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

using namespace std;

# include "fem_sample.H"

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

void basis_mn_t3 ( double t[2*3], int n, double p[], double phi[], 
  double dphidx[], double dphidy[] )

//****************************************************************************80
//
//  Purpose:
//
//    BASIS_MN_T3: all bases at N points for a T3 element.
//
//  Discussion:
//
//    The routine is given the coordinates of the vertices of a triangle.
//    It works directly with these coordinates, and does not refer to a 
//    reference element.
//
//    The sides of the triangle DO NOT have to lie along a coordinate
//    axis.
//
//    The routine evaluates the basis functions associated with each vertex,
//    and their derivatives with respect to X and Y.
//
//  Physical Element T3: 
//       
//            3
//           / \
//          /   \
//         /     \
//        /       \
//       1---------2
//   
//  Modified:
//
//    09 February 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double T[2*3], the coordinates of the vertices
//    of the triangle.  It is common to list these points in counter clockwise
//    order.
//
//    Input, int N, the number of evaluation points.
//
//    Input, double P[2*N], the points where the basis functions 
//    are to be evaluated.
//
//    Output, double PHI[3*N], the value of the basis functions 
//    at the evaluation points.
//
//    Output, double DPHIDX[3*N], DPHIDY[3*N], the value of the 
//    derivatives at the evaluation points.
//
//  Local parameters:
//
//    Local, double AREA, is (twice) the area of the triangle.
//
{
  double area;
  int i;
  int j;
  double temp;

  area = t[0+0*2] * ( t[1+1*2] - t[1+2*2] ) 
       + t[0+1*2] * ( t[1+2*2] - t[1+0*2] ) 
       + t[0+2*2] * ( t[1+0*2] - t[1+1*2] );

  if ( area == 0.0 )
  {
    cout << "\n";
    cout << "BASIS_MN_T3 - Fatal error!\n";
    cout << "  Element has zero area.\n";
    exit ( 1 );
  }

  for ( j = 0; j < n; j++ )
  {
    phi[0+j*3] =     (   ( t[0+2*2] - t[0+1*2] ) * ( p[1+j*2] - t[1+1*2] )     
                       - ( t[1+2*2] - t[1+1*2] ) * ( p[0+j*2] - t[0+1*2] ) );
    dphidx[0+j*3] =    - ( t[1+2*2] - t[1+1*2] );
    dphidy[0+j*3] =      ( t[0+2*2] - t[0+1*2] );

    phi[1+j*3] =     (   ( t[0+0*2] - t[0+2*2] ) * ( p[1+j*2] - t[1+2*2] )     
                       - ( t[1+0*2] - t[1+2*2] ) * ( p[0+j*2] - t[0+2*2] ) );
    dphidx[1+j*3] =    - ( t[1+0*2] - t[1+2*2] );
    dphidy[1+j*3] =      ( t[0+0*2] - t[0+2*2] );

    phi[2+j*3] =     (   ( t[0+1*2] - t[0+0*2] ) * ( p[1+j*2] - t[1+0*2] )     
                       - ( t[1+1*2] - t[1+0*2] ) * ( p[0+j*2] - t[0+0*2] ) );
    dphidx[2+j*3] =    - ( t[1+1*2] - t[1+0*2] );
    dphidy[2+j*3] =      ( t[0+1*2] - t[0+0*2] );
  }
//
//  Normalize.
//
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < 3; i++ )
    {
      phi[i+j*3]    = phi[i+j*3]    / area;
      dphidx[i+j*3] = dphidx[i+j*3] / area;
      dphidy[i+j*3] = dphidy[i+j*3] / area;
    }
  }

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

void basis_mn_t6 ( double t[2*6], int n, double p[], double phi[], 
  double dphidx[], double dphidy[] )

//****************************************************************************80
//
//  Purpose:
//
//    BASIS_MN_T6: all bases at N points for a T6 element.
//
//  Discussion:
//
//    The routine is given the coordinates of the vertices and midside
//    nodes of a triangle.  It works directly with these coordinates, and does 
//    not refer to a reference element.
//
//    This routine requires that the midside nodes be "in line"
//    with the vertices, that is, that the sides of the triangle be
//    straight.  However, the midside nodes do not actually have to
//    be halfway along the side of the triangle.  
//
//  The physical element T6:
//
//    This picture indicates the assumed ordering of the six nodes
//    of the triangle.
//
//    |
//    |   
//    |        3
//    |       / \
//    |      /   \
//    Y     6     5
//    |    /       \
//    |   /         \
//    |  1-----4-----2
//    |
//    +--------X-------->
//
//  Modified:
//
//    12 February 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double T[2*6], the nodal oordinates of the element.
//    It is common to list these points in counter clockwise order.
//
//    Input, int N, the number of evaluation points.
//
//    Input, double P[2*N], the coordinates of the point where
//    the basis functions are to be evaluated.
//
//    Output, double PHI[6*N], the value of the basis functions at P.
//
//    Output, double DPHIDX[6*N], DPHIDY[6*N], the value of the X 
//    and Y derivatives of the basis functions at P.
//
{
  double gn;
  double gx;
  double hn;
  double hx;
  int j;

  for ( j = 0; j < n; j++ )
  {
//
//  Basis function 1: PHI(X,Y) = G(3,2) * H(6,4) / normalization.
//
    gx = ( p[0+j*2] - t[0+1*2] ) * ( t[1+2*2] - t[1+1*2] ) 
       - ( t[0+2*2] - t[0+1*2] ) * ( p[1+j*2] - t[1+1*2] );

    gn = ( t[0+0*2] - t[0+1*2] ) * ( t[1+2*2] - t[1+1*2] ) 
       - ( t[0+2*2] - t[0+1*2] ) * ( t[1+0*2] - t[1+1*2] );

    hx = ( p[0+j*2] - t[0+3*2] ) * ( t[1+5*2] - t[1+3*2] ) 
       - ( t[0+5*2] - t[0+3*2] ) * ( p[1+j*2] - t[1+3*2] );

    hn = ( t[0+0*2] - t[0+3*2] ) * ( t[1+5*2] - t[1+3*2] ) 
       - ( t[0+5*2] - t[0+3*2] ) * ( t[1+0*2] - t[1+3*2] );

    phi[0+j*6] =     ( gx * hx ) / ( gn * hn );
    dphidx[0+j*6] =  (      ( t[1+2*2] - t[1+1*2] ) * hx 
                     + gx * ( t[1+5*2] - t[1+3*2] ) ) / ( gn * hn );
    dphidy[0+j*6] = -(      ( t[0+2*2] - t[0+1*2] ) * hx 
                     + gx * ( t[0+5*2] - t[0+3*2] ) ) / ( gn * hn );
//
//  Basis function 2: PHI(X,Y) = G(3,1) * H(4,5) / normalization.
//
    gx = ( p[0+j*2] - t[0+0*2] ) * ( t[1+2*2] - t[1+0*2] ) 
       - ( t[0+2*2] - t[0+0*2] ) * ( p[1+j*2] - t[1+0*2] );

