cycle_jumps

cycle_jumps([rng], [T], dims...;
    cycle_weight=0.1, jump_weight=0.1, jump_size=3, return_sparse=false,
    radius=nothing, cycle_kwargs=(), jump_kwargs=())

Create a cycle reservoir with jumps (Rodan and Tiňo, 2012).

\[W_{i,j} = \begin{cases} r, & \text{if } i = j + 1,\;\; j \in [1, D_{\mathrm{res}} - 1], \\[4pt] r, & \text{if } i = 1,\;\; j = D_{\mathrm{res}}, \\[8pt] r_j, & \text{if } i = j + \ell, \\[4pt] r_j, & \text{if } j = i + \ell, \\[4pt] r_j, & \text{if } (i,j) = (1+\ell, 1), \\[4pt] r_j, & \text{if } (i,j) = (1,\, D_{\mathrm{res}}+1-\ell), \\[8pt] 0, & \text{otherwise.} \end{cases}\]

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

• cycle_weight: The weight of cycle connections. 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 cycle you want to populate. Default is 0.1.

• jump_weight: The weight of jump connections. 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 jumps you want to populate. Default is 0.1.

• jump_size: The number of steps between jump connections. Default is 3.

• 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.

• cycle_kwargs and jump_kwargs: named tuples that control the kwargs for the cycle and jump weights respectively. The kwargs are as follows:

  • signs: Controls sign flips. Use RandomSigns, RegularSigns, or IrrationalDigitSigns. Pass nothing to leave signs unchanged. Default is nothing.

Examples

Default call:

julia> res_matrix = cycle_jumps(5, 5)
5×5 Matrix{Float32}:
 0.0  0.0  0.0  0.1  0.1
 0.1  0.0  0.0  0.0  0.0
 0.0  0.1  0.0  0.0  0.0
 0.1  0.0  0.1  0.0  0.0
 0.0  0.0  0.0  0.1  0.0

Changing weights:

julia> res_matrix = cycle_jumps(5, 5; jump_weight = 2, cycle_weight = -1);

julia> size(res_matrix) == (5, 5) && count(==(2.0f0), res_matrix) == 2 && count(==(-1.0f0), res_matrix) == 5
true

Changing weights to custom arrays:

julia> jump_weights = -Float32[0.2, 0.4, 0.6];

julia> cycle_weights = Float32[0.1, 0.3, 0.5, 0.7, 0.9];

julia> res_matrix = cycle_jumps(5, 5; jump_weight = jump_weights, cycle_weight = cycle_weights);

julia> size(res_matrix) == (5, 5) && eltype(res_matrix) == Float32 && count(!iszero, res_matrix) == 7
true

Changing sign of the weights with different sign patterns:

julia> cycle_sampled = cycle_jumps(
           MersenneTwister(123), 5, 5;
           cycle_kwargs = (; signs = RandomSigns()));

julia> jump_sampled = cycle_jumps(5, 5; jump_kwargs = (; signs = IrrationalDigitSigns()));

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

Changing cycle jumps length:

julia> res_matrix = cycle_jumps(5, 5; jump_size = 2)
5×5 Matrix{Float32}:
 0.0  0.0  0.1  0.0  0.1
 0.1  0.0  0.0  0.0  0.0
 0.1  0.1  0.0  0.0  0.1
 0.0  0.0  0.1  0.0  0.0
 0.0  0.0  0.1  0.1  0.0

julia> res_matrix = cycle_jumps(5, 5; jump_size = 4)
5×5 Matrix{Float32}:
 0.0  0.0  0.0  0.0  0.1
 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
 0.1  0.0  0.0  0.1  0.0

Return as a sparse matrix:

julia> using SparseArrays

julia> res_matrix = cycle_jumps(5, 5; return_sparse=true)
5×5 SparseMatrixCSC{Float32, Int64} with 7 stored entries:
  ⋅    ⋅    ⋅   0.1  0.1
 0.1   ⋅    ⋅    ⋅    ⋅
  ⋅   0.1   ⋅    ⋅    ⋅
 0.1   ⋅   0.1   ⋅    ⋅
  ⋅    ⋅    ⋅   0.1   ⋅