/usr/include/viennacl/linalg/amg.hpp is in libviennacl-dev 1.5.1-1.
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#define VIENNACL_LINALG_AMG_HPP_
/* =========================================================================
Copyright (c) 2010-2014, Institute for Microelectronics,
Institute for Analysis and Scientific Computing,
TU Wien.
Portions of this software are copyright by UChicago Argonne, LLC.
-----------------
ViennaCL - The Vienna Computing Library
-----------------
Project Head: Karl Rupp rupp@iue.tuwien.ac.at
(A list of authors and contributors can be found in the PDF manual)
License: MIT (X11), see file LICENSE in the base directory
============================================================================= */
/** @file viennacl/linalg/amg.hpp
@brief Main include file for algebraic multigrid (AMG) preconditioners. Experimental.
Implementation contributed by Markus Wagner
*/
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <vector>
#include <cmath>
#include "viennacl/forwards.h"
#include "viennacl/tools/tools.hpp"
#include "viennacl/linalg/prod.hpp"
#include "viennacl/linalg/direct_solve.hpp"
#include "viennacl/linalg/detail/amg/amg_base.hpp"
#include "viennacl/linalg/detail/amg/amg_coarse.hpp"
#include "viennacl/linalg/detail/amg/amg_interpol.hpp"
#include <map>
#ifdef VIENNACL_WITH_OPENMP
#include <omp.h>
#endif
#include "viennacl/linalg/detail/amg/amg_debug.hpp"
#define VIENNACL_AMG_COARSE_LIMIT 50
#define VIENNACL_AMG_MAX_LEVELS 100
namespace viennacl
{
namespace linalg
{
typedef detail::amg::amg_tag amg_tag;
/** @brief Setup AMG preconditioner
*
* @param A Operator matrices on all levels
* @param P Prolongation/Interpolation operators on all levels
* @param Pointvector Vector of points on all levels
* @param tag AMG preconditioner tag
*/
template <typename InternalType1, typename InternalType2>
void amg_setup(InternalType1 & A, InternalType1 & P, InternalType2 & Pointvector, amg_tag & tag)
{
typedef typename InternalType2::value_type PointVectorType;
unsigned int i, iterations, c_points, f_points;
detail::amg::amg_slicing<InternalType1,InternalType2> Slicing;
// Set number of iterations. If automatic coarse grid construction is chosen (0), then set a maximum size and stop during the process.
iterations = tag.get_coarselevels();
if (iterations == 0)
iterations = VIENNACL_AMG_MAX_LEVELS;
// For parallel coarsenings build data structures (number of threads set automatically).
if (tag.get_coarse() == VIENNACL_AMG_COARSE_RS0 || tag.get_coarse() == VIENNACL_AMG_COARSE_RS3)
Slicing.init(iterations);
for (i=0; i<iterations; ++i)
{
// Initialize Pointvector on level i and construct points.
Pointvector[i] = PointVectorType(static_cast<unsigned int>(A[i].size1()));
Pointvector[i].init_points();
// Construct C and F points on coarse level (i is fine level, i+1 coarse level).
detail::amg::amg_coarse (i, A, Pointvector, Slicing, tag);
// Calculate number of C and F points on level i.
c_points = Pointvector[i].get_cpoints();
f_points = Pointvector[i].get_fpoints();
#if defined (VIENNACL_AMG_DEBUG) //or defined(VIENNACL_AMG_DEBUGBENCH)
std::cout << "Level " << i << ": ";
std::cout << "No of C points = " << c_points << ", ";
std::cout << "No of F points = " << f_points << std::endl;
#endif
// Stop routine when the maximal coarse level is found (no C or F point). Coarsest level is level i.
if (c_points == 0 || f_points == 0)
break;
// Construct interpolation matrix for level i.
detail::amg::amg_interpol (i, A, P, Pointvector, tag);
// Compute coarse grid operator (A[i+1] = R * A[i] * P) with R = trans(P).
detail::amg::amg_galerkin_prod(A[i], P[i], A[i+1]);
// Test triple matrix product. Very slow for large matrix sizes (ublas).
