Optimization of nested "for" loops

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Olaf Popczyk
Olaf Popczyk 2021-5-3
编辑： Matt J 2021-5-3
Hi.
I would like to optimize my code. I examined it and found a serious bottle neck. Below is the chunk of code with nested "for" loops which in my opinion are very inefficient.
PHI = zeros(length(X),length(X));
PHI_X = zeros(length(X),length(X));
PHI_XX = zeros(length(X),length(X));
PHI_Y = zeros(length(X),length(X));
PHI_YY = zeros(length(X),length(X));
for i=1:length(X)
for j=1:length(Y)
x = X(i)-X(j);
y = Y(i)-Y(j);
PHI (i,j) = (x^2 + y^2 + e^2) ^ p;
PHI_X (i,j) = 2 * p * x * (x^2 + y^2 + e^2) ^ (p-1);
PHI_Y (i,j) = 2 * p * y * (x^2 + y^2 + e^2) ^ (p-1);
PHI_XX (i,j) = 2 * p * ((2*p-1)*x^2 + e^2) * (x^2 + y^2 + e^2) ^ (p-2);
PHI_YY (i,j) = 2 * p * ((2*p-1)*y^2 + e^2) * (x^2 + y^2 + e^2) ^ (p-2);
end
end
X and Y are vectors while e and p are real-valued coefficients. This part of the code is very important because it is executed even several hundred times (for different values of e and p) during one code execution. I would like to optimize it somehow but I don't know how because I'm quite a new user of MATLAB.
Kind regards

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采纳的回答

DGM
DGM 2021-5-3
Should be able to do something like this without the loop (don't need to preallocate either):
x = X'-X;
y = Y'-Y;
PHI = (x.^2 + y.^2 + e^2) .^ p;
PHI_X = 2 * p * x .* (x.^2 + y.^2 + e^2) .^ (p-1);
PHI_Y = 2 * p * y .* (x.^2 + y.^2 + e^2) .^ (p-1);
PHI_XX = 2 * p * ((2*p-1)*x.^2 + e^2) .* (x.^2 + y.^2 + e^2) .^ (p-2);
PHI_YY = 2 * p * ((2*p-1)*y.^2 + e^2) .* (x.^2 + y.^2 + e^2) .^ (p-2);
Those first couple lines will only work in R2016b or later, otherwise, you'd need to do:
x = bsxfun(@minus,X,X');
etc

更多回答（1 个）

Matt J
Matt J 2021-5-3
编辑：Matt J 2021-5-3
Replace the loop with,
x=X(:)-X(:).';
y=Y(:)-Y(:).';
xsq=x.^2;
ysq=y.^2;
xysq= xsq+ysq;
tmp1=xysq + e^2;
PHI = tmp1 .^ p;
tmp2=tmp1 .^ (p-1);
PHI_X = 2 * p * x .*tmp2;
PHI_Y = 2 * p * y .*tmp2;
clear tmp2
tmp3=tmp1 .^ (p-2);
PHI_XX = (2*p*(2*p-1)*xsq + 2*p*e^2) .* tmp3;
PHI_YY = (2*p*(2*p-1)*ysq + 2*p*e^2) .* tmp3;

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