for or while loops in matlab

Question

I've just started using for loops in matlab in programming class and the basic stuff is doing me fine, However I've been asked to "Use loops to create a 3 x 5 matrix in which the value of each element is its row number to the power of its column number divided by the sum of its row number and column number for example the value of element (2,3) is (2^3 / 2+3) = 1.6

So what sort of looping do I need to use to enable me to start new lines to form a matrix?

Answer 1

The command bsxfun is very helpful for such problems. It will do all the looping and preallocation for you.

eg:

bsxfun(@(x,y) x.^y./(x+y), (1:3)', 1:5)

Answer 2

Since you need to know the row and column numbers (and only because you have to use loops), for-loops are a natural choice. This is because a for-loop will automatically keep track of your row and column number for you if you set it up right. More specifically, you want a nested for loop, i.e. one for loop within another. The outer loop might loop through the rows and the inner loop through the columns for example.

As for starting new lines in a matrix, this is extremely bad practice to do in a loop. You should rather pre-allocate your matrix. This will have a major performance impact on your code. Pre-allocation is most commonly done using the zeros function.

e.g.

num_rows = 3;
num_cols = 5;
M = zeros(num_rows,num_cols); %// Preallocation of memory so you don't grow your matrix in your loop
for row = 1:num_rows
    for col = 1:num_cols
        M(row,col) = (row^col)/(row+col);
    end
end

But the most efficient way to do it is probably not to use loops at all but do it in one shot using ndgrid:

[R, C] =  ndgrid(1:num_rows, 1:num_cols);
M = (R.^C)./(R+C);