newton_impl.h

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/*
 * Copyright (c) 2010-2015:  G-CSC, Goethe University Frankfurt
 * Author: Andreas Vogel
 * 
 * This file is part of UG4.
 * 
 * UG4 is free software: you can redistribute it and/or modify it under the
 * terms of the GNU Lesser General Public License version 3 (as published by the
 * Free Software Foundation) with the following additional attribution
 * requirements (according to LGPL/GPL v3 §7):
 * 
 * (1) The following notice must be displayed in the Appropriate Legal Notices
 * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (2) The following notice must be displayed at a prominent place in the
 * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
 * 
 * (3) The following bibliography is recommended for citation and must be
 * preserved in all covered files:
 * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
 *   parallel geometric multigrid solver on hierarchically distributed grids.
 *   Computing and visualization in science 16, 4 (2013), 151-164"
 * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
 *   flexible software system for simulating pde based models on high performance
 *   computers. Computing and visualization in science 16, 4 (2013), 165-179"
 * 
 * This program 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 for more details.
 */
 
#ifndef __H__UG__LIB_DISC__OPERATOR__NON_LINEAR_OPERATOR__NEWTON_SOLVER__NEWTON_IMPL__
#define __H__UG__LIB_DISC__OPERATOR__NON_LINEAR_OPERATOR__NEWTON_SOLVER__NEWTON_IMPL__
 
#include <iostream>
#include <sstream>
 
#include "newton.h"
#include "lib_disc/function_spaces/grid_function_util.h"
#include "common/util/string_util.h"
 
#define PROFILE_NEWTON
#ifdef PROFILE_NEWTON
  #define NEWTON_PROFILE_FUNC()   PROFILE_FUNC_GROUP("Newton")
  #define NEWTON_PROFILE_BEGIN(name)  PROFILE_BEGIN_GROUP(name, "Newton")
  #define NEWTON_PROFILE_END()    PROFILE_END()
#else
  #define NEWTON_PROFILE_FUNC()
  #define NEWTON_PROFILE_BEGIN(name)
  #define NEWTON_PROFILE_END()
#endif
 
namespace ug{
 
template <typename TAlgebra>
NewtonSolver<TAlgebra>::
NewtonSolver(SmartPtr<ILinearOperatorInverse<vector_type> > LinearSolver,
      SmartPtr<IConvergenceCheck<vector_type> > spConvCheck,
      SmartPtr<ILineSearch<vector_type> > spLineSearch) :
      m_spLinearSolver(LinearSolver),
      m_spConvCheck(spConvCheck),
      m_spLineSearch(spLineSearch),
      m_N(NULL),
      m_J(NULL),
      m_spAss(NULL),
      m_reassembe_J_freq(0),
      m_dgbCall(0),
      m_lastNumSteps(0)
{};
 
template <typename TAlgebra>
NewtonSolver<TAlgebra>::
NewtonSolver() :
  m_spLinearSolver(NULL),
  m_spConvCheck(new StdConvCheck<vector_type>(10, 1e-8, 1e-10, true)),
  m_spLineSearch(NULL),
  m_N(NULL),
  m_J(NULL),
  m_spAss(NULL),
  m_reassembe_J_freq(0),
  m_dgbCall(0),
  m_lastNumSteps(0)
{};
 
template <typename TAlgebra>
NewtonSolver<TAlgebra>::
NewtonSolver(SmartPtr<IOperator<vector_type> > N) :
  m_spLinearSolver(NULL),
  m_spConvCheck(new StdConvCheck<vector_type>(10, 1e-8, 1e-10, true)),
  m_spLineSearch(NULL),
  m_N(NULL),
  m_J(NULL),
  m_spAss(NULL),
  m_reassembe_J_freq(0),
  m_dgbCall(0),
  m_lastNumSteps(0)
{
  init(N);
};
 
template <typename TAlgebra>
NewtonSolver<TAlgebra>::
NewtonSolver(SmartPtr<IAssemble<TAlgebra> > spAss) :
  m_spLinearSolver(NULL),
  m_spConvCheck(new StdConvCheck<vector_type>(10, 1e-8, 1e-10, true)),
  m_spLineSearch(NULL),
  m_N(NULL),
  m_J(NULL),
  m_spAss(NULL),
  m_reassembe_J_freq(0),
  m_dgbCall(0),
  m_lastNumSteps(0)
{
  m_spAss = spAss;
  m_N = SmartPtr<AssembledOperator<TAlgebra> >(new AssembledOperator<TAlgebra>(m_spAss));
};
 
template <typename TAlgebra>
void NewtonSolver<TAlgebra>::
set_convergence_check(SmartPtr<IConvergenceCheck<vector_type> > spConvCheck)
{
  m_spConvCheck = spConvCheck;
  m_spConvCheck->set_offset(3);
  m_spConvCheck->set_symbol('#');
  m_spConvCheck->set_name("Newton Solver");
}
 
