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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 bicg.h
* \brief Biconjugate Gradient (BiCG) method
*/
#pragma once
#include <cusp/detail/config.h>
namespace cusp
{
namespace krylov
{
/*! \addtogroup iterative_solvers Iterative Solvers
* \addtogroup krylov_methods Krylov Methods
* \ingroup iterative_solvers
* \{
*/
/*! \p bicg : Biconjugate Gradient method
*
* Solves the linear system A x = b using the default convergence criteria.
*/
template <class LinearOperator,
class Vector>
void bicg(LinearOperator& A,
LinearOperator& At,
Vector& x,
Vector& b);
/*! \p bicgstab : Biconjugate Gradient method
*
* Solves the linear system A x = b without preconditioning.
*/
template <class LinearOperator,
class Vector,
class Monitor>
void bicg(LinearOperator& A,
LinearOperator& At,
Vector& x,
Vector& b,
Monitor& monitor);
/*! \p bicg : Biconjugate Gradient method
*
* Solves the linear system A x = b with preconditioner \p M.
*
* \param A matrix of the linear system
* \param At conjugate tranpose of the matrix of the linear system
* \param x approximate solution of the linear system
* \param b right-hand side of the linear system
* \param monitor montiors iteration and determines stopping conditions
* \param M preconditioner for A
* \param Mt conjugate tranpose of the preconditioner for A
*
* \tparam LinearOperator is a matrix or subclass of \p linear_operator
* \tparam Vector vector
* \tparam Monitor is a monitor such as \p default_monitor or \p verbose_monitor
* \tparam Preconditioner is a matrix or subclass of \p linear_operator
*
* The following code snippet demonstrates how to use \p bicg to
* solve a 10x10 Poisson problem.
*
* \code
* #include <cusp/csr_matrix.h>
* #include <cusp/monitor.h>
* #include <cusp/krylov/bicg.h>
* #include <cusp/gallery/poisson.h>
*
* int main(void)
* {
* // create an empty sparse matrix structure (CSR format)
* cusp::csr_matrix<int, float, cusp::device_memory> A;
*
* // initialize matrix
* cusp::gallery::poisson5pt(A, 10, 10);
*
* // 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);
*
* // set stopping criteria:
* // iteration_limit = 100
* // relative_tolerance = 1e-6
* cusp::verbose_monitor<float> monitor(b, 100, 1e-6);
*
* // set preconditioner (identity)
* cusp::identity_operator<float, cusp::device_memory> M(A.num_rows, A.num_rows);
*
* // solve the linear system A x = b
* // because both A and M are hermitian we can use
* // them for their own conjugate transpose
* cusp::krylov::bicgstab(A, A, x, b, monitor, M, M);
*
* return 0;
* }
* \endcode
*
* \see \p default_monitor
* \see \p verbose_monitor
*/
template <class LinearOperator,
class Vector,
class Monitor,
class Preconditioner>
void bicg(LinearOperator& A,
LinearOperator& At,
Vector& x,
Vector& b,
Monitor& monitor,
Preconditioner& M,
Preconditioner& Mt);
/*! \}
*/
} // end namespace krylov
} // end namespace cusp
#include <cusp/krylov/detail/bicg.inl>
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