# include <math.h>
# include <stdbool.h>
# include <stdio.h>
# include <stdlib.h>
# include <string.h>
# include <time.h>

# include "lagrange.h"

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 );
char *s_escape_tex ( char *s1 );
void timestamp ( );

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    lagrange_test() tests lagrange().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    06 August 2025

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "lagrange_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test lagrange()\n" );

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

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

void lagrange_basis_antideriv_test ( )

/******************************************************************************/
/*
  Purpose:

    lagrange_basis_antideriv_test() tests lagrange_basis_antideriv().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    07 August 2025

  Author:

    John Burkardt
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  char data2_filename[255];
  FILE *data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  char output_filename[255];
  char prefix[100];
  char *prefix2;
  double *pcof_antideriv;
  double *xpol;
  double *xplot;
  double *yplot;

  printf ( "\n" );
  printf ( "lagrange_basis_antideriv_test():\n" );
  printf ( "  lagrange_basis_antideriv() evaluates the antiderivative\n" );
  printf ( "  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 = ( double * ) malloc ( nplot * sizeof ( double ) );
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = r8poly_value ( npol, pcof_antideriv, xplot[i] );
  }

  strcpy ( prefix, "lagrange_basis_antideriv" );
/*
  Create the data file.
*/
  sprintf ( data_filename, "%s_data.txt", prefix );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < nplot; i++ )
  {
    fprintf ( data_unit, "%g  %g\n", xplot[i], yplot[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );
/*
  Create the data2 file.
*/
  sprintf ( data2_filename, "%s_data2.txt", prefix );
  data2_unit = fopen ( data2_filename, "wt" );
  for ( i = 0; i < npol; i++ )
  {
    fprintf ( data2_unit, "%g  %g\n", xpol[i], 0.0 );
  }
  fclose ( data2_unit );
  printf ( "  Created graphics data file '%s'\n", data2_filename );
/*
  Plot the selected data.
*/
  sprintf ( command_filename, "%s_commands.txt", prefix );
  command_unit = fopen ( command_filename, "wt" );

  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set nokey\n" );
  sprintf ( output_filename, "%s.png", prefix );
  fprintf ( command_unit, "set output '%s\n", output_filename );
  fprintf ( command_unit, "set xlabel '<---X--->'\n" );
  fprintf ( command_unit, "set ylabel '<---Antideriv(L(i)(X))--->'\n" );
  prefix2 = s_escape_tex ( prefix );
  fprintf ( command_unit, "set title '%s'\n", prefix2 );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, "$AXIS << EOL\n" );
  fprintf ( command_unit, "-3.3  0.0\n" );
  fprintf ( command_unit, " 3.3  0.0\n" );
  fprintf ( command_unit, "EOL\n" );
  fprintf ( command_unit, "plot '%s' using 1:2 lw 3 linecolor rgb 'blue', \\\n", data_filename );
  fprintf ( command_unit, "     '%s' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n", data2_filename );
  fprintf ( command_unit, "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n" );
  fclose ( command_unit );
  printf ( "  Created graphics command file '%s'\n", command_filename );
/*
  Free memory.
*/
  free ( pcof_antideriv );
  free ( xplot );
  free ( xpol );
  free ( yplot );

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

void lagrange_basis_coef_test ( )

/******************************************************************************/
/*
  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;
  char s[15];
  double *xpol;

  printf ( "\n" );
  printf ( "lagrange_basis_coef_test():\n" );
  printf ( "  lagrange_basis_coef() returns the coefficients\n" );
  printf ( "  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 );

    sprintf ( s, "L(%d)(x)", ipol );
    r8poly_print ( npol, pcof, s );
    free ( pcof );
  }
/*
  Free memory.
*/
  free ( xpol );

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

void lagrange_basis_deriv_test ( )

/******************************************************************************/
/*
  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
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  char data2_filename[255];
  FILE *data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  char output_filename[255];
  char prefix[100];
  char *prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  printf ( "\n" );
  printf ( "lagrange_basis_deriv_test():\n" );
  printf ( "  lagrange_basis_deriv() evaluates the derivative\n" );
  printf ( "  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 = ( double * ) malloc ( nplot * sizeof ( double ) );
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_deriv ( npol, ipol, xpol, xplot[i] );
  }

  strcpy ( prefix, "lagrange_basis_deriv" );
/*
  Create the data file.
*/
  sprintf ( data_filename, "%s_data.txt", prefix );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < nplot; i++ )
  {
    fprintf ( data_unit, "%g  %g\n", xplot[i], yplot[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );
/*
  Create the data2 file.
*/
  sprintf ( data2_filename, "%s_data2.txt", prefix );
  data2_unit = fopen ( data2_filename, "wt" );
  for ( i = 0; i < npol; i++ )
  {
    fprintf ( data2_unit, "%g  %g\n", xpol[i], 0.0 );
  }
  fclose ( data2_unit );
  printf ( "  Created graphics data file '%s'\n", data2_filename );
/*
  Plot the selected data.
*/
  sprintf ( command_filename, "%s_commands.txt", prefix );
  command_unit = fopen ( command_filename, "wt" );

