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

using namespace std;

int main ( int argc, char *argv[] );
char ch_cap ( char ch );
bool ch_eqi ( char ch1, char ch2 );
int ch_to_digit ( char ch );
void dtable_close_write ( ofstream &output );
double *dtable_data_read ( char *input_filename, int m, int n );
void dtable_data_write ( ofstream &output, int m, int n, double table[] );
void dtable_header_read ( char *input_filename, int *m, int *n );
void dtable_header_write ( char *output_filename, ofstream &output, int m, 
  int n );
void dtable_write ( char *output_filename, int m, int n, double table[], 
  bool header );
int file_column_count ( char *input_filename );
void file_name_ext_get ( char *file_name, int *i, int *j );
char *file_name_ext_swap ( char *file_name, char *ext );
int file_row_count ( char *input_filename );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
int i4col_compare ( int m, int n, int a[], int i, int j );
void i4col_sort_a ( int m, int n, int a[] );
void i4col_swap ( int m, int n, int a[], int icol1, int icol2 );
void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
int *itable_data_read ( char *input_filename, int m, int n );
void itable_header_read ( char *input_filename, int *m, int *n );
double r8_epsilon ( void );
void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
int s_index_last_c ( char *s, char c );
int s_len_trim ( char *s );
int s_to_i4 ( char *s, int *last, bool *error );
bool s_to_i4vec ( char *s, int n, int ivec[] );
double s_to_r8 ( char *s, int *lchar, bool *error );
bool s_to_r8vec ( char *s, int n, double rvec[] );
int s_word_count ( char *s );
void sort_heap_external ( int n, int *indx, int *i, int *j, int isgn );
void timestamp ( void );
char *timestring ( void );
bool *triangulation_order3_boundary_node ( int node_num, int triangle_num, 
  int triangle_node[] );
bool *triangulation_order6_boundary_node ( int node_num, int triangle_num, 
  int triangle_node[] );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for TRIANGULATION_BOUNDARY_NODES.
//
//  Discussion:
//
//    TRIANGULATION_BOUNDARY_NODES outputs boundary nodes of a triangulation.
//
//    Each connected segment of the boundary is written to a separate file.
//
//  Modified:
//
//    01 January 2007
//
//  Author:
//
//    John Burkardt
//
//  Usage:
//
//    triangulation_boundary node_file triangle_file
//
{
  int dim_num;
  bool header;
  int i;
  char input_node_filename[81];
  char input_triangulation_filename[81];
  int node;
  bool *node_boundary;
  int node_boundary_num;
  int node_num;
  double *node_boundary_xy;
  double *node_xy;
  int node2;
  char *output_filename = "boundary_nodes.txt";
  int *triangle_node;
  int triangle_num;
  int triangle_order;

  cout << "\n";
  timestamp ( );

  cout << "\n";
  cout << "TRIANGULATION_BOUNDARY_NODES\n";
  cout << "  C++ version:\n";
  cout << "  Identify triangulation nodes that lie on the boundary.\n";
  cout << "\n";
  cout << "* Read a node dataset of NODE_NUM points in 2 dimensions;\n";
  cout << "\n";
  cout << "* Read an associated triangulation dataset of \n";
  cout << "  triangles using 3 or 6 nodes;\n";
  cout << "\n";
  cout << "* Determine which nodes are on the boundary;\n";
  cout << "\n";
  cout << "* Print a list of the node coordinates and indices;\n";
  cout << "\n";
  cout << "* Write a file of the node coordinates.\n";
  cout << "\n";
  cout << "  Compiled on " << __DATE__ << " at " << __TIME__ << ".\n";
//
//  Get the node file name.
//
  if ( argc <= 1 ) 
  {
    cout << "\n";
    cout << "TRIANGULATION_BOUNDARY_NODES:\n";
    cout << "  Please enter the name of the node file.\n";

    cin.getline ( input_node_filename, sizeof ( input_node_filename ) );
  }
  else 
  {
    strcpy ( input_node_filename, argv[1] );
  } 
//
//  Get the triangle file name.
//
  if ( argc <= 2 ) 
  {
    cout << "\n";
    cout << "TRIANGULATION_BOUNDARY_NODES:\n";
    cout << "  Please enter the name of the triangle file.\n";

    cin.getline ( input_triangulation_filename, 
      sizeof ( input_triangulation_filename ) );
  }
  else 
  {
    strcpy ( input_triangulation_filename, argv[2] );
  } 

  dtable_header_read (  input_node_filename, &dim_num, &node_num );

  cout << "\n";
  cout << "  Read the header of \"" << input_node_filename << "\".\n";
  cout << "\n";
  cout << "  Spatial dimension DIM_NUM = " << dim_num << "\n";
  cout << "  Number of nodes NODE_NUM  = " << node_num << "\n";