    gn = ( t[0+1*2] - t[0+0*2] ) * ( t[1+2*2] - t[1+0*2] ) 
       - ( t[0+2*2] - t[0+0*2] ) * ( t[1+1*2] - t[1+0*2] );

    hx = ( p[0+j*2] - t[0+4*2] ) * ( t[1+3*2] - t[1+4*2] ) 
       - ( t[0+3*2] - t[0+4*2] ) * ( p[1+j*2] - t[1+4*2] );

    hn = ( t[0+1*2] - t[0+4*2] ) * ( t[1+3*2] - t[1+4*2] ) 
       - ( t[0+3*2] - t[0+4*2] ) * ( t[1+1*2] - t[1+4*2] );

    phi[1+j*6] = ( gx * hx ) / ( gn * hn );
    dphidx[1+j*6] =  (      ( t[1+2*2] - t[1+0*2] ) * hx 
                     + gx * ( t[1+3*2] - t[1+4*2] ) ) / ( gn * hn );
    dphidy[1+j*6] = -(      ( t[0+2*2] - t[0+0*2] ) * hx 
                     + gx * ( t[0+3*2] - t[0+4*2] ) ) / ( gn * hn );
//
//  Basis function 3: PHI(X,Y) = G(1,2) * H(5,6) / normalization.
//
    gx = ( p[0+j*2] - t[0+1*2] ) * ( t[1+0*2] - t[1+1*2] ) 
       - ( t[0+0*2] - t[0+1*2] ) * ( p[1+j*2] - t[1+1*2] );

    gn = ( t[0+2*2] - t[0+1*2] ) * ( t[1+0*2] - t[1+1*2] ) 
       - ( t[0+0*2] - t[0+1*2] ) * ( t[1+2*2] - t[1+1*2] );

    hx = ( p[0+j*2] - t[0+5*2] ) * ( t[1+4*2] - t[1+5*2] ) 
       - ( t[0+4*2] - t[0+5*2] ) * ( p[1+j*2] - t[1+5*2] );

    hn = ( t[0+2*2] - t[0+5*2] ) * ( t[1+4*2] - t[1+5*2] ) 
       - ( t[0+4*2] - t[0+5*2] ) * ( t[1+2*2] - t[1+5*2] );

    phi[2+j*6] = ( gx * hx ) / ( gn * hn );
    dphidx[2+j*6] =  (      ( t[1+0*2] - t[1+1*2] ) * hx 
                     + gx * ( t[1+4*2] - t[1+5*2] ) ) / ( gn * hn );
    dphidy[2+j*6] = -(      ( t[0+0*2] - t[0+1*2] ) * hx 
                     + gx * ( t[0+4*2] - t[0+5*2] ) ) / ( gn * hn );
//
//  Basis function 4: PHI(X,Y) = G(1,3) * H(2,3) / normalization.
//
    gx = ( p[0+j*2] - t[0+2*2] ) * ( t[1+0*2] - t[1+2*2] ) 
       - ( t[0+0*2] - t[0+2*2] ) * ( p[1+j*2] - t[1+2*2] );

    gn = ( t[0+3*2] - t[0+2*2] ) * ( t[1+0*2] - t[1+2*2] ) 
       - ( t[0+0*2] - t[0+2*2] ) * ( t[1+3*2] - t[1+2*2] );

    hx = ( p[0+j*2] - t[0+2*2] ) * ( t[1+1*2] - t[1+2*2] ) 
       - ( t[0+1*2] - t[0+2*2] ) * ( p[1+j*2] - t[1+2*2] );

    hn = ( t[0+3*2] - t[0+2*2] ) * ( t[1+1*2] - t[1+2*2] ) 
       - ( t[0+1*2] - t[0+2*2] ) * ( t[1+3*2] - t[1+2*2] );

    phi[3+j*6] = ( gx * hx ) / ( gn * hn );
    dphidx[3+j*6] =  (      ( t[1+0*2] - t[1+2*2] ) * hx 
                     + gx * ( t[1+1*2] - t[1+2*2] ) ) / ( gn * hn );
    dphidy[3+j*6] = -(      ( t[0+0*2] - t[0+2*2] ) * hx 
                     + gx * ( t[0+1*2] - t[0+2*2] ) ) / ( gn * hn );
//
//  Basis function 5: PHI(X,Y) = G(2,1) * H(3,1) / normalization.
//
    gx = ( p[0+j*2] - t[0+0*2] ) * ( t[1+1*2] - t[1+0*2] ) 
       - ( t[0+1*2] - t[0+0*2] ) * ( p[1+j*2] - t[1+0*2] );

    gn = ( t[0+4*2] - t[0+0*2] ) * ( t[1+1*2] - t[1+0*2] ) 
       - ( t[0+1*2] - t[0+0*2] ) * ( t[1+4*2] - t[1+0*2] );

    hx = ( p[0+j*2] - t[0+0*2] ) * ( t[1+2*2] - t[1+0*2] ) 
       - ( t[0+2*2] - t[0+0*2] ) * ( p[1+j*2] - t[1+0*2] );

    hn = ( t[0+4*2] - t[0+0*2] ) * ( t[1+2*2] - t[1+0*2] ) 
       - ( t[0+2*2] - t[0+0*2] ) * ( t[1+4*2] - t[1+0*2] );

    phi[4+j*6] = ( gx * hx ) / ( gn * hn );
    dphidx[4+j*6] =  (      ( t[1+1*2] - t[1+0*2] ) * hx 
                     + gx * ( t[1+2*2] - t[1+0*2] ) ) / ( gn * hn );
    dphidy[4+j*6] = -(      ( t[0+1*2] - t[0+0*2] ) * hx 
                     + gx * ( t[0+2*2] - t[0+0*2] ) ) / ( gn * hn );
//
//  Basis function 6: PHI(X,Y) = G(1,2) * H(3,2) / normalization.
//
    gx = ( p[0+j*2] - t[0+1*2] ) * ( t[1+0*2] - t[1+1*2] ) 
       - ( t[0+0*2] - t[0+1*2] ) * ( p[1+j*2] - t[1+1*2] );

    gn = ( t[0+5*2] - t[0+1*2] ) * ( t[1+0*2] - t[1+1*2] ) 
       - ( t[0+0*2] - t[0+1*2] ) * ( t[1+5*2] - t[1+1*2] );

    hx = ( p[0+j*2] - t[0+1*2] ) * ( t[1+2*2] - t[1+1*2] ) 
       - ( t[0+2*2] - t[0+1*2] ) * ( p[1+j*2] - t[1+1*2] );

    hn = ( t[0+5*2] - t[0+1*2] ) * ( t[1+2*2] - t[1+1*2] ) 
       - ( t[0+2*2] - t[0+1*2] ) * ( t[1+5*2] - t[1+1*2] );

    phi[5+j*6] = ( gx * hx ) / ( gn * hn );
    dphidx[5+j*6] =  (      ( t[1+0*2] - t[1+1*2] ) * hx 
                     + gx * ( t[1+2*2] - t[1+1*2] ) ) / ( gn * hn );
    dphidy[5+j*6] = -(      ( t[0+0*2] - t[0+1*2] ) * hx 
                     + gx * ( t[0+2*2] - t[0+1*2] ) ) / ( gn * hn );
  }

