# 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 );
double *fem1d_approximate ( int sample_node_num, int sample_value_dim, 
  double sample_node_x[], double sample_value[], int fem_node_num, 
  double fem_node_x[], int fem_element_order, int fem_element_num, 
  int fem_value_dim, int fem_value_num );
int file_column_count ( string input_filename );
int file_row_count ( string input_filename );
int *i4mat_data_read ( string input_filename, int m, int n );
void i4mat_header_read ( string input_filename, int *m, int *n );
double piecewise_linear_product_quad ( double a, double b, int f_num, 
  double f_x[], double f_v[], int g_num, double g_x[], double g_v[] );
double r8_min ( double x, double y );
int r83_np_fa ( int n, double a[] );
double *r83_np_sl ( int n, double a_lu[], double b[], int job );
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[] );
double *r8mat_zero_new ( int m, int n );
void r8vec_bracket3 ( int n, double t[], double tval, int *left );
int s_len_trim ( string s );
int s_to_i4 ( string s, int *last, bool *error );
bool s_to_i4vec ( string s, int n, int ivec[] );
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 FEM1D_PROJECT.
//
//  Discussion:
//
//    FEM1D_PROJECT reads files defining a sampling of a (scalar or vector)
//    function of 1 argument, and a list of nodes and elements to use for
//    a finite element representation of the data.
//
//    It computes a set of finite element coefficients to be associated with
//    the given finite element mesh, and writes that information to a file
//    so that an FEM representation is formed by the node, element and value 
//    files.
//
//  Usage:
//
//    fem1d_project sample_prefix fem_prefix
//
//    where 'sample_prefix' is the common prefix for the SAMPLE files:
//
//    * sample_prefix_nodes.txt,  the node coordinates where samples were taken,
//    * sample_prefix_values.txt, the sample values.
//
//    and 'fem_prefix' is the common prefix for the FEM files:
//
//    * fem_prefix_nodes.txt,    the node coordinates.
//    * fem_prefix_elements.txt, the nodes that make up each element;
//    * fem_prefix_values.txt,   the values defined at each node.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    01 June 2009
//
//  Author:
//
//    John Burkardt
//
{
  string fem_element_filename;
  int *fem_element_node;
  int fem_element_num;
  int fem_element_order;
  int fem_node_dim;
  string fem_node_filename;
  int fem_node_num;
  double *fem_node_x;
  string fem_prefix;
  double *fem_value;
  int fem_value_dim;
  string fem_value_filename;
  int fem_value_num;
  string sample_prefix;
  int sample_node_dim;
  string sample_node_filename;
  int sample_node_num;
  double *sample_node_x;
  int sample_value_dim;
  int sample_value_num;
  double *sample_value;
  string sample_value_filename;

  timestamp ( );

  cout << "\n";
  cout << "FEM1D_PROJECT\n";
  cout << "  C++ version.\n";
  cout << "\n";
  cout << "  Read files defining a sampling of a function of 1 argument.\n";
  cout << "  Read files defining a finite element mesh.\n";
  cout << "  Project the sample data onto the mesh, and\n";
  cout << "  write a file of FEM coefficient values.\n";
//
//  Get the number of command line arguments.
//
  if ( 1 < argc )
  {
    sample_prefix = argv[1];
  }
  else
  {
    cout << "\n";
    cout << "Enter the sample file prefix:\n";
    cin >> sample_prefix;
  }

  if ( 2 < argc )
  {
    fem_prefix = argv[2];
  }
  else
  {
    cout << "\n";
    cout << "Enter the FEM file prefix:\n";
    cin >> fem_prefix;
  }
//
//  Create the filenames.
//
  sample_node_filename = sample_prefix + "_nodes.txt";
  sample_value_filename = sample_prefix + "_values.txt";

  fem_node_filename = fem_prefix + "_nodes.txt";
  fem_element_filename = fem_prefix + "_elements.txt";
  fem_value_filename = fem_prefix + "_values.txt";
//
//  Read the SAMPLE data.
//
  r8mat_header_read ( sample_node_filename, &sample_node_dim, 
    &sample_node_num );

