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

using namespace std;

# include "lagrange.hpp"

int main ( );
void lagrange_basis_antideriv_test ( );
void lagrange_basis_coef_test ( );
void lagrange_basis_deriv_test ( );
void lagrange_basis_deriv2_test ( );
void lagrange_basis_value_test ( );
double *r8vec_linspace_new ( int n, double a, double b );
string s_escape_tex ( string s1 );
void timestamp ( );

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

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_test() tests lagrange().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  timestamp ( );
  cout << "\n";
  cout << "lagrange_test():\n";
  cout << "  C++ version\n";
  cout << "  Test lagrange()\n";

  lagrange_basis_antideriv_test ( );
  lagrange_basis_coef_test ( );
  lagrange_basis_deriv_test ( );
  lagrange_basis_deriv2_test ( );
  lagrange_basis_value_test ( );
//
//  Terminate.
//
  cout << "\n";
  cout << "lagrange_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

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

void lagrange_basis_antideriv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_basis_antideriv_test() tests lagrange_basis_antideriv().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  string data2_filename;
  ofstream data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  string output_filename;
  string prefix;
  string prefix2;
  double *pcof_antideriv;
  double *xpol;
  double *xplot;
  double *yplot;

  cout << "\n";
  cout << "lagrange_basis_antideriv_test():\n";
  cout << "  lagrange_basis_antideriv() evaluates the antiderivative\n";
  cout << "  of a Lagrange basis polynomial.\n";

  npol = 7;
  ipol = 2;
  xpol = r8vec_linspace_new ( npol, -3.0, +3.0 );
//
//  Get coefficients of antiderivative.
//
  pcof_antideriv = lagrange_basis_antideriv ( npol, ipol, xpol );

  nplot = 101;
  xplot = r8vec_linspace_new ( nplot, -3.3, +3.5 );
  yplot = new double[nplot];
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = r8poly_value ( npol, pcof_antideriv, xplot[i] );
  }

  prefix = "lagrange_basis_antideriv";
//
//  Create the data file.
//
  data_filename = prefix + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < nplot; i++ )
  {
    data_unit << xplot[i] << "  "
              << yplot[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '"
       << data_filename << "'\n";
//
//  Create the data2 file.
//
  data2_filename = prefix + "_data2.txt";
  data2_unit.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < npol; i++ )
  {
    data2_unit << xpol[i] << "  "
               << 0.0 << "\n";
  }
  data2_unit.close ( );
  cout << "  Created graphics data file '"
       << data2_filename << "'\n";
//
//  Plot the selected data.
//
  command_filename = prefix + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );

  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 nokey\n";
  output_filename = prefix + ".png";
  command_unit << "set output '" << output_filename << "'\n";
  command_unit << "set xlabel '<---X--->'\n";
  command_unit << "set ylabel '<---Antideriv(L(i)(X))--->'\n";
  prefix2 = s_escape_tex ( prefix );
  command_unit << "set title '" << prefix2 << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << "$AXIS << EOL\n";
  command_unit << "-3.3  0.0\n";
  command_unit << " 3.3  0.0\n";
  command_unit << "EOL\n";
  command_unit << "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue', \\\n";
  command_unit << "     '" << data2_filename << "' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n";
  command_unit << "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n";
  command_unit.close ( );
  cout << "  Created graphics command file '"
       << command_filename << "'.";
//
//  Free memory.
//
  delete [] pcof_antideriv;
  delete [] xplot;
  delete [] xpol;
  delete [] yplot;

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

void lagrange_basis_coef_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_basis_coef_test() tests lagrange_basis_coef().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    06 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  int ipol;
  int npol;
  double *pcof;
  string s;
  double *xpol;

  cout << "\n";
  cout << "lagrange_basis_coef_test():\n";
  cout << "  lagrange_basis_coef() returns the coefficients\n";
  cout << "  for a Lagrange basis polynomial.\n";

  npol = 7;
 
  xpol = r8vec_linspace_new ( npol, -3.0, +3.0 );

  r8vec_print ( npol, xpol, "  Abscissas:" );

  for ( ipol = 0; ipol < npol; ipol++ )
  {
    pcof = lagrange_basis_coef ( npol, ipol, xpol );

    s = "L(" + to_string ( ipol ) + ")(x)";
    r8poly_print ( npol, pcof, s );
    delete [] pcof;
  }
//
//  Free memory.
//
  delete [] xpol;