template <typename TAlgebra>
bool NewtonSolver<TAlgebra>::init(SmartPtr<IOperator<vector_type> > N)
{
  NEWTON_PROFILE_BEGIN(NewtonSolver_init);
  m_N = N.template cast_dynamic<AssembledOperator<TAlgebra> >();
  if(m_N.invalid())
    UG_THROW("NewtonSolver: currently only works for AssembledDiscreteOperator.");
 
  m_spAss = m_N->discretization();
  return true;
}
 
template <typename TAlgebra>
bool NewtonSolver<TAlgebra>::prepare(vector_type& u)
{
//  todo: maybe remove this from interface
  return true;
}
 
template <typename TAlgebra>
bool NewtonSolver<TAlgebra>::apply(vector_type& u)
{
  NEWTON_PROFILE_BEGIN(NewtonSolver_apply);
//  increase call count
  m_dgbCall++;
 
//  Check for linear solver
  if(m_spLinearSolver.invalid())
    UG_THROW("NewtonSolver::apply: Linear Solver not set.");
 
//  Jacobian
  if(m_J.invalid() || m_J->discretization() != m_spAss) {
    m_J = make_sp(new AssembledLinearOperator<TAlgebra>(m_spAss));
  }
  m_J->set_level(m_N->level());
 
//  create tmp vectors
  SmartPtr<vector_type> spD = u.clone_without_values();
  SmartPtr<vector_type> spC = u.clone_without_values();
 
//  Set dirichlet values
  try{
    m_N->prepare(u);
  }
  UG_CATCH_THROW("NewtonSolver::prepare: Prepare of Operator failed.");
 
//  Compute first Defect
  try{
    NEWTON_PROFILE_BEGIN(NewtonComputeDefect1);
    m_N->apply(*spD, u);
    NEWTON_PROFILE_END();
  }UG_CATCH_THROW("NewtonSolver::apply: Computation of Start-Defect failed.");
 
//  loop counts (for the the convergence rate statistics etc.)
  int loopCnt = 0;
  m_lastNumSteps = 0;
  
//  write start defect for debug
  char debug_name_ext[20];
  if (this->debug_writer_valid())
  {
    sprintf(debug_name_ext, "_iter%03d", loopCnt);
    write_debug(*spD, std::string("NEWTON_Defect") + debug_name_ext);
    write_debug(u, "NEWTON_StartSolution");
  }
 
//  increase offset of output for linear solver
  const int stdLinOffset = m_spLinearSolver->standard_offset();
  m_spLinearSolver->convergence_check()->set_offset(stdLinOffset + 3);
 
//  set info string indicating the used linear solver
  std::stringstream ss; ss << "(Linear Solver: " << m_spLinearSolver->name() << ")";
  m_spConvCheck->set_info(ss.str());
 
//  start convergence check
  m_spConvCheck->start(*spD);
 
  for(size_t i = 0; i < m_stepUpdate.size(); ++i)
    m_stepUpdate[i]->update();
 
//  loop iteration
  while(!m_spConvCheck->iteration_ended())
  {
    m_lastNumSteps = loopCnt;
 
  //  set c = 0
    NEWTON_PROFILE_BEGIN(NewtonSetCorretionZero);
    spC->set(0.0);
    NEWTON_PROFILE_END();
 
    for(size_t i = 0; i < m_innerStepUpdate.size(); ++i)
      m_innerStepUpdate[i]->update();
 
  //  Compute Jacobian
    try{
      if(m_reassembe_J_freq == 0 || loopCnt % m_reassembe_J_freq == 0) // if we need to reassemble
      {
        NEWTON_PROFILE_BEGIN(NewtonComputeJacobian);
        m_J->init(u);
        NEWTON_PROFILE_END();
      }
    }UG_CATCH_THROW("NewtonSolver::apply: Initialization of Jacobian failed.");
 
  //  Write the current Jacobian for debug and prepare the section for the lin. solver
    if (this->debug_writer_valid())
    {
      write_debug(m_J->get_matrix(), std::string("NEWTON_Jacobian") + debug_name_ext);
      this->enter_debug_writer_section(std::string("NEWTON_LinSolver") + debug_name_ext);
    }
 
  //  Init Jacobi Inverse
    try{
      NEWTON_PROFILE_BEGIN(NewtonPrepareLinSolver);
      if(!m_spLinearSolver->init(m_J, u))
      {
        UG_LOG("ERROR in 'NewtonSolver::apply': Cannot init Inverse Linear "
            "Operator for Jacobi-Operator.\n");
        return false;
      }
      NEWTON_PROFILE_END();
    }UG_CATCH_THROW("NewtonSolver::apply: Initialization of Linear Solver failed.");
 
