simple_cycle

simple_cycle([rng], [T], dims...;
    cycle_weight=0.1, return_sparse=false,
    radius=nothing, kwargs...)

Create a simple cycle reservoir (Rodan and Tino, 2011).

\[W_{i,j} = \begin{cases} r, & \text{if } i = j + 1,\;\; j \in [1, D_{\mathrm{res}} - 1], \\[4pt] r, & \text{if } i = 1,\;\; j = D_{\mathrm{res}}, \\[6pt] 0, & \text{otherwise.} \end{cases}\]

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

• cycle_weight: Weight of the connections in the reservoir matrix. 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.
• 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.
• sampling_type: Sampling that decides the distribution of cycle_weight negative numbers. If set to :no_sample the sign is unchanged. If set to :bernoulli_sample! then each cycle_weight can be positive with a probability set by positive_prob. If set to :irrational_sample! the cycle_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 cycle_weight being positive when sampling_type is set to :bernoulli_sample!. Default is 0.5.
• irrational: Irrational number whose decimals decide the sign of cycle_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 call:

julia> res_matrix = simple_cycle(5, 5)
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
 0.0  0.0  0.0  0.1  0.0

Changing weights:

julia> res_matrix = simple_cycle(5, 5; cycle_weight=0.99)
5×5 Matrix{Float32}:
 0.0   0.0   0.0   0.0   0.99
 0.99  0.0   0.0   0.0   0.0
 0.0   0.99  0.0   0.0   0.0
 0.0   0.0   0.99  0.0   0.0
 0.0   0.0   0.0   0.99  0.0

Changing weights to a custom array:

julia> res_matrix = simple_cycle(5, 5; cycle_weight=rand(5))
5×5 Matrix{Float32}:
 0.0       0.0        0.0       0.0       0.471823
 0.534782  0.0        0.0       0.0       0.0
 0.0       0.0764598  0.0       0.0       0.0
 0.0       0.0        0.507883  0.0       0.0
 0.0       0.0        0.0       0.546656  0.0

Changing sign of the weights with different samplings:

julia> res_matrix = simple_cycle(5, 5; sampling_type=:irrational_sample!)
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
  0.0  0.0   0.0  -0.1   0.0

julia> res_matrix = simple_cycle(5, 5; sampling_type=:bernoulli_sample!)
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
 0.0   0.0  0.0  -0.1  0.0

Returning as sparse:

julia> using SparseArrays

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