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

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_evaluate ( int node_num, double node_x[], int element_order, 
  int element_num, int value_dim, double value[], int sample_node_num, 
  double sample_node_x[] );
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 *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_bracket4 ( int nt, double t[], int ns, double s[], 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_SAMPLE.
//
//  Discussion:
//
//    FEM1D_SAMPLE reads files defining a 2D FEM representation of data,
//    and a set of sample points, and writes out a file containing the 
//    value of the finite element function at the sample points.
//
//  Usage:
//
//    fem1d_sample fem_prefix sample_prefix
//
//    where '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.
//
//    and 'sample_prefix' is the common prefix for the SAMPLE files.
//    (the node file is input, and the values file is created by the program.)
//
//    * sample_prefix_nodes.txt,  the node coordinates where samples are desired.
//    * sample_prefix_values.txt, the values computed at each sample node.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    03 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_SAMPLE\n";
  cout << "  C++ version.\n";
  cout << "\n";
  cout << "  Read files defining an FEM function of 1 argument.\n";
  cout << "  Read a file of sample arguments.\n";
  cout << "  Write a file of function values at the arguments.\n";
//
//  Get the number of command line arguments.
//
  if ( 1 < argc )
  {
    fem_prefix = argv[1];
  }
  else
  {
    cout << "\n";
    cout << "Enter the FEM file prefix:\n";
    cin >> fem_prefix;
  }

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

  sample_node_filename = sample_prefix + "_nodes.txt";
  sample_value_filename = sample_prefix + "_values.txt";
//
//  Read the FEM data.
//
  r8mat_header_read ( fem_node_filename, &fem_node_dim, &fem_node_num );

  fem_node_x = r8mat_data_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_SAMPLE - Fatal error!\n";
    cout << "  Spatial dimension of the nodes is not 1.\n";
    exit ( 1 );
  }

  i4mat_header_read ( fem_element_filename, &fem_element_order, &fem_element_num );

  fem_element_node = i4mat_data_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";

  r8mat_header_read ( fem_value_filename, &fem_value_dim, &fem_value_num );

  cout << "  The FEM value order is           " << fem_value_dim << "\n";
  cout << "  the FEM value number is          " << fem_value_num << "\n";

  if ( fem_value_num != fem_node_num )
  {
    cout << "\n";
    cout << "FEM1D_SAMPLE - Fatal error!\n";
    cout << "  Number of FEM values and FEM nodes differ.\n";
    exit ( 1 );
  }
  fem_value = r8mat_data_read ( fem_value_filename, fem_value_dim, fem_value_num );
//
//  Read the SAMPLE node 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_SAMPLE - Fatal error!\n";
    cout << "  Spatial dimension of the sample nodes is not 1.\n";
    exit ( 1 );
  }
//
//  Compute the SAMPLE values.
//
  sample_value_dim = fem_value_dim;
  sample_value_num = sample_node_num;

  sample_value = fem1d_evaluate ( fem_node_num, fem_node_x, fem_element_order, 
    fem_element_num, fem_value_dim, fem_value, sample_node_num, sample_node_x );
//
//  Write the sample values.
//
  r8mat_write ( sample_value_filename, sample_value_dim, sample_value_num, 
    sample_value );

  cout << "\n";
  cout << "  Interpolated FEM data written to \"" << sample_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_SAMPLE\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

double *fem1d_evaluate ( int node_num, double node_x[], int element_order, 
  int element_num, int value_dim, double value[], int sample_node_num, 
  double sample_node_x[] )

//****************************************************************************80
//
//  Purpose:
//
//    FEM1D_EVALUATE evaluates a 1D FEM function at sample points.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    30 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of FEM nodes.
//
//    Input, double NODE_X[NODE_NUM], the nodes.  
//
//    Input, int ELEMENT_ORDER, the element order.
//
//    Input, int ELEMENT_NUM, the number of elements.
//
//    Input, int VALUE_DIM, the value dimension.
//
//    Input, double VALUE[VALUE_DIM*NODE_NUM], the FEM values.
//
//    Input, int SAMPLE_NODE_NUM, the number of sample points.
//
//    INput, double SAMPLE_NODE_X[SAMPLE_NODE_NUM], the sample nodes.
//
//    Output, double FEM1D_EVALUATE[VALUE_DIM*SAMPLE_NODE_NUM],
//    the interpolated FEM values at sample nodes.
//
{
  int i;
  int l;
  int r;;
  int sample;
  int *sample_left;
  double *sample_value;
//
//  For each sample point, find NODE_LEFT and NODE_RIGHT that bracket it.
//
  sample_left = new int[sample_node_num];

  r8vec_bracket4 ( node_num, node_x, sample_node_num, sample_node_x, 
    sample_left );

