Particle Swarm Optimization to solve matrix inversion

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Nurulhuda Ismail 2019-1-7

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https://ww2.mathworks.cn/matlabcentral/answers/438678-particle-swarm-optimization-to-solve-matrix-inversion

评论： Walter Roberson 2019-1-8

Hi everyone,

I am Huda, and I am working with matrix inversion. I am really new with PSO and I would like to know is it possible to use PSO for a large size matrix inversion (eg., 16x16, or 64x64)? From a linear equation, Ax=b, we can find x by several techniques such as Gauss-Jordan elimination, and we know that AA^(-1) =I. Thus, I wonder if PSO can solve this problem by computing A^(-1) iteratively.

If yes, can you share with me any material that can guide me to start my work. But, If matrix inversion with PSO will give bad result, can you advise any technique that suitable to use?

Thank you for your response.

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Nurulhuda Ismail 2019-1-8

Ok then, thank you for your comment.

Nurulhuda Ismail 2019-1-8

Instead of PSO, is there any other optimizer that suitable for matrix inversion? Your idea is really appreciated.Thank you.

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采纳的回答

Walter Roberson 2019-1-8

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https://ww2.mathworks.cn/matlabcentral/answers/438678-particle-swarm-optimization-to-solve-matrix-inversion#answer_355430

在 MATLAB Online 中打开

N = 8;
rng(12345);
M = randi([-50 50], N, N);
obj = @(v) sum(sum((M * reshape(v,N,N) - eye(N)).^2));
N2 = N.^2;
LB = []; UB = []; 
options = optimoptions(@particleswarm, 'Display', 'final', 'MaxIterations', 500*N2, 'PlotFcn', @pswplotbestf );
tic
[bestinv, fval] = particleswarm(obj, N2, LB, UB, options);
time_needed_ps = toc;
Minvps = reshape(bestinv, N, N);
tic
Minv = inv(M);
time_needed_numeric = toc;
residue = sum((Minvps(:) - Minv(:)).^2);
fprintf('\nResidue between particle swarm inverse and numeric inverse is: %.6g\n', residue);
fprintf('\nDifference between particle swarm inverse and numeric inverse is: \n\n')
disp(Minvps - Minv)
fprintf('\ntime required for particle swarm partial inverse: %.6gs\n', time_needed_ps);
fprintf('time required for numeric inverse:                %.6gs\n', time_needed_numeric);

Approximate time multiplication for the particle swarm approach: 620000 times more expensive. The calculated inverse will not necessarily be especially close -- it is not bad for 5 x 5, but by 8 x 8 the residue is still about a million.

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Nurulhuda Ismail 2019-1-8

Thank you. I got an error while I run in MATLAB which is because I dont install the Global Optimizaion Toolbox. I will re-run the codes once I install this toolbox.

Regarding to a matrix inversion, instead of PSO, do you know any other optimizer that I can be used to do matrix inversion?

Walter Roberson 2019-1-8

On my system inv() of a 64x64 array takes less than 1e-4 seconds. Any optimization routine would have to finish faster than that to be worth bothering with.

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