how can i sum over to variable in matlab?

Hi, i have a function as below in a for loop:

for i=1:20

end;

i'm trying to sum over variables N,N', as simple as it looks, it confused me? can any one help?

thanyou so much in advance

[Stephen23]

@Joseph: What are F, N, N', G, and K ? Arrays, functions, symbolic variables , ... ?

[Joseph]

F, G and K are functions (which are called Wigner 3j symbols), and N and N' are array of numbers from 1 to 20.

[Stephen23]

@Joseph: and what have you written so far?

[Guillaume]

And can these function operate on matrices, or do they only accept scalars?

Answer 1

[Jorge Mario Guerra González]

you mean something like this....

I'm supposing F,K,G are random arrays,

are N and N' independent values??? because the notation N, N' is a little tricky for me.

F=rand(20,20);
G=rand(1,20);
K=rand(1,20);
suma=0;
for i=1:20
  for j=1:20
      suma=suma+F(i,j)*G(i)*K(j);
  end
end
disp(suma);
%where i and j are your N and N'

[Guillaume]

Never ever call a variable sum, since it prevents you from using the sum function. In particular, in your example, you could get rid of the loop and use that sum function to obtain the same result in just one line:

result = sum(sum(F .* G .* K.'));  %R2016b only
%in versions < R2016b
%result = sum(sum(F .* bsxfun(@times, G, K.')));

However, I don't believe that's what the OP is asking.

[Joseph]

F,G and K are not random arrays, they are some type of functions of (N,N'). and N=N'-1, and N'=(1:20)

[Jorge Mario Guerra González]

@Guillaume sorry, that's true I wrote it as a fast script, I edit it rigth away.

[Jorge Mario Guerra González]

@Joseph you should've specified that N=N'-1 in the question. So, since N=N'-1 the range of N is 0:19?. why does the equation you posted say N=1:20.

[Joseph]

i apologize. corrected it.

Answer 2

[Guillaume]

Without any a priori knowledge of F, G, K, this is guaranteed to work:

[NN1, NN2] = ndgrid(0:19, 1:20);  %all combinations of N and N'
FN = arrayfun(@F, NN1, NN2);
GN = arrayfun(@G, NN1);
KN = arrayfun(@K, NN2);
result = sum(sum(FN .* GN .* KN));  %or sum(FN(:) .* GN(:) .* KN(:)) which is probably faster but more cryptic.

If the F, G, K functions support implicit expansion or can work directly with vectors and matrices then the arrayfun lines would not even be needed.