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

using namespace std;

# include "latinize.H"

//****************************************************************************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, char 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 real table data from a 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_data_write ( int m, int n, double table[], ofstream &output )

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

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

  output.close ( );

  return;
}
//****************************************************************************80
 
 void dtable_header_read ( char *input_filename, int *m, int *n )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_READ reads the header from a TABLE file.
//
//  Modified:
//
//    03 October 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *INPUT_FILENAME, the name of the input file.
//
//    Output, int *M, the number of spatial dimensions.
//
//    Output, int *N, the number of points
//
{
  *m = file_column_count ( input_filename );
 
  if ( *m <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_COLUMN_COUNT failed.\n";
    *n = -1;
    return;
  }
 
  *n = file_row_count ( input_filename );
 
  if ( *n <= 0 )
  {
    cout << "\n";
    cout << "DTABLE_HEADER_READ - Fatal error!\n";
    cout << "  FILE_ROW_COUNT failed.\n";
    return;
  }
 
  return;
}
//****************************************************************************80
 
void dtable_header_write ( int m, int n, char *output_filename, ofstream &output )
 
//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_HEADER_WRITE writes the header of a TABLE file.
//
//  Modified:
//
//    04 June 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of points.
//
//    Input, char *OUTPUT_FILENAME, the output filename.
//
//    Input, ofstream &OUTPUT, the output stream.
//
{
  double roundoff;
  char *s;
 
  s = timestring ( );
  roundoff = r8_epsilon ( );

  output << "#  " << output_filename << "\n";
  output << "#  created by LATINIZE.CC\n";
  output << "#  at " << s << "\n";
  output << "#\n";
  output << "#  Spatial dimension M = " << m << "\n";
  output << "#  Number of points N =  " << n << "\n";
  output << "#  EPSILON (unit roundoff) = " << roundoff << "\n";
  output << "#\n";
 
  return;
}
//*****************************************************************************

void dtable_latinize ( int m, int n, double table[] )

//*****************************************************************************
//
//  Purpose:
//
//    DTABLE_LATINIZE "Latinizes" a real table dataset.
//
//  Discussion:
//
//    It is assumed, though not necessary, that the input dataset
//    has points that lie in the unit hypercube.
//
//    In any case, the output dataset will have this property.
//
//  Modified:
//
//    06 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, the number of cells.
//
//    Input/output, double TABLE[M*N].  On input, the dataset to
//    be "Latinized".  On output, the Latinized dataset.
//
{
  double *column;
  int i;
  int *indx;
  int j;

  column = new double[n];

  for ( i = 0; i < m; i++ )
  {
    for ( j = 0; j < n; j++ )
    {
      column[j] = table[i+j*m];
    }
    indx = r8vec_sort_heap_index_a ( n, column );

    for ( j = 0; j < n; j++ )
    {
      table[i+indx[j]*m] = ( double ) ( 2 * j + 1 ) / ( double ) ( 2 * n );
    }

    delete [] indx;
  }

  delete [] column;

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_PRINT prints a double precision matrix, with an optional title.
//
//  Discussion:
//
//    The doubly dimensioned array A is treated as a one dimensional vector,
//    stored by COLUMNS.  Entry A(I,J) is stored as A[I+J*M]
//
//  Modified:
//
//    29 August 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows in A.
//
//    Input, int N, the number of columns in A.
//
//    Input, double A[M*N], the M by N matrix.
//
//    Input, char *TITLE, a title to be printed.
//
{
  dtable_print_some ( m, n, a, 1, 1, m, n, title );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_PRINT_SOME prints some of a double precision matrix.
//
//  Modified:
//
//    09 April 2004
//
//  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, double 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 5

  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 5.
//
  for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX )
  {
    j2hi = j2lo + INCX - 1;
    j2hi = i4_min ( j2hi, n );
    j2hi = i4_min ( j2hi, jhi );

    cout << "\n";
//
//  For each column J in the current range...
//
//  Write the header.
//
    cout << "  Col:    ";
    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(7) << j << "       ";
    }
    cout << "\n";
    cout << "  Row\n";
    cout << "  ---\n";
//
//  Determine the range of the rows in this strip.
//
    i2lo = i4_max ( ilo, 1 );
    i2hi = i4_min ( ihi, m );

    for ( i = i2lo; i <= i2hi; i++ )
    {
//
//  Print out (up to) 5 entries in row I, that lie in the current strip.
//
      cout << setw(5) << i << "  ";
      for ( j = j2lo; j <= j2hi; j++ )
      {
        cout << setw(12) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }

  }

  cout << "\n";

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_TRANSPOSE_PRINT prints a real matrix, 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.
//
{
  dtable_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

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

//****************************************************************************80
//
//  Purpose:
//
//    DTABLE_TRANSPOSE_PRINT_SOME prints some of a real matrix, 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 file_column_count ( char *input_filename )

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

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

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

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

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

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

    got_one = true;
    break;

  }

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

    input.open ( input_filename );

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

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

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

      got_one = true;
      break;

    }

  }

  input.close ( );

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

  column_num = s_word_count ( line );

