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

using namespace std;

int main ( int argc, char *argv[] );
char ch_cap ( char ch );
bool ch_eqi ( char ch1, char ch2 );
int ch_to_digit ( char ch );
void dtable_close_write ( ofstream &output );
double *dtable_data_read ( char *input_filename, int m, int n );
void dtable_data_write ( ofstream &output, int m, int n, double table[] );
void dtable_header_read ( char *input_filename, int *m, int *n );
void dtable_header_write ( char *output_filename, ofstream &output, int m, 
  int n );
void dtable_write ( char *output_filename, int m, int n, double table[], 
  bool header );
int file_column_count ( char *input_filename );
int file_row_count ( char *input_filename );
int i4_power ( int i, int j );
void product_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 product_rule_size ( int point_num_1d, int dim_num );
double r8_epsilon ( void );
int s_len_trim ( char *s );
int s_to_i4 ( char *s, int *last, bool *error );
double s_to_r8 ( char *s, int *lchar, bool *error );
bool s_to_r8vec ( char *s, int n, double rvec[] );
int s_word_count ( char *s );
void timestamp ( void );
char *timestring ( void );
void tuple_next ( int m1, int m2, int n, int *rank, int x[] );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for PRODUCT_RULE.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 May 2007
//
//  Author:
//
//    John Burkardt
//
{
  int dim;
  int dim_num;
  int dim_num_1d;
  bool error;
  bool header;
  int last;
  bool more;
  int point_num;
  int point_num_1d;
  int point_num_1d2;
  char quad_1d_filename[81];
  char quad_filename[] = "product";
  char quad_r_1d_filename[81];
  char quad_r_filename[81];
  char quad_w_1d_filename[81];
  char quad_w_filename[81];
  char quad_x_1d_filename[81];
  char quad_x_filename[81];
  double *r;
  double *r_1d;
  double *w;
  double *w_1d;
  double *x;
  double *x_1d;

  timestamp ( );
  cout << "\n";
  cout << "PRODUCT_RULE\n";
  cout << "  C++ version\n";
  cout << "\n";
  cout << "  Compiled on " << __DATE__ << " at " << __TIME__ << ".\n";
  cout << "\n";
  cout << "  Create a multidimensional product rule\n";
  cout << "  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
  {
    cout << "\n";
    cout << "PRODUCT_RULE:\n";
    cout << "  Enter the \"root\" name of the 1D quadrature files.\n";

    cin.getline ( quad_1d_filename, sizeof ( quad_1d_filename ) );
  }
//
//  Create the names of:
//    the quadrature X file;
//    the quadrature W file;
//    the quadrature R file;
//
  if ( 0 < s_len_trim ( quad_1d_filename ) )
  {
    strcpy ( quad_x_1d_filename, quad_1d_filename );
    strcat ( quad_x_1d_filename, "_x.txt" );
    strcpy ( quad_w_1d_filename, quad_1d_filename );
    strcat ( quad_w_1d_filename, "_w.txt" );
    strcpy ( quad_r_1d_filename, quad_1d_filename );
    strcat ( quad_r_1d_filename, "_r.txt" );
  }
  else
  {
    strcpy ( quad_x_1d_filename, "x.txt" );
    strcpy ( quad_w_1d_filename, "w.txt" );
    strcpy ( quad_r_1d_filename, "r.txt" );
  }
//
//  The second command line argument is the spatial dimension of the product.
//
  if ( 2 < argc )
  {
    dim_num = s_to_i4 ( argv[2], &last, &error );
  }
  else
  {
    cout << "\n";
    cout << "PRODUCT_RULE:\n";
    cout << "  Please enter the desired spatial dimension of the product rule.\n";

    cin >> dim_num;
  }
//
//  Summarize the input.
//
  cout << "\n";
  cout << "PRODUCT_RULE: User input:\n";
  cout << "  Quadrature rule X file = \"" << quad_x_1d_filename
             << "\".\n";
  cout << "  Quadrature rule W file = \"" << quad_w_1d_filename
             << "\".\n";
  cout << "  Quadrature rule R file = \"" << quad_r_1d_filename
             << "\".\n";
  cout << "  Spatial dimension of product = " << dim_num << "\n";
//
//  Read the X file.
//
  dtable_header_read ( quad_x_1d_filename, &dim_num_1d, &point_num_1d );

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

  cout << "\n";
  cout << "  Number of points in 1D rule = " << point_num_1d << "\n";

  x_1d = dtable_data_read ( quad_x_1d_filename, dim_num_1d, point_num_1d );
//
//  Read the W file.
//
  dtable_header_read ( quad_w_1d_filename, &dim_num_1d, &point_num_1d2 );

