Can I calculate the inverse of a matrix using arrayfun?
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Dear All,
I have a sparse matrix A. I want to calculate its inverse. I used the following way to calculate invA.
invA = A \ speye(size(A));
My matrix size is 3000 by 3000. I found it took me 1.3 seconds to get invA. It is longer than I expected.
I am wondering if I could use arrayfun to calculate invA. The idea is to calculate each column in invA by invA(:,i) = A \ ei, where ei is a zero column vector except its ith element is 1.0.
I tried the following code to implement the above idea:
invA = arrayfun(@(x) A\x ,speye(size(A,1)));
But I got error message.
Thanks a lot.
Benson
1 Comment
Matt J
on 25 Jun 2021
I don't see how arrayfun could help, unless this is on the GPU.
Accepted Answer
Walter Roberson
on 25 Jun 2021
Edited: Walter Roberson
on 25 Jun 2021
invA = cell2mat(arrayfun(@(C) A\sparse(C,1,1,size(A,1),1), 1:size(A,2), 'uniform', 0))
I would be surprised if it is faster.
8 Comments
A = sprand(20,20, .01)
tic
invA = cell2mat(arrayfun(@(C) A\sparse(C,1,1,size(A,1),1), 1:size(A,2), 'uniform', 0))
toc
tic
invA = A\speye(size(A))
toc
Walter Roberson
on 25 Jun 2021
Much slower!
Benson Gou
on 25 Jun 2021
Walter Roberson
on 25 Jun 2021
Well, you could try matrix decomposition, https://www.mathworks.com/help/matlab/ref/decomposition.html
Benson Gou
on 25 Jun 2021
Walter Roberson
on 25 Jun 2021
You decompose the matrix. Then you use the decomposition on the left side of \ with speye() on the right hand side.
Most of the time you should not be using the inverse in calculations, and should instead be using the \ operator . inv(A)*b + inv(A)*c --> dA = decompose(A), dA\b +dA\c
Benson Gou
on 29 Jun 2021
Walter Roberson
on 29 Jun 2021
decomposition()
More Answers (1)
Sulaymon Eshkabilov
on 25 Jun 2021
Edited: Sulaymon Eshkabilov
on 25 Jun 2021
In fact, you can employ arrayfun for the matric inverse calc, e.g.:
tic;
iA =arrayfun(@inv,A);
toc;
Note that arrayfun is not the best option and does not take the sparse matrix.
Just direct inv() is the fastest so far.
In fact, for solving linear systems, to compute the inverse is not advised.
4 Comments
Walter Roberson
on 25 Jun 2021
iA =arrayfun(@inv,A);
That code would be the equivalent of
iA = 1./A
A = sprand(20,20, .01)
iA = arrayfun(@inv, full(A))
iA2 = 1./A
Walter Roberson
on 25 Jun 2021
By the way, you cannot apply arrayfun() directly to a sparse matrix.
Benson Gou
on 29 Jun 2021
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