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Re^4: Fast sliding submatrix sums with PDL (inspired by PWC 248 task 2)

by Anonymous Monk
on Dec 28, 2023 at 11:35 UTC ( [id://11156576]=note: print w/replies, xml ) Need Help??


in reply to Re^3: Fast sliding submatrix sums with PDL (inspired by PWC 248 task 2)
in thread Fast sliding submatrix sums with PDL (inspired by PWC 248 task 2)

Interesting. FFT for this task, who would have thought a few days ago. Looks like it runs in almost constant time, regardless of kernel size; and of course slower than special solutions. I had to add a couple of checks to accommodate for (unimportant) corner test case of submatrix with dims (4,3) and example matrix.

sub sms_WxH_PDL_fftconvolve ( $m, $w, $h ) { my ( $W, $H ) = $m-> dims; my $small = ones( $w%2?$w:$w+1, $h%2?$h:$h+1 ); $small-> slice( -1 ) .= 0 unless $w%2; # zero row and/or column + for even kernels $small-> slice( [],-1 ) .= 0 unless $h%2; my $result = $m-> copy; $result = append( $result, 0 ) if $W == $w and not $W % 2; $result = append( $result-> transpose, 0 )-> transpose if $H == $h and not $H % 2; my $kernel = kernctr( $result, $small ); #full kernel $result-> fftconvolve( $kernel ); $result = $result-> slice( '0:-2','' ) if $W == $w and not $W % 2; $result = $result-> slice( '','0:-2' ) if $H == $h and not $H % 2; return $result-> slice( [floor(($w-1)/2),floor(-($w+1)/2)], [floor(($h-1)/2),floor(-($h+1)/2)] ) } __END__ Time (s) vs. N (NxN submatrix, PDL: Double D [1500,1500] matrix) +-----------------------------------------------------------+ | + + + + + + + + | | A | | | | | 2 |-+ +-| | B B B B B | | BB B B B B B B | | B B B B B | | C C | | C C | 1.5 |-+ A C +-| | C | | C | | | | C | 1 |-+ C +-| | A | | C C | | | | | | C | 0.5 |-+ A +-| | C | | C | | A | | D D | | CC D D D D D D D D D D D D | 0 |-+ D +-| | + + + + + + + + | +-----------------------------------------------------------+ 0 200 400 600 800 1000 1200 1400 sms_WxH_PDL_conv2d A sms_WxH_PDL_fftconvolve B sms_WxH_PDL_lags C sms_WxH_PDL_sliding D +------+-------+-------+-------+-------+ | N | A | B | C | D | +------+-------+-------+-------+-------+ | 2 | 0.023 | 1.792 | 0.021 | | | 4 | 0.065 | 1.854 | 0.036 | | | 8 | 0.237 | 1.896 | 0.031 | | | 12 | 0.534 | 1.865 | 0.049 | | | 16 | 0.930 | 1.740 | 0.039 | | | 20 | 1.432 | 1.812 | 0.057 | | | 25 | 2.224 | 1.716 | 0.081 | 0.099 | | 100 | | 1.899 | 0.380 | 0.107 | | 200 | | 1.779 | 0.826 | 0.075 | | 300 | | 1.836 | 1.143 | 0.089 | | 400 | | 1.760 | 1.393 | 0.065 | | 500 | | 1.826 | 1.560 | 0.047 | | 600 | | 1.740 | 1.659 | 0.036 | | 700 | | 1.818 | 1.620 | 0.049 | | 800 | | 1.919 | 1.589 | 0.031 | | 900 | | 1.917 | 1.484 | 0.026 | | 1000 | | 1.789 | 1.260 | 0.008 | | 1100 | | 1.880 | 1.068 | 0.010 | | 1200 | | 1.745 | 0.823 | 0.010 | | 1300 | | 1.841 | 0.562 | 0.008 | | 1400 | | 1.841 | 0.273 | 0.003 | +------+-------+-------+-------+-------+
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