Added ExtendedSquare

docs/src/api/states.md

@@ -17,6 +17,7 @@
     NLAT2
     NLAT3
     PartialSquare
+    ExtendedSquare
 ```
 
 ## Internals

src/ReservoirComputing.jl

@@ -33,7 +33,7 @@ include("esn/esn_predict.jl")
 include("reca/reca.jl")
 include("reca/reca_input_encodings.jl")
 
-export NLADefault, NLAT1, NLAT2, NLAT3, PartialSquare
+export NLADefault, NLAT1, NLAT2, NLAT3, PartialSquare, ExtendedSquare
 export StandardStates, ExtendedStates, PaddedStates, PaddedExtendedStates
 export StandardRidge
 export scaled_rand, weighted_init, informed_init, minimal_init, chebyshev_mapping,

src/states.jl

@@ -726,3 +726,71 @@ function (ps::PartialSquare)(x_old::AbstractVector)
 
     return x_new
 end
+
+@doc raw"""
+
+    ExtendedSquare()
+
+Extension of the Lu initialization proposed in [^herteux2020].
+The state vector is extended with the squared elements of the initial
+state
+
+# Equations
+
+```math
+\begin{equation}
+    \vec{x} = \{x_1, x_2, \dots, x_N, x_1^2, x_2^2, \dots, x_N^2\}
+\end{equation}
+```
+
+# Examples
+
+```jldoctest
+julia> x_old = [1, 2, 3, 4, 5, 6, 7, 8, 9]
+9-element Vector{Int64}:
+ 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
+
+julia> es = ExtendedSquare()
+ExtendedSquare()
+
+julia> x_new = es(x_old)
+18-element Vector{Int64}:
+  1
+  2
+  3
+  4
+  5
+  6
+  7
+  8
+  9
+  1
+  4
+  9
+ 16
+ 25
+ 36
+ 49
+ 64
+ 81
+
+```
+
+[^herteux2020]: Herteux, Joschka, and Christoph Räth.
+    "Breaking symmetries of the reservoir equations in echo state networks."
+    Chaos: An Interdisciplinary Journal of Nonlinear Science 30.12 (2020).
+"""
+struct ExtendedSquare <: NonLinearAlgorithm end
+
+function (::ExtendedSquare)(x_old::AbstractVector)
+    x_new = copy(x_old)
+    return vcat(x_new, x_new .^ 2)
+end

test/test_states.jl

@@ -9,7 +9,8 @@ nlas = [(NLADefault(), test_array),
     (NLAT1(), [1, 2, 9, 4, 25, 6, 49, 8, 81]),
     (NLAT2(), [1, 2, 2, 4, 12, 6, 30, 8, 9]),
     (NLAT3(), [1, 2, 8, 4, 24, 6, 48, 8, 9]),
-    (PartialSquare(0.6), [1, 4, 9, 16, 25, 6, 7, 8, 9])]
+    (PartialSquare(0.6), [1, 4, 9, 16, 25, 6, 7, 8, 9]),
+    (ExtendedSquare(), [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 4, 9, 16, 25, 36, 49, 64, 81])]
 
 pes = [(StandardStates(), test_array),
     (PaddedStates(; padding=padding),