line_search.h

Go to the documentation of this file.

/*
 * 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__LINE_SEARCH__
#define __H__UG__LIB_DISC__OPERATOR__NON_LINEAR_OPERATOR__LINE_SEARCH__
 
#include <ostream>
#include <string>
#include <vector>
#include <cmath>
#include <sstream>
 
#include "common/common.h"
 
namespace ug{
 
// Line Search
 
template <typename TVector>
class ILineSearch
{
  public:
    typedef TVector vector_type;
 
  public:
    virtual void set_offset(std::string offset) = 0;
 
    virtual bool search(SmartPtr<IOperator<vector_type> > spOp,
                        vector_type& u, vector_type& p,
                        vector_type& d, number defect) = 0;
 
 
    virtual std::string config_string() const = 0;
 
    virtual ~ILineSearch() {}
};
 
template <typename TVector>
class StandardLineSearch : public ILineSearch<TVector>
{
  public:
  //  type of
    typedef TVector vector_type;
 
  public:
    StandardLineSearch()
     :   m_maxSteps(10), m_lambdaStart(1.0), m_lambdaReduce(0.5), m_alpha(0.25),
         m_maxDefect(1e+10), m_verbose(true), m_bAcceptBest(false), m_bCheckAll(false), m_offset("")
       {};
 
    StandardLineSearch(int maxSteps, number lambdaStart, number lambdaReduce, bool bAcceptBest)
     :   m_maxSteps(maxSteps), m_lambdaStart(lambdaStart), m_lambdaReduce(lambdaReduce), m_alpha(0.25),
       m_maxDefect(1e+10), m_verbose(true), m_bAcceptBest(bAcceptBest), m_bCheckAll(false), m_offset("")
       {};
 
    StandardLineSearch(int maxSteps, number lambdaStart, number lambdaReduce, bool bAcceptBest, bool bCheckAll)
     :   m_maxSteps(maxSteps), m_lambdaStart(lambdaStart), m_lambdaReduce(lambdaReduce), m_alpha(0.25),
       m_maxDefect(1e+10), m_verbose(true), m_bAcceptBest(bAcceptBest), m_bCheckAll(bCheckAll), m_offset("")
       {};
 
    virtual std::string config_string() const
    {
      std::stringstream ss;
      ss << "StandardLineSearch( maxSteps = " << m_maxSteps << ", lambdaStart = " << m_lambdaStart << ", lambdaReduce = " << m_lambdaReduce << ", accept best = " <<
          (m_bAcceptBest ? "true" : "false") << " check all = " << (m_bCheckAll ? "true" : "false");
      return ss.str();
 
    }
 
    void set_maximum_steps(int steps) {m_maxSteps = steps;}
 
    void set_lambda_start(number start) {m_lambdaStart = start;}
 
    void set_reduce_factor(number factor) {m_lambdaReduce = factor;}
    
    void set_suff_descent_factor(number factor) {m_alpha = factor;}
 
    void set_accept_best(bool bAcceptBest) {m_bAcceptBest = bAcceptBest;}
 
    void set_check_all(bool bCheckAll) {m_bCheckAll = bCheckAll;}
 
    void set_maximum_defect(number maxDef) {m_maxDefect = maxDef;}
 
    void set_verbose(bool level) {m_verbose = level;}
 
    virtual void set_offset(std::string offset) {m_offset = offset;};
 
    virtual bool search(SmartPtr<IOperator<vector_type> > spOp,
                        vector_type& u, vector_type& p,
                        vector_type& d, number defect)
    {
      PROFILE_BEGIN_GROUP(StandardLineSearch_search, ""); // group?
    //  clone pattern for s
      s.resize(u.size());
 
    //  start factor
      number lambda = m_lambdaStart;
 
    //  some values
      number norm, norm_old = defect;
      bool converged = false;
      std::vector<number> vRho;
 
    // remember u
      s = u;
 
    //  print heading line
    if(m_verbose)
      UG_LOG(m_offset << "   ++++ Line Search:\n"
              << "   +  Iter       lambda        Defect          Rate \n");
 
 
    //  loop line search steps
      for(int k = 1; k <= m_maxSteps; ++k)
      {
      //  try on line u := u - lambda*p
        VecScaleAdd(u, 1.0, u, (-1)*lambda, p);
 
      //  compute new Defect
        spOp->prepare(u);
        spOp->apply(d, u);
 
      //  compute new Residuum
        norm = d.norm();
 
      //  compute reduction
        vRho.push_back(norm/norm_old);
 
      //  print rate
        if(m_verbose)
          UG_LOG(m_offset << "   + " << std::setw(4)
              << k << ":   " << std::setw(11)
              << std::resetiosflags( ::std::ios::scientific )<<
              lambda << "     "
              << std::scientific << norm << "   " << vRho.back() <<"\n");
 
      //  check if reduction fits
        if(vRho.back() <= 1 - m_alpha * std::fabs(lambda))
        {
          converged = true;
          if(!m_bCheckAll) break;
        }
 
        lambda *= m_lambdaReduce;
 
      //  check if maximum number of steps reached
        if(k == m_maxSteps)
        {
        //  if not accept best, line search failed
          if(!m_bAcceptBest)
          {
            UG_LOG(m_offset << "   ++++ Line Search did not converge.\n");
            return false;
          }
 
        //  search minimum
          size_t best = 0;
          number rho_min = vRho.front();
          for(size_t i = 1; i < vRho.size(); ++i)
          {
            if(rho_min > vRho[i])
            {
              rho_min = vRho[i];
              best = i;
            }
          }
 
        /*  check if best is converging (i.e. rho < 1)
          if(vRho[best] >= 1)
          {
            UG_LOG(m_offset << "   ++++ Accept Best: No try with "
                "Rate < 1, cannot accept any line search step.\n");
            UG_LOG(m_offset << "   ++++ Line Search did not converge.\n");
            return false;
          }*/
 
        //  accept best
          if(m_verbose)
            UG_LOG(m_offset << "   ++++ Accept Best: Accepting step " <<
              best+1 << ", Rate = "<< vRho[best] <<".\n");
 
        //  try on line u := u - lambda*p
          VecScaleAdd(u, 1.0, s, (-1)*m_lambdaStart*std::pow(m_lambdaReduce, (number)best), p);
 
        //  compute new Defect
          spOp->prepare(u);
          spOp->apply(d, u);
 
          // compute new Residuum
          norm = d.norm();
 
          // check if defect-norm is smaller than maximum allowed defect value
          if (norm > m_maxDefect)
          {
            UG_LOG("ERROR in 'StandardLineSearch::search':"
                " maximum defect-limit is reached.\n");
            return false;
          }
 
        //  break to finish
          break;
        }
 
      //  reset u
        u = s;
      }
 
    //  print end line
      if(m_verbose)
      {
        //only for rate < 1, we call it "Line Search converged"
        if(converged)
          UG_LOG(m_offset << "   ++++ Line Search converged.\n");
      }
 
    //  we're done
      return true;
    }
 
  protected:
    vector_type s;
 
  protected:
    int m_maxSteps;
 
    number m_lambdaStart;
 
    number m_lambdaReduce;
    
    number m_alpha;
 
    number m_maxDefect;
 
    bool m_verbose;
 
    bool m_bAcceptBest;
 
    bool m_bCheckAll;
 
    std::string m_offset;
};
 
} // end namespace ug
 
#endif /* __H__UG__LIB_DISC__OPERATOR__NON_LINEAR_OPERATOR__LINE_SEARCH__ */