Double sum with upper limits

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H Lange 2020-3-2

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https://ww2.mathworks.cn/matlabcentral/answers/508491-double-sum-with-upper-limits

评论： Luna 2020-3-3

采纳的回答： Guillaume

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 :)

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darova 2020-3-2

Luna 2020-3-2

编辑：Luna 2020-3-2

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

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Guillaume 2020-3-2

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编辑：Guillaume 2020-3-2

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

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

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Guillaume 2020-3-2

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 2020-3-3

You are right.

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Luna 2020-3-2

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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