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‎.devel/sphinx/index.md

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* supports multiprocessing via OpenMP (on selected platforms).
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Possible applications in data analysis:
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Possible applications in topological data analysis:
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clustering ([HDBSCAN\*](https://hdbscan.readthedocs.io/en/latest/index.html),
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[Genie](https://genieclust.gagolewski.com/), Lumbermark, Single linkage, etc.),
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classification and regression (k-nearest neighbours),
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density estimation, dimensionality reduction,
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outlier and noise point detection, and many more.
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## Contributing
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**quitefastmst** is distributed under the open source GNU AGPL v3 license.
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Its source code can be downloaded from [GitHub](https://github.com/gagolews/quitefastmst).
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## How to Install
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### Python Version
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To install from [PyPI](https://pypi.org/project/quitefastmst), call:
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```bash
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pip3 install quitefastmst # python3 -m pip install quitefastmst
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```
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*To learn more about Python, check out my open-access textbook*
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[Minimalist Data Wrangling in Python](https://datawranglingpy.gagolewski.com/).
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For best performance, advanced users will benefit from compiling the package
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from sources:
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```bash
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CPPFLAGS="-O3 -march=native" pip3 install quitefastmst --force --no-binary="quitefastmst"
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```
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🚧 TO DO (help needed): How to enable OpenMP support on macOS/Darwin in `setup.py`?
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### R Version
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To install from [CRAN](https://CRAN.R-project.org/package=quitefastmst), call:
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```r
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install.packages("quitefastmst")
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```
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*To learn more about R, check out my open-access textbook*
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[Deep R Programming](https://deepr.gagolewski.com/).
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For best performance, advanced users will benefit from compiling the package
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from sources:
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```r
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Sys.setenv(CXX_DEFS="-O3 -march=native") # for gcc and clang
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install.packages("quitefastmst", type="source")
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```
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## Contributing
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The Python version is available from [PyPI](https://pypi.org/project/quitefastmst)
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and the R one from [CRAN](https://CRAN.R-project.org/package=quitefastmst).
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*quitefastmst* is distributed under the open source GNU AGPL v3 license
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and can be downloaded from [GitHub](https://github.com/gagolews/quitefastmst).
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The core functionality is implemented in the form of a C++ library,
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However, the core functionality is implemented in the form of a C++ library,
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so it may be adapted to new projects relatively easily:
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any valuable contributions are welcome (Julia or Matlab bindings, etc.).
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::::{toctree}
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:maxdepth: 1
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:caption: Reference Manual
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:caption: Documentation
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:hidden:
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weave/definitions
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weave/benchmarks
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weave/python
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pythonapi
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weave/r
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rapi
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::::
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‎.devel/sphinx/pythonapi.rst

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=======================================
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.. autosummary::
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quitefastmst.mst_euclid
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quitefastmst.knn_euclid
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quitefastmst.mst_euclid
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.. automodule:: quitefastmst
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:members: mst_euclid, knn_euclid
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:members: knn_euclid, mst_euclid

‎.devel/sphinx/rapi/mst_euclid.md

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## Description
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The function determines the/a(\*) minimum spanning tree (MST) of a set of $n$ points, i.e., an acyclic undirected graph whose vertices represent the points, and $n-1$ edges with the minimal sum of weights, given by the pairwise distances. MSTs have many uses in, amongst others, topological data analysis (clustering, dimensionality reduction, etc.).
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The function determines the/a(\*) minimum spanning tree (MST) of a set of $n$ points, i.e., an acyclic undirected connected graph whose vertices represent the points, edges are weighted by the distances between point pairs, and have minimal total weight.
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For $M\leq 2$, we get a spanning tree that minimises the sum of Euclidean distances between the points. If $M=2$, the function additionally returns the distance to each point\'s nearest neighbour.
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MSTs have many uses in, amongst others, topological data analysis (clustering, density estimation, dimensionality reduction, outlier detection, etc.).
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If $M>2$, the spanning tree is the smallest wrt the degree-M mutual reachability distance (Campello et al., 2013) given by $d_M(i, j)=\max\{ c_M(i), c_M(j), d(i, j)\}$, where $d(i,j)$ is the Euclidean distance between the $i$-th and the $j$-th point, and $c_M(i)$ is the $i$-th $M$-core distance defined as the distance between the $i$-th point and its $(M-1)$-th nearest neighbour (not including the query points themselves). In clustering and density estimation, M plays the role of a smoothing factor; see (Campello et al. 2015) and the references therein for discussion.
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In clustering and density estimation, the parameter `M` plays the role of a smoothing factor; see (Campello et al. 2015) and the references therein for discussion. It corresponds to the <span class="pkg">hdbscan</span> Python package\'s `min_samples=M-1`.
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For $M\leq 2$, we get a spanning tree that minimises the sum of uclidean distances between the points, i.e., the classic Euclidean minimum spanning tree (EMST). If $M=2$, the function additionally returns the distance to each point\'s nearest neighbour.
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If $M>2$, the spanning tree is the smallest wrt the degree-M mutual reachability distance (Campello et al., 2013) given by $d_M(i, j)=\max\{ c_M(i), c_M(j), d(i, j)\}$, where $d(i,j)$ is the Euclidean distance between the $i$-th and the $j$-th point, and $c_M(i)$ is the $i$-th $M$-core distance defined as the distance between the $i$-th point and its $(M-1)$-th nearest neighbour (not including the query points themselves).
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## Usage
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‎.devel/sphinx/weave/Makefile

