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

# include "pwl_interp_1d.h"
# include "test_interp.h"

int main ( );
void pwl_basis_1d_test ( );
void pwl_value_1d_test ( );
void pwl_interp_1d_test01 ( int prob );
void r8mat_print ( int m, int n, double a[], char *title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title );
void r8mat_transpose_print ( int m, int n, double a[], char *title );
void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo,
  int ihi, int jhi, char *title );
double r8vec_diff_norm ( int n, double a[], double b[] );
double *r8vec_linspace_new ( int n, double a, double b );
double r8vec_max ( int n, double r8vec[] );
double r8vec_min ( int n, double r8vec[] );
void r8vec2_print ( int n, double a1[], double a2[], char *title );
void timestamp ( );

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

int main ( )

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

    pwl_interp_1d_test() tests pwl_interp_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 July 2015

  Author:

    John Burkardt
*/
{
  int prob;
  int prob_num;

  timestamp ( );
  printf ( "\n" );
  printf ( "pwl_interp_1d_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test pwl_interp_1d().\n" );
  printf ( "  The test needs the test_interp() library.\n" );

  pwl_basis_1d_test ( );

  pwl_value_1d_test ( );

  prob_num = p00_prob_num ( );
  for ( prob = 1; prob <= prob_num; prob++ )
  {
    pwl_interp_1d_test01 ( prob );
  }
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "pwl_interp_1d_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

void pwl_basis_1d_test ( )

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

    pwl_basis_1d_test() tests pwl_basis_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 July 2015

  Author:

    John Burkardt
*/
{
  double *lb;
  int nd = 4;
  int ni = 21;
  double x_max;
  double x_min;
  double xd[4] = { 0.0, 2.0, 5.0, 10.0 };
  double *xi;

  printf ( "\n" );
  printf ( "pwl_basis_1d_test():\n" );
  printf ( "  pwl_basis_1d() evaluates the piecewise linear 1D basis\n" );
  printf ( "  functions.\n" );

  x_min = 0.0;
  x_max = 10.0;
  xi = r8vec_linspace_new ( ni, x_min, x_max );

  lb = pwl_basis_1d ( nd, xd, ni, xi );

  r8mat_print ( ni, nd, lb, "  The piecewise linear basis functions:" );

  free ( lb );
  free ( xi );

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

void pwl_value_1d_test ( )

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

    pwl_value_1d_test() tests pwl_value_1d().

  Discussion:

    f(x) = x^3 - 12 x^2 + 39 x - 28 = ( x - 1 ) * ( x - 4 ) * ( x - 7 )

  Licensing:

    This code is distributed under the MIT license.

  Modified: 

    01 July 2015

  Author:

    John Burkardt
*/
{
  int nd = 4;
  int ni = 21;
  double x_max;
  double x_min;
  double xd[4] = { 0.0, 2.0, 5.0, 10.0 };
  double yd[4] = { -28.0, +10.0, -8.0, +162.0 };
  double *xi;
  double *yi;
 
  printf ( "\n" );
  printf ( "pwl_value_1d_test():\n" );
  printf ( "  pwl_value_1d() evaluates a piecewise linear 1D interpolant.\n" );

  x_min = 0.0;
  x_max = 10.0;
  xi = r8vec_linspace_new ( ni, x_min, x_max );

  yi = pwl_value_1d ( nd, xd, yd, ni, xi );

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

  free ( xi );
  free ( yi );

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

void pwl_interp_1d_test01 ( int prob )

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

    pwl_interp_1d_test01() tests pwl_interp_1d().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    31 May 2012

  Author:

    John Burkardt

  Parameters:

    Input, int PROB, the problem index.
*/
{
  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;
  int nd;
  int ni;
  char output_filename[255];
  double *xd;
  double *xi;
  double *xy;
  double xmax;
  double xmin;
  double *yd;
  double *yi;

  printf ( "\n" );
  printf ( "pwl_interp_1d_test01():\n" );
  printf ( "  pwl_interp_1d() evaluates the piecewise linear interpolant.\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 );
  
  r8mat_transpose_print ( 2, nd, xy, "  Data array:" );

  xd = ( double * ) malloc ( nd * sizeof ( double ) );
  yd = ( double * ) malloc ( nd * sizeof ( double ) );

  for ( i = 0; i < nd; i++ )
  {
    xd[i] = xy[0+2*i];
    yd[i] = xy[1+2*i];
  }
/*
  Does interpolant match function at interpolation points?
*/
  ni = nd;

  xi = ( double * ) malloc ( ni * sizeof ( double ) );
  for ( i = 0; i < ni; i++ )
  {
    xi[i] = xd[i];
  }

  yi = pwl_value_1d ( nd, xd, yd, ni, xi );

  interp_error = r8vec_diff_norm ( ni, yi, yd ) / ( double ) ( ni );

  printf ( "\n" );
  printf ( "  L2 interpolation error averaged per interpolant node = %g\n", interp_error );
/*
  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.
*/
  free ( xi );
  free ( yi );

  ni = 501;
  xmin = r8vec_min ( nd, xd );
  xmax = r8vec_max ( nd, xd );
  xi = r8vec_linspace_new ( ni, xmin, xmax );
  yi = pwl_value_1d ( nd, xd, yd, 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 piecewise linear 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 ( xd );
  free ( xi );
  free ( xy );
  free ( yd );
  free ( yi );

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

void r8mat_print ( int m, int n, double a[], char *title )

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

    r8mat_print() prints an R8MAT.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

    Entry A(I,J) is stored as A[I+J*M]

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    28 May 2008

  Author:

    John Burkardt

  Input:

    int M, the number of rows in A.

    int N, the number of columns in A.

    double A[M*N], the M by N matrix.

    char *TITLE, a title.
*/
{
  r8mat_print_some ( m, n, a, 1, 1, m, n, title );

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

void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title )

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

    r8mat_print_some() prints some of an R8MAT.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 June 2013

  Author:

    John Burkardt

  Input:

    int M, the number of rows of the matrix.
    M must be positive.

    int N, the number of columns of the matrix.
    N must be positive.

    double A[M*N], the matrix.

    int ILO, JLO, IHI, JHI, designate the first row and
    column, and the last row and column to be printed.

    char *TITLE, a title.
*/
{
# define INCX 5

  int i;
  int i2hi;
  int i2lo;
  int j;
  int j2hi;
  int j2lo;

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

  if ( m <= 0 || n <= 0 )
  {
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  (None)\n" );
    return;
  }
/*
  Print the columns of the matrix, in strips of 5.
*/
  for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX )
  {
    j2hi = j2lo + INCX - 1;
    if ( n < j2hi )
    {
      j2hi = n;
    }
    if ( jhi < j2hi )
    {
      j2hi = jhi;
    }

    fprintf ( stdout, "\n" );
/*
  For each column J in the current range...

  Write the header.
*/
    fprintf ( stdout, "  Col:  ");
    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "  %7d     ", j - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row\n" );
    fprintf ( stdout, "\n" );
/*
  Determine the range of the rows in this strip.
*/
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( m < ihi )
    {
      i2hi = m;
    }
    else
    {
      i2hi = ihi;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
/*
  Print out (up to) 5 entries in row I, that lie in the current strip.
*/
      fprintf ( stdout, "%5d:", i - 1 );
      for ( j = j2lo; j <= j2hi; j++ )
      {
        fprintf ( stdout, "  %14g", a[i-1+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

  return;
# undef INCX
}
/******************************************************************************/

void r8mat_transpose_print ( int m, int n, double a[], char *title )

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

    r8mat_transpose_print() prints an R8MAT, transposed.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    28 May 2008

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A[M*N], an M by N matrix to be printed.

    Input, char *TITLE, a title.
*/
{
  r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo,
  int ihi, int jhi, char *title )

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

    r8mat_transpose_print_some() prints some of an R8MAT, transposed.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    10 September 2013

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A[M*N], an M by N matrix to be printed.

    Input, int ILO, JLO, the first row and column to print.

    Input, int IHI, JHI, the last row and column to print.

    Input, char *TITLE, a title.
*/
{
# define INCX 5

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int i2lo_hi;
  int i2lo_lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

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

  if ( m <= 0 || n <= 0 )
  {
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  (None)\n" );
    return;
  }

  if ( ilo < 1 )
  {
    i2lo_lo = 1;
  }
  else
  {
    i2lo_lo = ilo;
  }

  if ( ihi < m )
  {
    i2lo_hi = m;
  }
  else
  {
    i2lo_hi = ihi;
  }

  for ( i2lo = i2lo_lo; i2lo <= i2lo_hi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;

    if ( m < i2hi )
    {
      i2hi = m;
    }
    if ( ihi < i2hi )
    {
      i2hi = ihi;
    }

    inc = i2hi + 1 - i2lo;

    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row:" );
    for ( i = i2lo; i <= i2hi; i++ )
    {
      fprintf ( stdout, "  %7d     ", i - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Col\n" );
    fprintf ( stdout, "\n" );

    if ( jlo < 1 )
    {
      j2lo = 1;
    }
    else
    {
      j2lo = jlo;
    }
    if ( n < jhi )
    {
      j2hi = n;
    }
    else
    {
      j2hi = jhi;
    }
    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "%5d:", j - 1 );
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        fprintf ( stdout, "  %14g", a[(i-1)+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

  return;
# undef INCX
}
/******************************************************************************/

double r8vec_diff_norm ( int n, double a[], double b[] )

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

    r8vec_diff_norm() returns the L2 norm of the difference of R8VEC's.

  Discussion:

    An R8VEC is a vector of R8's.

    The vector L2 norm is defined as:

      R8VEC_NORM_L2 = sqrt ( sum ( 1 <= I <= N ) A(I)^2 ).

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 June 2011

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of entries in A.

    Input, double A[N], B[N], the vectors.

    Output, double R8VEC_DIFF_NORM, the L2 norm of A - B.
*/
{
  int i;
  double value;

  value = 0.0;

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

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

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

  Parameters:

    Input, int N, the number of entries in the vector.

    Input, 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

  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;

  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

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

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:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  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
}