# Pagemtimes accuracy versus for loop

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Morten Nissov on 5 May 2021
Edited: Matt J on 5 May 2021
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.

Matt J on 5 May 2021
Edited: Matt J on 5 May 2021
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
##### 2 CommentsShowHide 1 older comment
Matt J on 5 May 2021
If the difference were greater than, say,
1000*eps(class(c1))
ans = 2.2204e-13
I might start to wonder what was going on.

R2020b

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