Double sum with upper limits

Hi

I am trying to do the following calululation in matlab:

But I do not how how to do the two sums in the front. Our data (d) is a 67x120 array.

Any suggestions would be appreciated :)

[darova]

[Luna]

What have you done so far as coding? And what is d?

Answer 1

[Guillaume]

s = (1:size(d, 1)).';
result = sum(sum(d .* cos(s))) / sum(cos(s));

Loops not needed, they're just a waste of time.

[Luna]

My understanding of /Sigma[cos(s)] part, it should be divided into sum of cos(s) from 1 to what s is until that iteration. For example if s is 20 while j = 3;

d(20,3)*cos(20) / ( cos(1)+cos(2)+...+cos(20) )

so your result gives a vector (1x67). I assume that result must be a scalar.

[Guillaume]

Yes, I made a mistake, there was a sum missing in the denominator. I assumed that the could be taken out of the double sum, i.e. it's over the whole range. It's not clear and we didn't get an answer to Darova's question. So, my code implement:

If it's a partial sum as you think, then:

s = (1:size(d, 1)).';
result = sum(sum(d .* cos(s) ./ cumsum(cos(s))));

which implements

[Luna]

You are right.

Answer 2

[Luna]

Maybe something like that would help:

d = rand(67,120);
sum_of_cos_s = 0;
result = 0;

for s = 1:67 
    for j = 1:120
       sum_of_cos_s = sum_of_cos_s+cos(s);
       result = result + (d(s,j)*cos(s))/sum_of_cos_s;        
    end
end