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

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 );
int file_column_count ( string input_filename );
int file_row_count ( string input_filename );
int product_rule_size ( string list_filename, int list_num );
double *r8mat_data_read ( string input_filename, int m, int n );
void r8mat_header_read ( string input_filename, int *m, int *n );
void r8mat_write ( string output_filename, int m, int n, double table[] );
void r8vec_direct_product ( int factor_index, int factor_order, 
  double factor_value[], int factor_num, int point_num, double x[] );
void r8vec_direct_product2 ( int factor_index, int factor_order, 
  double factor_value[], int factor_num, int point_num, double w[] );
int s_len_trim ( string s );
int s_to_i4 ( string s, int *last, bool *error );
double s_to_r8 ( string s, int *lchar, bool *error );
bool s_to_r8vec ( string s, int n, double rvec[] );
int s_word_count ( string s );
void timestamp ( );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for PRODUCT_RULE.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    13 May 2007
//
//  Author:
//
//    John Burkardt
//
{
  int dim;
  int dim_num;
  int dim_num_1d;
  string list_filename;
  int list_num;
  ifstream list_unit;
  int point;
  int point_num;
  int point_num_1d;
  int point_num_1d2;
  string quad_filename;
  string quad_1d_filename;
  string quad_r_1d_filename;
  string quad_r_filename;
  string quad_w_1d_filename;
  string quad_w_filename;
  string quad_x_1d_filename;
  string quad_x_filename;
  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 distinct 1D integration rules.\n";
//
//  Get the list filename:
//
  if ( 1 < argc ) 
  {
    list_filename = argv[1];
  }
  else
  {
    cout << "\n";
    cout << "PRODUCT_RULE:\n";
    cout << "  Enter the name of the file listing the factors.\n";

    cin >> list_filename;
  }
//
//  Get the product file root name:
//
  if ( 2 < argc ) 
  {
    quad_filename = argv[2];
  }
  else
  {
    cout << "\n";
    cout << "PRODUCT_RULE:\n";
    cout << "  Enter the file prefix to use for the output files\n";
    cout << "  describing the product rule.\n";

    cin >> quad_filename;
  }
//
//  Count the items in the list file.
//
  list_num = file_row_count ( list_filename );
//
//  Determine the spatial dimension and number of points in the product.
//
  dim_num = list_num;
  point_num = product_rule_size ( list_filename, list_num );
//
//  Allocate the product items.
//
  x = new double[dim_num*point_num];
  w = new double[point_num];
  r = new double[dim_num*2];

  for ( point = 0; point < point_num; point++ )
  {
    for ( dim = 0; dim < dim_num; dim++ )
    {
      x[dim+point*dim_num] = 0.0;
    }
  }
  for ( point = 0; point < point_num; point++ )
  {
    w[point] = 1.0;
  }
  for ( point = 0; point < 2; point++ )
  {
    for ( dim = 0; dim < dim_num; dim++ )
    {
      r[dim+point*dim_num] = 0.0;
    }
  }

  list_unit.open ( list_filename.c_str ( ) );

  if ( !list_unit )
  {
    cout << "\n";
    cout << "PRODUCT_RULE - Fatal error!\n";
    cout << "  Could not open the list file.\n";
    exit ( 1 );
  }
//
//  Read the factor information and apply it.
//
  for ( dim = 0; dim < dim_num; dim++ )
  {
    list_unit >> quad_1d_filename;

    quad_x_1d_filename = quad_1d_filename + "_x.txt";
    quad_w_1d_filename = quad_1d_filename + "_w.txt";
    quad_r_1d_filename = quad_1d_filename + "_r.txt";
//
//  Read the X file.
//
    r8mat_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 = 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 ) 
    {
      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 = 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 )
    { 
      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 = r8mat_data_read ( quad_r_1d_filename, 1, 2 );
//
//  Update the X, W, and R of the product rule.
//
    r8vec_direct_product ( dim, point_num_1d, x_1d, dim_num, point_num, x );

    r8vec_direct_product2 ( dim, point_num_1d, w_1d, dim_num, point_num, w );

    r[dim+0*dim_num] = r_1d[0];
    r[dim+1*dim_num] = r_1d[1];

    delete [] x_1d;
    delete [] w_1d;
    delete [] r_1d;
  }
//
//  Write product rule to files.
//
  quad_x_filename = quad_filename + "_x.txt";
  quad_w_filename = quad_filename + "_w.txt";
  quad_r_filename = quad_filename + "_r.txt";

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

  r8mat_write ( quad_x_filename, dim_num, point_num, x );

