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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.
*/
/*! \file diagonal.h
* \brief Diagonal preconditioner.
*
* Contributed by Andrew Trachenko and Nikita Styopin
* at SALD Laboratory ( http://www.saldlab.com )
*/
#pragma once
#include <cusp/detail/config.h>
#include <cusp/linear_operator.h>
namespace cusp
{
namespace precond
{
/*! \addtogroup preconditioners Preconditioners
* \ingroup preconditioners
* \{
*/
/*! \p diagonal : diagonal preconditoner (aka Jacobi preconditioner)
*
* Given a matrix \c A to precondition, the diagonal preconditioner
* simply extracts the main diagonal \c D of a \c A and implements
* <tt>y = D^-1 x</tt> when applied to a vector \p x.
*
* Diagonal preconditioning is very inexpensive to use, but has
* limited effectiveness. However, if the matrix \p A has poorly
* scaled rows then diagonal preconditioning can substantially
* reduce the number of solver iterations required to reach
* convergence.
*
* \tparam ValueType Type used for matrix values (e.g. \c float or \c double).
* \tparam MemorySpace A memory space (e.g. \c cusp::host_memory or cusp::device_memory)
*
* The following code snippet demonstrates how to use a
* \p diagonal preconditioner to solve a linear system.
*
* \code
* #include <cusp/precond/diagonal.h>
* ...
*
* // allocate storage for solution (x) and right hand side (b)
* cusp::array1d<float, cusp::device_memory> x(A.num_rows, 0);
* cusp::array1d<float, cusp::device_memory> b(A.num_rows, 1);
*
* cusp::default_monitor<float> monitor(b, 100, 1e-6);
*
* // setup preconditioner
* cusp::precond::diagonal<float, cusp::device_memory> M(A);
*
* // solve
* cusp::krylov::bicgstab(A, x, b, monitor, M);
*
* \endcode
*
*/
template <typename ValueType, typename MemorySpace>
class diagonal : public linear_operator<ValueType, MemorySpace>
{
typedef linear_operator<ValueType, MemorySpace> Parent;
cusp::array1d<ValueType, MemorySpace> diagonal_reciprocals;
public:
/*! construct a \p diagonal preconditioner
*
* \param A matrix to precondition
* \tparam MatrixType matrix
*/
template<typename MatrixType>
diagonal(const MatrixType& A);
/*! 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/diagonal.inl>
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