# manhattan_pairwise_distance¶

manhattan_pairwise_distance(X: , y: = None) [source]

Compute the manhattan pairwise distance between a set of time series.

Parameters:
Xnp.ndarray or List of np.ndarray

A collection of time series instances of shape `(n_cases, n_timepoints)` or `(n_cases, n_channels, n_timepoints)`.

ynp.ndarray or List of np.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)`. If None, then the manhattan pairwise distance between the instances of X is calculated.

Returns:
np.ndarray (n_cases, n_cases)

manhattan 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.

Examples

```>>> import numpy as np
>>> from aeon.distances import manhattan_pairwise_distance
>>> X = np.array([[[1, 2, 3, 4]],[[4, 5, 6, 3]], [[7, 8, 9, 3]]])
>>> manhattan_pairwise_distance(X)
array([[ 0., 10., 19.],
[10.,  0.,  9.],
[19.,  9.,  0.]])
```
```>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y = np.array([[[11, 12, 13]],[[14, 15, 16]], [[17, 18, 19]]])
>>> manhattan_pairwise_distance(X, y)
array([[30., 39., 48.],
[21., 30., 39.],
[12., 21., 30.]])
```
```>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> manhattan_pairwise_distance(X, y_univariate)
array([[30.],
[21.],
[12.]])
```
```>>> # Distance between each TS in a collection of unequal-length time series
>>> X = [np.array([1, 2, 3]), np.array([4, 5, 6, 7]), np.array([8, 9, 10, 11, 12])]
>>> manhattan_pairwise_distance(X)
array([[ 0.,  9., 21.],
[ 9.,  0., 16.],
[21., 16.,  0.]])
```