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

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_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

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

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;
}
//********************************************************************

unsigned long get_seed ( void )

//********************************************************************
//
//  Purpose:
//
//    GET_SEED returns a random seed for the random number generator.
//
//  Modified:
//
//    17 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, unsigned long GET_SEED, a random seed value.
//
{
# define UNSIGNED_LONG_MAX 4294967295UL

  time_t clock;
  int i;
  int hours;
  int minutes;
  int seconds;
  struct tm *lt;
  static unsigned long seed = 0;
  time_t tloc;
//
//  If the internal seed is 0, generate a value based on the time.
//
  if ( seed == 0 )
  {
    clock = time ( &tloc );
    lt = localtime ( &clock );
//
//  Extract HOURS.
//
    hours = lt->tm_hour;
//
//  In case of 24 hour clocks, shift so that HOURS is between 1 and 12.
//
    if ( 12 < hours )
    {
      hours = hours - 12;
    }
//
//  Move HOURS to 0, 1, ..., 11
//
    hours = hours - 1;

    minutes = lt->tm_min;

    seconds = lt->tm_sec;

    seed = seconds + 60 * ( minutes + 60 * hours );
//
//  We want values in [1,43200], not [0,43199].
//
    seed = seed + 1;
//
//  Remap SEED from [1,43200] to [1,UNSIGNED_LONG_MAX].
//
    seed = ( unsigned long ) 
      ( ( ( double ) seed )
      * ( ( double ) UNSIGNED_LONG_MAX ) / ( 60.0 * 60.0 * 12.0 ) );
  }
//
//  Never use a seed of 0.
//
  if ( seed == 0 )
  {
    seed = 1;
  }

  return seed;

# undef UNSIGNED_LONG_MAX
}
//****************************************************************************80

void grid_sample ( int node_num, double node_xy[], int triangle_order, 
  int triangle_num, int triangle_node[], int triangle_neighbor[], 
  double coef_node[], int x_number, int y_number, double x_vec[], 
  double y_vec[], double u_grid[] )

//****************************************************************************80
//
//  Purpose:
//
//    GRID_SAMPLE samples a (scalar) FE function on a T3 or T6 triangulation.
//
//  Discussion:
//
//    Note that the values of U returned are true values of the underlying
//    finite element function.  They are NOT produced by constructing some
//    other function that interpolates the data at the finite element nodes
//    (something which MATLAB's griddata function can easily do.)  Instead, 
//    each sampling node is located within one of the associated finite
//    element triangles, and the finite element function is developed and 
//    evaluated there.  
//
//    MATLAB's scattered data interpolation is wonderful, but it cannot
//    be guaranteed to reproduce the finite element function corresponding
//    to nodal data.  This routine can.
// 
//    So if you are using finite elements, then using THIS routine
//    (but not MATLAB's griddata function), what you see is what you have//
//
//  Modified:
//
//    13 October 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the nodes.
//
//    Input, int TRIANGLE_ORDER, the order of the triangles, either
//    3 or 6.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[TRIANGLE_ORDER*TRIANGLE_NUM], the
//    nodes that make up each triangle.
//
//    Input, int TRIANGLE_NEIGHBOR[3*TRIANGLE_NUM], the index of the
//    neighboring triangle on each side, or -1 if no neighbor there.
//
//    Input, double COEF_NODE[NODE_NUM], the finite element 
//    coefficient value at each node.
//
//    Input, int X_NUMBER, Y_NUMBER, the number of sampling points in the 
//    X and Y directions.
//
//    Output, double X_VEC[X_NUMBER], Y_VEC[Y_NUMBER],
//    U_GRID[X_NUMBER*Y_NUMBER], the coordinates of the X and Y sampling
//    points, and the value of the finite element function U at those
//    sampling points. 
//
{
  double *b;
  double *dbdx;
  double *dbdy;
  int edge;
  int i;
  double inc;
  int j;
  int node;
  int order;
  double p_xy[2];
  int t;
  int *t_node;
  double *t_xy;
  double x_frac;
  double x_hi;
  double x_lo;
  double y_frac;
  double y_hi;
  double y_lo;

  b = new double[triangle_order];
  dbdx = new double[triangle_order];
  dbdy = new double[triangle_order];
  t_node = new int[triangle_order];
  t_xy = new double[2*triangle_order];
//
//  Generate the X and Y coordinates of the grid.
//
  x_lo =  r8_huge ( );
  x_hi = -r8_huge ( );
  y_lo =  r8_huge ( );
  y_hi = -r8_huge ( );

  for ( node = 0; node < node_num; node++ )
  {
    x_lo = r8_min ( x_lo, node_xy[0+node*2] );
    x_hi = r8_max ( x_hi, node_xy[0+node*2] );
    y_lo = r8_min ( y_lo, node_xy[1+node*2] );
    y_hi = r8_max ( y_hi, node_xy[1+node*2] );
  }

  if ( x_number <= 1 && y_number <= 1 )
  {
    x_vec[0] = 0.5 * ( x_lo + x_hi );
    y_vec[0] = 0.5 * ( y_lo + y_hi );
  }
  else if ( y_number < x_number )
  {
    inc = ( x_hi - x_lo ) / ( double ) ( x_number - 1 );

    y_frac = 0.5 * ( ( y_hi - y_lo ) - ( double ) ( y_number - 1 ) * inc );

    for ( i = 0; i < x_number; i++ )
    {
      x_vec[i] = ( ( double ) ( x_number - i - 1 ) * x_lo   
                 + ( double ) (            i     ) * x_hi ) 
                 / ( double ) ( x_number     - 1 );
    }

    for ( j = 0; j < y_number; j++ )
    {
      y_vec[j] = ( ( double ) ( y_number - j - 1 ) * ( y_lo + y_frac )   
                 + ( double ) (            j     ) * ( y_hi - y_frac ) ) 
                 / ( double ) ( y_number     - 1 );
    }
  }
  else
  {
    inc = ( y_hi - y_lo ) / ( double ) ( y_number - 1 );

    x_frac = 0.5 * ( ( x_hi - x_lo ) - ( double ) ( x_number - 1 ) * inc );

    for ( i = 0; i < x_number; i++ )
    {
      x_vec[i] = ( ( double ) ( x_number - i - 1 ) * ( x_lo + x_frac )   
                 + ( double ) (            i     ) * ( x_hi - x_frac ) ) 
                 / ( double ) ( x_number     - 1 );
    }

    for ( j = 0; j < y_number; j++ )
    {
      y_vec[j] = ( ( double ) ( y_number - j - 1 ) * y_lo   
                 + ( double ) (            j     ) * y_hi ) 
                 / ( double ) ( y_number     - 1 );
    }

