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

int main ( int argc, char *argv[] );
char ch_cap ( char ch );
int ch_eqi ( char ch1, char ch2 );
int ch_to_digit ( char ch );
int file_column_count ( char *input_filename );
int file_row_count ( char *input_filename );
int i4_power ( int i, int j );
void power_rule_set ( int point_num_1d, double x_1d[], double w_1d[], 
  double r_1d[], int dim_num, int point_num, double x[], 
  double w[], double r[] );
int power_rule_size ( int point_num_1d, int dim_num );
double *r8mat_data_read ( char *input_filename, int m, int n );
void r8mat_header_read ( char *input_filename, int *m, int *n );
void r8mat_write ( char *output_filename, int m, int n, double table[] );
int s_len_trim ( char *s );
int s_to_i4 ( char *s, int *last, int *error );
double s_to_r8 ( char *s, int *lchar, int *error );
int s_to_r8vec ( char *s, int n, double rvec[] );
int s_word_count ( char *s );
void timestamp ( );
void tuple_next ( int m1, int m2, int n, int *rank, int x[] );

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

int main ( int argc, char *argv[] )

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

    power_rule() constructs a quadrature rule as a power of a given rule.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    05 February 2014

  Author:

    John Burkardt
*/
{
  int dim_num;
  int dim_num_1d;
  int error;
  int last;
  int point_num;
  int point_num_1d;
  int point_num_1d2;
  char quad_1d_filename[80];
  char quad_r_1d_filename[80];
  char quad_r_filename[] = "power_r.txt";
  char quad_w_1d_filename[80];
  char quad_w_filename[] = "power_w.txt";
  char quad_x_1d_filename[80];
  char quad_x_filename[] = "power_x.txt";
  double *r;
  double *r_1d;
  double *w;
  double *w_1d;
  double *x;
  double *x_1d;

  timestamp ( );
  printf ( "\n" );
  printf ( "power_rule():\n" );
  printf ( "  C version\n" );
  printf ( "  Create a multidimensional power rule\n" );
  printf ( "  as a product of identical 1D integration rules.\n" );
/*
  Get the quadrature file root name:
*/
  if ( 1 < argc ) 
  {
    strcpy ( quad_1d_filename, argv[1] );
  }
  else
  {
    printf ( "\n" );
    printf ( "POWER_RULE:\n" );
    printf ( "  Enter the \"root\" name of the 1D quadrature files.\n" );

    scanf ( "%s", quad_1d_filename );
  }
/*
  Create the names of:
    the quadrature X file;
    the quadrature W file;
    the quadrature R file;
*/
  strcpy ( quad_r_1d_filename, quad_1d_filename );
  strcat ( quad_r_1d_filename, "_r.txt" );
  strcpy ( quad_w_1d_filename, quad_1d_filename );
  strcat ( quad_w_1d_filename, "_w.txt" );
  strcpy ( quad_x_1d_filename, quad_1d_filename );
  strcat ( quad_x_1d_filename, "_x.txt" );
/*
  The second command line argument is the spatial dimension.
*/
  if ( 2 < argc )
  {
    dim_num = s_to_i4 ( argv[2], &last, &error );
  }
  else
  {
    printf ( "\n" );
    printf ( "POWER_RULE:\n" );
    printf ( "  Please enter the desired spatial dimension of the rule.\n" );

    scanf ( "%d", &dim_num );
  }
/*
  Summarize the input.
*/
  printf ( "\n" );
  printf ( "POWER_RULE: User input:\n" );
  printf ( "  Quadrature rule X file = \"%s\"\n", quad_x_1d_filename );
  printf ( "  Quadrature rule W file = \"%s\"\n", quad_w_1d_filename );
  printf ( "  Quadrature rule R file = \"%s\"\n", quad_r_1d_filename );
  printf ( "  Spatial dimension = %d\n", dim_num );
/*
  Read the X file.
*/
  r8mat_header_read ( quad_x_1d_filename, &dim_num_1d, &point_num_1d );

