// newtonalg.H
// created by ADP
// last modified 06/17/04

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#ifndef __RVL_OPTALG
#define __RVL_OPTALG

#include "cgalg.hh"
#include "lnsrchBT.hh"
#include "conoptstep.hh"

namespace RVLUmin {
  using namespace RVLAlg;
  using namespace RVL;

  /** A general framework for Newton--like optimization methods  
      with globalization in terms of a variable step length.
      
      The state in this algorithm is the vector x
      which is the current best point.
  */

template<class Scalar>
class NewtonStep: public ConOptStep<Scalar> {
public:
  NewtonStep(Functional<Scalar> const & f, Vector<Scalar> const & x0)
    : ConOptStep<Scalar>(f, x0)
  {}

  ~NewtonStep() {}

  virtual bool run() {
    try {
      Vector<Scalar> dir(ConOptStep<Scalar>::getFunctionalEvaluation().getDomain(), true);
      bool cd = calcDir(dir);
      bool cs = calcStep(dir);
      return (cd && cs);      }
    } catch(RVLException & e) {
      e << "called from NewtonStep::run()\n";
      throw e;
    } catch( std::exception & e) {
      RVLException es;
      es << "Exception caught in NewtonStep::run() with error message";
      es << e.what(); 
      throw e;
    }
    return true;
  }

protected:
  // Methods which must/may be implemented by children
  //@{

  // Fill in the vector with the search direction
  virtual bool calcDir(Vector<Scalar> & dir) = 0;

  //@}

  // Methods which may be implemented by children
  //@{

  /** Find the step length in this search direction,
      and updates x.
      Default implementation always sets the step to 1.
  */
  virtual bool calcStep(Vector<Scalar> & dir) {
    Scalar step = 1.0;  
    (this->getTrialPoint()).copy(this->getBasePoint());
    (this->getTrialPoint()).linComb(step, dir);
    return true;
  }

  //@}  
};

/** This Truncated Newton Algorithm is described in
    Numerical Optimization by Nocedal & Wright.
    It is listed as Algorithm 6.1 on page 140.

    It uses a CGStep to find a search direction and
    then a LineSearchAlg to determine the step length.
*/
template <class Scalar>
class TruncatedNewtonStep: public NewtonStep<Scalar> {
public:
  /** Takes the functional to be minimized and
      a vector containing the current location x*/
  TruncatedNewtonStep(Functional<Scalar> & _f, const Vector<Scalar> & _x): 
    NewtonStep<Scalar>(_f,_x), bs(_f.getDomain())
  {}

  /** Takes a vector containing the starting location x0
      and a functional evaluation to be manipulated.
  */
  TruncatedNewtonStep(const Vector<Scalar> & _x0, FunctionalEvaluation<Scalar> & _fx): 
    NewtonStep<Scalar>(_x0, _fx), bs(_fx.getDomain())
  {}

  ~TruncatedNewtonStep() {}

protected:

  /** Find the step length in this search direction,
      and update x and fx.
      
      Returning a non-positive step length is 
      an algorithmic failure, and will cause the run()
      method to return false.

      Use a backtracking line search.
  */
  //  virtual bool calcStep(Vector<Scalar> & dir, Scalar & step) {
  virtual bool calcStep(Vector<Scalar> & dir) {
    bs.set(dir,ConOptStep<Scalar>::getFunctionalEvaluation());
    bool res = bs.run();
    //    step = bs.getStep();  
    return res;
  }

  /** Fill in the vector with the search direction
      Find a search direction using CG.
  */
  virtual bool calcDir(Vector<Scalar> & dir) {
    Scalar rho, tol;
    dir.zero();
    FunctionalEvaluation<Scalar> & fx = ConOptStep<Scalar>::getFunctionalEvaluation();
    Vector<Scalar> g(fx.getDomain());
    g.copy(fx.getGradient());
    g.negate();

    CGStep<Scalar> cgs(dir, fx.getHessian(), g, rho);

    /* We want tol = min(0.5, sqrt(g.norm())) * g.norm() */
    tol = g.norm();
    if( tol < 0.25 ) {
      tol = sqrt(tol)*tol;
    } else {
      tol = 0.5 * tol;
    }
    
    tol = tol *tol; // We will compare r.norm2() to tol^2

    MinTerminator<Scalar> t1(rho, tol);
    MinTerminator<Scalar> t2(cgs. getCurvature(), cgs.getCurvatureTol());
    OrTerminator t(t1,t2);

    LoopAlg la(cgs, t);

    return la.run();
  }
 
  BacktrackingLineSearchAlg<Scalar> bs;
};

}

#endif