8f34-1129f9865b12", + "metadata": {}, + "source": [ + "Nothings plotting! NaNs cause some serious issues in the actual results of your solver, even breaking the code in some cases. Let's try to move forward at a more uniform step by setting `no_adaptive_step` to true, and see what the error looks like after 100000 steps." + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "9b2c9cca", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.00001; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 4; // How many equations are in our system?\n", + " int number_of_constants = 1; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 100000; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = true; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oCData2.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "c06cfe4d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OUCH! Found main in outC_function_master_list.\n", + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverComplicated2 `...\n", + "(BENCH): Finished executing in 0.41 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " \n", + " desc = \"Complicated Example: TOV Solver\"\n", + " \n", + " c_type = \"int\" \n", + " \n", + " name = \"main\"\n", + " \n", + " params = \"\"\n", + " \n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + "\n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "\n", + "os.chdir(\"../\")\n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverComplicated2\", compiler_opt_option=\"fast\")\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "\n", + "cmd.Execute(\"ODESolverComplicated2\", \"\", \"terminalOutput.txt\")" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "id": "bdf5b9fc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 59, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "positionList = []\n", + "calculatedList0 = []\n", + "calculatedList1 = []\n", + "calculatedList2 = []\n", + "calculatedList3 = []\n", + "\n", + "with open(sys.path[0] + '/outputTOVpolytropeMedium.txt') as f: # Data from Original NRPy+ TOV Solver\n", + " reader = csv.reader(f, delimiter=' ')\n", + " for row in reader:\n", + " positionList.append(float(row[0]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[1]))\n", + " calculatedList2.append(float(row[4]))\n", + " calculatedList3.append(float(row[7]))\n", + "\n", + "apositionList = []\n", + "acalculatedList0 = []\n", + "acalculatedList1 = []\n", + "acalculatedList2 = []\n", + "acalculatedList3 = []\n", + "acalculatedList4 = []\n", + "\n", + "with open('oCData2.txt') as f: \n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " apositionList.append(float(row[1]))\n", + " acalculatedList0.append(float(row[3]))\n", + " acalculatedList1.append(float(row[5]))\n", + " acalculatedList2.append(float(row[7]))\n", + " acalculatedList3.append(float(row[9]))\n", + " acalculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.set_xlabel('normalized radius')\n", + "ax.set_ylabel('relative error')\n", + "ax.set_title('Relative Errors Treating Cubically Interpolated Original NRPy+ TOV as Truth.')\n", + "\n", + "R_Schw = apositionList[-1]\n", + "M = acalculatedList2[-1]\n", + "Rbar_Schw = acalculatedList3[-1]\n", + "\n", + "C = 0.5*(np.sqrt(R_Schw*(R_Schw - 2.0*M)) + R_Schw - M) / Rbar_Schw\n", + "\n", + "interpList0 = scy.interp1d(positionList, np.array(calculatedList0))\n", + "xNew = np.arange(0.63,0.8)\n", + "yNew = interpList0(np.arange(0.63,0.8))\n", + "\n", + "from scipy import interpolate\n", + "x0 = np.array(positionList)\n", + "y0 = np.array(calculatedList0) \n", + "f0 = interpolate.interp1d(x0, y0, \"cubic\")\n", + "xnew = apositionList \n", + "xnew.pop(0)\n", + "ynew = f0(xnew) \n", + "ynew2 = acalculatedList0 \n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'blue', label=\"PRESSURE\")\n", + "\n", + "from scipy import interpolate\n", + "x2 = np.array(positionList)\n", + "y2 = np.array(calculatedList2)\n", + "f2 = interpolate.interp1d(x2, y2, \"cubic\")\n", + "ynew = f2(xnew) \n", + "ynew2 = acalculatedList2\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'green', label=\"MASS\")\n", + "\n", + "from scipy import interpolate\n", + "x3 = np.array(positionList)\n", + "y3 = np.array(calculatedList3)\n", + "f3 = interpolate.interp1d(x3, y3, \"cubic\")\n", + "ynew = f3(xnew) \n", + "ynew2 = acalculatedList3\n", + "ynew2.pop(0) \n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-np.array(ynew2)*C)/ynew), 'olive', label=\"POLYTROPIC RADIUS\")\n", + "\n", + "from scipy import interpolate\n", + "x4 = np.array(positionList)\n", + "y4 = np.array(calculatedList1)\n", + "f4 = interpolate.interp1d(x4, y4, \"cubic\")\n", + "ynew = f4(xnew) \n", + "ynew2 = acalculatedList4\n", + "ynew2.pop(0)\n", + "plt.plot(np.array(xnew)*(1.0/R_Schw), abs((ynew-ynew2)/ynew), 'purple', label=\"DENSITY\")\n", + "\n", + "# plt.ylim(0,0.001)\n", + "plt.xlim(0.0,1)\n", + "# https://stackoverflow.com/questions/332289/how-do-i-change-the-size-of-figures-drawn-with-matplotlib \n", + "# Setting size was annoying.\n", + "fig.set_size_inches(9,9)\n", + "ax.set_yscale(\"log\") # Found in matplotlib's documentation.\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "18ee68a0-918e-43c1-aff6-987f740d58f1", + "metadata": {}, + "source": [ + "After a certain point, look at the error spike! It only gets worse from there, giving us useless plots. This illustrates how important the exception handler is. Even though mathematically you may remain in the domain of your system, computers work a little differently. Even just slightly going \"out of bounds\" of your domain (like when the pressure here dips only slightly below zero) can cause a serious effect on your error. Make sure to always write out an exception handler that keeps you within the domain of your functions when even small roundoff errors occur." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d29b7c75-58e4-47ab-8a90-20eacc83a18a", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/OdieSolutions/NRPy+_OdieGM_Exercise_6_Solution.ipynb b/OdieSolutions/NRPy+_OdieGM_Exercise_6_Solution.ipynb new file mode 100644 index 00000000..6ad161af --- /dev/null +++ b/OdieSolutions/NRPy+_OdieGM_Exercise_6_Solution.ipynb @@ -0,0 +1,2456 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "be802a21", + "metadata": {}, + "source": [ + "# Ordinary Differential Equation Solver \"Odie:\" Exercise 6 Solution\n", + "\n", + "## Authors: Gabriel M Steward\n", + "\n", + "## Solutions: David Boyer\n", + "\n", + "### May 2023\n", + "\n", + "### NRPy+ Source Code for this module:\n", + "[cmdline_helper.py](/edit/cmdline_helper.py) (Multiplatform command line interface) \n", + "\n", + "[outputC.py](/edit/outputC.py) (NRPy+ code for packaging and compiling C)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb (template for using outputC.py)\n", + "\n", + "https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Solving_the_Scalar_Wave_Equation_with_NumPy.ipynb (basic Python plotting code)\n", + "\n", + "(All of this will need to be adjusted when properly inside the actual nrpytutorial repository). \n", + "\n", + "[Examples](NRPy+_OdieGM_Examples.ipynb)\n", + "\n", + "[Quickstart](NRPy+_OdieGM_Quickstart.ipynb)\n", + "\n", + "[Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb)\n", + "\n", + "[Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb)\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------\n" + ] + }, + { + "cell_type": "markdown", + "id": "3f26e008-2a8f-4842-8e7b-9b10742d9932", + "metadata": {}, + "source": [ + "\n", + "## Introduction:\n", + "This is the Odie Exercise Solution repository. In these six notebooks, I describe the solution to each of the exercise presented in the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook. Solutions to the other problems can be found here:\n", + "\n", + "1. [Exercise 1](NRPy+_OdieGM_Exercise_1_Solution.ipynb)\n", + "2. [Exercise 2](NRPy+_OdieGM_Exercise_2_Solution.ipynb)\n", + "3. [Exercise 3](NRPy+_OdieGM_Exercise_3_Solution.ipynb)\n", + "4. [Exercise 4](NRPy+_OdieGM_Exercise_4_Solution.ipynb)\n", + "5. [Exercise 5](NRPy+_OdieGM_Exercise_5_Solution.ipynb)\n", + "6. [Exercise 6](NRPy+_OdieGM_Exercise_6_Solution.ipynb)\n", + "\n", + "More detailed information about what Odie is and how it operates can be found in the [Full Documentation](NRPy+_OdieGM_Full_Documentation.ipynb) notebook. There are other notebooks as well; the [Examples](NRPy+_OdieGM_Examples.ipynb) notebook contains two examples of how to use Odie to solve problems, and the [Code Regeneration](NRPy+_OdieGM_Code_Regeneration.ipynb) notebook can produce Odie's C-files in case they are lost are changed in a way that can't be reversed. For new users, I'd recommend starting in the [Quickstart](NRPY+_OdieGM_Quickstart.ipynb) notebook to learn what each of the user functions do and how to use the main function template.\n", + "\n", + "-------------------------------------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "e4e130c0", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Table of Contents\n", + "$$\\label{toc}$$" + ] + }, + { + "cell_type": "markdown", + "id": "1fce59cd-2d43-4018-b285-bebbf9c557b9", + "metadata": {}, + "source": [ + "1. [Exercise 6](#E6)\n", + "\n", + "2. [Preliminary Code](#PC)\n", + "\n", + "3. [The Solution](#SOL)\n", + "\n", + "---------------------------------------------------------------------------------------------------------------" + ] + }, + { + "cell_type": "markdown", + "id": "954c37d8-59a9-4753-979b-7321267550e8", + "metadata": {}, + "source": [ + "\n", + "# Exercise 6 \\[Back to [top](#toc)\\]\n", + "\n", + "This is an updated exercise, as the prevoius exercise 6 was impossible to solve. As of writing this solution, it has not yet been changed in the NRPy+ repository, but should be changed within a few weeks of writing this solution.\n", + "\n", + "\"6) Use the custom area in the [Quickstart](NRPy+_OdieGM_Quickstart.ipynb) notebook, find the solution to the system of differential equations $z' = az+y^b+y^{1/c}; y' = bz+y^c$ with $z(0)$ = -1 and $y(0)$=1. Note the constants $a$, $b$, and $c$. They are defined as $a=2y$, $b=yz$, $c=z/5$. These values should be treated as constants and reported with the values of $y$ and $z$. Evaluate to at least $x$=0.443. This is a highly precise value for a reason—try evolving past it, see what happens!\"\n", + "\n", + "Now, the system is already setup in a format for Odie (coupled 1st-ordered ODEs). To solve this problem, we need to use our `const_eval` function." + ] + }, + { + "cell_type": "markdown", + "id": "cb835e91-5dea-4cda-9771-e4260a4e2d61", + "metadata": {}, + "source": [ + "\n", + "# Preliminary Code \\[Back to [top](#toc)\\]\n", + "This code needs to be run to work, but you do not need to look into it. Just execute the cells and move on." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8d7093cd", + "metadata": {}, + "outputs": [], + "source": [ + "import outputC as outC # NRPy+: Core C code output module.\n", + "import cmdline_helper as cmd # NRPy+: Multi-platform Python command-line interface\n", + "import os # Python: Miscellaneous operating system interfaces\n", + "import shutil # Python: High level file operations\n", + "\n", + "# https://github.com/zachetienne/nrpytutorial/blob/master/Tutorial-Start_to_Finish-Finite_Difference_Playground.ipynb\n", + "\n", + "# Create a C code output directory\n", + "# First, name it.\n", + "Ccodesrootdir = os.path.join(\"nrpy_odiegm_notebook_codes/\")\n", + "# Remove any previously existing files there.