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

# include "newton_interp_1d.h"
# include "test_interp.h"

int main ( );
void newton_coef_1d_test ( );
void newton_value_1d_test ( );
void newton_interp_1d_test01 ( int prob );
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[], char *title );
void r8vec2_print ( int n, double a1[], double a2[], char *title );
void timestamp ( );

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

int main ( )

/******************************************************************************/
/*
  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 ( );
  printf ( "\n" );
  printf ( "newton_interp_1d_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test newton_interp_1d().\n" );
  printf ( "  This test needs the test_interp() library as well.\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.
*/
  printf ( "\n" );
  printf ( "newton_interp_1d_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void newton_coef_1d_test ( )

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

    newton_coef_1d_test() tests newton_coef_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 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 };

  printf ( "\n" );
  printf ( "newton_coef_1d_test():\n" );
  printf ( "  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:" );

  free ( cd );

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

void newton_value_1d_test ( )

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

    newton_value_1d_test() tests newton_value_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 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;

  printf ( "\n" );
  printf ( "newton_value_1d_test():\n" );
  printf ( "  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:" );

  free ( xi );
  free ( yi );

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

void newton_interp_1d_test01 ( int prob )

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

    newton_interp_1d_test01() tests newton_interp_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 July 2015

  Author:

    John Burkardt
*/
{
  double *cd;
  char command_filename[255];
  FILE *command_unit;
  char data_filename[255];
  FILE *data_unit;
  int i;
  double interp_error;
  char interp_filename[255];
  FILE *interp_unit;
  int j;
  double ld;
  double li;
  int nd;
  int ni;
  char output_filename[255];
  double *xd;
  double *xi;
  double xmax;
  double xmin;
  double *xy;
  double *yd;
  double *yi;
  double ymax;
  double ymin;

  printf ( "\n" );
  printf ( "newton_interp_1d_test01():\n" );
  printf ( "  Interpolate data from test_interp() problem #%d\n", prob );

  nd = p00_data_num ( prob );
  printf ( "  Number of data points = %d\n", nd );

  xy = p00_data ( prob, 2, nd );
  
  xd = ( double * ) malloc ( nd * sizeof ( double ) );
  yd = ( double * ) malloc ( nd * sizeof ( double ) );

  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 );

  printf ( "\n" );
  printf ( "  L2 interpolation error averaged per interpolant node = %g\n", interp_error );

  free ( xi );
  free ( 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 ) );
  }

  printf ( "\n" );
  printf ( "  Normalized length of piecewise linear interpolant = %g\n", ld );
  printf ( "  Normalized length of Newton interpolant           = %g\n", li );

  free ( xi );
  free ( yi );
/*
  Create data file.
*/
  sprintf ( data_filename, "data%02d.txt", prob );
  data_unit = fopen ( data_filename, "wt" );
  for ( j = 0; j < nd; j++ )
  {
    fprintf ( data_unit, "  %14g  %14g\n", xd[j], yd[j] );
  }
  fclose ( data_unit );
  printf ( "\n" );
  printf ( "  Created graphics data file \"%s\".\n", data_filename );
/*
  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 );

  sprintf ( interp_filename, "interp%02d.txt", prob );
  interp_unit = fopen ( interp_filename, "wt" );
  for ( j = 0; j < ni; j++ )
  {
    fprintf ( interp_unit, "  %g  %g\n", xi[j], yi[j] );
  }
  fclose ( interp_unit );
  printf ( "  Created graphics interp file \"%s\".\n", interp_filename );
/*
  Plot the data and the interpolant.
*/
  sprintf ( command_filename, "commands%02d.txt", prob );
  command_unit = fopen ( command_filename, "wt" );

  sprintf ( output_filename, "plot%02d.png", prob );

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

  fclose ( command_unit );
  printf ( "  Created graphics command file \"%s\".\n", command_filename );
/*
  Free memory.
*/
  free ( cd );
  free ( xd );
  free ( xi );
  free ( yd );
  free ( yi );

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

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

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

    r8vec_copy_new() copies an R8VEC.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 August 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 = ( double * ) malloc ( n * sizeof ( double ) );

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

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

double r8vec_max ( int n, double r8vec[] )

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

    r8vec_max() returns the value of the maximum element in a R8VEC.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    05 May 2006

  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;

  if ( n <= 0 )
  {
    value = 0.0;
    return value;
  }

  value = r8vec[0];

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

double r8vec_min ( int n, double r8vec[] )

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

    r8vec_min() returns the value of the minimum element in a R8VEC.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    05 May 2006

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

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

/******************************************************************************/
/*
  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 whose affine L2 norm is desired.

  Output:

    double R8VEC_NORM_AFFINE, the affine L2 norm of V1.
*/
{
  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;
}
/******************************************************************************/

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

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

    08 April 2009

  Author:

    John Burkardt

  Input:

    int N, the number of components of the vector.

    double A[N], the vector to be printed.

    char *TITLE, a title.
*/
{
  int i;

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );
  fprintf ( stdout, "\n" );
  for ( i = 0; i < n; i++ )
  {
    fprintf ( stdout, "  %8d: %14g\n", i, a[i] );
  }

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

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

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

    26 March 2009

  Author:

    John Burkardt

  Input:

    int N, the number of components of the vector.

    double A1[N], double A2[N], the vectors to be printed.

    char *TITLE, a title.
*/
{
  int i;

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );
  fprintf ( stdout, "\n" );
  for ( i = 0; i < n; i++ )
  {
    fprintf ( stdout, "  %4d: %14g  %14g\n", i, a1[i], a2[i] );
  }

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

void timestamp ( )

/******************************************************************************/
/*
  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
*/
{
# 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 );

  fprintf ( stdout, "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}