libtrilinos-rol-dev 12.12.1-5 / usr / include / trilinos / ROL_LeastSquares.hpp

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/** \file
    \brief  Contains definitions for least squares function.
    \author Created by D. Ridzal and D. Kouri.
 */

#ifndef USE_HESSVEC 
#define USE_HESSVEC 1
#endif

#ifndef ROL_LEASTSQUARES_HPP
#define ROL_LEASTSQUARES_HPP

#include "ROL_StdVector.hpp"
#include "ROL_Objective.hpp"

namespace ROL {
namespace ZOO {

/** \brief Least squares function.
 */
template<class Real>
class Objective_LeastSquares : public Objective<Real> {
  typedef typename std::vector<Real>::size_type uint; 

public:

  Real value( const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<const std::vector<Real> > ex
      = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();

    uint n    = ex->size();
    Real h   = 1.0/((Real)n+1.0);
    Real val = 0.0;
    Real res = 0.0;
    for (uint i=0; i<n; i++) {
      if ( i == 0 ) {
        res = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i+1]-2.0*(*ex)[i]);
      }
      else if ( i == n-1 ) {
        res = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]);
      }
      else {
        res = 2.0*h + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]+(*ex)[i+1]);
      }
      val += 0.5*res*res;
    }
    return val;
  }

  void gradient( Vector<Real> &g, const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<std::vector<Real> > eg
      = Teuchos::dyn_cast<StdVector<Real> >(g).getVector();
    Teuchos::RCP<const std::vector<Real> > ex
      = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();

    uint n  = ex->size();
    Real h = 1.0/((Real)n+1.0);
    std::vector<Real> res(n,0.0);
    for (uint i=0; i<n; i++) {
      if ( i == 0 ) {
        res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i+1]-2.0*(*ex)[i]);
      }
      else if ( i == n-1 ) {
        res[i] = 2.0*h*(5.0/6.0) + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]);
      }
      else {
        res[i] = 2.0*h + 1.0/h*((*ex)[i-1]-2.0*(*ex)[i]+(*ex)[i+1]);
      }
    }

    for (uint i=0; i<n; i++) {
      if ( i == 0 ) {
        (*eg)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
      }
      else if ( i == n-1 ) {
        (*eg)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
      }
      else {
        (*eg)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
      }
    }
  }
#if USE_HESSVEC
  void hessVec( Vector<Real> &hv, const Vector<Real> &v, const Vector<Real> &x, Real &tol ) {
    Teuchos::RCP<std::vector<Real> > ehv
      = Teuchos::dyn_cast<StdVector<Real> >(hv).getVector();
    Teuchos::RCP<const std::vector<Real> > ev
      = Teuchos::dyn_cast<const StdVector<Real> >(v).getVector();
    Teuchos::RCP<const std::vector<Real> > ex
      = Teuchos::dyn_cast<const StdVector<Real> >(x).getVector();

    uint n  = ex->size();
    Real h = 1.0/((Real)n+1.0);
    std::vector<Real> res(n,0.0);
    for (uint i=0; i<n; i++) {
      if ( i == 0 ) {
        res[i] = 1.0/h*((*ev)[i+1]-2.0*(*ev)[i]);
      }
      else if ( i == n-1 ) {
        res[i] = 1.0/h*((*ev)[i-1]-2.0*(*ev)[i]);
      }
      else {
        res[i] = 1.0/h*((*ev)[i-1]-2.0*(*ev)[i]+(*ev)[i+1]);
      }
    }

    for (uint i=0; i<n; i++) {
      if ( i == 0 ) {
        (*ehv)[i] = 1.0/h*(res[i+1]-2.0*res[i]);
      }
      else if ( i == n-1 ) {
        (*ehv)[i] = 1.0/h*(res[i-1]-2.0*res[i]);
      }
      else {
        (*ehv)[i] = 1.0/h*(res[i-1]-2.0*res[i]+res[i+1]);
      }
    }
  }
#endif
};

template<class Real>
void getLeastSquares( Teuchos::RCP<Objective<Real> > &obj,
                      Teuchos::RCP<Vector<Real> >    &x0,
                      Teuchos::RCP<Vector<Real> >    &x ) {
  // Problem dimension
  int n = 32;

  // Get Initial Guess
  Teuchos::RCP<std::vector<Real> > x0p = Teuchos::rcp(new std::vector<Real>(n,0.0));
  for ( int i = 0; i < n; i++ ) {
    (*x0p)[i] = 0.0;
  }
  x0 = Teuchos::rcp(new StdVector<Real>(x0p));

  // Get Solution
  Teuchos::RCP<std::vector<Real> > xp = Teuchos::rcp(new std::vector<Real>(n,0.0));
  Real h = 1.0/((Real)n+1.0), pt = 0.0;
  for( int i = 0; i < n; i++ ) {
    pt = (Real)(i+1)*h;
    (*xp)[i] = pt*(1.0-pt);
  }
  x = Teuchos::rcp(new StdVector<Real>(xp));

  // Instantiate Objective Function
  obj = Teuchos::rcp(new Objective_LeastSquares<Real>);
}

} // End ZOO Namespace
} // End ROL Namespace

#endif