Why stock DOT function is suboptimally implemented

Followup the discussion in

https://www.mathworks.com/matlabcentral/answers/612051-calculation-precision-changed-in-2020b

and

https://www.mathworks.com/matlabcentral/answers/618088-column-operator-erases-complex-property

and do so tic/toc and I think the option selected by TMW (R2020b) is suboptimal in term of speed for complex data as show as this benchmark that one can speed up almost 10 times (!):

z=randn(1,1e7)+1i*randn(1,1e7);

tic
p1=dot(z,z);
toc % Elapsed time is 0.162930 seconds.

tic
p2 = sum(conj(z).*z);
toc % Elapsed time is 0.092252 seconds.

tic 
p3=z(:)'*z(:); % (:) copy data ?
toc % Elapsed time is 0.100122 seconds.

tic
zc=z(:); % (:) copy data ?
p4=zc'*zc;
toc % Elapsed time is 0.053257 seconds.

tic 
zr=reshape(z,[],1); % reshape does not?
p5=zr'*zr;
toc % Elapsed time is 0.016140 seconds.

Any comment would be welcome.

Just to have a formal question: what is the reason of TMW choice?

[Bruno Luong]

Update: results with R2021a

Elapsed time is 0.167038 seconds. % p1=dot(z,z)
Elapsed time is 0.088275 seconds. % p2 = sum(conj(z).*z)
Elapsed time is 0.114969 seconds. % p3=z(:)'*z(:)
Elapsed time is 0.051793 seconds. % zc=z(:); p4=zc'*zc
Elapsed time is 0.007295 seconds. % zr=reshape(z,[],1); p5=zr'*zr

[Jan]

Wow, 0.007 is fast.

Answer 1

[Jan]

Just a comment: Under Matlab 2018b, Core i5-3320M CPU @ 2.60GHz:

Elapsed time is 0.249669 seconds.   dot(z,z)
Elapsed time is 0.168906 seconds.   sum(conj(z).*z)
Elapsed time is 0.204284 seconds.   z(:)'*z(:)
Elapsed time is 0.114597 seconds.   zc=z(:); p4=zc'*zc
Elapsed time is 0.018371 seconds.   zr=reshape(z,[],1); p5=zr'*zr

When I copy the code into a function and repeat the calls 5 times in a FOR loop:

Elapsed time is 0.865391 seconds.
Elapsed time is 0.844665 seconds.
Elapsed time is 1.021389 seconds.
Elapsed time is 0.484573 seconds.
Elapsed time is 0.047871 seconds.

Answer 2

[Jan]

In dot.m we find a test for integer types, checks by isvector, comparison of lengths, both vectors are shaped by (:) and after a test with isreal(), either a'*b or sum(conj(a).*b) is called.

Your measurement

% Elapsed time is 0.167038 seconds.  % p1 = dot(z,z)
% Elapsed time is 0.088275 seconds.  % p2 = sum(conj(z).*z)

means, that the tests are expensive and the two (:) operations also, because they create deep data copies in modern Matlab versions for complex data:

a = rand(1,100) + 1i * rand(1,100);
ShowDataPointer(a)

pr = 7fe94d7f3d20

b = a(:);
ShowDataPointer(b)

pr = 7fe94d36e5e0

function ShowDataPointer(x)
orig = format('debug');
s = formattedDisplayText(x);
c = strtrim(strsplit(s, '\n'));
disp(c(startsWith(c, 'pr')));
format(orig);
end

With real values only, the data are shared. (For other readers. I'm aware, that you, Bruno, know this.)

My conclusion: dot.m is not efficiently implemented. Why? For future improvements.

I do not see a reason, why (:) creates a deep data copy, so I'd consider this as a bug. Did you ask MathWorks already for an explanation?

By the way, Matlab's cross() could be 10 times faster when implemented as MEX function.