  }
//
//  Generate points on the uniform grid, find them in the triangulation,
//  and evaluate.
//
  for ( j = 0; j < y_number; j++ )
  {
    p_xy[1] = y_vec[j];

    for ( i = 0; i < x_number; i++ )
    {
      p_xy[0] = x_vec[i];

      triangulation_search ( node_num, node_xy, triangle_order, 
        triangle_num, triangle_node, triangle_neighbor, p_xy, &t, &edge );
//
//  Evaluate U by getting element_node nodes, coefficients, 
//  basis function values.
//
//  NOTE:
//  If EDGE is negative, then point P_XY is actually outside the triangulation.
//  For now, we simply evaluate U as though the basis function in the triangle
//  extended on out to the point.  But this is probably unwise in most cases.
//  The value should probably be set to a flag value, or truncated to the
//  value at the nearest point on the triangle to P...
//
//  Also note that in the following loop, we assume that TRIANGLE_NODE
//  is 1-based, and that for convenience we can get away with making
//  T_NODE 0-based.
//
      for ( order = 0; order < triangle_order; order++ )
      {
        t_node[order] = triangle_node[order+(t-1)*triangle_order] - 1;
      }

      for ( order = 0; order < triangle_order; order++ )
      {
        t_xy[0+order*2] = node_xy[0+t_node[order]*2];
        t_xy[1+order*2] = node_xy[1+t_node[order]*2];
      }

      if ( triangle_order == 3 )
      {
        basis_mn_t3 ( t_xy, 1, p_xy, b, dbdx, dbdy );
      }
      else if ( triangle_order == 6 )
      {
        basis_mn_t6 ( t_xy, 1, p_xy, b, dbdx, dbdy );
      }

      u_grid[i+j*x_number] = 0.0;
      for ( order = 0; order < triangle_order; order++ )
      {
        u_grid[i+j*x_number] = u_grid[i+j*x_number] +
          coef_node[t_node[order]] * b[order];
      }
    }

  }
  delete [] b;
  delete [] dbdx;
  delete [] dbdy;
  delete [] t_node;
  delete [] t_xy;

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

void grid_sample_size ( int node_num, double node_xy[], int number, 
  int *x_number, int *y_number )

//****************************************************************************80
//
//  Purpose:
//
//    GRID_SAMPLE_SIZE determines sizes for a uniform grid.
//
//  Discussion:
//
//    We are given a set of node coordinates.  We are going to want
//    to sample points in the rectangle defined by the range of the
//    nodes.  We want to have NUMBER equally spaced points in the
//    widest of the two coordinate directions.
//
//    This routine determines X_NUMBER and Y_NUMBER, the number of
//    nodes to use in the X and Y directions, so that this requirement
//    is met.  Aside from special cases, one of X_NUMBER and Y_NUMBER 
//    will be equal to NUMBER.
//
//  Modified:
//
//    12 October 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the nodes.
//
//    Input, int NUMBER, the number of sampling points desired in
//    the widest direction.  NUMBER should be at least 1.
//
//    Output, int *NUMBER_X, *NUMBER_Y, the number of sampling points in the 
//    X and Y directions.
//
{
  double inc;
  int node;
  double x_hi;
  double x_lo;
  double y_hi;
  double y_lo;
//
//  A special case.
//
  if ( number <= 1 )
  {
    *x_number = 1;
    *y_number = 1;
  }
//
//  Determine the coordinate ranges for the nodes.
//
  else
  {
    x_lo =  r8_huge ( );
    x_hi = -r8_huge ( );
    y_lo =  r8_huge ( );
    y_hi = -r8_huge ( );

    for ( node = 0; node < node_num; node++ )
    {
      x_lo = r8_min ( x_lo, node_xy[0+node*2] );
      x_hi = r8_max ( x_hi, node_xy[0+node*2] );
      y_lo = r8_min ( y_lo, node_xy[1+node*2] );
      y_hi = r8_max ( y_hi, node_xy[1+node*2] );
    }
//
//  We want NUMBER nodes in the widest direction.
//
    if ( y_hi - y_lo < x_hi - x_lo )
    {
      *x_number = number;

      inc = ( x_hi - x_lo ) / ( double ) ( *x_number - 1 );

      *y_number = 1 + r8_nint ( ( y_hi - y_lo ) / inc );
    }
    else
    {
      *y_number = number;
 
      inc = ( y_hi - y_lo ) / ( double ) ( *y_number - 1 );
 
      *x_number = 1 + r8_nint ( ( x_hi - x_lo ) / inc );
    }
  }
  
  return;
}
//****************************************************************************80

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two integers.
//
//  Modified:
//
//    05 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MAX, the larger of I1 and I2.
//
{
  if ( i2 < i1 ) 
  {
    return i1;
  }
  else 
  {
    return i2;
  }

}
//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MIN returns the smaller of two integers.
//
//  Modified:
//
//    05 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MIN, the smaller of I1 and I2.
//
{
  if ( i1 < i2 ) 
  {
    return i1;
  }
  else 
  {
    return i2;
  }

}
//****************************************************************************80

int i4_uniform ( int a, int b, int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    I4_UNIFORM returns a scaled pseudorandom I4.
//
//  Discussion:
//
//    The pseudorandom number should be uniformly distributed
//    between A and B.
//
//  Modified:
//
//    12 November 2006
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley Interscience, page 95, 1998.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, pages 362-376, 1986.
//
//    Peter Lewis, Allen Goodman, James Miller
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, pages 136-143, 1969.
//
//  Parameters:
//
//    Input, int A, B, the limits of the interval.
//
//    Input/output, int *SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, int I4_UNIFORM, a number between A and B.
//
{
  int k;
  float r;
  int value;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "I4_UNIFORM - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  k = *seed / 127773;

  *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

  if ( *seed < 0 )
  {
    *seed = *seed + 2147483647;
  }

  r = ( float ) ( *seed ) * 4.656612875E-10;
//
//  Scale R to lie between A-0.5 and B+0.5.
//
  r = ( 1.0 - r ) * ( ( float ) ( i4_min ( a, b ) ) - 0.5 ) 
    +         r   * ( ( float ) ( i4_max ( a, b ) ) + 0.5 );
//
//  Use rounding to convert R to an integer between A and B.
//
  value = r4_nint ( r );

  value = i4_max ( value, i4_min ( a, b ) );
  value = i4_min ( value, i4_max ( a, b ) );

