Added gradient descent method.

/***************************************************************************

                          Timer.h  -  description

                             -------------------

    begin                : Mar 14, 2016

    copyright            : (C) 2016 by Tomas Oberhuber

    email                : tomas.oberhuber@fjfi.cvut.cz

 ***************************************************************************/

/* See Copyright Notice in tnl/Copyright */

#pragma once

#include <TNL/Solvers/IterativeSolver.h>

namespace TNL {

   namespace Solvers {

      namespace Optimization {

template< typename Vector, typename SolverMonitor =  IterativeSolverMonitor< typename Vector::RealType, typename Vector::IndexType > >

class GradientDescent : public IterativeSolver< typename Vector::RealType, typename Vector::IndexType, SolverMonitor >

{

   using RealType = typename Vector::RealType;

   using DeviceType = typename Vector::DeviceType;

   using IndexType = typename Vector::IndexType;

   using VectorType = Vector;

   using VectorView = typename Vector::ViewType;

   GradientDescent() = default;

   static void

   configSetup( Config::ConfigDescription& config, const String& prefix = "" );

   bool

   setup( const Config::ParameterContainer& parameters, const String& prefix = "" );

   void

   setRelaxation( const RealType& lambda );

   const RealType&

   getRelaxation() const;

   template< typename GradientGetter >

   bool

   solve( VectorView& w, GradientGetter&& getGradient );

protected:

   RealType relaxation = 1.0;

   VectorType aux;

};

      } //namespace Optimization

   } //namespace Solvers

} //namespace TNL

#include <TNL/Solvers/Optimization/GradientDescent.hpp>

/***************************************************************************

                          Timer.h  -  description

                             -------------------

    begin                : Mar 14, 2016

    copyright            : (C) 2016 by Tomas Oberhuber

    email                : tomas.oberhuber@fjfi.cvut.cz

 ***************************************************************************/

/* See Copyright Notice in tnl/Copyright */

#pragma once

#include <TNL/Solvers/Optimization/GradientDescent.h>

namespace TNL {

   namespace Solvers {

      namespace Optimization {

template< typename Vector, typename SolverMonitor >

void

GradientDescent< Vector, SolverMonitor >::

configSetup( Config::ConfigDescription& config, const String& prefix )

{

   IterativeSolver< RealType, IndexType, SolverMonitor >::configSetup( config, prefix );

   config.addEntry< double >( prefix + "gd-relaxation", "Relaxation parameter for the gradient descent.", 1.0 )

}

template< typename Vector, typename SolverMonitor >

bool

GradientDescent< Vector, SolverMonitor >::

setup( const Config::ParameterContainer& parameters, const String& prefix )

{

   this->setRelaxation( parameters.getParameter< double >( prefix + "gd-relaxation" ) );

   return IterativeSolver< RealType, IndexType, SolverMonitor >::setup( parameters, prefix );

}

template< typename Vector, typename SolverMonitor >

void

GradientDescent< Vector, SolverMonitor >::

setRelaxation( const RealType& lambda )

{

   this->relaxation = lambda;

}

template< typename Vector, typename SolverMonitor >

auto

GradientDescent< Vector, SolverMonitor >::

getRelaxation() const -> RealType&

{

   return this->relaxation;

}

template< typename Vector, typename SolverMonitor >

   template< typename GradientGetter >

bool

GradientDescent< Vector, SolverMonitor >::

solve( VectorView& w, GradientGetter&& getGradient )

{

   this->aux.setLike( w );

   auto aux_view = aux.getView();

   auto w_view = w.getView();

   aux = 0.0;

   /////

   // Set necessary parameters

   this->resetIterations();

   this->setResidue( this->getConvergenceResidue() + 1.0 );

   /////

   // Start the main loop

   while( 1 )

   {

      /////

      // Compute the gradient

      getGradient( w_view, aux_view );

      RealType lastResidue = this->getResidue();

      this->setResidue( addAndReduceAbs( w_view, this->relaxation * aux_view, TNL::Plus(), ( RealType ) 0.0 ) / ( this->relaxation * ( RealType ) w.getSize() ) );

      if( ! this->nextIteration() )

         return this->checkConvergence();

      /////

      // Check the stop condition

      if( this -> getConvergenceResidue() != 0.0 && this->getResidue() < this -> getConvergenceResidue() )

         return true;

   }

   return false; // just to avoid warnings

}

      } //namespace Optimization

   } //namespace Solvers

} //namespace TNL