# Licensed under a 3-clause BSD style license - see LICENSE.rst from __future__ import (absolute_import, division, print_function, unicode_literals) import timeit import numpy as np # pylint: disable=W0611 # largest image size to use for "linear" and fft convolutions max_exponents_linear = {1: 15, 2: 7, 3: 5} max_exponents_fft = {1: 15, 2: 10, 3: 7} if __name__ == "__main__": for ndims in [1, 2, 3]: print("\n%i-dimensional arrays ('n' is the size of the image AND the kernel)" % ndims) print(" ".join(["%17s" % n for n in ("n", "convolve", "convolve_fft")])) for ii in range(3, max_exponents_fft[ndims]): # array = np.random.random([2**ii]*ndims) # test ODD sizes too if ii < max_exponents_fft[ndims]: setup = (""" import numpy as np from astropy.convolution.convolve import convolve from astropy.convolution.convolve import convolve_fft array = np.random.random([%i]*%i) kernel = np.random.random([%i]*%i)""") % (2 ** ii - 1, ndims, 2 ** ii - 1, ndims) print("%16i:" % (int(2 ** ii - 1)), end=' ') if ii <= max_exponents_linear[ndims]: for ffttype, extra in zip(("", "_fft"), ("", "fft_pad=False")): statement = "convolve%s(array, kernel, boundary='fill', %s)" % (ffttype, extra) besttime = min(timeit.Timer(stmt=statement, setup=setup).repeat(3, 10)) print("%17f" % (besttime), end=' ') else: print("%17s" % "skipped", end=' ') statement = "convolve_fft(array, kernel, boundary='fill')" besttime = min(timeit.Timer(stmt=statement, setup=setup).repeat(3, 10)) print("%17f" % (besttime), end=' ') print() setup = (""" import numpy as np from astropy.convolution.convolve import convolve from astropy.convolution.convolve import convolve_fft array = np.random.random([%i]*%i) kernel = np.random.random([%i]*%i)""") % (2 ** ii - 1, ndims, 2 ** ii - 1, ndims) print("%16i:" % (int(2 ** ii)), end=' ') if ii <= max_exponents_linear[ndims]: for ffttype in ("", "_fft"): statement = "convolve%s(array, kernel, boundary='fill')" % ffttype besttime = min(timeit.Timer(stmt=statement, setup=setup).repeat(3, 10)) print("%17f" % (besttime), end=' ') else: print("%17s" % "skipped", end=' ') statement = "convolve_fft(array, kernel, boundary='fill')" besttime = min(timeit.Timer(stmt=statement, setup=setup).repeat(3, 10)) print("%17f" % (besttime), end=' ') print() """ Unfortunately, these tests are pretty strongly inconclusive RESULTS on a 2011 Mac Air: 1-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.000408 0.002334 0.005571 0.002677 8: 0.000399 0.002818 0.006505 0.003094 15: 0.000361 0.002491 0.005648 0.002678 16: 0.000371 0.002997 0.005983 0.003036 31: 0.000535 0.002450 0.005988 0.002880 32: 0.000452 0.002618 0.007102 0.004366 63: 0.000509 0.002876 0.008003 0.002981 64: 0.000453 0.002706 0.005520 0.003049 127: 0.000801 0.004080 0.008513 0.003932 128: 0.000749 0.003332 0.006236 0.003159 255: 0.002453 0.003111 0.007518 0.003564 256: 0.002478 0.003341 0.006325 0.004290 511: 0.008394 0.006224 0.010247 0.005991 512: 0.007934 0.003764 0.006840 0.004106 1023: 0.028741 0.007538 0.009591 0.007696 1024: 0.027900 0.004871 0.009628 0.005118 2047: 0.106323 0.021575 0.022041 0.020682 2048: 0.108916 0.008107 0.011049 0.007596 4095: 0.411936 0.021675 0.019761 0.020939 4096: 0.408992 0.018870 0.016663 0.012890 8191: 1.664517 8.278320 