// test_triplematprod(A[i],P[i],A[i+1]);
Pointvector[i].delete_points();
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Coarse Grid Operator Matrix:" << std::endl;
printmatrix (A[i+1]);
#endif
// If Limit of coarse points is reached then stop. Coarsest level is level i+1.
if (tag.get_coarselevels() == 0 && c_points <= VIENNACL_AMG_COARSE_LIMIT)
{
tag.set_coarselevels(i+1);
return;
}
}
tag.set_coarselevels(i);
}
/** @brief Initialize AMG preconditioner
*
* @param mat System matrix
* @param A Operator matrices on all levels
* @param P Prolongation/Interpolation operators on all levels
* @param Pointvector Vector of points on all levels
* @param tag AMG preconditioner tag
*/
template <typename MatrixType, typename InternalType1, typename InternalType2>
void amg_init(MatrixType const & mat, InternalType1 & A, InternalType1 & P, InternalType2 & Pointvector, amg_tag & tag)
{
//typedef typename MatrixType::value_type ScalarType;
typedef typename InternalType1::value_type SparseMatrixType;
if (tag.get_coarselevels() > 0)
{
A.resize(tag.get_coarselevels()+1);
P.resize(tag.get_coarselevels());
Pointvector.resize(tag.get_coarselevels());
}
else
{
A.resize(VIENNACL_AMG_MAX_LEVELS+1);
P.resize(VIENNACL_AMG_MAX_LEVELS);
Pointvector.resize(VIENNACL_AMG_MAX_LEVELS);
}
// Insert operator matrix as operator for finest level.
SparseMatrixType A0 (mat);
A.insert_element (0, A0);
}
/** @brief Save operators after setup phase for CPU computation.
*
* @param A Operator matrices on all levels on the CPU
* @param P Prolongation/Interpolation operators on all levels on the CPU
* @param R Restriction operators on all levels on the CPU
* @param A_setup Operators matrices on all levels from setup phase
* @param P_setup Prolongation/Interpolation operators on all levels from setup phase
* @param tag AMG preconditioner tag
*/
template <typename InternalType1, typename InternalType2>
void amg_transform_cpu (InternalType1 & A, InternalType1 & P, InternalType1 & R, InternalType2 & A_setup, InternalType2 & P_setup, amg_tag & tag)
{
//typedef typename InternalType1::value_type MatrixType;
// Resize internal data structures to actual size.
A.resize(tag.get_coarselevels()+1);
P.resize(tag.get_coarselevels());
R.resize(tag.get_coarselevels());
// Transform into matrix type.
for (unsigned int i=0; i<tag.get_coarselevels()+1; ++i)
{
A[i].resize(A_setup[i].size1(),A_setup[i].size2(),false);
A[i] = A_setup[i];
}
for (unsigned int i=0; i<tag.get_coarselevels(); ++i)
{
P[i].resize(P_setup[i].size1(),P_setup[i].size2(),false);
P[i] = P_setup[i];
}
for (unsigned int i=0; i<tag.get_coarselevels(); ++i)
{
R[i].resize(P_setup[i].size2(),P_setup[i].size1(),false);
P_setup[i].set_trans(true);
R[i] = P_setup[i];
P_setup[i].set_trans(false);
}
}
/** @brief Save operators after setup phase for GPU computation.
*
* @param A Operator matrices on all levels on the GPU
* @param P Prolongation/Interpolation operators on all levels on the GPU
* @param R Restriction operators on all levels on the GPU
* @param A_setup Operators matrices on all levels from setup phase
* @param P_setup Prolongation/Interpolation operators on all levels from setup phase
* @param tag AMG preconditioner tag
* @param ctx Optional context in which the auxiliary objects are created (one out of multiple OpenCL contexts, CUDA, host)
*/
template <typename InternalType1, typename InternalType2>
void amg_transform_gpu (InternalType1 & A, InternalType1 & P, InternalType1 & R, InternalType2 & A_setup, InternalType2 & P_setup, amg_tag & tag, viennacl::context ctx)
{
// Resize internal data structures to actual size.
