// @HEADER
// ************************************************************************
//
//               Rapid Optimization Library (ROL) Package
//                 Copyright (2014) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION OR THE
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Questions? Contact lead developers:
//              Drew Kouri   (dpkouri@sandia.gov) and
//              Denis Ridzal (dridzal@sandia.gov)
//
// ************************************************************************
// @HEADER

/** \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