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# Copyright (c) 2013-2025, Marek Gagolewski <https://www.gagolewski.com>
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FILES_RMD =
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FILES_RMD = \
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definitions.Rmd \
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benchmarks.Rmd \
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python.Rmd \
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r.Rmd
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RMD_MD_OUTPUTS=$(patsubst %.Rmd,%.md,$(FILES_RMD))
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‎.devel/sphinx/weave/benchmarks.Rmd

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# Benchmarks

‎.devel/sphinx/weave/benchmarks.md

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# Benchmarks

‎.devel/sphinx/weave/definitions.Rmd

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# Definitions
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The minimum spanning tree (MST) of a set of *n* points is an acyclic undirected
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connected graph whose:
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* vertices represent the points,
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* edges are weighted by the distances between point pairs,
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* edges have minimal total weight.
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MSTs have many uses in, amongst others, topological data analysis
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(clustering, density estimation, dimensionality reduction,
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outlier detection, etc.).
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The `mst_euclid` function can determine the classic
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Euclidean minimum spanning trees (EMST) as well as ones
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corresponding to mutual reachability distances {cite}`hdbscan`.
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::::{note}
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This section is a work in progress.
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In the meantime, take a look at the
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[Python](../pythonapi) or
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[R](../rapi)
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package reference manual.
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::::

‎.devel/sphinx/weave/definitions.md

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# Definitions
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The minimum spanning tree (MST) of a set of *n* points is an acyclic undirected
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connected graph whose:
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* vertices represent the points,
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* edges are weighted by the distances between point pairs,
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* edges have minimal total weight.
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MSTs have many uses in, amongst others, topological data analysis
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(clustering, density estimation, dimensionality reduction,
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outlier detection, etc.).
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The `mst_euclid` function can determine the classic
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Euclidean minimum spanning trees (EMST) as well as ones
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corresponding to mutual reachability distances {cite}`hdbscan`.
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::::{note}
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This section is a work in progress.
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In the meantime, take a look at the
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[Python](../pythonapi) or
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[R](../rapi)
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package reference manual.
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::::

‎.devel/sphinx/weave/python.Rmd

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# Python Examples
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*To learn more about Python, check out my open-access textbook*
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[Minimalist Data Wrangling in Python](https://datawranglingpy.gagolewski.com/).
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## How to Install
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To install the package from [PyPI](https://pypi.org/project/quitefastmst), call:
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```bash
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pip3 install quitefastmst # python3 -m pip install quitefastmst
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```
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For best performance, advanced users will benefit from compiling the package
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from sources:
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```bash
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CPPFLAGS="-O3 -march=native" pip3 install quitefastmst --force --no-binary="quitefastmst"
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```
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🚧 TO DO (help needed): How to enable OpenMP support on macOS/Darwin in `setup.py`?
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## Basic Use
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<!--
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```python3
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import quitefastmst
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quitefastmst.knn_euclid(X, k, ...)
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quitefastmst.mst_euclid(X, M=1, ...)
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```
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-->
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::::{note}
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This section is a work in progress.
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In the meantime, take a look at the examples in the [reference manual](../pythonapi).
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::::

‎.devel/sphinx/weave/python.md

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# Python Examples
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*To learn more about Python, check out my open-access textbook*
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[Minimalist Data Wrangling in Python](https://datawranglingpy.gagolewski.com/).
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## How to Install
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To install the package from [PyPI](https://pypi.org/project/quitefastmst), call:
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```bash
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pip3 install quitefastmst # python3 -m pip install quitefastmst
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```
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For best performance, advanced users will benefit from compiling the package
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from sources:
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```bash
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CPPFLAGS="-O3 -march=native" pip3 install quitefastmst --force --no-binary="quitefastmst"
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```
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🚧 TO DO (help needed): How to enable OpenMP support on macOS/Darwin in `setup.py`?
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## Basic Use
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::::{note}
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This section is a work in progress.
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In the meantime, take a look at the examples in the [reference manual](../pythonapi).
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::::

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