embedding

embedding

Functions:

Name	Description
embed	Delay vectors for an arbitrary choice of variables and lags.

embed

embed(coordinates: np.ndarray, x: np.ndarray) -> tuple[np.ndarray, np.ndarray]

Delay vectors for an arbitrary choice of variables and lags.

Parameters:

Name	Type	Description	Default
coordinates	ndarray	Integer array of shape (E, 2). Row j is (variable, lag), selecting observation x[t - lag, variable] for the delay vector at time t. A negative lag selects an observation taken after time t.	required
x	ndarray	Observations of shape (T, d), or (T,).	required

Returns:

Name	Type	Description
X	ndarray	Delay vectors of shape (N, E), one row per time in t.
t	ndarray	Times of shape (N,) at which every coordinate is available, that is lags.max() <= t <= T - 1 + lags.min(). A time outside [0, T - 1] is included when every coordinate still reads an observation inside x.

Raises:

Type	Description
ValueError	- If coordinates is not an integer array of shape (E, 2) with E >= 1. - If x is not a 1D or 2D array. - If a variable index lies outside x. - If no time has every coordinate available.

Examples:

import numpy as np

from edmkit.embedding import embed

x = np.arange(20).reshape(10, 2)  # ten times, two variables

# Classical univariate delay coordinates.
tau, E = 2, 3
coordinates = np.array([[0, tau * j] for j in range(E)])
X, t = embed(coordinates, x)
print(X)
print(t)
# [[ 8  4  0]
#  [10  6  2]
#  [12  8  4]
#  [14 10  6]
#  [16 12  8]
#  [18 14 10]]
# [4 5 6 7 8 9]

# One step ahead of the same coordinates, as iterated forecasting needs.
Y, t_ahead = embed(coordinates - [0, 1], x)