diagonal_init

diagonal_init([rng], [T], dims...;
    return_sparse=false, weight=randn,
    kwargs...)

Creates a diagonal reservoir (Fette and Eggert, 2005).

Arguments

• rng: Random number generator. Default is Utils.default_rng()from WeightInitializers.
• T: Type of the elements in the reservoir matrix. Default is Float32.
• dims: Dimensions of the reservoir matrix.

Keyword arguments

• weight: Weight used for the initial self-loop initialization. Can be a single number, vector, or function to generate an array. Default is randn.
• return_sparse: flag for returning a sparse matrix. true requires SparseArrays to be loaded. Default is false.
• return_diag: flag for returning a Diagonal matrix. If both return_diag and return_sparse are set to true priority is given to return_diag. Default is false.
• radius: The desired spectral radius of the reservoir. If nothing is passed, no scaling takes place. Defaults to nothing.
• sampling_type: Sampling that decides the distribution of weight negative numbers. If set to :no_sample the sign is unchanged. If set to :bernoulli_sample! then each forward_weight can be positive with a probability set by positive_prob. If set to :irrational_sample! the weight is negative if the decimal number of the irrational number chosen is odd. If set to :regular_sample!, each weight will be assigned a negative sign after the chosen strides. strides can be a single number or an array. Default is :no_sample.
• positive_prob: probability of the weight being positive when sampling_type is set to :bernoulli_sample!. Default is 0.5.
• irrational: Irrational number whose decimals decide the sign of weight. Default is pi.
• start: Which place after the decimal point the counting starts for the irrational sign counting. Default is 1.
• strides: number of strides for assigning negative value to a weight. It can be an integer or an array. Default is 2.

Examples

Default kwargs:

julia> rr = diagonal_init(5, 5)
5×5 Matrix{Float32}:
 -0.359729  0.0       0.0      0.0      0.0
  0.0       1.08721   0.0      0.0      0.0
  0.0       0.0      -0.41959  0.0      0.0
  0.0       0.0       0.0      0.71891  0.0
  0.0       0.0       0.0      0.0      0.420247

Changing the weights magnitudes to a different unique value:

julia> rr = diagonal_init(5, 5; weight=0.1)
5×5 Matrix{Float32}:
 0.1  0.0  0.0  0.0  0.0
 0.0  0.1  0.0  0.0  0.0
 0.0  0.0  0.1  0.0  0.0
 0.0  0.0  0.0  0.1  0.0
 0.0  0.0  0.0  0.0  0.1

Changing the weights signs with different sampling techniques:

Changing the weights to random numbers. Note that the length of the given array must be at least as long as the subdiagonal one wants to fill:

julia> rr = diagonal_init(5, 5; weight=0.1, sampling_type=:bernoulli_sample!)
5×5 Matrix{Float32}:
 0.1   0.0  0.0   0.0  0.0
 0.0  -0.1  0.0   0.0  0.0
 0.0   0.0  0.1   0.0  0.0
 0.0   0.0  0.0  -0.1  0.0
 0.0   0.0  0.0   0.0  0.1

julia> rr = diagonal_init(5, 5; weight=0.1, sampling_type=:irrational_sample!)
5×5 Matrix{Float32}:
 -0.1  0.0   0.0   0.0   0.0
  0.0  0.1   0.0   0.0   0.0
  0.0  0.0  -0.1   0.0   0.0
  0.0  0.0   0.0  -0.1   0.0
  0.0  0.0   0.0   0.0  -0.1

Returning a sparse matrix:

julia> using SparseArrays

julia> rr = diagonal_init(5, 5; return_sparse=true)
5×5 SparseMatrixCSC{Float32, Int64} with 5 stored entries:
 -0.359729   ⋅         ⋅        ⋅        ⋅
   ⋅        1.08721    ⋅        ⋅        ⋅
   ⋅         ⋅       -0.41959   ⋅        ⋅
   ⋅         ⋅         ⋅       0.71891   ⋅
   ⋅         ⋅         ⋅        ⋅       0.420247

Returning a diagonal matrix:

julia> rr = diagonal_init(5, 5; return_diag=true)
5×5 LinearAlgebra.Diagonal{Float32, Vector{Float32}}:
 -0.359729   ⋅         ⋅        ⋅        ⋅
   ⋅        1.08721    ⋅        ⋅        ⋅
   ⋅         ⋅       -0.41959   ⋅        ⋅
   ⋅         ⋅         ⋅       0.71891   ⋅
   ⋅         ⋅         ⋅        ⋅       0.420247