function table_latinize ( input_filename )

%*****************************************************************************80
%
%% TABLE_LATINIZE "latinizes" a dataset.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    08 October 2004
%
%  Author:
%
%    John Burkardt
%
%  Usage:
%
%    latinize ( input_filename )
%
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'TABLE_LATINIZE:\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Read a dataset of N points in M dimensions,\n' );
  fprintf ( 1, '  modify it into a Latin hypercube,\n' );
  fprintf ( 1, '  write the modified dataset to a file.\n' );
%
%  If at least one command line argument, it's the input file name.
%
  if ( nargin < 1 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'TABLE_LATINIZE:\n' );
    input_filename = input ( 'Enter the name of the input file:' );

  end
%
%  Need to create the output file name from the input filename.
%
  output_filename = file_name_ext_swap ( input_filename, 'latin.txt' );

  [ m, n ] = r8mat_header_read (  input_filename );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of "%s".\n', input_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Spatial dimension M = %d\n', m );
  fprintf ( 1, '  Number of points N  = %d\n', n );

  table = r8mat_data_read ( input_filename, m, n );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the data in "%s".', input_filename );

  r8mat_transpose_print_some ( m, n, table, 1, 1, 5, 5, ...
    '  Small portion of data read from file:' )

  table = r8mat_latinize ( m, n, table );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Latinized the data.\n' );

  r8mat_transpose_print_some ( m, n, table, 1, 1, 5, 5, ...
    '  Small portion of Latinized data:' );

  r8mat_write ( output_filename, m, n, table );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Wrote the latinized data to "%s".\n', output_filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'TABLE_LATINIZE\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

  fprintf ( 1, '\n' );
  timestamp ( );

  return
end
function column_num = file_column_count ( input_file_name )

%*****************************************************************************80
%
%% FILE_COLUMN_COUNT counts the columns in the first line of a file.
%
%  Discussion:
%
%    The file is assumed to be a simple text file.
%
%    Most lines of the file are presumed to consist of COLUMN_NUM words,
%    separated by spaces.  There may also be some blank lines, and some 
%    comment lines, which have a "#" in column 1.
%
%    The routine tries to find the first non-comment non-blank line and
%    counts the number of words in that line.
%
%    If all lines are blanks or comments, it goes back and tries to analyze
%    a comment line.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license. 
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILE_NAME, the name of the file.
%
%    Output, integer COLUMN_NUM, the number of columns in the file.
%
  FALSE = 0;
  TRUE = 1;
%
%  Open the file.
%
  input_unit = fopen ( input_file_name );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'FILE_COLUMN_COUNT - Error!\n' );
    fprintf ( 1, '  Could not open the file "%s".\n', input_file_name );
    error ( 'FILE_COLUMN_COUNT - Error!' );
  end
%
%  Read one line, but skip blank lines and comment lines.
%  Use FGETL so we drop the newline character!
%
  got_one = FALSE;

  while ( 1 )

    line = fgetl ( input_unit );

    if ( line == -1 )
      break;
    end

    if ( s_len_trim ( line ) == 0 )

    elseif ( line(1) == '#' )

    else
      got_one = TRUE;
      break;
    end

  end

  fclose ( input_unit );

  if ( got_one == FALSE ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'FILE_COLUMN_COUNT - Warning!\n' );
    fprintf ( 1, '  The file does not seem to contain any data.\n' );
    column_num = -1;
    return
  end

  column_num = s_word_count ( line );

  return
end
function file_name_new = file_name_ext_swap ( file_name, ext )

%*****************************************************************************80
%
%% FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
%
%  Discussion:
%
%    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.
%
%  Example:
%
%          Input           Output
%    ================     =============
%    FILE_NAME    EXT     FILE_NAME_NEW
%    
%    bob.for      obj     bob.obj
%    bob.bob.bob  txt     bob.bob.txt
%    bob          yak     bob.yak
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    15 August 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character FILE_NAME(*), a file name.
%    On output, the extension of the file has been changed.
%
%    Input, character EXT(*), the extension to be used on the output
%    copy of FILE_NAME, replacing the current extension if any.
%
%    Output, character FILE_NAME_NEW(*), a copy of the input file name,
%    with the new extension.
%
  file_name_len = length ( file_name );

  ext_len = length ( ext );

  period = file_name_len + 1;

  for i = file_name_len : -1 : 1
    if ( file_name(i:i) == '.' )
      period = i;
      break
    end
  end

  file_name_new(1:period-1) = file_name(1:period-1);
  file_name_new(period) = '.';
  file_name_new(period+1:period+ext_len) = ext(1:ext_len);

  return
end
function row_num = file_row_count ( input_file_name )

