4949
5050Create and return a matrix representing a weighted input layer.
5151This initializer generates a weighted input matrix with random non-zero
52- elements distributed uniformly within the range [-`scaling`, `scaling`] [^lu2017].
52+ elements distributed uniformly within the range
53+ [-`scaling`, `scaling`] [Lu2017](@cite).
5354
5455# Arguments
5556
@@ -78,11 +79,6 @@ julia> res_input = weighted_init(8, 3)
7879 0.0 0.0 0.0577838
7980 0.0 0.0 -0.0562827
8081```
81-
82- [^lu2017]: Lu, Zhixin, et al.
83- "Reservoir observers: Model-free inference of unmeasured variables in
84- chaotic systems."
85- Chaos: An Interdisciplinary Journal of Nonlinear Science 27.4 (2017): 041102.
8682"""
8783function weighted_init (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
8884 scaling:: Number = T (0.1 ), return_sparse:: Bool = false ) where {T <: Number }
109105Create and return a minimal weighted input layer matrix.
110106This initializer generates a weighted input matrix with equal, deterministic
111107elements in the same construction as [`weighted_minimal]`(@ref),
112- inspired by [^lu2017] .
108+ inspired by [Lu2017](@cite) .
113109
114110Please note that this initializer computes its own reservoir size! If
115111the computed reservoir size is different than the provided one it will raise a
@@ -188,11 +184,6 @@ julia> res_input = weighted_minimal(9, 3; sampling_type = :bernoulli_sample!)
188184 -0.0 -0.0 0.1
189185 0.0 -0.0 0.1
190186```
191-
192- [^lu2017]: Lu, Zhixin, et al.
193- "Reservoir observers: Model-free inference of unmeasured variables in
194- chaotic systems."
195- Chaos: An Interdisciplinary Journal of Nonlinear Science 27.4 (2017): 041102.
196187"""
197188function weighted_minimal (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
198189 weight:: Number = T (0.1 ), return_sparse:: Bool = false ,
216207 informed_init([rng], [T], dims...;
217208 scaling=0.1, model_in_size, gamma=0.5)
218209
219- Create an input layer for informed echo state networks [^pathak2018].
210+ Create an input layer for informed echo state
211+ networks [Pathak2018](@cite).
220212
221213# Arguments
222214
@@ -234,10 +226,6 @@ Create an input layer for informed echo state networks [^pathak2018].
234226 - `gamma`: The gamma value. Default is 0.5.
235227
236228# Examples
237-
238- [^pathak2018]: Pathak, Jaideep, et al. "Hybrid forecasting of chaotic processes:
239- Using machine learning in conjunction with a knowledge-based model."
240- Chaos: An Interdisciplinary Journal of Nonlinear Science 28.4 (2018).
241229"""
242230function informed_init (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
243231 scaling:: Number = T (0.1 ), model_in_size:: Integer ,
281269 sampling_type=:bernoulli_sample!, weight=0.1, irrational=pi,
282270 start=1, p=0.5)
283271
284- Create a layer matrix with uniform weights determined by `weight` [^rodan2010].
285- The sign difference is randomly determined by the `sampling` chosen.
272+ Create a layer matrix with uniform weights determined by
273+ `weight` [Rodan2011](@cite). The sign difference is randomly
274+ determined by the `sampling` chosen.
286275
287276# Arguments
288277
@@ -358,10 +347,6 @@ julia> res_input = minimal_init(8, 3; p = 0.8)# higher p -> more positive signs
358347 -0.1 0.1 0.1
359348 0.1 0.1 0.1
360349```
361-
362- [^rodan2010]: Rodan, Ali, and Peter Tino.
363- "Minimum complexity echo state network."
364- IEEE transactions on neural networks 22.1 (2010): 131-144.
365350"""
366351function minimal_init (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
367352 weight:: Number = T (0.1 ), sampling_type:: Symbol = :bernoulli_sample! ,
@@ -1034,7 +1019,7 @@ end
10341019 weight=0.1, return_sparse=false,
10351020 kwargs...)
10361021
1037- Create and return a delay line reservoir matrix [^rodan2010] .
1022+ Create and return a delay line reservoir matrix [Rodan2011](@cite) .
10381023
10391024# Arguments
10401025
@@ -1089,10 +1074,6 @@ julia> res_matrix = delay_line(5, 5; weight = 1)
10891074 0.0 0.0 1.0 0.0 0.0
10901075 0.0 0.0 0.0 1.0 0.0
10911076```
1092-
1093- [^rodan2010]: Rodan, Ali, and Peter Tino.
1094- "Minimum complexity echo state network."
1095- IEEE transactions on neural networks 22.1 (2010): 131-144.
10961077"""
10971078function delay_line (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
10981079 weight:: Union{Number, AbstractVector} = T (0.1 ), shift:: Integer = 1 ,
@@ -1106,11 +1087,11 @@ end
11061087
11071088"""
11081089 delay_line_backward([rng], [T], dims...;
1109- weight=0.1, fb_weight=0.2 , return_sparse=false,
1090+ weight=0.1, fb_weight=0.1 , return_sparse=false,
11101091 delay_kwargs=(), fb_kwargs=())
11111092
11121093Create a delay line backward reservoir with the specified by `dims` and weights.
1113- Creates a matrix with backward connections as described in [^rodan2010] .
1094+ Creates a matrix with backward connections as described in [Rodan2011](@cite) .
11141095
11151096# Arguments
11161097
@@ -1134,7 +1115,7 @@ Creates a matrix with backward connections as described in [^rodan2010].
11341115 This can be provided as a single value or an array. In case it is provided as an
11351116 array please make sure that the lenght of the array matches the lenght of the sub-diagonal
11361117 you want to populate.
1137- Default is 0.2 .
1118+ Default is 0.1 .
11381119 - `fb_shift`: How far the backward connection will be from the diagonal.
11391120 Default is 2.
11401121 - `return_sparse`: flag for returning a `sparse` matrix.
@@ -1163,24 +1144,20 @@ Creates a matrix with backward connections as described in [^rodan2010].
11631144```jldoctest
11641145julia> res_matrix = delay_line_backward(5, 5)
116511465×5 Matrix{Float32}:
1166- 0.0 0.2 0.0 0.0 0.0
1167- 0.1 0.0 0.2 0.0 0.0
1168- 0.0 0.1 0.0 0.2 0.0
1169- 0.0 0.0 0.1 0.0 0.2
1147+ 0.0 0.1 0.0 0.0 0.0
1148+ 0.1 0.0 0.1 0.0 0.0
1149+ 0.0 0.1 0.0 0.1 0.0
1150+ 0.0 0.0 0.1 0.0 0.1
11701151 0.0 0.0 0.0 0.1 0.0
11711152
11721153julia> res_matrix = delay_line_backward(Float16, 5, 5)
117311545×5 Matrix{Float16}:
1174- 0.0 0.2 0.0 0.0 0.0
1175- 0.1 0.0 0.2 0.0 0.0
1176- 0.0 0.1 0.0 0.2 0.0
1177- 0.0 0.0 0.1 0.0 0.2
1155+ 0.0 0.1 0.0 0.0 0.0
1156+ 0.1 0.0 0.1 0.0 0.0
1157+ 0.0 0.1 0.0 0.1 0.0
1158+ 0.0 0.0 0.1 0.0 0.1
11781159 0.0 0.0 0.0 0.1 0.0
11791160```
1180-
1181- [^rodan2010]: Rodan, Ali, and Peter Tino.
1182- "Minimum complexity echo state network."
1183- IEEE transactions on neural networks 22.1 (2010): 131-144.
11841161"""
11851162function delay_line_backward (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
11861163 weight:: Union{Number, AbstractVector} = T (0.1 ),
@@ -1201,7 +1178,7 @@ end
12011178 cycle_weight=0.1, jump_weight=0.1, jump_size=3, return_sparse=false,
12021179 cycle_kwargs=(), jump_kwargs=())
12031180
1204- Create a cycle jumps reservoir [^Rodan2012] .
1181+ Create a cycle jumps reservoir [Rodan2011](@cite) .
12051182
12061183# Arguments
12071184
@@ -1266,10 +1243,6 @@ julia> res_matrix = cycle_jumps(5, 5; jump_size = 2)
12661243 0.0 0.0 0.1 0.0 0.0
12671244 0.0 0.0 0.1 0.1 0.0
12681245```
1269-
1270- [^rodan2012]: Rodan, Ali, and Peter Tiňo.
1271- "Simple deterministically constructed cycle reservoirs with regular jumps."
1272- Neural computation 24.7 (2012): 1822-1852.
12731246"""
12741247function cycle_jumps (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
12751248 cycle_weight:: Union{Number, AbstractVector} = T (0.1 ),
@@ -1291,7 +1264,7 @@ end
12911264 weight=0.1, return_sparse=false,
12921265 kwargs...)
12931266
1294- Create a simple cycle reservoir [^rodan2010] .
1267+ Create a simple cycle reservoir [Rodan2011](@cite) .
12951268
12961269# Arguments
12971270
@@ -1344,10 +1317,6 @@ julia> res_matrix = simple_cycle(5, 5; weight = 11)
13441317 0.0 0.0 11.0 0.0 0.0
13451318 0.0 0.0 0.0 11.0 0.0
13461319```
1347-
1348- [^rodan2010]: Rodan, Ali, and Peter Tino.
1349- "Minimum complexity echo state network."
1350- IEEE transactions on neural networks 22.1 (2010): 131-144.
13511320"""
13521321function simple_cycle (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
13531322 weight:: Union{Number, AbstractVector} = T (0.1 ),
@@ -1424,7 +1393,7 @@ end
14241393 return_sparse=false)
14251394
14261395Creates a true double cycle reservoir, ispired by [^fu2023],
1427- with cycles built on the definition by [^rodan2010] .
1396+ with cycles built on the definition by [Rodan2011](@cite) .
14281397
14291398# Arguments
14301399
@@ -1476,9 +1445,6 @@ julia> true_double_cycle(5, 5; cycle_weight = 0.1, second_cycle_weight = 0.3)
14761445[^fu2023]: Fu, Jun, et al.
14771446 "A double-cycle echo state network topology for time series prediction."
14781447 Chaos: An Interdisciplinary Journal of Nonlinear Science 33.9 (2023).
1479- [^rodan2010]: Rodan, Ali, and Peter Tino.
1480- "Minimum complexity echo state network."
1481- IEEE transactions on neural networks 22.1 (2010): 131-144.
14821448"""
14831449function true_double_cycle (rng:: AbstractRNG , :: Type{T} , dims:: Integer... ;
14841450 cycle_weight:: Union{Number, AbstractVector} = T (0.1 ),
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