  if ( dim_num_1d != 1 ) 
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "POWER_RULE - Fatal error!\n" );
    fprintf ( stderr, "  The 1D quadrature abscissa file should have exactly\n" );
    fprintf ( stderr, "  one value on each line.\n" );
    exit ( 1 );
  }

  printf ( "\n" );
  printf ( "  Number of points in 1D rule = %d\n", point_num_1d );

  x_1d = r8mat_data_read ( quad_x_1d_filename, dim_num_1d, point_num_1d );
/*
  Read the W file.
*/
  r8mat_header_read ( quad_w_1d_filename, &dim_num_1d, &point_num_1d2 );

  if ( dim_num_1d != 1 ) 
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "POWER_RULE - Fatal error!\n" );
    fprintf ( stderr, "  The 1D quadrature weight file should have exactly\n" );
    fprintf ( stderr, "  one value on each line.\n" );
    exit ( 1 );
  }

  if ( point_num_1d2 != point_num_1d )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "POWER_RULE - Fatal error!\n" );
    fprintf ( stderr, "  The 1D quadrature weight file should have exactly\n" );
    fprintf ( stderr, "  the same number of lines as the abscissa file.\n" );
    exit ( 1 );
  }

  w_1d = r8mat_data_read ( quad_w_1d_filename, dim_num_1d, point_num_1d );
/*
  Read the R file.
*/
  r8mat_header_read ( quad_r_1d_filename, &dim_num_1d, &point_num_1d2 );

  if ( dim_num_1d != 1 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "POWER_RULE - Fatal error!\n" );
    fprintf ( stderr, "  The 1D quadrature region file should have exactly\n" );
    fprintf ( stderr, "  one value on each line.\n" );
    exit ( 1 );
  }

  if ( point_num_1d2 != 2 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "POWER_RULE - Fatal error!\n" );
    fprintf ( stderr, "  The 1D quadrature region file should have two lines.\n" );
    exit ( 1 );
  }

  r_1d = r8mat_data_read ( quad_r_1d_filename, 1, 2 );
/*
  Determine size of the rule.
*/
  point_num = power_rule_size ( point_num_1d, dim_num );

  printf ( "\n" );
  printf ( "  Number of points in rule = %d\n", point_num );
/*
  Compute the rule.
*/
  w = ( double * ) malloc ( point_num * sizeof ( double ) );
  x = ( double * ) malloc ( dim_num * point_num * sizeof ( double ) );
  r = ( double * ) malloc ( dim_num * 2 * sizeof ( double ) );

  power_rule_set ( point_num_1d, x_1d, w_1d, r_1d, dim_num, point_num, 
    x, w, r );
/*
  Write rule to files.
*/
  printf ( "\n" );
  printf ( "  Creating quadrature rule X file = \"%s\"\n", quad_x_filename );

  r8mat_write ( quad_x_filename, dim_num, point_num, x );

  printf ( "  Creating quadrature rule W file = \"%s\"\n", quad_w_filename );

  r8mat_write ( quad_w_filename, 1, point_num, w );
 
  printf ( "  Creating quadrature rule R file = \"%s\"\n", quad_r_filename );

  r8mat_write ( quad_r_filename, dim_num, 2, r );
/*
  Free memory.
*/
  free ( w );
  free ( w_1d );
  free ( x );
  free ( x_1d );
  free ( r );
  free ( r_1d );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "power_rule():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

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

char ch_cap ( char ch )

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

    ch_cap() capitalizes a single character.

  Discussion:

    This routine should be equivalent to the library "toupper" function.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    19 July 1998

  Author:

    John Burkardt

  Input:

    char CH, the character to capitalize.

  Output:

    char CH_CAP, the capitalized character.
*/
{
  if ( 97 <= ch && ch <= 122 ) 
  {
    ch = ch - 32;
  }   

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

int ch_eqi ( char ch1, char ch2 )

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

    ch_eqi() is TRUE (1) if two characters are equal, disregarding case.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Input:

    char CH1, CH2, the characters to compare.

