# dtaidistance.dtw¶

Dynamic Time Warping (DTW)

author: Wannes Meert Copyright 2017-2022 KU Leuven, DTAI Research Group. Apache License, Version 2.0, see LICENSE for details.
`dtaidistance.dtw.``best_path`(paths, row=None, col=None, use_max=False)

Compute the optimal path from the nxm warping paths matrix.

Parameters: row – If given, start from this row (instead of lower-right corner) col – If given, start from this column (instead of lower-right corner) Array of (row, col) representing the best path
`dtaidistance.dtw.``best_path2`(paths)

Compute the optimal path from the nxm warping paths matrix.

`dtaidistance.dtw.``distance`(s1, s2, window=None, max_dist=None, max_step=None, max_length_diff=None, penalty=None, psi=None, use_c=False, use_pruning=False, only_ub=False, inner_dist='squared euclidean')

Dynamic Time Warping.

This function keeps a compact matrix, not the full warping paths matrix.

Uses dynamic programming to compute:

wps[i, j] = (s1[i]-s2[j])**2 + min(
wps[i-1, j ] + penalty, // vertical / insertion / expansion wps[i , j-1] + penalty, // horizontal / deletion / compression wps[i-1, j-1]) // diagonal / match

dtw = sqrt(wps[-1, -1])

Parameters: s1 – First sequence s2 – Second sequence window – Only allow for maximal shifts from the two diagonals smaller than this number. It includes the diagonal, meaning that an Euclidean distance is obtained by setting window=1. max_dist – Stop if the returned values will be larger than this value max_step – Do not allow steps larger than this value max_length_diff – Return infinity if length of two series is larger penalty – Penalty to add if compression or expansion is applied psi – Psi relaxation parameter (ignore start and end of matching). If psi is a single integer, it is used for both start and end relaxations of both series. If psi is a 4-tuple, it is used as the psi-relaxation for (begin series1, end series1, begin series2, end series2) Useful for cyclical series. use_c – Use fast pure c compiled functions use_pruning – Prune values based on Euclidean distance. This is the same as passing ub_euclidean() to max_dist only_ub – Only compute the upper bound (Euclidean). inner_dist – Distance between two points in the time series. One of ‘squared euclidean’ (default), ‘euclidean’. When using the pure Python implementation (thus use_c=False) then the argument can also be an object that has as callable arguments ‘inner_dist’ and ‘result’. The ‘inner_dist’ function computes the distance between two points (e.g., squared euclidean) and ‘result’ is the function to apply to the final distance (e.g., sqrt when using squared euclidean). You can also inherit from the ‘innerdistance.CustomInnerDist’ class.

Returns: DTW distance

`dtaidistance.dtw.``distance_fast`(s1, s2, window=None, max_dist=None, max_step=None, max_length_diff=None, penalty=None, psi=None, use_pruning=False, only_ub=False, inner_dist='squared euclidean')

Same as `distance()` but with different defaults to chose the fast C-based version of the implementation (use_c = True).

Note: the series are expected to be arrays of the type `double`. Thus `numpy.array([1,2,3], dtype=numpy.double)` or `array.array('d', [1,2,3])`

`dtaidistance.dtw.``distance_matrix`(s, max_dist=None, use_pruning=False, max_length_diff=None, window=None, max_step=None, penalty=None, psi=None, block=None, compact=False, parallel=False, use_c=False, use_mp=False, show_progress=False, only_triu=False)

Distance matrix for all sequences in s.

Parameters: s – Iterable of series max_dist – see `distance()` use_pruning – Prune values based on Euclidean distance. This is the same as passing ub_euclidean() to max_dist max_length_diff – see `distance()` window – see `distance()` max_step – see `distance()` penalty – see `distance()` psi – see `distance()` block – Only compute block in matrix. Expects tuple with begin and end, e.g. ((0,10),(20,25)) will only compare rows 0:10 with rows 20:25. compact – Return the distance matrix as an array representing the upper triangular matrix. parallel – Use parallel operations use_c – Use c compiled Python functions use_mp – Force use Multiprocessing for parallel operations (not OpenMP) show_progress – Show progress using the tqdm library. This is only supported for the pure Python version (thus not the C-based implementations). only_triu – Only compute upper traingular matrix of warping paths. This is useful if s1 and s2 are the same series and the matrix would be mirrored around the diagonal. The distance matrix or the condensed distance matrix if the compact argument is true
`dtaidistance.dtw.``distance_matrix_fast`(s, max_dist=None, use_pruning=False, max_length_diff=None, window=None, max_step=None, penalty=None, psi=None, block=None, compact=False, parallel=True, use_mp=False, only_triu=False)

Same as `distance_matrix()` but with different defaults to choose the fast parallized C version (use_c = True and parallel = True).