0.073001 7.803563 8192: 1.657573 0.037967 0.034227 0.028390 16383: 6.654678 0.251661 0.202271 0.222171 16384: 6.611977 0.073630 0.067616 0.055591 2-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.000552 0.003524 0.006667 0.004318 8: 0.000646 0.004443 0.007354 0.003958 15: 0.002986 0.005093 0.012941 0.005951 16: 0.003549 0.005688 0.008818 0.006300 31: 0.074360 0.033973 0.031800 0.036937 32: 0.077338 0.017708 0.025637 0.011883 63: 0.848471 0.057407 0.052192 0.053213 64: 0.773061 0.029657 0.033409 0.028230 127: 14.656414 1.005329 0.402113 0.955279 128: 15.867796 0.266233 0.268551 0.237930 255: skipped 1.715546 1.566876 1.745338 256: skipped 1.515616 1.268220 1.036881 511: skipped 4.066155 4.303350 3.930661 512: skipped 3.976139 4.337525 3.968935 3-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.009239 0.012957 0.011957 0.015997 8: 0.012405 0.011328 0.011677 0.012283 15: 0.772434 0.075621 0.056711 0.079508 16: 0.964635 0.105846 0.072811 0.104611 31: 62.824051 2.295193 1.189505 2.351136 32: 79.507060 1.169182 0.821779 1.275770 63: skipped 11.250225 10.982726 10.585744 64: skipped 10.013558 11.507645 12.665557 On a 2009 Mac Pro: 1-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.000360 0.002269 0.004986 0.002476 8: 0.000361 0.002468 0.005242 0.002696 15: 0.000364 0.002255 0.005244 0.002471 16: 0.000365 0.002506 0.005286 0.002727 31: 0.000385 0.002380 0.005422 0.002588 32: 0.000385 0.002531 0.005543 0.002737 63: 0.000474 0.002407 0.005392 0.002637 64: 0.000484 0.002602 0.005631 0.002823 127: 0.000752 0.004122 0.007827 0.003966 128: 0.000757 0.002763 0.005844 0.002958 255: 0.004316 0.003258 0.006566 0.003324 256: 0.004354 0.003180 0.006120 0.003245 511: 0.011517 0.007158 0.009898 0.006238 512: 0.011482 0.003873 0.006777 0.003820 1023: 0.034105 0.009211 0.009468 0.008260 1024: 0.034609 0.005504 0.008399 0.005080 2047: 0.113620 0.028097 0.020662 0.021603 2048: 0.112828 0.008403 0.010939 0.007331 4095: 0.403373 0.023211 0.018767 0.020065 4096: 0.403316 0.017550 0.017853 0.013651 8191: 1.519329 8.454573 0.211436 7.212381 8192: 1.519082 0.033148 0.030370 0.025905 16383: 5.887481 0.317428 0.153344 0.237119 16384: 5.888222 0.069379 0.065264 0.052847 2-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.000474 0.003470 0.006131 0.003503 8: 0.000503 0.003565 0.006400 0.003586 15: 0.002011 0.004481 0.007825 0.004496 16: 0.002236 0.004744 0.007078 0.004680 31: 0.027291 0.019433 0.014841 0.018034 32: 0.029283 0.009244 0.010161 0.008964 63: 0.445680 0.038171 0.026753 0.037404 64: 0.460616 0.028128 0.029487 0.029149 127: 7.003774 0.925921 0.282591 0.762671 128: 7.063657 0.110838 0.104402 0.133523 255: skipped 0.804682 0.708849 0.869368 256: skipped 0.797800 0.721042 0.880848 511: skipped 3.643626 3.687562 4.584770 512: skipped 3.715215 4.893539 5.538462 3-dimensional arrays ('n' is the size of the image AND the kernel) n convolve convolve_fftnp convolve_fftw convolve_fftsp 7: 0.004520 0.011519 0.009464 0.012335 8: 0.006422 0.010294 0.010220 0.011711 15: 0.329566 0.060978 0.045495 0.073692 16: 0.405275 0.069999 0.040659 0.086114 31: 24.935228 1.654920 0.710509 1.773879 32: 27.524226 0.724053 0.543507 1.027568 63: skipped 8.982771 12.407683 16.900078 64: skipped 8.956070 11.934627 17.296447 """