pydtw
Fast Implementation of Dynamic Time Warping for Python.
install
pip install pydtw
interface
All functions accept anything numpy.asarray understands: numpy arrays, pandas Series / DataFrame, lists. C-contiguous float64 input is used in place without a copy, including read-only views such as pandas Series under copy-on-write; other dtypes and layouts are converted to a C-contiguous float64 copy. Inputs are never modified. Input containing NaN raises ValueError. 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 the local distance (metric) over the aligned pairs.
Alignment
dtw1d(a, b, window=None, ub=None, return_cost_matrix=True, metric="abs")
dtw2d(a, b, window=None, metric="euclidean", ub=None, return_cost_matrix=True)
-> (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]. With return_cost_matrix=False the matrix is not built: the alignment comes from a one-byte-per-cell direction matrix, cost_matrix is None, memory drops to an eighth and long sequences get several times faster (see below).
Distance only
dtw1d_dist(a, b, window=None, ub=None, method="eap", metric="abs")
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). The inner loop runs at about 2.2 ns per cell independent of the data; pruning costs nothing on hard pairs and pays off as soon as the sequences are similar. eap is the default because it was equal or fastest in every case.
case |
no prune |
pruned |
eap |
|---|---|---|---|
uniform noise |
0.056 s |
0.056 s |
0.059 s |
random walk |
0.056 s |
0.057 s |
0.057 s |
similar (shifted sine + noise) |
0.056 s |
0.023 s |
0.023 s |
near-identical (a, a + 0.01 noise) |
0.063 s |
0.003 s |
0.000 s |
random walk, window = 10% |
0.010 s |
0.011 s |
0.011 s |
2-d dim = 8 random walk |
0.168 s |
0.136 s |
0.104 s |
1-NN search, 101 candidates, n = 1000 |
0.229 s |
0.094 s |
0.084 s |
In the 1-NN row the best distance so far is passed as ub, so candidates that cannot win are abandoned early.
Alignment, same machine (no matrix is return_cost_matrix=False):
case |
dtw1d |
no matrix |
pruned |
pr+no mat |
|---|---|---|---|---|
uniform noise, n = 5000 |
0.094 s |
0.059 s |
0.144 s |
0.105 s |
random walk, n = 5000 |
0.098 s |
0.059 s |
0.148 s |
0.101 s |
similar (shifted sine + noise) |
0.094 s |
0.064 s |
0.078 s |
0.030 s |
near-identical (a, a + 0.01 noise) |
0.094 s |
0.057 s |
0.058 s |
0.005 s |
random walk, n = 20000 |
13.8 s |
2.5 s |
At n = m = 20000 the float64 cost matrix is 3.0 GiB and the direction matrix 0.38 GiB.
Pruned alignment
pruned_dtw1d(a, b, window=None, method="eap", return_cost_matrix=True, metric="abs")
pruned_dtw2d(a, b, window=None, metric="euclidean", method="eap", return_cost_matrix=True)
-> (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.
- return_cost_matrix
False skips the cost matrix (None is returned in its place) and derives the alignment from a direction matrix of one byte per cell.
- metric
Local distance between aligned elements. 1-d: "abs" (default, |a[i] - b[j]|; "cityblock" and "euclidean" are accepted as aliases) or "sqeuclidean" ((a[i] - b[j]) ** 2). 2-d, between rows: "euclidean" (default), "sqeuclidean", "cityblock", "chebyshev". Each metric is compiled into its own specialisation of the inner loop, so none of them pays for the choice at run time.
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. cost_matrix is None when return_cost_matrix=False.
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, al_q, al_c = pruned_dtw1d(query, candidates[best_i], window=50,
return_cost_matrix=False)
development
pip install -e . pytest
1 maintainer
Metadata
1 maintainer
Release files for pydtw 3.1.0
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