Efficient 3D element-wise operations in MATLAB - matlab

Question

Say i have two martrices:
A=50;
B=50;
C=1000;
X = rand(A,B);
Y = rand(A,B,C);
I want to subtract X from each slice C of Y. This is a fairly common problem and i have found three alternative solutions:
% Approach 1: for-loop
tic
Z1 = zeros(size(Y));
for i=1:C
Z1(:,:,i) = Y(:,:,i) - X;
end
toc
% Approach 2: repmat
tic
Z2 = Y - repmat(X,[1 1 C]);
toc
% Approach 3: bsxfun
tic
Z3=bsxfun(#minus,Y,X);
toc
I'm building a program which frequently (i.e., many thousands of times) solves problems like this, so i'm looking for the most efficient solution. Here is a common pattern of results:
Elapsed time is 0.013527 seconds.
Elapsed time is 0.004080 seconds.
Elapsed time is 0.006310 seconds.
The loop is clearly slower, and bsxfun is a little slower than repmat. I find the same pattern when i element-wise multiply (rather than subtract) X against slices of Y, though repmat and bsxfun are a little closer in multiplication.
Increasing the size of the data...
A=500;
B=500;
C=1000;
Elapsed time is 2.049753 seconds.
Elapsed time is 0.570809 seconds.
Elapsed time is 1.016121 seconds.
Here, repmat is the clear winner. I'm wondering if anyone in the SO community has a cool trick up their sleeves to speed this operation up at all.

Answer 1

Depending on your real case scenario, bsxfun and repmat will sometimes have some advantage over the other, just like #rayryeng suggested. There is one other option you can consider : mex. I hard coded some parameters for better performance here.
#include "mex.h"
#include "matrix.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
double *A, *B, *C;
int ind_1, ind_2, ind_3, ind_21, ind_32, ind_321, Dims[3] = {500,500,5000};
plhs[0] = mxCreateNumericArray(3, Dims, mxDOUBLE_CLASS, mxREAL);
A = mxGetPr(prhs[0]);
B = mxGetPr(prhs[1]);
C = mxGetPr(plhs[0]);
for ( int ind_3 = 0; ind_3 < 5000; ind_3++)
{
ind_32 = ind_3*250000;
for ( int ind_2 = 0; ind_2 < 500; ind_2++)
{
ind_21 = ind_2*500; // taken out of the innermost loop to save some calculation
ind_321 = ind_32 + ind_21;
for ( int ind_1 = 0 ; ind_1 < 500; ind_1++)
{
C[ind_1 + ind_321] = A[ind_1 + ind_321] - B[ind_1 + ind_21];
}
}
}
}
To use it, type this into command window ( assuming you name the above c file mexsubtract.c )
mex -WIN64 mexsubtract.c
Then you can use it like this:
Z4 = mexsubtract(Y,X);
Here are some test results on my computer using A=500, B=500, C=5000:
(repmat) Elapsed time is 3.441695 seconds.
(bsxfun) Elapsed time is 3.357830 seconds.
(cmex) Elapsed time is 3.391378 seconds.
It's a close contender and in some more extreme case, it'll have an edge. For example, this is what I got with A = 10, B = 500, C = 200000 :
(repmat) Elapsed time is 2.769177 seconds.
(bsxfun) Elapsed time is 3.178385 seconds.
(cmex) Elapsed time is 2.552115 seconds.