  Output:

    int CH_EQI, is TRUE (1) if the two characters are equal,
    disregarding case and FALSE (0) otherwise.
*/
{
  int value;

  if ( 97 <= ch1 && ch1 <= 122 ) 
  {
    ch1 = ch1 - 32;
  } 
  if ( 97 <= ch2 && ch2 <= 122 ) 
  {
    ch2 = ch2 - 32;
  }     
  if ( ch1 == ch2 )
  {
    value = 1;
  }
  else
  {
    value = 0;
  }
  return value;
}
/******************************************************************************/

int ch_to_digit ( char ch )

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

    ch_to_digit() returns the integer value of a base 10 digit.

  Example:

     CH  DIGIT
    ---  -----
    '0'    0
    '1'    1
    ...  ...
    '9'    9
    ' '    0
    'X'   -1

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Input:

    char CH, the decimal digit, '0' through '9' or blank are legal.

  Output:

    int CH_TO_DIGIT, the corresponding integer value.  If the 
    character was 'illegal', then DIGIT is -1.
*/
{
  int digit;

  if ( '0' <= ch && ch <= '9' )
  {
    digit = ch - '0';
  }
  else if ( ch == ' ' )
  {
    digit = 0;
  }
  else
  {
    digit = -1;
  }

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

int file_column_count ( char *input_filename )

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

    file_column_count() counts the number of columns in the first line of a file.

  Discussion:

    The file is assumed to be a simple text file.

    Most lines of the file is presumed to consist of COLUMN_NUM words, separated
    by spaces.  There may also be some blank lines, and some comment lines,
    which have a "#" in column 1.

    The routine tries to find the first non-comment non-blank line and
    counts the number of words in that line.

    If all lines are blanks or comments, it goes back and tries to analyze
    a comment line.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Input:

    char *INPUT_FILENAME, the name of the file.

  Output:

    int FILE_COLUMN_COUNT, the number of columns assumed 
    to be in the file.
*/
{
# define LINE_MAX 255

  int column_num;
  char *error;
  FILE *input;
  int got_one;
  char line[LINE_MAX];
/*
  Open the file.
*/
  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "FILE_COLUMN_COUNT - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the input file: \"%s\"\n",
      input_filename );
    exit ( 1 );
  }
/*
  Read one line, but skip blank lines and comment lines.
*/
  got_one = 0;

  for ( ; ; )
  {
    error = fgets ( line, LINE_MAX, input );

    if ( !error )
    {
      break;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      continue;
    }

    if ( line[0] == '#' )
    {
      continue;
    }

    got_one = 1;
    break;

  }

  if ( got_one == 0 )
  {
    fclose ( input );

    input = fopen ( input_filename, "r" );

    for ( ; ; )
    {
      error = fgets ( line, LINE_MAX, input );

      if ( !error )
      {
        break;
      }

      if ( s_len_trim ( line ) == 0 )
      {
        continue;
      }

      got_one = 1;
      break;
    }
  }

  fclose ( input );

  if ( got_one == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "FILE_COLUMN_COUNT - Warning!\n" );
    fprintf ( stderr, "  The file does not seem to contain any data.\n" );
    exit ( 1 );
  }

  column_num = s_word_count ( line );

  return column_num;

# undef LINE_MAX
}
/******************************************************************************/

int file_row_count ( char *input_filename )

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

    file_row_count() counts the number of row records in a file.

  Discussion:

    It does not count lines that are blank, or that begin with a
    comment symbol '#'.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Input:

    char *INPUT_FILENAME, the name of the input file.

