ENH: Use np.dot to speedup spatial.distance.correlation

[lgeiger]

What does this implement/fix?

This PR changes the implementation of spatial.distance.correlation to rely on dot products for computing the distance (7e85a88). 77f135d switches to builtin math operations when working on scalars as they have less overhead compared to numpy.

Overall this reduces the runtime of spatial.distance.cosine by ~6 x and the weighted version by ~3.5 x 🚀

Additional information

The above numbers where measured using the script below.

import numpy as np
import scipy.spatial

x = np.random.normal(size=512)
y = np.random.normal(size=512)
w = np.random.uniform(size=512)

%timeit scipy.spatial.distance.cosine(x, y)
# main: 19.2 µs ± 358 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
# this PR: 3.15 µs ± 54.9 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

%timeit scipy.spatial.distance.cosine(x, y, w)
# main: 46.6 µs ± 1.79 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
# this PR: 13.6 µs ± 530 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

%timeit scipy.spatial.distance.correlation(x, y)
# main: 34.1 µs ± 326 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
# this PR: 14.2 µs ± 168 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

%timeit scipy.spatial.distance.correlation(x, y, w)
# main: 71.3 µs ± 2.42 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
# this PR: 17.7 µs ± 89 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

Here are the results of the XdistWeighted (Xdist doesn't show a difference since it uses C code instead):

spatial.XdistWeighted.time_cdist (main)    spatial.XdistWeighted.time_cdist (this PR)
============ ============ =============    ============ ============= =============
--                     metric              --                      metric
------------ --------------------------    ------------ ---------------------------
 num_points     cosine     correlation      num_points      cosine     correlation
============ ============ =============    ============ ============= =============
     10       3.99±0.1ms    6.37±0.2ms          10       1.38±0.1ms   1.54±0.07ms
     20       16.5±0.2ms     25.7±1ms           20       5.40±0.5ms    6.14±0.2ms
    100        420±20ms      652±30ms          100        134±10ms      154±20ms
============ ============ =============    ============ ============= =============


spatial.XdistWeighted.time_pdist (main)    spatial.XdistWeighted.time_pdist (this PR)
============ ============= =============   ============ ============= =============
--                      metric             --                      metric
------------ ---------------------------   ------------ ---------------------------
 num_points      cosine     correlation     num_points      cosine     correlation
============ ============= =============   ============ ============= =============
     10       1.99±0.08ms    3.13±0.5ms         10       635±100μs      707±50μs
     20        7.97±0.3ms   11.9±0.03ms         20       2.56±0.1ms    3.07±0.2ms
    100         208±10ms      313±10ms         100        61.8±2ms      79.9±4ms
============ ============= =============   ============ ============= =============

[lgeiger]

From what I can tell the CI failure seems to be unrelated but happy to have a closer look if you think that's not the case.

[lucascolley]

From what I can tell the CI failure seems to be unrelated but happy to have a closer look if you think that's not the case.

Yeah, that's unrelated.

Out of interest, is u @ w any faster/slower than np.dot(u, w)?

[lgeiger]

Out of interest, is u @ w any faster/slower than np.dot(u, w)?

In an isolated test u @ w seems to be 30% slower than np.dot(u, w) when multiplying two vectors since it uses np.matmul under the hood.

[tylerjereddy]

Checking the benchmarks on x86_64 Linux with asv continuous -e -b ".*Xdist.*" main spatial-correlation-dot yields nothing but improvements:

| Change   | Before [ae9dc131] <main>   | After [4141d2f4] <spatial-correlation-dot>   |   Ratio | Benchmark (Parameter)                                |
|----------|----------------------------|----------------------------------------------|---------|------------------------------------------------------|
| -        | 1.88±0.01ms                | 544±1μs                                      |    0.29 | spatial.XdistWeighted.time_cdist(10, 'cosine')       |
| -        | 186±0.1ms                  | 53.7±0.3ms                                   |    0.29 | spatial.XdistWeighted.time_cdist(100, 'cosine')      |
| -        | 7.49±0.01ms                | 2.19±0.05ms                                  |    0.29 | spatial.XdistWeighted.time_cdist(20, 'cosine')       |
| -        | 847±2μs                    | 247±1μs                                      |    0.29 | spatial.XdistWeighted.time_pdist(10, 'cosine')       |
| -        | 92.9±0.2ms                 | 26.6±0.07ms                                  |    0.29 | spatial.XdistWeighted.time_pdist(100, 'cosine')      |
| -        | 3.54±0.01ms                | 1.03±0.02ms                                  |    0.29 | spatial.XdistWeighted.time_pdist(20, 'cosine')       |
| -        | 1.30±0ms                   | 308±8μs                                      |    0.24 | spatial.XdistWeighted.time_pdist(10, 'correlation')  |
| -        | 2.88±0ms                   | 663±0.8μs                                    |    0.23 | spatial.XdistWeighted.time_cdist(10, 'correlation')  |
| -        | 288±0.6ms                  | 66.0±0.1ms                                   |    0.23 | spatial.XdistWeighted.time_cdist(100, 'correlation') |
| -        | 11.5±0.01ms                | 2.63±0ms                                     |    0.23 | spatial.XdistWeighted.time_cdist(20, 'correlation')  |
| -        | 142±0.08ms                 | 32.7±0.1ms                                   |    0.23 | spatial.XdistWeighted.time_pdist(100, 'correlation') |
| -        | 5.47±0.01ms                | 1.25±0ms                                     |    0.23 | spatial.XdistWeighted.time_pdist(20, 'correlation')  |

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
PERFORMANCE INCREASED.

Same thing on ARM Mac (M2 Max):

| Change   | Before [ae9dc131] <main>   | After [4141d2f4] <spatial-correlation-dot>   |   Ratio | Benchmark (Parameter)                                |
|----------|----------------------------|----------------------------------------------|---------|------------------------------------------------------|
| -        | 680±5μs                    | 571±70μs                                     |    0.84 | spatial.Xdist.time_pdist(1000, 'chebyshev')          |
| -        | 799±3μs                    | 262±2μs                                      |    0.33 | spatial.XdistWeighted.time_pdist(10, 'cosine')       |
| -        | 1.74±0.01ms                | 558±2μs                                      |    0.32 | spatial.XdistWeighted.time_cdist(10, 'cosine')       |
| -        | 175±0.5ms                  | 55.4±0.6ms                                   |    0.32 | spatial.XdistWeighted.time_cdist(100, 'cosine')      |
| -        | 3.38±0ms                   | 1.07±0ms                                     |    0.32 | spatial.XdistWeighted.time_pdist(20, 'cosine')       |
| -        | 7.09±0.09ms                | 2.22±0.01ms                                  |    0.31 | spatial.XdistWeighted.time_cdist(20, 'cosine')       |
| -        | 88.7±2ms                   | 27.3±0.08ms                                  |    0.31 | spatial.XdistWeighted.time_pdist(100, 'cosine')      |
| -        | 10.9±0.08ms                | 2.79±0.01ms                                  |    0.26 | spatial.XdistWeighted.time_cdist(20, 'correlation')  |
| -        | 2.74±0.07ms                | 694±3μs                                      |    0.25 | spatial.XdistWeighted.time_cdist(10, 'correlation')  |
| -        | 273±1ms                    | 69.2±2ms                                     |    0.25 | spatial.XdistWeighted.time_cdist(100, 'correlation') |
| -        | 1.24±0.02ms                | 316±1μs                                      |    0.25 | spatial.XdistWeighted.time_pdist(10, 'correlation')  |
| -        | 137±0.1ms                  | 34.1±0.07ms                                  |    0.25 | spatial.XdistWeighted.time_pdist(100, 'correlation') |
| -        | 5.40±0.03ms                | 1.34±0ms                                     |    0.25 | spatial.XdistWeighted.time_pdist(20, 'correlation')  |

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
PERFORMANCE INCREASED.

Combined with the fact that code complexity hasn't increased much/we haven't added more compiled code, it is a pretty easy decision to merge, thanks.

[tylerjereddy]

and thanks for your first contribution to SciPy

[lgeiger]

Great, thanks for properly running the benchmarks and the fast review.