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-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2011-2014 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, Index& 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;
-  Index maxIters = iters;
-
-  Index n = mat.cols();
-  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*rhs_sqnorm;
-  RealScalar eps2 = NumTraits<Scalar>::epsilon()*NumTraits<Scalar>::epsilon();
-  Index i = 0;
-  Index restarts = 0;
-
-  while ( r.squaredNorm() > tol2 && i<maxIters )
-  {
-    Scalar rho_old = rho;
-
-    rho = r0.dot(r);
-    if (abs(rho) < eps2*r0_sqnorm)
-    {
-      // The new residual vector became too orthogonal to the arbitrarily chosen direction r0
-      // Let's restart with a new r0:
-      r  = rhs - mat * x;
-      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
-  *
-  * \implsparsesolverconcept
-  *
-  * 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.
-  * 
-  * The tolerance corresponds to the relative residual error: |Ax-b|/|b|
-  * 
-  * \b Performance: when using sparse matrices, best performance is achied for a row-major sparse matrix format.
-  * Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
-  * See \ref TopicMultiThreading for details.
-  * 
-  * 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.
-  * 
-  * BiCGSTAB can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
-  *
-  * \sa class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
-  */
-template< typename _MatrixType, typename _Preconditioner>
-class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> >
-{
-  typedef IterativeSolverBase<BiCGSTAB> Base;
-  using Base::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::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.
-    */
-  template<typename MatrixDerived>
-  explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
-
-  ~BiCGSTAB() {}
-
-  /** \internal */
-  template<typename Rhs,typename Dest>
-  void _solve_with_guess_impl(const Rhs& b, Dest& x) const
-  {    
-    bool failed = false;
-    for(Index j=0; j<b.cols(); ++j)
-    {
-      m_iterations = Base::maxIterations();
-      m_error = Base::m_tolerance;
-      
-      typename Dest::ColXpr xj(x,j);
-      if(!internal::bicgstab(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 */
-  using Base::_solve_impl;
-  template<typename Rhs,typename Dest>
-  void _solve_impl(const MatrixBase<Rhs>& b, Dest& x) const
-  {
-    x.resize(this->rows(),b.cols());
-    x.setZero();
-    _solve_with_guess_impl(b,x);
-  }
-
-protected:
-
-};
-
-} // end namespace Eigen
-
-#endif // EIGEN_BICGSTAB_H