MATLAB: How should I compute the eigenvectors of a sparse, real, symmetric matrix

eigeigssparsesymmetric

I need to compute all the eigenvectors of a sparse, real, symmetric matrix, A.
I've tried the following:
>> [V, D] = eig(A);
Error using eig
For standard eigenproblem EIG(A) when A is sparse, EIG does not support computing eigenvectors. Use EIGS instead.
>> [V, D] = eigs(A, size(A, 1));
Warning: For real symmetric problems, must have number of eigenvalues k < n.
Using eig instead.
So MATLAB gives me conflicting advice: first, to use eigs, and then to use eig! What it does internally is convert my sparse matrix to a full one. This seems inefficient if I have lots of sparsity. Any better suggestions?

Best Answer

Just convert the matrix to a full one, and use eig. Unless less you want just a few eigenvectors, then the decomposition using the sparse matrix will generally be slower anyway. E.g.:
>> A = sprand(2e3, 2e3, 2e-3);
>> A = A' + A;
>> tic; [V, D] = eigs(A, 2e3-2); toc;
Elapsed time is 21.727999 seconds.
>> tic; [V, D] = eig(full(A)); toc
Elapsed time is 2.488241 seconds.
Moral of the story: sparse isn't always faster!
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