  node_xy = dtable_data_read ( input_node_filename, dim_num, node_num );

  cout << "\n";
  cout << "  Read the data in \"" << input_node_filename << "\".\n";

  r8mat_transpose_print_some ( dim_num, node_num, node_xy, 1, 1, dim_num, 5, 
    "  Portion of coordinate data from file:" );
//
//  Read the triangulation data.
//
  itable_header_read (  input_triangulation_filename, &triangle_order, 
    &triangle_num );

  cout << "\n";
  cout << " Read the header of \"" << input_triangulation_filename << "\".\n";
  cout << "\n";
  cout << "  Triangle order TRIANGLE_ORDER = " << triangle_order << "\n";
  cout << "  Number of triangles TRIANGLE_NUM  = " << triangle_num << "\n";

  triangle_node = itable_data_read ( input_triangulation_filename, 
    triangle_order, triangle_num );

  cout << "\n";
  cout << "  Read the data in \"" << input_triangulation_filename << "\".\n";

  i4mat_transpose_print_some ( triangle_order, triangle_num, triangle_node, 1, 1, 
    triangle_order, 5, "  Portion of data read from file:" );
//
//  Determine which nodes lie on the boundary.
//
  if ( triangle_order == 3 )
  {
    node_boundary = triangulation_order3_boundary_node ( node_num, 
      triangle_num, triangle_node );
  }
  else if ( triangle_order == 6 )
  {
    node_boundary = triangulation_order6_boundary_node ( node_num, 
      triangle_num, triangle_node );
  }
//
//  Write the output file.
//
  node_boundary_num = 0;
  for ( node = 0; node < node_num; node++ )
  {
    if ( node_boundary[node] )
    {
      node_boundary_num = node_boundary_num + 1;
    }
  }

  node_boundary_xy = new double[2*node_boundary_num];

  cout << "\n";
  cout << "  Boundary nodes:\n";
  cout << "\n";
  cout << "     New     Old\n";
  cout << "   Index   Index         X and Y Coordinates\n";
  cout << "\n";

  node2 = 0;
  for ( node = 0; node < node_num; node++ )
  {
    if ( node_boundary[node] )
    {
      node_boundary_xy[0+node2*2] = node_xy[0+node*2];
      node_boundary_xy[1+node2*2] = node_xy[1+node*2];
      cout << "  " << setw(8) << node2
           << "  " << setw(8) << node
           << "  " << setw(14) << node_xy[0+node*2]
           << "  " << setw(14) << node_xy[1+node*2] << "\n";
      node2 = node2 + 1;
    }
  }

  header = true;

  dtable_write ( output_filename, dim_num, node_boundary_num, 
    node_boundary_xy, header );

  cout << "\n";
  cout << "  Created the boundary node coordinate file \""
       << output_filename << "\"\n";

  delete [] node_boundary;
  delete [] node_boundary_xy;
  delete [] node_xy;
  delete [] triangle_node;

  cout << "\n";
  cout << "TRIANGULATION_BOUNDARY_NODES:\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.
//
//  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.
//
//  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
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char CH, the decimal digit, '0' through '9' or blank are legal.
//
//    Output, int CH_TO_DIGIT, the corresponding integer value.  If the character was
//    'illegal', then DIGIT is -1.
//
{
  int digit;

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

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

void dtable_close_write ( ofstream &output )

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_CLOSE_WRITE closes a file to which a DTABLE was to be written.
//
//  Modified:
//
//    27 September 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, ofstream output, the output file stream.
//
{
  output.close ( );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_DATA_READ reads the data from a DTABLE file.
//
//  Discussion:
//
//    The file is assumed to contain one record per line.
//
//    Records beginning with the '#' character are comments, and are ignored.
//    Blank lines are also ignored.
//
//    Each line that is not ignored is assumed to contain exactly (or at least)
//    M real numbers, representing the coordinates of a point.
//
//    There are assumed to be exactly (or at least) N such records.
//
//  Modified:
//
//    27 January 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Input, int M, the number of spatial dimensions.
//
//    Input, int N, the number of points.  The program
//    will stop reading data once N values have been read.
//
//    Output, double DTABLE_DATA_READ[M*N], the table data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  char line[255];
  double *table;
  double *x;

  input.open ( input_filename );

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

  table = new double[m*n];

  x = new double[m];

  j = 0;

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

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

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

    error = s_to_r8vec ( line, m, x );

    if ( error )
    {
      continue;
    }

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

  }

  input.close ( );

  delete [] x;

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

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

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

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << setw(10) << table[i+j*m] << "  ";
    }
    output << "\n";
  }

  output.close ( );

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

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

  *n = file_row_count ( input_filename );

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

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

  s = timestring ( );

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

  delete [] s;