%*****************************************************************************80
%
%% FILE_ROW_COUNT counts the number of row records in a file.
%
%  Discussion:
%
%    Each input line is a "RECORD".
%
%    The records are divided into three groups:
%    
%    * BLANK LINES (nothing but blanks)
%    * COMMENT LINES (begin with a '#')
%    * DATA RECORDS (anything else)
%
%    The value returned by the function is the number of data records.
%
%    By the way, if the MATLAB routine FGETS is used, instead of
%    FGETL, then the variable LINE will include line termination 
%    characters, which means that a blank line would not actually
%    have zero characters.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license. 
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILE_NAME, the name of the input file.
%
%    Output, integer ROW_NUM, the number of rows found. 
%
  input_unit = fopen ( input_file_name );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'FILE_ROW_COUNT - Error!\n' );
    fprintf ( 1, '  Could not open the file "%s".\n', input_file_name );
    error ( 'FILE_ROW_COUNT - Error!' );
  end

  blank_num = 0;
  comment_num = 0;
  row_num = 0;
  
  record_num = 0;

  while ( 1 )

    line = fgetl ( input_unit );

    if ( line == -1 )
      break;
    end

    record_num = record_num + 1;
    record_length = s_len_trim ( line );
    
    if ( record_length <= 0 )
      blank_num = blank_num + 1;
    elseif ( line(1) == '#' )
      comment_num = comment_num + 1;
    else
      row_num = row_num + 1;
    end

  end

  fclose ( input_unit );

  return
end
function table = r8mat_data_read ( input_filename, m, n )

%*****************************************************************************80
%
%% R8MAT_DATA_READ reads data from an R8MAT file.
%
%  Discussion:
%
%    An R8MAT is an array of R8's.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILENAME, the name of the input file.
%
%    Input, integer M, N, the number of rows and columns of data.
%
%    Output, real TABLE(M,N), the point coordinates.
%

%
%  Build up the format string for reading M real numbers.
%
  string = ' ';

  for i = 0 : m
    string = strcat ( string, ' %f' );
  end

  input_unit = fopen ( input_filename );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_DATA_READ - Error!\n' );
    fprintf ( 1, '  Could not open the file.\n' );
    error ( 'R8MAT_DATA_READ - Error!' );
  end

  table = zeros(m,n);

  i = 0;

  while ( i < n )

    line = fgets ( input_unit );

    if ( line == -1 )
      break;
    end

    if ( line(1) == '#' )

    elseif ( s_len_trim ( line ) == 0 )
      
    else

      [ x, count ] = sscanf ( line, string );

      if ( count == m )
        i = i + 1;
        table(1:m,i) = x(1:m);
      end

    end

  end

  fclose ( input_unit );

  return
end
function [ m, n ] = r8mat_header_read ( input_filename )

%*****************************************************************************80
%
%% R8MAT_HEADER_READ reads the header from an R8MAT file.
%
%  Discussion:
%
%    An R8MAT is an array of R8's.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 October 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILENAME, the name of the input file.
%
%    Output, integer M, the spatial dimension.
%
%    Output, integer N, the number of points.
%
  m = file_column_count ( input_filename );

  if ( m <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_HEADER_READ - Fatal error!\n' );
    fprintf ( 1, '  There was some kind of I/O problem while trying\n' );
    fprintf ( 1, '  to count the number of data columns in\n' );
    fprintf ( 1, '  the file %s.\n', input_filename );
  end

  n = file_row_count ( input_filename );

  if ( n <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_HEADER_READ - Fatal error!\n' );
    fprintf ( 1, '  There was some kind of I/O problem while trying\n' );
    fprintf ( 1, '  to count the number of data rows in\n' );
    fprintf ( 1, '  the file %s\n', input_filename );
  end

  return
end
function table = r8mat_latinize ( dim_num, n, table )

%******************************************************************************
%
%% R8MAT_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.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license. 
%
%  Modified:
%
%    30 March 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer DIM_NUM, the spatial dimension.
%
%    Input, integer N, the number of cells.
%
%    Input/output, real TABLE(DIM_NUM,N).  On input, the dataset to
%    be "Latinized".  On output, the Latinized dataset.
%
  for i = 1 : dim_num
    indx = r8vec_sort_heap_index_a ( n, table(i,1:n) );
    for j = 1 : n
      table(i,indx(j)) = ( 2 * j - 1 ) / ( 2 * n );
    end
  end

  return
  end
  function r8mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title )