  sample_node_x = r8mat_data_read ( sample_node_filename, sample_node_dim, 
    sample_node_num );

  cout << "\n";
  cout << "  Sample node spatial dimension is " << sample_node_dim << "\n";
  cout << "  Sample node number is            " << sample_node_num << "\n";

  if ( sample_node_dim != 1 )
  {
    cout << "\n";
    cout << "FEM1D_PROJECT - Fatal error!\n";
    cout << "  Spatial dimension of the sample nodes is not 1.\n";
    exit ( 1 );
  }

  r8mat_header_read ( sample_value_filename, &sample_value_dim,
    &sample_value_num );

  cout << "  The SAMPLE value dimension is    " << sample_value_dim << "\n";
  cout << "  the SAMPLE value number is        " << sample_value_num << "\n";

  if ( sample_value_num != sample_node_num )
  {
    cout << "\n";
    cout << "FEM1D_PROJECT - Fatal error!\n";
    cout << "  Number of sample values and nodes differ.\n";
    exit ( 1 );
  }
  sample_value = r8mat_data_read ( sample_value_filename, sample_value_dim, 
    sample_value_num );
//
//  Read the FEM data.
//
  r8mat_header_read ( fem_node_filename, &fem_node_dim, &fem_node_num );

  cout << "\n";
  cout << "  The FEM node dimension is        " << fem_node_dim << "\n";
  cout << "  The FEM node number is           " << fem_node_num << "\n";

  if ( fem_node_dim != 1 )
  {
    cout << "\n";
    cout << "FEM1D_PROJECT - Fatal error!\n";
    cout << "  Spatial dimension of the nodes is not 1.\n";
    exit ( 1 );
  }

  fem_node_x = r8mat_data_read ( fem_node_filename, fem_node_dim, fem_node_num );

  i4mat_header_read ( fem_element_filename, &fem_element_order, &fem_element_num );

  cout << "  The FEM element order is         " << fem_element_order << "\n";
  cout << "  The FEM element number is        " << fem_element_num << "\n";

  fem_element_node = i4mat_data_read ( fem_element_filename, fem_element_order, 
    fem_element_num );
//
//  Compute the FEM values.
//
  fem_value_dim = sample_value_dim;
  fem_value_num = fem_node_num;

  fem_value = fem1d_approximate ( sample_node_num, sample_value_dim, sample_node_x, 
    sample_value, fem_node_num, fem_node_x, fem_element_order, 
    fem_element_num, fem_value_dim, fem_value_num );
//
//  Write the FEM values.
//
  r8mat_write ( fem_value_filename, fem_value_dim, fem_value_num, 
    fem_value );

  cout << "\n";
  cout << "  Projected FEM values written to \"" << fem_value_filename << "\"\n";
//
//  Free memory.
//
  delete [] fem_element_node;
  delete [] fem_node_x;
  delete [] fem_value;
  delete [] sample_node_x;
  delete [] sample_value;
//
//  Terminate.
//
  cout << "\n";
  cout << "FEM1D_PROJECT\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 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

double *fem1d_approximate ( int sample_node_num, int sample_value_dim, 
  double sample_node_x[], double sample_value[], int fem_node_num, 
  double fem_node_x[], int fem_element_order, int fem_element_num, 
  int fem_value_dim, int fem_value_num )

//****************************************************************************80
//
//  Purpose:
//
//    FEM1D_APPROXIMATE approximates data at sample points with an FEM function.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    01 May 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int SAMPLE_NODE_NUM, the number of sample points.
//
//    Input, int SAMPLE_VALUE_DIM, the value dimension.
//
//    Input, double SAMPLE_NODE_X[SAMPLE_NODE_NUM], the sample nodes.
//
//    Input, double SAMPLE_VALUE[VALUE_DIM*SAMPLE_NODE_NUM],
//    the values at sample nodes.
//
//    Input, int FEM_NODE_NUM, the number of FEM nodes.
//
//    Input, double FEM_NODE_X[FEM_NODE_NUM], the FEM nodes.  
//
//    Input, int FEM_ELEMENT_ORDER, the element order.
//
//    Input, int FEM_ELEMENT_NUM, the number of elements.
//
//    Input, int FEM_VALUE_DIM, the FEM value dimension.
//
//    Input, int FEM_VALUE_NUM, the number of FEM values.
//
//    Output, double FEM1D_APPROXIMATE[FEM_VALUE_DIM*FEM_VALUE_NUM], 
//    the FEM values.
//
{
# define QUAD_NUM 2

