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);