A.resize(tag.get_coarselevels()+1);
P.resize(tag.get_coarselevels());
R.resize(tag.get_coarselevels());
// Copy to GPU using the internal sparse matrix structure: std::vector<std::map>.
for (unsigned int i=0; i<tag.get_coarselevels()+1; ++i)
{
viennacl::switch_memory_context(A[i], ctx);
//A[i].resize(A_setup[i].size1(),A_setup[i].size2(),false);
viennacl::copy(*(A_setup[i].get_internal_pointer()),A[i]);
}
for (unsigned int i=0; i<tag.get_coarselevels(); ++i)
{
viennacl::switch_memory_context(P[i], ctx);
//P[i].resize(P_setup[i].size1(),P_setup[i].size2(),false);
viennacl::copy(*(P_setup[i].get_internal_pointer()),P[i]);
//viennacl::copy((boost::numeric::ublas::compressed_matrix<ScalarType>)P_setup[i],P[i]);
}
for (unsigned int i=0; i<tag.get_coarselevels(); ++i)
{
viennacl::switch_memory_context(R[i], ctx);
//R[i].resize(P_setup[i].size2(),P_setup[i].size1(),false);
P_setup[i].set_trans(true);
viennacl::copy(*(P_setup[i].get_internal_pointer()),R[i]);
P_setup[i].set_trans(false);
}
}
/** @brief Setup data structures for precondition phase.
*
* @param result Result vector on all levels
* @param rhs RHS vector on all levels
* @param residual Residual vector on all levels
* @param A Operators matrices on all levels from setup phase
* @param tag AMG preconditioner tag
*/
template <typename InternalVectorType, typename SparseMatrixType>
void amg_setup_apply (InternalVectorType & result, InternalVectorType & rhs, InternalVectorType & residual, SparseMatrixType const & A, amg_tag const & tag)
{
typedef typename InternalVectorType::value_type VectorType;
result.resize(tag.get_coarselevels()+1);
rhs.resize(tag.get_coarselevels()+1);
residual.resize(tag.get_coarselevels());
for (unsigned int level=0; level < tag.get_coarselevels()+1; ++level)
{
result[level] = VectorType(A[level].size1());
result[level].clear();
rhs[level] = VectorType(A[level].size1());
rhs[level].clear();
}
for (unsigned int level=0; level < tag.get_coarselevels(); ++level)
{
residual[level] = VectorType(A[level].size1());
residual[level].clear();
}
}
/** @brief Setup data structures for precondition phase for later use on the GPU
*
* @param result Result vector on all levels
* @param rhs RHS vector on all levels
* @param residual Residual vector on all levels
* @param A Operators matrices on all levels from setup phase
* @param tag AMG preconditioner tag
* @param ctx Optional context in which the auxiliary objects are created (one out of multiple OpenCL contexts, CUDA, host)
*/
template <typename InternalVectorType, typename SparseMatrixType>
void amg_setup_apply (InternalVectorType & result, InternalVectorType & rhs, InternalVectorType & residual, SparseMatrixType const & A, amg_tag const & tag, viennacl::context ctx)
{
typedef typename InternalVectorType::value_type VectorType;
result.resize(tag.get_coarselevels()+1);
rhs.resize(tag.get_coarselevels()+1);
residual.resize(tag.get_coarselevels());
for (unsigned int level=0; level < tag.get_coarselevels()+1; ++level)
{
result[level] = VectorType(A[level].size1(), ctx);
rhs[level] = VectorType(A[level].size1(), ctx);
}
for (unsigned int level=0; level < tag.get_coarselevels(); ++level)
{
residual[level] = VectorType(A[level].size1(), ctx);
}
}
/** @brief Pre-compute LU factorization for direct solve (ublas library).
* @brief Speeds up precondition phase as this is computed only once overall instead of once per iteration.