  double *a;
  double a1;
  double *b;
  double b1;
  int dim;
  double *fem_value;
  int i;
  double integral;
  int j;
  int job;
  int l;
  int phi_num;
  double phi_v[3];
  double phi_x[3];
  double phil;
  double phir;
  int quad;
  int quad_num = QUAD_NUM;
  double quad_x[QUAD_NUM] = {
    -0.577350269189625764509148780502, 
     0.577350269189625764509148780502 };
  double quad_w[QUAD_NUM] = { 1.0, 1.0 };
  int r;
  double *v;
  double wq;
  double *x;
  double xl;
  double xq;
  double xr;
//
//  Set up the matrix A.
//
  a = r8mat_zero_new ( 3, fem_node_num );

  for ( l = 0; l < fem_node_num - 1; l++ )
  {
    r = l + 1;
    xl = fem_node_x[l];
    xr = fem_node_x[r];

    for ( quad = 0; quad < quad_num; quad++ )
    {
      xq = ( ( 1.0 - quad_x[quad] ) * xl   
           + ( 1.0 + quad_x[quad] ) * xr ) 
           /   2.0;

      wq = quad_w[quad] * ( xr - xl ) / 2.0;

      phil = (      xq - xr ) 
           / ( xl      - xr );

      phir = ( xl - xq      ) 
           / ( xl      - xr );

      a[1+l*3] = a[1+l*3] + wq * phil * phil;
      a[2+l*3] = a[2+l*3] + wq * phil * phir;

      a[0+r*3] = a[0+r*3] + wq * phir * phil;
      a[1+r*3] = a[1+r*3] + wq * phir * phir;
    }
  }
  r83_np_fa ( fem_node_num, a );
//
//  Set up the right hand side b.
//
  b = new double[fem_node_num];
  v = new double[sample_node_num];
  fem_value = new double[fem_value_dim*fem_value_num];

  for ( dim = 0; dim < fem_value_dim; dim++ )
  {
    for ( i = 0; i < fem_node_num; i++ )
    {
      if ( i == 0 )
      {
        phi_num = 2;
        phi_x[0] = fem_node_x[0];
        phi_x[1] = fem_node_x[1];
        phi_v[0] = 1.0;
        phi_v[1] = 0.0;
      }
      else if ( i < fem_node_num - 1 )
      {
        phi_num = 3;
        phi_x[0] = fem_node_x[i-1];
        phi_x[1] = fem_node_x[i];
        phi_x[2] = fem_node_x[i+1];
        phi_v[0] = 0.0;
        phi_v[1] = 1.0;
        phi_v[2] = 0.0;
      }
      else if ( i == fem_node_num - 1 )
      {
        phi_num = 2;
        phi_x[0] = fem_node_x[fem_node_num-2];
        phi_x[1] = fem_node_x[fem_node_num-1];
        phi_v[0] = 0.0;
        phi_v[1] = 1.0;
      }

      a1 = phi_x[0];
      b1 = phi_x[phi_num-1];

      for ( j = 0; j < sample_node_num; j++ )
      {
        v[j] = sample_value[dim+j*sample_value_dim];
      }

      integral = piecewise_linear_product_quad ( a1, b1, phi_num, phi_x, 
        phi_v, sample_node_num, sample_node_x, v );

      b[i] = integral;
    }
    job = 0;
    x = r83_np_sl ( fem_node_num, a, b, job );

    for ( i = 0; i < fem_node_num; i++ )
    {
      fem_value[dim+i*fem_value_dim] = x[i];
    }
    delete [] x;
  }

  delete [] a;
  delete [] b;
  delete [] v;

  return fem_value;
# undef QUAD_NUM
}
//****************************************************************************80

int file_column_count ( string 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 MIT license. 
//
//  Modified:
//
//    23 February 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string 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[255];
//
//  Open the file.
//
  input.open ( input_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 << "  \"" << 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.c_str ( ) );

