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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/copy.h>
#include <cusp/array1d.h>
#include <cusp/convert.h>
#include <cusp/csr_matrix.h>
#include <cusp/detail/format_utils.h>
#include <thrust/count.h>
#include <thrust/functional.h>
#include <thrust/iterator/zip_iterator.h>
#include <thrust/iterator/permutation_iterator.h>
namespace cusp
{
namespace precond
{
namespace aggregation
{
namespace detail
{
template <typename ValueType>
__host__ __device__
ValueType absolute_value(const ValueType& x)
{
return (x < 0) ? -x : x;
}
////////////////
// Host Paths //
////////////////
template <typename Matrix1, typename Matrix2>
void symmetric_strength_of_connection(const Matrix1& A, Matrix2& S, const double theta,
cusp::csr_format, cusp::host_memory,
cusp::csr_format, cusp::host_memory)
{
typedef typename Matrix1::index_type IndexType;
typedef typename Matrix1::value_type ValueType;
// extract matrix diagonal
cusp::array1d<ValueType,cusp::host_memory> diagonal;
cusp::detail::extract_diagonal(A, diagonal);
IndexType num_entries = 0;
// count num_entries in output
for(size_t i = 0; i < A.num_rows; i++)
{
const ValueType Aii = diagonal[i];
for(IndexType jj = A.row_offsets[i]; jj < A.row_offsets[i + 1]; jj++)
{
const IndexType j = A.column_indices[jj];
const ValueType Aij = A.values[jj];
const ValueType Ajj = diagonal[j];
// |A(i,j)| >= theta * sqrt(|A(i,i)|*|A(j,j)|)
if(Aij*Aij >= (theta * theta) * absolute_value(Aii * Ajj))
num_entries++;
}
}
// resize output
S.resize(A.num_rows, A.num_cols, num_entries);
// reset counter for second pass
num_entries = 0;
// copy strong connections to output
for(size_t i = 0; i < A.num_rows; i++)
{
const ValueType Aii = diagonal[i];
S.row_offsets[i] = num_entries;
for(IndexType jj = A.row_offsets[i]; jj < A.row_offsets[i + 1]; jj++)
{
const IndexType j = A.column_indices[jj];
const ValueType Aij = A.values[jj];
const ValueType Ajj = diagonal[j];
// |A(i,j)| >= theta * sqrt(|A(i,i)|*|A(j,j)|)
if(Aij*Aij >= (theta * theta) * absolute_value(Aii * Ajj))
{
S.column_indices[num_entries] = j;
S.values[num_entries] = Aij;
num_entries++;
}
}
}
S.row_offsets[S.num_rows] = num_entries;
}
//////////////////
// Device Paths //
//////////////////
/* none for now */
///////////////////
// Generic Paths //
///////////////////
template <typename ValueType>
struct is_strong_connection
{
ValueType theta;
is_strong_connection(const ValueType theta) : theta(theta) {}
template <typename Tuple>
__host__ __device__
bool operator()(const Tuple& t) const
{
ValueType Aij = thrust::get<0>(t);
ValueType Aii = thrust::get<1>(t);
ValueType Ajj = thrust::get<2>(t);
// square everything to eliminate the sqrt()
return (Aij * Aij) >= (theta * theta) * absolute_value(Aii * Ajj);
}
};
template <typename Matrix1, typename Matrix2, typename MemorySpace>
void symmetric_strength_of_connection(const Matrix1& A, Matrix2& S, const double theta,
cusp::coo_format, MemorySpace,
cusp::coo_format, MemorySpace)
{
typedef typename Matrix1::index_type IndexType;
typedef typename Matrix1::value_type ValueType;
cusp::array1d<ValueType,MemorySpace> diagonal;
cusp::detail::extract_diagonal(A, diagonal);
is_strong_connection<ValueType> pred(theta);
// compute number of entries in output
IndexType num_entries = thrust::count_if
(thrust::make_zip_iterator(thrust::make_tuple
(A.values.begin(),
thrust::make_permutation_iterator(diagonal.begin(), A.row_indices.begin()),
thrust::make_permutation_iterator(diagonal.begin(), A.column_indices.begin()))),
thrust::make_zip_iterator(thrust::make_tuple
(A.values.begin(),
thrust::make_permutation_iterator(diagonal.begin(), A.row_indices.begin()),
thrust::make_permutation_iterator(diagonal.begin(), A.column_indices.begin()))) + A.num_entries,
pred);
// this is just zipping up (A[i,j],A[i,i],A[j,j]) and applying is_strong_connection to each tuple
// resize output
S.resize(A.num_rows, A.num_cols, num_entries);
// copy strong connections to output
thrust::copy_if(thrust::make_zip_iterator(thrust::make_tuple(A.row_indices.begin(), A.column_indices.begin(), A.values.begin())),
thrust::make_zip_iterator(thrust::make_tuple(A.row_indices.begin(), A.column_indices.begin(), A.values.begin())) + A.num_entries,
thrust::make_zip_iterator(thrust::make_tuple
(A.values.begin(),
thrust::make_permutation_iterator(diagonal.begin(), A.row_indices.begin()),
thrust::make_permutation_iterator(diagonal.begin(), A.column_indices.begin()))),
thrust::make_zip_iterator(thrust::make_tuple(S.row_indices.begin(), S.column_indices.begin(), S.values.begin())),
pred);
}
//////////////////
// Default Path //
//////////////////
template <typename Matrix1, typename Matrix2,
typename Format1, typename MemorySpace1,
typename Format2, typename MemorySpace2>
void symmetric_strength_of_connection(const Matrix1& A, Matrix2& S, const double theta,
Format1, MemorySpace1,
Format2, MemorySpace2)
{
typedef typename Matrix1::index_type IndexType1;
typedef typename Matrix1::value_type ValueType1;
typedef typename Matrix2::index_type IndexType2;
typedef typename Matrix2::value_type ValueType2;
// do everything on the host using the CSR format
cusp::csr_matrix<IndexType1,ValueType1,cusp::host_memory> A_csr(A);
cusp::csr_matrix<IndexType2,ValueType2,cusp::host_memory> S_csr;
cusp::precond::aggregation::symmetric_strength_of_connection(A_csr, S_csr, theta);
cusp::convert(S_csr, S);
}
} // end namepace detail
/////////////////
// Entry Point //
/////////////////
template <typename Matrix1, typename Matrix2>
void symmetric_strength_of_connection(const Matrix1& A, Matrix2& S, const double theta)
{
CUSP_PROFILE_SCOPED();
if (theta == 0.0)
{
// everything is a strong connection
cusp::copy(A,S);
}
else
{
// dispatch based on format and memory_space
detail::symmetric_strength_of_connection
(A, S, theta,
typename Matrix1::format(), typename Matrix1::memory_space(),
typename Matrix2::format(), typename Matrix2::memory_space());
}
}
} // end namespace aggregation
} // end namespace precond
} // end namespace cusp
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