What is the fastest way of doing this computation in MATLAB?

Question

I'm using the profiler on my MATLAB code, and the following line is taking 50% of the code's computation time:

firstSide = -1*HessianInverse*(eye(n,n)- ...
currentA'(currentA*HessianInverse*currentA')^-1*currentA*HessianInverse)*currentG;

HessianInverse is an n x n matrix
currentG is an n x n matrix
currentA is an n x n matrix as well

What would be the fastest way of doing this computation?

Use `inv` rather than `^-1`. Also should `currentA'(currentA*Hes...` have a `*` or something? — David, Mar 26 '14 at 02:41
Shouldn't `currentA'*(currentA*HessianInverse*currentA)^-1*currentA*HessianInverse=eye(n,n)`? In which case this equation should be zero? — David, Mar 26 '14 at 03:11
If it's resolved, post your answer and accept it, don't wipe out the contents of your question. — LittleBobbyTables - Au Revoir, Apr 29 '14 at 13:34

score 2 · Answer 1 · answered Mar 26 '14 at 02:56

You can do two simple things:

Compute currentA*HessianInverse once and store the result, since your are using the same matrix multiplication in two different places.
Replace ^-1 with the \ operator, since the latter is about twice as fast:

For example

>> A = rand(1000);
>> B = rand(1000);

>> tic; A^-1*B; toc
Elapsed time is 0.592531 seconds.
>> tic; A^-1*B; toc
Elapsed time is 0.578318 seconds.

>> tic; A\B; toc
Elapsed time is 0.275542 seconds.
>> tic; A\B; toc
Elapsed time is 0.262008 seconds.

What is the fastest way of doing this computation in MATLAB?

1 Answers1