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

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

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

  output.open ( output_filename );

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

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

  dtable_data_write ( output, m, n, table );

  dtable_close_write ( output );

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

int file_column_count ( char *input_filename )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
//
//  Discussion:
//
//    The file is assumed to be a simple text file.
//
//    Most lines of the file is presumed to consist of COLUMN_NUM words, separated
//    by spaces.  There may also be some blank lines, and some comment lines,
//    which have a "#" in column 1.
//
//    The routine tries to find the first non-comment non-blank line and
//    counts the number of words in that line.
//
//    If all lines are blanks or comments, it goes back and tries to analyze
//    a comment line.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the file.
//
//    Output, int FILE_COLUMN_COUNT, the number of columns assumed 
//    to be in the file.
//
{
  int column_num;
  ifstream input;
  bool got_one;
  char line[256];
//
//  Open the file.
//
  input.open ( input_filename );

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

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

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

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

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

    got_one = true;
    break;

  }

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

    input.open ( input_filename );

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

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

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

      got_one = true;
      break;

    }

  }

  input.close ( );

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

  column_num = s_word_count ( line );

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

void file_name_ext_get ( char *file_name, int *i, int *j )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_NAME_EXT_GET determines the "extension" of a file name.
//
//  Definition:
//
//    The "extension" of a file name is the string of characters
//    that appears after the LAST period in the name.  A file
//    with no period, or with a period as the last character
//    in the name, has a "null" extension.
//
//  Note:
//
//    Blanks are unusual in file names.  This routine ignores all
//    trailing blanks, but will treat initial or internal blanks
//    as regular characters acceptable in a file name.
//
//  Examples:
//
//    FILE_NAME   I  J
//
//    bob.for     3  6
//    N.B.C.D     5  6
//    Naomi.      5  5
//    Arthur     -1 -1
//    .com        0  0
//
//  Modified:
//
//    17 July 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, a file name to be examined.
//
//    Output, int *I, *J, the indices of the first and last characters
//    in the file extension.
//
//    If no period occurs in FILE_NAME, then
//      I = J = -1;
//    Otherwise,
//      I is the position of the LAST period in FILE_NAME, and J is the
//      position of the last nonblank character following the period.
//
{
  *i = s_index_last_c ( file_name, '.' );

  if ( *i == -1 )
  {
    *j = -1;
  }
  else
  {
    *j = s_len_trim ( file_name ) - 1;
  }

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

char *file_name_ext_swap ( char *file_name, char *ext )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
//
//  Discussion:
//
//    NO THANKS: The creation of this routine was made more difficult by the clumsy
//    construction and misleading documentation of the C library routines STRNCAT
//    and STRCAT, which I was planning to use.
//
//  Definition:
//
//    The "extension" of a file name is the string of characters
//    that appears after the LAST period in the name.  A file
//    with no period, or with a period as the last character
//    in the name, has a "null" extension.
//
//  Examples:
//
//          Input           Output
//    ================     ==================
//    FILE_NAME    EXT     FILE_NAME_EXT_SWAP
//
//    bob.for      obj     bob.obj
//    bob.bob.bob  txt     bob.bob.txt
//    bob          yak     bob.yak
//
//  Modified:
//
//    06 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, a file name.
//
//    Input, char *EXT, the extension to be used on the output
//    copy of FILE_NAME, replacing the current extension if any.
//
//    Output, char *FILE_NAME_EXT_SWAP, the file name with the new extension.
//
{
  int ext_len;
  int file_name_len;
  char *file_name2;
  int i;
  int j;
  int period;
  char *s;
  char *t;

  ext_len = s_len_trim ( ext );
  file_name_len = s_len_trim ( file_name );
//
//  Call FILE_NAME_EXT_GET to get I, the index of the period character
//  beginning the file extension.
//
  file_name_ext_get ( file_name, &period, &j );
//
//  If there is no extension, point to where the "." should be.
//
  if ( period == -1 )
  {
    period = file_name_len;
  }

  file_name2 = new char[ period + 1 + ext_len + 1];

  s = file_name2;
  t = file_name;
  for ( i = 0; i < period; i++ )
  {
    *s = *t;
    s++;
    t++;
  }
  *s = '.';
  s++;

  t = ext;
  for ( i = 0; i < ext_len; i++ )
  {
    *s = *t;
    s++;
    t++;
  }

  *s = '\0';

  return file_name2;
}
//****************************************************************************80

int file_row_count ( char *input_filename )

//****************************************************************************80
//
//  Purpose:
//
//    FILE_ROW_COUNT counts the number of row records in a file.
//
//  Discussion:
//
//    It does not count lines that are blank, or that begin with a
//    comment symbol '#'.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Output, int FILE_ROW_COUNT, the number of rows found.
//
{
  int bad_num;
  int comment_num;
  ifstream input;
  int i;
  char line[100];
  int record_num;
  int row_num;

