NullPointerException in OrderedComplexEigenDecomposition

[axkr]

Follow up from #248:

Thanks for the change, which works for most cases, but this case for matrix

Array2DRowRealMatrix{{1.0,0.0,0.0},{-2.0,1.0,0.0},{0.0,0.0,1.0}}

and the following call:

ComplexEigenDecomposition ced = new OrderedComplexEigenDecomposition(matrix, //
          ComplexEigenDecomposition.DEFAULT_EIGENVECTORS_EQUALITY, //
          ComplexEigenDecomposition.DEFAULT_EPSILON, //
          ComplexEigenDecomposition.DEFAULT_EPSILON_AV_VD_CHECK, //
          (c1, c2) -> Double.compare(c2.norm(), c1.norm()));

throws a NullPointerException

java.lang.NullPointerException: null
	at org.hipparchus.linear.AbstractFieldMatrix.setColumnVector(AbstractFieldMatrix.java:566) ~[classes/:?]
	at org.hipparchus.linear.ComplexEigenDecomposition.<init>(ComplexEigenDecomposition.java:143) ~[classes/:?]
	at org.hipparchus.linear.OrderedComplexEigenDecomposition.<init>(OrderedComplexEigenDecomposition.java:98) ~[classes/:?]

The eigenvectors contain a nullvalue at line ComplexEigenDecomposition.java:143

I would have expected a 0-vector {0.0,0.0,0.0} instead of the null value.

[maisonobe]

I think that instead of returning a zero vector (as mentioned in #248 discussion), we should trigger an exception.
The eigen decomposition theorem is that decomposition is always possible "if the matrix P of eigen vectors is a square matrix". The example in MathWorld is about a 2x2 matrix where the space of eigenvectors is only 1, and the matrix in this issue is a 3x3 matrix where the space of eigenvectors is only 2.
In both cases, the eigen decomposition theorem does not apply, the matrix P is not square.

[axkr]

We want to implement the MMA behavior; how can we do it, if hipparchus triggers an exception?

https://reference.wolfram.com/language/ref/Eigenvectors.html

[maisonobe]

OK, then I'll add the zeros, with some documentation.
It nevertheless looks strange to me as Wolfram Alpha really returns two eigenvectors for this matrix.

[axkr]

Yes there are some "conventions" described in the reference for symbolic and numerical evaluations.

The first 2 examples are symbolic evaluations the last 2 are numerical: