squared_distance¶

squared_distance(x: ndarray, y: ndarray) → float[source]¶

Compute the squared distance between two time series.

The squared distance between two time series is defined as:

\[sd(x, y) = \sum_{i=1}^{n} (x_i - y_i)^2\]

Parameters:

xnp.ndarray: First time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).
ynp.ndarray: Second time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).

Returns:

float: Squared distance between x and y.

Raises:

ValueError: If x and y are not 1D or 2D arrays.

Examples

>>> import numpy as np
>>> from aeon.distances import squared_distance
>>> x = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
>>> y = np.array([[11, 12, 13, 14, 15, 16, 17, 18, 19, 20]])
>>> squared_distance(x, y)
1000.0