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

void lagrange_basis_deriv_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_basis_deriv_test() tests lagrange_basis_deriv().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    06 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  string data2_filename;
  ofstream data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  string output_filename;
  string prefix;
  string prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  cout << "\n";
  cout << "lagrange_basis_deriv_test():\n";
  cout << "  lagrange_basis_deriv() evaluates the derivative\n";
  cout << "  of a Lagrange basis polynomial.\n";

  npol = 7;
  ipol = 2;
  xpol = r8vec_linspace_new ( npol, -3.0, +3.0 );

  nplot = 101;
  xplot = r8vec_linspace_new ( nplot, -3.3, +3.5 );
  yplot = new double[nplot];
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_deriv ( npol, ipol, xpol, xplot[i] );
  }

  prefix = "lagrange_basis_deriv";
//
//  Create the data file.
//
  data_filename = prefix + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < nplot; i++ )
  {
    data_unit << xplot[i] << "  "
              << yplot[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '"
       << data_filename << "'\n";
//
//  Create the data2 file.
//
  data2_filename = prefix + "_data2.txt";
  data2_unit.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < npol; i++ )
  {
    data2_unit << xpol[i] << "  "
               << 0.0 << "\n";
  }
  data2_unit.close ( );
  cout << "  Created graphics data file '"
       << data2_filename << "'\n";
//
//  Plot the selected data.
//
  command_filename = prefix + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );

  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 nokey\n";
  output_filename = prefix + ".png";
  command_unit << "set output '" << output_filename << "\n";
  command_unit << "set xlabel '<---X--->'\n";
  command_unit << "set ylabel '<---dL(i)(X)/dx)--->'\n";
  prefix2 = s_escape_tex ( prefix );
  command_unit << "set title '" << prefix2 << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << "$AXIS << EOL\n";
  command_unit << "-3.3  0.0\n";
  command_unit << " 3.3  0.0\n";
  command_unit << "EOL\n";
  command_unit << "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue', \\\n";
  command_unit << "     '" << data2_filename << "' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n";
  command_unit << "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n";
  command_unit.close ( );
  cout << "  Created graphics command file '"
       << command_filename << "'.";
//
//  Free memory.
//
  delete [] xplot;
  delete [] xpol;
  delete [] yplot;

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

void lagrange_basis_deriv2_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_basis_deriv2_test() tests lagrange_basis_deriv2().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    06 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  string data2_filename;
  ofstream data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  string output_filename;
  string prefix;
  string prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  cout << "\n";
  cout << "lagrange_basis_deriv2_test():\n";
  cout << "  lagrange_basis_deriv2() evaluates the second derivative\n";
  cout << "  of a Lagrange basis polynomial.\n";

  npol = 7;
  ipol = 2;
  xpol = r8vec_linspace_new ( npol, -3.0, +3.0 );

  nplot = 101;
  xplot = r8vec_linspace_new ( nplot, -3.3, +3.5 );
  yplot = new double[nplot];
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_deriv2 ( npol, ipol, xpol, xplot[i] );
  }

  prefix = "lagrange_basis_deriv2";
//
//  Create the data file.
//
  data_filename = prefix + "_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < nplot; i++ )
  {
    data_unit << xplot[i] << "  "
              << yplot[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '"
       << data_filename << "'\n";
//
//  Create the data2 file.
//
  data2_filename = prefix + "_data2.txt";
  data2_unit.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < npol; i++ )
  {
    data2_unit << xpol[i] << "  "
               << 0.0 << "\n";
  }
  data2_unit.close ( );
  cout << "  Created graphics data file '"
       << data2_filename << "'\n";
//
//  Plot the selected data.
//
  command_filename = prefix + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );

  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 nokey\n";
  output_filename = prefix + ".png";
  command_unit << "set output '" << output_filename << "\n";
  command_unit << "set xlabel '<---X--->'\n";
  command_unit << "set ylabel '<---d2L(i)(X)/dx2)--->'\n";
  prefix2 = s_escape_tex ( prefix );
  command_unit << "set title '" << prefix2 << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << "$AXIS << EOL\n";
  command_unit << "-3.3  0.0\n";
  command_unit << " 3.3  0.0\n";
  command_unit << "EOL\n";
  command_unit << "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue', \\\n";
  command_unit << "     '" << data2_filename << "' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n";
  command_unit << "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n";
  command_unit.close ( );
  cout << "  Created graphics command file '"
       << command_filename << "'.";
//
//  Free memory.
//
  delete [] xplot;
  delete [] xpol;
  delete [] yplot;

