Eigen decomp for non-symmetric matrices?

ND4J
1

I’ve been trying to figure out why the eigenvalue decomposition provided by ND4J is returning incorrect results in my unit tests. I worked out the matrix decomp by hand and calculated it with several other libraries (EJML, Parallel Colt, and JAMA).

I’ve tried both the standard and the generalized method (setting B to the identity matrix). Both give the same incorrect values:

        double[][] array = new double[][]{{1, 2, 1}, {6, -1, 0}, {-1, -2, -1}};
        INDArray matrix = Nd4j.create(array);

        INDArray values = Eigen.symmetricGeneralizedEigenvalues(matrix);
        // INDArray values = Eigen.symmetricGeneralizedEigenvalues(matrix, Nd4j.eye(matrix.row));
        System.out.println(values);

With either method I get:

[-6.2408, -1.3996, 6.6403]

However, the actual eigenvalues are

[-4.0, 0.0, 3.0]

I figure this has something to do with the fact that the docs say A should be symmetric… but I see no other class in the library that does eigenvalue decomposition and symmetric matrices are a pretty narrow scope (or so I thought?).

Does anyone have any ideas? Thanks!