CODEWITHSUNDEEP
matlabmatrix
Jawoe
Jawoe

Reputation: 31

Accuracy Matlab's slash matrix operators

Suppose we have these 3 matrices:

A=[1 3; 2 2];    B=[4 5; 1 3];     C=[0 2; 2 1]

Usually, I try to avoid using inv() or A^(-1) and try to use forward- and backslash operators instead. But if I want to calculate the following: 

A*B^(-1)*C

which way is the best:

A/B*C

or

A*(B\C)

Although both use the slash operators and no "explicit inverse" is being calculated, the result is a different and interestingly, A*(B\C) calculates the same as the one I'm trying to avoid, which is

A*inv(B)*C

as

isequal(A*(B\C),A*inv(B)*C)

shows. Can anyone explain what is happening here and which way I should go? Thanks!

Upvotes: 3

Views: 223

Answers (1)

MeMyselfAndI
MeMyselfAndI

Reputation: 1320

MATLAB has some serious strategy behind mldivide: see the Algorithm section of the documentation. I can image that it decides that inversing matrices of size 2×2 is the quickest way for solving and hence it calls inv and hence explicitely computes the inverse of B. For larger matrices, this is not the case and if I pick random matrices of size 4×4, executing the isequal-sentence returns false.

Anyway, the 'best' approach highly depends on your matrices A, B and C.

After some testing, I found that A*inv(B)*C always takes more time than A*(B\C), which means that it can also just be a machine-precision thing (see Dang Khoa's useful comment). Still, there is no single 'best' approach for mldivide versus mrdivide.

Upvotes: 0

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