Implicit casting overhead from real to complex when multiplying two matrices

2022 8 11
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更新时间：2023 7 10
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Is there an implicit casting overhead when multiplying a complex matrix by a real matrix to upcast the real matrix to complex or is it a natively-supported operation?
I have tried the following sample code but I get inconsistent results when changing the matrices dimension N.
N = 100;
A = rand(N);
B = rand(N);
C = complex(A);
tic
D1 = B*A;
toc
tic
D2 = B*C;
toc

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Benjamin Thompson
Benjamin Thompson 2022-8-11

0 个投票

Multiplying a complex matrix by a real matrix requires fewer calculations so should take less time. Your test is a little too simple since B would have already been cached into memory for the second part. If you do B*A twice, it is a lot faster the second time.

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Daniele Giovannini
Daniele Giovannini 2022-8-23
You are right. I have tried to eliminate the cache from playing a role in two ways:
  • having variables small enough to fit in the cache (my CPU cache is 3 MB) at the same time and repeating many times each matrix product
  • having variables so big that they cannot possibly be cached and perform each matrix product only once
Both ways seem to confirm your answer. I am reporting my test code for completeness.
% Test 1
N = 150;
C = crand(N);
A_R = rand(N);
A_C = complex(A_R);
whos
tic
for n = 1:1e4
D1 = C*A_R;
end
toc
tic
for n = 1:1e4
D2 = C*A_C;
end
toc
% Test 2
N = 3000;
C = crand(N);
A_R = rand(N);
A_C = complex(A_R);
whos
tic
D1 = C*A_R;
toc
tic
D2 = C*A_C;
toc

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更多回答（1 个）

James Tursa
James Tursa 2023-7-10

1 个投票

This is not a natively supported operation (to use your terms). Yes, the real matrix must be first upconverted to a complex matrix (deep data copy with interleaved 0's) in order to call the BLAS matrix multiply routines in the background, since the BLAS library has no mixed complex-real routines. This will be a performance hit because of the deep data copy and all those unnecessary 0 multiplies. See the related discussion and explanations here:
https://www.mathworks.com/matlabcentral/answers/1993193-complex-matrix-multiplication-with-pagemtimes?s_tid=srchtitle

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