pydtw
Fast, exact Dynamic Time Warping for Python: alignments and distances of 1-d and multivariate sequences, Sakoe-Chiba windows, PrunedDTW / EAPrunedDTW pruning, SIMD kernels (AVX2, NEON) with runtime dispatch, batch and all-pairs distances, float64 or float32. Inputs can be numpy arrays, pandas Series / DataFrame or lists.
Install
pip install pydtw
Wheels are provided for Linux (x86-64, AArch64), macOS (Intel, Apple Silicon) and Windows; building from source needs a C++ compiler and Cython.
Quick start
Alignment of two sequences:
import numpy as np from pydtw import dtw1d, dtw2d a, b = np.random.rand(100), np.random.rand(120) cost_matrix, cost, alignment_a, alignment_b = dtw1d(a, b) # alignment_a[k] is aligned with alignment_b[k] x, y = np.random.rand(100, 4), np.random.rand(120, 4) # (len, dim) cost_matrix, cost, alignment_x, alignment_y = dtw2d(x, y, window=20) # long sequences: skip the cost matrix (1/8 of the memory, faster) _, cost, alignment_a, alignment_b = dtw1d(a, b, return_cost_matrix=False)
Distance only (much faster, O(len(a) + len(b)) memory):
from pydtw import dtw1d_dist d = dtw1d_dist(a, b) # exact; EAPrunedDTW pruning, SIMD when available d = dtw1d_dist(a, b, window=20) # Sakoe-Chiba window d = dtw1d_dist(a, b, method="none") # no pruning d = dtw1d_dist(a, b, dtype=np.float32) # twice the SIMD lanes, ~1e-6 accuracy
Nearest neighbour with a tightening bound:
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 as soon as 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)
Many short series at once:
from pydtw import dtw1d_dist_batch, dtw1d_dist_matrix X = np.random.rand(1000, 50) # 1000 series of length 50 Y = np.random.rand(1000, 50) costs = dtw1d_dist_batch(X, Y) # pairs (X[k], Y[k]), one per SIMD lane costs = dtw1d_dist_batch(query[None, :], Y) # one query against all of Y D = dtw1d_dist_matrix(X) # all pairs, symmetric (1000, 1000) D = dtw1d_dist_matrix(X, Y, dtype=np.float32) # (1000, 1000), float32
API
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 with inf outside the window and in pruned cells; 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 and cost_matrix is None.
pruned_dtw1d(a, b, window=None, method="auto", return_cost_matrix=True, metric="abs")
pruned_dtw2d(a, b, window=None, metric="euclidean", method="auto", 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 only cells that can lie on an optimal path are expanded.
Distance
dtw1d_dist(a, b, window=None, ub=None, method="eap", metric="abs", dtype=numpy.float64, simd=True)
dtw2d_dist(a, b, window=None, metric="euclidean", ub=None, method="eap", dtype=numpy.float64, simd=True)
-> cost
Cost only, O(len(a) + len(b)) memory, pruned according to method, computed with the SIMD kernel when the CPU has AVX2 or NEON and with the scalar row kernels otherwise.
Batches
dtw1d_dist_batch(X, Y, window=None, ub=None, method="eap", metric="abs", dtype=numpy.float64)
dtw2d_dist_batch(X, Y, window=None, metric="euclidean", ub=None, method="eap", dtype=numpy.float64)
-> costs, shape (N,)
dtw1d_dist_matrix(X, Y=None, window=None, method="eap", metric="abs", dtype=numpy.float64)
dtw2d_dist_matrix(X, Y=None, window=None, metric="euclidean", method="eap", dtype=numpy.float64)
-> costs, shape (N, M)
*_batch computes the N pairs (X[k], Y[k]) with one pair per SIMD lane (X is (N, n) or (N, n, dim), Y is (N, m) or (N, m, dim); a batch of size 1 is broadcast). ub may be a scalar or one bound per pair. *_matrix computes all pairs between the rows of X and Y; with Y=None the symmetric matrix of X with itself. Series inside a batch must share their length; group ragged data by length. Batches pay off for many short series; for a few long series the per-pair kernel with a good ub is faster.
Introspection
simd_info() -> {"simd": "avx2" | "neon" | "scalar", "lanes_float64": ..., "lanes_float32": ...}
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 of the distance-only functions: "eap" (EAPrunedDTW, Herrmann & Webb 2021, default), "pruned" (PrunedDTW, Silva & Batista 2016) or "none". All return the exact cost; they differ in how many cells they skip. All three are implemented in both the SIMD anti-diagonal kernel and the scalar row kernels, so the pruning pays off on every CPU (see the benchmark grid below); which kernel runs is decided by the CPU, not by method.
