function distance_to_position ( input_filename )

%*****************************************************************************80
%
%% distance_to_position() computes positions from pairwise distances.
%
%  Discussion:
%
%    DISTANCE_TO_POSITION is the main routine of a program that tries to 
%    determine relative distances of a set of N objects, based on their
%    pairwise distances.
%
%    The input file is an N by N distance table.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    14 February 2009
%
%  Author:
%
%    John Burkardt
%
%  Usage:
%
%    distance_to_position ( 'input_filename' )
%
%  Input:
%
%    character input_filename, the name of the distance file.
%
  timestamp ( );
  fprintf ( 1, '\n' );
  fprintf ( 1, 'DISTANCE_TO_POSITION():\n' );
  fprintf ( 1, '  MATLAB/Octave version %s\n', version ( ) );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read a distance table for N points or cities;\n' );
  fprintf ( 1, '  assign coordinates to each point which will\n' );
  fprintf ( 1, '  reproduce the distance table with the lowest\n' );
  fprintf ( 1, '  discrepancy, in the least squares sense.\n' );

  if ( nargin < 1 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'DISTANCE_TO_POSITION:\n' );
    input_filename = input ( '  Enter the name of the input file, in quotes:  ' );
  end
%
%  For now, we will assume the spatial dimension is 2.
%  Later, this could be a second input argument.
%
  city_dim = 2;
%
%  Read the distance data.
%
  [ n1, n2 ] = r8mat_header_read ( input_filename );

  if ( n1 ~= n2 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'DISTANCE_TO_POSITION - Fatal error!\n' );
    fprintf ( 1, '  The input data does not seem to have the same\n' );
    fprintf ( 1, '  number of rows as columns.\n' );
    fprintf ( 1, '  N1 = %d\n', n1 );
    fprintf ( 1, '  N2 = %d\n', n2 );
    error ( 'DISTANCE_TO_POSITION - Fatal error!' );
  end

  city_num = n1;

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

  distance = r8mat_data_read ( input_filename, city_num, city_num );

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

  r8mat_print_some ( city_num, city_num, distance, 1, 1, 5, 5, ...
    '  5 by 5 portion of distance table:' );
%
%  Compute the positions.
%
  position = compute_position_from_distance ( city_dim, city_num, distance );

  f = map ( position, city_dim, city_num, distance );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Least squares residual for solution is %e\n', norm ( f ) );

  r8mat_transpose_print ( city_dim, city_num, position, '  Computed positions:' );

  distance2 = position_to_distance ( city_dim, city_num, position );

  r8mat_print_some ( city_num, city_num, distance2, 1, 1, 5, 5, ...
    '  5 by 5 portion of computed distance table:' );
%
%  Output the position data.
%
  output_filename = file_name_ext_swap ( input_filename, 'coord.txt' );
  r8mat_write ( output_filename, city_dim, city_num, position );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Wrote the position data to "%s".\n', output_filename );
%
%  Plot the data.
%
  plot ( position(1,1:city_num), position(2,1:city_num), 'b.', 'MarkerSize', 30 );
  t = max ( max ( position(1,1:city_num) ) - min ( position(1,1:city_num) ), ...
            max ( position(2,1:city_num) ) - min ( position(2,1:city_num) ) );
  for city = 1 : city_num
    txt = sprintf ( '%d', city );
    x = position(1,city) + 0.025 * t;
    y = position(2,city) + 0.025 * t;
    text ( x, y, txt, 'FontSize', 16 );
  end
  grid on
  xlabel ( '<---X--->' );
  ylabel ( '<---Y--->' );
  title ( 'Estimated Positions from Distance Matrix', 'FontSize', 16 );
  png_filename = file_name_ext_swap ( input_filename, 'png' );
  print ( '-dpng', png_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Saved the coordinate plot in "%s"\n', png_filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'DISTANCE_TO_POSITION\n' );
  fprintf ( 1, '  Normal end of execution.\n' );
  fprintf ( 1, '\n' );
  timestamp ( );

  return
end
function position = compute_position_from_distance ( city_dim, city_num, ...
  distance )

%*****************************************************************************80
%
%% compute_position_from_distance() determines position from distance.
%
%  Discussion:
%
%    The form of the data and the function which evaluates the residuals
%    is dictated by the software that solves the nonlinear least squares
%    problem.
%
%    In this case, we are calling MATLAB's LSQNONLIN.
%
%    The selection of LSQNONLIN, the construction of the appropriate
%    anonymous function, and the setting of the options for LSQNONLIN
%    were initially devised by Gene Cliff, to whom grateful acknowledgement
%    is made.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    15 February 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer CITY_DIM, the spatial dimension.
%
%    integer CITY_NUM, the number of cities.
%
%    real DISTANCE(CITY_NUM,CITY_NUM), the city-to-city distances.
%
%  Output:
%
%    real POSITION(CITY_DIM,CITY_NUM), positions that may be assigned
%    to the cities, which would result in a good match to the distance table.

