cusp::relaxation::polynomial< ValueType, MemorySpace > Class Template Reference

#include <polynomial.h>

Inheritance diagram for cusp::relaxation::polynomial< ValueType, MemorySpace >:

Public Methods
	polynomial (void)
template<typename MatrixType >
	polynomial (const MatrixType &A)
template<typename MatrixType , typename VectorType >
	polynomial (const MatrixType &A, const VectorType &coefficients)
template<typename MemorySpace2 >
	polynomial (const polynomial< ValueType, MemorySpace2 > &A)
template<typename MatrixType , typename VectorType1 , typename VectorType2 >
void	operator() (const MatrixType &A, const VectorType1 &b, VectorType2 &x)
template<typename MatrixType , typename VectorType1 , typename VectorType2 , typename VectorType3 >
void	operator() (const MatrixType &A, const VectorType1 &b, VectorType2 &x, const VectorType3 &coefficients)
Public Methods inherited from cusp::linear_operator< ValueType, MemorySpace, IndexType >
	linear_operator (void)
	linear_operator (IndexType num_rows, IndexType num_cols)
	linear_operator (IndexType num_rows, IndexType num_cols, IndexType num_entries)

Detailed description

template<typename ValueType, typename MemorySpace>
class cusp::relaxation::polynomial< ValueType, MemorySpace >

Represents a Polynomial relaxation scheme.

Template Parameters

ValueType	value_type of the array
MemorySpace	memory space of the array (cusp::host_memory or cusp::device_memory)

Overview

Performs 3rd degree Polynomial relaxation

Example

#include <cusp/array1d.h>
#include <cusp/csr_matrix.h>
#include <cusp/monitor.h>
 
#include <cusp/blas/blas.h>
#include <cusp/linear_operator.h>
#include <cusp/gallery/poisson.h>
 
// include cusp polynomial header file
#include <cusp/relaxation/polynomial.h>
 
int main()
{
   // Construct 5-pt Poisson example
   cusp::csr_matrix<int, float, cusp::device_memory> A;
   cusp::gallery::poisson5pt(A, 5, 5);
 
   // Initialize data
   cusp::array1d<float, cusp::device_memory> x(A.num_rows, 0);
   cusp::array1d<float, cusp::device_memory> b(A.num_rows, 1);
 
   // Allocate temporaries
   cusp::array1d<float, cusp::device_memory> r(A.num_rows);
   cusp::array1d<float, cusp::host_memory> coefficients;
 
   // Compute spectral radius of A
   float rho = cusp::detail::ritz_spectral_radius_symmetric(A, 8);
   // Compute 3rd degree Chebyshev polynomial
   cusp::relaxation::detail::chebyshev_polynomial_coefficients(rho, coefficients);
   // Construct polynomial relaxation class
   cusp::relaxation::polynomial<float, cusp::device_memory> M(A, coefficients);
 
   // Compute initial residual
   cusp::multiply(A, x, r);
   cusp::blas::axpy(b, r, float(-1));
 
   // Construct monitor with stopping criteria of 100 iterations or 1e-4 residual error
   cusp::monitor<float> monitor(b, 100, 1e-4, 0, true);
 
   // Iteratively solve system
   while (!monitor.finished(r))
   {
       M(A, b, x);
       cusp::multiply(A, x, r);
       cusp::blas::axpy(b, r, float(-1));
       ++monitor;
   }
 }

Definition at line 101 of file polynomial.h.

Constructor & Destructor Documentation

polynomial() [1/4]

template<typename ValueType , typename MemorySpace >

cusp::relaxation::polynomial< ValueType, MemorySpace >::polynomial ( void  )

inline

This constructor creates an empty polynomial smoother.

Definition at line 115 of file polynomial.h.

polynomial() [2/4]

template<typename ValueType , typename MemorySpace >

template<typename MatrixType >

cusp::relaxation::polynomial< ValueType, MemorySpace >::polynomial

(

const MatrixType &

A

)

This constructor creates a polynomial smoother using a given matrix.

Template Parameters

MatrixType

Type of input matrix used to create this polynomial smoother.

Parameters

A	Input matrix used to create smoother.

polynomial() [3/4]

template<typename ValueType , typename MemorySpace >

template<typename MatrixType , typename VectorType >

cusp::relaxation::polynomial< ValueType, MemorySpace >::polynomial	(	const MatrixType &	A,
		const VectorType &	coefficients
	)

This constructor creates a polynomial smoother using a given matrix and coefficients.

Template Parameters

MatrixType

Type of input matrix used to create this polynomial smoother.

Parameters

A	Input matrix used to create smoother.
coefficients	Used in polynomial smoother.

polynomial() [4/4]

template<typename ValueType , typename MemorySpace >

template<typename MemorySpace2 >

cusp::relaxation::polynomial< ValueType, MemorySpace >::polynomial ( const polynomial< ValueType, MemorySpace2 > &  A )

inline

Copy constructor for polynomial smoother.

Template Parameters

MemorySpace2

Memory space of input polynomial smoother.

Parameters

A	Input polynomial smoother.

Definition at line 147 of file polynomial.h.

Member Function Documentation

operator()() [1/2]

template<typename ValueType , typename MemorySpace >

template<typename MatrixType , typename VectorType1 , typename VectorType2 >

void cusp::relaxation::polynomial< ValueType, MemorySpace >::operator()	(	const MatrixType &	A,
		const VectorType1 &	b,
		VectorType2 &	x
	)

Perform polynomial relaxation using default coefficients specified during construction of this polynomial smoother

Template Parameters

MatrixType	Type of input matrix.
VectorType1	Type of input right-hand side vector.
VectorType2	Type of input approximate solution vector.

Parameters

A	matrix of the linear system
x	approximate solution of the linear system
b	right-hand side of the linear system

operator()() [2/2]

template<typename ValueType , typename MemorySpace >

template<typename MatrixType , typename VectorType1 , typename VectorType2 , typename VectorType3 >

void cusp::relaxation::polynomial< ValueType, MemorySpace >::operator()	(	const MatrixType &	A,
		const VectorType1 &	b,
		VectorType2 &	x,
		const VectorType3 &	coefficients
	)

Perform polynomial relaxation using specified coefficients

Template Parameters

MatrixType	Type of input matrix.
VectorType1	Type of input right-hand side vector.
VectorType2	Type of input approximate solution vector.
VectorType3	Type of input coefficients vector.

Parameters

A	matrix of the linear system
x	approximate solution of the linear system
b	right-hand side of the linear system
coefficients	Used in polynomial smoother.