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

  input.open ( input_filename );

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

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

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

    record_num = record_num + 1;

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

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

    row_num = row_num + 1;

  }

  input.close ( );

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

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two I4's.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, are two integers to be compared.
//
//    Output, int I4_MAX, the larger of I1 and I2.
//
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MIN returns the minimum of two I4's.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MIN, the smaller of I1 and I2.
//
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4col_compare ( int m, int n, int a[], int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4COL_COMPARE compares columns I and J of a integer array.
//
//  Example:
//
//    Input:
//
//      M = 3, N = 4, I = 2, J = 4
//
//      A = (
//        1  2  3  4
//        5  6  7  8
//        9 10 11 12 )
//
//    Output:
//
//      I4COL_COMPARE = -1
//
//  Modified:
//
//    12 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, int A[M*N], an array of N columns of vectors of length M.
//
//    Input, int I, J, the columns to be compared.
//    I and J must be between 1 and N.
//
//    Output, int I4COL_COMPARE, the results of the comparison:
//    -1, column I < column J,
//     0, column I = column J,
//    +1, column J < column I.
//
{
  int k;
//
//  Check.
//
  if ( i < 1 )
  {
    cout << "\n";
    cout << "I4COL_COMPARE - Fatal error!\n";
    cout << "  Column index I = " << i << " is less than 1.\n";
    exit ( 1 );
  }

  if ( n < i )
  {
    cout << "\n";
    cout << "I4COL_COMPARE - Fatal error!\n";
    cout << "  N = " << n << " is less than column index I = " << i << ".\n";
    exit ( 1 );
  }

  if ( j < 1 )
  {
    cout << "\n";
    cout << "I4COL_COMPARE - Fatal error!\n";
    cout << "  Column index J = " << j << " is less than 1.\n";
    exit ( 1 );
  }

  if ( n < j )
  {
    cout << "\n";
    cout << "I4COL_COMPARE - Fatal error!\n";
    cout << "  N = " << n << " is less than column index J = " << j << ".\n";
    exit ( 1 );
  }

  if ( i == j )
  {
    return 0;
  }

  k = 1;

  while ( k <= m )
  {
    if ( a[k-1+(i-1)*m] < a[k-1+(j-1)*m] )
    {
      return (-1);
    }
    else if ( a[k-1+(j-1)*m] < a[k-1+(i-1)*m] )
    {
      return 1;
    }
    k = k + 1;
  }

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

void i4col_sort_a ( int m, int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4COL_SORT_A ascending sorts the columns of an integer array.
//
//  Definition:
//
//    In lexicographic order, the statement "X < Y", applied to two
//    vectors X and Y of length M, means that there is some index I, with
//    1 <= I <= M, with the property that
//
//      X(J) = Y(J) for J < I,
//    and
//      X(I) < Y(I).
//
//    In other words, X is less than Y if, at the first index where they
//    differ, the X value is less than the Y value.
//
//  Modified:
//
//    12 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows of A.
//
//    Input, int N, the number of columns of A.
//
//    Input/output, int A[M*N].
//    On input, the array of N columns of M vectors;
//    On output, the columns of A have been sorted in ascending
//    lexicographic order.
//
{
  int i;
  int indx;
  int isgn;
  int j;
//
//  Initialize.
//
  i = 0;
  indx = 0;
  isgn = 0;
  j = 0;
//
//  Call the external heap sorter.
//
  for ( ; ; )
  {
    sort_heap_external ( n, &indx, &i, &j, isgn );
//
//  Interchange the I and J objects.
//
    if ( 0 < indx )
    {
      i4col_swap ( m, n, a, i, j );
    }
//
//  Compare the I and J objects.
//
    else if ( indx < 0 )
    {
      isgn = i4col_compare ( m, n, a, i, j );
    }
    else if ( indx == 0 )
    {
      break;
    }

  }

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

void i4col_swap ( int m, int n, int a[], int icol1, int icol2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4COL_SWAP swaps two columns of an integer array.
//
//  Discussion:
//
//    The two dimensional information is stored as a one dimensional
//    array, by columns.
//
//    The row indices are 1 based, NOT 0 based!  However, a preprocessor
//    variable, called OFFSET, can be reset from 1 to 0 if you wish to
//    use 0-based indices.
//
//  Modified:
//
//    03 April 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input/output, int A[M*N], an array of data.
//
//    Input, int ICOL1, ICOL2, the two columns to swap.
//    These indices should be between 1 and N.
//
{
# define OFFSET 1

  int i;
  int t;
//
//  Check.
//
  if ( icol1 - OFFSET < 0 || n-1 < icol1 - OFFSET )
  {
    cout << "\n";
    cout << "I4COL_SWAP - Fatal error!\n";
    cout << "  ICOL1 is out of range.\n";
    exit ( 1 );
  }