%
%  Generate a random initial estimate for POSITION.
%  LSQNONLIN needs POSITION to be a vector, not a matrix.
%
  position = rand ( city_dim * city_num, 1 );
%
%  Create a handle to the function which evaluates the discrepancies.
%
  r_hndl = @(z) map ( z, city_dim, city_num, distance );
%
%  Set options to LSQNONLIN.
%
  OPTIONS = optimset ( 'lsqnonlin' ); 
  OPTIONS = optimset ( OPTIONS, 'Display', 'iter', 'TolFun', 1.e-10 );
%
%  LSQNONLIN computes a solution POSITION that minimizes the sum of the
%  squares of the residuals.
%    
  position = lsqnonlin ( r_hndl, position(:), [], [], OPTIONS );
%
%  Reshape POSITION into a 2D array.
%
  position = reshape ( position(:), city_dim, city_num );
   
  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 MIT license.
%
%  Modified:
%
%    21 February 2004
%
%  Author:
%
%    John Burkardt
%
%  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 ( true )

    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 MIT license.
%
%  Modified:
%
%    15 August 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    character FILE_NAME(*), a file name.
%    On the extension of the file has been changed.
%
%    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 MIT license.
%
%  Modified:
%
%    31 December 2006
%
%  Author:
%
%    John Burkardt
%
%  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 ( true )

    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 f = map ( x, city_dim, city_num, distance )

%*****************************************************************************80
%
%% map() is the function to be minimized for city positions.
%
%  Discussion:
%
%    In 1D, we must set city #1 to have coordinate 0.
%
%    In 2D, we set city #1 at (0,0) and city #2 at (?,0).
%
%    This extends to higher dimensions.
%
%    The function used to minimize the sum of squares of the residuals
%    needs the city position data to be a vector, not a matrix.
%
%    The number of residuals is N1 + N2.
%
%    N1 counts the constraints used to remove nonuniqueness by setting
%    some coordinates to 0.
%
%    N2 counts the residuals that measure the discrepancy between computed
%    and prescribed distances between cities.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    15 February 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real X(CITY_DIM*CITY_NUM), the city positions, stored as
%    a vector.
%
%    integer CITY_DIM, the spatial dimension.
%
%    integer CITY_NUM, the number of cities.
%
%    real DISTANCE(CITY_NUM,CITY_NUM), the pairwise city distances.
%
%  Output:
%
%    real F(N1+N2), the residuals.
%
  if ( city_num < city_dim )
    n1 = ( city_num * ( city_num + 1 ) ) / 2;
  else
    n1 = ( city_dim * ( city_dim + 1 ) ) / 2;
  end

  n2 = ( city_num * ( city_num - 1 ) ) / 2;

  f = zeros ( n1 + n2, 1 );

  k = 0;
%
%  City #1 is at the origin.
%  City #2 must have zero components for entries 2 through CITY_DIM.
%  City #3 must mave zero components for entries 3 through CITY_DIM.
%  up to 
%  CITY #DIM_NUM must have zero component for entry CITY_DIM.
%
  for city = 1 : min ( city_dim, city_num)
    for dim = city : min ( city_dim, city_num)
      k = k + 1;
      f(k) = x((city-1)*city_dim+dim);
    end
  end
%
%  Now measure discrepancies with the distance table.
%
  for city1 = 1 : city_num
    for city2 = city1 + 1 : city_num

      i1 = (city1-1)*city_dim;
      i2 = (city2-1)*city_dim;

      k = k + 1;
      f(k) = distance(city1,city2) ...
        - norm ( x(i1+1:i1+city_dim) - x(i2+1:i2+city_dim) );

    end
  end

  return
end
function distance = position_to_distance ( city_dim, city_num, position )

