Strategies for a matrix containing values very close to zero, when passing it to EigenDecompositionSymmetric()?

[mjw99]

I am in the process of refactoring a codebase that made use of EigenDecomposition() in Hipparchus version 2.3 to use EigenDecompositionSymmetric() in Hipparchus 3.1.

However, it is now failing some of its unittests due to there being double values very close to zero in a matrix that I pass to the EigenDecompositionSymmetric() constructor; resulting in a "MathIllegalArgumentException: non symmetric matrix..." being thrown. This is being generated by MatrixUtils.checkSymmetric() and the following example can reproduce something very similar to what I am seeing:

    @Test
    void testIsSymmetricToleranceMjw() {
        // Default
        final double eps = 1e-12;

        final double[][] dataSym1 = {
            {    1,      1, 1.0E-16 },
            {    1,      1, 1       },
            {1.0E-17,    1, 1       },
        };
        
        RealMatrix matrix = MatrixUtils.createRealMatrix(dataSym1);       
         
        System.out.println(MatrixUtils.isSymmetric(matrix, eps));      
        new EigenDecompositionSymmetric(matrix,eps,true);
    }

The above will trigger this condition here

Are there any utility methods that can actually zero double values close to zero or any other hints/tips for this situation?

Thank you.

[maisonobe]

Thanks for the report!

The issue is due to the tolerance being in fact a relative tolerance check, not an absolute tolerance check. In this case the difference between the two entries 1.0e-16 and 1.0e-17 is 9.0e-17, and the relative check compares this to 1.0e-28 (which is max(1.0e-16, 1.0e-17) * 1.0e-12.

Hipparchus does not by itself provide a way to collapse small entries, but you could use the following to achieve this result by changing small values in-place:

        matrix.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
            public double visit(final int row, final int column, final double value) {
                return FastMath.abs(value) < 2.0e-16 ? 0 : value;
            }
        });

[mjw99]

Dear Luc,

Many thanks for looking at this and offering this suggestion; I will follow this.

Thanks again.