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

using namespace std;

# include "newton_interp_1d.hpp"
# include "test_interp.hpp"

int main ( );
void newton_coef_1d_test ( );
void newton_value_1d_test ( );
void newton_interp_1d_test01 ( int prob );
string i4_to_string ( int i4 );
double *r8mat_copy_new ( int m, int n, double a1[] );
double *r8vec_copy_new ( int n, double a1[] );
double *r8vec_linspace_new ( int n, double a, double b );
double r8vec_max ( int n, double r8vec[] );
double r8vec_min ( int n, double r8vec[] );
double r8vec_norm_affine ( int n, double v0[], double v1[] );
void r8vec_print ( int n, double a[], string title );
void r8vec2_print ( int n, double a1[], double a2[], string title );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    newton_interp_1d_test() tests newton_interp_1d().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 September 2022
//
//  Author:
//
//    John Burkardt
//
{
  int prob;
  int prob_num;

  timestamp ( );
  cout << "\n";
  cout << "newton_interp_1d_test():\n";
  cout << "  C++ version\n";
  cout << "  Test newton_interp_1d().\n";
  cout << "  This test needs the test_interp() library.\n";

  newton_coef_1d_test ( );

  newton_value_1d_test ( );

  prob_num = p00_prob_num ( );

  for ( prob = 1; prob <= prob_num; prob++ )
  {
     newton_interp_1d_test01 ( prob );
  }
//
//  Terminate.
//
  cout << "\n";
  cout << "newton_interp_1d_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void newton_coef_1d_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    newton_coef_1d_test() tests newton_coef_1d().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 July 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *cd;
  int nd = 5;
  double xd[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
  double yd[5] = { 24.0, 0.0, 0.0, 0.0, 0.0 };

  cout << "\n";
  cout << "newton_coef_1d_test():\n";
  cout << "  newton_coef_1d() sets the coefficients for a 1D Newton interpolation.\n";

  r8vec2_print ( nd, xd, yd, "  Interpolation data:" );

  cd = newton_coef_1d ( nd, xd, yd );

  r8vec_print ( nd, cd, "  Newton interpolant coefficients:" );

  delete [] cd;

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

void newton_value_1d_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    newton_value_1d_test() tests newton_value_1d().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 July 2015
//
//  Author:
//
//    John Burkardt
//
{
  double cd[5] = { 24.0, -24.0, +12.0, -4.0, 1.0 };
  int nd = 5;
  int ni = 16;
  double x_hi;
  double x_lo;
  double xd[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
  double *xi;
  double *yi;

  cout << "\n";
  cout << "newton_value_1d_test():\n";
  cout << "  newton_value_1d() evaluates a Newton 1d interpolant.\n";

  r8vec2_print ( nd, xd, cd, "  The Newton interpolant data:" );

  x_lo = 0.0;
  x_hi = 5.0;
  xi = r8vec_linspace_new ( ni, x_lo, x_hi );
  yi = newton_value_1d ( nd, xd, cd, ni, xi );

  r8vec2_print ( ni, xi, yi, "  Newton interpolant values:" );

  delete [] xi;
  delete [] yi;

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

void newton_interp_1d_test01 ( int prob )

//****************************************************************************80
//
//  Purpose:
//
//    newton_interp_1d_test01() tests newton_interp_1d().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    10 July 2015
//
//  Author:
//
//    John Burkardt
//
{
  double *cd;
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  int i;
  double interp_error;
  string interp_filename;
  ofstream interp_unit;
  int j;
  double ld;
  double li;
  int nd;
  int ni;
  string output_filename;
  string title;
  double *xd;
  double *xi;
  double xmax;
  double xmin;
  double *xy;
  double *yd;
  double *yi;
  double ymax;
  double ymin;

  cout << "\n";
  cout << "newton_interp_1d_test01():\n";
  cout << "  Interpolate data from test_interp() problem #" << prob << "\n";

  nd = p00_data_num ( prob );
  cout << "  Number of data points = " << nd << "\n";

  xy = p00_data ( prob, 2, nd );
  
  xd = new double[nd];
  yd = new double[nd];

  for ( i = 0; i < nd; i++ )
  {
    xd[i] = xy[0+i*2];
    yd[i] = xy[1+i*2];
  }

  r8vec2_print ( nd, xd, yd, "  X, Y data:" );
//
//  Get the Newton coefficients.
//
  cd = newton_coef_1d ( nd, xd, yd );
//
//  #1:  Does interpolant match function at interpolation points?
//
  ni = nd;
  xi = r8vec_copy_new ( ni, xd );
  yi = newton_value_1d ( nd, xd, cd, ni, xi );

  interp_error = r8vec_norm_affine ( ni, yi, yd ) / ( double ) ( ni );

  cout << "\n";
  cout << "  L2 interpolation error averaged per interpolant node = " << interp_error << "\n";

