delay_line

delay_line([rng], [T], dims...;
    delay_weight=0.1, delay_shift=1,
    return_sparse=false, radius=nothing, kwargs...)

Create and return a delay line reservoir matrix (Rodan and Tino, 2011).

\[W_{i,j} = \begin{cases} r, & \text{if } i = j + 1, j \in [1, D_{\mathrm{res}} - 1], \\[6pt] 0, & \text{otherwise.} \end{cases}\]

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

• delay_weight: Determines the value of all connections in the reservoir. This can be provided as a single value or an array. In case it is provided as an array please make sure that the length of the array matches the length of the sub-diagonal you want to populate. Default is 0.1.
• delay_shift: delay line shift. Default is 1.
• radius: The desired spectral radius of the reservoir. If nothing is passed, no scaling takes place. Defaults to nothing.
• return_sparse: flag for returning a sparse matrix. true requires SparseArrays to be loaded. Default is false.
• signs: Controls sign flips. Use RandomSigns, RegularSigns, or IrrationalDigitSigns. Pass nothing to leave signs unchanged. Default is nothing.

Examples

Default call:

julia> res_matrix = delay_line(5, 5)
5×5 Matrix{Float32}:
 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  0.0

Changing weights:

julia> res_matrix = delay_line(5, 5; delay_weight = 1)
5×5 Matrix{Float32}:
 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  1.0  0.0

Changing weights to a custom array:

julia> delay_weights = Float32[0.2, 0.4, 0.6, 0.8];

julia> res_matrix = delay_line(5, 5; delay_weight = delay_weights);

julia> res_matrix[2:end, 1:end-1] == Diagonal(delay_weights)
true

Changing sign of the weights with different sign patterns:

julia> irrational_matrix = delay_line(5, 5; signs = IrrationalDigitSigns());

julia> bernoulli_matrix = delay_line(MersenneTwister(123), 5, 5; signs = RandomSigns());

julia> all(abs.(irrational_matrix[irrational_matrix .!= 0]) .== 0.1f0) &&
       all(abs.(bernoulli_matrix[bernoulli_matrix .!= 0]) .== 0.1f0)
true

Shifting the delay line:

julia> res_matrix = delay_line(5, 5; delay_shift = 3)
5×5 Matrix{Float32}:
 0.0  0.0  0.0  0.0  0.0
 0.0  0.0  0.0  0.0  0.0
 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

Returning as sparse:

julia> using SparseArrays

julia> res_matrix = delay_line(5, 5; return_sparse=true)
5×5 SparseMatrixCSC{Float32, Int64} with 4 stored entries:
  ⋅    ⋅    ⋅    ⋅    ⋅
 0.1   ⋅    ⋅    ⋅    ⋅
  ⋅   0.1   ⋅    ⋅    ⋅
  ⋅    ⋅   0.1   ⋅    ⋅
  ⋅    ⋅    ⋅   0.1   ⋅