reservoirpy.datasets.narma#

reservoirpy.datasets.narma(
n_timesteps: int,
order: int = 30,
a1: float = 0.2,
a2: float = 0.04,
b: float = 1.5,
c: float = 0.001,
x0: list | ndarray = [0.0],
seed: int | Generator | None = None,
u: ndarray | None = None,
) → tuple[ndarray, ndarray][source]#

Non-linear Autoregressive Moving Average (NARMA) timeseries, as first defined in [14], and as used in [15].

NARMA n-th order dynamical system is defined by the recurrent relation:

\[y[t+1] = a_1 y[t] + a_2 y[t] (\sum_{i=0}^{n-1} y[t-i]) + b u[t-( n-1)]u[t] + c\]

where \(u[t]\) are sampled following a uniform distribution in \([0, 0.5]\).

Parameters:

  • n_timesteps (int) – Number of timesteps to generate.

  • order (int, default to 30) – Order of the system.

  • a1 (float, default to 0.2) – \(a_1\) parameter of the system.

  • a2 (float, default to 0.04) – \(a_2\) parameter of the system.

  • b (float, default to 1.5) – \(b\) parameter of the system.

  • c (float, default to 0.001) – \(c\) parameter of the system.

  • x0 (array-like of shape (init_steps,), default to [0.0]) – Initial conditions of the system.

  • seed (int or numpy.random.Generator, optional) – Random state seed for reproducibility.

  • u (array of shape (n_timesteps + order, 1), default to None.) – Input timeseries (usually uniformly distributed).

Returns:

Input timeseries u and output NARMA timeseries.

Return type:

tuple of arrays of shape (n_timesteps + order, 1) and (n_timesteps, 1)

Example

>>> import numpy as np
>>> from reservoirpy.nodes import Reservoir, Ridge
>>> from reservoirpy.datasets import narma
>>> reservoir = Reservoir(100)
>>> model = reservoir >> Ridge()
>>> n_timesteps, order = 2000, 30
>>> rng = np.random.default_rng(seed=2341)
>>> u, y = narma(n_timesteps=n_timesteps, order=order)
>>> reservoir.run(u[:order]) # warmup
>>> model = model.fit(u[order:], y)
../../_images/reservoirpy-datasets-narma-1.png

References