- dtype
Precision of the computation and of the internal buffers, as for numpy ufuncs: numpy.float64 (default) or numpy.float32. Inputs are converted to it, the dynamic programming runs in it and the result is returned in it (Python float / float32 array). float32 doubles the SIMD lanes (8 instead of 4 with AVX2, 4 instead of 2 with NEON) and halves the memory traffic, which is where its speed-up comes from; the cost is then accurate to about 1e-6 relative (more for very long paths). float32 always uses the anti-diagonal kernel (scalar on CPUs without SIMD).
- simd
True (default) uses the SIMD anti-diagonal kernel when the CPU has one; False forces the scalar row kernels. Exists for benchmarking the kernels against each other; results are identical up to rounding.
- 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; the cost of a path is its sum over the aligned pairs. 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 above ub are not guaranteed to hold their exact value in cost_matrix, only a value above ub.
Input handling
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 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.
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).
Performance
SIMD
The distance kernels are compiled three times: scalar, AVX2 + FMA and NEON. At first use the CPU is probed (CPUID on x86-64; NEON is always present on AArch64) and the best available version is selected; the wheels therefore run on any x86-64 or AArch64 machine. PYDTW_SIMD=scalar|avx2|neon|auto in the environment overrides the choice (an unavailable choice falls back to scalar), which the test suite uses to check the scalar path. All kernels give the same results up to floating-point rounding.
Distance
python bench/bench_dist.py, 1-d, n = m = 5000, best of 3, one core with AVX2. Rows are data sets, columns are pruning scheme (method) by kernel: scalar is the row kernels (simd=False), simd f64 / simd f32 the anti-diagonal kernel in float64 / float32.
scalar |
simd f64 |
simd f32 |
|||||||
|---|---|---|---|---|---|---|---|---|---|
case |
none |
pruned |
eap |
none |
pruned |
eap |
none |
pruned |
eap |
uniform noise |
0.055 s |
0.057 s |
0.058 s |
0.015 s |
0.015 s |
0.014 s |
0.010 s |
0.008 s |
0.009 s |
random walk |
0.070 s |
0.060 s |
0.056 s |
0.014 s |
0.015 s |
0.014 s |
0.006 s |
0.007 s |
0.006 s |
similar (shifted sine + noise) |
0.064 s |
0.029 s |
0.027 s |
0.020 s |
0.005 s |
0.005 s |
0.009 s |
0.002 s |
0.002 s |
near-identical (a, a + 0.01 noise) |
0.073 s |
0.005 s |
0.001 s |
0.019 s |
0.000 s |
0.000 s |
0.009 s |
0.000 s |
0.000 s |
random walk, window = 10% |
0.014 s |
0.013 s |
0.014 s |
0.002 s |
0.002 s |
0.002 s |
0.001 s |
0.001 s |
0.001 s |
2-d dim = 8 random walk |
0.226 s |
0.199 s |
0.115 s |
0.048 s |
0.045 s |
0.046 s |
0.024 s |
0.023 s |
0.023 s |
1-NN, 101 candidates, n = 1000 |
0.240 s |
0.110 s |
0.103 s |
0.052 s |
0.023 s |
0.021 s |
0.030 s |
0.011 s |
0.014 s |
In the 1-NN row the best distance so far is passed as ub, so candidates that cannot win are abandoned early. The same search as one dtw1d_dist_batch call takes 0.103 s (float64) / 0.053 s (float32): a batch cannot exploit a tightening bound, so it wins only on short series. All pairs of 200 series of length 100: 0.405 s as a loop over dtw1d_dist, 0.188 s with dtw1d_dist_matrix (0.097 s in float32).
Alignment
Same machine; no matrix is return_cost_matrix=False, pruned is pruned_dtw1d (its bound comes from the SIMD kernel).
case |
dtw1d |
no matrix |
pruned |
pr+no mat |
|---|---|---|---|---|
uniform noise, n = 5000 |
0.116 s |
0.067 s |
0.117 s |
0.084 s |
random walk, n = 5000 |
0.104 s |
0.062 s |
0.098 s |
0.057 s |
similar (shifted sine + noise) |
0.100 s |
0.083 s |
0.063 s |
0.011 s |
near-identical (a, a + 0.01 noise) |
0.109 s |
0.089 s |
0.062 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.
Development
pip install -e ".[test]" pytest PYDTW_SIMD=scalar pytest # exercise the scalar kernel python bench/bench_dist.py
1 maintainer
Metadata
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