\n", + "shutil.rmtree(Ccodesrootdir,ignore_errors=True)\n", + "# Create the fresh directory. \n", + "cmd.mkdir(Ccodesrootdir)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6dfcfc4a", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_h = r\"\"\" \n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// Note: math.h requries the \"-lm\" arg be added at the END of tasks.json's arguments.\n", + "// https://askubuntu.com/questions/332884/how-to-compile-a-c-program-that-uses-math-h\n", + "\n", + "// ODE Solver \"Odie\"\n", + "// By G. M. Steward\n", + "// The main goal of this project is to solve Ordinary Differential Equation Systems\n", + "// in complete generality.\n", + "// This tenth version seeks to make this code functional as a drop-in replacement for GSL's solver. \n", + "\n", + "// Heavily influenced by Numerical Mathematics and Computing 6E by Cheney and Kincaid\n", + "// and GSL's ODE Solver, especially the method for adaptive time step and high-level funcitonality. \n", + "\n", + "// https://git.ligo.org/lscsoft/lalsuite/-/blob/master/lalsimulation/lib/LALSimIMRTEOBResumS.c\n", + "// Lalsuite section for what parts of GSL this was designed to replace. \n", + "\n", + "// This is the header file for Odie. \n", + "// It contains the structure definitions. \n", + "// The structs are defined below largely in accordance with GSL definitions. \n", + "// However, unecessary variables were removed, and many new ones were added. \n", + "// Butcher tables can be found at the bottom of this file. \n", + "// Function prototypes can be found in nrpy_odiegm_proto.c\n", + "\n", + "\n", + "typedef struct {\n", + " int (*function) (double x, double y[], double dydx[], void *params);\n", + " // The function passed to this struct contains the definitions of the differnetial equations. \n", + " // int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[], void *params); \n", + " // The Jacobian was a holdover from GSL, it will not be used in this program.\n", + " int (*true_function) (double x, double y[]);\n", + " // INSTEAD we will use the Jacobian's slot slot to allow passing of a true value! \n", + " // Naturally, this is only used if desired.\n", + " size_t dimension; //For storing how big our system of equations is. \n", + " // Just pass it an int, usually. \n", + " void *params; // For storing extra constants needed to evaluate the functions. \n", + " // params->dimension stores how many there are. \n", + " // Struct definition can be found in nrpy_odiegm_user_methods.c\n", + "} nrpy_odiegm_system;\n", + "\n", + "\n", + "typedef struct {\n", + " // Unlike with the system struct above, this step_type struct does not need\n", + " // to match GSL's form explicitly, it just needs to define the method.\n", + " int rows; \n", + " int columns; // Size of table for used method.\n", + " // Since we're dealing with void pointers we need a way to know how big everything is. \n", + " int order; // record the order.\n", + " // These are set at the bottom of this file. \n", + " void *butcher;\n", + " // Make sure to put this at the end of the struct\n", + " // in case we add more parts to it. Nonspecific arrays must be the last element.\n", + "\n", + " //Two of these step_type \"objects\" might be needed at once, depending on implementation. \n", + " //Fortunately you can make as many as you want. \n", + "} nrpy_odiegm_step_type;\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_step_type *type; \n", + " int rows; \n", + " int columns; // Since we are passing a void pointer to do this, we need a way\n", + " // to know how large it is in the end.\n", + " // Purposefully redundant with step_type's rows and columns value. \n", + " int method_type; // What type of method we are using? 0,1,2 values. \n", + " int adams_bashforth_order; // Order if an AB method is used.\n", + " void *y_values; // The extremely funky parameter that hides a 2D array, used when\n", + " // the past steps are important for AB method. \n", + " // Stored in step struct since it needs access to adams_bashforth_order for allocation.\n", + "} nrpy_odiegm_step;\n", + "\n", + "typedef struct {\n", + " // Various error parameters\n", + " double abs_lim; // Absolute error limiter\n", + " double rel_lim; // Relative error limiter\n", + " double scale_factor; // A scale factor used in the error comparison formula.\n", + " double error_safety; // A factor that limits how drastically things can change for stability.\n", + " double ay_error_scaler; // Weight given to error estimates related to the function itself.\n", + " double ady_error_scaler; // Weight given to error estimates related to the function's derivative.\n", + " double max_step_adjustment; // What is the largest growing step adjustment we'll allow?\n", + " double min_step_adjustment; // What is the smallest shrinking step adjustment we'll allow?\n", + " double absolute_max_step; // Largest allowed step?\n", + " double absolute_min_step; // Smallest allowed step?\n", + " double error_upper_tolerance; // If estimated error is higher than this, it is too high. \n", + " double error_lower_tolerance; // If estimated error is lower than this, it is too low.\n", + " // We added these ourselves. Control the error!\n", + " // We suppose this means that our control struct acts NOTHING like GSL's control struct\n", + " // save that it stores error limits. \n", + "} nrpy_odiegm_control;\n", + "\n", + "typedef struct\n", + "{\n", + " double *y0; // The values of the system of equations\n", + " double *yerr; // The estimated errors, if needed \n", + " double last_step; // Set to 1 when we are at the last step.\n", + " // Probably not used but the user may want it for some reason. \n", + " // Could be used as a termination condition. \n", + " double bound; // The point at which we started is sometimes important. \n", + " double current_position; // It's a good idea to know where we are at any given time. \n", + " unsigned long int count; // Equivalent to i. Keeps track of steps taken.\n", + " bool no_adaptive_step; // A simple toggle for forcing the steps to be the same or not.\n", + "} nrpy_odiegm_evolve;\n", + "\n", + "\n", + "\n", + "typedef struct {\n", + " const nrpy_odiegm_system *sys; // ODE system \n", + " nrpy_odiegm_evolve *e; // evolve struct \n", + " nrpy_odiegm_control *c; // control struct \n", + " nrpy_odiegm_step *s; // step struct, will contain step type \n", + " double h; // step size \n", + " // Curiously, this is where the step size is held. \n", + " // Usually it's passed to functions directly though. \n", + "} nrpy_odiegm_driver;\n", + "\n", + "\n", + "\n", + "// A collection of butcher tables, courtesy of NRPy+.\n", + "// This section just has definitions. \n", + "// Specifically of all the various kinds of stepper methods we have on offer. \n", + "\n", + "double butcher_Euler[2][2] = {{0.0,0.0},{1.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_euler0 = {2,2,1,&butcher_Euler};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_euler = &nrpy_odiegm_step_euler0;\n", + "\n", + "double butcher_RK2H[3][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_Heun0 = {3,3,2,&butcher_RK2H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Heun = &nrpy_odiegm_step_RK2_Heun0;\n", + "\n", + "double butcher_RK2MP[3][3] = {{0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0},{2.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_MP0 = {3,3,2,&butcher_RK2MP};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_MP = &nrpy_odiegm_step_RK2_MP0;\n", + "\n", + "double butcher_RK2R[3][3] = {{0.0,0.0,0.0},{2.0/3.0,2.0/3.0,0.0},{2.0,1.0/4.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK2_R0 = {3,3,2,&butcher_RK2R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK2_Ralston = &nrpy_odiegm_step_RK2_R0;\n", + "\n", + "double butcher_RK3[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{1.0,-1.0,2.0,0.0},{3.0,1.0/6.0,2.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_0 = {4,4,3,&butcher_RK3};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3 = &nrpy_odiegm_step_RK3_0;\n", + "\n", + "double butcher_RK3H[4][4] = {{0.0,0.0,0.0,0.0},{1.0/3.0,1.0/3.0,0.0,0.0},{2.0/3.0,0.0,2.0/3.0,0.0},{3.0,1.0/4.0,0.0,3.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_H0 = {4,4,3,&butcher_RK3H};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Heun = &nrpy_odiegm_step_RK3_H0;\n", + "\n", + "double butcher_RK3R[4][4] = {{0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_R0 = {4,4,3,&butcher_RK3R};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK3_Ralston = &nrpy_odiegm_step_RK3_R0;\n", + "\n", + "double butcher_RK3S[4][4] = {{0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0},{1.0/2.0,1.0/4.0,1.0/4.0,0.0},{3.0,1.0/6.0,1.0/6.0,2.0/3.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK3_S0 = {4,4,3,&butcher_RK3S};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_SSPRK3 = &nrpy_odiegm_step_RK3_S0;\n", + "\n", + "double butcher_RK4[5][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{1.0/2.0,0.0,1.0/2.0,0.0,0.0},{1.0,0.0,0.0,1.0,0.0},{4.0,1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_RK4_0 = {5,5,4,&butcher_RK4};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_RK4 = &nrpy_odiegm_step_RK4_0;\n", + "// This alternate name is declared for gsl drop in requirements. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk4 = &nrpy_odiegm_step_RK4_0;\n", + "\n", + "double butcher_DP5[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5_0 = {8,8,5,&butcher_DP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5 = &nrpy_odiegm_step_DP5_0;\n", + "\n", + "double butcher_DP5A[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0},{5.0,821.0/10800.0,0.0,19683.0/71825.0,175273.0/912600.0,395.0/3672.0,785.0/2704.0,3.0/50.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP5A_0 = {8,8,5,&butcher_DP5A};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP5alt = &nrpy_odiegm_step_DP5A_0;\n", + "\n", + "double butcher_CK5[7][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_CK5_0 = {7,7,5,&butcher_CK5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_CK5 = &nrpy_odiegm_step_CK5_0;\n", + "\n", + "double butcher_DP6[9][9] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/10.0,1.0/10.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{2.0/9.0,-2.0/81.0,20.0/81.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/7.0,615.0/1372.0,-270.0/343.0,1053.0/1372.0,0.0,0.0,0.0,0.0,0.0},{3.0/5.0,3243.0/5500.0,-54.0/55.0,50949.0/71500.0,4998.0/17875.0,0.0,0.0,0.0,0.0},{4.0/5.0,-26492.0/37125.0,72.0/55.0,2808.0/23375.0,-24206.0/37125.0,338.0/459.0,0.0,0.0,0.0},{1.0,5561.0/2376.0,-35.0/11.0,-24117.0/31603.0,899983.0/200772.0,-5225.0/1836.0,3925.0/4056.0,0.0,0.0},{1.0,465467.0/266112.0,-2945.0/1232.0,-5610201.0/14158144.0,10513573.0/3212352.0,-424325.0/205632.0,376225.0/454272.0,0.0,0.0},{6.0,61.0/864.0,0.0,98415.0/321776.0,16807.0/146016.0,1375.0/7344.0,1375.0/5408.0,-37.0/1120.0,1.0/10.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP6_0 = {9,9,6,&butcher_DP6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP6 = &nrpy_odiegm_step_DP6_0;\n", + "\n", + "// This one is left in terms of floating points, as the form stored in \n", + "// the butcher table includes irrational numbers and other stuff. \n", + "// double butcher_L6[8][8] = {{0.0,0,0,0,0,0,0,0},{1.0,1.0,0,0,0,0,0,0},{0.5,0.375,0.125,0,0,0,0,0},{0.6666666666666666,0.2962962962962963,0.07407407407407407,0.2962962962962963,0,0,0,0},{0.17267316464601143,0.051640768506639186,-0.04933518989886041,0.2960111393931624,-0.1256435533549298,0,0,0},{0.8273268353539885,-1.1854881643947648,-0.2363790958154253,-0.7481756236662596,0.8808545802392703,2.116515138991168,0,0},{1.0,4.50650248872424,0.6666666666666666,6.017339969931307,-4.111704479703632,-7.018914097580199,0.9401094519616178,0},{6.0,0.05,0.0,0.35555555555555557,0.0,0.2722222222222222,0.2722222222222222,0.05}};\n", + "// const double sqrt21 = 4.58257569495584; //explicitly declared to avoid the funky problems with consts. \n", + "// Manually added to the below definition since Visual Studio complained sqrt21 wasn't a constant.