function mesh_bandwidth ( element_file_name )

%*****************************************************************************80
%
%% MAIN is the main program for MESH_BANDWIDTH.
%
%  Discussion:
%
%    MESH_BANDWIDTH determines the geometric bandwidth of a mesh of elements.
%
%    The user supplies an element file, listing the indices of the nodes that
%    make up each element.
%
%    The program computes the geometric bandwidth associated with the mesh.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    02 January 2007
%
%  Author:
%
%    John Burkardt
%
%  Usage:
%
%    mesh_bandwidth ( 'element_file' )
%
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'MESH_BANDWIDTH\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Read a mesh file which defines\n' );
  fprintf ( 1, '  a "triangulation" of a region in the plane,\n' );
  fprintf ( 1, '  or a "tetrahedronization" of a region in space,\n' );
  fprintf ( 1, '  or any division of a regino in ND space into elements,\n' );
  fprintf ( 1, '  using a mesh of elements of uniform order.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Determine the geometric mesh bandwidth.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '    M = ML + 1 + MU.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  which is the bandwidth of the vertex connectivity\n' );
  fprintf ( 1, '  matrix.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Note that a matrix associated with variables defined\n' );
  fprintf ( 1, '  at the  nodes could have a greater bandwidth than M,\n' );
  fprintf ( 1, '  since you might have multiple variables at a vertex,\n' );
  fprintf ( 1, '  or the variable might be a vector quantity,\n' );
  fprintf ( 1, '  or physical effects might link two variables that are\n' );
  fprintf ( 1, '  not associated with vertices that are connected.\n' );
%
%  If at least one command line argument, it's the element file.
%
  if ( nargin < 1 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BANDWIDTH\n' );
    element_file_name = input ( ...
      '  Please enter the name of the element file.' );

  end
%
%  Read the triangulation data.
%
  [ element_order, element_num ] = itable_header_read (  element_file_name );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of "%s".\n', element_file_name );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Element order ELEMENT_ORDER = %d\n', element_order );
  fprintf ( 1, '  Element number ELEMENT_NUM  = %d\n', element_num );

  element_node = itable_data_read ( element_file_name, element_order, ...
    element_num );

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

  i4mat_transpose_print_some ( element_order, element_num, element_node, ...
    1, 1, element_order, 5, '  First 5 elements:' );
%
%  Compute the bandwidth.
%
  [ ml, mu, m ] = bandwidth_mesh ( element_order, element_num, element_node );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Lower bandwidth ML = %d\n', ml );
  fprintf ( 1, '  Upper bandwidth MU = %d\n', mu );
  fprintf ( 1, '  Total bandwidth M  = %d\n', m );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'MESH_BANDWIDTH\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

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

  return
end
function [ ml, mu, m ] = bandwidth_mesh ( element_order, element_num, ...
  element_node )

%*****************************************************************************80
%
%% 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.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    31 December 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer ELEMENT_ORDER, the order of the elements.
%
%    Input, integer ELEMENT_NUM, the number of elements.
%
%    Input, integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM);
%    ELEMENT_NODE(I,J) is the global index of local node I in element J.
%
%    Output, integer ML, MU, the lower and upper bandwidths of the matrix.
%
%    Output, integer M, the bandwidth of the matrix.
%
  ml = 0;
  mu = 0;

  for element = 1 : element_num

    for local_i = 1 : element_order
      global_i = element_node(local_i,element);

      for local_j = 1 : element_order
        global_j = element_node(local_j,element);

        mu = max ( mu, global_j - global_i );
        ml = max ( ml, global_i - global_j );

      end
    end
  end

  m = ml + 1 + mu;

  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:
%
%    21 February 2004
%
%  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 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:
%
%    31 December 2006
%
%  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 i4mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title )

%*****************************************************************************80
%
%% I4MAT_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    21 June 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer M, N, the number of rows and columns.
%
%    Input, integer 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 = 10;

  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' );
    fprintf ( 1, '\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, '%7d  ', a(i,j) );
      end
      fprintf ( 1, '\n' );

    end

  end

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

%*****************************************************************************80
%
%% ITABLE_DATA_READ reads an integer table from a table file.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    27 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILENAME, the name of the input file.
%
%    Input, integer M, N, the number of rows and columns in the data.
%
%    Output, integer 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, ' %d' );
  end

  input_unit = fopen ( input_filename );

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

  i = 0;

  while ( i < n )

    line = fgets ( input_unit );

    if ( line == -1 )
      fprintf ( 1, '\n' );
      fprintf ( 1, 'ITABLE_DATA_READ - Error!\n' );
      fprintf ( 1, '  End of input while reading data.\n' );
      error ( 'ITABLE_DATA_READ - Error!' );
    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 ] = itable_header_read ( input_filename )

%*****************************************************************************80
%
%% ITABLE_HEADER_READ reads the header from an integer table file.
%
%  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, 'ITABLE_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, 'ITABLE_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 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