  Output:

    int FILE_ROW_COUNT, the number of rows found.
*/
{
# define LINE_MAX 255

  int comment_num;
  char *error;
  FILE *input;
  char line[LINE_MAX];
  int record_num;
  int row_num;

  row_num = 0;
  comment_num = 0;
  record_num = 0;

  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "FILE_ROW_COUNT - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the input file: \"%s\"\n",
      input_filename );
    exit ( 1 );
  }

  for ( ; ; )
  {
    error = fgets ( line, LINE_MAX, input );

    if ( !error )
    {
      break;
    }

    record_num = record_num + 1;

    if ( line[0] == '#' )
    {
      comment_num = comment_num + 1;
      continue;
    }

    if ( s_len_trim ( line ) == 0 )
    {
      comment_num = comment_num + 1;
      continue;
    }

    row_num = row_num + 1;
  }

  fclose ( input );

  return row_num;

# undef LINE_MAX
}
/******************************************************************************/

int i4_power ( int i, int j )

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

    i4_power() returns the value of I^J.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    23 October 2007

  Author:

    John Burkardt

  Input:

    int I, J, the base and the power.  J should be nonnegative.

  Output:

    int I4_POWER, the value of I^J.
*/
{
  int k;
  int value;

  if ( j < 0 )
  {
    if ( i == 1 )
    {
      value = 1;
    }
    else if ( i == 0 )
    {
      printf ( "\n" );
      printf ( "I4_POWER - Fatal error!\n" );
      printf ( "  I^J requested, with I = 0 and J negative.\n" );
      exit ( 1 );
    }
    else
    {
      value = 0;
    }
  }
  else if ( j == 0 )
  {
    if ( i == 0 )
    {
      printf ( "\n" );
      printf ( "I4_POWER - Fatal error!\n" );
      printf ( "  I^J requested, with I = 0 and J = 0.\n" );
      exit ( 1 );
    }
    else
    {
      value = 1;
    }
  }
  else if ( j == 1 )
  {
    value = i;
  }
  else
  {
    value = 1;
    for ( k = 1; k <= j; k++ )
    {
      value = value * i;
    }
  }
  return value;
}
/******************************************************************************/

void power_rule_set ( int point_num_1d, double x_1d[], double w_1d[], 
  double r_1d[], int dim_num, int point_num, double x[], 
  double w[], double r[] )

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

    power_rule_set() sets up a power rule.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    05 February 2014

  Author:

    John Burkardt

  Input:

    int POINT_NUM_1D, the order of the 1D rule.

    double X_1D[POINT_NUM_1D], the points of the 1D rule.

    double W_1D[POINT_NUM_1D], the weights of the
    1D rule.

    double R_1D[2], the extreme points that define
    the range of the 1D region.

    int DIM_NUM, the spatial dimension.

    int POINT_NUM, the number of points in the rule.

  Output:

    double X[DIM_NUM*POINT_NUM], the points of the rule.

    double W[POINT_NUM], the weights of the rule.

    double R[DIM_NUM*2], the extreme points 
    that define the range of the product rule region.
*/
{
  int dim;
  int *indx;
  int k;

  indx = ( int * ) malloc ( dim_num * sizeof ( int ) );
  k = 0;

  for ( ; ; )
  {
    tuple_next ( 0, point_num_1d-1, dim_num, &k, indx );

    if ( k == 0 )
    {
      break;
    }

    w[k-1] = 1.0;
    for ( dim = 0; dim < dim_num; dim++ )
    {
      w[k-1] = w[k-1] * w_1d[indx[dim]];
    }

    for ( dim = 0; dim < dim_num; dim++ )
    {
      x[dim+(k-1)*dim_num] = x_1d[indx[dim]];
    }
  }

  free ( indx );

  for ( dim = 0; dim < dim_num; dim++ )
  {
    r[dim+0*dim_num] = r_1d[0];
    r[dim+1*dim_num] = r_1d[1];
  }

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

int power_rule_size ( int point_num_1d, int dim_num )

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

    power_rule_size() returns the size of a power rule.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    05 Febraury 2014

  Author:

    John Burkardt

  Input:

    int POINT_NUM_1D, the number of points in the 1D rule.

    int DIM_NUM, the spatial dimension.

  Output:

    int POWER_RULE_SIZE, the number of points in the rule.
*/
{
  int point_num;

  point_num = i4_power ( point_num_1d, dim_num );

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

double *r8mat_data_read ( char *input_filename, int m, int n )

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

    r8mat_data_read() reads the data from an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

    The file is assumed to contain one record per line.