\n", + "double butcher_L6[8][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/2.0,3.0/8.0,1.0/8.0,0.0,0.0,0.0,0.0,0.0},{2.0/3.0,8.0/27.0,2.0/27.0,8.0/27.0,0.0,0.0,0.0,0.0},{1.0/2.0 - 4.58257569495584/14.0,-3.0/56.0 + 9.0*4.58257569495584/392.0,-1.0/7.0 + 4.58257569495584/49.0,6.0/7.0 - 6.0*4.58257569495584/49.0,-9.0/56.0 + 3.0*4.58257569495584/392.0,0.0,0.0,0.0},{4.58257569495584/14.0 + 1.0/2.0,-51.0*4.58257569495584/392.0 - 33.0/56.0,-1.0/7.0 - 4.58257569495584/49.0,-8.0*4.58257569495584/49.0,9.0/280.0 + 363.0*4.58257569495584/1960.0,4.58257569495584/5.0 + 6.0/5.0,0.0,0.0},{1.0,11.0/6.0 + 7.0*4.58257569495584/12.0,2.0/3.0,-10.0/9.0 + 14.0*4.58257569495584/9.0,7.0/10.0 - 21.0*4.58257569495584/20.0,-343.0/90.0 - 7.0*4.58257569495584/10.0,49.0/18.0 - 7.0*4.58257569495584/18.0,0.0},{6.0,1.0/20.0,0.0,16.0/45.0,0.0,49.0/180.0,49.0/180.0,1.0/20.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_L6_0 = {8,8,6,&butcher_L6};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_L6 = &nrpy_odiegm_step_L6_0;\n", + "\n", + "double butcher_DP8[14][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_DP8_0 = {14,14,8,&butcher_DP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_DP8 = &nrpy_odiegm_step_DP8_0;\n", + "\n", + "// Adaptive Methods\n", + "double butcher_AHE[4][3] = {{0.0,0.0,0.0},{1.0,1.0,0.0},{2.0,1.0/2.0,1.0/2.0},{2.0,1.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AHE_0 = {4,3,2,&butcher_AHE};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AHE = &nrpy_odiegm_step_AHE_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk2 = &nrpy_odiegm_step_AHE_0;\n", + "\n", + "double butcher_ABS[6][5] = {{0.0,0.0,0.0,0.0,0.0},{1.0/2.0,1.0/2.0,0.0,0.0,0.0},{3.0/4.0,0.0,3.0/4.0,0.0,0.0},{1.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,2.0/9.0,1.0/3.0,4.0/9.0,0.0},{3.0,7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ABS_0 = {6,5,3,&butcher_ABS};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ABS = &nrpy_odiegm_step_ABS_0;\n", + "\n", + "double butcher_ARKF[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/4.0,1.0/4.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/32.0,9.0/32.0,0.0,0.0,0.0,0.0},{12.0/13.0,1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0.0,0.0,0.0},{1.0,439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0.0,0.0},{1.0/2.0,-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0.0},{5.0,16.0/135.0,0.0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},{5.0,25.0/216.0,0.0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ARKF_0 = {8,7,5,&butcher_ARKF};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ARKF = &nrpy_odiegm_step_ARKF_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkf45 = &nrpy_odiegm_step_ARKF_0;\n", + "\n", + "double butcher_ACK[8][7] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0},{3.0/5.0,3.0/10.0,-9.0/10.0,6.0/5.0,0.0,0.0,0.0},{1.0,-11.0/54.0,5.0/2.0,-70.0/27.0,35.0/27.0,0.0,0.0},{7.0/8.0,1631.0/55296.0,175.0/512.0,575.0/13824.0,44275.0/110592.0,253.0/4096.0,0.0},{5.0,37.0/378.0,0.0,250.0/621.0,125.0/594.0,0.0,512.0/1771.0},{5.0,2825.0/27648.0,0.0,18575.0/48384.0,13525.0/55296.0,277.0/14336.0,1.0/4.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ACK_0 = {8,7,5,&butcher_ACK};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ACK = &nrpy_odiegm_step_ACK_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rkck = &nrpy_odiegm_step_ACK_0;\n", + "\n", + "double butcher_ADP5[9][8] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/5.0,1.0/5.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/10.0,3.0/40.0,9.0/40.0,0.0,0.0,0.0,0.0,0.0},{4.0/5.0,44.0/45.0,-56.0/15.0,32.0/9.0,0.0,0.0,0.0,0.0},{8.0/9.0,19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0.0,0.0,0.0},{1.0,9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0.0,0.0},{1.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,35.0/384.0,0.0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0.0},{5.0,5179.0/57600.0,0.0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP5_0 = {9,8,5,&butcher_ADP5};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP5 = &nrpy_odiegm_step_ADP5_0;\n", + "\n", + "double butcher_ADP8[15][14] = {{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/18.0,1.0/18.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/12.0,1.0/48.0,1.0/16.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{1.0/8.0,1.0/32.0,0.0,3.0/32.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{5.0/16.0,5.0/16.0,0.0,-75.0/64.0,75.0/64.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{3.0/8.0,3.0/80.0,0.0,0.0,3.0/16.0,3.0/20.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{59.0/400.0,29443841.0/614563906.0,0.0,0.0,77736538.0/692538347.0,-28693883.0/1125000000.0,23124283.0/1800000000.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0},{93.0/200.0,16016141.0/946692911.0,0.0,0.0,61564180.0/158732637.0,22789713.0/633445777.0,545815736.0/2771057229.0,-180193667.0/1043307555.0,0.0,0.0,0.0,0.0,0.0,0.0},{5490023248.0/9719169821.0,39632708.0/573591083.0,0.0,0.0,-433636366.0/683701615.0,-421739975.0/2616292301.0,100302831.0/723423059.0,790204164.0/839813087.0,800635310.0/3783071287.0,0.0,0.0,0.0,0.0,0.0},{13.0/20.0,246121993.0/1340847787.0,0.0,0.0,-37695042795.0/15268766246.0,-309121744.0/1061227803.0,-12992083.0/490766935.0,6005943493.0/2108947869.0,393006217.0/1396673457.0,123872331.0/1001029789.0,0.0,0.0,0.0,0.0},{1201146811.0/1299019798.0,-1028468189.0/846180014.0,0.0,0.0,8478235783.0/508512852.0,1311729495.0/1432422823.0,-10304129995.0/1701304382.0,-48777925059.0/3047939560.0,15336726248.0/1032824649.0,-45442868181.0/3398467696.0,3065993473.0/597172653.0,0.0,0.0,0.0},{1.0,185892177.0/718116043.0,0.0,0.0,-3185094517.0/667107341.0,-477755414.0/1098053517.0,-703635378.0/230739211.0,5731566787.0/1027545527.0,5232866602.0/850066563.0,-4093664535.0/808688257.0,3962137247.0/1805957418.0,65686358.0/487910083.0,0.0,0.0},{1.0,403863854.0/491063109.0,0.0,0.0,-5068492393.0/434740067.0,-411421997.0/543043805.0,652783627.0/914296604.0,11173962825.0/925320556.0,-13158990841.0/6184727034.0,3936647629.0/1978049680.0,-160528059.0/685178525.0,248638103.0/1413531060.0,0.0,0.0},{8.0,14005451.0/335480064.0,0.0,0.0,0.0,0.0,-59238493.0/1068277825.0,181606767.0/758867731.0,561292985.0/797845732.0,-1041891430.0/1371343529.0,760417239.0/1151165299.0,118820643.0/751138087.0,-528747749.0/2220607170.0,1.0/4.0},{8.0,13451932.0/455176623.0,0.0,0.0,0.0,0.0,-808719846.0/976000145.0,1757004468.0/5645159321.0,656045339.0/265891186.0,-3867574721.0/1518517206.0,465885868.0/322736535.0,53011238.0/667516719.0,2.0/45.0,0.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_ADP8_0 = {15,14,8,&butcher_ADP8};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_ADP8 = &nrpy_odiegm_step_ADP8_0;\n", + "// This alternate name is declared because of the need for GSL drop in. \n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_rk8pd = &nrpy_odiegm_step_ADP8_0;\n", + "\n", + "// Adams-Bashforth Method. Could be set to arbitrary size, but we chose 19. \n", + "// Should never need all 19.\n", + "double butcher_AB[19][19] = {{333374427829017307697.0/51090942171709440000.0,-5148905233415267713.0/109168679854080000.0,395276943631267674287.0/1548210368839680000.0,-2129159630108649501931.0/2128789257154560000.0,841527158963865085639.0/283838567620608000.0,-189774312558599272277.0/27646613729280000.0,856822959645399341657.0/67580611338240000.0,-13440468702008745259589.0/709596419051520000.0,196513123964380075325537.0/8515157028618240000.0,-57429776853357830333.0/2494674910728000.0,53354279746900330600757.0/2838385676206080000.0,-26632588461762447833393.0/2128789257154560000.0,4091553114434184723167.0/608225502044160000.0,-291902259907317785203.0/101370917007360000.0,816476630884557765547.0/851515702861824000.0,-169944934591213283591.0/709596419051520000.0,239730549209090923561.0/5676771352412160000.0,-19963382447193730393.0/4257578514309120000.0,12600467236042756559.0/51090942171709440000.0},{0.0,57424625956493833.0/9146248151040000.0,-3947240465864473.0/92386344960000.0,497505713064683651.0/2286562037760000.0,-511501877919758129.0/640237370572800.0,65509525475265061.0/29640619008000.0,-38023516029116089751.0/8002967132160000.0,129650088885345917773.0/16005934264320000.0,-19726972891423175089.0/1778437140480000.0,3146403501110383511.0/256094948229120.0,-70617432699294428737.0/6402373705728000.0,14237182892280945743.0/1778437140480000.0,-74619315088494380723.0/16005934264320000.0,17195392832483362153.0/8002967132160000.0,-4543527303777247.0/5928123801600.0,653581961828485643.0/3201186852864000.0,-612172313896136299.0/16005934264320000.0,2460247368070567.0/547211427840000.0,-85455477715379.0/342372925440000.0},{0.0,0.0,14845854129333883.0/2462451425280000.0,-55994879072429317.0/1455084933120000.0,2612634723678583.0/14227497123840.0,-22133884200927593.0/35177877504000.0,5173388005728297701.0/3201186852864000.0,-5702855818380878219.0/1778437140480000.0,80207429499737366711.0/16005934264320000.0,-3993885936674091251.0/640237370572800.0,2879939505554213.0/463134672000.0,-324179886697104913.0/65330343936000.0,7205576917796031023.0/2286562037760000.0,-2797406189209536629.0/1778437140480000.0,386778238886497951.0/640237370572800.0,-551863998439384493.0/3201186852864000.0,942359269351333.0/27360571392000.0,-68846386581756617.0/16005934264320000.0,8092989203533249.0/32011868528640000.0},{0.0,0.0,0.0,362555126427073.0/62768369664000.0,-2161567671248849.0/62768369664000.0,740161300731949.0/4828336128000.0,-4372481980074367.0/8966909952000.0,72558117072259733.0/62768369664000.0,-131963191940828581.0/62768369664000.0,62487713370967631.0/20922789888000.0,-70006862970773983.0/20922789888000.0,62029181421198881.0/20922789888000.0,-129930094104237331.0/62768369664000.0,10103478797549069.0/8966909952000.0,-2674355537386529.0/5706215424000.0,9038571752734087.0/62768369664000.0,-1934443196892599.0/62768369664000.0,36807182273689.0/8966909952000.0,-25221445.0/98402304.0},{0.0,0.0,0.0,0.0,13325653738373.0/2414168064000.0,-60007679150257.0/1961511552000.0,3966421670215481.0/31384184832000.0,-25990262345039.0/70053984000.0,25298910337081429.0/31384184832000.0,-2614079370781733.0/1961511552000.0,17823675553313503.0/10461394944000.0,-2166615342637.0/1277025750.0,13760072112094753.0/10461394944000.0,-1544031478475483.0/1961511552000.0,1600835679073597.0/4483454976000.0,-58262613384023.0/490377888000.0,859236476684231.0/31384184832000.0,-696561442637.0/178319232000.0,1166309819657.0/4483454976000.0},{0.0,0.0,0.0,0.0,0.0,905730205.0/172204032.0,-140970750679621.0/5230697472000.0,89541175419277.0/871782912000.0,-34412222659093.0/124540416000.0,570885914358161.0/1046139494400.0,-31457535950413.0/38745907200.0,134046425652457.0/145297152000.0,-350379327127877.0/435891456000.0,310429955875453.0/581188608000.0,-10320787460413.0/38745907200.0,7222659159949.0/74724249600.0,-21029162113651.0/871782912000.0,6460951197929.0/1743565824000.0,-106364763817.0/402361344000.0},{0.0,0.0,0.0,0.0,0.0,0.0,13064406523627.0/2615348736000.0,-931781102989.0/39626496000.0,5963794194517.0/72648576000.0,-10498491598103.0/52306974720.0,20730767690131.0/58118860800.0,-34266367915049.0/72648576000.0,228133014533.0/486486000.0,-2826800577631.0/8072064000.0,2253957198793.0/11623772160.0,-20232291373837.0/261534873600.0,4588414555201.0/217945728000.0,-169639834921.0/48432384000.0,703604254357.0/2615348736000.