# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iostream>
# include <iomanip>


using namespace std;

# include "toms178.hpp"

//****************************************************************************80

double best_nearby ( double delta[], double point[], double prevbest, 
  int nvars, double f ( double x[], int nvars ), int *funevals )

//****************************************************************************80
//
//  Purpose:
//
//    BEST_NEARBY looks for a better nearby point, one coordinate at a time.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    12 February 2008
//
//  Author:
//
//    The ALGOL original is by Arthur Kaupe.
//    C version by Mark Johnson
//    C++ version by John Burkardt
//
//  Reference:
//
//    M Bell, Malcolm Pike,
//    Remark on Algorithm 178: Direct Search,
//    Communications of the ACM,
//    Volume 9, Number 9, September 1966, page 684.
//
//    Robert Hooke, Terry Jeeves,
//    Direct Search Solution of Numerical and Statistical Problems,
//    Journal of the ACM,
//    Volume 8, Number 2, April 1961, pages 212-229.
//
//    Arthur Kaupe,
//    Algorithm 178:
//    Direct Search,
//    Communications of the ACM,
//    Volume 6, Number 6, June 1963, page 313.
//
//    FK Tomlin, LB Smith,
//    Remark on Algorithm 178: Direct Search,
//    Communications of the ACM,
//    Volume 12, Number 11, November 1969, page 637-638.
//
//  Parameters:
//
//    Input, double DELTA(NVARS), the size of a step in each direction.
//
//    Input/output, double POINT(NVARS); on input, the current candidate.
//    On output, the value of POINT may have been updated.
//
//    Input, double PREVBEST, the minimum value of the function seen
//    so far.
//
//    Input, int NVARS, the number of variables.
//
//    Input, F, the name of the function routine,
//    which should have the form:
//      double f ( double x[], int n )
//
//    Input/output, int *FUNEVALS, the number of function evaluations.
//
//    Output, double BEST_NEARBY, the minimum value of the function seen
//    after checking the nearby neighbors.
//
{
  double ftmp;
  int i;
  double minf;
  double *z;

  z = new double[nvars];

  minf = prevbest;

  for ( i = 0; i < nvars; i++ )
  {
   z[i] = point[i];
  }

  for ( i = 0; i < nvars; i++ )
  {
    z[i] = point[i] + delta[i];

    ftmp = f ( z, nvars );
    *funevals = *funevals + 1;

    if ( ftmp < minf )
    {
      minf = ftmp;
    }
    else
    {
      delta[i] = - delta[i];
      z[i] = point[i] + delta[i];
      ftmp = f ( z, nvars );
      *funevals = *funevals + 1;

      if ( ftmp < minf )
      {
        minf = ftmp;
      }
      else
      {
        z[i] = point[i];
      }
    }
  }

  for ( i = 0; i < nvars; i++ )
  {
    point[i] = z[i];
  }

  delete [] z;

  return minf;
}
//****************************************************************************80

int hooke ( int nvars, double startpt[], double endpt[], double rho, double eps, 
  int itermax, double f ( double x[], int nvars ) )   

