CODEWITHSUNDEEP
c++matlabarmadillo
farhanhubble
farhanhubble

Reputation: 494

Right function for computing a limited number of eigenvectors of a complex symmetric matrix in Armadillo

I am using the Armadillo library to manually port a piece of Matlab code. The matlab code uses the eigs() function to find a small number (~3) of eigen vectors of a relative large(200x200) covariance matrix R. The code looks like this:

[E,D] = eigs(R,3,"lm");

In Armadillo there are two functions eigs_sym() and eigs_gen() however the former only support real symmetric matrix and the latter requires ARPACK (I'm building the code for Android). Is there a reason eigs_sym doesn't support complex matrices? Is there any other way to find the eigenvectors of a complex symmetric matrix?

Upvotes: 0

Views: 241

Answers (2)

Hans Olsson
Hans Olsson

Reputation: 12527

Have you tested constructing a 400x400 real symmetric matrix by replacing each complex value, a+bi, by a 2x2 matrix [a,b;-b,a] (alternatively using a block variant of this)?

This should construct a real symmetric matrix that in some way correspond to the complex one. There will be a slow-down due to the larger size, and all eigenvalues will be duplicated (which may slow down the algorithm), but it seems straightforward to test.

Upvotes: 0

mtall
mtall

Reputation: 3620

The eigs_sym() and eigs_gen() functions (where the s in eigs stands for sparse) in Armadillo are for large sparse matrices. A "large" size in this context is roughly 5000x5000 or larger.

Your R matrix has a size of 200x200. This is very small by current standards. It would be much faster to simply use the dense eigendecomposition eig_sym() or eig_gen() functions to get all the eigenvalues / eigenvectors, followed by extracting a subset of them using submatrix operations like .tail_cols()

Upvotes: 2

Related Questions