2D summation loop

How do I create this in MATLAB?

[James Tursa]

What have you done so far? What specific problems are you having with your code? Do you know how to write a for-loop, or use the sum( ) function, or use the diff( ) function, or use the .* operator?

[John Allen]

Yes, I know all of those, just never did it like this, so totally confused how to structure this one.

Answer 1

[James Tursa]

Take the denominator for instance. Literally written out, this would be

denominator = 0;
for k=1:K
    denominator = denominator + B(k,j)^2;
end

Or, assuming the first dimension of B is K, then you could use the sum( ) function:

denominator = sum(B(:,j).^2);

You can construct similar code for the numerator.

Probably best if you code everything up using for-loops just to get something running that works. Then you can simplify things with the sum( ) and diff( ) functions. It is possible to do the entire operation to construct ds without loops.

[John Allen]

In my application, it is NMF based operation, so the matrix is K x T and I have J components, let's say 20 of them, and then after I apply NMF, I will get B = K x J and G = J x T.

This summation happens after I get B. So, wouldn't I need a nested 2d loop to go over both K and J ?

I understand your code, but I am trying to understand this in my head.

[James Tursa]

"So, wouldn't I need a nested 2d loop to go over both K and J ?"

Yes. The code I had written above was only for the denominator part of the j'th element of ds.

I would still suggest you write out the looping code first to get some correct code running. Then you can worry about simplifying it using sum( ) and diff( ) etc.

[John Allen]

OK, thank you very much, I think I get it now, I marked answer as accepted.

Thanks again! :)

[James Tursa]

If you have trouble, don't hesitate to post your current code and the problems you are having and we can still help you.