  //  Solve Linearized System
    try{
      NEWTON_PROFILE_BEGIN(NewtonApplyLinSolver);
      if(!m_spLinearSolver->apply(*spC, *spD))
      {
        UG_LOG("ERROR in 'NewtonSolver::apply': Cannot apply Inverse Linear "
            "Operator for Jacobi-Operator.\n");
        return false;
      }
      NEWTON_PROFILE_END();
    }UG_CATCH_THROW("NewtonSolver::apply: Application of Linear Solver failed.");
 
    this->leave_debug_writer_section();
    
  //  store convergence history
    const int numSteps = m_spLinearSolver->step();
    if(loopCnt >= (int)m_vTotalLinSolverSteps.size()) m_vTotalLinSolverSteps.resize(loopCnt+1);
    if(loopCnt >= (int)m_vLinSolverCalls.size()) m_vLinSolverCalls.resize(loopCnt+1, 0);
    if(loopCnt >= (int)m_vLinSolverRates.size()) m_vLinSolverRates.resize(loopCnt+1, 0);
    m_vTotalLinSolverSteps[loopCnt] += numSteps;
    m_vLinSolverCalls[loopCnt] += 1;
    m_vLinSolverRates[loopCnt] += m_spLinearSolver->convergence_check()->avg_rate();
 
    try{
    //  Line Search
      if(m_spLineSearch.valid())
      {
        m_spLineSearch->set_offset("   #  ");
        NEWTON_PROFILE_BEGIN(NewtonLineSearch);
        if(!m_spLineSearch->search(m_N, u, *spC, *spD, m_spConvCheck->defect()))
        {
          UG_LOG("ERROR in 'NewtonSolver::apply': "
              "Newton Solver did not converge.\n");
          return false;
        }
        NEWTON_PROFILE_END();
      }
    //  No line search: Compute new defect
      else
      {
      //  update solution
        u -= *spC;
  
      //  compute new Defect
        NEWTON_PROFILE_BEGIN(NewtonComputeDefect);
        m_N->prepare(u);
        m_N->apply(*spD, u);
        NEWTON_PROFILE_END();
      }
    }UG_CATCH_THROW("NewtonSolver::apply: Line Search update failed.");
 
 
  //  update counter
    loopCnt++;
 
  //  check convergence
    m_spConvCheck->update(*spD);
    if(loopCnt-1 >= (int)m_vNonLinSolverRates.size()) m_vNonLinSolverRates.resize(loopCnt, 0);
    m_vNonLinSolverRates[loopCnt-1] += m_spConvCheck->rate();
 
  //  write defect for debug
    if (this->debug_writer_valid())
    {
      sprintf(debug_name_ext, "_iter%03d", loopCnt);
      write_debug(*spD, std::string("NEWTON_Defect") + debug_name_ext);
      write_debug(*spC, std::string("NEWTON_Correction") + debug_name_ext);
      write_debug(u, std::string("NEWTON_Solution") + debug_name_ext);
    }
  }
 
  // reset offset of output for linear solver to previous value
  m_spLinearSolver->convergence_check()->set_offset(stdLinOffset);
 
  return m_spConvCheck->post();
}
 
template <typename TAlgebra>
void NewtonSolver<TAlgebra>::print_average_convergence() const
{
  UG_LOG("\nNewton solver convergence history:\n");
  UG_LOG("Newton Step | Num Calls | Total Lin Iters | Avg Lin Iters | Avg Nonlin Rates | Avg Lin Rates \n");
  int allCalls = 0, allLinSteps = 0;
  number allLinRatesProduct = 1.0, allNonLinRatesProduct = 1.0;
  for(int call = 0; call < (int)m_vLinSolverCalls.size(); ++call)
  {
    UG_LOG( " " << std::setw(10) << call+1 << " | ");
    UG_LOG(std::setw(9) << m_vLinSolverCalls[call] << " | ");
    allCalls += m_vLinSolverCalls[call];
    UG_LOG(std::setw(15) << m_vTotalLinSolverSteps[call] << " | ");
    allLinSteps += m_vTotalLinSolverSteps[call];
    UG_LOG(std::setw(13) << std::setprecision(2) << std::fixed << m_vTotalLinSolverSteps[call] / (double)m_vLinSolverCalls[call] << " | ");
    allNonLinRatesProduct *= pow((number)m_vNonLinSolverRates[call]/(double)m_vLinSolverCalls[call],(double)m_vLinSolverCalls[call]);
    UG_LOG(std::setw(16) << std::setprecision(6) << std::scientific << m_vNonLinSolverRates[call] / (double)m_vLinSolverCalls[call] << " | ");
    allLinRatesProduct *= (number)std::pow((number)m_vLinSolverRates[call]/(double)m_vLinSolverCalls[call],(number)m_vTotalLinSolverSteps[call]);
    UG_LOG(std::setw(13) << std::setprecision(6) << std::scientific << m_vLinSolverRates[call] / (double)m_vLinSolverCalls[call]);
    UG_LOG("\n");
  }
  UG_LOG( "        all | ");
  UG_LOG(std::setw(9) << allCalls << " | ");
  UG_LOG(std::setw(15) << allLinSteps << " | ");
  UG_LOG(std::setw(13) << std::setprecision(2) << std::fixed << allLinSteps / (number)allCalls << " | ");
  UG_LOG(std::setw(16) << std::setprecision(6) << std::scientific << std::pow((number)allNonLinRatesProduct,(number)1.0/(number)allCalls) << " | ");
  UG_LOG(std::setw(13) << std::setprecision(6) << std::scientific << std::pow((number)allLinRatesProduct,(number)1.0/(number)allLinSteps));
  UG_LOG("\n");
}
 