*
* @param op Operator matrix for direct solve
* @param Permutation Permutation matrix which saves the factorization result
* @param A Operator matrix on coarsest level
*/
template <typename ScalarType, typename SparseMatrixType>
void amg_lu(boost::numeric::ublas::compressed_matrix<ScalarType> & op, boost::numeric::ublas::permutation_matrix<> & Permutation, SparseMatrixType const & A)
{
typedef typename SparseMatrixType::const_iterator1 ConstRowIterator;
typedef typename SparseMatrixType::const_iterator2 ConstColIterator;
// Copy to operator matrix. Needed
op.resize(A.size1(),A.size2(),false);
for (ConstRowIterator row_iter = A.begin1(); row_iter != A.end1(); ++row_iter)
for (ConstColIterator col_iter = row_iter.begin(); col_iter != row_iter.end(); ++col_iter)
op (col_iter.index1(), col_iter.index2()) = *col_iter;
// Permutation matrix has to be reinitialized with actual size. Do not clear() or resize()!
Permutation = boost::numeric::ublas::permutation_matrix<> (op.size1());
boost::numeric::ublas::lu_factorize(op,Permutation);
}
/** @brief AMG preconditioner class, can be supplied to solve()-routines
*/
template <typename MatrixType>
class amg_precond
{
typedef typename MatrixType::value_type ScalarType;
typedef boost::numeric::ublas::vector<ScalarType> VectorType;
typedef detail::amg::amg_sparsematrix<ScalarType> SparseMatrixType;
typedef detail::amg::amg_pointvector PointVectorType;
typedef typename SparseMatrixType::const_iterator1 InternalConstRowIterator;
typedef typename SparseMatrixType::const_iterator2 InternalConstColIterator;
typedef typename SparseMatrixType::iterator1 InternalRowIterator;
typedef typename SparseMatrixType::iterator2 InternalColIterator;
boost::numeric::ublas::vector <SparseMatrixType> A_setup;
boost::numeric::ublas::vector <SparseMatrixType> P_setup;
boost::numeric::ublas::vector <MatrixType> A;
boost::numeric::ublas::vector <MatrixType> P;
boost::numeric::ublas::vector <MatrixType> R;
boost::numeric::ublas::vector <PointVectorType> Pointvector;
mutable boost::numeric::ublas::compressed_matrix<ScalarType> op;
mutable boost::numeric::ublas::permutation_matrix<> Permutation;
mutable boost::numeric::ublas::vector <VectorType> result;
mutable boost::numeric::ublas::vector <VectorType> rhs;
mutable boost::numeric::ublas::vector <VectorType> residual;
mutable bool done_init_apply;
amg_tag tag_;
public:
amg_precond(): Permutation(0) {}
/** @brief The constructor. Saves system matrix, tag and builds data structures for setup.
*
* @param mat System matrix
* @param tag The AMG tag
*/
amg_precond(MatrixType const & mat, amg_tag const & tag): Permutation(0)
{
tag_ = tag;
// Initialize data structures.
amg_init (mat,A_setup,P_setup,Pointvector,tag_);
done_init_apply = false;
}
/** @brief Start setup phase for this class and copy data structures.
*/
void setup()
{
// Start setup phase.
amg_setup(A_setup,P_setup,Pointvector,tag_);
// Transform to CPU-Matrixtype for precondition phase.
amg_transform_cpu(A,P,R,A_setup,P_setup,tag_);
done_init_apply = false;
}
/** @brief Prepare data structures for preconditioning:
* Build data structures for precondition phase.
* Do LU factorization on coarsest level.
*/
void init_apply() const
{
// Setup precondition phase (Data structures).
amg_setup_apply(result,rhs,residual,A_setup,tag_);
// Do LU factorization for direct solve.
amg_lu(op,Permutation,A_setup[tag_.get_coarselevels()]);
done_init_apply = true;
}
/** @brief Returns complexity measures.
