Sparse and binary mask
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I am working on saving computations and speeding up my Matlab code. Here's what I do Perform thresholding on an image and make most of its components as zero run it inside a loop with element by element multiplication with another matrix(full matrix) of the same size
Here is a detailed version of what I am doing
CASE I:When I dont avoid multiplication with zeros
matrix(matrix<threshold) = 0 ;
while the condition is true
matrix = matrix.*phase;
other lines of code ;
end
Result: From MATLAB profiler I see that matrix = matrix.*phase; takes 80 seconds
CASE II:When I avoid multiplication with zeros using SPARSE
matrix(matrix<threshold) = 0 ;
matrix = sparse(matrix);
while the condition is true
matrix = matrix.*phase;
other lines of code ;
end
Result: From MATLAB profiler I see that matrix = matrix.*phase takes 110 seconds
CASE III:When I avoid multiplication with zeros using a mask
matrix(matrix<threshold) = 0 ;
mask = matrix~=0;
while the condition is true
matrix(mask) = matrix(mask).*phase(mask);
other lines of code ;
end
Result: From MATLAB profiler I see that matrix = matrix.*phase takes 130 seconds
Why is my code slow if I try to avoid multiplications with zeros? Since the matrix after thresholding has 75% zeros my speed should be up by 75% as I am avoiding multiplication with zeros. But my time is increased Is there any other way to achieve avoiding multiplication with zeros and speeding up of the code?
MY PRIORITY IS TO SPEED UP THE CODE EXECUTION AND SAVE MUTLIPLICATIONS
4 Commenti
James Tursa
il 14 Set 2018
What is the class of your image variable? Do you have a supported C compiler installed for a mex routine?
Risposta accettata
Bruno Luong
il 15 Set 2018
Modificato: Bruno Luong
il 15 Set 2018
Instead of matrix(mask) = matrix(mask).*phase(mask)
you might work on index
idx = find(mask & matrix~=0);
while ...
matrix(idx) = matrix(idx).*phase(idx);
end
You might want to compute phase(idx) outside the loop if they do not change, or update idx if the matrix elements become zero. As you don't give any detail, we have no idea if those are applicable for you.
If matrix does not share any copy, you might do element inplace replacement using MEX.
17 Commenti
Bruno Luong
il 20 Set 2018
Modificato: Bruno Luong
il 20 Set 2018
a = [ 0 0 3 0; 2 5 0 1; 0 0 0 3];
b = [ 4 3 2 1; 5 3 6 2; 7 1 -2 3];
idx = find(a)
[m,n] = size(a);
col = floor((idx-1)/m)+1;
sumcol = accumarray(col,a(idx).*b(idx)).'
% check
prod = a.*b;
sum(prod,1)
row = mod((idx-1),m)+1;
sumrow = accumarray(row,a(idx).*b(idx))
% check
sum(prod,2)
Più risposte (2)
James Tursa
il 15 Set 2018
Modificato: James Tursa
il 15 Set 2018
Try this simple C mex routine. It avoids the overhead you are creating with your sparse alternate stuff. Could maybe be improved further by multi-threading for large variables but it is currently not coded that way. (Caution, no input checking so it will crash MATLAB if not used properly)
/*
* File: times_threshold.c
*
* C = times_threshold(A,B,threshold) does
*
* C = A .* B but only where A > threshold (C = 0 in the other spots)
*
* A = full real double variable
* B = full real double variable (same size as A)
* C = full real double variable (same size as A)
* threshold = numeric scalar
*
* CAUTION: Bare bones with no argument checking! Will crash MATLAB if the
* inputs are not exactly as expected.
*/
#include "mex.h"
void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
double *Apr, *Bpr, *Cpr;
double threshold;
mwSize n;
n = mxGetNumberOfElements(prhs[0]);
plhs[0] = mxCreateNumericArray(mxGetNumberOfDimensions(prhs[0]),
mxGetDimensions(prhs[0]),
mxDOUBLE_CLASS, mxREAL);
Apr = mxGetPr(prhs[0]);
Bpr = mxGetPr(prhs[1]);
Cpr = mxGetPr(plhs[0]);
threshold = mxGetScalar(prhs[2]);
while( n-- ) {
if( *Apr > threshold ) {
*Cpr = *Apr * *Bpr;
}
Apr++; Bpr++; Cpr++;
}
}
8 Commenti
Walter Roberson
il 15 Set 2018
matrix<threshold and matrix~=0 both generate values the same size as matrix. matrix(mask) and phase(mask) and matrix(mask).*phase(mask) generate values with the same number of entries as the number of non-zero values in mask. Those variables get stored in memory and have to be processed.
At the MATLAB level, matrix = matrix.*phase gets dispatched to the high performance libraries that operate on multiple cores. One temporary value the same size as matrix would be involved to hold the results.
The high performance libraries would probably be scheduling multiple multiplies simultaneously, perhaps with SIMD type instructions, possibly able to graduate one result per cycle, or whatever the maximum graduation rate is.
When you select part of the array it has to be conditionally moved to other memory locations, and then that array processed, and then selectively moved back. That involves memory bandwidth and comparisons and loops. Those cost, and the tradeoffs are potentially just not worth the effort compared to SIMD or vector instructions.
You would face different tradeoffs in your FPGA.
To reduce multiplications, it might be worth creating an explicit loop, along the lines of
new_matrix = zeros(size(matrix));
for idx = 1 : numel(matrix)
M = matrix(idx); P = phase(idx);
if M && P; new_matrix(idx) = M .* P;
end
If phase is certain to be non-zero then
new_matrix = zeros(size(matrix));
for idx = 1 : numel(matrix)
M = matrix(idx);
if M; new_matrix(idx) = M .* phase(idx);
end
9 Commenti
Walter Roberson
il 15 Set 2018
new_matrix = zeros(size(matrix));
for idx = 1 : numel(matrix)
M = matrix(idx);
if M ~= 0; new_matrix(idx) = M .* phase(idx); end
end
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