  if ( icol2 - OFFSET < 0 || n-1 < icol2 - OFFSET )
  {
    cout << "\n";
    cout << "I4COL_SWAP - Fatal error!\n";
    cout << "  ICOL2 is out of range.\n";
    exit ( 1 );
  }

  if ( icol1 == icol2 )
  {
    return;
  }
  for ( i = 0; i < m; i++ )
  {
    t                     = a[i+(icol1-OFFSET)*m];
    a[i+(icol1-OFFSET)*m] = a[i+(icol2-OFFSET)*m];
    a[i+(icol2-OFFSET)*m] = t;
  }

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

void i4mat_transpose_print_some ( int m, int n, int a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.
//
//  Modified:
//
//    14 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows of the matrix.
//    M must be positive.
//
//    Input, int N, the number of columns of the matrix.
//    N must be positive.
//
//    Input, int A[M*N], the matrix.
//
//    Input, int ILO, JLO, IHI, JHI, designate the first row and
//    column, and the last row and column to be printed.
//
//    Input, char *TITLE, a title for the matrix.
{
# define INCX 10

  int i;
  int i2hi;
  int i2lo;
  int j;
  int j2hi;
  int j2lo;

  if ( 0 < s_len_trim ( title ) )
  {
    cout << "\n";
    cout << title << "\n";
  }
//
//  Print the columns of the matrix, in strips of INCX.
//
  for ( i2lo = ilo; i2lo <= ihi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

    cout << "\n";
//
//  For each row I in the current range...
//
//  Write the header.
//
    cout << "  Row: ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(6) << i << "  ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
//
//  Print out (up to INCX) entries in column J, that lie in the current strip.
//
      cout << setw(5) << j << "  ";
      for ( i = i2lo; i <= i2hi; i++ )
      {
        cout << setw(6) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }

  }

  cout << "\n";

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

int *itable_data_read ( char *input_filename, int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    ITABLE_DATA_READ reads data from an ITABLE file.
//
//  Discussion:
//
//    The file is assumed to contain one record per line.
//
//    Records beginning with the '#' character are comments, and are ignored.
//    Blank lines are also ignored.
//
//    Each line that is not ignored is assumed to contain exactly (or at least)
//    M real numbers, representing the coordinates of a point.
//
//    There are assumed to be exactly (or at least) N such records.
//
//  Modified:
//
//    11 October 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Input, int M, the number of spatial dimensions.
//
//    Input, int N, the number of points.  The program
//    will stop reading data once N values have been read.
//
//    Output, int ITABLE_DATA_READ[M*N], the table data.
//
{
  bool error;
  ifstream input;
  int i;
  int j;
  char line[255];
  int *table;
  int *x;

  input.open ( input_filename );

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

  table = new int[m*n];

  x = new int[m];

  j = 0;

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

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

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

    error = s_to_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 itable_header_read ( char *input_filename, int *m, int *n )
 
//****************************************************************************80
//
//  Purpose:
//
//    ITABLE_HEADER_READ reads the header from an ITABLE file.
//
//  Modified:
//
//    04 June 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Output, int *M, the number of spatial dimensions.
//
//    Output, int *N, the number of points
//
{
  *m = file_column_count ( input_filename );
 
  if ( *m <= 0 )
  {
    cout << "\n";
    cout << "ITABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_COLUMN_COUNT failed.\n";
    *n = -1;
    return;
  }
 
  *n = file_row_count ( input_filename );
 
  if ( *n <= 0 )
  {
    cout << "\n";
    cout << "ITABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_ROW_COUNT failed.\n";
    return;
  }
 
  return;
}
//****************************************************************************80

double r8_epsilon ( void )

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

  r = 1.0;

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

  return ( 2.0 * r );
}
//****************************************************************************80

void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
//
//  Modified:
//
//    11 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, double A[M*N], an M by N matrix to be printed.
//
//    Input, int ILO, JLO, the first row and column to print.
//
//    Input, int IHI, JHI, the last row and column to print.
//
//    Input, char *TITLE, an optional title.
//
{
# define INCX 5

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

  if ( 0 < s_len_trim ( title ) )
  {
    cout << "\n";
    cout << title << "\n";
  }

  for ( i2lo = i4_max ( ilo, 1 ); i2lo <= i4_min ( ihi, m ); i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;
    i2hi = i4_min ( i2hi, m );
    i2hi = i4_min ( i2hi, ihi );

    inc = i2hi + 1 - i2lo;

    cout << "\n";
    cout << "  Row: ";
    for ( i = i2lo; i <= i2hi; i++ )
    {
      cout << setw(7) << i << "       ";
    }
    cout << "\n";
    cout << "  Col\n";
    cout << "\n";

    j2lo = i4_max ( jlo, 1 );
    j2hi = i4_min ( jhi, n );