  sample_value = new double[value_dim*sample_node_num];

  if ( element_order == 1 )
  {
    for ( sample = 0; sample < sample_node_num; sample++ )
    {
      for ( i = 0; i < value_dim; i++ )
      {
        sample_value[i+sample*value_dim] = value[i+sample_left[sample]*value_dim]; 
      }
    }
  }
  else if ( element_order == 2 )
  {
    for ( sample = 0; sample < sample_node_num; sample++ )
    {
      l = sample_left[sample];
      r = sample_left[sample]+1;
      for ( i = 0; i < value_dim; i++ )
      {
        sample_value[i+sample*value_dim] = 
          ( value[i+l*value_dim] * ( node_x[r] - sample_node_x[sample]             ) 
          + value[i+r*value_dim] * (             sample_node_x[sample] - node_x[l] ) )
          /                        ( node_x[r]                         - node_x[l] );
      }
    }
  }
  else
  {
    cerr << "\n";
    cerr << "FEM_EVALUATE - Fatal error!\n";
    cerr << "  Cannot handle elements of this order.\n";
    exit ( 1 );
  }

  delete [] sample_left;

  return sample_value;
}
//****************************************************************************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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 *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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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

void r8vec_bracket4 ( int nt, double t[], int ns, double s[], int left[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_BRACKET4 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[NT-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 GNU LGPL license. 
//
//  Modified:
//
//    30 April 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NT, length of the input array.
//
//    Input, double T[NT], an array that has been sorted
//    into ascending order.
//
//    Input, int NS, the number of points to be bracketed.
//
//    Input, double S[NS], values to be bracketed by entries of T.
//
//    Output, int LEFT[NS].
//    LEFT[I] is set so that the interval [ T[LEFT[I]], T[LEFT[I]+1] ]
//    is the closest to S[I]; it either contains S[I], or else S[I]
//    lies outside the interval [ T[0], T[NT-1] ].
//
{
  int high;
  int i;
  int low;
  int mid;
//  
//  Check the input data.
//
  if ( nt < 2 ) 
  {
    cout << "\n";
    cout << "R8VEC_BRACKET4 - Fatal error!\n";
    cout << "  NT must be at least 2.\n";
    exit ( 1 );
  }

  for ( i = 0; i < ns; i++ )
  {
    left[i] = ( nt - 1 ) / 2;
//
//  CASE 1: S[I] < T[LEFT]:
//  Search for S[I] in (T[I],T[I+1]), for I = 0 to LEFT-1.
//
    if ( s[i] < t[left[i]] ) 
    {
      if ( left[i] == 0 ) 
      {
        continue;
      }
      else if ( left[i] == 1 ) 
      {
        left[i] = 0;
        continue;
      }
      else if ( t[left[i]-1] <= s[i] )
      {
        left[i] = left[i] - 1;
        continue;
      }
      else if ( s[i] <= t[1] ) 
      {
        left[i] = 0;
        continue;
      }
// 
//  ...Binary search for S[I] in (T[I],T[I+1]), for I = 1 to *LEFT-2.
//
      low = 1;
      high = left[i] - 2;
 
      for ( ; ; )
      {
        if ( low == high )
        {
          left[i] = low;
          break;
        }

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

        if ( t[mid] <= s[i] ) 
        {
          low = mid;
        }
        else 
        {
          high = mid - 1;
        }
      }
    }
// 
//  CASE 2: T[LEFT+1] < S[I]:
//  Search for S[I] in (T[I],T[I+1]) for intervals I = LEFT+1 to NT-2.
//
    else if ( t[left[i]+1] < s[i] ) 
    {
      if ( left[i] == nt - 2 ) 
      {
        continue;
      }
      else if ( left[i] == nt - 3 ) 
      {
        left[i] = left[i] + 1;
        continue;
      }
      else if ( s[i] <= t[left[i]+2] )
      {
        left[i] = left[i] + 1;
        continue;
      }
      else if ( t[nt-2] <= s[i] ) 
      {
        left[i] = nt - 2;
        continue;
      }
// 
//  ...Binary search for S[I] in (T[I],T[I+1]) for intervals I = LEFT+2 to NT-3.
//
      low = left[i] + 2;
      high = nt - 3;

      for ( ; ; ) 
      {

        if ( low == high ) 
        {
          left[i] = low;
          break;
        }

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

        if ( t[mid] <= s[i] ) 
        {
          low = mid;
        }
        else 
        {
          high = mid - 1;
        }
      }
    }
//
//  CASE 3: T[LEFT] <= S[I] <= T[LEFT+1]:
//
    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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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 GNU LGPL 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:
//
//    May 31 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    02 October 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

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

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

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}