Problem with the implementation of the quadruple sum

Question

Przemyslaw Gontar 2017-12-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/373131-problem-with-the-implementation-of-the-quadruple-sum

回答： Walter Roberson 2017-12-18

采纳的回答： Walter Roberson

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Hello, I'm trying write code for quadruple sum:

where x and y are matrix NxN. Output matrix also is NxN. I wrote something like that:

function v = RCPM(x,y,a,b,N,mi,V,n)
  m = n - 1;
  v = zeros(N,N);
  for i = 1:m
      disp(i);
      for j = 1:m
          for k = 1:m
              for l = 1:m
                  s = mi^((a(j) - a(k + 1))^2 + (b(i) - b(l+1))^2) ...
                      * cos(V * (x * (a(j) - a(k + 1)) + ...
                      y * (b(i) - b(l+1))));
                  v = v + s;
              end
          end
      end
  end
end

But looks like it don't work well. Could anyone have a look at whether I implemented the above formula well?

3 个评论
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Walter Roberson 2017-12-18

I see no reason to remove the function command. function is a good thing there.

Walter Roberson 2017-12-18

It is not obvious to me that the formula definitely intends algebraic matrix multiplication like you implemented by using the * operators. It seems plausible to me that element-by-element multiplication should be used instead -- but I cannot tell for sure either way.

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Answer 1

Walter Roberson 2017-12-18

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/373131-problem-with-the-implementation-of-the-quadruple-sum#answer_296711

You are iterating 1:m for each variable, which is m iterations each. However, your formula have 0 to M, which is M+1 iterations each. You define m as N-1 . It is not at all obvious that m = M+1, which would require that M = N-2

You code a(j) - a(k + 1) and b(i) - b(l+1), corresponding to alpha_lx - alpha_lx1 and beta_ly - beta_ly1 . Anyone reading this is going to assume that you got confused with the variable name lx1 as thinking that should be lx+1 but it is a completely different variable name. None of the subscripts should have +1 in them.

It is confusing that you have used i, j, k, l as the variable names controlling the loops and not ly, lx, lx1, ly1 (or Ly, Lx, Lx1, Ly1 for readability)

(a(lx)-a(lx1)) and (b(ly)-b(ly1)) occur twice in the expression, so it would probably make sense to compute them into separate variables.

For efficiency, pull expressions out of the inner loops. For example V * (x * (a(j) - a(k + 1)) does not need to be recalculated for each iteration of for l since it does not involve l