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

using namespace std;

int main ( int argc, char *argv[] );
double alpha_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] );
double arc_cosine ( double c );
double area_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] );
void bandwidth_mesh ( int element_order, int element_num, int element_node[],
  int *ml, int *mu, int *m );
char ch_cap ( char c );
bool ch_eqi ( char c1, char c2 );
int ch_to_digit ( char c );
double *dtable_data_read ( char *input_filename, int m, int n );
void dtable_header_read ( char *input_filename, int *m, int *n );
int file_column_count ( char *input_filename );
int file_row_count ( char *input_filename );
int i4_max ( int i1, int i2 );
int i4_min ( int i1, int i2 );
void i4mat_transpose_print ( int m, int n, int a[], char *title );
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 q_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] );
double r8_huge ( void );
double r8_max ( double x, double y );
double r8_min ( double x, double y );
void r8mat_transpose_print ( int m, int n, double a[], char *title );
void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo, 
  int ihi, int jhi, char *title );
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 timestamp ( void );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for TRIANGULATION_QUALITY.
//
//  Discussion:
//
//    TRIANGULATION_QUALITY determines quality measures for a triangulation.
//
//    The code has been modified to 'allow' 6-node triangulations.
//    However, no effort is made to actually process the midside nodes.
//    Only information from the vertices is used.
//
//    The three quality measures are:
//
//      ALPHA_MEASURE
//      AREA_MEASURE
//      Q_MEASURE
//
//    In each case, the ideal value of the quality measure is 1, and
//    the worst possible value is 0.
//
//    The program also prints out the geometric bandwidth, which is the
//    bandwidth of the adjacency matrix of the nodes.
//
//  Modified:
//
//    03 September 2006
//
//  Author:
//
//    John Burkardt
//
//  Local parameters:
//
//    Local, int DIM_NUM, the spatial dimension.
//
//    Local, int NODE_NUM, the number of nodes.
//
//    Local, double NODE_XY[DIM_NUM*NODE_NUM], the point set.
//
//    Local, int TRIANGLE_NODE[TRIANGLE_ORDER*TRIANGLE_NUM], 
//    lists the nodes that make up each triangle.
//
//    Local, int TRIANGLE_NUM, the number of triangles.
//
//    Local, int TRIANGLE_ORDER, the order of the triangles, either 3 or 6.
//
{ 
  int dim_num;
  int iarg;
  int iargc;
  char input_node_filename[256];
  char input_triangulation_filename[256];
  int m;
  int ml;
  int mu;
  int node_num;
  double *node_xy;
  int *triangle_node;
  int triangle_num;
  int triangle_order;
  double value;

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

  cout << "\n";
  cout << "TRIANGULATION_QUALITY:\n";
  cout << "  C++ version:\n";
  cout << "  Compute triangulation quality measures.\n";
  cout << "\n";
  cout << "  Compiled on " << __DATE__ << " at " << __TIME__ << ".\n";
//
//  Get the node file name.
//
  if ( argc <= 1 ) 
  {
    cout << "\n";
    cout << "TRIANGULATION_QUALITY:\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 triangulation file name.
//
  if ( argc <= 2 ) 
  {
    cout << "\n";
    cout << "TRIANGULATION_QUALITY:\n";
    cout << "  Please enter the name of the triangulation file.\n";

    cin.getline ( input_triangulation_filename, 
      sizeof ( input_triangulation_filename ) );
  }
  else 
  {
    strcpy ( input_triangulation_filename, argv[2] );
  } 
//
//  Read the node data.
//
  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, 5, 5, 
    "  5 by 5 portion of data read 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, 5, 5, "  5 by 5 portion of data read from file:" );

  value = alpha_measure ( node_num, node_xy, triangle_order, triangle_num, 
    triangle_node );
  cout << "  The minimum angle measure    Alpha = " << value << "\n";

  value = area_measure ( node_num, node_xy, triangle_order, triangle_num, 
    triangle_node );
  cout << "  The area ratio measure     A-Ratio = " << value << "\n";

  value = q_measure ( node_num, node_xy, triangle_order, triangle_num, 
    triangle_node );
  cout << "  The triangle uniformity measure  Q = " << value << "\n";

  bandwidth_mesh ( triangle_order, triangle_num, triangle_node, &ml, &mu, &m );

  cout << "  The geometric bandwidth          M = " << m << "\n";

  delete [] node_xy;
  delete [] triangle_node;

  cout << "\n";
  cout << "TRIANGULATION_QUALITY:\n";
  cout << "  Normal end of execution.\n";

