I'm working on the LinearOperator stuff for MAHOUT-672 and have gotten to
the point when I'm modifying the new LanczosSolver as implemented in the
MAHOUT-319 patch applied to Jake's github repo.
One quick question: on lines 165-167 of LanczosSolver.java we have the
lines:
if (isSymmetric) {
e = Math.sqrt(e);
}
Unless I'm misunderstanding something, isn't this backwards? My
understanding is that Lanczos is an eigendecomposition algorithm, so for a
symmetric A, it's going to compute eigenvector matrix U and diagonal
eigenvalue matrix S such that A ~= USU'. To use it to compute the SVD, you
use the fact that for non-symmetric A = USV', we have A'A = V(S^2)V', so by
taking the eigendecomposition of A'A, you get the right singular vectors as
the eigenvectors and the singular values as the sqrt of the eigenvalues. So,
shouldn't these lines be:
if (!isSymmetric) {
e = Math.sqrt(e);
}
-Jon
