# Double integral over array

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steve solomon on 1 Feb 2020
Commented: steve solomon on 2 Feb 2020
Hi,
Evaluating a double integral over a large number of pixels takes an hour, even with the parallel toolbox. I can't figure out how to vectoirze this calculation to speed it up...suggestions welcome!
parfor iRow = 1:nRows
for iCol = 1:nCols
X = pitch_mm * (iRow - nRows/2 - 0.5);
Y = pitch_mm * (iCol - nCols/2 - 0.5);
% projected solid angle differential
dOmega = @(Xap,Yap) (apDist_mm ./ ((apDist_mm)^2 + (X-Xap).^2 + (Y-Yap).^2)).^2;
% convert to polar & integrate
dOmegaPolar = @(theta,r) dOmega(r.*cos(theta),r.*sin(theta)).*r;
cos4(iRow,iCol) = integral2(dOmegaPolar,0,2*pi,0,apDiam_mm/2);
end
end

David Hill on 1 Feb 2020
X=pitch_mm*([1:nRows]-nRows/2-.5);
Y=pitch_mm*([1:nCols]-nCols/2-.5);
dOmegaPolar = @(theta,r) dOmega(r.*cos(theta),r.*sin(theta)).*r;
dOmega = @(Xap,Yap) (apDist_mm ./ ((apDist_mm)^2 + (x-Xap).^2 + (y-Yap).^2)).^2;
cos4=zeros(nRows,nCols);%preallocate
parfor iRow = 1:nRows
x=X(iRow);
for iCol = 1:nCols
y=Y(iCol);
cos4(iRow,iCol) = integral2(dOmegaPolar,0,2*pi,0,apDiam_mm/2);
end
end
Above should speed things up some.
##### 2 CommentsShow 1 older commentHide 1 older comment
steve solomon on 2 Feb 2020
thanks David. That looks like it should be faster but it's not, about an hour of run time.

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