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wigner_init

ReservoirComputing.wigner_init — Function
wigner_init([rng], [T], dim.;
    std=1.0, std_diag=0.5, return_symmetric)

Create and return a dense random wigner initialized reservoir matrix. We follow as outlined in (Verzelli et al., 2021) and previously (Inubushi and Yoshimura, 2017) The off-diagonal elements will be scaled by std while the diagonal elements will be scaled by std_diag. if 2 std_diag == std, then std machtes the resulting spectral radius of the matrix.

Arguments

  • rng: Random number generator.
  • T: Type of the elements in the reservoir matrix. Default is Float32.
  • dims: Dimension of the (symmetric) reservoir matrix. Either a single integer or a pair of integers. Pair of integers must match.

Keyword arguments

  • std: The desired scaling for the standard deviation of the off_diagonal elements. Defaults to 1.0.

  • std_diag: The desired scaling for the standard deviation of the diagonal elements. Defaults to 0.5.

  • return_symmetric: If true, returns a LinearAlgebra.Symmetric type matrix. Defaults to false.

    Examples

    Default kwargs:

    julia> rr = wigner_init(5, 5)
5×5 Matrix{Float32}:
  0.000769674   0.126007   -0.277637   -0.126593   -0.389
  0.126007     -0.0176753   0.541007   -0.392352    0.435318
 -0.277637      0.541007    0.448532   -0.0991032  -0.357256
 -0.126593     -0.392352   -0.0991032  -0.0637784  -0.373899
 -0.389         0.435318   -0.357256   -0.373899   -0.0403503

    Returning a Symmetric matrix:

    julia> rr = wigner_init(5, 5; return_symmetric=true)
 5×5 LinearAlgebra.Symmetric{Float32, Matrix{Float32}}:
  -0.0874871   0.0666034   0.520725   0.454877  -0.503613
   0.0666034  -0.2203     -0.497137   0.805205   0.0580209
   0.520725   -0.497137    0.489767  -0.792692   0.571714
   0.454877    0.805205   -0.792692  -0.126786  -0.414994
  -0.503613    0.0580209   0.571714  -0.414994  -0.0372717

    Returning with different standard deviation on diagonal and off diagonal:

    julia> rr = wigner_init(5, 5; std_diag=5, std=1e-3)
5×5 Matrix{Float32}:
  0.685752      0.000850898  -0.000109755  -0.000211195  -0.000102981
  0.000850898  -0.327889     -0.000201935   0.000673213   7.9558f-5
 -0.000109755  -0.000201935  -2.77398       0.00010618   -0.000488676
 -0.000211195   0.000673213   0.00010618    1.15882       0.000629446
 -0.000102981   7.9558f-5    -0.000488676   0.000629446  -3.25089
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