    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 )
  {
    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 ( line );

  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;
  char line[255];
  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";
    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 *i4mat_data_read ( string input_filename, int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_DATA_READ reads data from an I4MAT file.
//
//  Discussion:
//
//    An I4MAT is an array of I4'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, int I4MAT_DATA_READ[M*N], the data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  string line;
  int *table;
  int *x;

  input.open ( input_filename.c_str ( ) );

  if ( !input )
  {
    cerr << "\n";
    cerr << "I4MAT_DATA_READ - Fatal error!\n";
    cerr << "  Could not open the input file: \"" << input_filename << "\"\n";
    exit ( 1 );
  }

  table = new int[m*n];

  x = new int[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_i4vec ( 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 i4mat_header_read ( string input_filename, int *m, int *n )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_HEADER_READ reads the header from an I4MAT file.
//
//  Discussion:
//
//    An I4MAT is an array of I4'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 << "I4MAT_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 << "I4MAT_HEADER_READ - Fatal error!\n";
    cerr << "  FILE_ROW_COUNT failed.\n";
    exit ( 1 );
  }

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

double piecewise_linear_product_quad ( double a, double b, int f_num, 
  double f_x[], double f_v[], int g_num, double g_x[], double g_v[] )

//****************************************************************************80
//
//  Purpose:
//
//    PIECEWISE_LINEAR_PRODUCT_QUAD: piecewise linear product integral.
//
//  Discussion:
//
//    We are given two piecewise linear functions F(X) and G(X) and we wish
//    to compute the exact value of the integral
//
//      INTEGRAL = Integral ( A <= X <= B ) F(X) * G(X) dx
//
//    The functions F(X) and G(X) are defined as tables of coordinates X and
//    values V.  A piecewise linear function is evaluated at a point X by 
//    evaluating the interpolant to the data at the endpoints of the interval 
//    containing X.  
//
//    It must be the case that A <= B.
//
//    It must be the case that the node coordinates F_X(*) and G_X(*) are
//    given in ascending order.
//
//    It must be the case that:
//
//      F_X(1) <= A and B <= F_X(F_NUM)
//      G_X(1) <= A and B <= G_X(G_NUM)
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    30 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double A, B, the limits of integration.
//
//    Input, int F_NUM, the number of nodes for F.
//
//    Input, double F_X[F_NUM], the node coordinates for F.
//
//    Input, double F_V[F_NUM], the nodal values for F.
//
//    Input, int G_NUM, the number of nodes for G.
//
//    Input, double G_X[G_NUM], the node coordinates for G.
//
//    Input, double G_V[G_NUM], the nodal values for G.
//
//    Output, double INTEGRAL, the integral of F(X) * G(X)
//    from A to B.
//
{
  double bit;
  int f_left;
  double f0;
  double f1;
  double fl;
  double fr;
  int g_left;
  double g0;
  double g1;
  double gl;
  double gr;
  double h0;
  double h1;
  double h2;
  int i;
  double integral;
  double xl;
  double xr;
  double xr_max;

  integral = 0.0;

  if ( f_x[f_num-1] <= a || g_x[g_num-1] <= a )
  {
    return integral;
  }

  if ( f_num < 2 || g_num < 2 )
  {
    return integral;
  }

  xr = a;

  f_left = 0;
  r8vec_bracket3 ( f_num, f_x, xr, &f_left );
  fr = f_v[f_left] + ( xr - f_x[f_left] ) * ( f_v[f_left+1] - f_v[f_left] ) 
    / ( f_x[f_left+1] - f_x[f_left] );

  g_left = 0;
  r8vec_bracket3 ( g_num, g_x, xr, &g_left );
  gr = g_v[g_left] + ( xr - g_x[g_left] ) * ( g_v[g_left+1] - g_v[g_left] ) 
    / ( g_x[g_left+1] - g_x[g_left] );

