I don't see how arrayfun could help, unless this is on the GPU.
Can I calculate the inverse of a matrix using arrayfun?
1 次查看（过去 30 天）
显示 更早的评论
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 个评论
采纳的回答
Walter Roberson
2021-6-25
编辑：Walter Roberson
2021-6-25
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 个评论
Walter Roberson
2021-6-25
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
(12,1) NaN
(13,1) NaN
(14,1) NaN
(15,1) NaN
(16,1) NaN
(18,1) NaN
(19,1) NaN
(20,1) Inf
(1,2) NaN
(3,2) NaN
(6,2) NaN
(7,2) NaN
(8,2) NaN
(9,2) NaN
(10,2) NaN
(11,2) NaN
(12,2) NaN
(13,2) NaN
(14,2) NaN
(15,2) NaN
(16,2) NaN
(18,2) NaN
(19,2) Inf
(20,2) NaN
(1,3) NaN
(3,3) NaN
(6,3) NaN
(7,3) NaN
(8,3) NaN
(9,3) NaN
(10,3) NaN
(11,3) NaN
(12,3) NaN
(13,3) NaN
(14,3) NaN
(15,3) NaN
(16,3) NaN
(18,3) Inf
(19,3) NaN
(20,3) NaN
(1,4) NaN
(3,4) NaN
(4,4) 1.0387
(6,4) NaN
(7,4) NaN
(8,4) NaN
(9,4) NaN
(10,4) NaN
(11,4) NaN
(12,4) NaN
(13,4) NaN
(14,4) NaN
(15,4) NaN
(16,4) NaN
(18,4) NaN
(19,4) NaN
(20,4) NaN
(1,5) NaN
(2,5) 3.7094
(3,5) NaN
(6,5) NaN
(7,5) NaN
(8,5) NaN
(9,5) NaN
(10,5) NaN
(11,5) NaN
(12,5) NaN
(13,5) NaN
(14,5) NaN
(15,5) NaN
(16,5) NaN
(18,5) NaN
(19,5) NaN
(20,5) NaN
(1,6) NaN
(3,6) NaN
(6,6) NaN
(7,6) NaN
(8,6) NaN
(9,6) NaN
(10,6) NaN
(11,6) NaN
(12,6) NaN
(13,6) NaN
(14,6) NaN
(15,6) NaN
(16,6) Inf
(18,6) NaN
(19,6) NaN
(20,6) NaN
(1,7) NaN
(3,7) NaN
(6,7) NaN
(7,7) NaN
(8,7) NaN
(9,7) NaN
(10,7) NaN
(11,7) NaN
(12,7) NaN
(13,7) NaN
(14,7) NaN
(15,7) Inf
(16,7) NaN
(18,7) NaN
(19,7) NaN
(20,7) NaN
(1,8) NaN
(3,8) NaN
(6,8) NaN
(7,8) NaN
(8,8) NaN
(9,8) NaN
(10,8) NaN
(11,8) NaN
(12,8) NaN
(13,8) NaN
(14,8) Inf
(15,8) NaN
(16,8) NaN
(18,8) NaN
(19,8) NaN
(20,8) NaN
(1,9) NaN
(3,9) NaN
(5,9) 10.0885
(6,9) NaN
(7,9) NaN
(8,9) NaN
(9,9) NaN
(10,9) NaN
(11,9) NaN
(12,9) NaN
(13,9) NaN
(14,9) NaN
(15,9) NaN
(16,9) NaN
(18,9) NaN
(19,9) NaN
(20,9) NaN
(1,10) NaN
(3,10) NaN
(6,10) NaN
(7,10) NaN
(8,10) NaN
(9,10) NaN
(10,10) NaN
(11,10) NaN
(12,10) NaN
(13,10) Inf
(14,10) NaN
(15,10) NaN
(16,10) NaN
(18,10) NaN
(19,10) NaN
(20,10) NaN
(1,11) NaN
(3,11) NaN
(6,11) NaN
(7,11) NaN
(8,11) NaN
(9,11) NaN
(10,11) NaN
(11,11) NaN
(12,11) Inf
(13,11) NaN
