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

using namespace std;

# include "newton_interp_1d.hpp"

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

double *newton_coef_1d ( int nd, double xd[], double yd[] )

//****************************************************************************80
//
//  Purpose:
//
//    NEWTON_COEF_1D computes coefficients of a Newton 1D interpolant.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 July 2015
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Carl deBoor,
//    A Practical Guide to Splines,
//    Springer, 2001,
//    ISBN: 0387953663,
//    LC: QA1.A647.v27.
//
//  Parameters:
//
//    Input, int ND, the number of data points.
//
//    Input, double XD[ND], the X values at which data was taken.
//    These values must be distinct.
//
//    Input, double YD[ND], the corresponding Y values.
//
//    Output, double NEWTON_COEF_1D[ND], the divided difference coefficients.
//
{
  double *cd;
  int i;
  int j;
//
//  Copy the data values.
//
  cd = new double[nd];

  for ( i = 0; i < nd; i++ )
  {
    cd[i] = yd[i];
  }
//
//  Make sure the abscissas are distinct.
//
  for ( i = 0; i < nd; i++ )
  {
    for ( j = i + 1; j < nd; j++ )
    {
      if ( xd[i] - xd[j] == 0.0 )
      {
        cerr << "\n";
        cerr << "NEWTON_COEF_1D - Fatal error!\n";
        cerr << "  Two entries of XD are equal!\n";
        cerr << "  XD[" << i << "] = " << xd[i] << "\n";
        cerr << "  XD[" << j << "] = " << xd[j] << "\n";
        exit ( 1 );
      }
    }
  }
//
//  Compute the divided differences.
//
  for ( i = 1; i <= nd - 1; i++ )
  {
    for ( j = nd - 1; i <= j; j-- )
    {
      cd[j] = ( cd[j] - cd[j-1] ) / ( xd[j] - xd[j-i] );
    }
  }
  return cd;
}
//****************************************************************************80

double *newton_value_1d ( int nd, double xd[], double cd[], int ni, double xi[] )

//****************************************************************************80
//
//  Purpose:
//
//    NEWTON_VALUE_1D evaluates a Newton 1D interpolant.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 July 2015
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Carl deBoor,
//    A Practical Guide to Splines,
//    Springer, 2001,
//    ISBN: 0387953663,
//    LC: QA1.A647.v27.
//
//  Parameters:
//
//    Input, int ND, the order of the difference table.
//
//    Input, double XD[ND], the X values of the difference table.
//
//    Input, double CD[ND], the divided differences.
//
//    Input, int NI, the number of interpolation points.
//
//    Input, double XI[NI], the interpolation points.
//
//    Output, double NEWTON_VALUE_1D[NI], the interpolation values.
//
{
  int i;
  int j;
  double *yi;

  yi = new double[ni];

  for ( j = 0; j < ni; j++ )
  {
    yi[j] = cd[nd-1];
    for ( i = 2; i <= nd; i++ )
    {
      yi[j] = cd[nd-i] + ( xi[j] - xd[nd-i] ) * yi[j];
    }
  }
  return yi;
}
//****************************************************************************80

double *r8mat_copy_new ( int m, int n, double a1[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8's, which
//    may be stored as a vector in column-major order.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, double A1[M*N], the matrix to be copied.
//
//    Output, double R8MAT_COPY_NEW[M*N], the copy of A1.
//
{
  double *a2;
  int i;
  int j;

  a2 = new double[m*n];

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      a2[i+j*m] = a1[i+j*m];
    }
  }
  return a2;
}
//****************************************************************************80

double *r8vec_copy_new ( int n, double a1[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_COPY_NEW copies an R8VEC to a new R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vectors.
//
//    Input, double A1[N], the vector to be copied.
//
//    Output, double R8VEC_COPY_NEW[N], the copy of A1.
//
{
  double *a2;
  int i;

  a2 = new double[n];

  for ( i = 0; i < n; i++ )
  {
    a2[i] = a1[i];
  }
  return a2;
}
//****************************************************************************80

double *r8vec_linspace_new ( int n, double a_first, double a_last )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_LINSPACE_NEW creates a vector of linearly spaced values.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
//
//    In other words, the interval is divided into N-1 even subintervals,
//    and the endpoints of intervals are used as the points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    29 March 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double A_FIRST, A_LAST, the first and last entries.
//
//    Output, double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
//
{
  double *a;
  int i;

  a = new double[n];

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - 1 - i ) * a_first 
             + ( double ) (         i ) * a_last ) 
             / ( double ) ( n - 1     );
    }
  }
  return a;
}
//****************************************************************************80

double r8vec_max ( int n, double r8vec[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_MAX returns the value of the maximum element in an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    22 August 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, double R8VEC[N], a pointer to the first entry of the array.
//
//    Output, double R8VEC_MAX, the value of the maximum element.  This
//    is set to 0.0 if N <= 0.
//
{
  int i;
  double value;

  value = r8vec[0];

  for ( i = 1; i < n; i++ )
  {
    if ( value < r8vec[i] )
    {
      value = r8vec[i];
    }
  }
  return value;
}
//****************************************************************************80

double r8vec_min ( int n, double r8vec[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_MIN returns the value of the minimum element in an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    02 July 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, double R8VEC[N], the array to be checked.
//
//    Output, double R8VEC_MIN, the value of the minimum element.
//
{
  int i;
  double value;

  value = r8vec[0];

  for ( i = 1; i < n; i++ )
  {
    if ( r8vec[i] < value )
    {
      value = r8vec[i];
    }
  }
  return value;
}
//****************************************************************************80

double r8vec_norm_affine ( int n, double v0[], double v1[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORM_AFFINE returns the affine L2 norm of an R8VEC.
//
//  Discussion:
//
//    The affine vector L2 norm is defined as:
//
//      R8VEC_NORM_AFFINE(V0,V1)
//        = sqrt ( sum ( 1 <= I <= N ) ( V1(I) - V0(I) )^2 )
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    27 October 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the dimension of the vectors.
//
//    Input, double V0[N], the base vector.
//
//    Input, double V1[N], the vector.
//
//    Output, double R8VEC_NORM_AFFINE, the affine L2 norm.
//
{
  int i;
  double value;

  value = 0.0;

  for ( i = 0; i < n; i++ )
  {
    value = value + ( v1[i] - v0[i] ) * ( v1[i] - v0[i] );
  }
  value = sqrt ( value );

  return value;
}
//****************************************************************************80

void r8vec_print ( int n, double a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_PRINT prints an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    16 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, double A[N], the vector to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << setw(8)  << i
         << ": " << setw(14) << a[i]  << "\n";
  }

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

void r8vec2_print ( int n, double a1[], double a2[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC2_PRINT prints an R8VEC2.
//
//  Discussion:
//
//    An R8VEC2 is a dataset consisting of N pairs of real values, stored
//    as two separate vectors A1 and A2.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    19 November 2002
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, double A1[N], double A2[N], the vectors to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i <= n - 1; i++ )
  {
    cout << setw(6)  << i
         << ": " << setw(14) << a1[i]
         << "  " << setw(14) << a2[i] << "\n";
  }

  return;
}
//****************************************************************************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 GNU LGPL license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

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

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}