fixed docstrings in inits

Author: MartinuzziFrancesco

src/esn/esn_inits.jl

@@ -13,6 +13,9 @@ a range defined by `scaling`.
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
+
+# Keyword arguments
+
   - `scaling`: A scaling factor to define the range of the uniform distribution.
     The matrix elements will be randomly chosen from the
     range `[-scaling, scaling]`. Defaults to `0.1`.
@@ -55,6 +58,9 @@ elements distributed uniformly within the range [-`scaling`, `scaling`] [^Lu2017
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
+
+# Keyword arguments
+
   - `scaling`: The scaling factor for the weight distribution.
     Defaults to `0.1`.
   - `return_sparse`: flag for returning a `sparse` matrix.
@@ -106,6 +112,9 @@ Create an input layer for informed echo state networks [^Pathak2018].
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
+
+# Keyword arguments
+
   - `scaling`: The scaling factor for the input matrix.
     Default is 0.1.
   - `model_in_size`: The size of the input model.
@@ -167,6 +176,9 @@ is randomly determined by the `sampling` chosen.
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
+
+# Keyword arguments
+
   - `weight`: The weight used to fill the layer matrix. Default is 0.1.
   - `sampling_type`: The sampling parameters used to generate the input matrix.
     Default is `:bernoulli`.
@@ -282,7 +294,7 @@ function _create_irrational(irrational::Irrational, start::Int, res_size::Int,
     return T.(input_matrix)
 end
 
-"""
+@doc raw"""
     chebyshev_mapping([rng], [T], dims...;
         amplitude=one(T), sine_divisor=one(T),
         chebyshev_parameter=one(T), return_sparse=true)
@@ -292,14 +304,15 @@ using a sine function and subsequent rows are iteratively generated
 via the Chebyshev mapping. The first row is defined as:
 
 ```math
-    w(1, j) = amplitude * sin(j * π / (sine_divisor * n_cols))
+    W[1, j] = \text{amplitude} \cdot \sin(j \cdot \pi / (\text{sine_divisor} 
+        \cdot \text{n_cols}))
 ```
 
 for j = 1, 2, …, n_cols (with n_cols typically equal to K+1, where K is the number of input layer neurons).
 Subsequent rows are generated by applying the mapping:
 
 ```math
-    w(i+1, j) = cos(chebyshev_parameter * acos(w(i, j)))
+    W[i+1, j] = \cos( \text{chebyshev_parameter} \cdot \acos(W[pi, j]))
 ```
 
 # Arguments
@@ -364,22 +377,23 @@ function chebyshev_mapping(rng::AbstractRNG, ::Type{T}, dims::Integer...;
 end
 
 @doc raw"""
-    logistic_mapping(rng::AbstractRNG, ::Type{T}, dims::Integer...;
-        amplitude=0.3, sine_divisor=5.9, logistic_parameter = 3.7,
+    logistic_mapping([rng], [T], dims...;
+        amplitude=0.3, sine_divisor=5.9, logistic_parameter=3.7,
         return_sparse=true)
 
 Generate an input weight matrix using a logistic mapping [^wang2022].The first
 row is initialized using a sine function:
 
 ```math
-    W(1, j) = amplitude * sin(j * π / (sine_divisor * in_size))
+    W[1, j] = \text{amplitude} \cdot \sin(j \cdot \pi / 
+        (\text{sine_divisor} \cdot in_size))
 ```
 
 for each input index `j`, with `in_size` being the number of columns provided in `dims`. Subsequent rows
 are generated recursively using the logistic map recurrence:
 
 ```math
-    W(i+1, j) = logistic_parameter * W(i, j) * (1 - W(i, j))
+    W[i+1, j] = \text{logistic_parameter} \cdot W(i, j) \cdot (1 - W[i, j])
 ```
 
 # Arguments
@@ -389,7 +403,8 @@ are generated recursively using the logistic map recurrence:
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
 
-# keyword arguments
+# Keyword arguments
+
   - `amplitude`: Scaling parameter used in the sine initialization of the
     first row. Default is 0.3.
   - `sine_divisor`: Parameter used to adjust the phase in the sine initialization.
@@ -452,14 +467,15 @@ as follows:
 - The first element of the chain is initialized using a sine function:
 
 ```math
-      W(1,j) = amplitude * sin( (j * π) / (factor * n * sine_divisor) )
+      W[1,j] = \text{amplitude} \cdot \sin( (j \cdot \pi) / 
+          (\text{factor} \cdot \text{n} \cdot \text{sine_divisor}) )
 ```
   where `j` is the index corresponding to the input and `n` is the number of inputs.
 
