Assess Superlet Performance Issues

[pantaray]

Computing a spectrum using superlets is at times significantly slower than a (comparable) wavelet setup, e.g., same data-set (3 trials, 4 channels), auto-freq selection (0-500Hz), ca. 90 seconds for max_order = 2 superlets compared to around 8 seconds for Morlet.
The increase in computational time seems non-linear wrt max_order too (for max_order = 10 the runtime for the same dataset is ca. 20 minutes)

[tensionhead]

So I just ran a few ad-hoc backend timing tests, and these are the results for a single 25 000 sample signal:

order_max	run time
2	667ms
10	3340ms
20	6860ms

I see pretty perfect linear scaling 😄

[pantaray]

Hm, can't reproduce this with the frontend. Using the synthetic data-set from the testing module defined in _make_tf_signal

syncopy/syncopy/tests/test_specest.py

Line 38 in 9af9d5a

def _make_tf_signal(nChannels, nTrials, seed, fadeIn=None, fadeOut=None):

(using as mentioned 4 channels and 3 trials) the timing for order_min = 1 and order_max = 2 is:

Syncopy <freqanalysis> INFO: Automatic superlet frequency selection from 0.0Hz to 500.0Hz
100% |███████████████████████ 3/3 [01:21<00:00]

for order_max = 4 I get

Syncopy <freqanalysis> INFO: Automatic superlet frequency selection from 0.0Hz to 500.0Hz
100% |███████████████████████| 3/3 [04:05<00:00]

and order_max = 8 gives

Syncopy <freqanalysis> INFO: Automatic superlet frequency selection from 0.0Hz to 500.0Hz
100% |███████████████████████| 3/3 [13:56<00:00]

[tensionhead]

I did a few frontend tests, so simple calls ala freqanalysis(data, method='superlet', order_max=..), the data has 3 Trials. 10 Channels and 2600 samples:

order_max = 2 gives 3.1s runtime and profiled:

 ncalls  tottime  percall  cumtime  percall filename:lineno(function)
      954    2.006    0.002    2.006    0.002 {built-in method scipy.fft._pocketfft.pypocketfft.c2c}
        3    0.685    0.228    3.094    1.031 superlet.py:107(multiplicativeSLT)
      318    0.153    0.000    0.153    0.000 superlet.py:286(time)
      318    0.141    0.000    2.209    0.007 signaltools.py:334(_freq_domain_conv)
      642    0.036    0.000    0.036    0.000 {built-in method numpy.zeros}
        6    0.015    0.003    2.409    0.401 superlet.py:336(cwtSL)
        3    0.013    0.004    0.022    0.007 dataset.py:584(__setitem__)

order_max = 4 gives 9.2s runtime and profiled:

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
     1908    6.594    0.003    6.594    0.003 {built-in method scipy.fft._pocketfft.pypocketfft.c2c}
        3    1.332    0.444    9.164    3.055 superlet.py:107(multiplicativeSLT)
      636    0.490    0.001    0.490    0.001 superlet.py:286(time)
      636    0.467    0.001    7.223    0.011 signaltools.py:334(_freq_domain_conv)
     1284    0.098    0.000    0.098    0.000 {built-in method numpy.zeros}
       12    0.052    0.004    7.832    0.653 superlet.py:336(cwtSL)
     1908    0.029    0.000    0.120    0.000 helper.py:109(_fix_shape)
        3    0.014    0.005    0.022    0.007 dataset.py:584(__setitem__)

order_max = 8 gives 33.2s runtime and profiled:

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
     3816   26.142    0.007   26.142    0.007 {built-in method scipy.fft._pocketfft.pypocketfft.c2c}
        3    2.665    0.888   33.175   11.058 superlet.py:107(multiplicativeSLT)
     1272    1.754    0.001   28.438    0.022 signaltools.py:334(_freq_domain_conv)
     1272    1.742    0.001    1.742    0.001 superlet.py:286(time)
     2568    0.365    0.000    0.365    0.000 {built-in method numpy.zeros}
       24    0.156    0.006   30.510    1.271 superlet.py:336(cwtSL)
     3816    0.094    0.000    0.445    0.000 helper.py:109(_fix_shape)
     1276    0.041    0.000    0.041    0.000 {built-in method numpy.arange}
     1272    0.028    0.000    0.028    0.000 {method 'copy' of 'numpy.ndarray' objects}
     1272    0.025    0.000    0.065    0.000 superlet.py:383(_get_superlet_support)
     8949    0.019    0.000    0.019    0.000 {built-in method numpy.array}
     1272    0.018    0.000   28.531    0.022 signaltools.py:432(fftconvolve)
     5088    0.017    0.000    0.048    0.000 helper.py:41(_init_nd_shape_and_axes)
     1272    0.016    0.000    0.027    0.000 signaltools.py:263(_centered)
     3816    0.015    0.000   26.665    0.007 basic.py:141(c2cn)
        3    0.014    0.005    0.022    0.007 dataset.py:584(__setitem__)

So there is indeed some unexpected scaling, order_max doubles but runtime triples. However not in that ludicrous range (seconds vs. minutes) that @pantaray reported for a smaller dataset with only 12 signals (here we have 3 * 10 = 30 signals).

EDIT: small inspection of the profiles shows, that scipy.fft._... itself does not scale with a factor of 2 but rather more 3ish :D