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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_BASIC_PRECONDITIONERS_H
#define EIGEN_BASIC_PRECONDITIONERS_H
namespace Eigen {
/** \ingroup IterativeLinearSolvers_Module
* \brief A preconditioner based on the digonal entries
*
* This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
* In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
* \code
* A.diagonal().asDiagonal() . x = b
* \endcode
*
* \tparam _Scalar the type of the scalar.
*
* This preconditioner is suitable for both selfadjoint and general problems.
* The diagonal entries are pre-inverted and stored into a dense vector.
*
* \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
*
*/
template <typename _Scalar>
class DiagonalPreconditioner
{
typedef _Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> Vector;
typedef typename Vector::Index Index;
public:
typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
DiagonalPreconditioner() : m_isInitialized(false) {}
template<typename MatrixType>
DiagonalPreconditioner(const MatrixType& mat) : m_invdiag(mat.cols())
{
compute(mat);
}
Index rows() const { return m_invdiag.size(); }
Index cols() const { return m_invdiag.size(); }
template<typename MatrixType>
DiagonalPreconditioner& analyzePattern(const MatrixType& )
{
return *this;
}
template<typename MatrixType>
DiagonalPreconditioner& factorize(const MatrixType& mat)
{
m_invdiag.resize(mat.cols());
for(int j=0; j<mat.outerSize(); ++j)
{
typename MatrixType::InnerIterator it(mat,j);
while(it && it.index()!=j) ++it;
if(it && it.index()==j)
m_invdiag(j) = Scalar(1)/it.value();
else
m_invdiag(j) = 0;
}
m_isInitialized = true;
return *this;
}
template<typename MatrixType>
DiagonalPreconditioner& compute(const MatrixType& mat)
{
return factorize(mat);
}
template<typename Rhs, typename Dest>
void _solve(const Rhs& b, Dest& x) const
{
x = m_invdiag.array() * b.array() ;
}
template<typename Rhs> inline const internal::solve_retval<DiagonalPreconditioner, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
eigen_assert(m_invdiag.size()==b.rows()
&& "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<DiagonalPreconditioner, Rhs>(*this, b.derived());
}
protected:
Vector m_invdiag;
bool m_isInitialized;
};
namespace internal {
template<typename _MatrixType, typename Rhs>
struct solve_retval<DiagonalPreconditioner<_MatrixType>, Rhs>
: solve_retval_base<DiagonalPreconditioner<_MatrixType>, Rhs>
{
typedef DiagonalPreconditioner<_MatrixType> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
}
/** \ingroup IterativeLinearSolvers_Module
* \brief A naive preconditioner which approximates any matrix as the identity matrix
*
* \sa class DiagonalPreconditioner
*/
class IdentityPreconditioner
{
public:
IdentityPreconditioner() {}
template<typename MatrixType>
IdentityPreconditioner(const MatrixType& ) {}
template<typename MatrixType>
IdentityPreconditioner& analyzePattern(const MatrixType& ) { return *this; }
template<typename MatrixType>
IdentityPreconditioner& factorize(const MatrixType& ) { return *this; }
template<typename MatrixType>
IdentityPreconditioner& compute(const MatrixType& ) { return *this; }
template<typename Rhs>
inline const Rhs& solve(const Rhs& b) const { return b; }
};
} // end namespace Eigen
#endif // EIGEN_BASIC_PRECONDITIONERS_H
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