%*****************************************************************************80
%
%% R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    23 May 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer M, N, the number of rows and columns.
%
%    Input, real A(M,N), an M by N matrix to be printed.
%
%    Input, integer ILO, JLO, the first row and column to print.
%
%    Input, integer IHI, JHI, the last row and column to print.
%
%    Input, string TITLE, an optional title.
%
  incx = 5;

  if ( 0 < s_len_trim ( title ) )
    fprintf ( 1, '\n' );
    fprintf ( 1, '%s\n', title );
  end

  for i2lo = max ( ilo, 1 ) : incx : min ( ihi, m )

    i2hi = i2lo + incx - 1;
    i2hi = min ( i2hi, m );
    i2hi = min ( i2hi, ihi );

    inc = i2hi + 1 - i2lo;
    
    fprintf ( 1, '\n' );
    fprintf ( 1, '  Row: ' );
    for i = i2lo : i2hi
      fprintf ( 1, '%7d       ', i );
    end
    fprintf ( 1, '\n' );
    fprintf ( 1, '  Col\n' );

    j2lo = max ( jlo, 1 );
    j2hi = min ( jhi, n );

    for j = j2lo : j2hi

      fprintf ( 1, '%5d ', j );
      for i2 = 1 : inc
        i = i2lo - 1 + i2;
        fprintf ( 1, '%12f', a(i,j) );
      end
      fprintf ( 1, '\n' );

    end

  end

  return
end
function r8mat_write ( output_filename, m, n, table )

%*****************************************************************************80
%
%% R8MAT_WRITE writes an R8MAT file.
%
%  Discussion:
%
%    An R8MAT is an array of R8's.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string OUTPUT_FILENAME, the output filename.
%
%    Input, integer M, the spatial dimension.
%
%    Input, integer N, the number of points.
%
%    Input, real TABLE(M,N), the points.
%

%
%  Open the file.
%
  output_unit = fopen ( output_filename, 'wt' );

  if ( output_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'R8MAT_WRITE - Error!' );
  end
%
%  Write the data.
%
%  For smaller data files, and less precision, try:
%
%     fprintf ( output_unit, '  %14.6e', table(i,j) );
%
  for j = 1 : n
    for i = 1 : m
      fprintf ( output_unit, '  %24.16e', table(i,j) );
    end
    fprintf ( output_unit, '\n' );
  end
%
%  Close the file.
%
  fclose ( output_unit );

  return
end
function indx = r8vec_sort_heap_index_a ( n, a )

%*****************************************************************************80
%
%% 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,
%
%    or explicitly, by the call
%
%      call R8VEC_PERMUTE ( N, A, INDX )
%
%    after which A(I), I = 1 to N is sorted.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    30 March 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer N, the number of entries in the array.
%
%    Input, real A(N), an array to be index-sorted.
%
%    Output, integer INDX(N), the sort index.  The
%    I-th element of the sorted array is A(INDX(I)).
%
  if ( n < 1 )
    indx = [];
    return;
  end

  indx(1:n) = 1:n;

  if ( n == 1 )
    return;
  end

  l = floor ( n / 2 ) + 1;
  ir = n;

  while ( 1 )

    if ( 1 < l )

      l = l - 1;
      indxt = indx(l);
      aval = a(indxt);

    else

      indxt = indx(ir);
      aval = a(indxt);
      indx(ir) = indx(1);
      ir = ir - 1;

      if ( ir == 1 )
        indx(1) = indxt;
        break;
      end

    end

    i = l;
    j = l + l;

    while ( j <= ir )

      if ( j < ir )
        if ( a(indx(j)) < a(indx(j+1)) )
          j = j + 1;
        end
      end

      if ( aval < a(indx(j)) )
        indx(i) = indx(j);
        i = j;
        j = j + j;
      else
        j = ir + 1;
      end

    end

    indx(i) = indxt;

  end

  return
end
function len = s_len_trim ( s )

%*****************************************************************************80
%
%% S_LEN_TRIM returns the length of a character string to the last nonblank.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    14 June 2003
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string S, the string to be measured.
%
%    Output, integer LEN, the length of the string up to the last nonblank.
%
  len = length ( s );

  while ( 0 < len )
    if ( s(len) ~= ' ' )
      return
    end
    len = len - 1;
  end

  return
end
function word_num = s_word_count ( s )

%*****************************************************************************80
%
%% S_WORD_COUNT counts the number of "words" in a string.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    30 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string S, the string to be examined.
%
%    Output, integer WORD_NUM, the number of "words" in the string.
%    Words are presumed to be separated by one or more blanks.
%
  FALSE = 0;
  TRUE = 1;

  word_num = 0;
  s_length = length ( s );

  if ( s_length <= 0 )
    return;
  end

  blank = TRUE;

  for i = 1 : s_length

    if ( s(i) == ' ' )
      blank = TRUE;
    elseif ( blank == TRUE )
      word_num = word_num + 1;
      blank = FALSE;
    end

  end

  return
end
function timestamp ( )

%*****************************************************************************80
%
%% TIMESTAMP prints the current YMDHMS date as a timestamp.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    14 February 2003
%
%  Author:
%
%    John Burkardt
%
  t = now;
  c = datevec ( t );
  s = datestr ( c, 0 );
  fprintf ( 1, '%s\n', s );

  return
end