# erp_alignment_path¶

erp_alignment_path(x: ndarray, y: ndarray, window: = None, g: float = 0.0, g_arr: = None, itakura_max_slope: = None) Tuple[List[Tuple[int, int]], float][source]

Compute the ERP alignment path between two time series.

The optimal value of g is selected from the range [σ/5, σ], where σ is the The optimal value of g is selected from the range [σ/5, σ], where σ is the standard deviation of the training data. When there is > 1 channel, g should be a np.ndarray where the nth value is the standard deviation of the nth channel.

Parameters:
xnp.ndarray

First time series, shape `(n_channels, n_timepoints)` or `(n_timepoints,)`.

ynp.ndarray

Second time series, shape `(m_channels, m_timepoints)` or `(m_timepoints,)`.

windowfloat, default=None

The window to use for the bounding matrix. If None, no bounding matrix is used.

gfloat, default=0.0.

The reference value to penalise gaps. The default is 0.

g_arrnp.ndarray, of shape (n_channels), default=None

Numpy array that must be the length of the number of channels in x and y.

itakura_max_slopefloat, default=None

Maximum slope as a proportion of the number of time points used to create Itakura parallelogram on the bounding matrix. Must be between 0. and 1.

Returns:
List[Tuple[int, int]]

The alignment path between the two time series where each element is a tuple of the index in x and the index in y that have the best alignment according to the cost matrix.

float

The erp distance betweeen the two time series.

Raises:
ValueError

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

Examples

```>>> import numpy as np
>>> from aeon.distances import erp_alignment_path
>>> x = np.array([[1, 2, 3, 6]])
>>> y = np.array([[1, 2, 3, 4]])
>>> erp_alignment_path(x, y)
([(0, 0), (1, 1), (2, 2), (3, 3)], 2.0)
```