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

int i4row_compare ( int m, int n, int a[], int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4ROW_COMPARE compares two rows of a integer array.
//
//  Discussion:
//
//    The two dimensional information is stored in a one dimensional array,
//    by columns.  The entry A(I,J) is stored in A[I+J*M].
//
//    The input arguments I and J are row indices.  They DO NOT use the
//    C convention of starting at 0, but rather start at 1.
//
//  Example:
//
//    Input:
//
//      M = 3, N = 4, I = 2, J = 3
//
//      A = (
//        1  2  3  4
//        5  6  7  8
//        9 10 11 12 )
//
//    Output:
//
//      I4ROW_COMPARE = -1
//
//  Modified:
//
//    13 October 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input, int  A[M*N], the array of data.
//
//    Input, int I, J, the rows to be compared.
//    I and J must be between 1 and M.
//
//    Output, int I4ROW_COMPARE, the results of the comparison:
//    -1, row I < row J,
//     0, row I = row J,
//    +1, row J < row I.
//
{
  int k;
//
//  Check that I and J are legal.
//
  if ( i < 1 )
  {
    cout << "\n";
    cout << "I4ROW_COMPARE - Fatal error!\n";
    cout << "  Row index I is less than 1.\n";
    cout << "  I = " << i << "\n";
    exit ( 1 );
  }
  else if ( m < i )
  {
    cout << "\n";
    cout << "I4ROW_COMPARE - Fatal error!\n";
    cout << "  Row index I is out of bounds.\n";
    cout << "  I = " << i << "\n";
    cout << "  Maximum legal value is M = " << m << "\n";
    exit ( 1 );
  }

  if ( j < 1 )
  {
    cout << "\n";
    cout << "I4ROW_COMPARE - Fatal error!\n";
    cout << "  Row index J is less than 1.\n";
    cout << "  J = " << j << "\n";
    exit ( 1 );
  }
  else if ( m < j )
  {
    cout << "\n";
    cout << "I4ROW_COMPARE - Fatal error!\n";
    cout << "  Row index J is out of bounds.\n";
    cout << "  J = " << j << "\n";
    cout << "  Maximum legal value is M = " << m << "\n";
    exit ( 1 );
  }

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

  for ( k = 0; k < n; k++ )
  {
    if ( a[(i-1)+k*m] < a[(j-1)+k*m] )
    {
      return -1;
    }
    else if ( a[(j-1)+k*m] < a[(i-1)+k*m] )
    {
      return +1;
    }
  }

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

void i4row_sort_a ( int m, int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4ROW_SORT_A ascending sorts the rows of an I4ROW.
//
//  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.
//
//  Example:
//
//    Input:
//
//      M = 5, N = 3
//
//      A =
//        3  2  1
//        2  4  3
//        3  1  8
//        2  4  2
//        1  9  9
//
//    Output:
//
//      A =
//        1  9  9
//        2  4  2
//        2  4  3
//        3  1  8
//        3  2  1
//
//  Modified:
//
//    17 September 2003
//
//  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 M rows of N-vectors.
//    On output, the rows 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 ( m, &indx, &i, &j, isgn );
//
//  Interchange the I and J objects.
//
    if ( 0 < indx )
    {
      i4row_swap ( m, n, a, i, j );
    }
//
//  Compare the I and J objects.
//
    else if ( indx < 0 )
    {
      isgn = i4row_compare ( m, n, a, i, j );
    }
    else if ( indx == 0 )
    {
      break;
    }

  }

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

void i4row_swap ( int m, int n, int a[], int irow1, int irow2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4ROW_SWAP swaps two rows of an I4ROW.
//
//  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:
//
//    16 September 2003
//
//  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 IROW1, IROW2, the two rows to swap.
//    These indices should be between 1 and M.
//
{
# define OFFSET 1

  int j;
  int t;
//
//  Check.
//
  if ( irow1 < 0+OFFSET || m-1+OFFSET < irow1 )
  {
    cout << "\n";
    cout << "I4ROW_SWAP - Fatal error!\n";
    cout << "  IROW1 is out of range.\n";
    exit ( 1 );
  }

  if ( irow2 < 0+OFFSET || m-1+OFFSET < irow2 )
  {
    cout << "\n";
    cout << "I4ROW_SWAP - Fatal error!\n";
    cout << "  IROW2 is out of range.\n";
    exit ( 1 );
  }

  if ( irow1 == irow2 )
  {
    return;
  }
  for ( j = 0; j < n; j++ )
  {
    t                   = a[irow1-OFFSET+j*m];
    a[irow1-OFFSET+j*m] = a[irow2-OFFSET+j*m];
    a[irow2-OFFSET+j*m] = t;
  }

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

float r4_abs ( float x )

//*********************************************************************
//
//  Purpose:
//
//    R4_ABS returns the absolute value of an R4.
//
//  Modified:
//
//    01 December 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, float X, the quantity whose absolute value is desired.
//
//    Output, float R4_ABS, the absolute value of X.
//
{
  float value;

  if ( 0.0 <= x )
  {
    value = x;
  } 
  else
  {
    value = -x;
  }
  return value;
}
//****************************************************************************80

int r4_nint ( float x )

//****************************************************************************80
//
//  Purpose:
//
//    R4_NINT returns the nearest integer to an R4.
//
//  Examples:
//
//        X         R4_NINT
//
//      1.3         1
//      1.4         1
//      1.5         1 or 2
//      1.6         2
//      0.0         0
//     -0.7        -1
//     -1.1        -1
//     -1.6        -2
//
//  Modified:
//
//    14 November 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, float X, the value.
//
//    Output, int R4_NINT, the nearest integer to X.
//
{
  int value;

  if ( x < 0.0 )
  {
    value = - ( int ) ( r4_abs ( x ) + 0.5 );
  }
  else
  {
    value =   ( int ) ( r4_abs ( x ) + 0.5 );
  }

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

float r4_uniform_01 ( int *seed )

//****************************************************************************80
//
//  Purpose:
//
//    R4_UNIFORM_01 returns a unit pseudorandom R4.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = 16807 * seed mod ( 2**31 - 1 )
//      r4_uniform_01 = seed / ( 2**31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//    If the initial seed is 12345, then the first three computations are
//
//      Input     Output      R4_UNIFORM_01
//      SEED      SEED
//
//         12345   207482415  0.096616
//     207482415  1790989824  0.833995
//    1790989824  2035175616  0.947702
//
//  Modified:
//
//    16 November 2004
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation
//    edited by Jerry Banks,
//    Wiley Interscience, page 95, 1998.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, pages 362-376, 1986.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, pages 136-143, 1969.
//
//  Parameters:
//
//    Input/output, int *SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has been updated.
//
//    Output, float R4_UNIFORM_01, a new pseudorandom variate, strictly between
//    0 and 1.
//
{
  int k;
  float r;

  if ( *seed == 0 )
  {
    cerr << "\n";
    cerr << "R4_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  k = *seed / 127773;

