How to speed this up - large variable

Question

Alex Kurek 2016-7-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/296682-how-to-speed-this-up-large-variable

回答： Walter Roberson 2016-7-22

Hello,

Is there a way to speed this up? This if within a function and i can use codegen - and I do. But I need to speed this up more. I think the problem is that one variable is huge and the access to it takes long? What should be done in such a case?

xElements = 1201;
maxN = 100;
umnHolder = complex(zeros(maxN + 1, maxN + 1));
betaSumSq1 = zeros(xElements, xElements); % preallocate
besselsFisher = zeros(1201, 1201, 101); % just to show the size     LARGE, ~780 MB
XY = zeros(xElements, xElements);       % just to show the size
acosContainer = XY;                     % just to show the size
parfor i = 1 : xElements
    for j = 1 : xElements
        umn = umnHolder;
        for n = 0:maxN
            mm = 1;
            for m = -n:2:n
                nn = n + 1; % for indexing
                  if m > 0
                      umn(nn, mm) = sqrt(n+1) * XY(i, j) * besselsFisher(i, j, nn) * cos( abs(m)*acosContainer(i, j) );
                  end
                  if m < 0
                      umn(nn, mm) = sqrt(n+1) * XY(i, j) * besselsFisher(i, j, nn) * sin( abs(m)*sign(x(i))*acosContainer(i, j) );
                  end
                  if m == 0
                      umn(nn, mm) = sqrt(n+1) * XY(i, j) * besselsFisher(i, j, nn);
                  end  
                  mm = mm + 1;
              end % m
          end % n
          beta1 = sum(sum(Aj1.*umn));
          betaSumSq1(i, j) = abs(beta1).^2;
          beta2 = sum(sum(Aj2.*umn));
          betaSumSq2(i, j) = abs(beta2).^2;
      end % j
  end % i

Best regards, Alex

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Thorsten 2016-7-22

编辑：Thorsten 2016-7-22

The first step before optimising would be to identify where most of the time is spent using profile.

Alex Kurek 2016-7-22

在 MATLAB Online 中打开

Most of the time is spent here:

 umn(nn, mm) = sqrt(n+1) * XY(i, j) * besselsFisher(i, j, nn) * cos( abs(m)*acosContainer(i, j) );
 umn(nn, mm) = sqrt(n+1) * XY(i, j) * besselsFisher(i, j, nn) * sin( abs(m)*sign(x(i))*acosContainer(i, j) );

This makes sense, since if you multiply

besselsFisher = zeros(1201, 1201, 101);

by e.g. 2 it takes ~1.6 seconds.

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Answer 1

Walter Roberson 2016-7-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/296682-how-to-speed-this-up-large-variable#answer_229502

You should factor out common sub-expressions. acosContainer(i, j) is the same for all m and n so assign it to a variable outside the m loop. Taking abs(m) is a waste of time when you know that m > 0 . sign(x(1)) is the same for all j, m, n so assign it to a variable. Multiplying by sign(x(1)) is done for the vector -n to -1 so you can vectorize to precalculate, sin((-n : 2 : -1) .* sign(x(1)) .* acosContainer(i, j)); you can probably vectorize the rest of that case as well.

All of the cases for any one n are multiplied by sqrt(n+1) so hold off on that multiplication until you have done the entire set of m values, and then multiply them all by sqrt(n+1) to get economy of scale.

And so on.