BiCGSTAB.h

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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
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
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::abs;
  using std::sqrt;
  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;
}
 
}  // namespace internal
 
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;
};
 
}  // namespace internal
 
template <typename MatrixType_, typename Preconditioner_>
class BiCGSTAB : public IterativeSolverBase<BiCGSTAB<MatrixType_, Preconditioner_> > {
  typedef IterativeSolverBase<BiCGSTAB> Base;
  using Base::m_error;
  using Base::m_info;
  using Base::m_isInitialized;
  using Base::m_iterations;
  using Base::matrix;
 
 public:
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef Preconditioner_ Preconditioner;
 
 public:
  BiCGSTAB() : Base() {}
 
  template <typename MatrixDerived>
  explicit BiCGSTAB(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
 
  ~BiCGSTAB() {}
 
  template <typename Rhs, typename Dest>
  void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const {
    m_iterations = Base::maxIterations();
    m_error = Base::m_tolerance;
 
    bool ret = internal::bicgstab(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
 
    m_info = (!ret) ? NumericalIssue : m_error <= Base::m_tolerance ? Success : NoConvergence;
  }
 
 protected:
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_BICGSTAB_H