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

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

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

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

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

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

//****************************************************************************80
//
//  Purpose:
//
//    FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
//
//  Discussion:
//
//    NO THANKS: The creation of this routine was made more difficult by the clumsy
//    construction and misleading documentation of the C library routines STRNCAT
//    and STRCAT, which I was planning to use.
//
//  Definition:
//
//    The "extension" of a filename is the string of characters
//    that appears after the LAST period in the name.  A file
//    with no period, or with a period as the last character
//    in the name, has a "null" extension.
//
//  Examples:
//
//          Input           Output
//    ================     ==================
//    FILE_NAME    EXT     FILE_NAME_EXT_SWAP
//
//    bob.for      obj     bob.obj
//    bob.bob.bob  txt     bob.bob.txt
//    bob          yak     bob.yak
//
//  Modified:
//
//    06 December 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *FILE_NAME, a file name.
//
//    Input, char *EXT, the extension to be used on the output
//    copy of FILE_NAME, replacing the current extension if any.
//
//    Output, char *FILE_NAME_EXT_SWAP, the file name with the new extension.
//
{
  int ext_len;
  int file_name_len;
  char *file_name2;
  int i;
  int j;
  int period;
  char *s;
  char *t;
//
  ext_len = s_len_trim ( ext );
  file_name_len = s_len_trim ( file_name );
//
//  Call FILE_NAME_EXT_GET to get I, the index of the period character
//  beginning the file extension.
//
  file_name_ext_get ( file_name, &period, &j );
//
//  If there is no extension, point to where the "." should be.
//
  if ( period == -1 )
  {
    period = file_name_len;
  }

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

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

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

  *s = '\0';

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

int file_row_count ( char *input_filename )

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

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

  input.open ( input_filename );

  if ( !input )
  {
    cout << "\n";
    cout << "FILE_ROW_COUNT - Fatal error!\n";
    cout << "  Could not open the input file: \"" << input_filename << "\"\n";
    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:
//
//    11 September 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1 and 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 I4's.
//
//  Modified:
//
//    11 September 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1 and 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

double r8_epsilon ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_EPSILON returns the R8 round off unit.
//
//  Discussion:
//
//    R8_EPSILON is a number R which is a power of 2 with the property that,
//    to the precision of the computer's arithmetic,
//      1 < 1 + R
//    but 
//      1 = ( 1 + R / 2 )
//
//  Modified:
//
//    06 May 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_EPSILON, the doubleing point round-off unit.
//
{
  double r;

  r = 1.0;

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

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

int *r8vec_sort_heap_index_a ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_SORT_HEAP_INDEX_A does an indexed heap ascending sort of an R8VEC.
//
//  Discussion:
//
//    The sorting is not actually carried out.  Rather an index array is
//    created which defines the sorting.  This array may be used to sort
//    or index the array, or to sort or index related arrays keyed on the
//    original array.
//
//    Once the index array is computed, the sorting can be carried out
//    "implicitly:
//
//      A(INDX(I)), I = 1 to N is sorted,
//
//    after which A(I), I = 1 to N is sorted.
//
//  Modified:
//
//    30 March 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input, double A[N], an array to be index-sorted.
//
//    Output, int R8VEC_SORT_HEAP_INDEX_A[N], contains the sort index.  The
//    I-th element of the sorted array is A(INDX(I)).
//
{
  double aval;
  int i;
  int *indx;
  int indxt;
  int ir;
  int j;
  int l;

  indx = new int[n];

  for ( i = 1; i <= n; i++ )
  {
    indx[i-1] = i;
  }

  l = n / 2 + 1;
  ir = n;

  for ( ; ; )
  {
    if ( 1 < l )
    {
      l = l - 1;
      indxt = indx[l-1];
      aval = a[indxt-1];
    }
    else
    {
      indxt = indx[ir-1];
      aval = a[indxt-1];
      indx[ir-1] = indx[0];
      ir = ir - 1;

      if ( ir == 1 )
      {
        indx[0] = indxt;
        for ( i = 0; i < n; i++ )
        {
          indx[i] = indx[i] - 1;
        }
        return indx;
      }

    }

    i = l;
    j = l + l;

    while ( j <= ir )
    {
      if ( j < ir )
      {
        if ( a[indx[j-1]-1] < a[indx[j]-1] )
        {
          j = j + 1;
        }
      }

      if ( aval < a[indx[j-1]-1] )
      {
        indx[i-1] = indx[j-1];
        i = j;
        j = j + j;
      }
      else
      {
        j = ir + 1;
      }
    }
    indx[i-1] = indxt;
  }
}
//****************************************************************************80

int s_index_last_c ( char *s, char c )

//****************************************************************************80
//
//  Purpose:
//
//    S_INDEX_LAST_C returns a pointer to the last occurrence of a given character.
//
//  Modified:
//
//    10 October 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, char *S, a pointer to a string.
//
//    Input, char C, the character to search for.
//
//    Output, int S_INDEX_LAST_C, the index in S of the last occurrence of the character,
//    or -1 if it does not occur.
//
{
  int n;
  char *t;

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

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

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

int s_len_trim ( char *s )

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

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

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

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

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, ( double ) rexp );
    }

  }

  r = isgn * rexp * rtop / rbot;

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

bool s_to_r8vec ( char *s, int n, double dvec[] )

//****************************************************************************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 DVEC[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++ )
  {
    dvec[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;
}
//**********************************************************************

void timestamp ( void )

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

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

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

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

  cout << time_buffer << "\n";

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

char *timestring ( void )

//**********************************************************************
//
//  Purpose:
//
//    TIMESTRING returns the current YMDHMS date as a string.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, char *TIMESTRING, a string containing the current YMDHMS date.
//
{
# define TIME_SIZE 40

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

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

  s = new char[TIME_SIZE];

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

  return s;
# undef TIME_SIZE
}