eigs with big sparse matrix has Internal error

I am using 9m by 9m K_matrix_sys and M_matrix_sys to calculate the frequence with eigs.

fre = eigs(K_matrix_sys,M_matrix_sys,3,0);

The error is showing below. I don't know how set up eigs other value to make this work.

Error using matlab.internal.decomposition.builtin.UMFPACKWrapper
Decomposition built-in error: Algorithm did not succeed.
Internal error in library UMFPACK.

Error in eigs>AminusSigmaBSolve (line 1220)
        umf = matlab.internal.decomposition.builtin.UMFPACKWrapper(AminusSigmaB, 0.1, 0.001, true, 0);

Error in eigs>getOps (line 1122)
        applyOP = AminusSigmaBSolve(A, B, innerOpts.sigma, Amatrix, n, ...

Error in eigs (line 122)
[applyOP, applyM] = getOps(A, B, n, spdB, shiftAndInvert, R, cholB, permB,...
    

[Christine Tobler]

The error is happening while computing a factorization of K_matrix_sys so that we can then solve linear systems K_matrix_sys \ x.

Could you try to solve a linear system? That is, calling

K_matrix_sys \ rand(size(K_matrix_sys, 1), 1);

Does this also error, and if yes, what error message is given?

[Benyang Hu]

I just finished the running. There is no error for the line you give to me. Do you mean the error is from M_matrix_sys?

Update: The error is saying

Error using  \ 
Out of memory. Type "help memory" for your options.

So is there no enought memory for this calculation?

[Bruno Luong]

How much memory do you have?

May be you can try to save K and M the load them again in clean matlab enviroment and calling eigs.

[Benyang Hu]

I have 128GB memory. There is no difference after I "clear" in matlab. I tried before.

[Bruno Luong]

"So is there no enought memory for this calculation?"

Obviously no, as I have suspected.

[Christine Tobler]

eigs should have given the out-of-memory error directly, instead of the "internal error" message you had originally received. This has been addressed for R2019b, so in that and later releases the error message should be less confusing.

Unfortunately there isn't much to be done for the case of an out-of-memory error. For some sparse matrices, their factorization contains a lot of "fill-in", meaning the factors of this matrix contain many more nonzeros than the original matrix and therefore need much more memory.

If you happen to know that all eigenvalues are positive, you could try to instead use the "smallestreal" option, which doesn't compute a factorization of the first input matrix. That can be a bit of a mixed bag, as convergence of the iteration inside eigs can be much slower (or not happen in practical time at all), but in some cases it works very well.

% If you know all eigenvalues are >= 0:
fre = eigs(K_matrix_sys,M_matrix_sys,3,'smallestreal')

Answer 1

[Andrew Knyazev]

try running Locally Optimal Block Preconditioned Conjugate Gradient - File Exchange - MATLAB Central (mathworks.com)