function tet_mesh_to_xml ( prefix )

%*****************************************************************************80
%
%% tet_mesh_to_xml() converts a tet mesh to dolfin() XML mesh format.
%
%  Usage:
%
%    tet_mesh_to_xml ( 'prefix' )
%
%    where
%
%    * 'prefix'_nodes.txt contains nodal coordinates;
%    * 'prefix'_elements.txt contains the element definitions;
%    * 'prefix'.xml contains the DOLFIN XML mesh file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    04 June 2013
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Anders Logg, Kent-Andre Mardal, Garth Wells,
%    Automated Solution of Differential Equations by the Finite Element
%    Method: The FEniCS Book,
%    Lecture Notes in Computational Science and Engineering,
%    Springer, 2011,
%    ISBN13: 978-3642230981,
%
%  Input:
%
%    string PREFIX, the common filename prefix.
%  
  timestamp ( );
  fprintf ( 1, '\n' );
  fprintf ( 1, 'TET_MESH_TO_XML:\n' );
  fprintf ( 1, '  MATLAB/Octave version %s\n', version ( ) );
  fprintf ( 1, '  Read a tet mesh defined by node and element data files.\n' );
  fprintf ( 1, '  Create an equivalent file in DOLFIN XML mesh format.\n' );
%
%  Argument 1 is the common file prefix.
%
  if ( 1 <= nargin )

  else

    fprintf ( 1, '\n' );
    fprintf ( 1, 'TET_MESH_TO_XML:\n' );
    prefix = input ( '  Please enter the filename prefix:' );

  end
%
%  Create the filenames.
%
  node_filename = strcat ( prefix, '_nodes.txt' );
  element_filename = strcat ( prefix, '_elements.txt' );
  xml_filename = strcat ( prefix, '.xml' );
%
%  Read the node data.
%
  [ dim_num, node_num ] = r8mat_header_read ( node_filename );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of "%s".\n', node_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Spatial dimension  = %d\n', dim_num );
  fprintf ( 1, '  Number of points   = %d\n', node_num );

  node_xyz = r8mat_data_read ( node_filename, dim_num, node_num );

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

  r8mat_transpose_print_some ( dim_num, node_num, node_xyz, ...
    1, 1, dim_num, 5, '  Coordinates of first 5 nodes:' );
%
%  Read the element data.
%
  [ element_order, element_num ] = i4mat_header_read ( element_filename );

  if ( element_order == 4 )
  elseif ( element_order == 10 )
  elseif ( element_order == 20 )
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, 'TET_MESH_TO_XML - Fatal error!\n' );
    fprintf ( 1, '  Data must be for a 4, 10 or 20 node tet mesh.\n' );
    error ( 'TET_MESH_TO_XML - Fatal error!' );
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of "%s".\n', element_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Element order = %d\n', element_order );
  fprintf ( 1, '  Number of elements  = %d\n', element_num );

  element_node = i4mat_data_read ( element_filename, element_order, ...
    element_num );

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

  i4mat_transpose_print_some ( element_order, element_num, ...
    element_node, 1, 1, element_order, 5, '  First 5 elements:' );
%
%  Enforce 0-based indexing.
%
  element_node = mesh_base_zero ( node_num, element_order, element_num, ...
    element_node );
%
%  Write the XML file.
%
  xml_write ( xml_filename, dim_num, node_num, node_xyz, ...
    element_order, element_num, element_node );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Saved XML mesh in file "%s"\n', xml_filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'TET_MESH_TO_XML:\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 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 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 table = i4mat_data_read ( input_filename, m, n )

%*****************************************************************************80
%
%% i4mat_data_read() reads data from an I4MAT 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 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, 'I4MAT_DATA_READ - Error!\n' );
    fprintf ( 1, '  Could not open the input file.\n' );
    error ( 'I4MAT_DATA_READ - Error!' );
  end

  i = 0;

  while ( i < n )

    line = fgets ( input_unit );

    if ( line == -1 )
      fprintf ( 1, '\n' );
      fprintf ( 1, 'I4MAT_DATA_READ - Error!\n' );
      fprintf ( 1, '  End of input while reading data.\n' );
      error ( 'I4MAT_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 ] = i4mat_header_read ( input_filename )

