[eigen] How to compute the inverse of a sparse matrix? And how ist computeInverseWithCheck(..) used correctly?

[Mathias Goldau <math@xxxxxxxxxxxxxxxxxxxxxxxxx>]

Is there a way in Eigen to compute the inverse of a sparse matrix?

ATM I try to do that for dense matrix, and read the doc so I am aware that in
case of non invertibility the result is undefined. So I looked into the repos
and found: computeInverseWithCheck(..) function.
But if I try to use it it aborts with:

In file included from /usr/local/eigen/include/eigen3/Eigen/LU:27,
                 from
/home/math/repos/Wassermann/src/modules/detTract2GPConvert/WGaussProcess.cpp:25:
/usr/local/eigen/include/eigen3/Eigen/src/LU/Inverse.h: In member function
‘void Eigen::MatrixBase<Derived>::computeInverseAndDetWithCheck(ResultType&,
typename ResultType::Scalar&, bool&, const typename Eigen::NumTraits<typename
Eigen::ei_traits<Derived>::Scalar>::Real&) const [with ResultType =
Eigen::Matrix<double, -0x00000000000000001, -0x00000000000000001, 0,
-0x00000000000000001, -0x00000000000000001>, Derived = Eigen::Matrix<double,
-0x00000000000000001, -0x00000000000000001, 0, -0x00000000000000001,
-0x00000000000000001>]’:
/usr/local/eigen/include/eigen3/Eigen/src/LU/Inverse.h:400:   instantiated
from ‘void Eigen::MatrixBase<Derived>::computeInverseWithCheck(ResultType&,
bool&, const typename Eigen::NumTraits<typename
Eigen::ei_traits<Derived>::Scalar>::Real&) const [with ResultType =
Eigen::MatrixXd, Derived = Eigen::Matrix<double, -0x00000000000000001,
-0x00000000000000001, 0, -0x00000000000000001, -0x00000000000000001>]’
/home/math/repos/Wassermann/src/modules/detTract2GPConvert/WGaussProcess.cpp:53:
  instantiated from here
/usr/local/eigen/include/eigen3/Eigen/src/LU/Inverse.h:368: error: ‘run’ is
not a member of
‘Eigen::ei_compute_inverse_and_det_with_check<Eigen::Matrix<double,
-0x00000000000000001, -0x00000000000000001, 0, -0x00000000000000001,
-0x00000000000000001>, Eigen::Matrix<double, -0x00000000000000001,
-0x00000000000000001, 0, -0x00000000000000001, -0x00000000000000001>,
-0x00000000000000001>’

The calling code looks like this:

Eigen::MatrixXd Cff( static_cast< int >( tract.size() ), static_cast< int >(
tract.size() ) );
size_t i = 0, j = 0;
for( WFiber::const_iterator cit = tract.begin(); cit != tract.end(); ++cit, ++i )
{
    for( WFiber::const_iterator cit2 = tract.begin(); cit2 != tract.end();
++cit2, ++j )
    {
        Cff( i, j ) = cov( *cit, *cit2 );
    }
}
bool isInvertible = false;
Cff.computeInverseWithCheck( m_CffInverse, isInvertible );

I want to use eigen for many covariance matrix which I assume to be sparse.
But until I know how to compute the inverse of a spares matrix with eigen, I
will use dense matrices at first...

best regards
Mathias

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