solver_cg.h

// ---------------------------------------------------------------------
//
// Copyright (C) 1998 - 2018 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, 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 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii_solver_cg_h
#define dealii_solver_cg_h


#include <deal.II/base/config.h>
#include <deal.II/lac/tridiagonal_matrix.h>
#include <deal.II/lac/solver.h>
#include <deal.II/lac/solver_control.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/logstream.h>
#include <deal.II/base/subscriptor.h>
#include <cmath>

DEAL_II_NAMESPACE_OPEN

// forward declaration
class PreconditionIdentity;



template <typename VectorType = Vector<double> >
class SolverCG : public Solver<VectorType>
{
public:
  typedef types::global_dof_index size_type;

  struct AdditionalData {};

  SolverCG (SolverControl            &cn,
            VectorMemory<VectorType> &mem,
            const AdditionalData     &data = AdditionalData());

  SolverCG (SolverControl        &cn,
            const AdditionalData &data=AdditionalData());

  virtual ~SolverCG () = default;

  template <typename MatrixType, typename PreconditionerType>
  void
  solve (const MatrixType         &A,
         VectorType               &x,
         const VectorType         &b,
         const PreconditionerType &preconditioner);

  boost::signals2::connection
  connect_coefficients_slot(
    const std::function<void (double,double)> &slot);

  boost::signals2::connection
  connect_condition_number_slot(const std::function<void (double)> &slot,
                                const bool every_iteration=false);

  boost::signals2::connection
  connect_eigenvalues_slot(
    const std::function<void (const std::vector<double> &)> &slot,
    const bool every_iteration=false);

protected:
  virtual void print_vectors(const unsigned int step,
                             const VectorType   &x,
                             const VectorType   &r,
                             const VectorType   &d) const;

  static void
  compute_eigs_and_cond(
    const std::vector<double> &diagonal,
    const std::vector<double> &offdiagonal,
    const boost::signals2::signal<void (const std::vector<double> &)> &eigenvalues_signal,
    const boost::signals2::signal<void (double)> &cond_signal);

  AdditionalData additional_data;

  boost::signals2::signal<void (double,double)> coefficients_signal;

  boost::signals2::signal<void (double)> condition_number_signal;

  boost::signals2::signal<void (double)> all_condition_numbers_signal;

  boost::signals2::signal<void (const std::vector<double> &)> eigenvalues_signal;

  boost::signals2::signal<void (const std::vector<double> &)> all_eigenvalues_signal;
};

/*------------------------- Implementation ----------------------------*/

#ifndef DOXYGEN

template <typename VectorType>
SolverCG<VectorType>::SolverCG (SolverControl        &cn,
                                VectorMemory<VectorType> &mem,
                                const AdditionalData     &data)
  :
  Solver<VectorType>(cn,mem),
  additional_data(data)
{}



template <typename VectorType>
SolverCG<VectorType>::SolverCG (SolverControl        &cn,
                                const AdditionalData &data)
  :
  Solver<VectorType>(cn),
  additional_data(data)
{}



template <typename VectorType>
void
SolverCG<VectorType>::print_vectors(const unsigned int,
                                    const VectorType &,
                                    const VectorType &,
                                    const VectorType &) const
{}



template <typename VectorType>
inline void
SolverCG<VectorType>::compute_eigs_and_cond
(const std::vector<double> &diagonal,
 const std::vector<double> &offdiagonal,
 const boost::signals2::signal<void (const std::vector<double> &)> &eigenvalues_signal,
 const boost::signals2::signal<void (double)>                      &cond_signal)
{
  //Avoid computing eigenvalues unless they are needed.
  if (!cond_signal.empty()|| !eigenvalues_signal.empty())
    {
      TridiagonalMatrix<double> T(diagonal.size(), true);
      for (size_type i=0; i<diagonal.size(); ++i)
        {
          T(i,i) = diagonal[i];
          if (i< diagonal.size()-1)
            T(i,i+1) = offdiagonal[i];
        }
      T.compute_eigenvalues();
      //Need two eigenvalues to estimate the condition number.
      if (diagonal.size()>1)
        {
          double condition_number=T.eigenvalue(T.n()-1)/T.eigenvalue(0);
          cond_signal(condition_number);
        }
      //Avoid copying the eigenvalues of T to a vector unless a signal is
      //connected.
      if (!eigenvalues_signal.empty())
        {
          std::vector<double> eigenvalues(T.n());
          for (unsigned int j = 0; j < T.n(); ++j)
            {
              eigenvalues.at(j)=T.eigenvalue(j);
            }
          eigenvalues_signal(eigenvalues);
        }
    }