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

  r8mat_write ( quad_w_filename, 1, point_num, w );
 
  cout << "\n";
  cout << "  Creating product quadrature rule R file = \""
       << quad_r_filename << "\".\n";

  r8mat_write ( quad_r_filename, dim_num, 2, r );
//
//  Free memory.
//
  delete [] w;
  delete [] x;
  delete [] r;
//
//  Terminate.
//
  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 MIT 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 MIT 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 MIT 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 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

int file_column_count ( string filename )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_COLUMN_COUNT counts the columns in the first line of a file.
//
//  Discussion:
//
//    The file is assumed to be a simple text file.
//
//    Most lines of the file are 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:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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;
  string text;
//
//  Open the file.
//
  input.open ( filename.c_str ( ) );

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

  for ( ; ; )
  {
    getline ( input, text );

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

    if ( s_len_trim ( text ) <= 0 )
    {
      continue;
    }

    if ( text[0] == '#' )
    {
      continue;
    }
    got_one = true;
    break;
  }

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

    input.open ( filename.c_str ( ) );

    for ( ; ; )
    {
      input >> text;

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

      if ( s_len_trim ( text ) == 0 )
      {
        continue;
      }
      got_one = true;
      break;
    }
  }

  input.close ( );

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

  column_num = s_word_count ( text );

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

int file_row_count ( string 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 MIT license.
//
//  Modified:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string INPUT_FILENAME, the name of the input file.
//
//    Output, int FILE_ROW_COUNT, the number of rows found.
//
{
  int comment_num;
  ifstream input;
  string line;
  int record_num;
  int row_num;

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

  input.open ( input_filename.c_str ( ) );

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

  for ( ; ; )
  {
    getline ( input, 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 product_rule_size ( string list_filename, int list_num )

//****************************************************************************80
//
//  Purpose:
//
//    PRODUCT_RULE_SIZE returns the size of a product rule of distinct factors.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    11 May 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string LIST_FILENAME, a file containing a list
//    of prefixes defining quadrature rules.
//
//    Input, int LIST_NUM, the number of prefixes in the file.
//
//    Output, int PRODUCT_RULE_SIZE, the number of points in the product rule.
//
{
  int dim_num_1d;
  int list;
  ifstream list_unit;
  int point_num;
  int point_num_1d;
  string quad_1d_filename;
  string quad_x_1d_filename;

  point_num = 1;

  list_unit.open ( list_filename.c_str ( ) );

  if ( !list_unit )
  {
    cout << "\n";
    cout << "PRODUCT_RULE_SIZE - Fatal error!\n";
    cout << "  Nonzero value of IOS while opening list file.\n";
    exit ( 1 );
  }

  for ( list = 1; list <= list_num; list++ )
  {
    list_unit >> quad_1d_filename;

    quad_x_1d_filename = quad_1d_filename + "_x.txt";
    
    r8mat_header_read ( quad_x_1d_filename, &dim_num_1d, &point_num_1d );

    point_num = point_num * point_num_1d;
  }

  list_unit.close ( );

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

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

//****************************************************************************80
//
//  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 '#' 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:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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 R8MAT_DATA_READ[M*N], the data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  string line;
  double *table;
  double *x;

  input.open ( input_filename.c_str ( ) );

  if ( !input )
  {
    cerr << "\n";
    cerr << "R8MAT_DATA_READ - Fatal error!\n";
    cerr << "  Could not open the input file: \"" << input_filename << "\"\n";
    exit ( 1 );
  }

  table = new double[m*n];

  x = new double[m];

  j = 0;

  while ( j < n )
  {
    getline ( input, 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 r8mat_header_read ( string input_filename, int *m, int *n )

//****************************************************************************80
//
//  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:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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 )
  {
    cerr << "\n";
    cerr << "R8MAT_HEADER_READ - Fatal error!\n";
    cerr << "  FILE_COLUMN_COUNT failed.\n";
    exit ( 1 );
  }

  *n = file_row_count ( input_filename );

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

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

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

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_WRITE writes an R8MAT file with no header.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    29 June 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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.
//
{
  int i;
  int j;
  ofstream output;
//
//  Open the file.
//
  output.open ( output_filename.c_str ( ) );

  if ( !output )
  {
    cerr << "\n";
    cerr << "R8MAT_WRITE - Fatal error!\n";
    cerr << "  Could not open the output file.\n";
    return;
  }
//
//  Write the data.
//
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << "  " << setw(24) << setprecision(16) << table[i+j*m];
    }
    output << "\n";
  }
//
//  Close the file.
//
  output.close ( );