    Records beginning with the '#' character are comments, and are ignored.
    Blank lines are also ignored.

    Each line that is not ignored is assumed to contain exactly (or at least)
    M real numbers, representing the coordinates of a point.

    There are assumed to be exactly (or at least) N such records.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    27 January 2005

  Author:

    John Burkardt

  Input:

    char *INPUT_FILENAME, the name of the input file.

    int M, the number of spatial dimensions.

    int N, the number of points.  The program
    will stop reading data once N values have been read.

  Output:

    double R8MAT_DATA_READ[M*N], the data.
*/
{
# define LINE_MAX 255

  int error;
  char *got_string;
  FILE *input;
  int i;
  int j;
  char line[255];
  double *table;
  double *x;

  input = fopen ( input_filename, "r" );

  if ( !input )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_DATA_READ - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the input file: \"%s\"\n", input_filename );
    exit ( 1 );
  }

  table = ( double * ) malloc ( m * n * sizeof ( double ) );

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

  j = 0;

  while ( j < n )
  {
    got_string = fgets ( line, LINE_MAX, input );

    if ( !got_string )
    {
      break;
    }

    if ( line[0] == '#' || s_len_trim ( line ) == 0 )
    {
      continue;
    }

    error = s_to_r8vec ( line, m, x );

    if ( error == 1 )
    {
      continue;
    }

    for ( i = 0; i < m; i++ )
    {
      table[i+j*m] = x[i];
    }
    j = j + 1;

  }

  fclose ( input );

  free ( x );

  return table;

# undef LINE_MAX
}
/******************************************************************************/
 
void r8mat_header_read ( char *input_filename, int *m, int *n )
 
/******************************************************************************/
/*
  Purpose:

    r8mat_header_read() reads the header from an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    04 June 2004

  Author:

    John Burkardt

  Input:

    char *INPUT_FILENAME, the name of the input file.

  Output:

    int *M, the number of spatial dimensions.

    int *N, the number of points.
*/
{
  *m = file_column_count ( input_filename );

  if ( *m <= 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_HEADER_READ - Fatal error!\n" );
    fprintf ( stderr, "  FILE_COLUMN_COUNT failed.\n" );
    exit ( 1 );
  }

  *n = file_row_count ( input_filename );

  if ( *n <= 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_HEADER_READ - Fatal error!\n" );
    fprintf ( stderr, "  FILE_ROW_COUNT failed.\n" );
    exit ( 1 );
  }

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

void r8mat_write ( char *output_filename, int m, int n, double table[] )

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

    r8mat_write() writes an R8MAT file.

  Discussion:

    An R8MAT is an array of R8's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 June 2009

  Author:

    John Burkardt

  Input:

    char *OUTPUT_FILENAME, the output filename.

    int M, the spatial dimension.

    int N, the number of points.

    double TABLE[M*N], the data.
*/
{
  int i;
  int j;
  FILE *output;
/*
  Open the file.
*/
  output = fopen ( output_filename, "wt" );

  if ( !output )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8MAT_WRITE - Fatal error!\n" );
    fprintf ( stderr, "  Could not open the output file.\n" );
    exit ( 1 );
  }
/*
  Write the data.
*/
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      fprintf ( output, "  %24.16g", table[i+j*m] );
    }
    fprintf ( output, "\n" );
  }
/*
  Close the file.
*/
  fclose ( output );

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

int s_len_trim ( char *s )

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

    s_len_trim() returns the length of a string to the last nonblank.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    26 April 2003

  Author:

    John Burkardt

  Input:

    char *S, a pointer to a string.

  Output:

    int S_LEN_TRIM, the length of the string to the last nonblank.
    If S_LEN_TRIM is 0, then the string is entirely blank.
*/
{
  int n;
  char *t;

  n = strlen ( s );
  t = s + strlen ( s ) - 1;

  while ( 0 < n ) 
  {
    if ( *t != ' ' )
    {
      return n;
    }
    t--;
    n--;
  }

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

int s_to_i4 ( char *s, int *last, int *error )

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

    s_to_i4() reads an I4 from a string.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 June 2003

  Author:

    John Burkardt

  Input:

    char *S, a string to be examined.

