Sparse LU solver
================

Inverse of sparse matrix are modelled in a "lazy" manner.
When creating an object :math:`\texttt{invA}` that models the
inverse :math:`A^{-1}` of a sparse matrix :math:`A`, the LU
factorization :math:`A = L\cdot U` is computed and stored
according to an algorithm that takes advantage of the sparsity.

After creation of this "lazy inverse" :math:`\texttt{invA}`, only
matrix-vector products :math:`y \mapsto x = \texttt{invA}(y)` can
be performed, and each matrix-vector product triggers the solution
of a linear system :math:`A(x)=y` by means of the sparse LU factorization.

Sparse LU factorizations are performed relying on the routines of
the `Eigen3 library`_.

.. _Eigen3 library: https://eigen.tuxfamily.org/index.php?title=Main_Page

.. doxygenclass:: InvCooMatrix
   :members: