Pagemtimes accuracy versus for loop

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Morten Nissov 2021-5-5

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https://ww2.mathworks.cn/matlabcentral/answers/822425-pagemtimes-accuracy-versus-for-loop

编辑： Matt J 2021-5-5

I was using pagemtimes for some calculations an I get results which are not quite what I expect, for example

N = 1e3;
a = randn(3, 3, N);
b = randn(2, 3);
c1 = zeros(2, 2, N);
for i=1:N
	c1(:,:,i) = b * a(:,:,i) * b';
end
c2 = pagemtimes(pagemtimes(b, a), b');
c3 = pagemtimes(b, pagemtimes(a, b'));
isequal(c1,c2)
isequal(c1,c3)

returns a logical no for both isequal queries.

I assume this is due to numerical deviations? Or is there something non-equivalent between the different fomulations of the "c" matrix.

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Answer 1

Matt J 2021-5-5

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/822425-pagemtimes-accuracy-versus-for-loop#answer_692890

编辑：Matt J 2021-5-5

在 MATLAB Online 中打开

I assume this is due to numerical deviations?

Yes, there is no expectation that both approaches will produce the same floating point noise. Clearly the percent errors are very small, though:

N = 1e3;
a = randn(3, 3, N);
b = randn(2, 3);
c1 = zeros(2, 2, N);
for i=1:N
	c1(:,:,i) = b * a(:,:,i) * b';
end
c2 = pagemtimes(pagemtimes(b, a), b');
c3 = pagemtimes(b, pagemtimes(a, b'));
%Percent errors
relError=@(a,b)norm(a(:)-b(:),inf)/norm(b(:),inf)*100;
relError(c1,c2)
ans = 2.1378e-14
relError(c1,c3)
ans = 2.1378e-14

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Morten Nissov 2021-5-5

Okay sounds good, is there any metric for how small these deviations should be? Like for example differences in 1e-10 indicate different matrices but 1e-12 or less is likely numerical noise.