//****************************************************************************80
//
//  Purpose:
//
//    HOOKE seeks a minimizer of a scalar function of several variables.
//
//  Discussion:
//
//    This routine find a point X where the nonlinear objective function 
//    F(X) has a local minimum.  X is an N-vector and F(X) is a scalar.  
//    The objective function F(X) is not required to be differentiable
//    or even continuous.  The program does not use or require derivatives 
//    of the objective function. 
//
//    The user supplies three things: 
//    1) a subroutine that computes F(X), 
//    2) an initial "starting guess" of the minimum point X, 
//    3) values for the algorithm convergence parameters.  
//
//    The program searches for a local minimum, beginning from the    
//    starting guess, using the Direct Search algorithm of Hooke and  
//    Jeeves.
//
//    This program is adapted from the Algol pseudocode found in the
//    paper by Kaupe, and includes improvements suggested by Bell and Pike,
//    and by Tomlin and Smith.
//
//    The algorithm works by taking "steps" from one estimate of
//    a minimum, to another (hopefully better) estimate.  Taking 
//    big steps gets to the minimum more quickly, at the risk of 
//    "stepping right over" an excellent point.  The stepsize is 
//    controlled by a user supplied parameter called RHO.  At each 
//    iteration, the stepsize is multiplied by RHO  (0 < RHO < 1), 
//    so the stepsize is successively reduced. 
//
//    Small values of rho correspond to big stepsize changes, 
//    which make the algorithm run more quickly.  However, there 
//    is a chance (especially with highly nonlinear functions) 
//    that these big changes will accidentally overlook a 
//    promising search vector, leading to nonconvergence. 
//
//    Large values of RHO correspond to small stepsize changes, 
//    which force the algorithm to carefully examine nearby points 
//    instead of optimistically forging ahead.  This improves the 
//    probability of convergence. 
//
//    The stepsize is reduced until it is equal to (or smaller 
//    than) EPS.  So the number of iterations performed by 
//    Hooke-Jeeves is determined by RHO and EPS:
// 
//      RHO^(number_of_iterations) = EPS
//
//    In general it is a good idea to set RHO to an aggressively 
//    small value like 0.5 (hoping for fast convergence).  Then, 
//    if the user suspects that the reported minimum is incorrect 
//    (or perhaps not accurate enough), the program can be run 
//    again with a larger value of RHO such as 0.85, using the 
//    result of the first minimization as the starting guess to 
//    begin the second minimization.
//
//    Normal use: 
//    (1) Code your function F() in the C language;
//    (2) Install your starting guess;
//    (3) Run the program.
//
//    If there are doubts about the result, the computed minimizer 
//    can be used as the starting point for a second minimization attempt.
//
//    To apply this method to data fitting, code your function F() to be 
//    the sum of the squares of the errors (differences) between the 
//    computed values and the measured values.  Then minimize F() 
//    using Hooke-Jeeves. 
//
//    For example, you have 20 datapoints (T[i], Y[i]) and you want to
//    find A, B and C so that:
//
//      A*t*t + B*exp(t) + C*tan(t)
//
//    fits the data as closely as possible.  Then the objective function
//    F() to be minimized is just
//
//      F(A,B,C) = sum ( 1 <= i <= 20 )
//        ( y[i] - A*t[i]*t[i] - B*exp(t[i]) - C*tan(t[i]) )^2.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    12 February 2008
//
//  Author:
//
//    ALGOL original by Arthur Kaupe.
//    C version by Mark Johnson.
//    C++ version by John Burkardt.
//
//  Reference:
//
//    M Bell, Malcolm Pike,
//    Remark on Algorithm 178: Direct Search,
//    Communications of the ACM,
//    Volume 9, Number 9, September 1966, page 684.
//
//    Robert Hooke, Terry Jeeves,
//    Direct Search Solution of Numerical and Statistical Problems,
//    Journal of the ACM,
//    Volume 8, Number 2, April 1961, pages 212-229.
//
//    Arthur Kaupe,
//    Algorithm 178:
//    Direct Search,
//    Communications of the ACM,
//    Volume 6, Number 6, June 1963, page 313.
//
//    FK Tomlin, LB Smith,
//    Remark on Algorithm 178: Direct Search,
//    Communications of the ACM,
//    Volume 12, Number 11, November 1969, page 637-638.
//
//  Parameters:
//
//    Input, int NVARS, the number of spatial dimensions.
//
//    Input, double STARTPT(NVARS), the user-supplied
//    initial estimate for the minimizer. 
//
//    Output, double ENDPT(NVARS), the estimate for the
//    minimizer, as calculated by the program.
//
//    Input, double RHO, a user-supplied convergence parameter
//    which should be set to a value between 0.0 and 1.0.  Larger values 
//    of RHO give greater probability of convergence on highly nonlinear 
//    functions, at a cost of more function evaluations.  Smaller     
//    values of RHO reduce the number of evaluations and the program 
//    running time, but increases the risk of nonconvergence. 
//
//    Input, double EPS, the criterion for halting   
//    the search for a minimum.  When the algorithm   
//    begins to make less and less progress on each   
//    iteration, it checks the halting criterion: if  
//    the stepsize is below EPS, terminate the    
//    iteration and return the current best estimate  
//    of the minimum.  Larger values of EPS (such 
//    as 1.0e-4) give quicker running time, but a     
//    less accurate estimate of the minimum.  Smaller 
//    values of EPS (such as 1.0e-7) give longer  
//    running time, but a more accurate estimate of   
//    the minimum.            
//
//    Input, int ITERMAX, a limit on the number of iterations.
//
///    Input, F, the name of the function routine,
//    which should have the form:
//      double f ( double x[], int n )
//
//    Output, int HOOKE, the number of iterations taken.
//
{
  double *delta;
  double fbefore;
  int funevals;
  int i;
  int iters;
  int keep;
  double newf;
  double *newx;
  double steplength;
  double tmp;
  bool verbose = false;
  double *xbefore;

