eye(2rheolef) [debian man page]

eye(2rheolef)							    rheolef-6.1 						     eye(2rheolef)

NAME

       eye - the identity matrix

DESCRIPTION

       Following  matlab,  the name eye() is used in place of I to denote identity matrices because I is often used as a subscript or as sqrt(-1).
       The dimensions of eye() are determined by context.  The preconditioner interface is usefull when calling algorithms without  any  precondi-
       tioners, e.g.

	   int status = pcg (a, x, b, eye(), 100, 1e-7);

IMPLEMENTATION

       class eye {
       public:
	 eye() {}
	 template<class T> const vec<T>& operator* (const vec<T>& x) const { return x; }
	 template<class T> const vec<T>& solve (const vec<T>& x) const { return x; }
	 template<class T> const vec<T>& trans_solve (const vec<T>& x) const { x; }
       };

rheolef-6.1							    rheolef-6.1 						     eye(2rheolef)

dia(2rheolef)							    rheolef-6.1 						     dia(2rheolef)

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 @emph{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)

rheolef-6.1							    rheolef-6.1 						     dia(2rheolef)