%*****************************************************************************80
%
%% i4mat_header_read() reads the header from an I4MAT 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, 'I4MAT_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, 'I4MAT_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 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 MIT license.
%
%  Modified:
%
%    21 June 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    integer 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, 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 element_node = mesh_base_zero ( node_num, element_order, ...
  element_num, element_node )

%*****************************************************************************80
%
%% mesh_base_zero() ensures that the element definition is zero-based.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    04 June 2013
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer NODE_NUM, the number of nodes.
%
%    integer ELEMENT_ORDER, the order of the elements.
%
%    integer ELEMENT_NUM, the number of elements.
%
%    integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM), the element definitions.
%
%  Output:
%
%    integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM), the element definitions.
%
  node_min = min ( min ( element_node(1:element_order,1:element_num) ) );
  node_max = max ( max ( element_node(1:element_order,1:element_num) ) );

  if ( node_min == 0 && node_max == node_num - 1 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BASE_ZERO:\n' );
    fprintf ( 1, '  The element indexing appears to be 0-based!\n' );
    fprintf ( 1, '  No conversion is necessary.\n' );
  elseif ( node_min == 1 && node_max == node_num )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BASE_ZERO:\n' );
    fprintf ( 1, '  The element indexing appears to be 1-based!\n' );
    fprintf ( 1, '  This will be converted to 0-based.\n' );
    element_node(1:element_order,1:element_num) = ...
      element_node(1:element_order,1:element_num) - 1;
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BASE_ZERO - Warning!\n' );
    fprintf ( 1, '  The element indexing is not of a recognized type.\n' );
  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_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, 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 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
function xml_write ( xml_filename, dim_num, node_num, node_xyz, ...
  element_order, element_num, element_node )

%*****************************************************************************80
%
%% xml_write() writes the triangulation data as a DOLFIN XML mesh file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    04 June 2013
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Anders Logg, Kent-Andre Mardal, Garth Wells,
%    Automated Solution of Differential Equations by the Finite Element
%    Method: The FEniCS Book,
%    Lecture Notes in Computational Science and Engineering,
%    Springer, 2011,
%    ISBN13: 978-3642230981
%
%  Input:
%
%    string XML_FILENAME, the name of the DOLFIN XML file to create.
%
%    integer DIM_NUM, the spatial dimension.
%
%    integer NODE_NUM, the number of nodes.
%
%    real NODE_XYZ(3,NODE_NUM), the node coordinates.
%
%    integer ELEMENT_ORDER, the order of the elements.
%
%    integer ELEMENT_NUM, the number of elements.
%
%    integer ELEMENT_NODE(ELEMENT_ORDER,ELEMENT_NUM), the nodes
%    that make up each element.
%

%
%  Open the file.
%
  xml = fopen ( xml_filename, 'wt' );

  if ( xml < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'XML_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'XML_WRITE - Error!' );
  end
%
%  Write the data.
%
  fprintf ( xml, '<?xml version="1.0" encoding="UTF-8"?>\n' );
  fprintf ( xml, '\n' );
  fprintf ( xml, '<dolfin xmlns:dolfin="http://www.fenics.org/dolfin/">\n' );
  fprintf ( xml, '  <mesh celltype="tetrahedron" dim="3">\n' );

  fprintf ( xml, '    <vertices size="%d">\n', node_num );
  for node = 1 : node_num
    fprintf ( xml, '      <vertex index ="%d" x ="%g" y ="%g" z ="%g"/>\n', ...
      node - 1, node_xyz(1:3,node) );
  end
  fprintf ( xml, '    </vertices>\n' );

  fprintf ( xml, '    <cells size="%d">\n', element_num );
  for element = 1 : element_num
    fprintf ( xml, ...
      '      <tetrahedron index ="%d" v0 ="%d" v1 ="%d" v2 ="%d" v3 ="%d"/>\n', ...
      element - 1, element_node(1:4,element) );
  end
  fprintf ( xml, '    </cells>\n' );
  fprintf ( xml, '  </mesh>\n' );
  fprintf ( xml, '</dolfin>\n' );

  fclose ( xml );

  return
end
 