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,4527766399.0/958003200.0,-6477936721.0/319334400.0,12326645437.0/191600640.0,-15064372973.0/106444800.0,35689892561.0/159667200.0,-41290273229.0/159667200.0,35183928883.0/159667200.0,-625551749.0/4561920.0,923636629.0/15206400.0,-17410248271.0/958003200.0,30082309.0/9123840.0,-4777223.0/17418240.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2132509567.0/479001600.0,-2067948781.0/119750400.0,1572737587.0/31933440.0,-1921376209.0/19958400.0,3539798831.0/26611200.0,-82260679.0/623700.0,2492064913.0/26611200.0,-186080291.0/3991680.0,2472634817.0/159667200.0,-52841941.0/17107200.0,26842253.0/95800320.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4325321.0/1036800.0,-104995189.0/7257600.0,6648317.0/181440.0,-28416361.0/453600.0,269181919.0/3628800.0,-222386081.0/3628800.0,15788639.0/453600.0,-2357683.0/181440.0,20884811.0/7257600.0,-25713.0/89600.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,14097247.0/3628800.0,-21562603.0/1814400.0,47738393.0/1814400.0,-69927631.0/1814400.0,862303.0/22680.0,-45586321.0/1814400.0,19416743.0/1814400.0,-4832053.0/1814400.0,1070017.0/3628800.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,16083.0/4480.0,-1152169.0/120960.0,242653.0/13440.0,-296053.0/13440.0,2102243.0/120960.0,-115747.0/13440.0,32863.0/13440.0,-5257.0/17280.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,198721.0/60480.0,-18637.0/2520.0,235183.0/20160.0,-10754.0/945.0,135713.0/20160.0,-5603.0/2520.0,19087.0/60480.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4277.0/1440.0,-2641.0/480.0,4991.0/720.0,-3649.0/720.0,959.0/480.0,-95.0/288.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1901.0/720.0,-1387.0/360.0,109.0/30.0,-637.0/360.0,251.0/720.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,55.0/24.0,-59.0/24.0,37.0/24.0,-3.0/8.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,23.0/12.0,-4.0/3.0,5.0/12.0},{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.0/2.0,-1.0/2.0},{0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0}};\n", + "const nrpy_odiegm_step_type nrpy_odiegm_step_AB0 = {19,19,19,&butcher_AB};\n", + "const nrpy_odiegm_step_type *nrpy_odiegm_step_AB = &nrpy_odiegm_step_AB0;\n", + "// NOT comparable to GSL's AB method, so it is not named as such.\n", + "// Not adaptive, has to use constant time steps. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c5d4ba59", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_proto_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm.h\"\n", + "\n", + "// This file contains all the function prototypes that would usually be in the header.\n", + "// However, we split them off so the struct \"objects\" would occupy different files. \n", + "// The actual function definitions can be found in nrpy_odiegm_funcs.c\n", + "\n", + "// Allocation methods\n", + "nrpy_odiegm_step * nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim);\n", + "nrpy_odiegm_evolve * nrpy_odiegm_evolve_alloc (size_t dim);\n", + "nrpy_odiegm_control * nrpy_odiegm_control_y_new (double eps_abs, double eps_rel);\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel);\n", + "\n", + "// Memory freeing methods\n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c);\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e);\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s);\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state);\n", + "\n", + "// The actual stepping functions are below.\n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "// This is the primary function, it does most of the actual work. \n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]);\n", + "\n", + "// The rest of these are just modifications on the above, \n", + "// in fact all of them call nrpy_odiegm_evolve_apply when run. \n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]);\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]);\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]);\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b0fa46aa", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_funcs_c = r\"\"\"\n", + "\n", + "// #include \"nrpy_odiegm_proto.c\"\n", + "\n", + "// This file contains the actual definitions for the funcitons outlined in nrpy_odiegm_proto.c\n", + "\n", + "// Memory allocation functions.\n", + "nrpy_odiegm_step *\n", + "nrpy_odiegm_step_alloc (const nrpy_odiegm_step_type * T, size_t dim)\n", + "{\n", + " // Allocate the step \"object\", set all values, even those that may not be used. \n", + " nrpy_odiegm_step *s = (nrpy_odiegm_step *) malloc (sizeof (nrpy_odiegm_step));\n", + " s->type = T;\n", + " s->method_type = 1;\n", + " s->adams_bashforth_order = 0;\n", + " s->rows = T->rows;\n", + " s->columns = T->columns;\n", + " // these last two assignments might be unecessary, but it will be convenient if this number\n", + " // can be acessed at both levels. \n", + " if (T->rows == T->columns) {\n", + " s->method_type = 0; // aka, normal RK-type method. \n", + " }\n", + " if (T->rows == 19) {\n", + " s->method_type = 2; // AB method. \n", + " s->adams_bashforth_order = 4; // default order chosen, if user wants control they will \n", + " // specify elsewhere after allocation is run. \n", + " }\n", + "\n", + " s->y_values = (double *) malloc ((double)19.0 * dim * sizeof (double));\n", + " // This here is the array used to store past values.\n", + " // Only used for AB methods, but it still needs to be dynamically allocated. \n", + " // Having an adams_bashforth_order of 0 doesn't throw any errors, which is conveinent.\n", + "\n", + " return s;\n", + "}\n", + "\n", + "nrpy_odiegm_evolve *\n", + "nrpy_odiegm_evolve_alloc (size_t dim)\n", + "{\n", + " // Allocate the evolve \"object\" and set all values, even those that may not be used.\n", + " nrpy_odiegm_evolve *e = (nrpy_odiegm_evolve *) malloc (sizeof (nrpy_odiegm_evolve));\n", + " e->y0 = (double *) malloc (dim * sizeof (double));\n", + " e->yerr = (double *) malloc (dim * sizeof (double));\n", + " // Fill these with 0 just in case someone tries to allocate something. \n", + " for (int n = 0; n < dim; n++) {\n", + " e->y0[n] = 0.0;\n", + " e->yerr[n] = 0.0;\n", + " }\n", + " \n", + " e->count = 0;\n", + " e->last_step = 0.0; // By default we don't use this value. \n", + " e->bound = 0.0; // This will be adjusted when the first step is taken.\n", + " e->current_position = 0.0; //This will be regularly adjusted as the program goes on. \n", + " e->no_adaptive_step = false; // We assume adaptive by default. \n", + " return e;\n", + "}\n", + "\n", + "nrpy_odiegm_control *\n", + "nrpy_odiegm_control_y_new (double eps_abs, double eps_rel)\n", + "{\n", + " // Allocate the control \"object.\" Unusual wording of function name is due to us needing\n", + " // a GSL replacement. \n", + " nrpy_odiegm_control *c = (nrpy_odiegm_control *) malloc (sizeof (nrpy_odiegm_control));\n", + " c->abs_lim = eps_abs;\n", + " c->rel_lim = eps_rel;\n", + "\n", + " c->scale_factor = 0.9;\n", + " c->error_safety = 4.0/15.0;\n", + " c->ay_error_scaler = 1.0;\n", + " c->ady_error_scaler = 1.0;\n", + " c->max_step_adjustment = 5.0;\n", + " c->min_step_adjustment = 0.2;\n", + " c->absolute_max_step = 0.1;\n", + " c->absolute_min_step = 1e-10;\n", + " c->error_upper_tolerance = 1.1;\n", + " c->error_lower_tolerance = 0.5;\n", + " // These are all the default values, virtually all responsible for adaptive timestep and \n", + " // error estimation.\n", + "\n", + " return c;\n", + "}\n", + "\n", + "nrpy_odiegm_driver * nrpy_odiegm_driver_alloc_y_new (const nrpy_odiegm_system * sys,\n", + " const nrpy_odiegm_step_type * T,\n", + " const double hstart,\n", + " const double epsabs, const double epsrel)\n", + "{\n", + " // Initializes an ODE driver \"object\" which contains all the \"objets\" above, making a system\n", + " // that is prepared to evaluate a system of differential equations. \n", + "\n", + " nrpy_odiegm_driver *state;\n", + " state = (nrpy_odiegm_driver *) calloc (1, sizeof (nrpy_odiegm_driver));\n", + " const size_t dim = sys->dimension; \n", + " state->sys = sys;\n", + " state->s = nrpy_odiegm_step_alloc (T, dim);\n", + "\n", + " state->e = nrpy_odiegm_evolve_alloc (dim);\n", + " state->h = hstart; // the step size. \n", + "\n", + " state->c = nrpy_odiegm_control_y_new (epsabs, epsrel);\n", + "\n", + " // There were functions here in GSL that assigned the driver to the objects contained in the driver.\n", + " // We will not be doing that insanity. \n", + "\n", + " return state;\n", + "}\n", + "\n", + "// Memory freeing functions. \n", + "void nrpy_odiegm_control_free (nrpy_odiegm_control * c)\n", + "{\n", + " free (c);\n", + "}\n", + "void nrpy_odiegm_evolve_free (nrpy_odiegm_evolve * e)\n", + "{\n", + " free (e->yerr);\n", + " free (e->y0);\n", + " free (e);\n", + "}\n", + "void nrpy_odiegm_step_free (nrpy_odiegm_step * s)\n", + "{ \n", + " free (s->y_values);\n", + " free (s);\n", + "}\n", + "void nrpy_odiegm_driver_free (nrpy_odiegm_driver * state)\n", + "{\n", + " // In most cases, this method should be called alone, calling the others would be redundant. \n", + " if (state->c)\n", + " nrpy_odiegm_control_free (state->c);\n", + "\n", + " if (state->e)\n", + " nrpy_odiegm_evolve_free (state->e);\n", + "\n", + " if (state->s)\n", + " nrpy_odiegm_step_free (state->s);\n", + "\n", + " free (state);\n", + "}\n", + "\n", + "// The actual stepping functions follow. \n", + "\n", + "// The goal is for these functions to be completely agnostic to whatever the user is doing, \n", + "// they should always work regardless of the form of the system passed, the method passed, and even\n", + "// if the user does something dumb it shouldn't crash. It will spit out nonsense in those cases, though. \n", + "\n", + "int nrpy_odiegm_evolve_apply (nrpy_odiegm_evolve * e, nrpy_odiegm_control * c,\n", + " nrpy_odiegm_step * s,\n", + " const nrpy_odiegm_system * dydt, double *t,\n", + " double t1, double *h, double y[]) {\n", + " // This is the big one, the function that ACTUALLY performs the step.\n", + "\n", + " // First off, check if we're at the desired edge or not. \n", + " if (*t + *h > t1) {\n", + " *h = t1 - *t;\n", + " // If we're going past an endpoint we want, reduce the step size. \n", + " // Otherwise continue as normal. \n", + " // No need to stop the adaptive time step! If we need to increase the size, we\n", + " // Still report the smaller value, so it'll go through. \n", + " e->last_step = 1.0; // This is generally not used but the user might want it or something\n", + " // to tell that this has been triggered. \n", + " }\n", + "\n", + " // Gotta read in several things... improves readability.