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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/coo_matrix.h>
#include <cusp/csr_matrix.h>
#include <cusp/elementwise.h>
#include <cusp/detail/spectral_radius.h>
#include <thrust/extrema.h>
#include <thrust/fill.h>
#include <thrust/gather.h>
#include <thrust/transform.h>
#include <thrust/reduce.h>
#include <thrust/iterator/zip_iterator.h>
#include <thrust/iterator/constant_iterator.h>
#include <thrust/iterator/counting_iterator.h>
namespace cusp
{
namespace precond
{
namespace aggregation
{
namespace detail
{
using namespace thrust::placeholders;
template <typename MatrixType, typename ValueType>
void smooth_prolongator(const MatrixType& S,
const MatrixType& T,
MatrixType& P,
const ValueType omega,
const ValueType rho_Dinv_S,
cusp::coo_format,
cusp::device_memory)
{
CUSP_PROFILE_SCOPED();
typedef typename MatrixType::index_type IndexType;
// TODO handle case with unaggregated nodes more gracefully
if (T.num_entries == T.num_rows) {
const ValueType lambda = omega / rho_Dinv_S;
// temp <- -lambda * S(i,j) * T(j,k)
MatrixType temp(S.num_rows, T.num_cols, S.num_entries + T.num_entries);
thrust::copy(S.row_indices.begin(), S.row_indices.end(), temp.row_indices.begin());
thrust::gather(S.column_indices.begin(), S.column_indices.end(), T.column_indices.begin(), temp.column_indices.begin());
thrust::transform(S.values.begin(), S.values.end(),
thrust::make_permutation_iterator(T.values.begin(), S.column_indices.begin()),
temp.values.begin(),
-lambda * _1 * _2);
// temp <- D^-1
{
cusp::array1d<ValueType, cusp::device_memory> D(S.num_rows);
cusp::detail::extract_diagonal(S, D);
thrust::transform(temp.values.begin(), temp.values.begin() + S.num_entries,
thrust::make_permutation_iterator(D.begin(), S.row_indices.begin()),
temp.values.begin(),
thrust::divides<ValueType>());
}
// temp <- temp + T
thrust::copy(T.row_indices.begin(), T.row_indices.end(), temp.row_indices.begin() + S.num_entries);
thrust::copy(T.column_indices.begin(), T.column_indices.end(), temp.column_indices.begin() + S.num_entries);
thrust::copy(T.values.begin(), T.values.end(), temp.values.begin() + S.num_entries);
// sort by (I,J)
cusp::detail::sort_by_row_and_column(temp.row_indices, temp.column_indices, temp.values);
// compute unique number of nonzeros in the output
// throws a warning at compile (warning: expression has no effect)
IndexType NNZ = thrust::inner_product(thrust::make_zip_iterator(thrust::make_tuple(temp.row_indices.begin(), temp.column_indices.begin())),
thrust::make_zip_iterator(thrust::make_tuple(temp.row_indices.end (), temp.column_indices.end())) - 1,
thrust::make_zip_iterator(thrust::make_tuple(temp.row_indices.begin(), temp.column_indices.begin())) + 1,
IndexType(0),
thrust::plus<IndexType>(),
thrust::not_equal_to< thrust::tuple<IndexType,IndexType> >()) + 1;
// allocate space for output
P.resize(temp.num_rows, temp.num_cols, NNZ);
// sum values with the same (i,j)
thrust::reduce_by_key(thrust::make_zip_iterator(thrust::make_tuple(temp.row_indices.begin(), temp.column_indices.begin())),
thrust::make_zip_iterator(thrust::make_tuple(temp.row_indices.end(), temp.column_indices.end())),
temp.values.begin(),
thrust::make_zip_iterator(thrust::make_tuple(P.row_indices.begin(), P.column_indices.begin())),
P.values.begin(),
thrust::equal_to< thrust::tuple<IndexType,IndexType> >(),
thrust::plus<ValueType>());
} else {
cusp::array1d<ValueType, cusp::device_memory> D(S.num_rows);
cusp::detail::extract_diagonal(S, D);
// create D_inv_S by copying S then scaling
MatrixType D_inv_S(S);
// scale the rows of D_inv_S by D^-1
thrust::transform(D_inv_S.values.begin(), D_inv_S.values.begin() + S.num_entries,
thrust::make_permutation_iterator(D.begin(), S.row_indices.begin()),
D_inv_S.values.begin(),
thrust::divides<ValueType>());
const ValueType lambda = omega / rho_Dinv_S;
cusp::blas::scal( D_inv_S.values, lambda );
MatrixType temp;
cusp::multiply( D_inv_S, T, temp );
cusp::subtract( T, temp, P );
}
}
template <typename MatrixType, typename ValueType>
void smooth_prolongator(const MatrixType& S,
const MatrixType& T,
MatrixType& P,
const ValueType omega,
const ValueType rho_Dinv_S,
cusp::csr_format,
cusp::host_memory)
{
CUSP_PROFILE_SCOPED();
typedef typename MatrixType::index_type IndexType;
cusp::array1d<ValueType, cusp::host_memory> D(S.num_rows);
cusp::detail::extract_diagonal(S, D);
// create D_inv_S by copying S then scaling
MatrixType D_inv_S(S);
// scale the rows of D_inv_S by D^-1
for ( size_t row = 0; row < D_inv_S.num_rows; row++ )
{
const IndexType row_start = D_inv_S.row_offsets[row];
const IndexType row_end = D_inv_S.row_offsets[row+1];
const ValueType diagonal = D[row];
for ( IndexType index = row_start; index < row_end; index++ )
D_inv_S.values[index] /= diagonal;
}
const ValueType lambda = omega / rho_Dinv_S;
cusp::blas::scal( D_inv_S.values, lambda );
MatrixType temp;
cusp::multiply( D_inv_S, T, temp );
cusp::subtract( T, temp, P );
}
} // end namespace detail
template <typename MatrixType, typename ValueType>
void smooth_prolongator(const MatrixType& S,
const MatrixType& T,
MatrixType& P,
const ValueType omega,
const ValueType rho_Dinv_S)
{
detail::smooth_prolongator(S, T, P, omega, rho_Dinv_S, typename MatrixType::format(), typename MatrixType::memory_space());
}
} // end namespace aggregation
} // end namespace precond
} // end namespace cusp
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