(14,11) NaN
(15,11) NaN
(16,11) NaN
(18,11) NaN
(19,11) NaN
(20,11) NaN
(1,12) NaN
(3,12) NaN
(6,12) NaN
(7,12) NaN
(8,12) NaN
(9,12) NaN
(10,12) NaN
(11,12) Inf
(12,12) NaN
(13,12) NaN
(14,12) NaN
(15,12) NaN
(16,12) NaN
(18,12) NaN
(19,12) NaN
(20,12) NaN
(1,13) NaN
(3,13) NaN
(6,13) NaN
(7,13) NaN
(8,13) NaN
(9,13) NaN
(10,13) Inf
(11,13) NaN
(12,13) NaN
(13,13) NaN
(14,13) NaN
(15,13) NaN
(16,13) NaN
(18,13) NaN
(19,13) NaN
(20,13) NaN
(1,14) NaN
(3,14) NaN
(6,14) NaN
(7,14) NaN
(8,14) NaN
(9,14) Inf
(10,14) NaN
(11,14) NaN
(12,14) NaN
(13,14) NaN
(14,14) NaN
(15,14) NaN
(16,14) NaN
(18,14) NaN
(19,14) NaN
(20,14) NaN
(1,15) NaN
(3,15) NaN
(6,15) NaN
(7,15) NaN
(8,15) Inf
(9,15) NaN
(10,15) NaN
(11,15) NaN
(12,15) NaN
(13,15) NaN
(14,15) NaN
(15,15) NaN
(16,15) NaN
(18,15) NaN
(19,15) NaN
(20,15) NaN
(1,16) NaN
(3,16) NaN
(6,16) NaN
(7,16) Inf
(8,16) NaN
(9,16) NaN
(10,16) NaN
(11,16) NaN
(12,16) NaN
(13,16) NaN
(14,16) NaN
(15,16) NaN
(16,16) NaN
(18,16) NaN
(19,16) NaN
(20,16) NaN
(1,17) NaN
(3,17) NaN
(6,17) Inf
(7,17) NaN
(8,17) NaN
(9,17) NaN
(10,17) NaN
(11,17) NaN
(12,17) NaN
(13,17) NaN
(14,17) NaN
(15,17) NaN
(16,17) NaN
(18,17) NaN
(19,17) NaN
(20,17) NaN
(1,18) NaN
(3,18) NaN
(6,18) NaN
(7,18) NaN
(8,18) NaN
(9,18) NaN
(10,18) NaN
(11,18) NaN
(12,18) NaN
(13,18) NaN
(14,18) NaN
(15,18) NaN
(16,18) NaN
(17,18) 1.1435
(18,18) NaN
(19,18) NaN
(20,18) NaN
(1,19) NaN
(3,19) Inf
(6,19) NaN
(7,19) NaN
(8,19) NaN
(9,19) NaN
(10,19) NaN
(11,19) NaN
(12,19) NaN
(13,19) NaN
(14,19) NaN
(15,19) NaN
(16,19) NaN
(18,19) NaN
(19,19) NaN
(20,19) NaN
(1,20) Inf
(3,20) NaN
(6,20) NaN
(7,20) NaN
(8,20) NaN
(9,20) NaN
(10,20) NaN
(11,20) NaN
(12,20) NaN
(13,20) NaN
(14,20) NaN
(15,20) NaN
(16,20) NaN
(18,20) NaN
(19,20) NaN
(20,20) NaN
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
(12,1) NaN
(13,1) NaN
(14,1) NaN
(15,1) NaN
(16,1) NaN
(18,1) NaN
(19,1) NaN
(20,1) Inf
(1,2) NaN
(3,2) NaN
(6,2) NaN
(7,2) NaN
(8,2) NaN
(9,2) NaN
(10,2) NaN
(11,2) NaN
(12,2) NaN
(13,2) NaN
(14,2) NaN
(15,2) NaN
(16,2) NaN
(18,2) NaN
(19,2) Inf
(20,2) NaN
(1,3) NaN
(3,3) NaN
(6,3) NaN
(7,3) NaN
(8,3) NaN
(9,3) NaN
(10,3) NaN
(11,3) NaN
(12,3) NaN
(13,3) NaN