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

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

double alpha_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] )

//****************************************************************************80*
//
//  Purpose:
//
//    ALPHA_MEASURE determines the triangulated pointset quality measure ALPHA.
//
//  Discusion:
//
//    The ALPHA measure evaluates the uniformity of the shapes of the triangles
//    defined by a triangulated pointset.
//
//    We compute the minimum angle among all the triangles in the triangulated
//    dataset and divide by the maximum possible value (which, in degrees,
//    is 60).  The best possible value is 1, and the worst 0.  A good
//    triangulation should have an ALPHA score close to 1.
//
//    The code has been modified to 'allow' 6-node triangulations.
//    However, no effort is made to actually process the midside nodes.
//    Only information from the vertices is used.
//
//  Modified:
//
//    07 November 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of points.
//
//    Input, real ( kind = 8 ) Z(2,N), the points.
//
//    Input, int TRIANGLE_ORDER, the order of the triangles.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE(TRIANGLE_ORDER,TRIANGLE_NUM),
//    the triangulation.
//
//    Output, double ALPHA_MEASURE, the ALPHA quality measure.
//
{
  double a_angle;
  int a_index;
  double a_x;
  double a_y;
  double ab_len;
  double alpha;
  double b_angle;
  int b_index;
  double b_x;
  double b_y;
  double bc_len;
  double c_angle;
  int c_index;
  double c_x;
  double c_y;
  double ca_len;
  double pi = 3.141592653589793;
  int triangle;
  double value;

  alpha = r8_huge ( );

  for ( triangle = 0; triangle < triangle_num; triangle++ )
  {
    a_index = triangle_node[0+triangle*3];
    b_index = triangle_node[1+triangle*3];
    c_index = triangle_node[2+triangle*3];

    a_x = z[0+(a_index-1)*2];
    a_y = z[1+(a_index-1)*2];
    b_x = z[0+(b_index-1)*2];
    b_y = z[1+(b_index-1)*2];
    c_x = z[0+(c_index-1)*2];
    c_y = z[1+(c_index-1)*2];

    ab_len = sqrt ( pow ( a_x - b_x, 2 ) + pow ( a_y - b_y, 2 ) );
    bc_len = sqrt ( pow ( b_x - c_x, 2 ) + pow ( b_y - c_y, 2 ) );
    ca_len = sqrt ( pow ( c_x - a_x, 2 ) + pow ( c_y - a_y, 2 ) );
//
//  Take care of a ridiculous special case.
//
    if ( ab_len == 0.0 && bc_len == 0.0 && ca_len == 0.0 )
    {
      a_angle = 2.0 * pi / 3.0;
      b_angle = 2.0 * pi / 3.0;
      c_angle = 2.0 * pi / 3.0;
    }
    else
    {
      if ( ca_len == 0.0 || ab_len == 0.0 )
      {
        a_angle = pi;
      }
      else
      {
        a_angle = arc_cosine ( 
          ( ca_len * ca_len + ab_len * ab_len - bc_len * bc_len ) 
          / ( 2.0 * ca_len * ab_len ) );
      }

      if ( ab_len == 0.0 || bc_len == 0.0 )
      {
        b_angle = pi;
      }
      else
      {
        b_angle = arc_cosine ( 
          ( ab_len * ab_len + bc_len * bc_len - ca_len * ca_len ) 
          / ( 2.0 * ab_len * bc_len ) );
      }

      if ( bc_len == 0.0 || ca_len == 0.0 )
      {
        c_angle = pi;
      }
      else
      {
        c_angle = arc_cosine ( 
          ( bc_len * bc_len + ca_len * ca_len - ab_len * ab_len ) 
          / ( 2.0 * bc_len * ca_len ) );
      }
    }
    alpha = r8_min ( alpha, a_angle );
    alpha = r8_min ( alpha, b_angle );
    alpha = r8_min ( alpha, c_angle );
  }
//
//  Normalize angles from [0,60] degrees into qualities in [0,1].
//
  value = alpha * 3.0 / pi;