  xr_max = b;
  xr_max = r8_min ( xr_max, f_x[f_num-1] );
  xr_max = r8_min ( xr_max, g_x[g_num-1] );

  while ( xr < xr_max )
  {
//
//  Shift right values to left.
//
    xl = xr;
    fl = fr;
    gl = gr;
//
//  Determine the new right values.
//  The hard part is figuring out how to advance XR some, but not too much.
//
    xr = xr_max;

    for ( i = 1; i <= 2; i++ )
    {
      if ( f_left + i <= f_num - 1 )
      {
        if ( xl < f_x[f_left+i] && f_x[f_left+i] < xr )
        {
          xr = f_x[f_left+i];
          break;
        }
      }
    }

    for ( i = 1; i <= 2; i++ )
    {
      if ( g_left + i <= g_num - 1 )
      {
        if ( xl < g_x[g_left+i] && g_x[g_left+i] < xr )
        {
          xr = g_x[g_left+i];
          break;
        }
      }
    }

    r8vec_bracket3 ( f_num, f_x, xr, &f_left );
    fr = f_v[f_left] + ( xr - f_x[f_left] ) * ( f_v[f_left+1] - f_v[f_left] ) 
      / ( f_x[f_left+1] - f_x[f_left] );

    r8vec_bracket3 ( g_num, g_x, xr, &g_left );
    gr = g_v[g_left] + ( xr - g_x[g_left] ) * ( g_v[g_left+1] - g_v[g_left] ) 
      / ( g_x[g_left+1] - g_x[g_left] );
//
//  Form the linear polynomials for F(X) and G(X) over [XL,XR],
//  then the product H(X), integrate H(X) and add to the running total.
//
    if ( DBL_EPSILON <= fabs ( xr - xl ) )
    {
      f1 = fl - fr;
      f0 = fr * xl - fl * xr;

      g1 = gl - gr;
      g0 = gr * xl - gl * xr;

      h2 = f1 * g1;
      h1 = f1 * g0 + f0 * g1;
      h0 = f0 * g0;

      h2 = h2 / 3.0;
      h1 = h1 / 2.0;

      bit = ( ( h2 * xr + h1 ) * xr + h0 ) * xr 
          - ( ( h2 * xl + h1 ) * xl + h0 ) * xl;

      integral = integral + bit / ( xr - xl ) / ( xr - xl );
    }
  }

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

double r8_min ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MIN returns the minimum of two R8's.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    31 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MIN, the minimum of X and Y.
//
{
  double value;

  if ( y < x )
  {
    value = y;
  } 
  else
  {
    value = x;
  }
  return value;
}
//****************************************************************************80

int r83_np_fa ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R83_NP_FA factors a R83 system without pivoting.
//
//  Discussion:
//
//    The R83 storage format is used for a tridiagonal matrix.
//    The superdiagonal is stored in entries (1,2:N), the diagonal in
//    entries (2,1:N), and the subdiagonal in (3,1:N-1).  Thus, the
//    original matrix is "collapsed" vertically into the array.
//
//    Because this routine does not use pivoting, it can fail even when
//    the matrix is not singular, and it is liable to make larger
//    errors.
//
//    R83_NP_FA and R83_NP_SL may be preferable to the corresponding
//    LINPACK routine SGTSL for tridiagonal systems, which factors and solves
//    in one step, and does not save the factorization.
//
//  Example:
//
//    Here is how a R83 matrix of order 5 would be stored:
//
//       *  A12 A23 A34 A45
//      A11 A22 A33 A44 A55
//      A21 A32 A43 A54  *
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    11 January 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the matrix.
//    N must be at least 2.
//
//    Input/output, double A[3*N].
//    On input, the tridiagonal matrix.  On output, factorization information.
//
//    Output, int R83_NP_FA, singularity flag.
//    0, no singularity detected.
//    nonzero, the factorization failed on the INFO-th step.
//
{
  int i;