  delete [] xi;
  delete [] yi;
//
//  #2: Compare estimated curve length to piecewise linear (minimal) curve length.
//  Assume data is sorted, and normalize X and Y dimensions by (XMAX-XMIN) and
//  (YMAX-YMIN).
//
  xmin = r8vec_min ( nd, xd );
  xmax = r8vec_max ( nd, xd );
  ymin = r8vec_min ( nd, yd );
  ymax = r8vec_max ( nd, yd );

  ni = 501;
  xi = r8vec_linspace_new ( ni, xmin, xmax );
  yi = newton_value_1d ( nd, xd, cd, ni, xi );

  ld = 0.0;
  for ( i = 0; i < nd - 1; i++ )
  {
    ld = ld + sqrt ( pow ( ( xd[i+1] - xd[i] ) / ( xmax - xmin ), 2 )
                   + pow ( ( yd[i+1] - yd[i] ) / ( ymax - ymin ), 2 ) ); 
  }

  li = 0.0;
  for ( i = 0; i < ni - 1; i++ )
  {
    li = li + sqrt ( pow ( ( xi[i+1] - xi[i] ) / ( xmax - xmin ), 2 )
                   + pow ( ( yi[i+1] - yi[i] ) / ( ymax - ymin ), 2 ) );
  }

  cout << "\n";
  cout << "  Normalized length of piecewise linear interpolant = " << ld << "\n";
  cout << "  Normalized length of Newton interpolant           = " << li << "\n";

  delete [] xi;
  delete [] yi;
//
//  Create data file.
//
  data_filename = "data" + i4_to_string ( prob ) + ".txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( j = 0; j < nd; j++ )
  {
    data_unit << "  " << xd[j]
              << "  " << yd[j] << "\n";
  }
  data_unit.close ( );
  cout << "\n";
  cout << "  Created graphics data file \"" << data_filename << "\".\n";
//
//  Create interp file.
//
  ni = 501;
  xmin = r8vec_min ( nd, xd );
  xmax = r8vec_max ( nd, xd );
  xi = r8vec_linspace_new ( ni, xmin, xmax );
  yi = newton_value_1d ( nd, xd, cd, ni, xi );

  interp_filename = "interp" + i4_to_string ( prob ) + ".txt";
  interp_unit.open ( interp_filename.c_str ( ) );
  for ( j = 0; j < ni; j++ )
  {
    interp_unit << "  " << xi[j]
                << "  " << yi[j] << "\n";
  }
  interp_unit.close ( );
  cout << "  Created graphics interp file \"" << interp_filename << "\".\n";
//
//  Plot the data and the interpolant.
//
  command_filename = "commands" + i4_to_string ( prob ) + ".txt";
  command_unit.open ( command_filename.c_str ( ) );

  output_filename = "plot" + i4_to_string ( prob ) + ".png";

  command_unit << "# " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "# Usage:\n";
  command_unit << "#  gnuplot < " << command_filename << "\n";
  command_unit << "#\n";
  command_unit << "set term png\n";
  command_unit << "set output '" << output_filename << "'\n";
  command_unit << "set xlabel '<---X--->'\n";
  command_unit << "set ylabel '<---Y--->'\n";
  command_unit << "set title 'Data versus Newton polynomial interpolant'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << "plot '" << data_filename 
               << "' using 1:2 with points pt 7 ps 2 lc rgb 'blue',\\\n";
  command_unit << "     '" << interp_filename 
               << "' using 1:2 lw 3 linecolor rgb 'red'\n";

  command_unit.close ( );
  cout << "  Created graphics command file \"" << command_filename << "\".\n";
//
//  Free memory.
//
  delete [] cd;
  delete [] xd;
  delete [] xi;
  delete [] xy;
  delete [] yd;
  delete [] yi;

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

string i4_to_string ( int i4 )

//****************************************************************************80
//
//  Purpose:
//
//    i4_to_string() converts an I4 to a C++ string.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    16 January 2013
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int I4, an integer.
//
//    string FORMAT, the format string.
//
//  Output:
//
//    string I4_TO_STRING, the string.
//
{
  ostringstream fred;
  string value;

  fred << i4;

  value = fred.str ( );

  return value;
}
//****************************************************************************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 MIT license.
//
//  Modified:
//
//    03 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, N, the number of rows and columns.
//
//    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 MIT license.
//
//  Modified:
//
//    03 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the vectors.
//
//    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 MIT license.
//
//  Modified:
//
//    29 March 2011
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the vector.
//
//    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 MIT license.
//
//  Modified:
//
//    22 August 2010
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the array.
//
//    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 MIT license.
//
//  Modified:
//
//    02 July 2005
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the array.
//
//    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 MIT license.
//
//  Modified:
//
//    27 October 2010
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the dimension of the vectors.
//
//    double V0[N], the base vector.
//
//    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 MIT license.
//
//  Modified:
//
//    16 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of components of the vector.
//
//    double A[N], the vector to be printed.
//
//    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 MIT license.
//
//  Modified:
//
//    19 November 2002
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of components of the vector.
//
//    double A1[N], double A2[N], the vectors to be printed.
//
//    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 MIT license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
{
# 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
}