*
* @param avgstencil Average stencil sizes on all levels
* @return Operator complexity of AMG method
*/
template <typename VectorType>
ScalarType calc_complexity(VectorType & avgstencil)
{
avgstencil = VectorType (tag_.get_coarselevels()+1);
unsigned int nonzero=0, systemmat_nonzero=0, level_coefficients=0;
for (unsigned int level=0; level < tag_.get_coarselevels()+1; ++level)
{
level_coefficients = 0;
for (InternalRowIterator row_iter = A_setup[level].begin1(); row_iter != A_setup[level].end1(); ++row_iter)
{
for (InternalColIterator col_iter = row_iter.begin(); col_iter != row_iter.end(); ++col_iter)
{
if (level == 0)
systemmat_nonzero++;
nonzero++;
level_coefficients++;
}
}
avgstencil[level] = level_coefficients/static_cast<ScalarType>(A_setup[level].size1());
}
return nonzero/static_cast<ScalarType>(systemmat_nonzero);
}
/** @brief Precondition Operation
*
* @param vec The vector to which preconditioning is applied to (ublas version)
*/
template <typename VectorType>
void apply(VectorType & vec) const
{
// Build data structures and do lu factorization before first iteration step.
if (!done_init_apply)
init_apply();
int level;
// Precondition operation (Yang, p.3)
rhs[0] = vec;
for (level=0; level <static_cast<int>(tag_.get_coarselevels()); level++)
{
result[level].clear();
// Apply Smoother presmooth_ times.
smooth_jacobi (level, tag_.get_presmooth(), result[level], rhs[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After presmooth:" << std::endl;
printvector(result[level]);
#endif
// Compute residual.
residual[level] = rhs[level] - boost::numeric::ublas::prod (A[level],result[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Residual:" << std::endl;
printvector(residual[level]);
#endif
// Restrict to coarse level. Restricted residual is RHS of coarse level.
rhs[level+1] = boost::numeric::ublas::prod (R[level],residual[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Restricted Residual: " << std::endl;
printvector(rhs[level+1]);
#endif
}
// On highest level use direct solve to solve equation.
result[level] = rhs[level];
boost::numeric::ublas::lu_substitute(op,Permutation,result[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After direct solve: " << std::endl;
printvector (result[level]);
#endif
for (level=tag_.get_coarselevels()-1; level >= 0; level--)
{
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Coarse Error: " << std::endl;
printvector(result[level+1]);
#endif
// Interpolate error to fine level. Correct solution by adding error.
result[level] += boost::numeric::ublas::prod (P[level], result[level+1]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Corrected Result: " << std::endl;
printvector (result[level]);
#endif
// Apply Smoother postsmooth_ times.
smooth_jacobi (level, tag_.get_postsmooth(), result[level], rhs[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After postsmooth: " << std::endl;
printvector (result[level]);
#endif
}
vec = result[0];
}
/** @brief (Weighted) Jacobi Smoother (CPU version)
* @param level Coarse level to which smoother is applied to
* @param iterations Number of smoother iterations
* @param x The vector smoothing is applied to
* @param rhs The right hand side of the equation for the smoother
*/
template <typename VectorType>
void smooth_jacobi(int level, int const iterations, VectorType & x, VectorType const & rhs) const
{
VectorType old_result (x.size());
long index;
ScalarType sum = 0, diag = 1;
for (int i=0; i<iterations; ++i)
{
old_result = x;
x.clear();
#ifdef VIENNACL_WITH_OPENMP
#pragma omp parallel for private (sum,diag) shared (rhs,x)
#endif
for (index=0; index < static_cast<long>(A_setup[level].size1()); ++index)
{
InternalConstRowIterator row_iter = A_setup[level].begin1();
row_iter += index;
sum = 0;
diag = 1;
for (InternalConstColIterator col_iter = row_iter.begin(); col_iter != row_iter.end(); ++col_iter)
{
if (col_iter.index1() == col_iter.index2())
diag = *col_iter;
else
sum += *col_iter * old_result[col_iter.index2()];
}
x[index]= static_cast<ScalarType>(tag_.get_jacobiweight()) * (rhs[index] - sum) / diag + (1-static_cast<ScalarType>(tag_.get_jacobiweight())) * old_result[index];
}
}
}
amg_tag & tag() { return tag_; }
};
/** @brief AMG preconditioner class, can be supplied to solve()-routines.
