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/*
* Copyright 2008-2010 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.
*/
/*! \file ainv.h
* \brief Approximate Inverse (AINV) preconditioner.
*/
#pragma once
#include <cusp/detail/config.h>
#include <cusp/linear_operator.h>
#include <cusp/hyb_matrix.h>
namespace cusp
{
namespace precond
{
/*! \addtogroup preconditioners Preconditioners
* \ingroup preconditioners
* \{
*/
/*! \p scaled_bridson_ainv : Approximate Inverse preconditoner (from Bridson's "outer product" formulation)
* The diagonal matrix is folded into the factorization to reduce operation count during
* preconditioner application. Not sure if this is a good idea or not, yet.
* This preconditioner allows for a novel dropping strategy, where rather than a fixed
* drop tolerance, you can specify now many non-zeroes are allowed per row. The non-zeroes
* will be chosen based on largest magnitude. This idea has been applied to IC factorization,
* but not AINV as far as I'm aware. See:
* Lin, C. and More, J. J. 1999. Incomplete Cholesky Factorizations with Limited Memory.
* SIAM J. Sci. Comput. 21, 1 (Aug. 1999), 24-45.
* This preconditioner will only work for SPD matrices.
*
*/
template <typename ValueType, typename MemorySpace>
class scaled_bridson_ainv : public linear_operator<ValueType, MemorySpace>
{
typedef linear_operator<ValueType, MemorySpace> Parent;
public:
cusp::hyb_matrix<int, ValueType, MemorySpace> w;
cusp::hyb_matrix<int, ValueType, MemorySpace> w_t;
/*! construct a \p ainv preconditioner
*
* \param A matrix to precondition
* \tparam MatrixType matrix
* \param ValueType drop_tolerance Tolerance for dropping during factorization
* \param nonzero_per_row Count of non-zeroes allowed per row of the factored matrix. If negative or lin_dropping==true, this will be ignored.
* \param lin_dropping When true, this will use the dropping strategy from Lin & More, where the per-row count will be based on A's structure.
* \param lin_param when lin_dropping set to true, this indicates how many additional non-zeros per row to include
*/
template<typename MatrixTypeA>
scaled_bridson_ainv(const MatrixTypeA & A, ValueType drop_tolerance=0.1, int nonzero_per_row=-1, bool lin_dropping=false, int lin_param=1);
/*! apply the preconditioner to vector \p x and store the result in \p y
*
* \param x input vector
* \param y ouput vector
* \tparam VectorType1 vector
* \tparam VectorType2 vector
*/
template <typename VectorType1, typename VectorType2>
void operator()(const VectorType1& x, VectorType2& y) const;
};
/*! \}
*/
/*! \addtogroup preconditioners Preconditioners
* \ingroup preconditioners
* \{
*/
/*! \p bridson_ainv : Approximate Inverse preconditoner (from Bridson's "outer product" formulation)
* This preconditioner allows for a novel dropping strategy, where rather than a fixed
* drop tolerance, you can specify now many non-zeroes are allowed per row. The non-zeroes
* will be chosen based on largest magnitude. This idea has been applied to IC factorization,
* but not AINV as far as I'm aware. See:
* Lin, C. and More, J. J. 1999. Incomplete Cholesky Factorizations with Limited Memory.
* SIAM J. Sci. Comput. 21, 1 (Aug. 1999), 24-45.
* This preconditioner will only work for SPD matrices.
*/
template <typename ValueType, typename MemorySpace>
class bridson_ainv : public linear_operator<ValueType, MemorySpace>
{
typedef linear_operator<ValueType, MemorySpace> Parent;
public:
cusp::hyb_matrix<int, ValueType, MemorySpace> w;
cusp::hyb_matrix<int, ValueType, MemorySpace> w_t;
cusp::array1d<ValueType, MemorySpace> diagonals;
/*! construct a \p ainv preconditioner
*
* \param A matrix to precondition
* \tparam MatrixTypeA matrix
* \param ValueType drop_tolerance Tolerance for dropping during factorization
* \param nonzero_per_row Count of non-zeroes allowed per row of the factored matrix. If negative or lin_dropping==true, this will be ignored.
* \param lin_dropping When true, this will use the dropping strategy from Lin & More, where the per-row count will be based on A's structure.
* \param lin_param when lin_dropping set to true, this indicates how many additional non-zeros per row to include
*/
template<typename MatrixTypeA>
bridson_ainv(const MatrixTypeA & A, ValueType drop_tolerance=0.1, int nonzero_per_row =-1, bool lin_dropping=false, int lin_param=1);
/*! apply the preconditioner to vector \p x and store the result in \p y
*
* \param x input vector
* \param y ouput vector
* \tparam VectorType1 vector
* \tparam VectorType2 vector
*/
template <typename VectorType1, typename VectorType2>
void operator()(const VectorType1& x, VectorType2& y) const;
};
/*! \}
*/
/*! \addtogroup preconditioners Preconditioners
* \ingroup preconditioners
* \{
*/
/*! \p nonsym_bridson_ainv : Approximate Inverse preconditoner (from Bridson's "outer product" formulation)
* The non-symmetric form, which is identical to the standard form in the case of symmetric matrices, but
* handles non-symmtric matrices as well. The storage and cost of applying the preconditioner
* are about the same, but build time is 2x higher.
*/
template <typename ValueType, typename MemorySpace>
class nonsym_bridson_ainv : public linear_operator<ValueType, MemorySpace>
{
typedef linear_operator<ValueType, MemorySpace> Parent;
public:
cusp::hyb_matrix<int, ValueType, MemorySpace> w_t;
cusp::hyb_matrix<int, ValueType, MemorySpace> z;
cusp::array1d<ValueType, MemorySpace> diagonals;
/*! construct a \p ainv preconditioner
*
* \param A matrix to precondition
* \tparam MatrixTypeA matrix
* \param ValueType drop_tolerance Tolerance for dropping during factorization
* \param nonzero_per_row Count of non-zeroes allowed per row of the factored matrix. If negative or lin_dropping==true, this will be ignored.
* \param lin_dropping When true, this will use the dropping strategy from Lin & More, where the per-row count will be based on A's structure.
* \param lin_param when lin_dropping set to true, this indicates how many additional non-zeros per row to include
*/
template<typename MatrixTypeA>
nonsym_bridson_ainv(const MatrixTypeA & A, ValueType drop_tolerance=0.1, int nonzero_per_row=-1, bool lin_dropping=false, int lin_param=1);
/*! apply the preconditioner to vector \p x and store the result in \p y
*
* \param x input vector
* \param y ouput vector
* \tparam VectorType1 vector
* \tparam VectorType2 vector
*/
template <typename VectorType1, typename VectorType2>
void operator()(const VectorType1& x, VectorType2& y) const;
};
/*! \}
*/
} // end namespace precond
} // end namespace cusp
#include <cusp/precond/detail/ainv.inl>
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