(14,3) NaN
(15,3) NaN
(16,3) NaN
(18,3) Inf
(19,3) NaN
(20,3) NaN
(1,4) NaN
(3,4) NaN
(4,4) 1.0387
(6,4) NaN
(7,4) NaN
(8,4) NaN
(9,4) NaN
(10,4) NaN
(11,4) NaN
(12,4) NaN
(13,4) NaN
(14,4) NaN
(15,4) NaN
(16,4) NaN
(18,4) NaN
(19,4) NaN
(20,4) NaN
(1,5) NaN
(2,5) 3.7094
(3,5) NaN
(6,5) NaN
(7,5) NaN
(8,5) NaN
(9,5) NaN
(10,5) NaN
(11,5) NaN
(12,5) NaN
(13,5) NaN
(14,5) NaN
(15,5) NaN
(16,5) NaN
(18,5) NaN
(19,5) NaN
(20,5) NaN
(1,6) NaN
(3,6) NaN
(6,6) NaN
(7,6) NaN
(8,6) NaN
(9,6) NaN
(10,6) NaN
(11,6) NaN
(12,6) NaN
(13,6) NaN
(14,6) NaN
(15,6) NaN
(16,6) Inf
(18,6) NaN
(19,6) NaN
(20,6) NaN
(1,7) NaN
(3,7) NaN
(6,7) NaN
(7,7) NaN
(8,7) NaN
(9,7) NaN
(10,7) NaN
(11,7) NaN
(12,7) NaN
(13,7) NaN
(14,7) NaN
(15,7) Inf
(16,7) NaN
(18,7) NaN
(19,7) NaN
(20,7) NaN
(1,8) NaN
(3,8) NaN
(6,8) NaN
(7,8) NaN
(8,8) NaN
(9,8) NaN
(10,8) NaN
(11,8) NaN
(12,8) NaN
(13,8) NaN
(14,8) Inf
(15,8) NaN
(16,8) NaN
(18,8) NaN
(19,8) NaN
(20,8) NaN
(1,9) NaN
(3,9) NaN
(5,9) 10.0885
(6,9) NaN
(7,9) NaN
(8,9) NaN
(9,9) NaN
(10,9) NaN
(11,9) NaN
(12,9) NaN
(13,9) NaN
(14,9) NaN
(15,9) NaN
(16,9) NaN
(18,9) NaN
(19,9) NaN
(20,9) NaN
(1,10) NaN
(3,10) NaN
(6,10) NaN
(7,10) NaN
(8,10) NaN
(9,10) NaN
(10,10) NaN
(11,10) NaN
(12,10) NaN
(13,10) Inf
(14,10) NaN
(15,10) NaN
(16,10) NaN
(18,10) NaN
(19,10) NaN
(20,10) NaN
(1,11) NaN
(3,11) NaN
(6,11) NaN
(7,11) NaN
(8,11) NaN
(9,11) NaN
(10,11) NaN
(11,11) NaN
(12,11) Inf
(13,11) NaN
(14,11) NaN
(15,11) NaN
(16,11) NaN
(18,11) NaN
(19,11) NaN
(20,11) NaN
(1,12) NaN
(3,12) NaN
(6,12) NaN
(7,12) NaN
(8,12) NaN
(9,12) NaN
(10,12) NaN
(11,12) Inf
(12,12) NaN
(13,12) NaN
(14,12) NaN
(15,12) NaN
(16,12) NaN
(18,12) NaN
(19,12) NaN
(20,12) NaN
(1,13) NaN
(3,13) NaN
(6,13) NaN
(7,13) NaN
(8,13) NaN
(9,13) NaN
(10,13) Inf
(11,13) NaN
(12,13) NaN
(13,13) NaN
(14,13) NaN
(15,13) NaN
(16,13) NaN
(18,13) NaN
(19,13) NaN
(20,13) NaN
(1,14) NaN
(3,14) NaN
(6,14) NaN
(7,14) NaN
(8,14) NaN
(9,14) Inf
(10,14) NaN
(11,14) NaN
(12,14) NaN
(13,14) NaN
(14,14) NaN
(15,14) NaN
(16,14) NaN
(18,14) NaN
(19,14) NaN
(20,14) NaN
(1,15) NaN
(3,15) NaN
(6,15) NaN
(7,15) NaN
(8,15) Inf
(9,15) NaN
(10,15) NaN
(11,15) NaN
(12,15) NaN
(13,15) NaN
(14,15) NaN