*
* Specialization for compressed_matrix
*/
template <typename ScalarType, unsigned int MAT_ALIGNMENT>
class amg_precond< compressed_matrix<ScalarType, MAT_ALIGNMENT> >
{
typedef viennacl::compressed_matrix<ScalarType, MAT_ALIGNMENT> MatrixType;
typedef viennacl::vector<ScalarType> VectorType;
typedef detail::amg::amg_sparsematrix<ScalarType> SparseMatrixType;
typedef detail::amg::amg_pointvector PointVectorType;
typedef typename SparseMatrixType::const_iterator1 InternalConstRowIterator;
typedef typename SparseMatrixType::const_iterator2 InternalConstColIterator;
typedef typename SparseMatrixType::iterator1 InternalRowIterator;
typedef typename SparseMatrixType::iterator2 InternalColIterator;
boost::numeric::ublas::vector <SparseMatrixType> A_setup;
boost::numeric::ublas::vector <SparseMatrixType> P_setup;
boost::numeric::ublas::vector <MatrixType> A;
boost::numeric::ublas::vector <MatrixType> P;
boost::numeric::ublas::vector <MatrixType> R;
boost::numeric::ublas::vector <PointVectorType> Pointvector;
mutable boost::numeric::ublas::compressed_matrix<ScalarType> op;
mutable boost::numeric::ublas::permutation_matrix<> Permutation;
mutable boost::numeric::ublas::vector <VectorType> result;
mutable boost::numeric::ublas::vector <VectorType> rhs;
mutable boost::numeric::ublas::vector <VectorType> residual;
viennacl::context ctx_;
mutable bool done_init_apply;
amg_tag tag_;
public:
amg_precond(): Permutation(0) {}
/** @brief The constructor. Builds data structures.
*
* @param mat System matrix
* @param tag The AMG tag
*/
amg_precond(compressed_matrix<ScalarType, MAT_ALIGNMENT> const & mat, amg_tag const & tag): Permutation(0), ctx_(viennacl::traits::context(mat))
{
tag_ = tag;
// Copy to CPU. Internal structure of sparse matrix is used for copy operation.
std::vector<std::map<unsigned int, ScalarType> > mat2 = std::vector<std::map<unsigned int, ScalarType> >(mat.size1());
viennacl::copy(mat, mat2);
// Initialize data structures.
amg_init (mat2,A_setup,P_setup,Pointvector,tag_);
done_init_apply = false;
}
/** @brief Start setup phase for this class and copy data structures.
*/
void setup()
{
// Start setup phase.
amg_setup(A_setup,P_setup,Pointvector, tag_);
// Transform to GPU-Matrixtype for precondition phase.
amg_transform_gpu(A,P,R,A_setup,P_setup, tag_, ctx_);
done_init_apply = false;
}
/** @brief Prepare data structures for preconditioning:
* Build data structures for precondition phase.
* Do LU factorization on coarsest level.
*/
void init_apply() const
{
// Setup precondition phase (Data structures).
amg_setup_apply(result,rhs,residual,A_setup,tag_, ctx_);
// Do LU factorization for direct solve.
amg_lu(op,Permutation,A_setup[tag_.get_coarselevels()]);
done_init_apply = true;
}
/** @brief Returns complexity measures
*
* @param avgstencil Average stencil sizes on all levels
* @return Operator complexity of AMG method
*/
template <typename VectorType>
ScalarType calc_complexity(VectorType & avgstencil)
{
avgstencil = VectorType (tag_.get_coarselevels()+1);
unsigned int nonzero=0, systemmat_nonzero=0, level_coefficients=0;
for (unsigned int level=0; level < tag_.get_coarselevels()+1; ++level)
{
level_coefficients = 0;
for (InternalRowIterator row_iter = A_setup[level].begin1(); row_iter != A_setup[level].end1(); ++row_iter)
{
for (InternalColIterator col_iter = row_iter.begin(); col_iter != row_iter.end(); ++col_iter)
{
if (level == 0)
systemmat_nonzero++;
nonzero++;
level_coefficients++;
}
}
avgstencil[level] = level_coefficients/(double)A[level].size1();
}
return nonzero/static_cast<double>(systemmat_nonzero);
}
/** @brief Precondition Operation
*
* @param vec The vector to which preconditioning is applied to
*/
template <typename VectorType>
void apply(VectorType & vec) const
{
if (!done_init_apply)
init_apply();
int level;
// Precondition operation (Yang, p.3).
