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Can I calculate the inverse of a matrix using arrayfun?
조회 수: 2 (최근 30일)
이전 댓글 표시
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
댓글 수: 1
채택된 답변
Walter Roberson
2021년 6월 25일
편집: Walter Roberson
2021년 6월 25일
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.
댓글 수: 8
Walter Roberson
2021년 6월 25일
A = sprand(20,20, .01)
A =
(5,2) 0.2696
(4,4) 0.9628
(9,5) 0.0991
(18,17) 0.8745
tic
invA = cell2mat(arrayfun(@(C) A\sparse(C,1,1,size(A,1),1), 1:size(A,2), 'uniform', 0))
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
invA =
(1,1) NaN
(3,1) NaN
(6,1) NaN
(7,1) NaN
(8,1) NaN
(9,1) NaN
(10,1) NaN
(11,1) NaN
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toc
Elapsed time is 0.115353 seconds.
tic
invA = A\speye(size(A))
Warning: Matrix is singular to working precision.
invA =
(1,1) NaN
(3,1) NaN
(6,1) NaN
(7,1) NaN
(8,1) NaN
(9,1) NaN
(10,1) NaN
(11,1) NaN
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toc
Elapsed time is 0.018112 seconds.
Benson Gou
2021년 6월 25일
Hi, Walter,
Thanks for your help.
I compared your code and my original code. Your code took 3.7 sceonds while mine took 1.27 seconds.
I am wondering if there exists a faster code than my original code.
Thanks a lot, anyway.
Benso
Walter Roberson
2021년 6월 25일
Well, you could try matrix decomposition, https://www.mathworks.com/help/matlab/ref/decomposition.html
Benson Gou
2021년 6월 25일
Hi, Walter,
Yes, decomposition is a good way to solve linear systems. But I need the inverse of the matrix for other calculations, not just solve the linear system.
Thanks a lot.
Benson
Walter Roberson
2021년 6월 25일
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
2021년 6월 29일
Hi, Walter,
I do not have the Image Processing Toolbox. So I cannot run decompose(A).
But the goal that I want to obtain the inverse of A is becaus I need to find out the nonzero elements in invA. So I do not know if decompose(A) is able to be useful for my case.
Thanks a lot.
Benson
추가 답변 (1개)
Sulaymon Eshkabilov
2021년 6월 25일
편집: Sulaymon Eshkabilov
2021년 6월 25일
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.
댓글 수: 4
Walter Roberson
2021년 6월 25일
A = sprand(20,20, .01)
A =
(16,5) 0.5706
(10,12) 0.5464
(12,16) 0.7549
(4,17) 0.6957
iA = arrayfun(@inv, full(A))
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
Warning: Matrix is singular to working precision.
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iA = 20×20
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.4373 Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.8301 Inf Inf Inf Inf Inf Inf Inf Inf
iA2 = 1./A
iA2 = 20×20
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.4373 Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf
Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf 1.8301 Inf Inf Inf Inf Inf Inf Inf Inf
Benson Gou
2021년 6월 29일
Hi, Walter,
Yes, the decomposition is faster than \ operator. Thanks a lot.
Benson
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