# pairwise_distance¶

pairwise_distance(x: ndarray, y: = None, metric: = None, **kwargs: Unpack) [source]

Compute the pairwise distance matrix between two time series.

Parameters:
Xnp.ndarray
A collection of time series instances of shape `(n_cases, n_timepoints)`

or `(n_cases, n_channels, n_timepoints)`.

ynp.ndarray or None, default=None

A single series or a collection of time series of shape `(m_timepoints,)` or `(m_cases, m_timepoints)` or `(m_cases, m_channels, m_timepoints)`

metricstr or Callable

The distance metric to use. A list of valid distance metrics can be found in the documentation for `aeon.distances.get_distance_function` or by calling the function `aeon.distances.get_distance_function_names`.

kwargsAny

Extra arguments for metric. Refer to each metric documentation for a list of possible arguments.

Returns:
np.ndarray (n_cases, n_cases)

pairwise matrix between the instances of X.

Raises:
ValueError

If X is not 2D or 3D array when only passing X. If X and y are not 1D, 2D or 3D arrays when passing both X and y. If metric is not a valid string or callable.

Examples

```>>> import numpy as np
>>> from aeon.distances import pairwise_distance
>>> # Distance between each time series in a collection of time series
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> pairwise_distance(X, metric='dtw')
array([[  0.,  26., 108.],
[ 26.,   0.,  26.],
[108.,  26.,   0.]])
```
```>>> # Distance between two collections of time series
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y = np.array([[[11, 12, 13]],[[14, 15, 16]], [[17, 18, 19]]])
>>> pairwise_distance(X, y, metric='dtw')
array([[300., 507., 768.],
[147., 300., 507.],
[ 48., 147., 300.]])
```
```>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> pairwise_distance(X, y_univariate, metric='dtw')
array([[300.],
[147.],
[ 48.]])
```