syntax and doc correction

Author: mcosovic

.github/workflows/Build.yml

@@ -7,7 +7,7 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        julia-version: ['1.6.1']
+        julia-version: ['1.6.1', '1.7']
         julia-arch: [x64]
         os: [ubuntu-latest, windows-latest, macOS-latest]
         exclude:

README.md

@@ -36,7 +36,7 @@ The following examples are intended for a quick introduction to FactorGraph pack
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -52,7 +52,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -77,7 +77,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -105,7 +105,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1 0 0 0 0; 6 8 2 0 0; 0 5 0 0 0;       # jacobian matrix
+H = [1 0 0 0 0; 6 8 2 0 0; 0 5 0 0 0;       # coefficient matrix
      0 0 2 0 0; 0 0 3 8 2]
 z = [1; 2; 3; 4; 5]                         # observation vector
 v = [3; 4; 2; 5; 1]                         # variance vector

docs/src/index.md

@@ -48,7 +48,7 @@ The following examples are intended for a quick introduction to FactorGraph pack
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -64,7 +64,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -89,7 +89,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # jacobian matrix
+H = [1.0 0.0 0.0; 1.5 0.0 2.0; 0.0 3.1 4.6] # coefficient matrix
 z = [0.5; 0.8; 4.1]                         # observation vector
 v = [0.1; 1.0; 1.0]                         # variance vector
 
@@ -117,7 +117,7 @@ marginal(gbp)                               # compute marginals
 ```julia-repl
 using FactorGraph
 
-H = [1 0 0 0 0; 6 8 2 0 0; 0 5 0 0 0;       # jacobian matrix
+H = [1 0 0 0 0; 6 8 2 0 0; 0 5 0 0 0;       # coefficient matrix
      0 0 2 0 0; 0 0 3 8 2]
 z = [1; 2; 3; 4; 5]                         # observation vector
 v = [3; 4; 2; 5; 1]                         # variance vector

docs/src/man/continuousInference.md

@@ -55,11 +55,11 @@ Same as before, the function accepts only the composite type `ContinuousModel`.
 ---
 
 #### Dynamic inference
-This framework is an extension to the real-time model that operates continuously and accepts asynchronous mean and variance values. More precisely, in each GBP iteration user can change the mean and variance values of the corresponding factor nodes and continue the GBP iteration process. We advise the reader to read the section [dynamic GBP algorithm] (@ref dynamicGBP) which provides a detailed description of the input parameters.
+This framework is an extension to the real-time model that operates continuously and accepts asynchronous observation (i.e., mean) and variance values. More precisely, in each GBP iteration user can change the observation and variance values of the corresponding factor nodes and continue the GBP iteration process. We advise the reader to read the section [dynamic GBP algorithm] (@ref dynamicGBP) which provides a detailed description of the input parameters.
 ```julia-repl
-dynamicFactor!(gbp; factor = index, mean = value, variance = value)
+dynamicFactor!(gbp; factor = index, observation = value, variance = value)
 ```
-The function accepts the composite type `ContinuousModel` and keywords `factor`, `mean` and `variance`, which defines the dynamic update scheme of the factor nodes. The factor node index corresponding to the row index of the jacobian matrix. Note that during each function call, `ContinuousSystem.observation` and `ContinuousSystem.variance` fields also change values according to the scheme.
+The function accepts the composite type `ContinuousModel` and keywords `factor`, `observation` and `variance`, which defines the dynamic update scheme of the factor nodes. The factor node index corresponding to the row index of the coefficient matrix. Note that during each function call, `ContinuousSystem.observation` and `ContinuousSystem.variance` fields also change values according to the scheme.
 
 ---
 

docs/src/man/continuousInput.md

@@ -8,9 +8,9 @@ The FactorGraph package supports continuous random variables, where local functi
 ```math
   \mathcal{N}(z_i|\mathcal{X}_i,v_i) \propto \exp\Bigg\{-\cfrac{[z_i-h_i(\mathcal{X}_i)]^2}{2v_i}\Bigg\}.
 ```
-Hence, the local function is associated with mean ``z_i``, variance  ``v_i``, and linear equation ``h_i(\mathcal{X}_i)``. To describe the joint probability density function ``g(\mathcal{X})``, it is enough to define the Jacobian matrix containing coefficients of the equations, and vectors of mean and variance values. Then, the ``i``-th row of the Jacobian matrix, with consistent entries of mean and variance, defines the local function ``\psi_i(\mathcal{X}_i)``.
+Hence, the local function is associated with observation ``z_i``, variance  ``v_i``, and linear equation ``h_i(\mathcal{X}_i)``. To describe the joint probability density function ``g(\mathcal{X})``, it is enough to define the coefficient matrix containing coefficients of the equations, and vectors of observation and variance values. Then, the ``i``-th row of the coefficient matrix, with consistent entries of observation and variance, defines the local function ``\psi_i(\mathcal{X}_i)``.
 
-Thus, the input data structure includes the `jacobian` variable, while variables `observation` and `variance` represent mean and variance vectors, respectively. The functions `continuousModel()` and `continuousTreeModel()` accept variables `jacobian`, `observation` and `variance`.
+Thus, the input data structure includes the `coefficient` variable which describes coefficients of the equations, while variables `observation` and `variance` represent observation and variance vectors, respectively. The functions `continuousModel()` and `continuousTreeModel()` accept variables `coefficient`, `observation` and `variance`.
 
 ---
 
@@ -21,16 +21,16 @@ Let us observe the following joint probability density function:
     g(\mathcal{X}) \propto  \exp\Bigg\{-\cfrac{[2.5 - 0.2x_1]^2}{2\cdot 1.1}\Bigg\}\exp\Bigg\{-\cfrac{[0.6 - (2.1x_1 + 3.4x_2)]^2}{2\cdot 3.5}\Bigg\}
 ```
 