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

void r8vec_direct_product ( int factor_index, int factor_order, 
  double factor_value[], int factor_num, int point_num, double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_DIRECT_PRODUCT creates a direct product of R8VEC's.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    To explain what is going on here, suppose we had to construct
//    a multidimensional quadrature rule as the product of K rules
//    for 1D quadrature.
//
//    The product rule will be represented as a list of points and weights.
//
//    The J-th item in the product rule will be associated with
//      item J1 of 1D rule 1,
//      item J2 of 1D rule 2, 
//      ..., 
//      item JK of 1D rule K.
//
//    In particular, 
//      X(J) = ( X(1,J1), X(2,J2), ..., X(K,JK))
//    and
//      W(J) = W(1,J1) * W(2,J2) * ... * W(K,JK)
//
//    So we can construct the quadrature rule if we can properly
//    distribute the information in the 1D quadrature rules.
//
//    This routine carries out that task.
//
//    Another way to do this would be to compute, one by one, the
//    set of all possible indices (J1,J2,...,JK), and then index
//    the appropriate information.  An advantage of the method shown
//    here is that you can process the K-th set of information and
//    then discard it.
//
//  Example:
//
//    Rule 1: 
//      Order = 4
//      X(1:4) = ( 1, 2, 3, 4 )
//
//    Rule 2:
//      Order = 3
//      X(1:3) = ( 10, 20, 30 )
//
//    Rule 3:
//      Order = 2
//      X(1:2) = ( 100, 200 )
//
//    Product Rule:
//      Order = 24
//      X(1:24) = 
//        ( 1, 10, 100 )
//        ( 2, 10, 100 )
//        ( 3, 10, 100 )
//        ( 4, 10, 100 )
//        ( 1, 20, 100 )
//        ( 2, 20, 100 )
//        ( 3, 20, 100 )
//        ( 4, 20, 100 )
//        ( 1, 30, 100 )
//        ( 2, 30, 100 )
//        ( 3, 30, 100 )
//        ( 4, 30, 100 )
//        ( 1, 10, 200 )
//        ( 2, 10, 200 )
//        ( 3, 10, 200 )
//        ( 4, 10, 200 )
//        ( 1, 20, 200 )
//        ( 2, 20, 200 )
//        ( 3, 20, 200 )
//        ( 4, 20, 200 )
//        ( 1, 30, 200 )
//        ( 2, 30, 200 )
//        ( 3, 30, 200 )
//        ( 4, 30, 200 )
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    18 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int FACTOR_INDEX, the index of the factor being processed.
//    The first factor processed must be factor 0.
//
//    Input, int FACTOR_ORDER, the order of the factor.
//
//    Input, double FACTOR_VALUE[FACTOR_ORDER], the factor values
//    for factor FACTOR_INDEX.
//
//    Input, int FACTOR_NUM, the number of factors.
//
//    Input, int POINT_NUM, the number of elements in the direct product.
//
//    Input/output, double X[FACTOR_NUM*POINT_NUM], the elements of the
//    direct product, which are built up gradually.  
//
//  Local Parameters:
//
//    Local, int START, the first location of a block of values to set.
//
//    Local, int CONTIG, the number of consecutive values to set.
//
//    Local, int SKIP, the distance from the current value of START
//    to the next location of a block of values to set.
//
//    Local, int REP, the number of blocks of values to set.
//
{
  static int contig = 0;
  int i;
  int j;
  int k;
  static int rep = 0;
  static int skip = 0;
  int start;

  if ( factor_index == 0 )
  {
    contig = 1;
    skip = 1;
    rep = point_num;
    for ( j = 0; j < point_num; j++ )
    {
      for ( i = 0; i < factor_num; i++ )
      {
        x[i+j*factor_num] = 0.0;
      }
    }
  }

  rep = rep / factor_order;
  skip = skip * factor_order;

  for ( i = 0; i < factor_order; i++ )
  {
    start = 0 + i * contig;

    for ( k = 1; k <= rep; k++ )
    {
      for ( j = start; j < start + contig; j++ )
      {
        x[factor_index+j*factor_num] = factor_value[i];
      }
      start = start + skip;
    }
  }
  contig = contig * factor_order;