  Output:

    int *LAST, the last character of S used to make IVAL.

    int *ERROR is TRUE (1) if an error occurred and FALSE (0) otherwise.

    int *S_TO_I4, the integer value read from the string.
    If the string is blank, then IVAL will be returned 0.
*/
{
  char c;
  int i;
  int isgn;
  int istate;
  int ival;

  *error = 0;
  istate = 0;
  isgn = 1;
  i = 0;
  ival = 0;

  while ( *s ) 
  {
    c = s[i];
    i = i + 1;
/*
  Haven't read anything.
*/
    if ( istate == 0 )
    {
      if ( c == ' ' )
      {
      }
      else if ( c == '-' )
      {
        istate = 1;
        isgn = -1;
      }
      else if ( c == '+' )
      {
        istate = 1;
        isgn = + 1;
      }
      else if ( '0' <= c && c <= '9' )
      {
        istate = 2;
        ival = c - '0';
      }
      else
      {
        *error = 1;
        return ival;
      }
    }
/*
  Have read the sign, expecting digits.
*/
    else if ( istate == 1 )
    {
      if ( c == ' ' )
      {
      }
      else if ( '0' <= c && c <= '9' )
      {
        istate = 2;
        ival = c - '0';
      }
      else
      {
        *error = 1;
        return ival;
      }
    }
/*
  Have read at least one digit, expecting more.
*/
    else if ( istate == 2 )
    {
      if ( '0' <= c && c <= '9' )
      {
        ival = 10 * (ival) + c - '0';
      }
      else
      {
        ival = isgn * ival;
        *last = i - 1;
        return ival;
      }

    }
  }
/*
  If we read all the characters in the string, see if we're OK.
*/
  if ( istate == 2 )
  {
    ival = isgn * ival;
    *last = s_len_trim ( s );
  }
  else
  {
    *error = 1;
    *last = 0;
  }

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

double s_to_r8 ( char *s, int *lchar, int *error )

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

    s_to_r8() reads an R8 value from a string.

  Discussion:

    We have had some trouble with input of the form 1.0E-312.
    For now, let's assume anything less than 1.0E-20 is zero.

    This routine will read as many characters as possible until it reaches
    the end of the string, or encounters a character which cannot be
    part of the real number.

    Legal input is:

       1 blanks,
       2 '+' or '-' sign,
       2.5 spaces
       3 integer part,
       4 decimal point,
       5 fraction part,
       6 'E' or 'e' or 'D' or 'd', exponent marker,
       7 exponent sign,
       8 exponent integer part,
       9 exponent decimal point,
      10 exponent fraction part,
      11 blanks,
      12 final comma or semicolon.

    with most quantities optional.

  Example:

    S                 R

    '1'               1.0
    '     1   '       1.0
    '1A'              1.0
    '12,34,56'        12.0
    '  34 7'          34.0
    '-1E2ABCD'        -100.0
    '-1X2ABCD'        -1.0
    ' 2E-1'           0.2
    '23.45'           23.45
    '-4.2E+2'         -420.0
    '17d2'            1700.0
    '-14e-2'         -0.14
    'e2'              100.0
    '-12.73e-9.23'   -12.73 * 10.0^(-9.23)

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    24 June 2005

  Author:

    John Burkardt

  Input:

    char *S, the string containing the
    data to be read.  Reading will begin at position 1 and
    terminate at the end of the string, or when no more
    characters can be read to form a legal real.  Blanks,
    commas, or other nonnumeric data will, in particular,
    cause the conversion to halt.

