pydtw
Fast Implementation of Dynamic Time Warping for Python.
install
pip install pydtw
interface
All functions accept anything numpy.asarray understands (lists, integer or non-contiguous arrays are converted to C-contiguous float64). 1-d functions take sequences of shape (len,), 2-d functions take multivariate sequences of shape (len, dim) with the same dim. The cost of a path is the sum of abs(a[i] - b[j]) (1-d) or the Euclidean distance between rows (2-d) over the aligned pairs.
Alignment
dtw1d(a, b, window=None, ub=None)
dtw2d(a, b, window=None, metric="euclidean", ub=None)
-> (cost_matrix, cost, alignment_a, alignment_b)
Full cost matrix plus traceback. cost_matrix is an (len(a), len(b)) ndarray; alignment_a[k] is aligned with alignment_b[k].
Distance only
dtw1d_dist(a, b, window=None, ub=None, method="eap")
dtw2d_dist(a, b, window=None, metric="euclidean", ub=None, method="eap")
-> cost
Two-row buffer (O(len(b)) memory instead of O(len(a) * len(b))) with pruning. Use this when the alignment is not needed, e.g. for nearest-neighbour search or distance matrices.
Benchmark (python bench/bench_dist.py, 1-d, n = m = 5000, best of 3, one core; no prune is ub=numpy.inf, the others use the automatic bound). Pruning never costs anything on hard pairs and pays off as soon as the sequences are similar; eap is the default because it was the fastest or within noise in every case.
case |
no prune |
pruned |
eap |
|---|---|---|---|
uniform noise |
0.216 s |
0.220 s |
0.216 s |
random walk |
0.074 s |
0.126 s |
0.075 s |
similar (shifted sine + noise) |
0.095 s |
0.042 s |
0.031 s |
near-identical (a, a + 0.01 noise) |
0.075 s |
0.004 s |
0.001 s |
random walk, window = 10% |
0.014 s |
0.021 s |
0.015 s |
2-d dim = 8 random walk |
0.162 s |
0.158 s |
0.153 s |
1-NN search, 101 candidates, n = 1000 |
0.345 s |
0.190 s |
0.131 s |
In the 1-NN row the best distance so far is passed as ub, so candidates that cannot win are abandoned early.
Pruned alignment
pruned_dtw1d(a, b, window=None, method="eap")
pruned_dtw2d(a, b, window=None, metric="euclidean", method="eap")
-> (cost_matrix, cost, alignment_a, alignment_b)
Same result as dtw1d / dtw2d. The exact cost is computed first with dtw*_dist and then passed as ub to the alignment, so the full matrix only expands cells that can lie on an optimal path.
Arguments
- window
Sakoe-Chiba window. None searches the whole matrix; an integer w only evaluates cells with abs(i - j) <= w. A window smaller than abs(len(a) - len(b)) cannot reach the last cell and is widened to that value with a warning.
- ub
Upper bound on the cost. Cells whose partial cost exceeds it are pruned, which is exact as long as the true cost is at most ub. When the true cost exceeds ub, dtw*_dist returns inf and dtw1d / dtw2d return (cost_matrix, inf, [], []). In dtw*_dist, None (default) derives a bound from a simple warping path, which keeps the result exact; pass numpy.inf to disable pruning. In dtw1d / dtw2d, None disables pruning. Typical sources of a bound are the best distance found so far in a nearest-neighbour search, or the cost with a narrower window.
- method
Pruning scheme for the two-row implementation: "eap" (EAPrunedDTW, Herrmann & Webb 2021, default) or "pruned" (PrunedDTW, Silva & Batista 2016). Both return the exact cost.
- metric
Distance between rows for 2-d sequences. Only "euclidean" for now.
Cells outside the window or pruned are inf in cost_matrix. Cells above ub are not guaranteed to hold their exact value, only a value above ub.
Deprecated
constrained_dtw1d(a, b, constraint) and constrained_dtw2d(a, b, constraint, metric) are aliases for dtw1d(a, b, window=constraint) and dtw2d(a, b, window=constraint, metric=metric).
usage
Alignment for two 1-dimensional sequences
from pydtw import dtw1d import numpy as np a = np.random.rand(10) b = np.random.rand(15) cost_matrix, cost, alignment_a, alignment_b = dtw1d(a, b)
Alignment for two 2-dimensional sequences
from pydtw import dtw2d import numpy as np a = np.random.rand(10, 4) b = np.random.rand(15, 4) cost_matrix, cost, alignment_a, alignment_b = dtw2d(a, b)
Nearest neighbour with pruning
from pydtw import dtw1d_dist, pruned_dtw1d
best, best_i = float("inf"), None
for i, c in enumerate(candidates):
d = dtw1d_dist(query, c, window=50, ub=best) # inf once it exceeds best
if d < best:
best, best_i = d, i
cost_matrix, cost, al_q, al_c = pruned_dtw1d(query, candidates[best_i], window=50)
development
pip install -e . pytest
1 maintainer
Metadata
1 maintainer
Release files for pydtw 3.0.0
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