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

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

  w_1d = dtable_data_read ( quad_w_1d_filename, dim_num_1d, point_num_1d );
//
//  Read the R file.
//
  dtable_header_read ( quad_r_1d_filename, &dim_num_1d, &point_num_1d2 );

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

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

  r_1d = dtable_data_read ( quad_r_1d_filename, 1, 2 );
//
//  Determine size of product rule.
//
  point_num = product_rule_size ( point_num_1d, dim_num );

  cout << "\n";
  cout << "  Number of points in product rule = " << point_num << "\n";
//
//  Compute the product rule.
//
  w = new double [point_num];
  x = new double [dim_num*point_num];
  r = new double [dim_num*2];

  product_rule_set ( point_num_1d, x_1d, w_1d, r_1d, dim_num, point_num, 
    x, w, r );
//
//  Write product rule to files.
//
  strcpy ( quad_x_filename, quad_filename );
  strcat ( quad_x_filename, "_x.txt" );
  strcpy ( quad_w_filename, quad_filename );
  strcat ( quad_w_filename, "_w.txt" );
  strcpy ( quad_r_filename, quad_filename );
  strcat ( quad_r_filename, "_r.txt" );

  cout << "\n";
  cout << "  Creating product quadrature rule X file = \""
       << quad_x_filename << "\".\n";

  header = false;
  dtable_write ( quad_x_filename, dim_num, point_num, x, header );

  cout << "\n";
  cout << "  Creating product quadrature rule W file = \""
       << quad_w_filename << "\".\n";

  header = false;
  dtable_write ( quad_w_filename, 1, point_num, w, header );
 
  cout << "\n";
  cout << "  Creating product quadrature rule R file = \""
       << quad_r_filename << "\".\n";

  header = false;
  dtable_write ( quad_r_filename, dim_num, 2, r, header );

  delete [] w;
  delete [] w_1d;
  delete [] x;
  delete [] x_1d;
  delete [] r;
  delete [] r_1d;

  cout << "\n";
  cout << "PRODUCT_RULE:\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

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

char ch_cap ( char ch )

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    19 July 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the character to capitalize.
//
//    Output, char CH_CAP, the capitalized character.
//
{
  if ( 97 <= ch && ch <= 122 ) 
  {
    ch = ch - 32;
  }   

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

bool ch_eqi ( char ch1, char ch2 )

//****************************************************************************80
//
//  Purpose:
//
//    CH_EQI is true if two characters are equal, disregarding case.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH1, CH2, the characters to compare.
//
//    Output, bool CH_EQI, is true if the two characters are equal,
//    disregarding case.
//
{
  if ( 97 <= ch1 && ch1 <= 122 ) 
  {
    ch1 = ch1 - 32;
  } 
  if ( 97 <= ch2 && ch2 <= 122 ) 
  {
    ch2 = ch2 - 32;
  }     

  return ( ch1 == ch2 );
}
//****************************************************************************80

int ch_to_digit ( char ch )

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    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;
}
//****************************************************************************80

void dtable_close_write ( ofstream &output )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_CLOSE_WRITE closes a file to which a DTABLE was to be written.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    27 September 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream output, the output file stream.
//
{
  output.close ( );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_DATA_READ reads the data from a DTABLE file.
//
//  Discussion:
//
//    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 GNU LGPL license. 
//
//  Modified:
//
//    27 January 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Input, int M, the number of spatial dimensions.
//
//    Input, int N, the number of points.  The program
//    will stop reading data once N values have been read.
//
//    Output, double DTABLE_DATA_READ[M*N], the table data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  char line[255];
  double *table;
  double *x;

  input.open ( input_filename );

  if ( !input )
  {
    cout << "\n";
    cout << "DTABLE_DATA_READ - Fatal error!\n";
    cout << "  Could not open the input file: \"" << input_filename << "\"\n";
    return NULL;
  }

  table = new double[m*n];

  x = new double[m];

  j = 0;

  while ( j < n )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      break;
    }

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

    error = s_to_r8vec ( line, m, x );

    if ( error )
    {
      continue;
    }

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

  }

  input.close ( );

  delete [] x;

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

void dtable_data_write ( ofstream &output, int m, int n, double table[] )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_DATA_WRITE writes data to a DTABLE file.
//
//  Discussion:
//
//    The file should already be open.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    11 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream &OUTPUT, a pointer to the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, double TABLE[M*N], the table data.
//
{
  int i;
  int j;
  char *s;