-We can describe the joint probability density function using variables `jacobian`, `observation` and `variance`. Passing data directly via command-line support the following format, where the Jacobian matrix can be defined as a full or sparse matrix:
+We can describe the joint probability density function using variables `coefficient`, `observation` and `variance`. Passing data directly via command-line support the following format, where the coefficient matrix can be defined as a full or sparse matrix:
 ```julia-repl
-jacobian = zeros(2, 2)
-jacobian[1, 1] = 0.2; jacobian[2, 1] = 2.1; jacobian[2, 2] = 3.4
+coefficient = zeros(2, 2)
+coefficient[1, 1] = 0.2; coefficient[2, 1] = 2.1; coefficient[2, 2] = 3.4
 observation = [2.5; 0.6]
 variance = [1.1; 3.5]
 
-gbp = continuousModel(jacobian, observation, variance)
+gbp = continuousModel(coefficient, observation, variance)
 ```
 Here, the variable `gbp` holds the main composite type related to the continuous model. In the case of a tree factor graph, when you want to use a forward-backward GBP algorithm, then the following command can be used:
 ```julia-repl
-gbp = continuousTreeModel(jacobian, observation, variance)
+gbp = continuousTreeModel(coefficient, observation, variance)
 ```

docs/src/man/continuousModel.md

@@ -17,7 +17,7 @@ Input arguments of the function `continuousModel()` describe the graphical model
 
 Loads the system data passing arguments:
 ```julia-repl
-gbp = continuousModel(jacobian, observation, variances)
+gbp = continuousModel(coefficient, observation, variances)
 ```
 
 ---
@@ -64,7 +64,7 @@ freezeVariableFactor!(gbp; variable = index, factor = index)
 ```julia-repl
 freezeFactorVariable!(gbp; factor = index, variable = index)
 ```
-The functions accept following parameters: composite type `ContinuousModel`; the factor node index corresponding to the row index of the Jacobian matrix; and the variable node index corresponding to the column index of the Jacobian matrix. Note that the singly connected factor nodes can not be frozen because they always send the same message.
+The functions accept following parameters: composite type `ContinuousModel`; the factor node index corresponding to the row index of the coefficient matrix; and the variable node index corresponding to the column index of the coefficient matrix. Note that the singly connected factor nodes can not be frozen because they always send the same message.
 