  *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

  if ( *seed < 0 )
  {
    *seed = *seed + 2147483647;
  }
//
//  Although SEED can be represented exactly as a 32 bit integer,
//  it generally cannot be represented exactly as a 32 bit real number!
//
  r = ( float ) ( *seed ) * 4.656612875E-10;

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

double r8_huge ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_HUGE returns a "huge" R8.
//
//  Discussion:
//
//    HUGE_VAL is the largest representable legal double precision number, 
//    and is usually defined in math.h, or sometimes in stdlib.h.
//
//  Modified:
//
//    31 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_HUGE, a "huge" R8 value.
//
{
  return HUGE_VAL;
}
//*********************************************************************

double r8_max ( double x, double y )

//*********************************************************************
//
//  Purpose:
//
//    R8_MAX returns the maximum of two double precision values.
//
//  Modified:
//
//    18 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MAX, the maximum of X and Y.
//
{
  if ( y < x )
  {
    return x;
  } 
  else
  {
    return y;
  }
}
//*********************************************************************

double r8_min ( double x, double y )

//*********************************************************************
//
//  Purpose:
//
//    R8_MIN returns the minimum of two double precision values.
//
//  Modified:
//
//    31 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MIN, the minimum of X and Y.
//
{
  if ( y < x )
  {
    return y;
  } 
  else
  {
    return x;
  }
}
//****************************************************************************80

int r8_nint ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    R8_NINT returns the nearest integer to an R8.
//
//  Examples:
//
//        X         Value
//
//      1.3         1
//      1.4         1
//      1.5         1 or 2
//      1.6         2
//      0.0         0
//     -0.7        -1
//     -1.1        -1
//     -1.6        -2
//
//  Modified:
//
//    26 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, the value.
//
//    Output, int R8_NINT, the nearest integer to X.
//
{
  int s;
  int value;

  if ( x < 0.0 )
  {
    s = -1;
  }
  else
  {
    s = 1;
  }
  value = s * ( int ) ( fabs ( x ) + 0.5 );

  return value;
}
//****************************************************************************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 integer value 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 integer vector 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:
//
//    08 February 2005
//
//  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;
}
//********************************************************************

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

//********************************************************************
//
//  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;
}
//**********************************************************************

void timestamp ( void )

//**********************************************************************
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    02 October 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

void triangulation_order3_neighbor_triangles ( int triangle_num,
  int triangle_node[], int triangle_neighbor[] )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors.
//
//  Discussion:
//
//    A triangulation of a set of nodes can be completely described by
//    the coordinates of the nodes, and the list of nodes that make up
//    each triangle.  However, in some cases, it is necessary to know
//    triangle adjacency information, that is, which triangle, if any,
//    is adjacent to a given triangle on a particular side.
//
//    This routine creates a data structure recording this information.
//
//    The primary amount of work occurs in sorting a list of 3 * TRIANGLE_NUM
//    data items.
//
//  Example:
//
//    The input information from TRIANGLE_NODE:
//
//    Triangle   Nodes
//    --------   ---------------
//     1         3      4      1
//     2         3      1      2
//     3         3      2      8
//     4         2      1      5
//     5         8      2     13
//     6         8     13      9
//     7         3      8      9
//     8        13      2      5
//     9         9     13      7
//    10         7     13      5
//    11         6      7      5
//    12         9      7      6
//    13        10      9      6
//    14         6      5     12
//    15        11      6     12
//    16        10      6     11
//
//    The output information in TRIANGLE_NEIGHBOR:
//
//    Triangle  Neighboring Triangles
//    --------  ---------------------
//
//     1        -1     -1      2
//     2         1      4      3
//     3         2      5      7
//     4         2     -1      8
//     5         3      8      6
//     6         5      9      7
//     7         3      6     -1
//     8         5      4     10
//     9         6     10     12
//    10         9      8     11
//    11        12     10     14
//    12         9     11     13
//    13        -1     12     16
//    14        11     -1     15
//    15        16     14     -1
//    16        13     15     -1
//
//  Modified:
//
//    17 October 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[3*TRIANGLE_NUM], the nodes that make up each triangle.
//
//    Output, int TRIANGLE_NEIGHBOR[3*TRIANGLE_NUM], the three triangles that are direct
//    neighbors of a given triangle.  TRIANGLE_NEIGHBOR(1,I) is the index of the triangle
//    which touches side 1, defined by nodes 2 and 3, and so on.  TRIANGLE_NEIGHBOR(1,I)
//    is negative if there is no neighbor on that side.  In this case, that
//    side of the triangle lies on the boundary of the triangulation.
//
{
  int i;
  int irow;
  int j;
  int k;
  int *row;
  int side1;
  int side2;
  int tri;
  int tri1;
  int tri2;

  row = new int[3*triangle_num*4];
//
//  Step 1.
//  From the list of nodes for triangle T, of the form: (I,J,K)
//  construct the three neighbor relations:
//
//    (I,J,1,T) or (J,I,1,T),
//    (J,K,2,T) or (K,J,2,T),
//    (K,I,3,T) or (I,K,3,T)
//
//  where we choose (I,J,1,T) if I < J, or else (J,I,1,T)
//
  for ( tri = 0; tri < triangle_num; tri++ )
  {
    i = triangle_node[0+tri*3];
    j = triangle_node[1+tri*3];
    k = triangle_node[2+tri*3];

    if ( i < j )
    {
      row[3*tri+0*3*triangle_num] = i;
      row[3*tri+1*3*triangle_num] = j;
      row[3*tri+2*3*triangle_num] = 1;
      row[3*tri+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+0*3*triangle_num] = j;
      row[3*tri+1*3*triangle_num] = i;
      row[3*tri+2*3*triangle_num] = 1;
      row[3*tri+3*3*triangle_num] = tri + 1;
    }

    if ( j < k )
    {
      row[3*tri+1+0*3*triangle_num] = j;
      row[3*tri+1+1*3*triangle_num] = k;
      row[3*tri+1+2*3*triangle_num] = 2;
      row[3*tri+1+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+1+0*3*triangle_num] = k;
      row[3*tri+1+1*3*triangle_num] = j;
      row[3*tri+1+2*3*triangle_num] = 2;
      row[3*tri+1+3*3*triangle_num] = tri + 1;
    }