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << setprecision(16) << setw(24) << table[i+j*m] << "  ";
    }
    output << "\n";
  }

  output.close ( );

  return;
}
//****************************************************************************80
 
void dtable_header_read ( char *input_filename, int *m, int *n )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_READ reads the header from a DTABLE file.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    04 June 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Output, int *M, the number of spatial dimensions.
//
//    Output, int *N, the number of points.
//
{
  *m = file_column_count ( input_filename );

  if ( *m <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_COLUMN_COUNT failed.\n";
    *n = -1;
    return;
  }

  *n = file_row_count ( input_filename );

  if ( *n <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_ROW_COUNT failed.\n";
    return;
  }

  return;
}
//****************************************************************************80
 
void dtable_header_write ( char *output_filename, ofstream &output, int m, 
  int n )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_WRITE writes the header of a DTABLE file.
//
//  Discussion:
//
//    The file should already be open.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    22 March 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *OUTPUT_FILENAME, the output filename.
//
//    Input, ofstream &OUTPUT, the output stream.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
{
  char *s;

  s = timestring ( );

  output << "#  " << output_filename << "\n";
  output << "#  created by dtable_write in table_io.C" << "\n";
  output << "#  at " << s << "\n";
  output << "#\n";
  output << "#  Spatial dimension M = " << m << "\n";
  output << "#  Number of points N =  " << n << "\n";
  output << "#  EPSILON (unit roundoff) = " << r8_epsilon ( ) << "\n";
  output << "#\n";

  delete [] s;

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

void dtable_write ( char *output_filename, int m, int n, double table[], 
  bool header )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_WRITE writes information to a DTABLE file.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    20 July 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *OUTPUT_FILENAME, the output filename.
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, double TABLE[M*N], the table data.
//
//    Input, bool HEADER, is TRUE if the header is to be included.
//
{
  ofstream output;

  output.open ( output_filename );

  if ( !output )
  {
    cout << "\n";
    cout << "DTABLE_WRITE - Fatal error!\n";
    cout << "  Could not open the output file.\n";
    return;
  }

  if ( header )
  {
    dtable_header_write ( output_filename, output, m, n );
  }

  dtable_data_write ( output, m, n, table );

  dtable_close_write ( output );

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

int file_column_count ( char *input_filename )

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the file.
//
//    Output, int FILE_COLUMN_COUNT, the number of columns assumed 
//    to be in the file.
//
{
  int column_num;
  ifstream input;
  bool got_one;
  char line[256];
//
//  Open the file.
//
  input.open ( input_filename );

  if ( !input )
  {
    column_num = -1;
    cout << "\n";
    cout << "FILE_COLUMN_COUNT - Fatal error!\n";
    cout << "  Could not open the file:\n";
    cout << "  \"" << input_filename << "\"\n";
    return column_num;
  }
//
//  Read one line, but skip blank lines and comment lines.
//
  got_one = false;

  for ( ; ; )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      break;
    }

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

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

    got_one = true;
    break;

  }

  if ( !got_one )
  {
    input.close ( );

    input.open ( input_filename );

    for ( ; ; )
    {
      input.getline ( line, sizeof ( line ) );

      if ( input.eof ( ) )
      {
        break;
      }

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

      got_one = true;
      break;

    }

  }

  input.close ( );

  if ( !got_one )
  {
    cout << "\n";
    cout << "FILE_COLUMN_COUNT - Warning!\n";
    cout << "  The file does not seem to contain any data.\n";
    return -1;
  }

  column_num = s_word_count ( line );

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

int file_row_count ( char *input_filename )

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Output, int FILE_ROW_COUNT, the number of rows found.
//
{
  int bad_num;
  int comment_num;
  ifstream input;
  int i;
  char line[100];
  int record_num;
  int row_num;

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

  input.open ( input_filename );

  if ( !input )
  {
    cout << "\n";
    cout << "FILE_ROW_COUNT - Fatal error!\n";
    cout << "  Could not open the input file: \"" << input_filename << "\"\n";
    return (-1);
  }

  for ( ; ; )
  {
    input.getline ( line, sizeof ( line ) );

    if ( input.eof ( ) )
    {
      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;

  }

  input.close ( );

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

int i4_power ( int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4_POWER returns the value of I^J.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    01 April 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    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 )
    {
      cout << "\n";
      cout << "I4_POWER - Fatal error!\n";
      cout << "  I^J requested, with I = 0 and J negative.\n";
      exit ( 1 );
    }
    else
    {
      value = 0;
    }
  }
  else if ( j == 0 )
  {
    if ( i == 0 )
    {
      cout << "\n";
      cout << "I4_POWER - Fatal error!\n";
      cout << "  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;
}
//****************************************************************************80

void product_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[] )

