filling up an m X n X o size matrix without loops

Hi,

I am looking for an efficient way to 'fill up' a three-dimensional (m by n by o size) matrix M with elements based on a simple rule.

I have a number of matrices of size m X n X 1. I want the matrix M to contain weighted sums of these m X n X 1 size matrices. The weighted sums are obtained by the general formula

M(:,:,i) = f1(A, theta(i)) + f2(B, theta(i)) + f3(C, theta(i)) + ...

where f1, f2, f3, etc... are arbitrary functions and A, B, C, etc... are the m X n X 1 size matrices. theta is a 1 X o size vector containing angles (the functions f1, f2... are trigonometrical functions). The functions f1, f2... apply elementwise operations on A, B,... using a single value of theta, thus their outputs are also m X n X 1.

I can fill the matrix M up by looping through i=1:o and inserting the appropriate level M(:,:,i). However I feel that there must be a vectorized solution that works much faster.

I'd appreciate if you could give me ideas where to look for this functionality.

Thanks a lot,

Paul

[Azzi Abdelmalek]

what is the difference between nwmw1 and nxm?

theta is a 1x0 size? what does that mean?

Format your code http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

[Pal]

Azzi,

There is no difference between nXmX1 and nXm.

theta is 1 by 'o', not 1 by zero.

Answer 1

[Matt J]

I doubt that the loop over i is what's slowing you down. My bet is that it's the evaluation of f1(A,theta), f2(B,theta), etc.... However, one possibility to avoid the loop over i is as follows;

theta=reshape(theta,1,1,[]);

M = bsxfun(f1,A, theta) +  bsxfun(f2,B, theta) +  bsxfun(f2,C, theta)...

It still seems to me that you need a loop over f1,f2,f3, etc... but a vectorized solution to that will require knowledge of what those functions look like.

[Pal]

Thanks for your reply. The functions f1, f2... are all in the form

f1(A, theta) = A .* trig(theta)

where trig is a simple trigonometric function, like sin or cos. So they are basically elementwise multiplications of A by a single scalar. This is already vectorized by the .* operation.

The typical dimension of the matrices A, B,... is 1000 X 1000, while 'o' is around 50. Your solution is slower than the for loop for this size. It is faster though for smaller sizes, like 500 X 500 X 50.

[Matt J]

That will also depend greatly on the number of terms f1...fj that you have. In any case, BSXFUN is not my preferred solution. Now that we know the form of your f_i(), the more appropriate thing to do is,

theta=theta(:).'; %make sure it's a row vector

M=[A(:),B(:),C(:),...]*[trig1(theta); trig2(theta); trig3(theta);...];

M=reshape(M,m,n,[]);

[Pal]

That is about five times faster than the for loop. Brilliant!

Thank you very much.