NAME

       dia - diagonal matrix

DESCRIPTION

       The class implements a diagonal matrix.  A declaration whithout any parametrers correspond
       to a null size matrix:

               dia<Float> d;

       The constructor can be invocated whith a ownership parameter (see distributor(2)):

               dia<Float> d(ownership);

       or an initialiser, either a vector (see vec(2)):

               dia<Float> d(v);

       or a csr matrix (see csr(2)):

               dia<Float> d(a);

       The conversion from dia to vec or csr is explicit.

       When a diagonal matrix is constructed from a csr matrix, the definition of the diagonal of
       matrix  is  always a vector of size row_ownership which contains the elements in rows 1 to
       nrow of the matrix that are contained in the diagonal.   If  the  diagonal  element  falls
       outside the matrix, i.e. ncol < nrow then it is defined as a zero entry.

PRECONDITIONER INTERFACE

       The class presents a preconditioner interface, as the solver(2), so that it can be used as
       preconditioner to the iterative solvers suite (see pcg(4)).

IMPLEMENTATION

       template<class T, class M = rheo_default_memory_model>
       class dia : public vec<T,M> {
       public:

       // typedefs:

           typedef typename vec<T,M>::size_type       size_type;
           typedef typename vec<T,M>::iterator          iterator;
           typedef typename vec<T,M>::const_iterator    const_iterator;

       // allocators/deallocators:

           explicit dia (const distributor& ownership = distributor(),
                         const T&  init_val = std::numeric_limits<T>::max());

           explicit dia (const vec<T,M>& u);
           explicit dia (const csr<T,M>& a);
           dia<T,M>& operator= (const T& lambda);

       // preconditionner interface: solves d*x=b

           vec<T,M> solve (const vec<T,M>& b) const;
           vec<T,M> trans_solve (const vec<T,M>& b) const;
       };
       template <class T, class M>
       dia<T,M> operator/ (const T& lambda, const dia<T,M>& d);

       template <class T, class M>
       vec<T,M> operator* (const dia<T,M>& d, const vec<T,M>& x);

SEE ALSO

       distributor(2), vec(2), csr(2), solver(2), pcg(4)