    if ( k < i )
    {
      row[3*tri+2+0*3*triangle_num] = k;
      row[3*tri+2+1*3*triangle_num] = i;
      row[3*tri+2+2*3*triangle_num] = 3;
      row[3*tri+2+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+2+0*3*triangle_num] = i;
      row[3*tri+2+1*3*triangle_num] = k;
      row[3*tri+2+2*3*triangle_num] = 3;
      row[3*tri+2+3*3*triangle_num] = tri + 1;
    }
  }
//
//  Step 2. Perform an ascending dictionary sort on the neighbor relations.
//  We only intend to sort on columns 1 and 2; the routine we call here
//  sorts on columns 1 through 4 but that won't hurt us.
//
//  What we need is to find cases where two triangles share an edge.
//  Say they share an edge defined by the nodes I and J.  Then there are
//  two rows of ROW that start out ( I, J, ?, ? ).  By sorting ROW,
//  we make sure that these two rows occur consecutively.  That will
//  make it easy to notice that the triangles are neighbors.
//
  i4row_sort_a ( 3*triangle_num, 4, row );
//
//  Step 3. Neighboring triangles show up as consecutive rows with
//  identical first two entries.  Whenever you spot this happening,
//  make the appropriate entries in TRIANGLE_NEIGHBOR.
//
  for ( j = 0; j < triangle_num; j++ )
  {
    for ( i = 0; i < 3; i++ )
    {
      triangle_neighbor[i+j*3] = -1;
    }
  }

  irow = 1;

  for ( ; ; )
  {
    if ( 3 * triangle_num <= irow )
    {
      break;
    }

    if ( row[irow-1+0*3*triangle_num] != row[irow+0*3*triangle_num] || 
         row[irow-1+1*3*triangle_num] != row[irow+1*3*triangle_num] )
    {
      irow = irow + 1;
      continue;
    }

    side1 = row[irow-1+2*3*triangle_num];
    tri1 =  row[irow-1+3*3*triangle_num];
    side2 = row[irow  +2*3*triangle_num];
    tri2 =  row[irow  +3*3*triangle_num];

    triangle_neighbor[side1-1+(tri1-1)*3] = tri2;
    triangle_neighbor[side2-1+(tri2-1)*3] = tri1;

    irow = irow + 2;
  }
 
  delete [] row;

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

void triangulation_order6_neighbor_triangles ( int triangle_num,
  int triangle_node[], int triangle_neighbor[] )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES determines triangle neighbors.
//
//  Discussion:
//
//    A triangulation of a set of nodes can be completely described by
//    the coordinates of the nodes, and the list of nodes that make up
//    each triangle.  However, in some cases, it is necessary to know
//    triangle adjacency information, that is, which triangle, if any,
//    is adjacent to a given triangle on a particular side.
//
//    This routine creates a data structure recording this information.
//
//    The primary amount of work occurs in sorting a list of 3 * TRIANGLE_NUM
//    data items.
//
//  Modified:
//
//    13 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[6*TRIANGLE_NUM], the nodes that make up each triangle.
//
//    Output, int TRIANGLE_NEIGHBOR[3*TRIANGLE_NUM], the three triangles that are direct
//    neighbors of a given triangle.  TRIANGLE_NEIGHBOR(1,I) is the index of the triangle
//    which touches side 1, defined by nodes 2 and 3, and so on.  TRIANGLE_NEIGHBOR(1,I)
//    is negative if there is no neighbor on that side.  In this case, that
//    side of the triangle lies on the boundary of the triangulation.
//
{
  int i;
  int irow;
  int j;
  int k;
  int *row;
  int side1;
  int side2;
  int tri;
  int tri1;
  int tri2;

  row = new int[3*triangle_num*4];
//
//  Step 1.
//  From the list of nodes for triangle T, of the form: (I,J,K)
//  construct the three neighbor relations:
//
//    (I,J,1,T) or (J,I,1,T),
//    (J,K,2,T) or (K,J,2,T),
//    (K,I,3,T) or (I,K,3,T)
//
//  where we choose (I,J,1,T) if I < J, or else (J,I,1,T)
//
  for ( tri = 0; tri < triangle_num; tri++ )
  {
    i = triangle_node[0+tri*6];
    j = triangle_node[1+tri*6];
    k = triangle_node[2+tri*6];

    if ( i < j )
    {
      row[3*tri+0*3*triangle_num] = i;
      row[3*tri+1*3*triangle_num] = j;
      row[3*tri+2*3*triangle_num] = 1;
      row[3*tri+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+0*3*triangle_num] = j;
      row[3*tri+1*3*triangle_num] = i;
      row[3*tri+2*3*triangle_num] = 1;
      row[3*tri+3*3*triangle_num] = tri + 1;
    }

    if ( j < k )
    {
      row[3*tri+1+0*3*triangle_num] = j;
      row[3*tri+1+1*3*triangle_num] = k;
      row[3*tri+1+2*3*triangle_num] = 2;
      row[3*tri+1+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+1+0*3*triangle_num] = k;
      row[3*tri+1+1*3*triangle_num] = j;
      row[3*tri+1+2*3*triangle_num] = 2;
      row[3*tri+1+3*3*triangle_num] = tri + 1;
    }

    if ( k < i )
    {
      row[3*tri+2+0*3*triangle_num] = k;
      row[3*tri+2+1*3*triangle_num] = i;
      row[3*tri+2+2*3*triangle_num] = 3;
      row[3*tri+2+3*3*triangle_num] = tri + 1;
    }
    else
    {
      row[3*tri+2+0*3*triangle_num] = i;
      row[3*tri+2+1*3*triangle_num] = k;
      row[3*tri+2+2*3*triangle_num] = 3;
      row[3*tri+2+3*3*triangle_num] = tri + 1;
    }
  }
//
//  Step 2. Perform an ascending dictionary sort on the neighbor relations.
//  We only intend to sort on columns 1 and 2; the routine we call here
//  sorts on columns 1 through 4 but that won't hurt us.
//
//  What we need is to find cases where two triangles share an edge.
//  Say they share an edge defined by the nodes I and J.  Then there are
//  two rows of ROW that start out ( I, J, ?, ? ).  By sorting ROW,
//  we make sure that these two rows occur consecutively.  That will
//  make it easy to notice that the triangles are neighbors.
//
  i4row_sort_a ( 3*triangle_num, 4, row );
//
//  Step 3. Neighboring triangles show up as consecutive rows with
//  identical first two entries.  Whenever you spot this happening,
//  make the appropriate entries in TRIANGLE_NEIGHBOR.
//
  for ( j = 0; j < triangle_num; j++ )
  {
    for ( i = 0; i < 3; i++ )
    {
      triangle_neighbor[i+j*3] = -1;
    }
  }

  irow = 1;

  for ( ; ; )
  {
    if ( 3 * triangle_num <= irow )
    {
      break;
    }

    if ( row[irow-1+0*3*triangle_num] != row[irow+0*3*triangle_num] || 
         row[irow-1+1*3*triangle_num] != row[irow+1*3*triangle_num] )
    {
      irow = irow + 1;
      continue;
    }

    side1 = row[irow-1+2*3*triangle_num];
    tri1 =  row[irow-1+3*3*triangle_num];
    side2 = row[irow  +2*3*triangle_num];
    tri2 =  row[irow  +3*3*triangle_num];

    triangle_neighbor[side1-1+(tri1-1)*3] = tri2;
    triangle_neighbor[side2-1+(tri2-1)*3] = tri1;

    irow = irow + 2;
  }
 
  delete [] row;

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

void triangulation_search ( int node_num, double node_xy[], int triangle_order,
  int triangle_num, int triangle_node[], int triangle_neighbor[], 
  double p[2], int *triangle, int *edge )

//****************************************************************************80
//
//  Purpose:
//
//    TRIANGULATION_SEARCH searches a triangulation for a point.
//
//  Discussion:
//
//    The algorithm "walks" from one triangle to its neighboring triangle,
//    and so on, until a triangle is found containing point P, or P is found 
//    to be outside the convex hull.  
//
//    The algorithm computes the barycentric coordinates of the point with 
//    respect to the current triangle.  If all three quantities are positive,
//    the point is contained in the triangle.  If the I-th coordinate is
//    negative, then (X,Y) lies on the far side of edge I, which is opposite
//    from vertex I.  This gives a hint as to where to search next.
//
//    For a Delaunay triangulation, the search is guaranteed to terminate.
//    For other triangulations, a cycle may occur.
//
//    Note the surprising fact that, even for a Delaunay triangulation of
//    a set of nodes, the nearest point to (X,Y) need not be one of the
//    vertices of the triangle containing (X,Y).  
//
//    The code can be called for triangulations of any order, but only
//    the first three nodes in each triangle are considered.  Thus, if
//    higher order triangles are used, and the extra nodes are intended
//    to give the triangle a polygonal shape, these will have no effect,
//    and the results obtained here might be misleading.
//
//  Modified:
//
//    27 September 2006
//
//  Author:
//
//    Barry Joe,
//    Department of Computing Science,
//    University of Alberta,
//    Edmonton, Alberta, Canada  T6G 2H1
//
//  Reference:
//
//    Barry Joe,
//    GEOMPACK - a software package for the generation of meshes
//    using geometric algorithms,
//    Advances in Engineering Software,
//    Volume 13, pages 325-331, 1991.
//
//  Parameters:
//
//    Input, int NODE_NUM, the number of nodes.
//
//    Input, double NODE_XY[2*NODE_NUM], the coordinates of the nodes.
//
//    Input, int TRIANGLE_ORDER, the order of the triangles.
//
//    Input, int TRIANGLE_NUM, the number of triangles in the triangulation.
//
//    Input, int TRIANGLE_NODE[TRIANGLE_ORDER*TRIANGLE_NUM], 
//    the nodes of each triangle.
//
//    Input, int TRIANGLE_NEIGHBOR[3*TRIANGLE_NUM], the triangle neighbor list.
//
//    Input, double P[2], the coordinates of a point.
//
//    Output, int *TRIANGLE, the index of the triangle where the search ended.
//    If a cycle occurred, then TRIANGLE = -1.
//
//    Output, int *EDGE, indicates the position of the point (X,Y) in
//    triangle TRIANGLE:
//    0, the interior or boundary of the triangle;
//    -1, outside the convex hull of the triangulation, past edge 1;
//    -2, outside the convex hull of the triangulation, past edge 2;
//    -3, outside the convex hull of the triangulation, past edge 3.
//
{
  int a;
  double alpha;
  int b;
  double beta;
  int c;
  int count;
  double det;
  double dxp;
  double dxa;
  double dxb;
  double dyp;
  double dya;
  double dyb;
  double gamma;
  int seed;

  count = 0;
  edge = 0;

  seed = get_seed ( );

  *triangle = i4_uniform ( 1, triangle_num, &seed );

  for ( ; ; )
  {
    count = count + 1;

    if ( triangle_num < count )
    {
      cout << "\n";
      cout << "TRIANGULATION_SEARCH - Fatal error!\n";
      cout << "  The algorithm seems to be cycling.\n";
      cout << "  Current triangle is " << *triangle << "\n";
      *triangle = -1;
      *edge = -1;
      return;
    }
//
//  Get the vertices of triangle TRIANGLE.
//
    a = triangle_node[0+(*triangle-1)*triangle_order] - 1;
    b = triangle_node[1+(*triangle-1)*triangle_order] - 1;
    c = triangle_node[2+(*triangle-1)*triangle_order] - 1;
//
//  Using vertex C as a base, compute the distances to vertices A and B,
//  and the point (X,Y).
//
    dxa = node_xy[0+a*2] - node_xy[0+c*2];
    dya = node_xy[1+a*2] - node_xy[1+c*2];

    dxb = node_xy[0+b*2] - node_xy[0+c*2];
    dyb = node_xy[1+b*2] - node_xy[1+c*2];

    dxp = p[0]           - node_xy[0+c*2];
    dyp = p[1]           - node_xy[1+c*2];

    det = dxa * dyb - dya * dxb;
//
//  Compute the barycentric coordinates of the point (X,Y) with respect
//  to this triangle.
//
    alpha = ( dxp * dyb - dyp * dxb ) / det;
    beta =  ( dxa * dyp - dya * dxp ) / det;
    gamma = 1.0 - alpha - beta;
//
//  If the barycentric coordinates are all positive, then the point
//  is inside the triangle and we're done.
//
    if ( 0.0 <= alpha &&
         0.0 <= beta  &&
         0.0 <= gamma )
    {
      break;
    }
//
//  At least one barycentric coordinate is negative.
//
//  If there is a negative barycentric coordinate for which there exists
//  an opposing triangle neighbor closer to the point, move to that triangle.
//
//  (Two coordinates could be negative, in which case we could go for the
//  most negative one, or the most negative one normalized by the actual
//  distance it represents).
//
    if ( alpha < 0.0 && 0 <= triangle_neighbor[1+(*triangle-1)*3] )
    {
      *triangle = triangle_neighbor[1+(*triangle-1)*3];
      continue;
    }
    else if ( beta < 0.0 && 0 <= triangle_neighbor[2+(*triangle-1)*3] )
    {
      *triangle = triangle_neighbor[2+(*triangle-1)*3];
      continue;
    }
    else if ( gamma < 0.0 && 0 <= triangle_neighbor[0+(*triangle-1)*3] )
    {
      *triangle = triangle_neighbor[0+(*triangle-1)*3];
      continue;
    }
//
//  All negative barycentric coordinates correspond to vertices opposite
//  sides on the convex hull.
//
//  Note the edge and exit.
//
    if ( alpha < 0.0 )
    {
      *edge = -2;
      break;
    }
    else if ( beta < 0.0 )
    {
      *edge = -3;
      break;
    }
    else if ( gamma < 0.0 )
    {
      *edge = -1;
      break;
    }
    else
    {
      cout << "\n";
      cout << "TRIANGULATION_SEARCH - Fatal error!\n";
      cout << "  The algorithm seems to have reached a dead end\n";
      cout << "  after " << count << " steps.\n";
      *triangle = -1;
      *edge = -1;
      return;
    }
  }

  return;
}