Re: [eigen] Sparse Cholesky Factors

[Brad Bell <bradbell@xxxxxxxxxx>]

Looking at the source code
    eigen-3.2.1/Eigen/src/SparseCholesky/SimplicialCholesky.h
one can see the undocumented public member function

inline const VectorType vectorD() const {
        eigen_assert(Base::m_factorizationIsOk && "Simplicial Cholesky 
not factorized");
        return Base::m_diag;
}

Is vectorD() intended to be part of the Eigen API ?

It appears that in the case of an eigen LDL Cholesky factorization
http://eigen.tuxfamily.org/dox-devel/classEigen_1_1SimplicialLDLT.html
the LDL means the same as in
http://en.wikipedia.org/wiki/Cholesky_decomposition#LDL_decomposition
It also appears that vectorD() returns the diagonal of the D matrix for 
this case.

Is this is true ? If so, one can uses these facts to directly compute 
the log of the determinant.




On 4/3/2015 6:17 AM, Brad Bell wrote:
> Looking at the documentation
> http://eigen.tuxfamily.org/dox-devel/classEigen_1_1SimplicialLLT.html
> there is a determinant member function
>     Scalar Eigen::SimplicialLLT< _MatrixType, _UpLo, _Ordering 
> >::determinant() const
>
> For large matrices, the determinant often results in underflow or 
> overflow. Is there also a log-determinant function (to avoid this 
> problem) ?