  Output:

    int *LCHAR, the number of characters read from
    the string to form the number, including any terminating
    characters such as a trailing comma or blanks.

    int *ERROR, is TRUE (1) if an error occurred and FALSE (0)
    otherwise.

    double S_TO_R8, the value that was read from the string.
*/
{
  char c;
  int ihave;
  int isgn;
  int iterm;
  int jbot;
  int jsgn;
  int jtop;
  int nchar;
  int ndig;
  double r;
  double rbot;
  double rexp;
  double rtop;
  char TAB = 9;

  nchar = s_len_trim ( s );
  *error = 0;
  r = 0.0;
  *lchar = -1;
  isgn = 1;
  rtop = 0.0;
  rbot = 1.0;
  jsgn = 1;
  jtop = 0;
  jbot = 1;
  ihave = 1;
  iterm = 0;

  for ( ; ; )
  {
    c = s[*lchar+1];
    *lchar = *lchar + 1;
/*
  Blank or TAB character.
*/
    if ( c == ' ' || c == TAB )
    {
      if ( ihave == 2 )
      {
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        iterm = 1;
      }
      else if ( 1 < ihave )
      {
        ihave = 11;
      }
    }
/*
  Comma.
*/
    else if ( c == ',' || c == ';' )
    {
      if ( ihave != 1 )
      {
        iterm = 1;
        ihave = 12;
        *lchar = *lchar + 1;
      }
    }
/*
  Minus sign.
*/
    else if ( c == '-' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
        isgn = -1;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
        jsgn = -1;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Plus sign.
*/
    else if ( c == '+' )
    {
      if ( ihave == 1 )
      {
        ihave = 2;
      }
      else if ( ihave == 6 )
      {
        ihave = 7;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Decimal point.
*/
    else if ( c == '.' )
    {
      if ( ihave < 4 )
      {
        ihave = 4;
      }
      else if ( 6 <= ihave && ihave <= 8 )
      {
        ihave = 9;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Exponent marker.
*/
    else if ( ch_eqi ( c, 'E' ) || ch_eqi ( c, 'D' ) )
    {
      if ( ihave < 6 )
      {
        ihave = 6;
      }
      else
      {
        iterm = 1;
      }
    }
/*
  Digit.
*/
    else if ( ihave < 11 && '0' <= c && c <= '9' )
    {
      if ( ihave <= 2 )
      {
        ihave = 3;
      }
      else if ( ihave == 4 )
      {
        ihave = 5;
      }
      else if ( ihave == 6 || ihave == 7 )
      {
        ihave = 8;
      }
      else if ( ihave == 9 )
      {
        ihave = 10;
      }

      ndig = ch_to_digit ( c );

      if ( ihave == 3 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
      }
      else if ( ihave == 5 )
      {
        rtop = 10.0 * rtop + ( double ) ndig;
        rbot = 10.0 * rbot;
      }
      else if ( ihave == 8 )
      {
        jtop = 10 * jtop + ndig;
      }
      else if ( ihave == 10 )
      {
        jtop = 10 * jtop + ndig;
        jbot = 10 * jbot;
      }
    }
/*
  Anything else is regarded as a terminator.
*/
    else
    {
      iterm = 1;
    }
/*
  If we haven't seen a terminator, and we haven't examined the
  entire string, go get the next character.
*/
    if ( iterm == 1 || nchar <= *lchar + 1 )
    {
      break;
    }

  }
/*
  If we haven't seen a terminator, and we have examined the
  entire string, then we're done, and LCHAR is equal to NCHAR.
*/
  if ( iterm != 1 && (*lchar) + 1 == nchar )
  {
    *lchar = nchar;
  }
/*
  Number seems to have terminated.  Have we got a legal number?
  Not if we terminated in states 1, 2, 6 or 7!
*/
  if ( ihave == 1 || ihave == 2 || ihave == 6 || ihave == 7 )
  {
    *error = 1;
    return r;
  }
/*
  Number seems OK.  Form it.

  We have had some trouble with input of the form 1.0E-312.
  For now, let's assume anything less than 1.0E-20 is zero.
*/
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      if ( jsgn * jtop < -20 )
      {
        rexp = 0.0;
      }
      else
      {
        rexp = pow ( ( double ) 10.0, ( double ) ( jsgn * jtop ) );
      }
    }
    else
    {
      if ( jsgn * jtop < -20 * jbot )
      {
        rexp = 0.0;
      }
      else
      {
        rexp = jsgn * jtop;
        rexp = rexp / jbot;
        rexp = pow ( ( double ) 10.0, ( double ) rexp );
      }
    }

  }

  r = isgn * rexp * rtop / rbot;

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

int s_to_r8vec ( char *s, int n, double rvec[] )

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

    s_to_r8vec() reads an R8VEC from a string.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    19 February 2001

  Author:

    John Burkardt

  Input:

    char *S, the string to be read.

    int N, the number of values expected.

  Output:

    double RVEC[N], the values read from the string.

    int S_TO_R8VEC, is TRUE (1) if an error occurred and FALSE (0)
    otherwise.
*/
{
  int error;
  int i;
  int lchar;

  error = 0;

  for ( i = 0; i < n; i++ )
  {
    rvec[i] = s_to_r8 ( s, &lchar, &error );

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

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

int s_word_count ( char *s )

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

    s_word_count() counts the number of "words" in a string.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    16 September 2015

  Author:

    John Burkardt

  Input:

    char *S, the string to be examined.

  Output:

    int S_WORD_COUNT, the number of "words" in the string.
    Words are presumed to be separated by one or more blanks.
*/
{
  int blank;
  int word_num;
  char *t;

  word_num = 0;
  blank = 1;
  t = s;

  while ( *t )
  {
    if ( *t == ' ' || *t == '\n' )
    {
      blank = 1;
    }
    else if ( blank )
    {
      word_num = word_num + 1;
      blank = 0;
    }
    t++;
  }

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

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 );

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

  return;
# undef TIME_SIZE
}
/******************************************************************************/

void tuple_next ( int m1, int m2, int n, int *rank, int x[] )

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

    tuple_next() computes the next element of a tuple space.

  Discussion:

    The elements are N vectors.  Each entry is constrained to lie
    between M1 and M2.  The elements are produced one at a time.
    The first element is
      (M1,M1,...,M1),
    the second element is
      (M1,M1,...,M1+1),
    and the last element is
      (M2,M2,...,M2)
    Intermediate elements are produced in lexicographic order.

  Example:

    N = 2, M1 = 1, M2 = 3

    INPUT        OUTPUT
    -------      -------
    Rank  X      Rank   X
    ----  ---    -----  ---
    0     * *    1      1 1
    1     1 1    2      1 2
    2     1 2    3      1 3
    3     1 3    4      2 1
    4     2 1    5      2 2
    5     2 2    6      2 3
    6     2 3    7      3 1
    7     3 1    8      3 2
    8     3 2    9      3 3
    9     3 3    0      0 0

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    29 April 2003

  Author:

    John Burkardt

  Input:

    int M1, M2, the minimum and maximum entries.

    int N, the number of components.

    int *RANK, counts the elements.
    On first call, set RANK to 0.  

    int X[N]: the current tuple.

  Output:

    int *RANK, counts the elements.
    The output value of RANK
    will indicate the order of the element returned.  When there are no
    more elements, RANK will be returned as 0.

    int X[N]: the next tuple.

*/
{
  int i;
  int j;

  if ( m2 < m1 )
  {
    *rank = 0;
    return;
  }

  if ( *rank <= 0 )
  {
    for ( i = 0; i < n; i++ )
    {
      x[i] = m1;
    }
    *rank = 1;
  }
  else
  {
    *rank = *rank + 1;
    i = n - 1;

    for ( ; ; )
    {

      if ( x[i] < m2 )
      {
        x[i] = x[i] + 1;
        break;
      }

      x[i] = m1;

      if ( i == 0 )
      {
        *rank = 0;
        for ( j = 0; j < n; j++ )
        {
          x[j] = m1;
        }
        break;
      }
      i = i - 1;
    }
  }
  return;
}