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/*
* Copyright 2008-2009 NVIDIA Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <cusp/blas.h>
#include <cusp/multiply.h>
#include <cusp/monitor.h>
namespace cusp
{
template <typename MatrixType, typename SmootherType, typename SolverType>
template <typename MatrixType2, typename SmootherType2, typename SolverType2>
multilevel<MatrixType,SmootherType,SolverType>
::multilevel(const multilevel<MatrixType2,SmootherType2,SolverType2>& M)
: solver(M.solver)
{
for( size_t lvl = 0; lvl < M.levels.size(); lvl++ )
levels.push_back(M.levels[lvl]);
}
template <typename MatrixType, typename SmootherType, typename SolverType>
template <typename Array1, typename Array2>
void multilevel<MatrixType,SmootherType,SolverType>
::operator()(const Array1& b, Array2& x)
{
CUSP_PROFILE_SCOPED();
// perform 1 V-cycle
_solve(b, x, 0);
}
template <typename MatrixType, typename SmootherType, typename SolverType>
template <typename Array1, typename Array2>
void multilevel<MatrixType,SmootherType,SolverType>
::solve(const Array1& b, Array2& x)
{
CUSP_PROFILE_SCOPED();
cusp::default_monitor<ValueType> monitor(b);
solve(b, x, monitor);
}
template <typename MatrixType, typename SmootherType, typename SolverType>
template <typename Array1, typename Array2, typename Monitor>
void multilevel<MatrixType,SmootherType,SolverType>
::solve(const Array1& b, Array2& x, Monitor& monitor)
{
CUSP_PROFILE_SCOPED();
/* const MatrixType& A = levels[0].A; */
/* const size_t n = A.num_rows; */
const size_t n = levels[0].A.num_rows;
// use simple iteration
cusp::array1d<ValueType,MemorySpace> update(n);
cusp::array1d<ValueType,MemorySpace> residual(n);
// compute initial residual
/* cusp::multiply(A, x, residual); */
cusp::multiply(levels[0].A, x, residual);
cusp::blas::axpby(b, residual, residual, ValueType(1.0), ValueType(-1.0));
while(!monitor.finished(residual))
{
_solve(residual, update, 0);
// x += M * r
cusp::blas::axpy(update, x, ValueType(1.0));
// update residual
/* cusp::multiply(A, x, residual); */
cusp::multiply(levels[0].A, x, residual);
cusp::blas::axpby(b, residual, residual, ValueType(1.0), ValueType(-1.0));
++monitor;
}
}
template <typename MatrixType, typename SmootherType, typename SolverType>
template <typename Array1, typename Array2>
void multilevel<MatrixType,SmootherType,SolverType>
::_solve(const Array1& b, Array2& x, const size_t i)
{
CUSP_PROFILE_SCOPED();
if (i + 1 == levels.size())
{
// coarse grid solve
// TODO streamline
cusp::array1d<ValueType,cusp::host_memory> temp_b(b);
cusp::array1d<ValueType,cusp::host_memory> temp_x(x.size());
solver(temp_b, temp_x);
x = temp_x;
}
else
{
/* const MatrixType& A = levels[i].A; */
// presmooth
/* levels[i].smoother.presmooth(A, b, x); */
levels[i].smoother.presmooth(levels[i].A, b, x);
// compute residual <- b - A*x
/* cusp::multiply(A, x, levels[i].residual); */
cusp::multiply(levels[i].A, x, levels[i].residual);
cusp::blas::axpby(b, levels[i].residual, levels[i].residual, ValueType(1.0), ValueType(-1.0));
// restrict to coarse grid
cusp::multiply(levels[i].R, levels[i].residual, levels[i + 1].b);
// compute coarse grid solution
_solve(levels[i + 1].b, levels[i + 1].x, i + 1);
// apply coarse grid correction
cusp::multiply(levels[i].P, levels[i + 1].x, levels[i].residual);
cusp::blas::axpy(levels[i].residual, x, ValueType(1.0));
// postsmooth
/* levels[i].smoother.postsmooth(A, b, x); */
levels[i].smoother.postsmooth(levels[i].A, b, x);
}
}
template <typename MatrixType, typename SmootherType, typename SolverType>
void multilevel<MatrixType,SmootherType,SolverType>
::print( void )
{
size_t num_levels = levels.size();
std::cout << "\tNumber of Levels:\t" << num_levels << std::endl;
std::cout << "\tOperator Complexity:\t" << operator_complexity() << std::endl;
std::cout << "\tGrid Complexity:\t" << grid_complexity() << std::endl;
std::cout << "\tlevel\tunknowns\tnonzeros:\t" << std::endl;
double nnz = 0;
for(size_t index = 0; index < num_levels; index++)
nnz += levels[index].A.num_entries;
for(size_t index = 0; index < num_levels; index++)
{
double percent = levels[index].A.num_entries / nnz;
std::cout << "\t" << index << "\t" << levels[index].A.num_cols << "\t\t" \
<< levels[index].A.num_entries << " \t[" << 100*percent << "%]" \
<< std::endl;
}
}
template <typename MatrixType, typename SmootherType, typename SolverType>
double multilevel<MatrixType,SmootherType,SolverType>
::operator_complexity( void )
{
size_t nnz = 0;
for(size_t index = 0; index < levels.size(); index++)
nnz += levels[index].A.num_entries;
return (double) nnz / (double) levels[0].A.num_entries;
}
template <typename MatrixType, typename SmootherType, typename SolverType>
double multilevel<MatrixType,SmootherType,SolverType>
::grid_complexity( void )
{
size_t unknowns = 0;
for(size_t index = 0; index < levels.size(); index++)
unknowns += levels[index].A.num_rows;
return (double) unknowns / (double) levels[0].A.num_rows;
}
} // end namespace cusp
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