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

void r8vec_direct_product2 ( int factor_index, int factor_order, 
  double factor_value[], int factor_num, int point_num, double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_DIRECT_PRODUCT2 creates a direct product of R8VEC's.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    To explain what is going on here, suppose we had to construct
//    a multidimensional quadrature rule as the product of K rules
//    for 1D quadrature.
//
//    The product rule will be represented as a list of points and weights.
//
//    The J-th item in the product rule will be associated with
//      item J1 of 1D rule 1,
//      item J2 of 1D rule 2, 
//      ..., 
//      item JK of 1D rule K.
//
//    In particular, 
//      X(J) = ( X(1,J1), X(2,J2), ..., X(K,JK))
//    and
//      W(J) = W(1,J1) * W(2,J2) * ... * W(K,JK)
//
//    So we can construct the quadrature rule if we can properly
//    distribute the information in the 1D quadrature rules.
//
//    This routine carries out that task for the weights W.
//
//    Another way to do this would be to compute, one by one, the
//    set of all possible indices (J1,J2,...,JK), and then index
//    the appropriate information.  An advantage of the method shown
//    here is that you can process the K-th set of information and
//    then discard it.
//
//  Example:
//
//    Rule 1: 
//      Order = 4
//      W(1:4) = ( 2, 3, 5, 7 )
//
//    Rule 2:
//      Order = 3
//      W(1:3) = ( 11, 13, 17 )
//
//    Rule 3:
//      Order = 2
//      W(1:2) = ( 19, 23 )
//
//    Product Rule:
//      Order = 24
//      W(1:24) =
//        ( 2 * 11 * 19 )
//        ( 3 * 11 * 19 )
//        ( 4 * 11 * 19 )
//        ( 7 * 11 * 19 )
//        ( 2 * 13 * 19 )
//        ( 3 * 13 * 19 )
//        ( 5 * 13 * 19 )
//        ( 7 * 13 * 19 )
//        ( 2 * 17 * 19 )
//        ( 3 * 17 * 19 )
//        ( 5 * 17 * 19 )
//        ( 7 * 17 * 19 )
//        ( 2 * 11 * 23 )
//        ( 3 * 11 * 23 )
//        ( 5 * 11 * 23 )
//        ( 7 * 11 * 23 )
//        ( 2 * 13 * 23 )
//        ( 3 * 13 * 23 )
//        ( 5 * 13 * 23 )
//        ( 7 * 13 * 23 )
//        ( 2 * 17 * 23 )
//        ( 3 * 17 * 23 )
//        ( 5 * 17 * 23 )
//        ( 7 * 17 * 23 )
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    24 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int FACTOR_INDEX, the index of the factor being processed.
//    The first factor processed must be factor 0.
//
//    Input, int FACTOR_ORDER, the order of the factor.
//
//    Input, double FACTOR_VALUE[FACTOR_ORDER], the factor values for
//    factor FACTOR_INDEX.
//
//    Input, int FACTOR_NUM, the number of factors.
//
//    Input, int POINT_NUM, the number of elements in the direct product.
//
//    Input/output, double W[POINT_NUM], the elements of the
//    direct product, which are built up gradually.  
//
//  Local Parameters:
//
//    Local, integer START, the first location of a block of values to set.
//
//    Local, integer CONTIG, the number of consecutive values to set.
//
//    Local, integer SKIP, the distance from the current value of START
//    to the next location of a block of values to set.
//
//    Local, integer REP, the number of blocks of values to set.
//
{
  static int contig = 0;
  int i;
  int j;
  int k;
  static int rep = 0;
  static int skip = 0;
  int start;

  if ( factor_index == 0 )
  {
    contig = 1;
    skip = 1;
    rep = point_num;
    for ( i = 0; i < point_num; i++ )
    {
      w[i] = 1.0;
    }
  }

  rep = rep / factor_order;
  skip = skip * factor_order;

  for ( j = 0; j < factor_order; j++ )
  {
    start = 0 + j * contig;

    for ( k = 1; k <= rep; k++ )
    {
      for ( i = start; i < start + contig; i++ )
      {
        w[i] = w[i] * factor_value[j];
      }
      start = start + skip;
    }
  }

  contig = contig * factor_order;

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

int s_len_trim ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, 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;

  n = s.length ( );

  while ( 0 < n )
  {
    if ( s[n-1] != ' ' )
    {
      return n;
    }
    n = n - 1;
  }

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

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

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4 reads an I4 from a string.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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;

  for ( ; ; )
  {
    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 ( string s, int *lchar, bool *error )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8 reads an R8 from a string.
//
//  Discussion:
//
//    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:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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 real 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.
//
  if ( jtop == 0 )
  {
    rexp = 1.0;
  }
  else
  {
    if ( jbot == 1 )
    {
      rexp = pow ( 10.0, jsgn * jtop );
    }
    else
    {
      rexp = jsgn * jtop;
      rexp = rexp / jbot;
      rexp = pow ( 10.0, rexp );
    }

  }

  r = isgn * rexp * rtop / rbot;

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

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

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_R8VEC reads an R8VEC from a string.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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.
//
{
  int begin;
  bool error;
  int i;
  int lchar;
  int length;

  begin = 0;
  length = s.length ( );
  error = 0;

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

    if ( error )
    {
      return error;
    }
    begin = begin + lchar;
    length = length - lchar;
  }

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

int s_word_count ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_WORD_COUNT counts the number of "words" in a string.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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 char_count;
  int i;
  int word_count;

  word_count = 0;
  blank = true;

  char_count = s.length ( );

  for ( i = 0; i < char_count; i++ )
  {
    if ( isspace ( s[i] ) )
    {
      blank = true;
    }
    else if ( blank )
    {
      word_count = word_count + 1;
      blank = false;
    }
  }

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

void timestamp ( )

//****************************************************************************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 MIT license. 
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}