 ---
 
@@ -85,7 +85,7 @@ defreezeVariableFactor!(gbp; variable = index, factor = index)
 defreezeFactorVariable!(gbp; factor = index, variable = index)
 ```
 
-The functions accept following parameters: composite type `ContinuousModel`; the factor node index corresponding to the row index of the Jacobian matrix; and the variable node index corresponding to the column index of the Jacobian matrix. Since singly connected factors cannot be frozen, they cannot be unfreezed.
+The functions accept following parameters: composite type `ContinuousModel`; the factor node index corresponding to the row index of the coefficient matrix; and the variable node index corresponding to the column index of the coefficient matrix. Since singly connected factors cannot be frozen, they cannot be unfreezed.
 
 ---
 
@@ -94,14 +94,14 @@ Utilising a hiding mechanism, the function softly deletes factor node. Hence, th
 ```julia-repl
 hideFactor!(gbp; factor = index)
 ```
-If the function targets the singly connected factor node, the function obliterates the target factor only if there are two or more singly connected factor nodes at the same variable node. If there is only one singly connected factor node at the variable node, the function transforms the target factor node to the virtual factor node. Note that to maintain consistency, the function also affects `ContinuousSystem.observation`, `ContinuousSystem.jacobian` and `ContinuousSystem.jacobianTranspose` fields by setting non-zero elements to zero.
+If the function targets the singly connected factor node, the function obliterates the target factor only if there are two or more singly connected factor nodes at the same variable node. If there is only one singly connected factor node at the variable node, the function transforms the target factor node to the virtual factor node. Note that to maintain consistency, the function also affects `ContinuousSystem.observation`, `ContinuousSystem.coefficient` and `ContinuousSystem.coefficientTranspose` fields by setting non-zero elements to zero.
 
 ---
 
 #### Add factor nodes
 The function adds new factor nodes to the existing factor graph.
 ```julia-repl
-addFactors!(gbp; mean = vector, variance = vector, jacobian = matrix)
+addFactors!(gbp; coefficient = matrix, observation = vector, variance = vector)
 ```
-The function supports addition of the multiple factor nodes to initial (existing) formation of the factor graph using the same input data format. The function accepts the following parameters: composite type `ContinuousModel`; the `mean` and `variance` vectors representing new measurement values and variances, respectively. The keyword `jacobian` with corresponding coefficients defines the set of equations describing new factor nodes. Also, function initializes messages from variable nodes to a new factor node using results from the last GBP iteration. Note that the function also affects `ContinuousSystem.observation`, `ContinuousSystem.variance`, `ContinuousSystem.jacobian` and `ContinuousSystem.jacobianTranspose` fields.
+The function supports addition of the multiple factor nodes to initial (existing) formation of the factor graph using the same input data format. The function accepts the following parameters: composite type `ContinuousModel`; the `observation` and `variance` vectors representing new observation values and variances, respectively. The keyword `coefficient` with corresponding coefficients defines the set of equations describing new factor nodes. Also, function initializes messages from variable nodes to a new factor node using results from the last GBP iteration. Note that the function also affects `ContinuousSystem.observation`, `ContinuousSystem.variance`, `ContinuousSystem.coefficient` and `ContinuousSystem.coefficientTranspose` fields.
 

docs/src/man/continuousTreeModel.md

@@ -15,7 +15,7 @@ Input arguments of the function `continuousTreeModel()` describe the tree graphi
 
 Loads the system data passing arguments:
 ```julia-repl
-gbp = continuousTreeModel(jacobian, observation, variances)
+gbp = continuousTreeModel(coefficient, observation, variances)
 ```
 
 ---

docs/src/man/theoreticalBelief.md

@@ -9,7 +9,7 @@ Thus, as an input, we observe a noisy linear system of equations with real coeff
 ```math
         \mathbf{z}=\mathbf{h}(\mathbf{x})+\mathbf{u},
 ```
-where ``\mathbf {x}=[x_1,\dots,x_{n}]^{{T}}`` is the vector of the state variables, ``\mathbf{h}(\mathbf{x})= [h_1(\mathbf{x})``, ``\dots``, ``h_k(\mathbf{x})]^{{T}}`` is the vector of observation or measurement functions,  ``\mathbf{z} = [z_1,\dots,z_m]^{{T}}`` is the vector of observation values, and ``\mathbf{u} = [u_1,\dots,u_k]^{{T}}`` is the vector of uncorrelated observation errors. The linear system of equations is an overdetermined ``m>n`` arising in many technical fields, such as statistics, signal processing, and control theory.
+where ``\mathbf {x}=[x_1,\dots,x_{n}]^{{T}}`` is the vector of the state variables, ``\mathbf{h}(\mathbf{x})= [h_1(\mathbf{x})``, ``\dots``, ``h_k(\mathbf{x})]^{{T}}`` is the vector of observation functions, ``\mathbf{z} = [z_1,\dots,z_m]^{{T}}`` is the vector of observation values, and ``\mathbf{u} = [u_1,\dots,u_k]^{{T}}`` is the vector of uncorrelated observation errors. The linear system of equations is an overdetermined ``m>n`` arising in many technical fields, such as statistics, signal processing, and control theory.
 
 Each observation is associated with observed value ``z_i``, error  ``u_i``, and function ``h_i(\mathbf{x})``. Under the assumption that observation errors ``u_i`` follow a zero-mean Gaussian distribution, the probability density function associated with the ``i``-th observation is proportional to:
 ```math
@@ -156,9 +156,9 @@ The randomised damping parameter pairs lead to a trade-off between the number of
 ---
 