    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(5) << j << " ";
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        cout << setw(14) << a[(i-1)+(j-1)*m];
      }
      cout << "\n";
    }
  }
  cout << "\n";

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

int s_index_last_c ( char *s, char c )

//****************************************************************************80
//
//  Purpose:
//
//    S_INDEX_LAST_C returns a pointer to the last occurrence of a given character.
//
//  Modified:
//
//    06 December
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a pointer to a string.
//
//    Input, char C, the character to search for.
//
//    Output, int S_INDEX_LAST_C, the index in S of the last occurrence of the character,
//    or -1 if it does not occur.
//
{
  int n;
  char *t;

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

  while ( 0 <= n ) 
  {
    if ( *t == c )
    {
      return n;
    }
    t--;
    n--;
  }

  return (-1);
}
//****************************************************************************80

int s_len_trim ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Modified:
//
//    26 April 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a pointer to a string.
//
//    Output, int S_LEN_TRIM, the length of the string to the last nonblank.
//    If S_LEN_TRIM is 0, then the string is entirely blank.
//
{
  int n;
  char *t;

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

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

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

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

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4 reads an I4 from a string.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a string to be examined.
//
//    Output, int *LAST, the last character of S used to make IVAL.
//
//    Output, bool *ERROR is TRUE if an error occurred.
//
//    Output, int *S_TO_I4, the integer value read from the string.
//    If the string is blank, then IVAL will be returned 0.
//
{
  char c;
  int i;
  int isgn;
  int istate;
  int ival;

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

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

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

bool s_to_i4vec ( char *s, int n, int ivec[] )

//****************************************************************************80
//
//  Purpose:
//
//    S_TO_I4VEC reads an I4VEC from a string.
//
//  Modified:
//
//    08 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *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.
//
{
  bool error;
  int i;
  int lchar;
  double x;

  error = false;

  for ( i = 0; i < n; i++ )
  {
    ivec[i] = s_to_i4 ( s, &lchar, &error );

    if ( error )
    {
      cout << "\n";
      cout << "S_TO_I4VEC - Fatal error!\n";
      cout << "  S_TO_I4 returned error while reading item " << i << "\n";
      return error;
    }

    s = s + lchar;

  }

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

double s_to_r8 ( char *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.
//
//  Examples:
//
//    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)
//
//  Modified:
//
//    07 August 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string containing the
//    data to be read.  Reading will begin at position 1 and
//    terminate at the end of the string, or when no more
//    characters can be read to form a legal real.  Blanks,
//    commas, or other nonnumeric data will, in particular,
//    cause the conversion to halt.
//
//    Output, int *LCHAR, the number of characters read from
//    the string to form the number, including any terminating
//    characters such as a trailing comma or blanks.
//
//    Output, bool *ERROR, is true if an error occurred.
//
//    Output, double S_TO_R8, the 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 ( char *s, int n, double rvec[] )

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

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

    if ( error )
    {
      return error;
    }

    s = s + lchar;

  }

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

int s_word_count ( char *s )

//****************************************************************************80
//
//  Purpose:
//
//    S_WORD_COUNT counts the number of "words" in a string.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, the string to be examined.
//
//    Output, int S_WORD_COUNT, the number of "words" in the string.
//    Words are presumed to be separated by one or more blanks.
//
{
  bool blank;
  int i;
  int nword;

  nword = 0;
  blank = true;

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

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

void sort_heap_external ( int n, int *indx, int *i, int *j, int isgn )

//****************************************************************************80
//
//  Purpose:
//
//    SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
//
//  Discussion:
//
//    The actual list is not passed to the routine.  Hence it may
//    consist of integers, reals, numbers, names, etc.  The user,
//    after each return from the routine, will be asked to compare or
//    interchange two items.
//
//    The current version of this code mimics the FORTRAN version,
//    so the values of I and J, in particular, are FORTRAN indices.
//
//  Modified:
//
//    05 February 2004
//
//  Reference:
//
//    Albert Nijenhuis, Herbert Wilf,
//    Combinatorial Algorithms,
//    Academic Press, 1978, second edition,
//    ISBN 0-12-519260-6.
//
//  Parameters:
//
//    Input, int N, the length of the input list.
//
//    Input/output, int *INDX.
//    The user must set INDX to 0 before the first call.
//    On return,
//      if INDX is greater than 0, the user must interchange
//      items I and J and recall the routine.
//      If INDX is less than 0, the user is to compare items I
//      and J and return in ISGN a negative value if I is to
//      precede J, and a positive value otherwise.
//      If INDX is 0, the sorting is done.
//
//    Output, int *I, *J.  On return with INDX positive,
//    elements I and J of the user's list should be
//    interchanged.  On return with INDX negative, elements I
//    and J are to be compared by the user.
//
//    Input, int ISGN. On return with INDX negative, the
//    user should compare elements I and J of the list.  If
//    item I is to precede item J, set ISGN negative,
//    otherwise set ISGN positive.
//
{
  static int i_save = 0;
  static int j_save = 0;
  static int k = 0;
  static int k1 = 0;
  static int n1 = 0;
//
//  INDX = 0: This is the first call.
//
  if ( *indx == 0 )
  {