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

double arc_cosine ( double c )

//****************************************************************************80
//
//  Purpose:
//
//    ARC_COSINE computes the arc cosine function, with argument truncation.
//
//  Discussion:
//
//    If you call your system ACOS routine with an input argument that is
//    outside the range [-1.0, 1.0 ], you may get an unpleasant surprise.
//    This routine truncates arguments outside the range.
//
//  Modified:
//
//    13 June 2002
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double C, the argument, the cosine of an angle.
//
//    Output, double ARC_COSINE, an angle whose cosine is C.
//
{
# define PI 3.141592653589793

  if ( c <= -1.0 )
  {
    return PI;
  } 
  else if ( 1.0 <= c )
  {
    return 0.0;
  }
  else
  {
    return acos ( c );
  }
# undef PI
}
//****************************************************************************80

double area_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] )

//****************************************************************************80
//
//  Purpose:
//
//    AREA_MEASURE determines the area ratio quality measure.
//
//  Discusion:
//
//    This measure computes the area of every triangle, and returns
//    the ratio of the minimum to the maximum triangle.  A value of
//    1 is "perfect", indicating that all triangles have the same area.
//    A value of 0 is the worst possible result.
//
//    The code has been modified to 'allow' 6-node triangulations.
//    However, no effort is made to actually process the midside nodes.
//    Only information from the vertices is used.
//
//  Modified:
//
//    07 November 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of points.
//
//    Input, double Z[2*N], the points.
//
//    Input, int TRIANGLE_ORDER, the order of the triangles.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[TRIANGLE_ORDER*TRIANGLE_NUM],
//    the triangulation.
//
//    Output, double AREA_MEASURE, the AREA quality measure.
//
{
  double area;
  double area_max;
  double area_min;
  int triangle;
  double value;
  double x1;
  double x2;
  double x3;
  double y1;
  double y2;
  double y3;

  area_max = 0.0;
  area_min = r8_huge ( );

  for ( triangle = 0; triangle < triangle_num; triangle++ )
  {
    x1 = z[0+(triangle_node[0+triangle*3]-1)*2];
    y1 = z[1+(triangle_node[0+triangle*3]-1)*2];
    x2 = z[0+(triangle_node[1+triangle*3]-1)*2];
    y2 = z[1+(triangle_node[1+triangle*3]-1)*2];
    x3 = z[0+(triangle_node[2+triangle*3]-1)*2];
    y3 = z[1+(triangle_node[2+triangle*3]-1)*2];

    area = 0.5 * fabs ( x1 * ( y2 - y3 ) 
                      + x2 * ( y3 - y1 ) 
                      + x3 * ( y1 - y2 ) );

    area_min = r8_min ( area_min, area );
    area_max = r8_max ( area_max, area );
  }

  value = area_min / area_max;

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

void bandwidth_mesh ( int element_order, int element_num, int element_node[],
  int *ml, int *mu, int *m )

//****************************************************************************80
//
//  Purpose:
//
//    BANDWIDTH_MESH determines the bandwidth of the coefficient matrix.
//
//  Discussion:
//
//    The quantity computed here is the "geometric" bandwidth determined
//    by the finite element mesh alone.
//
//    If a single finite element variable is associated with each node
//    of the mesh, and if the nodes and variables are numbered in the
//    same way, then the geometric bandwidth is the same as the bandwidth
//    of a typical finite element matrix.
//
//    The bandwidth M is defined in terms of the lower and upper bandwidths:
//
//      M = ML + 1 + MU
//
//    where 
//
//      ML = maximum distance from any diagonal entry to a nonzero
//      entry in the same row, but earlier column,
//
//      MU = maximum distance from any diagonal entry to a nonzero
//      entry in the same row, but later column.
//
//    Because the finite element node adjacency relationship is symmetric,
//    we are guaranteed that ML = MU.
//
//  Modified:
//
//    06 January 2006
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int ELEMENT_ORDER, the order of the elements.
//
//    Input, int ELEMENT_NUM, the number of elements.
//
//    Input,  ELEMENT_NODE[ELEMENT_ORDER*ELEMENT_NUM];
//    ELEMENT_NODE(I,J) is the global index of local node I in element J.
//
//    Output, int *ML, *MU, the lower and upper bandwidths of the matrix.
//
//    Output, int *M, the bandwidth of the matrix.
//
{
  int element;
  int global_i;
  int global_j;
  int local_i;
  int local_j;

