How to multiply matrix having different size (without knowing exactly the size they will have)?

Question

I have to multiply 2 matrices (scalar multiplication) that have different sizes. For instance, the 1st has size n-by-m and the 2nd n+1-by-m+1. The fact is that it is not always the case. I mean, sometimes the first has size n+1-by-m+1 and the 2nd n-by-m or n+2-by-m+2 etc...

Example:

a = [ 1 2 3; 
      4 5 6]; 

b = [ 1 2 3; 
      4 5 6; 
      7 8 9]

I would like Matlab to check the size of each matrix, then multiply them using the smallest size available between the 2 i.e. ignoring the last rows and columns of the bigger matrix (or similarly, adding rows and columns of 0 to the smaller matrix).

With the example inputs I would like to obtain:

c = [1  4  9; 
     16 25 36] 

or

c = [1  4  9; 
     16 25 36; 
     0  0  0]

How can I write this?

Answer 1

Find the number of rows and columns of your final matrix:

n = min(size(a,1), size(b,1));
m = min(size(a,2), size(b,2));

Then extract only the relevant sections of a and b (using the : operator) for your multiplication:

c = a(1:n,1:m).*b(1:n,1:m)

Answer 2

If you only consider dot product, it means that size(a) must equal size(b), which allows to simply restrain the size of b, you can use a simple if statement if you like. For example:

if all(size(b) == size(a))
   answer = a.*b
else 
   minsize(:,1) = min(size(a,1),size(b,1));
   minsize(:,2) = min(size(a,2),size(b,2));
   answer = a(1:minsize(:,1),1:minsize(:,2)).*a(1:minsize(:,1),1:minsize(:,2));
end

I don't think this is easiest way to do it, but it is simple to understand :)

Answer 3

I am not always sure which one of the matrix is bigger, then I thought to use:

if size (a) > size (b)
   a = a(1:size(b,1),1:size(b,2));
elseif size (a) < size (b)
   b = b (1: size (a,1),1:size(a,2));
end

It seems to work like this.