    i_save = 0;
    j_save = 0;
    k = n / 2;
    k1 = k;
    n1 = n;
  }
//
//  INDX < 0: The user is returning the results of a comparison.
//
  else if ( *indx < 0 )
  {
    if ( *indx == -2 ) 
    {
      if ( isgn < 0 ) 
      {
        i_save = i_save + 1;
      }
      j_save = k1;
      k1 = i_save;
      *indx = -1;
      *i = i_save;
      *j = j_save;
      return;
    }

    if ( 0 < isgn ) 
    {
      *indx = 2;
      *i = i_save;
      *j = j_save;
      return;
    }

    if ( k <= 1 ) 
    {
      if ( n1 == 1 ) 
      {
        i_save = 0;
        j_save = 0;
        *indx = 0;
      }
      else 
      {
        i_save = n1;
        j_save = 1;
        n1 = n1 - 1;
        *indx = 1;
      }
      *i = i_save;
      *j = j_save;
      return;
    }
    k = k - 1;
    k1 = k;
  }
//
//  0 < INDX: the user was asked to make an interchange.
//
  else if ( *indx == 1 ) 
  {
    k1 = k;
  }

  for ( ; ; )
  {

    i_save = 2 * k1;

    if ( i_save == n1 ) 
    {
      j_save = k1;
      k1 = i_save;
      *indx = -1;
      *i = i_save;
      *j = j_save;
      return;
    }
    else if ( i_save <= n1 ) 
    {
      j_save = i_save + 1;
      *indx = -2;
      *i = i_save;
      *j = j_save;
      return;
    }

    if ( k <= 1 ) 
    {
      break;
    }

    k = k - 1;
    k1 = k;
  }

  if ( n1 == 1 ) 
  {
    i_save = 0;
    j_save = 0;
    *indx = 0;
    *i = i_save;
    *j = j_save;
  }
  else 
  {
    i_save = n1;
    j_save = 1;
    n1 = n1 - 1;
    *indx = 1;
    *i = i_save;
    *j = j_save;
  }

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

void timestamp ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

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

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

  cout << time_buffer << "\n";

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

char *timestring ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTRING returns the current YMDHMS date as a string.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, char *TIMESTRING, a string containing the current YMDHMS date.
//
{
# define TIME_SIZE 40

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

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

  s = new char[TIME_SIZE];

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

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

bool *triangulation_order3_boundary_node ( int node_num, int triangle_num, 
  int triangle_node[] )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_ORDER3_BOUNDARY_NODE indicates nodes on the boundary.
//
//  Discussion:
//
//    This routine is given a triangulation, an abstract list of triples
//    of nodes.  It is assumed that the nodes in each triangle are listed
//    in a counterclockwise order, although the routine should work
//    if the nodes are consistently listed in a clockwise order as well.
//
//    It is assumed that each edge of the triangulation is either
//    * an INTERIOR edge, which is listed twice, once with positive
//      orientation and once with negative orientation, or;
//    * a BOUNDARY edge, which will occur only once.
//
//    This routine should work even if the region has holes - as long
//    as the boundary of the hole comprises more than 3 edges!
//
//  Modified:
//
//    12 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[3*TRIANGLE_NUM], the nodes that make up the
//    triangles.  These should be listed in counterclockwise order.
//
//    Output, bool TRIANGULATION_ORDER3_BOUNDARY_NODE[NODE_NUM], 
//    is TRUE if the node is on a boundary edge.
//
{
  int e1;
  int e2;
  int *edge;
  bool equal;
  int i;
  int j;
  int m;
  int n;
  bool *node_boundary;

  m = 2;
  n = 3 * triangle_num;
//
//  Set up the edge array.
//
  edge = new int[m*n];