template <typename TAlgebra>
size_t NewtonSolver<TAlgebra>::num_newton_steps() const
{
  return m_vLinSolverCalls.size();
}
 
template <typename TAlgebra>
int NewtonSolver<TAlgebra>::num_linsolver_calls(size_t call) const
{
  return m_vLinSolverCalls[call];
}
 
template <typename TAlgebra>
int NewtonSolver<TAlgebra>::num_linsolver_steps(size_t call) const
{
  return m_vTotalLinSolverSteps[call];
}
 
template <typename TAlgebra>
double NewtonSolver<TAlgebra>::average_linear_steps(size_t call) const
{
  return m_vTotalLinSolverSteps[call] / ((double)m_vLinSolverCalls[call]);
}
 
template <typename TAlgebra>
int NewtonSolver<TAlgebra>::total_linsolver_calls() const
{
  int allCalls = 0;
  for(size_t call = 0; call < m_vLinSolverCalls.size(); ++call)
    allCalls += m_vLinSolverCalls[call];
  return allCalls;
}
 
template <typename TAlgebra>
int NewtonSolver<TAlgebra>::total_linsolver_steps() const
{
  int allSteps = 0;
  for(size_t call = 0; call < m_vLinSolverCalls.size(); ++call)
    allSteps += m_vTotalLinSolverSteps[call];
  return allSteps;
}
 
template <typename TAlgebra>
double NewtonSolver<TAlgebra>::total_average_linear_steps() const
{
  return total_linsolver_steps()/((double)total_linsolver_calls());
}
 
 
template <typename TAlgebra>
void NewtonSolver<TAlgebra>::clear_average_convergence()
{
  m_vLinSolverRates.clear();
  m_vNonLinSolverRates.clear();
  m_vLinSolverCalls.clear();
  m_vTotalLinSolverSteps.clear();
}
 
template <typename TAlgebra>
void NewtonSolver<TAlgebra>::write_debug(const vector_type& vec, std::string name)
{
//  add call count to name
  char ext[20]; sprintf(ext, "_call%03d", m_dgbCall);
 
//  write
  typedef DebugWritingObject<TAlgebra> base_writer_type;
  base_writer_type::write_debug(vec, name + ext);
}
 
template <typename TAlgebra>
void NewtonSolver<TAlgebra>::write_debug(const matrix_type& mat, std::string name)
{
//  add call count to name
  char ext[20]; sprintf(ext, "_call%03d", m_dgbCall);
 
//  write
  typedef DebugWritingObject<TAlgebra> base_writer_type;
  base_writer_type::write_debug(mat, name + ext);
}
 
template <typename TAlgebra>
std::string NewtonSolver<TAlgebra>::config_string() const
{
  std::stringstream ss;
  ss << "NewtonSolver\n";
  ss << " LinearSolver: ";
  if(m_spLinearSolver.valid())  ss << ConfigShift(m_spLinearSolver->config_string()) << "\n";
  else              ss << " NOT SET!\n";
  ss << " ConvergenceCheck: ";
  if(m_spConvCheck.valid())   ss << ConfigShift(m_spConvCheck->config_string()) << "\n";
  else              ss << " NOT SET!\n";
  ss << " LineSearch: ";
  if(m_spLineSearch.valid())    ss << ConfigShift(m_spLineSearch->config_string()) << "\n";
  else              ss << " not set.\n";
  if(m_reassembe_J_freq != 0)   ss << " Reassembling Jacobian only once per " << m_reassembe_J_freq << " step(s)\n";
  return ss.str();
}
 
 
}
 
#endif /* __H__UG__LIB_DISC__OPERATOR__NON_LINEAR_OPERATOR__NEWTON_SOLVER__NEWTON_IMPL__ */