\n", + " // Don't need a million arrows everywhere if we do this. \n", + " int number_of_equations = (int)(dydt->dimension);\n", + " double current_position = *t;\n", + " e->current_position = *t;\n", + " double step = *h; \n", + "\n", + " unsigned long int i = e->count;\n", + " if (i == 0) {\n", + " e->bound = current_position;\n", + " // If this is our first ever step, record what the starting position was. \n", + " }\n", + "\n", + " bool no_adaptive_step = e->no_adaptive_step;\n", + "\n", + " int method_type = s->method_type; \n", + " int rows = s->type->rows;\n", + " int columns = s->type->columns;\n", + " int adams_bashforth_order = s->adams_bashforth_order;\n", + "\n", + " double absolute_error_limit = c->abs_lim;\n", + " double relative_error_limit = c->rel_lim;\n", + " double scale_factor = c->scale_factor;\n", + " double error_safety = c->error_safety;\n", + " double ay_error_scaler = c->ay_error_scaler;\n", + " double ady_error_scaler = c->ady_error_scaler;\n", + " double max_step_adjustment = c-> max_step_adjustment;\n", + " double min_step_adjustment = c->min_step_adjustment;\n", + " double absolute_max_step = c->absolute_max_step;\n", + " double absolute_min_step = c->absolute_min_step;\n", + " double error_upper_tolerance = c->error_upper_tolerance;\n", + " double error_lower_tolerance = c->error_lower_tolerance;\n", + "\n", + " double y_values[number_of_equations][adams_bashforth_order];\n", + "\n", + " int counter = 0; // This counter is reused time and time again for sifting through memory\n", + " // Allow me to express my dislike of void pointers. \n", + "\n", + " // The following section only runs if we're using an AB method, otherwise it jumps over. \n", + " if (adams_bashforth_order != 0) {\n", + " if (i == 0) {\n", + " // First time initialization of the y_values array for AB methods. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y_values[n][0] = y[n];\n", + " for (int m = 1; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = 0; // These values shouldn't be used, but zero them anyway. \n", + " } \n", + " }\n", + " } else {\n", + " // Load values from known y_values if not first step for AB method. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " y_values[n][m] = *((double *)(*s).y_values+counter); // Gotta fill in an array... joy...\n", + " counter++;\n", + " // This has to be done this way due to the array being passed as a void pointer. \n", + " } \n", + " }\n", + " }\n", + " }\n", + "\n", + " // Read in the step type. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = s->type;\n", + "\n", + " counter = 0;\n", + " if (method_type == 2) {\n", + " rows = adams_bashforth_order;\n", + " columns = adams_bashforth_order;\n", + " }\n", + " double butcher[rows][columns];\n", + " // This is the butcher table that actually defines the method we use. \n", + " if (method_type != 2) { // If we aren't using AB method, just fill it without anything special. \n", + " for (int k=0; k < rows; k++) {\n", + " for (int j = 0; j < columns; j++) {\n", + " butcher[k][j] = *((double *)(*step_type).butcher+counter);\n", + " counter++;\n", + " }\n", + " }\n", + " } else { // If we ARE using an AB method, we need to construct it a little more carefully. \n", + " counter = counter + 19*(19-adams_bashforth_order);\n", + " // Every row has 19 elements, and we need to clear 19-order rows, \n", + " // leaving only the order behind. \n", + " for (int i=0; i < adams_bashforth_order; i++) {\n", + " counter = counter + 19-adams_bashforth_order; \n", + " // for every row, clear the unneeded zeroes. \n", + " for (int j = 0; j < adams_bashforth_order; j++) {\n", + " butcher[i][j] = *((double *)(*step_type).butcher+counter);\n", + " // This slowly counts through the array via complciated void pointer nonsense. \n", + " counter++;\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (method_type != 2) {\n", + " // To use adaptive time-step, we need to store data at different step values:\n", + " double y_big_step[number_of_equations];\n", + " double y_smol_steps[number_of_equations];\n", + "\n", + " // One could argue that since the small steps will become our result \n", + " // we shouldn't declare it, however we are actually\n", + " // NOT going to assign the results to the actual answer y until we compare and run the adaptive\n", + " // time-step algorithm. We might throw out all the data and need to run it again! \n", + " double error_estimate[number_of_equations];\n", + " // even if we aren't limiting the constants, we can still report their error. \n", + " \n", + " double original_step = step;\n", + " // We need to be able to refer to the original step so we can \n", + " // see if we're adjusting it too much at once. \n", + " double previous_step = step;\n", + " // if we end up in a situation where the adaptive method wants to oscillate back and forth, \n", + " // we will occasionally need to know what the step we found before the current step is. \n", + "\n", + " // We rather explicitly do not actually take any steps until we confirm the error is below what we want.\n", + " bool error_satisfactory = false;\n", + " bool under_error = false;\n", + " bool over_error = false;\n", + " // It's important to declare these outside the error_satisfactory loop \n", + " // since to update the stepper we need to know exactly what kind of step change we just did. \n", + "\n", + " // This is a slapped together solution for indexing. \n", + " // Uses multiplication by 1 or 0 instead of an if statement on a bool. \n", + " int quick_patch = 1;\n", + " if (method_type == 2) {\n", + " quick_patch = 0;\n", + " }\n", + " // This constant removes certain components from consideraiton. \n", + "\n", + " bool floored = false;\n", + " // This is for a check hard-coded in for if we hit the *absolute minimum* step size. \n", + " // We have to make sure to run the loop one more time, so rather than exiting the loop\n", + " // we set this to true and run once more. \n", + "\n", + " while (error_satisfactory == false) {\n", + " \n", + " // All of the bellow values start off thinking they are the values from the \n", + " // previous step or initial conditions. \n", + " // We must reset them every time we return here. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " y_big_step[n] = y[n];\n", + " y_smol_steps[n] = y[n];\n", + " } \n", + " for (int iteration = 1; iteration < 4; iteration++) {\n", + " // So, we want to use Adaptive Timestep methodology. \n", + " // This will involve evaluating each step three times, \n", + " // In order to compare the evolution of two different \n", + " // step sizes and get an error estimate. \n", + " // Iteration 1 performs a normal step. \n", + " // Iteration 2 perofrms a half step.\n", + " // Iteration 3 performs another half step after the previous one. \n", + " // Naturally the half-step results are reported as truth, \n", + " // but we get an error estimate from the difference\n", + " // between the two values. \n", + "\n", + " // For inherently adaptive methods we only go through iteration 1 and 2\n", + " // Though instead of doing a half step, we use a second evaluation built\n", + " // into the method. \n", + " \n", + " // For AB method we only go through once, but do so with some additional operations. \n", + "\n", + " if (i == 0 && iteration == 1 && method_type == 0 && adams_bashforth_order == 0) {\n", + " // Don't take unecessary steps, if we are on the first step \n", + " // and have no need for the large step, ignore it.\n", + " // Since we always want the first step to go through \n", + " // don't bother calculating things we don't need. \n", + " iteration = 2;\n", + " // This doesn't actually apply to inherently adaptive methods \n", + " // since we cheat and do it in one iteration. \n", + " }\n", + "\n", + " double scale = 1.0;\n", + " // This is the number we use to scale. It's either 1 or 1/2, \n", + " // Depending on what size step we want. \n", + " int shift = 0;\n", + " // This is the number we set if we want to shift where we are evaluating from. \n", + " if (iteration == 1.0) {\n", + " // Scale remains 1\n", + " // Shift remains 0\n", + " } else if (iteration == 2.0) {\n", + " scale = 0.5; // Using half-steps.\n", + " // Shfit remains 0\n", + " } else {\n", + " scale = 0.5; //Using half-steps.\n", + " shift = 1; \n", + " }\n", + " // Every time it's needed, we multiply the step by the scale. \n", + "\n", + " double K[rows-method_type*quick_patch][number_of_equations];\n", + " // These are the K-values that are required to evaluate RK-like methods. \n", + " // They will be determined based on the provided butcher table.\n", + " // This is a 2D matrix since each diffyQ has its own set of K-values. \n", + " // Note that we subtract the method type from the row: \n", + " // adaptive RK butcher tables are larger. \n", + "\n", + " // Since we'll be calling K while it's empty, \n", + " // even though there should be no errors due\n", + " // to the way it's set up, let's go ahead and fill it with zeroes.\n", + " for (int j = 0; jfunction(x_Insert, y_insert, dy_out, dydt->params);\n", + " // y_insert goes in, dy_out comes out.\n", + "\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " K[j][n] = step*scale*dy_out[n];\n", + " // Fill in the K-values we just calculated. \n", + " } \n", + " }\n", + "\n", + " // Now that we have all the K-values set, we need to find \n", + " // the actual result in one final loop.\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " K[0][n] = y_smol_steps[n]; // The 0th spot in the K-values is reserved for \n", + " // holding the final value while it's being calculated. \n", + " for (int j = 1; j < columns; j++) {\n", + " K[0][n] = K[0][n] + butcher[rows-1-method_type*quick_patch][j]*K[j][n]; \n", + " // This is where the actual approximation is finally performed. \n", + " }\n", + " y_smol_steps[n] = K[0][n]; // Set ySmol to the new estimated value. \n", + " }\n", + " // Note that we specifically set ySmol to the value, not anything else. \n", + " // This is because we wish to avoid abusing if statements.\n", + "\n", + " if (iteration == 1) {\n", + " for (int n = 0; nfunction(current_position+step,y_smol_steps, error_limiter, dydt->params);\n", + "\n", + " // Now SmolSteps is used to set the error_limiter. \n", + " for (int n = 0; n error_upper_tolerance) {\n", + " // If we are 10% (or whatever value is specified) over what the error we want is, adjust. \n", + " over_error = true;\n", + " } else if (ratio_ED <= error_lower_tolerance) {\n", + " // If we are 50% (or whatever value is specified) under what the error we want is, adjust. \n", + " under_error = true;\n", + " }\n", + " if (no_adaptive_step == false && step != (min_step_adjustment * original_step)) {\n", + " // Before adjusting, record what the step size was a second ago. \n", + " previous_step = step;\n", + " \n", + " // If we have no trouble...\n", + " if (under_error == false && over_error == false) {\n", + " error_satisfactory = true;\n", + " }\n", + " // ...Say that we're cleared to move to the next step. \n", + " // However, if one of them was triggered, we need to adjust. \n", + " // In these cases we change the actual step size. \n", + " // It is theoretically possible for both to be triggered on different equations. \n", + " // In that case, over_error takes prescedent. \n", + " // We would rather have more accuracy than less in odd situations like that. \n", + "\n", + " // These if statements perform step adjustment if needed. Based on GSL's algorithm. \n", + " else if (over_error == true) {\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/butcher[rows-1-method_type*quick_patch][0]);\n", + " } else { // If under_error is true and over_error is false \n", + " //is the only way to get here. The true-true situation is skipped.\n", + " step = step * scale_factor * pow(ratio_ED,-1.0/(butcher[rows-1-method_type*quick_patch][0]+1));\n", + " error_satisfactory = true;\n", + " }\n", + "\n", + " // Check to see if we're adjusting the step too much at once. \n", + " // If we are, declare that we're done. \n", + " if (step > max_step_adjustment * original_step) {\n", + " step = max_step_adjustment * original_step;\n", + " error_satisfactory = true;\n", + " } else if (step < min_step_adjustment * original_step){\n", + " step = min_step_adjustment * original_step;\n", + " // We still have to go through again to make sure this applies, though. \n", + " // Thus there is no errorSatisfacotry = true here. \n", + " }\n", + "\n", + " if (floored == true) {\n", + " error_satisfactory = true;\n", + " } \n", + "\n", + " // We also declare some minium and maximum step conditions. \n", + " if (step > absolute_max_step) {\n", + " step = absolute_max_step;\n", + " error_satisfactory = true;\n", + " } else if (step < absolute_min_step){\n", + " step = absolute_min_step;\n", + " floored = true;\n", + " // This is set here since we need to run through one more time, \n", + " // not end right here. \n", + " }\n", + "\n", + " } else {\n", + " error_satisfactory = true;\n", + " under_error = false;\n", + " // This area is triggered when we purposefully take single steps.\n", + " // Or, alternatively, when we hit the minimum step size \n", + " // adjustment on the *previous* step\n", + " // but still needed to go through one more time. \n", + " }\n", + " // With that, the step size has been changed. If error_satisfactory is still false, \n", + " // it goes back and performs everything again with the new step size. \n", + " } else {\n", + " error_satisfactory = true;\n", + " // We always want the *first* step to go through without change, \n", + " // often the first step is chosen for a specific reason. \n", + " // In our work this generally came from a need to plot data sets against each other. \n", + " // Also do this if we are using the AB method, as it has no error checks. \n", + " }\n", + " }\n", + " \n", + " // Finally, we actually update the real answer. \n", + " for (int n = 0; nbound + (i+1)*step;\n", + " } else {\n", + " current_position = current_position + step;\n", + " }\n", + " }\n", + "\n", + " // Before, the values were Printed here. This method no longer prints, \n", + " // printing is done outside any method. \n", + "\n", + " if (adams_bashforth_order > 0) {\n", + " // At the END of every loop, we \"shift\" the values in the array \"down\" one space, \n", + " // that is, into the \"past.\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order - 1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + " }\n", + " } else {\n", + " // This loop is for the Adams-Bashforth method, which is implemented \n", + " // entirely differnetly from all RK methods.\n", + " // As such it needs an entirely different algorithm. \n", + "\n", + " // This is normally where we would calulate the K values, \n", + " // but they are entirely unecessary here.\n", + "\n", + " double y_insert[number_of_equations];\n", + " // We also need an array for the inserted y-values for each equation. \n", + "\n", + " double dy_out[number_of_equations];\n", + " // GSL demands that we use two separate arrays for y and y', so here's y'. \n", + "\n", + " double x_Insert; // This is generally going to be rather simple. \n", + "\n", + " // First, determine which row to use in the AB butcher table. \n", + " int current_row;\n", + " if (i < adams_bashforth_order-1) {\n", + " current_row = adams_bashforth_order-1-i;\n", + " // Basically, keep track of how many steps we actually have on offer to use. \n", + " } else {\n", + " current_row = 0;\n", + " // The highest order part of the method is used when we hit a certain step. \n", + " }\n", + "\n", + " for (int m = adams_bashforth_order-current_row-1; m >= 0; m--) {\n", + " // We actually need m=0 in this case, the \"present\" is evaluated. \n", + " x_Insert = e->bound + step*(i-m);\n", + " // The \"current locaiton\" depends on how far in the past we are.\n", + " for (int j = 0; j < number_of_equations ; j++) {\n", + " y_insert[j] = y_values[j][m];\n", + " }\n", + " // Grab the correct y_values for the proper time/location. \n", + "\n", + " // Now we actually evaluate the differential equations.\n", + " dydt->function(x_Insert, y_insert, dy_out, dydt->params);\n", + "\n", + " // With that evaluation, we can change the value of y for each equation. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " y[n] = y[n] + step*butcher[current_row][m+current_row]*dy_out[n];\n", + "\n", + " }\n", + " // Keep in mind this is procedural, y isn't right until all \n", + " // values of m have been cycled through. \n", + " }\n", + "\n", + " // At the END of every loop, we \"shift\" the values in the array \n", + " // down one space, that is, into the \"past\"\n", + " // Present values are 0, previous step is 1, step before that is 2, etc. \n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " for (int m = adams_bashforth_order-1; m > 0; m--) {\n", + " y_values[n][m] = y_values[n][m-1];\n", + " // Note that we start at the last column, m, and move the adjacent column to it. \n", + " // This pushes off the value at the largest m value, \n", + " // since it's far enough in the past we no longer care.\n", + " }\n", + " y_values[n][0] = y[n]; \n", + " // Present values update to what we just calculated. \n", + " // We have now completed stepping. \n", + " } \n", + "\n", + " current_position = e->bound+step*(i+1);\n", + " \n", + " }\n", + " \n", + " // Now we adjust any values that changed so everything outside the function can know it. \n", + " *h = step;\n", + " *t = current_position;\n", + " e->current_position = current_position;\n", + " e->count = i+1;\n", + "\n", + " // Update y_values, very important. We spent all that time shifting everything, \n", + " // we need to be able to access it next time this function is called! \n", + " counter = 0;\n", + "\n", + " if (adams_bashforth_order != 0) {\n", + " // Put the new y_values back into the stored array. \n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " for (int m = 0; m < adams_bashforth_order; m++) {\n", + " *((double *)(*s).y_values+counter) = y_values[n][m]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " } \n", + " }\n", + " }\n", + "\n", + " // In case the user needs it for some reason we also save the result to the evolve object.\n", + " counter = 0;\n", + " for (int n = 0; n< number_of_equations; n++) {\n", + " *((double *)(*e).y0+counter) = y[n]; // Gotta fill in an array... joy...\n", + " counter++;\n", + " }\n", + "\n", + " return 0; \n", + "}\n", + "\n", + "int nrpy_odiegm_evolve_apply_fixed_step (nrpy_odiegm_evolve * e,\n", + " nrpy_odiegm_control * con,\n", + " nrpy_odiegm_step * step,\n", + " const nrpy_odiegm_system * dydt,\n", + " double *t, double h0,\n", + " double y[]){\n", + " // This method performs a single fixed time step. \n", + " e->no_adaptive_step = true;\n", + " nrpy_odiegm_evolve_apply(e, con, step, dydt, t, *t+h0, &h0, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "int nrpy_odiegm_driver_apply (nrpy_odiegm_driver * d, double *t,\n", + " const double t1, double y[]){\n", + " // Takes as many steps as requested at the driver level. \n", + " // Only really useful if you don't want to report anything until the end. Which. Sure.\n", + " while (*t < t1) {\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, d->sys, t, t1, &(d->h), y);\n", + " }\n", + "\n", + " return 0;\n", + "}\n", + "int nrpy_odiegm_driver_apply_fixed_step (nrpy_odiegm_driver * d, double *t,\n", + " const double h,\n", + " const unsigned long int n,\n", + " double y[]){\n", + " // This just forces a fixed-step extrapolation. \n", + " d->e->no_adaptive_step = true;\n", + " nrpy_odiegm_driver_apply(d, t, h*(double)n, y);\n", + "\n", + " return 0;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "245b247b", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_standard = r\"\"\"\n", + "\n", + " // We need to define a struct that can hold all possible constants. \n", + " struct constant_parameters cp; \n", + " cp.dimension = number_of_constants;\n", + " // We'll set the actual parameters later. \n", + " // Do note that cp itself needs to be declared in constant_parameters in \n", + " // nrpy_odiegm_user_methods.c manually.\n", + " // The methods that make use of it it need to be declared as well, if they are used.\n", + "\n", + " nrpy_odiegm_system system = {diffy_Q_eval,known_Q_eval,number_of_equations,&cp};\n", + " // This is the system of equations we solve.\n", + " // The second slot was originally the Jacobian in GSL, but we use it to pass a \n", + " // true answer function that may or may not be used.\n", + "\n", + " nrpy_odiegm_driver *d;\n", + " d = nrpy_odiegm_driver_alloc_y_new(&system, step_type, step, absolute_error_limit, relative_error_limit); \n", + " // This is the \"object\" (struct) that runs everything, contains every needed varaible, etc. \n", + " // Basically the master of the whole thing, hence why it's called the \"driver\"\n", + " // Contains three major sub-objects besides the step type. \n", + " // c is the controller, which is primarily used to store adaptive timestep values. \n", + " // s is the step, which has the step type in it, but also parameters that describe the steps.\n", + " // e is the evolver, which actually performs the update when it is requested. \n", + "\n", + " int method_type = 1;\n", + " if (step_type->rows == step_type->columns) {\n", + " method_type = 0; // AKA, normal RK-type method. \n", + " } // No need for an else, we set it to 1 earlier to represent Adaptive methods. \n", + " if (step_type->rows == 19) { \n", + " method_type = 2;\n", + " } else {\n", + " adams_bashforth_order = 0;\n", + " }\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = no_adaptive_step;\n", + " // Based on what type of method we are using, we adjust some parameters within the driver.\n", + "\n", + " if (method_type == 2) {\n", + " printf(\"Method Order: %i.\\n\",adams_bashforth_order);\n", + " } else {\n", + " printf(\"Method Order: %i.\\n\",step_type->order); \n", + " }\n", + " \n", + " double y[number_of_equations];\n", + " // These next few variables temporarily store the values calculated before they are \n", + " // printed to the output file and forgotten.\n", + " // y contains the values of the actual equations. \n", + " // Each array only holds values at one evaluation point, but one for each Equation.\n", + "\n", + " double c[number_of_constants];\n", + " // c is just used to hold any constants we wish to report. \n", + " // You'd think that, since we have the constants in a struct, we can avoid declaring this.\n", + " // No. Not as far as we can tell, anyway. Structs are a pain to iterate through,\n", + " // and we can't know what form the user is going to hand us the struct in. \n", + "\n", + " // This here sets the initial conditions as declared in get_initial_condition\n", + " get_initial_condition(y); \n", + " const_eval(current_position, y,&cp);\n", + " assign_constants(c,&cp); \n", + "\n", + " FILE *fp2;\n", + " fp2 = fopen(file_name,\"w\");\n", + " printf(\"Printing to file '%s'.\\n\",file_name);\n", + "\n", + " // Open the file we'll be writing data to. \n", + "\n", + " // First, print the location we are at. \n", + " printf(\"INITIAL: Position:,\\t%f,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " // Second, go through and print the result for every single equation in our system.\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + " // Third, print out desired constants.\n", + " assign_constants(c,&cp); \n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " }\n", + " // Lastly, the newline character. \n", + " printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + " // Comma delimiters are printed to the file so it can be read as .csv with ease. \n", + "\n", + " if (report_error_estimates == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // In order to keep things neat and regular in the file, print a first line of errors. \n", + " // Even though by necessity all of them must be zero. \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i:,\\t0.0,\\t\",n);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " // SECTION II: The Loop\n", + "\n", + " // This loop fills out all the data.\n", + " // It takes a provided butcher table and executes the method stored within. \n", + " // Any RK table should work, even one not included by default.\n", + " // Also handles AB methods up to 19th order. No one should ever need more. \n", + "\n", + " for (int i = 0; i < size; i++){\n", + " \n", + " // Hybrid Methods require some fancy footwork, hence the if statements below. \n", + " if (method_type == 2 && i == 0 && step_type_2 != nrpy_odiegm_step_AB) {\n", + " d->s->type = step_type_2;\n", + " d->s->rows = step_type_2->rows;\n", + " d->s->columns = step_type_2->columns;\n", + " d->s->method_type = 0;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " } else if (step_type != step_type_2 && method_type == 2 && i == adams_bashforth_order) {\n", + " d->s->type = step_type;\n", + " d->s->rows = step_type->rows;\n", + " d->s->columns = step_type->columns;\n", + " d->s->method_type = 2;\n", + " d->s->adams_bashforth_order = adams_bashforth_order;\n", + " d->e->no_adaptive_step = true;\n", + " }\n", + "\n", + " nrpy_odiegm_evolve_apply(d->e, d->c, d->s, &system, ¤t_position, current_position+step, &step, y);\n", + " // This is the line that actually performs the step.\n", + "\n", + " exception_handler(current_position,y);\n", + " const_eval(current_position,y,&cp);\n", + " assign_constants(c,&cp);\n", + " // These lines are to make sure the constant updates. \n", + " // And exception constraints are applied. \n", + "\n", + " // Printing section.\n", + " // Uncomment for live updates. Prints to the file automatically.\n", + " // printf(\"Position:,\\t%15.14e,\\t\",current_position);\n", + " fprintf(fp2, \"Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " fprintf(fp2, \"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " fprintf(fp2,\"\\n\");\n", + "\n", + " if (report_error_estimates == true) {\n", + " // Print the error estimates we already have. \n", + " fprintf(fp2, \"Error Estimates:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n,(d->e->yerr[n])); \n", + " }\n", + " // Constant estimates not reported, only differential equation values. \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + " \n", + " if (report_error_actual == true) {\n", + " // Now if we have an actual error to compare against, there's some more work to do. \n", + " double y_truth[number_of_equations];\n", + " double c_truth[number_of_constants];\n", + " struct constant_parameters cp_truth; \n", + " // True values for everything we compare with.\n", + " \n", + " known_Q_eval(current_position,y_truth);\n", + " const_eval(current_position,y_truth,&cp_truth);\n", + "\n", + " assign_constants(c,&cp); \n", + " assign_constants(c_truth,&cp_truth);\n", + " \n", + " fprintf(fp2, \"Errors:,\\t\");\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " fprintf(fp2, \"Equation %i:,\\t%15.14e,\\t\",n, y_truth[n]-y[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",y_truth[n]);\n", + " }\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " fprintf(fp2, \"Constant %i Error:,\\t%15.14e,\\t\",n, c_truth[n]-c[n]);\n", + " fprintf(fp2, \"Truth:,\\t%15.14e,\\t\",c_truth[n]);\n", + " } \n", + " fprintf(fp2,\"\\n\");\n", + " }\n", + "\n", + " if (do_we_terminate(current_position, y, &cp) == 1) {\n", + " i = size-1;\n", + " // If we need to bail, set i to size-1 to break the loop. The -1 is there to make sure final line printing works. \n", + " } \n", + " if (i == size-1) {\n", + " // Also potentially a good idea: print the final line. \n", + " printf(\"FINAL: Position:,\\t%15.14e,\\t\",current_position);\n", + " for (int n = 0; n < number_of_equations; n++) {\n", + " // printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " printf(\"Equation %i:,\\t%15.14e,\\t\",n, y[n]);\n", + " }\n", + "\n", + " for (int n = 0; n < number_of_constants; n++) {\n", + " // printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " printf(\"Constant %i:,\\t%15.14e,\\t\",n, c[n]);\n", + " // printf(\"Constant %i:,\\t%15.14e %15.14e,\\n\",n, c[n], y[n]);\n", + " }\n", + " // printf(\"\\n\");\n", + " printf(\"\\n\");\n", + " }\n", + " }\n", + "\n", + " // SECTION III: Analysis\n", + "\n", + " // Minor post-processing goes here. \n", + " // Anything advanced will need to be done in a data analysis program. \n", + " // We like to use matplotlib for python.\n", + "\n", + " fclose(fp2);\n", + "\n", + " nrpy_odiegm_driver_free(d);\n", + " // MEMORY SHENANIGANS\n", + "\n", + " printf(\"ODE Solver \\\"Odie\\\" V10 Shutting Down...\\n\");\n", + " return 0;\n", + " \n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "f4a00582-d2e6-4927-ad47-bc85d9ed81af", + "metadata": {}, + "source": [ + "\n", + "# The Solution \\[Back to [top](#toc)\\]\n", + "\n", + "While it may be pretty self-explanitory how to change our `diffy_Q_Eval`, the same can not be said about the `const_eval`. This is because of the pesky void pointers hiding throughout the code, which means we have to dereference our pointers to be able to use them in our `diffy_Q_eval` function, but that will be explained in the solution. Here are all the functions you need to make adjustments to.\n", + "\n", + "1. `struct constant_parameters`: For the struct right at the beginning, we need to make sure we have these constants in our parameters. This just initially defines them, so add under `int dimension`:\n", + "\n", + "`double a;`\n", + "\n", + "`double b;`\n", + "\n", + "`double c;`\n", + "\n", + "2. `const_eval`: This is where we evaluate the constants a,b, and c. Since they are dependent on the values of y and z at a given time, we must pass in those values into the function, which is already included in the template. The additions that need to be made are:\n", + "\n", + "`params->a = 2.0*y[1];`\n", + "\n", + "`params->b = y[1]*y[0];`\n", + "\n", + "`params->c = y[0]/5;`\n", + "\n", + "Remember, these parameters are in a struct, so you need to point to the memeber variables. Furthermore, for future reference, I set z to `y[0]` and y to `y[1]`, so you know which equation refers to which index in the array.\n", + "\n", + "3. `diffy_Q_eval`: For this one, were just setting up the equations like we normally do, with the exception that we also need to evaluate and use are constants. The difficult part about this is dereferencing the void pointers to the constants, and it is not obvious. Our function will take the form of:\n", + "\n", + "`const_eval(x,y,params);`\n", + " \n", + "`double a = (*(struct constant_parameters*)params).a;`\n", + "\n", + "`double b = (*(struct constant_parameters*)params).b;`\n", + "\n", + "`double c = (*(struct constant_parameters*)params).c;`\n", + "\n", + "`dydx[0] = a*y[0]+pow(y[1],b)+pow(y[1],1/c);`\n", + "\n", + "`dydx[1] = b*y[0]+pow(y[1],c);`\n", + "\n", + "Again, not super obvious, but once you know how, you can derefernece any void pointers. It would be nice if we DIDN'T have to do that, but c'est la vie...\n", + "\n", + "4. `get_initial_condition`: We're just putting in our initial conditions of `y[0] = -1.0` and `y[1] = 1.0`\n", + "\n", + "5. `assign_constants`: For the last part, we want to save and plot our constant values later, so we need to assign the constants to be stored:\n", + "\n", + "`c[0] = params->a;`\n", + "\n", + "`c[1] = params->b;`\n", + "\n", + "`c[2] = params->c;`" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "86414d51", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_user_methods_c = r\"\"\"\n", + "\n", + "// #include \n", + "// #include \n", + "// #include \n", + "// #include \n", + "\n", + "// This file holds all the functions and definitions for the user to edit. \n", + "// Note that it does not depend on any of the other files--so long as the formatting is maintained\n", + "// the operation of the code should be agnostic to what the user puts in here. \n", + "\n", + "// This struct here holds any constant parameters we may wish to report.\n", + "// Often this struct can be entirely empty if the system of equations is self-contained.\n", + "// But if we had a system that relied on an Equation of State, \n", + "// the parameters for that EOS would go here. \n", + "struct constant_parameters { \n", + " int dimension; // number that says how many constants we have. \n", + " double a;\n", + " double b;\n", + " double c;\n", + " // double parameter;\n", + " // add more as necessary. Label as desired. \n", + "};\n", + "\n", + "\n", + "// Here are the prototypes for the functions in this file, stated explicitly for the sake of clarity. \n", + "void exception_handler (double x, double y[]); \n", + "// Handles any exceptions the user may wish to define.\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params); \n", + "// User-defined endpoint.\n", + "// Generally used if the code won't terminate itself from outside, or if there's a variable condition. \n", + "void const_eval (double x, const double y[], struct constant_parameters *params);\n", + "// Assign constants to the constant_parameters struct based on values in y[]. \n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params);\n", + "// The definition for the system of equations itself goes here. \n", + "int known_Q_eval (double x, double y[]);\n", + "// If an exact solution is known, it goes here, otherwise leave empty. \n", + "void get_initial_condition (double y[]);\n", + "// Initial conditions for the system of differential equations. \n", + "void assign_constants (double c[], struct constant_parameters *params);\n", + "// Used to read values from constant_parameters into an array so they can be reported in sequence. \n", + "\n", + "// Note that nrpy_odiegm_funcs.c does not depend on these definitions at all. The user is free\n", + "// to rename the functions if desired, though since diffy_Q_eval and known_Q_eval are passed to \n", + "// one of nrpy_odiegm's structs the actual function parameters for those two should not be adjusted.\n", + "// NOTE: the given nrpy_odiegm_main.c file will only work with the same names as listed here,\n", + "// only change names if creating a new custom main function. \n", + "\n", + "void exception_handler (double x, double y[])\n", + "{\n", + " \n", + "}\n", + "\n", + "int do_we_terminate (double x, double y[], struct constant_parameters *params)\n", + "{\n", + " return 0;\n", + "}\n", + "\n", + "void const_eval (double x, const double y[], struct constant_parameters *params)\n", + "{\n", + "\n", + " params->a = 2.0*y[1];\n", + " params->b = y[1]*y[0];\n", + " params->c = y[0]/5;\n", + "\n", + "}\n", + "\n", + "int diffy_Q_eval (double x, double y[], double dydx[], void *params)\n", + "{\n", + " const_eval(x,y,params);\n", + " \n", + " double a = (*(struct constant_parameters*)params).a;\n", + " double b = (*(struct constant_parameters*)params).b;\n", + " double c = (*(struct constant_parameters*)params).c;\n", + "\n", + " dydx[0] = a*y[0]+pow(y[1],b)+pow(y[1],1/c);\n", + " dydx[1] = b*y[0]+pow(y[1],c);\n", + "\n", + " return 1;\n", + "}\n", + "\n", + "\n", + "//This is the function to evaluate the known solution. Must be set manually.