  delta = new double[nvars];
  newx = new double[nvars];
  xbefore = new double[nvars];

  for ( i = 0; i < nvars; i++ )
  {
    newx[i] = startpt[i];
  }

  for ( i = 0; i < nvars; i++ )
  {
    xbefore[i] = startpt[i];
  }

  for ( i = 0; i < nvars; i++ )
  {
    if ( startpt[i] == 0.0 )
    {
      delta[i] = rho;
    }
    else
    {
      delta[i] = rho * fabs ( startpt[i] );
    }
  }

  funevals = 0;
  steplength = rho;
  iters = 0;
  fbefore = f ( newx, nvars );
  funevals = funevals + 1;
  newf = fbefore;

  while ( iters < itermax && eps < steplength )
  {
    iters = iters + 1;

    if ( verbose )
    {
      cout << "\n";
      cout << "  FUNEVALS, = " << funevals
           << "  F(X) = " << fbefore << "\n";

      for ( i = 0; i < nvars; i++ )
      {
        cout << "  " << i + 1
             << "  " << xbefore[i] << "\n";
      }
    }
//
//  Find best new point, one coordinate at a time.
//
    for ( i = 0; i < nvars; i++ )
    {
      newx[i] = xbefore[i];
    }

    newf = best_nearby ( delta, newx, fbefore, nvars, f, &funevals );
//
//  If we made some improvements, pursue that direction.
//
    keep = 1;

    while ( newf < fbefore && keep == 1 )
    {
      for ( i = 0; i < nvars; i++ )
      {
//
//  Arrange the sign of DELTA.
//
        if ( newx[i] <= xbefore[i] )
        {
          delta[i] = - fabs ( delta[i] );
        }
        else
        {
          delta[i] = fabs ( delta[i] );
        }
//
//  Now, move further in this direction.
//
        tmp = xbefore[i];
        xbefore[i] = newx[i];
        newx[i] = newx[i] + newx[i] - tmp;
      }

      fbefore = newf;
      newf = best_nearby ( delta, newx, fbefore, nvars, f, &funevals );
//
//  If the further (optimistic) move was bad...
//
      if ( fbefore <= newf )
      {
        break;
      }
//
//  Make sure that the differences between the new and the old points 
//  are due to actual displacements; beware of roundoff errors that 
//  might cause NEWF < FBEFORE.
//
      keep = 0;

      for ( i = 0; i < nvars; i++ )
      {
        if ( 0.5 * fabs ( delta[i] ) < fabs ( newx[i] - xbefore[i] ) )
        {
          keep = 1;
          break;
        }
      }
    }

    if ( eps <= steplength && fbefore <= newf )
    {
      steplength = steplength * rho;
      for ( i = 0; i < nvars; i++ )
      {
        delta[i] = delta[i] * rho;
      }
    }

  }

  for ( i = 0; i < nvars; i++ )
  {
    endpt[i] = xbefore[i];
  }

  delete [] delta;
  delete [] newx;
  delete [] xbefore;

  return iters;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}