 ### [Dynamic GBP algorithm]  (@id dynamicGBP)
-To recall, each factor node is associated with the mean ``z_i`` and variance value ``v_i``. The dynamic framework allows the update of these values in any GBP iteration ``\tau``. This framework is an extension to the real-time model that operates continuously and accepts asynchronous data. Such data are continuously integrated into the running instances of the GBP algorithm. Hence, the GBP algorithm can update the state estimate vector in a time-continuous process.
+To recall, each factor node is associated with the observation ``z_i`` and variance value ``v_i``. The dynamic framework allows the update of these values in any GBP iteration ``\tau``. This framework is an extension to the real-time model that operates continuously and accepts asynchronous data. Such data are continuously integrated into the running instances of the GBP algorithm. Hence, the GBP algorithm can update the state estimate vector in a time-continuous process.
 
-Additionally, this framework allows for the artificial addition and removal of factor nodes. Then, the initial factor graph, described with the Jacobian matrix, should include all possible factor nodes. Factor nodes that are not active are then taken into account via extremely large values of variances (e.g., ``10^{60}``). Consequently, estimates will have a unique solution according to variances whose values are much smaller than ``10^{60}``.
+Additionally, this framework allows for the artificial addition and removal of factor nodes. Then, the initial factor graph, described with the coefficient matrix, should include all possible factor nodes. Factor nodes that are not active are then taken into account via extremely large values of variances (e.g., ``10^{60}``). Consequently, estimates will have a unique solution according to variances whose values are much smaller than ``10^{60}``.
 
 ---
 

docs/src/man/utility.md

@@ -8,7 +8,7 @@ The function provides the estimate obtained by the weighted least-squares (WLS)
 ```julia-repl
 exact = wls(gbp)
 ```
-The function returns the composite type `WeightedLeastSquares` with fields `estimate`, `rmse`, `mae`, `wrss`. Note that results are obtained according to variables `ContinuousSystem.jacobian`, `ContinuousSystem.observation` and `ContinuousSystem.variance`.
+The function returns the composite type `WeightedLeastSquares` with fields `estimate`, `rmse`, `mae`, `wrss`. Note that results are obtained according to variables `ContinuousSystem.coefficient`, `ContinuousSystem.observation` and `ContinuousSystem.variance`.
 
 ----
 #### The GBP error metrics