  *ml = 0;
  *mu = 0;

  for ( element = 0; element < element_num; element++ )
  {
    for ( local_i = 0; local_i < element_order; local_i++ )
    {
      global_i = element_node[local_i+element*element_order];

      for ( local_j = 0; local_j < element_order; local_j++ )
      {
        global_j = element_node[local_j+element*element_order];

        *mu = i4_max ( *mu, global_j - global_i );
        *ml = i4_max ( *ml, global_i - global_j );
      }
    }
  }

  *m = *ml + 1 + *mu;

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

char ch_cap ( char c )

//****************************************************************************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 C, the character to capitalize.
//
//    Output, char CH_CAP, the capitalized character.
//
{
  if ( 97 <= c && c <= 122 ) 
  {
    c = c - 32;
  }   

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

bool ch_eqi ( char c1, char c2 )

//****************************************************************************80
//
//  Purpose:
//
//    CH_EQI is true if two characters are equal, disregarding case.
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char C1, C2, the characters to compare.
//
//    Output, bool CH_EQI, is true if the two characters are equal,
//    disregarding case.
//
{
  if ( 97 <= c1 && c1 <= 122 ) 
  {
    c1 = c1 - 32;
  } 
  if ( 97 <= c2 && c2 <= 122 ) 
  {
    c2 = c2 - 32;
  }     

  return ( c1 == c2 );
}
//****************************************************************************80

int ch_to_digit ( char c )

//****************************************************************************80
//
//  Purpose:
//
//    CH_TO_DIGIT returns the integer value of a base 10 digit.
//
//  Example:
//
//     C   DIGIT
//    ---  -----
//    '0'    0
//    '1'    1
//    ...  ...
//    '9'    9
//    ' '    0
//    'X'   -1
//
//  Modified:
//
//    13 June 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char C, the decimal digit, '0' through '9' or blank are legal.
//
//    Output, int CH_TO_DIGIT, the corresponding integer value.  If C was
//    'illegal', then DIGIT is -1.
//
{
  int digit;

  if ( '0' <= c && c <= '9' )
  {
    digit = c - '0';
  }
  else if ( c == ' ' )
  {
    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 real TABLE 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, 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";
    exit ( 1 );
  }

  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 real TABLE 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";
    exit ( 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.
//
//
{
  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 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.
//
//
{
  if ( i1 < i2 )
  {
    return i1;
  }
  else
  {
    return i2;
  }

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

void i4mat_transpose_print ( int m, int n, int a[], char *title )

//****************************************************************************80
//
//  Purpose:
//
//    I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
//
//  Modified:
//
//    31 January 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows in A.
//
//    Input, int N, the number of columns in A.
//
//    Input, int A[M*N], the M by N matrix.
//
//    Input, char *TITLE, a title to be printed.
//
{
  int i;
  int j;
  int jhi;
  int jlo;

  i4mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

  return;
}
//****************************************************************************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 q_measure ( int n, double z[], int triangle_order, int triangle_num,
  int triangle_node[] )