}



template <typename VectorType>
template <typename MatrixType, typename PreconditionerType>
void
SolverCG<VectorType>::solve (const MatrixType         &A,
                             VectorType               &x,
                             const VectorType         &b,
                             const PreconditionerType &preconditioner)
{
  SolverControl::State conv=SolverControl::iterate;

  LogStream::Prefix prefix("cg");

  // Memory allocation
  typename VectorMemory<VectorType>::Pointer g_pointer(this->memory);
  typename VectorMemory<VectorType>::Pointer d_pointer(this->memory);
  typename VectorMemory<VectorType>::Pointer h_pointer(this->memory);

  // define some aliases for simpler access
  VectorType &g = *g_pointer;
  VectorType &d = *d_pointer;
  VectorType &h = *h_pointer;

  // Should we build the matrix for eigenvalue computations?
  const bool do_eigenvalues = !condition_number_signal.empty()
                              ||!all_condition_numbers_signal.empty()
                              ||!eigenvalues_signal.empty()
                              ||!all_eigenvalues_signal.empty();

  // vectors used for eigenvalue
  // computations
  std::vector<double> diagonal;
  std::vector<double> offdiagonal;

  int  it=0;
  double res = -std::numeric_limits<double>::max();

  double eigen_beta_alpha = 0;

  // resize the vectors, but do not set
  // the values since they'd be overwritten
  // soon anyway.
  g.reinit(x, true);
  d.reinit(x, true);
  h.reinit(x, true);

  double gh,beta;

  // compute residual. if vector is
  // zero, then short-circuit the
  // full computation
  if (!x.all_zero())
    {
      A.vmult(g,x);
      g.add(-1.,b);
    }
  else
    g.equ(-1.,b);
  res = g.l2_norm();

  conv = this->iteration_status(0, res, x);
  if (conv != SolverControl::iterate)
    return;

  if (std::is_same<PreconditionerType,PreconditionIdentity>::value == false)
    {
      preconditioner.vmult(h,g);

      d.equ(-1.,h);

      gh = g*h;
    }
  else
    {
      d.equ(-1.,g);
      gh = res*res;
    }

  while (conv == SolverControl::iterate)
    {
      it++;
      A.vmult(h,d);

      double alpha = d*h;
      Assert(alpha != 0., ExcDivideByZero());
      alpha = gh/alpha;

      x.add(alpha,d);
      res = std::sqrt(g.add_and_dot(alpha, h, g));

      print_vectors(it, x, g, d);

      conv = this->iteration_status(it, res, x);
      if (conv != SolverControl::iterate)
        break;

      if (std::is_same<PreconditionerType,PreconditionIdentity>::value
          == false)
        {
          preconditioner.vmult(h,g);

          beta = gh;
          Assert(beta != 0., ExcDivideByZero());
          gh   = g*h;
          beta = gh/beta;
          d.sadd(beta,-1.,h);
        }
      else
        {
          beta = gh;
          gh = res*res;
          beta = gh/beta;
          d.sadd(beta,-1.,g);
        }

      this->coefficients_signal(alpha,beta);
      // set up the vectors
      // containing the diagonal
      // and the off diagonal of
      // the projected matrix.
      if (do_eigenvalues)
        {
          diagonal.push_back(1./alpha + eigen_beta_alpha);
          eigen_beta_alpha = beta/alpha;
          offdiagonal.push_back(std::sqrt(beta)/alpha);
        }
      compute_eigs_and_cond(diagonal,offdiagonal,all_eigenvalues_signal,
                            all_condition_numbers_signal);
    }

  compute_eigs_and_cond(diagonal,offdiagonal,eigenvalues_signal,
                        condition_number_signal);

  // in case of failure: throw exception
  if (conv != SolverControl::success)
    AssertThrow(false, SolverControl::NoConvergence (it, res));
  // otherwise exit as normal
}



template <typename VectorType>
boost::signals2::connection
SolverCG<VectorType>::connect_coefficients_slot
(const std::function<void(double,double)> &slot)
{
  return coefficients_signal.connect(slot);
}



template <typename VectorType>
boost::signals2::connection
SolverCG<VectorType>::connect_condition_number_slot
(const std::function<void(double)> &slot,
 const bool                              every_iteration)
{
  if (every_iteration)
    {
      return all_condition_numbers_signal.connect(slot);
    }
  else
    {
      return condition_number_signal.connect(slot);
    }
}



template <typename VectorType>
boost::signals2::connection
SolverCG<VectorType>::connect_eigenvalues_slot
(const std::function<void (const std::vector<double> &)> &slot,
 const bool                                                    every_iteration)
{
  if (every_iteration)
    {
      return all_eigenvalues_signal.connect(slot);
    }
  else
    {
      return eigenvalues_signal.connect(slot);
    }
}



#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif