Pagemtimes accuracy versus for loop

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.

Answer 1

[Matt J]

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

[Morten Nissov]

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.

[Matt J]

If the difference were greater than, say,

1000*eps(class(c1))

ans = 2.2204e-13

I might start to wonder what was going on.