//****************************************************************************80
//
//  Purpose:
//
//    Q_MEASURE determines the triangulated pointset quality measure Q.
//
//  Discussion:
//
//    The Q measure evaluates the uniformity of the shapes of the triangles
//    defined by a triangulated pointset.
//
//    For a single triangle T, the value of Q(T) is defined as follows:
//
//      TAU_IN = radius of the inscribed circle,
//      TAU_OUT = radius of the circumscribed circle,
//
//      Q(T) = 2 * TAU_IN / TAU_OUT
//        = ( B + C - A ) * ( C + A - B ) * ( A + B - C ) / ( A * B * C )
//
//    where A, B and C are the lengths of the sides of the triangle T.
//
//    The Q measure computes the value of Q(T) for every triangle T in the
//    triangulation, and then computes the minimum of this
//    set of values:
//
//      Q_MEASURE = min ( all T in triangulation ) Q(T)
//
//    In an ideally regular mesh, all triangles would have the same
//    equilateral shape, for which Q = 1.  A good mesh would have
//    0.5 < Q.
//
//    Given the 2D coordinates of a set of N nodes, stored as Z(1:2,1:N),
//    a triangulation is a list of TRIANGLE_NUM triples of node indices that form
//    triangles.  Generally, a maximal triangulation is expected, namely,
//    a triangulation whose image is a planar graph, but for which the
//    addition of any new triangle would mean the graph was no longer planar.
//    A Delaunay triangulation is a maximal triangulation which maximizes
//    the minimum angle that occurs in any triangle.
//
//    The code has been modified to 'allow' 6-node triangulations.
//    However, no effort is made to actually process the midside nodes.
//    Only information from the vertices is used.
//
//  Modified:
//
//    30 December 2006
//
//  Author:
//
//    Max Gunzburger
//    John Burkardt
//
//  Reference:
//
//    Max Gunzburger and John Burkardt,
//    Uniformity Measures for Point Samples in Hypercubes.
//
//    Per-Olof Persson and Gilbert Strang,
//    A Simple Mesh Generator in MATLAB,
//    SIAM Review,
//    Volume 46, Number 2, pages 329-345, June 2004.
//
//  Parameters:
//
//    Input, int N, the number of points.
//
//    Input, double Z[2*N], the points.
//
//    Input, int TRIANGLE_ORDER, the order of the triangles.
//
//    Input, int TRIANGLE_NUM, the number of triangles.
//
//    Input, int TRIANGLE_NODE[TRIANGLE_ORDER*TRIANGLE_NUM],
//    the triangulation.
//
//    Output, double Q_MEASURE, the Q quality measure.
//
{
  int a_index;
  double ab_length;
  int b_index;
  double bc_length;
  int c_index;
  double ca_length;
  double q;
  double q_min;
  int triangle;
  double value;

  if ( triangle_num < 1 )
  {
    value = -1.0;
    return value;
  }

  q_min = r8_huge ( );

  for ( triangle = 0; triangle < triangle_num; triangle++ )
  {
    a_index = triangle_node[0+triangle*3];
    b_index = triangle_node[1+triangle*3];
    c_index = triangle_node[2+triangle*3];

    ab_length = sqrt ( 
        pow ( z[0+(a_index-1)*2] - z[0+(b_index-1)*2], 2 ) 
      + pow ( z[1+(a_index-1)*2] - z[1+(b_index-1)*2], 2 ) );

    bc_length = sqrt ( 
        pow ( z[0+(b_index-1)*2] - z[0+(c_index-1)*2], 2 ) 
      + pow ( z[1+(b_index-1)*2] - z[1+(c_index-1)*2], 2 ) );

    ca_length = sqrt ( 
        pow ( z[0+(c_index-1)*2] - z[0+(a_index-1)*2], 2 ) 
      + pow ( z[1+(c_index-1)*2] - z[1+(a_index-1)*2], 2 ) );

    q = ( bc_length + ca_length - ab_length ) 
      * ( ca_length + ab_length - bc_length ) 
      * ( ab_length + bc_length - ca_length ) 
      / ( ab_length * bc_length * ca_length );

    q_min = r8_min ( q_min, q );
  }

  value = q_min;

  return value;
}
//****************************************************************************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" double precision value.
//
{
  return HUGE_VAL;
}
//****************************************************************************80

double r8_max ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MAX returns the maximum of two R8's.
//
//  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;
  }
}
//****************************************************************************80

double r8_min ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MIN returns the minimum of two R8's.
//
//  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

void r8mat_transpose_print ( int m, int n, double a[], char *title )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_TRANSPOSE_PRINT prints 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, char *TITLE, an optional title.
//
{
  r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

    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_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 timestamp ( void )

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