  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set nokey\n" );
  sprintf ( output_filename, "%s.png", prefix );
  fprintf ( command_unit, "set output '%s\n", output_filename );
  fprintf ( command_unit, "set xlabel '<---X--->'\n" );
  fprintf ( command_unit, "set ylabel '<---dL(i)(X)/dx)--->'\n" );
  prefix2 = s_escape_tex ( prefix );
  fprintf ( command_unit, "set title '%s'\n", prefix2 );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, "$AXIS << EOL\n" );
  fprintf ( command_unit, "-3.3  0.0\n" );
  fprintf ( command_unit, " 3.3  0.0\n" );
  fprintf ( command_unit, "EOL\n" );
  fprintf ( command_unit, "plot '%s' using 1:2 lw 3 linecolor rgb 'blue', \\\n", data_filename );
  fprintf ( command_unit, "     '%s' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n", data2_filename );
  fprintf ( command_unit, "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n" );
  fclose ( command_unit );
  printf ( "  Created graphics command file '%s'\n", command_filename );
/*
  Free memory.
*/
  free ( xplot );
  free ( xpol );
  free ( yplot );

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

void lagrange_basis_deriv2_test ( )

/******************************************************************************/
/*
  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
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  char data2_filename[255];
  FILE *data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  char output_filename[255];
  char prefix[100];
  char *prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  printf ( "\n" );
  printf ( "lagrange_basis_deriv2_test():\n" );
  printf ( "  lagrange_basis_deriv2() evaluates the second derivative\n" );
  printf ( "  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 = ( double * ) malloc ( nplot * sizeof ( double ) );
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_deriv2 ( npol, ipol, xpol, xplot[i] );
  }

  strcpy ( prefix, "lagrange_basis_deriv2" );
/*
  Create the data file.
*/
  sprintf ( data_filename, "%s_data.txt", prefix );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < nplot; i++ )
  {
    fprintf ( data_unit, "%g  %g\n", xplot[i], yplot[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );
/*
  Create the data2 file.
*/
  sprintf ( data2_filename, "%s_data2.txt", prefix );
  data2_unit = fopen ( data2_filename, "wt" );
  for ( i = 0; i < npol; i++ )
  {
    fprintf ( data2_unit, "%g  %g\n", xpol[i], 0.0 );
  }
  fclose ( data2_unit );
  printf ( "  Created graphics data file '%s'\n", data2_filename );
/*
  Plot the selected data.
*/
  sprintf ( command_filename, "%s_commands.txt", prefix );
  command_unit = fopen ( command_filename, "wt" );

  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set nokey\n" );
  sprintf ( output_filename, "%s.png", prefix );
  fprintf ( command_unit, "set output '%s\n", output_filename );
  fprintf ( command_unit, "set xlabel '<---X--->'\n" );
  fprintf ( command_unit, "set ylabel '<---d2L(i)(X)/dx2)--->'\n" );
  prefix2 = s_escape_tex ( prefix );
  fprintf ( command_unit, "set title '%s'\n", prefix2 );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, "$AXIS << EOL\n" );
  fprintf ( command_unit, "-3.3  0.0\n" );
  fprintf ( command_unit, " 3.3  0.0\n" );
  fprintf ( command_unit, "EOL\n" );
  fprintf ( command_unit, "plot '%s' using 1:2 lw 3 linecolor rgb 'blue', \\\n", data_filename );
  fprintf ( command_unit, "     '%s' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n", data2_filename );
  fprintf ( command_unit, "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black'\n" );
  fclose ( command_unit );
  printf ( "  Created graphics command file '%s'\n", command_filename );
/*
  Free memory.
*/
  free ( xplot );
  free ( xpol );
  free ( yplot );

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

void lagrange_basis_value_test ( )