 - Subsequent elements are recursively computed using the logistic mapping:
 
 ```math
-      W(i+1,j) = logistic_parameter * W(i,j) * (1 - W(i,j))
+      W[i+1,j] = \text{logistic_parameter} \cdot W[i,j] \cdot (1 - W[i,j])
 ```
 
 The resulting matrix has dimensions `(factor * in_size) x in_size`, where
@@ -474,7 +490,8 @@ the number of rows is overridden.
     Default is `Float32`.
   - `dims`: Dimensions of the matrix. Should follow `res_size x in_size`.
 
-# keyword arguments
+# Keyword arguments
+
   - `factor`: The number of logistic map iterations (chain length) per input,
     determining the number of rows per input.
   - `amplitude`: Scaling parameter A for the sine-based initialization of
@@ -563,6 +580,8 @@ and scaled spectral radius according to `radius`.
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+# Keyword arguments
+
   - `radius`: The desired spectral radius of the reservoir.
     Defaults to 1.0.
   - `sparsity`: The sparsity level of the reservoir matrix,
@@ -609,6 +628,9 @@ Create and return a delay line reservoir matrix [^Rodan2010].
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+
+# Keyword arguments
+
   - `weight`: Determines the value of all connections in the reservoir.
     Default is 0.1.
   - `return_sparse`: flag for returning a `sparse` matrix.
@@ -652,7 +674,7 @@ end
 
 """
     delay_line_backward([rng], [T], dims...;
-        weight = 0.1, fb_weight = 0.2, return_sparse=true)
+        weight=0.1, fb_weight=0.2, return_sparse=true)
 
 Create a delay line backward reservoir with the specified by `dims` and weights.
 Creates a matrix with backward connections as described in [^Rodan2010].
@@ -664,6 +686,9 @@ Creates a matrix with backward connections as described in [^Rodan2010].
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+
+  # Keyword arguments
+
   - `weight`: The weight determines the absolute value of
     forward connections in the reservoir. Default is 0.1
   - `fb_weight`: Determines the absolute value of backward connections
@@ -709,7 +734,7 @@ end
 
 """
     cycle_jumps([rng], [T], dims...; 
-        cycle_weight = 0.1, jump_weight = 0.1, jump_size = 3, return_sparse=true)
+        cycle_weight=0.1, jump_weight=0.1, jump_size=3, return_sparse=true)
 
 Create a cycle jumps reservoir with the specified dimensions,
 cycle weight, jump weight, and jump size.
@@ -721,6 +746,9 @@ cycle weight, jump weight, and jump size.
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+
+# Keyword arguments
+
   - `cycle_weight`:  The weight of cycle connections.
     Default is 0.1.
   - `jump_weight`: The weight of jump connections.
@@ -779,7 +807,7 @@ end
 
 """
     simple_cycle([rng], [T], dims...; 
-        weight = 0.1, return_sparse=true)
+        weight=0.1, return_sparse=true)
 
 Create a simple cycle reservoir with the specified dimensions and weight.
 
@@ -789,6 +817,9 @@ Create a simple cycle reservoir with the specified dimensions and weight.
     from WeightInitializers.
   - `T`: Type of the elements in the reservoir matrix. Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+
+  # Keyword arguments
+
   - `weight`: Weight of the connections in the reservoir matrix.
     Default is 0.1.
   - `return_sparse`: flag for returning a `sparse` matrix.
@@ -831,7 +862,7 @@ end
 
 """
     pseudo_svd([rng], [T], dims...; 
-        max_value=1.0, sparsity=0.1, sorted = true, reverse_sort = false,
+        max_value=1.0, sparsity=0.1, sorted=true, reverse_sort=false,
         return_sparse=true)
 
 Returns an initializer to build a sparse reservoir matrix with the given
@@ -844,6 +875,9 @@ Returns an initializer to build a sparse reservoir matrix with the given
   - `T`: Type of the elements in the reservoir matrix.
     Default is `Float32`.
   - `dims`: Dimensions of the reservoir matrix.
+
+  # Keyword arguments
+
   - `max_value`: The maximum absolute value of elements in the matrix.
     Default is 1.0
   - `sparsity`: The desired sparsity level of the reservoir matrix.