Why is my call to "bsxfun" slower than a similar call using "repmat" in MATLAB (R2014b)?

I was under the impression that 'repmat' is typically slower than 'bsxfun' .  However, I am comparing the two methods when performing the same computation using 'timeit'  and I find that 'bsxfun' is slower:

>> x = 2*pi*rand(500,1);
>> y = x;
>> f1 = @() angle(repmat(exp(1i*x),1,length(y)) ./ repmat(exp(1i*y'),length(x),1));
>> timeit(f1)
ans =
    0.0059
>> f2 = @() bsxfun(@(x,y)angle(x/y),exp(1i*x),exp(1i*y'));
>> timeit(f2)
ans =
    0.0209

Why is 'repmat' faster in this case, and how can I improve the performance of 'bsxfun'?

Answer 1

[MathWorks Support Team]

One contributing factor to the performance difference is the fact that the 'bsxfun' call is using an anonymous function handle rather than built-in functions. A second factor is that, as a result of the way the 'bsxfun' call is formulated, the 'angle' function is called many times, rather than being called once on a full matrix. By contrast, the 'repmat' version involves only one call to 'angle', which results in more efficient computation.

The performance of 'bsxfun' can be dramatically improved (and a more accurate comparison against 'repmat' can be made) by instead writing the 'bsxfun' call as:

>> angle(bsxfun(@rdivide,exp(1i*x),exp(1i*y')));

This formulation produces the same result, but has two advantages:

1. The binary function used by 'bsxfun' will no longer be an anonymous function, but instead the built-in 'rdivide'.
2. The 'angle' call now operates on the entire matrix of combinations rather than individual entries.

On the same machine that generating the timing numbers listed above, this formulation produces the following result:

>> f3 = @() angle(bsxfun(@rdivide,exp(1i*x),exp(1i*y')));
>> timeit(f3)
ans =
    0.0036

From the results, the 'bsxfun' version is now faster than the 'repmat' version as one might expect.