  for ( i = 1; i <= n-1; i++ )
  {
    if ( a[1+(i-1)*3] == 0.0 )
    {
      cout << "\n";
      cout << "R83_NP_FA - Fatal error!\n";
      cout << "  Zero pivot on step " << i << "\n";
      return i;
    }
//
//  Store the multiplier in L.
//
    a[2+(i-1)*3] = a[2+(i-1)*3] / a[1+(i-1)*3];
//
//  Modify the diagonal entry in the next column.
//
    a[1+i*3] = a[1+i*3] - a[2+(i-1)*3] * a[0+i*3];
  }

  if ( a[1+(n-1)*3] == 0.0 )
  {
    cout << "\n";
    cout << "R83_NP_FA - Fatal error!\n";
    cout << "  Zero pivot on step " << n << "\n";
    return n;
  }

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

double *r83_np_sl ( int n, double a_lu[], double b[], int job )

//****************************************************************************80
//
//  Purpose:
//
//    R83_NP_SL solves a R83 system factored by R83_NP_FA.
//
//  Discussion:
//
//    The R83 storage format is used for a tridiagonal matrix.
//    The superdiagonal is stored in entries (1,2:N), the diagonal in
//    entries (2,1:N), and the subdiagonal in (3,1:N-1).  Thus, the
//    original matrix is "collapsed" vertically into the array.
//
//  Example:
//
//    Here is how a R83 matrix of order 5 would be stored:
//
//       *  A12 A23 A34 A45
//      A11 A22 A33 A44 A55
//      A21 A32 A43 A54  *
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    12 January 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the matrix.
//    N must be at least 2.
//
//    Input, double A_LU[3*N], the LU factors from R83_NP_FA.
//
//    Input, double B[N], the right hand side of the linear system.
//    On output, B contains the solution of the linear system.
//
//    Input, int JOB, specifies the system to solve.
//    0, solve A * x = b.
//    nonzero, solve A' * x = b.
//
//    Output, double R83_NP_SL[N], the solution of the linear system.
//
{
  int i;
  double *x;

  x = new double[n];

  for ( i = 0; i < n; i++ )
  {
    x[i] = b[i];
  }

  if ( job == 0 )
  {
//
//  Solve L * Y = B.
//
    for ( i = 1; i < n; i++ )
    {
      x[i] = x[i] - a_lu[2+(i-1)*3] * x[i-1];
    }
//
//  Solve U * X = Y.
//
    for ( i = n; 1 <= i; i-- )
    {
      x[i-1] = x[i-1] / a_lu[1+(i-1)*3];
      if ( 1 < i )
      {
        x[i-2] = x[i-2] - a_lu[0+(i-1)*3] * x[i-1];
      }
    }
  }
  else
  {
//
//  Solve U' * Y = B
//
    for ( i = 1; i <= n; i++ )
    {
      x[i-1] = x[i-1] / a_lu[1+(i-1)*3];
      if ( i < n )
      {
        x[i] = x[i] - a_lu[0+i*3] * x[i-1];
      }
    }
//
//  Solve L' * X = Y.
//
    for ( i = n-1; 1 <= i; i-- )
    {
      x[i-1] = x[i-1] - a_lu[2+(i-1)*3] * x[i];
    }
  }

  return x;
}
//****************************************************************************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.
//
//  Discussion:
//
//    An R8MAT is an array of R8's.
//
//  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 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";
    exit ( 1 );
  }
//
//  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

double *r8mat_zero_new ( int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_ZERO_NEW returns a new zeroed R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8 values,  stored as a vector 
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    03 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Output, double R8MAT_ZERO[M*N], the new zeroed matrix.
//
{
  double *a;
  int i;
  int j;

  a = new double[m*n];

