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Diffstat (limited to 'third_party/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h')
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1 files changed, 0 insertions, 254 deletions
diff --git a/third_party/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h b/third_party/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h deleted file mode 100644 index 7a46b51fa6..0000000000 --- a/third_party/eigen3/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h +++ /dev/null @@ -1,254 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> -// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr> -// -// This Source Code Form is subject to the terms of the Mozilla -// Public License v. 2.0. If a copy of the MPL was not distributed -// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. - -#ifndef EIGEN_BICGSTAB_H -#define EIGEN_BICGSTAB_H - -namespace Eigen { - -namespace internal { - -/** \internal Low-level bi conjugate gradient stabilized algorithm - * \param mat The matrix A - * \param rhs The right hand side vector b - * \param x On input and initial solution, on output the computed solution. - * \param precond A preconditioner being able to efficiently solve for an - * approximation of Ax=b (regardless of b) - * \param iters On input the max number of iteration, on output the number of performed iterations. - * \param tol_error On input the tolerance error, on output an estimation of the relative error. - * \return false in the case of numerical issue, for example a break down of BiCGSTAB. - */ -template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner> -bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, - const Preconditioner& precond, int& iters, - typename Dest::RealScalar& tol_error) -{ - using std::sqrt; - using std::abs; - typedef typename Dest::RealScalar RealScalar; - typedef typename Dest::Scalar Scalar; - typedef Matrix<Scalar,Dynamic,1> VectorType; - RealScalar tol = tol_error; - int maxIters = iters; - - int n = mat.cols(); - x = precond.solve(x); - VectorType r = rhs - mat * x; - VectorType r0 = r; - - RealScalar r0_sqnorm = r0.squaredNorm(); - RealScalar rhs_sqnorm = rhs.squaredNorm(); - if(rhs_sqnorm == 0) - { - x.setZero(); - return true; - } - Scalar rho = 1; - Scalar alpha = 1; - Scalar w = 1; - - VectorType v = VectorType::Zero(n), p = VectorType::Zero(n); - VectorType y(n), z(n); - VectorType kt(n), ks(n); - - VectorType s(n), t(n); - - RealScalar tol2 = tol*tol; - int i = 0; - int restarts = 0; - - while ( r.squaredNorm()/rhs_sqnorm > tol2 && i<maxIters ) - { - Scalar rho_old = rho; - - rho = r0.dot(r); - if (internal::isMuchSmallerThan(rho,r0_sqnorm)) - { - // The new residual vector became too orthogonal to the arbitrarily choosen direction r0 - // Let's restart with a new r0: - r0 = r; - rho = r0_sqnorm = r.squaredNorm(); - if(restarts++ == 0) - i = 0; - } - Scalar beta = (rho/rho_old) * (alpha / w); - p = r + beta * (p - w * v); - - y = precond.solve(p); - - v.noalias() = mat * y; - - alpha = rho / r0.dot(v); - s = r - alpha * v; - - z = precond.solve(s); - t.noalias() = mat * z; - - RealScalar tmp = t.squaredNorm(); - if(tmp>RealScalar(0)) - w = t.dot(s) / tmp; - else - w = Scalar(0); - x += alpha * y + w * z; - r = s - w * t; - ++i; - } - tol_error = sqrt(r.squaredNorm()/rhs_sqnorm); - iters = i; - return true; -} - -} - -template< typename _MatrixType, - typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> > -class BiCGSTAB; - -namespace internal { - -template< typename _MatrixType, typename _Preconditioner> -struct traits<BiCGSTAB<_MatrixType,_Preconditioner> > -{ - typedef _MatrixType MatrixType; - typedef _Preconditioner Preconditioner; -}; - -} - -/** \ingroup IterativeLinearSolvers_Module - * \brief A bi conjugate gradient stabilized solver for sparse square problems - * - * This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient - * stabilized algorithm. The vectors x and b can be either dense or sparse. - * - * \tparam _MatrixType the type of the sparse matrix A, can be a dense or a sparse matrix. - * \tparam _Preconditioner the type of the preconditioner. Default is DiagonalPreconditioner - * - * The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() - * and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations - * and NumTraits<Scalar>::epsilon() for the tolerance. - * - * This class can be used as the direct solver classes. Here is a typical usage example: - * \include BiCGSTAB_simple.cpp - * - * By default the iterations start with x=0 as an initial guess of the solution. - * One can control the start using the solveWithGuess() method. Here is a step by - * step execution example starting with a random guess and printing the evolution - * of the estimated error: - * \include BiCGSTAB_step_by_step.cpp - * Note that such a step by step excution is slightly slower. - * - * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner - */ -template< typename _MatrixType, typename _Preconditioner> -class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> > -{ - typedef IterativeSolverBase<BiCGSTAB> Base; - using Base::mp_matrix; - using Base::m_error; - using Base::m_iterations; - using Base::m_info; - using Base::m_isInitialized; -public: - typedef _MatrixType MatrixType; - typedef typename MatrixType::Scalar Scalar; - typedef typename MatrixType::Index Index; - typedef typename MatrixType::RealScalar RealScalar; - typedef _Preconditioner Preconditioner; - -public: - - /** Default constructor. */ - BiCGSTAB() : Base() {} - - /** Initialize the solver with matrix \a A for further \c Ax=b solving. - * - * This constructor is a shortcut for the default constructor followed - * by a call to compute(). - * - * \warning this class stores a reference to the matrix A as well as some - * precomputed values that depend on it. Therefore, if \a A is changed - * this class becomes invalid. Call compute() to update it with the new - * matrix A, or modify a copy of A. - */ - BiCGSTAB(const MatrixType& A) : Base(A) {} - - ~BiCGSTAB() {} - - /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A - * \a x0 as an initial solution. - * - * \sa compute() - */ - template<typename Rhs,typename Guess> - inline const internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess> - solveWithGuess(const MatrixBase<Rhs>& b, const Guess& x0) const - { - eigen_assert(m_isInitialized && "BiCGSTAB is not initialized."); - eigen_assert(Base::rows()==b.rows() - && "BiCGSTAB::solve(): invalid number of rows of the right hand side matrix b"); - return internal::solve_retval_with_guess - <BiCGSTAB, Rhs, Guess>(*this, b.derived(), x0); - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solveWithGuess(const Rhs& b, Dest& x) const - { - bool failed = false; - for(int j=0; j<b.cols(); ++j) - { - m_iterations = Base::maxIterations(); - m_error = Base::m_tolerance; - - typename Dest::ColXpr xj(x,j); - if(!internal::bicgstab(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_error)) - failed = true; - } - m_info = failed ? NumericalIssue - : m_error <= Base::m_tolerance ? Success - : NoConvergence; - m_isInitialized = true; - } - - /** \internal */ - template<typename Rhs,typename Dest> - void _solve(const Rhs& b, Dest& x) const - { -// x.setZero(); - x = b; - _solveWithGuess(b,x); - } - -protected: - -}; - - -namespace internal { - - template<typename _MatrixType, typename _Preconditioner, typename Rhs> -struct solve_retval<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs> - : solve_retval_base<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs> -{ - typedef BiCGSTAB<_MatrixType, _Preconditioner> Dec; - EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) - - template<typename Dest> void evalTo(Dest& dst) const - { - dec()._solve(rhs(),dst); - } -}; - -} // end namespace internal - -} // end namespace Eigen - -#endif // EIGEN_BICGSTAB_H |