I have discovered what appears to be a fairly serious bug in the FEAST MKL eigensolver that occurs when there are coupled eigenvalues (ie. multiple eigenvalues with the same value). When coupled eigenvalues occur, the FEAST module returns eigenvectors that are a combination of the eigenvectors for each eigenvalue rather than keeping them separate.
For example, if the 1st and 2nd eigenvalues have the same value, FEAST returns a 1st eigenvector that is a combination of what should be separate 1st and 2nd eigenvectors, each factored by a different apparently random value. Similarly, it returns the 2nd eigenvector that is also a combination of the 1st and 2nd eigenvectors.
Has anyone else experienced this and/or found a solution?
I can provide data that illustrates the problem if required.
It appears that there are an infinite number of eigenvector solutions for coupled eigenvalues. In such cases the eigenvector solutions involve any combinations of the separate eigenvectors. I am still looking at it and will post again if I can't figure it out.