%*****************************************************************************80
%
%% position_to_distance() creates a distance matrix from positions.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    14 February 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer CITY_DIM, the spatial dimension.
%
%    integer CITY_NUM, the number of cities.
%
%    real POSITION(CITY_DIM,CITY_NUM), the positions.
%
%  Output:
%
%    real DISTANCE(CITY_NUM,CITY_NUM), the distances.
%
  distance(1:city_num,1:city_num) = 0.0;

  for city1 = 1 : city_num
    for city2 = city1 + 1 : city_num
      for dim = 1 : city_dim
        distance(city1,city2) = distance(city1,city2) ...
          + ( position(dim,city1) - position(dim,city2) ).^2;
      end
      distance(city1,city2) = sqrt ( distance(city1,city2) );
      distance(city2,city1) = distance(city1,city2);
    end
  end

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

%*****************************************************************************80
%
%% r8mat_data_read() reads data from an R8MAT file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    27 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILENAME, the name of the input file.
%
%    integer M, N, the number of rows and columns of data.
%
%  Output:
%
%    real TABLE(M,N), the point coordinates.
%
  table = zeros ( m, n );
%
%  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

  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.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    22 October 2004
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILENAME, the name of the input file.
%
%  Output:
%
%    integer M, the spatial dimension.
%
%    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 r8mat_print_some ( m, n, a, ilo, jlo, ihi, jhi, title )

%*****************************************************************************80
%
%% r8mat_print_some() prints out a portion of an R8MAT.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    16 May 2008
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns of the matrix.
%
%    real A(M,N), an M by N matrix to be printed.
%
%    integer ILO, JLO, the first row and column to print.
%
%    integer IHI, JHI, the last row and column to print.
%
%    string TITLE, a title.
%
  incx = 5;

  fprintf ( 1, '\n' );
  fprintf ( 1, '%s\n', title );

  for j2lo = max ( jlo, 1 ): incx : min ( jhi, n )

    j2hi = j2lo + incx - 1;
    j2hi = min ( j2hi, n );
    j2hi = min ( j2hi, jhi );
    
    fprintf ( 1, '\n' );
    fprintf ( 1, '  Col: ' );

    for j = j2lo : j2hi
      fprintf ( 1, '%7d       ', j );
    end

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

    i2lo = max ( ilo, 1 );
    i2hi = min ( ihi, m );

    for i = i2lo : i2hi

      fprintf ( 1, '%7d  ', i );
      
      for j = j2lo : j2hi

        if ( a(i,j) == floor ( a(i,j) ) )
          fprintf ( 1, '%8d      ', a(i,j) );
        else
          fprintf ( 1, '%12g  ', a(i,j) );
        end

      end

      fprintf ( 1, '\n' );

    end

  end

  return
end
function r8mat_transpose_print ( m, n, a, title )

%*****************************************************************************80
%
%% r8mat_transpose_print() prints an R8MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 August 2004
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    real A(M,N), an M by N matrix to be printed.
%
%    string TITLE, a title.
%
  r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

  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 MIT license.
%
%  Modified:
%
%    23 May 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    real A(M,N), an M by N matrix to be printed.
%
%    integer ILO, JLO, the first row and column to print.
%
%    integer IHI, JHI, the last row and column to print.
%
%    string TITLE, a title.
%
  incx = 5;

  fprintf ( 1, '\n' );
  fprintf ( 1, '%s\n', title );

  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.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    11 August 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string OUTPUT_FILENAME, the output filename.
%
%    integer M, the spatial dimension.
%
%    integer N, the number of points.
%
%    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, '  %14.6f', table(i,j) );
%
  for j = 1 : n
    for i = 1 : m
      fprintf ( output_unit, '  %24.16f', table(i,j) );
    end
    fprintf ( output_unit, '\n' );
  end
%
%  Close the file.
%
  fclose ( output_unit );

  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 MIT license.
%
%  Modified:
%
%    14 June 2003
%
%  Author:
%
%    John Burkardt
%
%  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 MIT license.
%
%  Modified:
%
%    30 January 2006
%
%  Author:
%
%    John Burkardt
%
%  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 MIT license.
%
%  Modified:
%
%    14 February 2003
%
%  Author:
%
%    John Burkardt
%
  t = now;
  c = datevec ( t );
  s = datestr ( c, 0 );
  fprintf ( 1, '%s\n', s );

  return
end
 
