# Distances¶

The aeon.distances module contains time series specific distance functions that can be used in aeon and scikit learn estimators. It also contains tools for extracting the alignment paths for a distance calculation between two series, and tools for finding all pairwise distances

## Amerced Dynamic Time Warping (ADTW)¶

 adtw_distance(x, y[, window, ...]) Compute the ADTW distance between two time series. adtw_pairwise_distance(X[, y, window, ...]) Compute the ADTW pairwise distance between a set of time series. adtw_cost_matrix(x, y[, window, ...]) Compute the ADTW cost matrix between two time series. adtw_alignment_path(x, y[, window, ...]) Compute the ADTW alignment path between two time series.

## Dynamic Time Warping (DTW)¶

 dtw_distance(x, y[, window, itakura_max_slope]) Compute the DTW distance between two time series. dtw_pairwise_distance(X[, y, window, ...]) Compute the DTW pairwise distance between a set of time series. dtw_cost_matrix(x, y[, window, ...]) Compute the DTW cost matrix between two time series. dtw_alignment_path(x, y[, window, ...]) Compute the DTW alignment path between two time series.

## Edit Real Penalty (ERP)¶

 erp_distance(x, y[, window, g, g_arr, ...]) Compute the ERP distance between two time series. erp_pairwise_distance(X[, y, window, g, ...]) Compute the ERP pairwise distance between a set of time series. erp_cost_matrix(x, y[, window, g, g_arr, ...]) Compute the ERP cost matrix between two time series. erp_alignment_path(x, y[, window, g, g_arr, ...]) Compute the ERP alignment path between two time series.

## Edit distance for real sequences (EDR)¶

 edr_distance(x, y[, window, epsilon, ...]) Compute the EDR distance between two time series. edr_pairwise_distance(X[, y, window, ...]) Compute the pairwise EDR distance between a set of time series. edr_cost_matrix(x, y[, window, epsilon, ...]) Compute the EDR cost matrix between two time series. edr_alignment_path(x, y[, window, epsilon, ...]) Compute the EDR alignment path between two time series.

## Euclidean¶

 Compute the Euclidean distance between two time series. Compute the Euclidean pairwise distance between a set of time series.

## Longest Common Subsequence (LCSS)¶

 lcss_distance(x, y[, window, epsilon, ...]) Return the LCSS distance between x and y. lcss_pairwise_distance(X[, y, window, ...]) Compute the LCSS pairwise distance between a set of time series. lcss_cost_matrix(x, y[, window, epsilon, ...]) Return the LCSS cost matrix between x and y. lcss_alignment_path(x, y[, window, epsilon, ...]) Compute the LCSS alignment path between two time series.

## Manhattan¶

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

## Minkowski¶

 minkowski_distance(x, y[, p, w]) Compute the Minkowski distance between two time series. minkowski_pairwise_distance(X[, y, p, w]) Compute the Minkowski pairwise distance between a set of time series.

## Move-Split-Merge (MSM)¶

 msm_distance(x, y[, window, independent, c, ...]) Compute the MSM distance between two time series. msm_pairwise_distance(X[, y, window, ...]) Compute the msm pairwise distance between a set of time series. msm_cost_matrix(x, y[, window, independent, ...]) Compute the MSM cost matrix between two time series. msm_alignment_path(x, y[, window, ...]) Compute the msm alignment path between two time series.

## Shape-based Distance (SBD)¶

 sbd_distance(x, y[, standardize]) Compute the shape-based distance (SBD) between two time series. sbd_pairwise_distance(X[, y, standardize]) Compute the shape-based distance (SBD) between all pairs of time series.

## Shape Dynamic Time Warping (Shape DTW)¶

 shape_dtw_distance(x, y[, window, ...]) Compute the ShapeDTW distance function between two series x and y. shape_dtw_pairwise_distance(X[, y, window, ...]) Compute the ShapeDTW pairwise distance among a set of series. shape_dtw_cost_matrix(x, y[, window, ...]) Compute the ShapeDTW cost matrix between two series x and y. shape_dtw_alignment_path(x, y[, window, ...]) Compute the ShapeDTW alignment path between two series x and y.

## Squared¶

 Compute the squared distance between two time series. Compute the squared pairwise distance between a set of time series.

## Time Warp Edit (TWE)¶

 twe_distance(x, y[, window, nu, lmbda, ...]) Compute the TWE distance between two time series. twe_pairwise_distance(X[, y, window, nu, ...]) Compute the TWE pairwise distance between a set of time series. twe_cost_matrix(x, y[, window, nu, lmbda, ...]) Compute the TWE cost matrix between two time series. twe_alignment_path(x, y[, window, nu, ...]) Compute the TWE alignment path between two time series.

## Weighted Derivative Dynamic Time Warping (WDDTW)¶

 wddtw_distance(x, y[, window, g, ...]) Compute the WDDTW distance between two time series. wddtw_pairwise_distance(X[, y, window, g, ...]) Compute the WDDTW pairwise distance between a set of time series. wddtw_cost_matrix(x, y[, window, g, ...]) Compute the WDDTW cost matrix between two time series. wddtw_alignment_path(x, y[, window, g, ...]) Compute the WDDTW alignment path between two time series.

## Weighted Dynamic Time Warping (DTW)¶

 wdtw_distance(x, y[, window, g, ...]) Compute the WDTW distance between two time series. wdtw_pairwise_distance(X[, y, window, g, ...]) Compute the WDTW pairwise distance between a set of time series. wdtw_cost_matrix(x, y[, window, g, ...]) Compute the WDTW cost matrix between two time series. wdtw_alignment_path(x, y[, window, g, ...]) Compute the WDTW alignment path between two time series.

## General methods with distance argument¶

 distance(x, y, metric, **kwargs) Compute the distance between two time series. pairwise_distance(x[, y, metric]) Compute the pairwise distance matrix between two time series. cost_matrix(x, y, metric, **kwargs) Compute the alignment path and distance between two time series. alignment_path(x, y, metric, **kwargs) Compute the alignment path and distance between two time series. create_bounding_matrix(x_size, y_size[, ...]) Create a bounding matrix for an elastic distance.

## General methods to recover distance functions¶

 get_distance_function(metric) Get the distance function for a given metric string or callable. Get the pairwise distance function for a given metric string or callable. Get a list of distance function names in aeon. Get the cost matrix function for a given metric string or callable. Get the alignment path function for a given metric string or callable.