(15,15) NaN
(16,15) NaN
(18,15) NaN
(19,15) NaN
(20,15) NaN
(1,16) NaN
(3,16) NaN
(6,16) NaN
(7,16) Inf
(8,16) NaN
(9,16) NaN
(10,16) NaN
(11,16) NaN
(12,16) NaN
(13,16) NaN
(14,16) NaN
(15,16) NaN
(16,16) NaN
(18,16) NaN
(19,16) NaN
(20,16) NaN
(1,17) NaN
(3,17) NaN
(6,17) Inf
(7,17) NaN
(8,17) NaN
(9,17) NaN
(10,17) NaN
(11,17) NaN
(12,17) NaN
(13,17) NaN
(14,17) NaN
(15,17) NaN
(16,17) NaN
(18,17) NaN
(19,17) NaN
(20,17) NaN
(1,18) NaN
(3,18) NaN
(6,18) NaN
(7,18) NaN
(8,18) NaN
(9,18) NaN
(10,18) NaN
(11,18) NaN
(12,18) NaN
(13,18) NaN
(14,18) NaN
(15,18) NaN
(16,18) NaN
(17,18) 1.1435
(18,18) NaN
(19,18) NaN
(20,18) NaN
(1,19) NaN
(3,19) Inf
(6,19) NaN
(7,19) NaN
(8,19) NaN
(9,19) NaN
(10,19) NaN
(11,19) NaN
(12,19) NaN
(13,19) NaN
(14,19) NaN
(15,19) NaN
(16,19) NaN
(18,19) NaN
(19,19) NaN
(20,19) NaN
(1,20) Inf
(3,20) NaN
(6,20) NaN
(7,20) NaN
(8,20) NaN
(9,20) NaN
(10,20) NaN
(11,20) NaN
(12,20) NaN
(13,20) NaN
(14,20) NaN
(15,20) NaN
(16,20) NaN
(18,20) NaN
(19,20) NaN
(20,20) NaN
toc
Elapsed time is 0.018112 seconds.
Benson Gou
2021-6-25
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
2021-6-25
Well, you could try matrix decomposition, https://www.mathworks.com/help/matlab/ref/decomposition.html
Benson Gou
2021-6-25
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
2021-6-25
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
2021-6-29
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
更多回答（1 个）
Sulaymon Eshkabilov
2021-6-25
编辑：Sulaymon Eshkabilov
2021-6-25
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 个评论
Walter Roberson
2021-6-25
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
2021-6-29
Hi, Walter,
Yes, the decomposition is faster than \ operator. Thanks a lot.
Benson
另请参阅
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!发生错误
由于页面发生更改，无法完成操作。请重新加载页面以查看其更新后的状态。
Translated by 
您也可以从以下列表中选择网站：
如何获得最佳网站性能
选择中国网站（中文或英文）以获得最佳网站性能。其他 MathWorks 国家/地区网站并未针对您所在位置的访问进行优化。
美洲
- América Latina (Español)
- Canada (English)
- United States (English)
欧洲
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom(English)
亚太
- Australia (English)
- India (English)
- New Zealand (English)
- 中国
- 日本Japanese (日本語)
- 한국Korean (한국어)