\n", + "int known_Q_eval (double x, double y[]) //This function is the other one passed using GSL's formulation. \n", + "//Allows the specific_methods file to be completely agnostic to whatever the user is doing. \n", + "{\n", + "\n", + " //y[0] = exp(x);\n", + "\n", + " return 1;\n", + " //report \"success\"\n", + "}\n", + "\n", + "void get_initial_condition (double y[])\n", + "{\n", + " y[0] = -1.0;\n", + " y[1] = 1.0;\n", + "}\n", + "\n", + "void assign_constants (double c[], struct constant_parameters *params)\n", + "{\n", + " c[0] = params->a;\n", + " c[1] = params->b;\n", + " c[2] = params->c;\n", + "}\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "a7770b76-9c9b-4b5c-929b-ff0ed70dbbd5", + "metadata": {}, + "source": [ + "We still have to make some adjustments to a couple of these values:\n", + "\n", + "`number_of_equations`: You have 2 equations, so set to 2.\n", + "\n", + "`number_of_constants`: You have 3 constants, so set to 3.\n", + "\n", + "`const int size`: I just set to 500, that should be enough to illustrate to problem\n", + "\n", + "`no_adaptive_step`: DON'T change that, leave as false, you'll see why when we plot." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a565cd03", + "metadata": {}, + "outputs": [], + "source": [ + "nrpy_odiegm_main_c_modifiable = r\"\"\"\n", + "\n", + " printf(\"Beginning ODE Solver \\\"Odie\\\" V10...\\n\");\n", + "\n", + " // SECTION I: Preliminaries\n", + "\n", + " // Before the program actually starts, variables need to be created\n", + " // and set, as well as the functions chosen. \n", + " // The system of differential equations can be found declared in diffy_Q_eval\n", + " // in nrpy_odiegm_user_methods.c\n", + "\n", + " double step = 0.01; /// the \"step\" value. Initial step if using an adaptive method.\n", + " double current_position = 0.0; // where the boundary/initial condition is. \n", + " // Same for every equation in the system.\n", + " int number_of_equations = 2; // How many equations are in our system?\n", + " int number_of_constants = 3; // How many constants do we wish to separately evaluate and report? \n", + " // If altering the two \"numberOf\" ints, be careful it doesn't go over the actual number \n", + " // and cause an overflow in the functions in nrpy_odiegm_user_methods.c\n", + " const int size = 500; // How many steps are we going to take? \n", + " // This is the default termination condition. \n", + " int adams_bashforth_order = 4; // If using the AB method, specify which order you want.\n", + " // If we are not using the AB method this is set to 0 later automatically. 4 by default. \n", + " bool no_adaptive_step = false; // Sometimes we just want to step forward uniformly \n", + " // without using GSL's awkward setup. False by default. \n", + "\n", + " bool report_error_actual = false;\n", + " bool report_error_estimates = false;\n", + " // AB methods do not report error estimates. \n", + " // BE WARNED: setting reporError (either kind) to true makes\n", + " // it print out all error data on another line,\n", + " // the file will have to be read differently. \n", + "\n", + " // ERROR PARAMETERS: Use these to set limits on the erorr. \n", + " double absolute_error_limit = 1e-14; // How big do we let the absolute error be?\n", + " double relative_error_limit = 1e-14; // How big do we let the relative error be?\n", + " // Default: 1e-14 for both.\n", + " // Note: there are a lot more error control numbers that can be set inside the \n", + " // control \"object\" (struct) d->c.\n", + "\n", + " char file_name[] = \"oUData.txt\"; // Where do you want the data to print?\n", + "\n", + " // Now we set up the method. \n", + " const nrpy_odiegm_step_type * step_type;\n", + " step_type = nrpy_odiegm_step_RK4;\n", + " // Here is where the method is actually set, by specific name since that's what GSL does. \n", + "\n", + " const nrpy_odiegm_step_type * step_type_2;\n", + " step_type_2 = nrpy_odiegm_step_RK4;\n", + " // This is a second step type \"object\" (struct) for hybridizing. \n", + " // Only used if the original type is AB.\n", + " // Set to AB to use pure AB method. \n", + "\n", + " //AFTER THIS POINT THERE SHOULD BE NO NEED FOR USER INPUT, THE CODE SHOULD HANDLE ITSELF. \n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "6ffc1243", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(EXEC): Executing `make -j10`...\n", + "(BENCH): Finished executing in 0.41 seconds.\n", + "Finished compilation.\n", + "(EXEC): Executing `taskset -c 0,1,2,3 ./ODESolverCustom `...\n", + "(BENCH): Finished executing in 0.21 seconds.\n" + ] + } + ], + "source": [ + "def add_to_Cfunction_dict_ODESolver():\n", + " includes = [\"stdio.h\", \"stdlib.h\", \"math.h\", \"stdbool.h\"]\n", + " # What \"#include\" lines do we include at the top?\n", + " \n", + " prefunc = nrpy_odiegm_h+ nrpy_odiegm_proto_c+ nrpy_odiegm_funcs_c + nrpy_odiegm_user_methods_c\n", + " # Prefunctions are functions declared outside main.\n", + " # The specifics of what go here were declared above. \n", + " \n", + " desc = \"User Custom System\"\n", + " # Just put a guide as to what the code actually does here. \n", + " \n", + " c_type = \"int\" \n", + " # What does main return?\n", + " \n", + " name = \"main\"\n", + " # Will almost always just be \"main\", but could be otherwise. \n", + " \n", + " params = \"\"\n", + " # Various paremeters. Should be \"\" most often. \n", + " \n", + " # Below is where the actual main function itself goes, constructed from the variables\n", + " # defined in the customization section.\n", + " body = nrpy_odiegm_main_c_modifiable + nrpy_odiegm_main_c_standard\n", + " # Now everything is ready to be constructed. \n", + " outC.add_to_Cfunction_dict(\n", + " includes=includes,\n", + " prefunc=prefunc,\n", + " desc=desc,\n", + " c_type=c_type, name=name, params=params,\n", + " body=body, enableCparameters=False)\n", + " # Now all those things we defined above are put into a function from outC, \n", + " # Which generates the actual entry in the C function dictionary. \n", + " \n", + "add_to_Cfunction_dict_ODESolver()\n", + "# Call the function we just declared above. \n", + "\n", + "cmd.new_C_compile(Ccodesrootdir, \"ODESolverCustom\", compiler_opt_option=\"fast\")\n", + "# This just compiles the code into the specified file. \n", + "# Note to change the name if you want to run more than once, otherwise it is ODESolverCustom.\n", + "# Will override the previous ODESolverCustom.\n", + "\n", + "os.chdir(Ccodesrootdir)\n", + "# Change the file path to the folder we created earlier. \n", + "\n", + "cmd.Execute(\"ODESolverCustom\", \"\", \"terminalOutput.txt\")\n", + "# Evaluate the C-code and put the Terminal output into a text file. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "4cc9cc2d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Beginning ODE Solver \"Odie\" V10...\n", + "Method Order: 4.\n", + "Printing to file 'oUData.txt'.\n", + "INITIAL: Position:,\t0.000000,\tEquation 0:,\t-1.00000000000000e+00,\tEquation 1:,\t1.00000000000000e+00,\tConstant 0:,\t2.00000000000000e+00,\tConstant 1:,\t-1.00000000000000e+00,\tConstant 2:,\t-2.00000000000000e-01,\t\n", + "FINAL: Position:,\t4.24905910095493e-01,\tEquation 0:,\t-3.50404545584104e+00,\tEquation 1:,\t4.35927594279369e+00,\tConstant 0:,\t8.71855188558738e+00,\tConstant 1:,\t-1.52751010581034e+01,\tConstant 2:,\t-7.00809091168208e-01,\t\n", + "ODE Solver \"Odie\" V10 Shutting Down...\n", + "\n" + ] + } + ], + "source": [ + "with open(\"terminalOutput.txt\") as f:\n", + " print(f.read())" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f220b31c", + "metadata": {}, + 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print(f.read())" + ] + }, + { + "cell_type": "markdown", + "id": "e6cd44db-e858-4ea7-9eeb-81a5f02269f5", + "metadata": {}, + "source": [ + "Last but not least, there is a couple of adjustments we need to make to plot each of the constants and values for y and z:\n", + "\n", + "1. `calculatedList0` through `calculatedList4` Make sure to have five lists to be able to plot the values of z and y, as well as the three constants a, b, and c.\n", + "\n", + "2. Make sure you read in the data correctly in the csv.reader loop. These are always the odd indices, since the even indices are strings referencing what value is being printed (see the printed data in the above cell). Should use indices 1, 3, 5, 7, 9, and 11.\n", + "\n", + "3. Make sure to plot all the calculated lists along with respect to the position list. Should have five `ax.plot()`s" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "7483f657-5b57-4140-b4aa-dbe3d72a0435", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting code adapated from NRPy \"Solving the Scalar Wave Equation\"\n", + "import matplotlib.pyplot as plt\n", + "\n", + "positionList = []\n", + "\n", + "# truthList0 = []\n", + "# Uncomment or add more if validation is desired.\n", + "\n", + "calculatedList0 = [] #z\n", + "calculatedList1 = [] #y\n", + "calculatedList2 = [] #a\n", + "calculatedList3 = [] #b\n", + "calculatedList4 = [] #c\n", + "# Uncomment for plotting more than one value. \n", + "\n", + "# errorList0 = []\n", + "# Uncomment for lists to store errors. \n", + "\n", + "# i = 0\n", + "# Use this i if a check has to be performed as to which row we're on. \n", + "\n", + "# csv file interface from https://www.dataquest.io/blog/read-file-python/\n", + "import csv\n", + "import sys\n", + "# https://stackoverflow.com/questions/2753254/how-to-open-a-file-in-the-parent-directory-in-python-in-appengine\n", + "# to make sure we get the right file. \n", + "with open('oUData.txt') as f:\n", + " reader = csv.reader(f, delimiter=',')\n", + " for row in reader:\n", + " positionList.append(float(row[1]))\n", + " calculatedList0.append(float(row[3]))\n", + " calculatedList1.append(float(row[5]))\n", + " calculatedList2.append(float(row[7]))\n", + " calculatedList3.append(float(row[9]))\n", + " calculatedList4.append(float(row[11]))\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Here is where you would do any post-processing. Remember, use np.array() on the lists so operations\n", + "# can be performed properly. \n", + "\n", + "# Remember to change labels!\n", + "ax.set_xlabel('x (or t)')\n", + "ax.set_ylabel('y')\n", + "ax.set_title('Custom Graph')\n", + "ax.plot(positionList, calculatedList0, color='r', label=\"z\")\n", + "ax.plot(positionList, calculatedList1, color='r', label=\"y\") \n", + "ax.plot(positionList, calculatedList2, color='g', label=\"a\") \n", + "ax.plot(positionList, calculatedList3, color='olive', label=\"b\") \n", + "ax.plot(positionList, calculatedList4, color='purple', label=\"c\") # marker='o' (or whatever symbol) can be added here. \n", + "\n", + "fig.set_size_inches(9,9)\n", + "# plt.xlim(0.0,1.0)\n", + "# plt.ylim(0.0,1.0)\n", + "# The above two lines can control the region of the graph displayed. Comment out for auto scaling. \n", + "\n", + "# ax.set_yscale(\"log\") # Found in matplotlib's documentation. \n", + "# Uncommenting this sets the scale to logarithmic. \n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "id": "05c9c3eb-44a0-41f5-ac99-8edd2d7a8e9a", + "metadata": {}, + "source": [ + "Notice why we used the adaptive step. When we get around x=.443, we start to see asymptotic behavior. You see this more the more steps you take. If you choose to use a uniform step, it very quickly ends up with NaNs as you move past x=.443." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "777725d1-3c06-4ee3-b1f5-2e7c2fe847ae", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}