cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format > Class Template Reference

Detailed description

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>
class cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >

Algebraic multigrid preconditoner based on smoothed aggregation.

Template Parameters

IndexType	Type used for matrix values (e.g. int or size_t).
ValueType	Type used for matrix values (e.g. float or double).
MemorySpace	A memory space (e.g. cusp::host_memory or cusp::device_memory)

Overview

Given a matrix A to precondition, the smoothed aggregation preconditioner constructs a algebraic multigrid (AMG) operator.

Smoothed aggregation is expensive to use but is a very effective preconditioning technique to solve challenging linear systems. The default configuration uses a symmetric strength measure, MIS-based aggregation in device memory, sequential aggregation in host_memory, Jacobi smoothing is applied to the tentative prolongator, Jacobi relaxation on each level of hierarchy and LU to solve the coarse matrix in host memory.

Example

The following code snippet demonstrates how to use a smoothed_aggregation preconditioner to solve a linear system.

#include <cusp/csr_matrix.h>
#include <cusp/gallery/poisson.h>
#include <cusp/io/matrix_market.h>
#include <cusp/krylov/cg.h>
#include <cusp/precond/aggregation/smoothed_aggregation.h>

#include <iostream>

int main(int argc, char *argv[])
{
    typedef int                 IndexType;
    typedef double              ValueType;
    typedef cusp::device_memory MemorySpace;

    // create an empty sparse matrix structure
    cusp::hyb_matrix<IndexType, ValueType, MemorySpace> A;

    // construct 2d poisson matrix
    IndexType N = 256;
    cusp::gallery::poisson5pt(A, N, N);

    std::cout << "Generated matrix (poisson5pt) "
              << "with shape ("  << A.num_rows << "," << A.num_cols << ") and "
              << A.num_entries << " entries" << "\n";

    std::cout << "\nSolving with smoothed aggregation preconditioner and jacobi smoother" << std::endl;

    cusp::precond::aggregation::smoothed_aggregation<IndexType, ValueType, MemorySpace> M(A);

    // print AMG statistics
    M.print();

    // allocate storage for solution (x) and right hand side (b)
    cusp::array1d<ValueType, MemorySpace> x(A.num_rows, 0);
    cusp::array1d<ValueType, MemorySpace> b(A.num_rows, 1);

    // set stopping criteria (iteration_limit = 1000, relative_tolerance = 1e-10)
    cusp::monitor<ValueType> monitor(b, 1000, 1e-10);

    // solve
    cusp::krylov::cg(A, x, b, monitor, M);

    // report status
    monitor.print();

    return 0;
}

Examples:

custom_amg.cu, and smoothed_aggregation.cu.

Definition at line 160 of file smoothed_aggregation.h.

#include <smoothed_aggregation.h>

Inheritance diagram for cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >:

Public Methods
	smoothed_aggregation (void)
template<typename MatrixType >
	smoothed_aggregation (const MatrixType &A)
template<typename MatrixType , typename ArrayType >
	smoothed_aggregation (const MatrixType &A, const ArrayType &B, typename thrust::detail::enable_if_convertible< typename ArrayType::format, cusp::array1d_format >::type *=0)
template<typename MemorySpace2 , typename SmootherType2 , typename SolverType2 , typename Format2 >
	smoothed_aggregation (const smoothed_aggregation< IndexType, ValueType, MemorySpace2, SmootherType2, SolverType2, Format2 > &M)
template<typename MatrixType >
void	initialize (const MatrixType &A)
template<typename MatrixType , typename ArrayType >
void	initialize (const MatrixType &A, const ArrayType &B, typename thrust::detail::enable_if_convertible< typename MatrixType::format, cusp::known_format >::type *=0)

Constructor & Destructor Documentation

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::smoothed_aggregation ( void  )

inline

Construct an empty smoothed_aggregation preconditioner.

Definition at line 177 of file smoothed_aggregation.h.

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

template<typename MatrixType >

cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::smoothed_aggregation

(

const MatrixType &

A

)

Construct a smoothed_aggregation preconditioner from a matrix.

Parameters

A	matrix used to create the AMG hierarchy.

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

template<typename MatrixType , typename ArrayType >

cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::smoothed_aggregation	(	const MatrixType &	A,
		const ArrayType &	B,
		typename thrust::detail::enable_if_convertible< typename ArrayType::format, cusp::array1d_format >::type *	= 0
	)

Construct a smoothed_aggregation preconditioner from a matrix and specified near nullspace vector.

Parameters

A	matrix used to create the AMG hierarchy.
B	candidate near nullspace vector.

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

template<typename MemorySpace2 , typename SmootherType2 , typename SolverType2 , typename Format2 >

cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::smoothed_aggregation

(

const smoothed_aggregation< IndexType, ValueType, MemorySpace2, SmootherType2, SolverType2, Format2 > &

M

)

Construct a smoothed_aggregation preconditioner from a existing SA smoothed_aggregation preconditioner.

Parameters

M	other smoothed_aggregation preconditioner.

Member Function Documentation

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

template<typename MatrixType >

void cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::initialize

(

const MatrixType &

A

)

Initialize a smoothed_aggregation preconditioner from a matrix. Used to initialize a smoothed_aggregation preconditioner constructed with no input matrix specified.

Parameters

A	matrix used to create the AMG hierarchy.

template<typename IndexType, typename ValueType, typename MemorySpace, typename SmootherType = thrust::use_default, typename SolverType = thrust::use_default, typename Format = thrust::use_default>

template<typename MatrixType , typename ArrayType >

void cusp::precond::aggregation::smoothed_aggregation< IndexType, ValueType, MemorySpace, SmootherType, SolverType, Format >::initialize	(	const MatrixType &	A,
		const ArrayType &	B,
		typename thrust::detail::enable_if_convertible< typename MatrixType::format, cusp::known_format >::type *	= 0
	)

Initialize a smoothed_aggregation preconditioner from a matrix and initial near nullspace vector. Used to initialize a smoothed_aggregation preconditioner constructed with no input matrix specified.

Parameters

A	matrix used to create the AMG hierarchy.
B	candidate near nullspace vector.