wigner_init

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., 2022) 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(MersenneTwister(123), 5, 5);
  
  julia> size(rr) == (5, 5) && eltype(rr) == Float32 && issymmetric(rr)
  true

  Returning a Symmetric matrix:

  julia> rr = wigner_init(MersenneTwister(123), 5, 5; return_symmetric=true);
  
  julia> rr isa Symmetric{Float32} && size(rr) == (5, 5)
  true

  Returning with different standard deviation on diagonal and off diagonal:

  julia> rr = wigner_init(MersenneTwister(123), 5, 5; std_diag=5, std=1e-3);
  
  julia> issymmetric(rr) && maximum(abs, diag(rr)) > maximum(abs, rr .- Diagonal(diag(rr)))
  true