/******************************************************************************/
/*
  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
*/
{
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  char data2_filename[255];
  FILE *data2_unit;
  int i;
  int ipol;
  int nplot;
  int npol;
  char output_filename[255];
  char prefix[100];
  char *prefix2;
  double *xpol;
  double *xplot;
  double *yplot;

  printf ( "\n" );
  printf ( "lagrange_basis_value_test():\n" );
  printf ( "  lagrange_basis_value() evaluates\n" );
  printf ( "  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 = ( double * ) malloc ( nplot * sizeof ( double ) );
  for ( i = 0; i < nplot; i++ )
  {
    yplot[i] = lagrange_basis_value ( npol, ipol, xpol, xplot[i] );
  }

  strcpy ( prefix, "lagrange_basis_value" );
/*
  Create the data file.
*/
  sprintf ( data_filename, "%s_data.txt", prefix );
  data_unit = fopen ( data_filename, "wt" );
  for ( i = 0; i < nplot; i++ )
  {
    fprintf ( data_unit, "%g  %g\n", xplot[i], yplot[i] );
  }
  fclose ( data_unit );
  printf ( "  Created graphics data file '%s'\n", data_filename );
/*
  Create the data2 file.
*/
  sprintf ( data2_filename, "%s_data2.txt", prefix );
  data2_unit = fopen ( data2_filename, "wt" );
  for ( i = 0; i < npol; i++ )
  {
    fprintf ( data2_unit, "%g  %g\n", xpol[i], 0.0 );
  }
  fclose ( data2_unit );
  printf ( "  Created graphics data file '%s'\n", data2_filename );
/*
  Plot the selected data.
*/
  sprintf ( command_filename, "%s_commands.txt", prefix );
  command_unit = fopen ( command_filename, "wt" );

  fprintf ( command_unit, "# %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "# Usage:\n" );
  fprintf ( command_unit, "#  gnuplot < %s\n", command_filename );
  fprintf ( command_unit, "#\n" );
  fprintf ( command_unit, "set term png\n" );
  fprintf ( command_unit, "set nokey\n" );
  sprintf ( output_filename, "%s.png", prefix );
  fprintf ( command_unit, "set output '%s\n", output_filename );
  fprintf ( command_unit, "set xlabel '<---X--->'\n" );
  fprintf ( command_unit, "set ylabel '<---L(i)(X)--->'\n" );
  prefix2 = s_escape_tex ( prefix );
  fprintf ( command_unit, "set title '%s'\n", prefix2 );
  fprintf ( command_unit, "set grid\n" );
  fprintf ( command_unit, "set style data lines\n" );
  fprintf ( command_unit, "$AXIS << EOL\n" );
  fprintf ( command_unit, "-3.3  0.0\n" );
  fprintf ( command_unit, " 3.3  0.0\n" );
  fprintf ( command_unit, "EOL\n" );
  fprintf ( command_unit, "$BLIP << EOL\n" );
  fprintf ( command_unit, "-1.0  0.0\n" );
  fprintf ( command_unit, "-1.0  1.0\n" );
  fprintf ( command_unit, "EOL\n" );
  fprintf ( command_unit, "plot '%s' using 1:2 lw 3 linecolor rgb 'blue', \\\n", data_filename );
  fprintf ( command_unit, "     '%s' using 1:2 with points pt 7 ps 2 lc rgb 'red', \\\n", data2_filename );
  fprintf ( command_unit, "     $AXIS using 1:2 with lines lw 3 linecolor rgb 'black', \\\n" );
  fprintf ( command_unit, "     $BLIP using 1:2 with lines lw 3 linecolor rgb 'red'\n" );
  fclose ( command_unit );
  printf ( "  Created graphics command file '%s'\n", command_filename );
/*
  Free memory.
*/
  free ( xplot );
  free ( xpol );
  free ( yplot );

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

double *r8vec_linspace_new ( int n, double a, double b )

/******************************************************************************/
/*
  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, B, the first and last entries.

  Output:

    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
*/
{
  int i;
  double *x;

  x = ( double * ) malloc ( n * sizeof ( double ) );

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

char *s_escape_tex ( char *s1 )

/******************************************************************************/
/*
  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:

    19 January 2007

  Author:

    John Burkardt

  Input:

    char *S1, the string to be de-escaped.

  Output:

    char *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_length;
  int s2_pos;
  int slash_count;

  s1_length = strlen ( s1 );
/*
  We need to know how many slashes occur in S1, so we
  can allocate S2.

  Note that, alas, the backslash is also the escape in C++,
  so we have to say '\\' when we mean '\'!
*/
  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_length = s1_length + slash_count;
  s2 = ( char * ) malloc ( ( s2_length + 1 ) * sizeof ( char ) );
/*
  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;

  return s2;
}
/******************************************************************************/

void timestamp ( )

/******************************************************************************/
/*
  Purpose:

    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 June 2014

  Author:

    John Burkardt
*/
{
# 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 );

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}