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

void lagrange_basis_value_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    lagrange_basis_value_test() tests lagrange_basis_value().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    06 August 2025
//
//  Author:
//
//    John Burkardt
//
{
  string command_filename;
  ofstream command_unit;
  string data_filename;
  ofstream data_unit;
  string data2_filename;
  ofstream data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  string output_filename;
  string prefix;
  string prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  cout << "\n";
  cout << "lagrange_basis_value_test():\n";
  cout << "  lagrange_basis_value() evaluates\n";
  cout << "  a Lagrange basis polynomial.\n";

  npol = 7;
  ipol = 2;
  xpol = r8vec_linspace_new ( npol, -3.0, +3.0 );

  nplot = 101;
  xplot = r8vec_linspace_new ( nplot, -3.3, +3.5 );
  yplot = new double[nplot];
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_value ( npol, ipol, xpol, xplot[i] );
  }

  prefix = "lagrange_basis_value";
//
//  Create the data file.
//
  data_filename = prefix +"_data.txt";
  data_unit.open ( data_filename.c_str ( ) );
  for ( i = 0; i < nplot; i++ )
  {
    data_unit << xplot[i] << "  "
              << yplot[i] << "\n";
  }
  data_unit.close ( );
  cout << "  Created graphics data file '"
       << data_filename << "'\n";
//
//  Create the data2 file.
//
  data2_filename = prefix + "_data2.txt";
  data2_unit.open ( data2_filename.c_str ( ) );
  for ( i = 0; i < npol; i++ )
  {
    data2_unit << xpol[i] << "  "
               << 0.0 << "\n";
  }
  data2_unit.close ( );
  cout << "  Created graphics data file '"
       << data2_filename << "'\n";
//
//  Plot the selected data.
//
  command_filename = prefix + "_commands.txt";
  command_unit.open ( command_filename.c_str ( ) );

  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 nokey\n";
  output_filename = prefix + ".png";
  command_unit << "set output '" << output_filename << "\n";
  command_unit << "set xlabel '<---X--->'\n";
  command_unit << "set ylabel '<---L(i)(X)--->'\n";
  prefix2 = s_escape_tex ( prefix );
  command_unit << "set title '" << prefix2 << "'\n";
  command_unit << "set grid\n";
  command_unit << "set style data lines\n";
  command_unit << "$AXIS << EOL\n";
  command_unit << "-3.3  0.0\n";
  command_unit << " 3.3  0.0\n";
  command_unit << "EOL\n";
  command_unit << "$BLIP << EOL\n";
  command_unit << "-1.0  0.0\n";
  command_unit << "-1.0  1.0\n";
  command_unit << "EOL\n";
  command_unit << "plot '" << data_filename << "' using 1:2 lw 3 linecolor rgb 'blue', \\\n";
  command_unit << "     '" << data2_filename << "' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n";
  command_unit << "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black', \\\n";
  command_unit << "     $BLIP using 1:2 with lines lw 3 linecolor rgb 'red'\n";
  command_unit.close ( );
  cout << "  Created graphics command file '"
       << command_filename << "'.";
//
//  Free memory.
//
  delete [] xplot;
  delete [] xpol;
  delete [] yplot;

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

string s_escape_tex ( string s1 )

//****************************************************************************80
//
//  Purpose:
//
//    s_escape_tex() de-escapes TeX escape sequences.
//
//  Discussion:
//
//    In particular, every occurrence of the characters '\', '_',
//    '^', '{' and '}' will be replaced by '\\', '\_', '\^',
//    '\{' and '\}'.  A TeX interpreter, on seeing these character
//    strings, is then likely to return the original characters.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    29 August 2009
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    string S1, the string to be de-escaped.
//
//  Output:
//
//    string S_ESCAPE_TEX, a copy of the string,
//    modified to avoid TeX escapes.
//
{
  char ch;
  int s1_length;
  int s1_pos;
  char *s2;
  int s2_pos;
  string s3;
  int slash_count;

  s1_length = s1.length ( );

  slash_count = 0;
  for ( s1_pos = 0; s1_pos < s1_length; s1_pos++ )
  {
    ch = s1[s1_pos];

    if ( ch == '\\' ||
         ch == '_' ||
         ch == '^' ||
         ch == '{' ||
         ch == '}' )
    {
      slash_count = slash_count + 1;
    }
  }
  s2 = new char[s1_length + slash_count + 1];
//
//  Now copy S1 into S2.
//
  s1_pos = 0;
  s2_pos = 0;

  for ( s1_pos = 0; s1_pos < s1_length; s1_pos++ )
  {
    ch = s1[s1_pos];

    if ( ch == '\\' ||
         ch == '_' ||
         ch == '^' ||
         ch == '{' ||
         ch == '}' )
    {
      s2[s2_pos] = '\\';
      s2_pos = s2_pos + 1;
    }

    s2[s2_pos] = ch;
    s2_pos = s2_pos + 1;
  }

  s2[s2_pos] = '\0';
  s2_pos = s2_pos + 1;

  s3 = string ( s2 );

  return s3;
}
//****************************************************************************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:
//
//    19 March 2018
//
//  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
}