rhs[0] = vec;
for (level=0; level <static_cast<int>(tag_.get_coarselevels()); level++)
{
result[level].clear();
// Apply Smoother presmooth_ times.
smooth_jacobi (level, tag_.get_presmooth(), result[level], rhs[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After presmooth: " << std::endl;
printvector(result[level]);
#endif
// Compute residual.
//residual[level] = rhs[level] - viennacl::linalg::prod (A[level],result[level]);
residual[level] = viennacl::linalg::prod (A[level],result[level]);
residual[level] = rhs[level] - residual[level];
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Residual: " << std::endl;
printvector(residual[level]);
#endif
// Restrict to coarse level. Result is RHS of coarse level equation.
//residual_coarse[level] = viennacl::linalg::prod(R[level],residual[level]);
rhs[level+1] = viennacl::linalg::prod(R[level],residual[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Restricted Residual: " << std::endl;
printvector(rhs[level+1]);
#endif
}
// On highest level use direct solve to solve equation (on the CPU)
//TODO: Use GPU direct solve!
result[level] = rhs[level];
boost::numeric::ublas::vector <ScalarType> result_cpu (result[level].size());
copy (result[level],result_cpu);
boost::numeric::ublas::lu_substitute(op,Permutation,result_cpu);
copy (result_cpu, result[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After direct solve: " << std::endl;
printvector (result[level]);
#endif
for (level=tag_.get_coarselevels()-1; level >= 0; level--)
{
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Coarse Error: " << std::endl;
printvector(result[level+1]);
#endif
// Interpolate error to fine level and correct solution.
result[level] += viennacl::linalg::prod(P[level],result[level+1]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "Corrected Result: " << std::endl;
printvector (result[level]);
#endif
// Apply Smoother postsmooth_ times.
smooth_jacobi (level, tag_.get_postsmooth(), result[level], rhs[level]);
#ifdef VIENNACL_AMG_DEBUG
std::cout << "After postsmooth: " << std::endl;
printvector (result[level]);
#endif
}
vec = result[0];
}
/** @brief Jacobi Smoother (GPU version)
* @param level Coarse level to which smoother is applied to
* @param iterations Number of smoother iterations
* @param x The vector smoothing is applied to
* @param rhs The right hand side of the equation for the smoother
*/
template <typename VectorType>
void smooth_jacobi(int level, unsigned int iterations, VectorType & x, VectorType const & rhs) const
{
VectorType old_result = x;
viennacl::ocl::context & ctx = const_cast<viennacl::ocl::context &>(viennacl::traits::opencl_handle(x).context());
viennacl::linalg::opencl::kernels::compressed_matrix<ScalarType>::init(ctx);
viennacl::ocl::kernel & k = ctx.get_kernel(viennacl::linalg::opencl::kernels::compressed_matrix<ScalarType>::program_name(), "jacobi");
for (unsigned int i=0; i<iterations; ++i)
{
if (i > 0)
old_result = x;
x.clear();
viennacl::ocl::enqueue(k(A[level].handle1().opencl_handle(), A[level].handle2().opencl_handle(), A[level].handle().opencl_handle(),
static_cast<ScalarType>(tag_.get_jacobiweight()),
viennacl::traits::opencl_handle(old_result),
viennacl::traits::opencl_handle(x),
viennacl::traits::opencl_handle(rhs),
static_cast<cl_uint>(rhs.size())));
}
}
amg_tag & tag() { return tag_; }
};
}
}
#endif
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