This method uses the C-compiled version of the DTW algorithm and uses parallelization. By default this is the OMP C parallelization. If the OMP functionality is not available the parallelization is changed to use Python’s multiprocessing library.

`dtaidistance.dtw.``distances_array_to_matrix`(dists, nb_series, block=None, only_triu=False)

Transform a condensed distances array to a full matrix representation.

The upper triangular matrix will contain all the distances.

`dtaidistance.dtw.``lb_keogh`(s1, s2, window=None, max_dist=None, max_step=None, max_length_diff=None, use_c=False, inner_dist='squared euclidean')

Lowerbound LB_KEOGH

`dtaidistance.dtw.``ub_euclidean`(s1, s2, inner_dist='squared euclidean')

See ed.euclidean_distance

`dtaidistance.dtw.``warp`(from_s, to_s, path=None, **kwargs)

Warp a function to optimally match a second function.

Parameters: from_s – First sequence to_s – Second sequence path – (Optional) Path to use wrap the ‘from_s’ sequence to the ‘to_s’ sequence If provided, this function will use it. If not provided, this function will calculate it using the warping_path function kwargs – Same options as `warping_paths()`.
`dtaidistance.dtw.``warping_amount`(path)

Returns the number of compressions and expansions performed to obtain the best path. Can be used as a metric for the amount of warping.

Parameters: path – path to be tested

:returns number of compressions or expansions

`dtaidistance.dtw.``warping_path`(from_s, to_s, include_distance=False, **kwargs)

Compute warping path between two sequences.

`dtaidistance.dtw.``warping_path_fast`(from_s, to_s, include_distance=False, **kwargs)

Compute warping path between two sequences.

`dtaidistance.dtw.``warping_path_penalty`(s1, s2, penalty_post=0, **kwargs)

Dynamic Time Warping with an alternative penalty.

This function supports two different penalties. The traditional DTW penalty penalty is used in the matrix during calculation of the warping path (see `distance()`).

The second penalty penalty_post measures the amount of warping. This penalty doesn’t affect the warping path and is added to the DTW distance after the warping for every compression or expansion.

Same options as `warping_paths()`

Parameters: s1 – First sequence s2 – Second sequence penalty_post – Penalty to be added after path calculation, for compression/extension

:returns [DTW distance, best path, DTW distance between 2 path elements, DTW matrix]

`dtaidistance.dtw.``warping_path_prob`(from_s, to_s, avg, include_distance=False, use_c=True, **kwargs)

Compute warping path between two sequences.

`dtaidistance.dtw.``warping_paths`(s1, s2, window=None, max_dist=None, use_pruning=False, max_step=None, max_length_diff=None, penalty=None, psi=None, psi_neg=True, use_c=False, use_ndim=False, inner_dist='squared euclidean')

Dynamic Time Warping.

The full matrix of all warping paths (or accumulated cost matrix) is built.

Parameters: s1 – First sequence s2 – Second sequence window – see `distance()` max_dist – see `distance()` use_pruning – Prune values based on Euclidean distance. This is the same as passing ub_euclidean() to max_dist max_step – see `distance()` max_length_diff – see `distance()` penalty – see `distance()` psi – see `distance()` psi_neg – Replace values that should be skipped because of psi-relaxation with -1. use_c – Use the C implementation instead of Python use_ndim – The input series is >1 dimensions. Use cost = EuclideanDistance(s1[i], s2[j]) inner_dist – Distance between two points in the time series. One of ‘squared euclidean’ (default), ‘euclidean’ (DTW distance, DTW matrix)
`dtaidistance.dtw.``warping_paths_affinity`(s1, s2, window=None, only_triu=False, penalty=None, psi=None, psi_neg=True, gamma=1, tau=0, delta=0, delta_factor=1, exp_avg=None, use_c=False)

Dynamic Time Warping warping paths using an affinity/similarity matrix instead of a distance matrix.

The full matrix of all warping paths (or accumulated cost matrix) is built.

Parameters: s1 – First sequence s2 – Second sequence window – see `distance()` only_triu – Only compute upper traingular matrix of warping paths. This is useful if s1 and s2 are the same series and the matrix would be mirrored around the diagonal. penalty – see `distance()` psi – see `distance()` psi_neg – Replace values that should be skipped because of psi-relaxation with -1. (DTW distance, DTW matrix)
`dtaidistance.dtw.``warping_paths_affinity_fast`(s1, s2, window=None, only_triu=False, penalty=None, psi=None, psi_neg=True, gamma=1, tau=0, delta=0, delta_factor=1, exp_avg=None, compact=False, use_ndim=False)

Fast C version of `warping_paths()`.

`dtaidistance.dtw.``warping_paths_fast`(s1, s2, window=None, max_dist=None, use_pruning=False, max_step=None, max_length_diff=None, penalty=None, psi=None, psi_neg=True, compact=False, use_ndim=False, inner_dist='squared euclidean')
Fast C version of `warping_paths()`.