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      a[i+j*m] = 0.0;
    }
  }
  return a;
}
//****************************************************************************80

void r8vec_bracket3 ( int n, double t[], double tval, int *left )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_BRACKET3 finds the interval containing or nearest a given value.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    The routine always returns the index LEFT of the sorted array
//    T with the property that either
//    *  T is contained in the interval [ T[LEFT], T[LEFT+1] ], or
//    *  T < T[LEFT] = T[0], or
//    *  T > T[LEFT+1] = T[N-1].
//
//    The routine is useful for interpolation problems, where
//    the abscissa must be located within an interval of data
//    abscissas for interpolation, or the "nearest" interval
//    to the (extreme) abscissa must be found so that extrapolation
//    can be carried out.
//
//    This version of the function has been revised so that the value of
//    LEFT that is returned uses the 0-based indexing natural to C++.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    30 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, length of the input array.
//
//    Input, double T[N], an array that has been sorted into ascending order.
//
//    Input, double TVAL, a value to be bracketed by entries of T.
//
//    Input/output, int *LEFT.
//    On input, if 0 <= LEFT <= N-2, LEFT is taken as a suggestion for the
//    interval [ T[LEFT-1] T[LEFT] ] in which TVAL lies.  This interval
//    is searched first, followed by the appropriate interval to the left
//    or right.  After that, a binary search is used.
//    On output, LEFT is set so that the interval [ T[LEFT], T[LEFT+1] ]
//    is the closest to TVAL; it either contains TVAL, or else TVAL
//    lies outside the interval [ T[0], T[N-1] ].
//
{
  int high;
  int low;
  int mid;
//  
//  Check the input data.
//
  if ( n < 2 ) 
  {
    cout << "\n";
    cout << "R8VEC_BRACKET3 - Fatal error//\n";
    cout << "  N must be at least 2.\n";
    exit ( 1 );
  }
//
//  If *LEFT is not between 0 and N-2, set it to the middle value.
//
  if ( *left < 0 || n - 2 < *left ) 
  {
    *left = ( n - 1 ) / 2;
  }
//
//  CASE 1: TVAL < T[*LEFT]:
//  Search for TVAL in (T[I],T[I+1]), for I = 0 to *LEFT-1.
//
  if ( tval < t[*left] ) 
  {
    if ( *left == 0 ) 
    {
      return;
    }
    else if ( *left == 1 ) 
    {
      *left = 0;
      return;
    }
    else if ( t[*left-1] <= tval )
    {
      *left = *left - 1;
      return;
    }
    else if ( tval <= t[1] ) 
    {
      *left = 0;
      return;
    }
// 
//  ...Binary search for TVAL in (T[I],T[I+1]), for I = 1 to *LEFT-2.
//
    low = 1;
    high = *left - 2;

    for ( ; ; )
    {
      if ( low == high )
      {
        *left = low;
        return;
      }

      mid = ( low + high + 1 ) / 2;

      if ( t[mid] <= tval ) 
      {
        low = mid;
      }
      else 
      {
        high = mid - 1;
      }
    }
  }
// 
//  CASE 2: T[*LEFT+1] < TVAL:
//  Search for TVAL in (T[I],T[I+1]) for intervals I = *LEFT+1 to N-2.
//
  else if ( t[*left+1] < tval ) 
  {
    if ( *left == n - 2 ) 
    {
      return;
    }
    else if ( *left == n - 3 ) 
    {
      *left = *left + 1;
      return;
    }
    else if ( tval <= t[*left+2] )
    {
      *left = *left + 1;
      return;
    }
    else if ( t[n-2] <= tval ) 
    {
      *left = n - 2;
      return;
    }
// 
//  ...Binary search for TVAL in (T[I],T[I+1]) for intervals I = *LEFT+2 to N-3.
//
    low = *left + 2;
    high = n - 3;

    for ( ; ; ) 
    {

      if ( low == high ) 
      {
        *left = low;
        return;
      }

      mid = ( low + high + 1 ) / 2;

      if ( t[mid] <= tval ) 
      {
        low = mid;
      }
      else 
      {
        high = mid - 1;
      }
    }
  }
//
//  CASE 3: T[*LEFT] <= TVAL <= T[*LEFT+1]:
//  T is just where the user said it might be.
//
  else 
  {
  }

  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

bool s_to_i4vec ( string s, int n, int ivec[] )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4VEC reads an I4VEC 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, int IVEC[N], the values read from the string.
//
//    Output, bool S_TO_I4VEC, 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++ )
  {
    ivec[i] = s_to_i4 ( s.substr(begin,length), &lchar, &error );

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

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