NAME

       solver - direct or interative solver interface

DESCRIPTION

        The class implements a matrix factorization:
        LU factorization for an unsymmetric matrix and
        Choleski fatorisation for a symmetric one.

        Let a be a square invertible matrix in
        csr format (see csr(2)).

               csr<Float> a;

        We get the factorization by:

               solver<Float> sa (a);

        Each call to the direct solver for a*x = b writes either:

               vec<Float> x = sa.solve(b);

        When the matrix is modified in a computation loop but
        conserves its sparsity pattern, an efficient re-factorization
        writes:

               sa.update_values (new_a);
               x = sa.solve(b);

        This approach skip the long step of the symbolic factization step.

ITERATIVE SOLVER

        The factorization can also be incomplete, i.e. a pseudo-inverse,
        suitable for preconditionning iterative methods.
        In that case, the sa.solve(b) call runs a conjugate gradient
        when the matrix is symmetric, or a generalized minimum residual
        algorithm when the matrix is unsymmetric.

AUTOMATIC CHOICE AND CUSTOMIZATION

        The symmetry of the matrix is tested via the a.is_symmetric() property
        (see csr(2)) while the choice between direct or iterative solver
        is switched from the a.pattern_dimension() value. When the pattern
        is 3D, an iterative method is faster and less memory consuming.
        Otherwhise, for 1D or 2D problems, the direct method is prefered.

        These default choices can be supersetted by using explicit options:

               solver_option_type opt;
               opt.iterative = true;
               solver<Float> sa (a, opt);

        See the solver.h header for the complete list of available options.

IMPLEMENTATION NOTE

        The implementation bases on the pastix library.

IMPLEMENTATION

       template <class T, class M = rheo_default_memory_model>
       class solver_basic : public smart_pointer<solver_rep<T,M> > {
       public:
       // typedefs:

         typedef solver_rep<T,M>    rep;
         typedef smart_pointer<rep> base;

       // allocator:

         solver_basic ();
         explicit solver_basic (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
         void update_values (const csr<T,M>& a);

       // accessors:

         vec<T,M> trans_solve (const vec<T,M>& b) const;
         vec<T,M> solve       (const vec<T,M>& b) const;
       };
       // factorizations:
       template <class T, class M>
       solver_basic<T,M> ldlt(const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
       template <class T, class M>
       solver_basic<T,M> lu  (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
       template <class T, class M>
       solver_basic<T,M> ic0 (const csr<T,M>& a, const solver_option_type& opt = solver_option_type());
       template <class T, class M>
       solver_basic<T,M> ilu0(const csr<T,M>& a, const solver_option_type& opt = solver_option_type());

       typedef solver_basic<Float> solver;

SEE ALSO

       csr(2), csr(2)