Hi,
I'm working with V3 of Eigen.

I'm looking at the test case of the matrix.
[1,0]
[0,-1]

This matrix isn't semi-positive definite. Nor is it semi-negative definite.
Running it through LDLT I get the following results:

reconstructedMatrix ;
[1,0]
[0,-1]
isPositive : True (Which is wrong!)
isNegative : False
info : Success

If you contrast this to the same input for LLT I get a failure code from info(), which is what I would expect since LLT only works on SPD matrices.
In the docs it says that we can use LDLT on semi-positive definite or semi-negative matrices. If the input isn't one of these, as in the above case, it seems it should either fail or give a correct output. Is it possible to have this behaviour, please? Or is it not easy to do with this algo? Certainly it would help in the sense I that I wouldn't need an independent check on the correctness of the input in my code.

Thanks very much. Really impressed with Eigen by the way.

Hi,

your matrix is a special case because it is diagonal. Therefore, the factorization went well, and it assumed the matrix was positive because the first pivot was 1. In a more general case, the factorization would have failed. I'm not sure we want to abort the factorization if it can really be done. So I propose the following simple fix: line 284 add:

Code: Select all

      else if(sign)
      {
        // LDLT does not support non positive or non negative matrices, except if the matrix is diagonal.
        int newSign = real(mat.diagonal().coeff(index_of_biggest_in_corner)) > 0;
        if(newSign!=*sign)
          m_sign = 0;
      }


Thanks very much for clearing this up.

ggael wrote:your matrix is a special case because it is diagonal. Therefore, the factorization went well, and it assumed the matrix was positive because the first pivot was 1. In a more general case, the factorization would have failed.

In what sense would it fail? I tried a couple of indefinite matrices, and the LDLT class seems to work fine. Perhaps you mean that the algorithm can be unstable if the matrix is close to singular?

I'm not sure we want to abort the factorization if it can really be done. So I propose the following simple fix: line 284 add: [...]

I cannot see anything wrong with that, so I committed your fix to the development branch.