//****************************************************************************80
//
//  Purpose:
//
//    PRODUCT_RULE_SET sets up a product rule.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    08 May 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int POINT_NUM_1D, the order of the 1D rule.
//
//    Input, double X_1D[POINT_NUM_1D], the points of the 1D rule.
//
//    Input, double W_1D[POINT_NUM_1D], the weights of the
//    1D rule.
//
//    Input, double R_1D[2], the extreme points that define
//    the range of the 1D region.
//
//    Input, int DIM_NUM, the spatial dimension.
//
//    Input, int POINT_NUM, the number of points in the product rule.
//
//    Output, double X[DIM_NUM*POINT_NUM], the points of the 
//    product rule.
//
//    Output, double W[POINT_NUM], the weights of the
//    product rule.
//
//    Output, double R[DIM_NUM*2], the extreme points 
//    that define the range of the  product rule region.
//
{
  int dim;
  int *indx;
  int k;

  indx = new int[dim_num];
  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]];
    }
  }

  delete [] 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;
}
//****************************************************************************80

int product_rule_size ( int point_num_1d, int dim_num )

//****************************************************************************80
//
//  Purpose:
//
//    PRODUCT_RULE_SIZE returns the size of a product rule.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    05 May 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int POINT_NUM_1D, the number of points in the 1D rule.
//
//    Input, int DIM_NUM, the spatial dimension.
//
//    Output, int PRODUCT_RULE_SIZE, the number of points in the product rule.
//
{
  int point_num;

  point_num = i4_power ( point_num_1d, dim_num );

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

double r8_epsilon ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_EPSILON returns the R8 roundoff unit.
//
//  Discussion:
//
//    The roundoff unit is a number R which is a power of 2 with the 
//    property that, to the precision of the computer's arithmetic,
//      1 < 1 + R
//    but 
//      1 = ( 1 + R / 2 )
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    01 July 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_EPSILON, the R8 round-off unit.
//
{
  double value;

  value = 1.0;

  while ( 1.0 < ( double ) ( 1.0 + value )  )
  {
    value = value / 2.0;
  }

  value = 2.0 * value;

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

int s_len_trim ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    26 April 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    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;
}
//****************************************************************************80

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

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4 reads an I4 from a string.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a string to be examined.
//
//    Output, int *LAST, the last character of S used to make IVAL.
//
//    Output, bool *ERROR is TRUE if an error occurred.
//
//    Output, 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 = false;
  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 = true;
        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 = true;
        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 = true;
    *last = 0;
  }

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

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

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    24 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    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.
//
//    Output, bool *ERROR, is true if an error occurred.
//
//    Output, 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 = false;
  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 = true;
    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;
}
//****************************************************************************80

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

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8VEC reads an R8VEC from a string.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 February 2001
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string to be read.
//
//    Input, int N, the number of values expected.
//
//    Output, double RVEC[N], the values read from the string.
//
//    Output, bool S_TO_R8VEC, is true if an error occurred.
//
{
  bool error;
  int i;
  int lchar;
  double x;

  error = false;

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

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

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

int s_word_count ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_WORD_COUNT counts the number of "words" in a string.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    30 January 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    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.
//
{
  bool blank;
  int i;
  int word_num;

  word_num = 0;
  blank = true;

  while ( *s ) 
  {
    if ( *s == ' ' )
    {
      blank = true;
    }
    else if ( blank )
    {
      word_num = word_num + 1;
      blank = false;
    }
    *s++;
  }

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

void timestamp ( void )

//****************************************************************************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 GNU LGPL license. 
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  size_t len;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  len = strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}
//****************************************************************************80

char *timestring ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTRING returns the current YMDHMS date as a string.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, char *TIMESTRING, a string containing the current YMDHMS date.
//
{
# define TIME_SIZE 40

  const struct tm *tm;
  size_t len;
  time_t now;
  char *s;

  now = time ( NULL );
  tm = localtime ( &now );

  s = new char[TIME_SIZE];

  len = strftime ( s, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  return s;
# undef TIME_SIZE
}
//****************************************************************************80

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

//****************************************************************************80
//
//  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 GNU LGPL license. 
//
//  Modified:
//
//    29 April 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M1, M2, the minimum and maximum entries.
//
//    Input, int N, the number of components.
//
//    Input/output, int *RANK, counts the elements.
//    On first call, set RANK to 0.  Thereafter, 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.
//
//    Input/output, int X[N], on input the previous tuple.
//    On output, 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;
}