  for ( j = 0; j < triangle_num; j++ )
  {
    edge[0+(j               )*m] = triangle_node[0+j*3];
    edge[1+(j               )*m] = triangle_node[1+j*3];
    edge[0+(j+  triangle_num)*m] = triangle_node[1+j*3];
    edge[1+(j+  triangle_num)*m] = triangle_node[2+j*3];
    edge[0+(j+2*triangle_num)*m] = triangle_node[2+j*3];
    edge[1+(j+2*triangle_num)*m] = triangle_node[0+j*3];
  }
//
//  In each column, force the smaller entry to appear first.
//
  for ( j = 0; j < n; j++ )
  {
    e1 = i4_min ( edge[0+j*m], edge[1+j*m] );
    e2 = i4_max ( edge[0+j*m], edge[1+j*m] );
    edge[0+j*m] = e1;
    edge[1+j*m] = e2;
  }
//
//  Ascending sort the column array.
//
  i4col_sort_a ( m, n, edge );
//
//  Records which appear twice are internal edges and can be ignored.
//
  node_boundary = new bool[node_num];

  for ( i = 0; i < node_num; i++ )
  {
    node_boundary[i] = false;
  }

  j = 0;

  while ( j < 3 * triangle_num )
  {
    j = j + 1;

    if ( j == 3 * triangle_num )
    {
      for ( i = 0; i < m; i++ )
      {
        node_boundary[edge[i+(j-1)*m]-1] = true;
      }
      break;
    }

    equal = true;

    for ( i = 0; i < m; i++ )
    {
      if ( edge[i+(j-1)*m] != edge[i+j*m] )
      {
        equal = false;
      }
    }

    if ( equal )
    {
      j = j + 1;
    }
    else
    {
      for ( i = 0; i < m; i++ )
      {
        node_boundary[edge[i+(j-1)*m]-1] = true;
      }
    }

  }

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

bool *triangulation_order6_boundary_node ( int node_num, int triangle_num, 
  int triangle_node[] )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_ORDER6_BOUNDARY_NODE indicates nodes on the boundary.
//
//  Discussion:
//
//    This routine is given an order 6 triangulation, an abstract list of
//    sets of six nodes.  The vertices are listed clockwise, then the 
//    midside nodes.
//
//    It is assumed that each edge of the triangulation is either
//    * an INTERIOR edge, which is listed twice, once with positive
//      orientation and once with negative orientation, or;
//    * a BOUNDARY edge, which will occur only once.
//
//    This routine should work even if the region has holes - as long
//    as the boundary of the hole comprises more than 3 edges!
//
//  Modified:
//
//    14 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[6*TRIANGLE_NUM], the nodes that make up the
//    triangles.  
//
//    Output, bool TRIANGULATION_ORDER6_BOUNDARY_NODE[NODE_NUM], 
//    is TRUE if the node is on a boundary edge.
//
{
  int e1;
  int e2;
  int *edge;
  bool equal;
  int i;
  int j;
  int m;
  int n;
  bool *node_boundary;

  m = 3;
  n = 3 * triangle_num;
//
//  Set up the edge array.
//
  edge = new int[m*n];

  for ( j = 0; j < triangle_num; j++ )
  {
    edge[0+(j               )*m] = triangle_node[0+j*6];
    edge[1+(j               )*m] = triangle_node[3+j*6];
    edge[2+(j               )*m] = triangle_node[1+j*6];

    edge[0+(j+  triangle_num)*m] = triangle_node[1+j*6];
    edge[1+(j+  triangle_num)*m] = triangle_node[4+j*6];
    edge[2+(j+  triangle_num)*m] = triangle_node[2+j*6];

    edge[0+(j+2*triangle_num)*m] = triangle_node[2+j*6];
    edge[1+(j+2*triangle_num)*m] = triangle_node[5+j*6];
    edge[2+(j+2*triangle_num)*m] = triangle_node[0+j*6];
  }
//
//  In each column, force the smaller entry to appear first.
//
  for ( j = 0; j < n; j++ )
  {
    e1 = i4_min ( edge[0+j*m], edge[2+j*m] );
    e2 = i4_max ( edge[0+j*m], edge[2+j*m] );
    edge[0+j*m] = e1;
    edge[2+j*m] = e2;
  }
//
//  Ascending sort the column array.
//
  i4col_sort_a ( m, n, edge );
//
//  Records which appear twice are internal edges and can be ignored.
//
  node_boundary = new bool[node_num];

  for ( i = 0; i < node_num; i++ )
  {
    node_boundary[i] = false;
  }

  j = 0;

  while ( j < 3 * triangle_num )
  {
    j = j + 1;

    if ( j == 3 * triangle_num )
    {
      for ( i = 0; i < m; i++ )
      {
        node_boundary[edge[i+(j-1)*m]-1] = true;
      }
      break;
    }

    equal = true;

    for ( i = 0; i < m; i++ )
    {
      if ( edge[i+(j-1)*m] != edge[i+j*m] )
      {
        equal = false;
      }
    }

    if ( equal )
    {
      j = j + 1;
    }
    else
    {
      for ( i = 0; i < m; i++ )
      {
        node_boundary[edge[i+(j-1)*m]-1] = true;
      }
    }

  }

  return node_boundary;
}