function fem_to_gmsh ( prefix )

%*****************************************************************************80
%
%% fem_to_gmsh() converts a 1D, 2D or 3D mesh from FEM to GMSH format.   
%
%  Usage:
%
%    fem_to_gmsh ( 'prefix' )
%
%    where 'prefix' is the common filename prefix:
%
%    * 'prefix'_nodes.txt contains the node coordinates,
%    * 'prefix'_elements.txt contains the element definitions.
%    * 'prefix'.msh will contain the Gmsh version of the data.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    07 October 2014
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Christophe Geuzaine, Jean-Francois Remacle,
%    Gmsh: a three-dimensional finite element mesh generator with
%    built-in pre- and post-processing facilities,
%    International Journal for Numerical Methods in Engineering,
%    Volume 79, Number 11, pages 1309-1331, 2009.
%
%  Input:
%
%    character PREFIX, the common file prefix.
%
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_TO_GMSH\n' );
  fprintf ( 1, '  MATLAB/Octave version %s\n', version ( ) );
  fprintf ( 1, ...
    '  Convert a 1D, 2D or 3D mesh from FEM to GMSH  format.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read "prefix"_nodes.txt, node coordinates.\n' );
  fprintf ( 1, '  Read "prefix"_elements.txt, 3 or 6 node element definitions.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Create "prefix".msh, a corresponding Gmsh mesh file.\n' );
%
%  The command line argument is the common filename prefix.
%
  if ( nargin < 1 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'FEM_TO_GMSH:\n' );

    prefix = input ( ...
      'Please enter the filename prefix:' );

  end
%
%  Create the filenames.
%
  node_filename = strcat ( prefix, '_nodes.txt' );
  element_filename = strcat ( prefix, '_elements.txt' );
  gmsh_filename = strcat ( prefix, '.msh' );
%
%  Read the data.
%
  [ m, 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', m );
  fprintf ( 1, '  Number of points  = %d\n', node_num );

  node_x(1:m,1:node_num) = r8mat_data_read ( node_filename, ...
    m, node_num );

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

  r8mat_transpose_print_some ( m, node_num, node_x, 1, 1, m, 5, ...
    '  Initial portion of node coordinate data:' );
%
%  Read the element data.
%
  [ element_order, element_num ] = i4mat_header_read ( element_filename );

  if ( m == 1 )

    if ( element_order == 2 )

    else
      fprintf ( 1, '\n' );
      fprintf ( 1, 'FEM_TO_GMSH - Fatal error!\n' );
      fprintf ( 1, '  1D data must use 2 nodes.\n' );
      error ( 'FEM_TO_GMSH - Fatal error!' );
    end

  elseif ( m == 2 )

    if ( element_order == 3 )
    elseif ( element_order == 6 )
    else
      fprintf ( 1, '\n' );
      fprintf ( 1, 'FEM_TO_GMSH - Fatal error!\n' );
      fprintf ( 1, '  2D mesh data must use 3 or 6 nodes.\n' );
      error ( 'FEM_TO_GMSH - Fatal error!' );
    end

  elseif ( m == 3 )

    if ( element_order == 4 )
    elseif ( element_order == 10 )
    elseif ( element_order == 20 )
    else
      fprintf ( 1, '\n' );
      fprintf ( 1, 'FEM_TO_GMSH - Fatal error!\n' );
      fprintf ( 1, '  3D mesh data must use 4, 10 or 20 nodes.\n' );
      error ( 'FEM_TO_GMSH - Fatal error!' );
    end

  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(1:element_order,1:element_num) = 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, 10, '  Initial portion of element data:' );
%
%  Write out the Gmsh version of the data.
%
  if ( m == 1 )
    gmsh_mesh1d_write ( gmsh_filename, m, node_num, node_x, ...
      element_order, element_num, element_node );
  elseif ( m == 2 )
    gmsh_mesh2d_write ( gmsh_filename, m, node_num, node_x, ...
      element_order, element_num, element_node );
  elseif ( m == 3 )
    gmsh_mesh3d_write ( gmsh_filename, m, node_num, node_x, ...
      element_order, element_num, element_node );
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Saved GMSH mesh in file "%s"\n', gmsh_filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_TO_GMSH\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 gmsh_mesh1d_write ( gmsh_filename, m, node_num, node_x, ...
  element_order, element_num, element_node )

%*****************************************************************************80
%
%% gmsh_mesh1d_write() writes 1D mesh data as a Gmsh mesh file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    07 October 2014
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Christophe Geuzaine, Jean-Francois Remacle,
%    Gmsh: a three-dimensional finite element mesh generator with
%    built-in pre- and post-processing facilities,
%    International Journal for Numerical Methods in Engineering,
%    Volume 79, Number 11, pages 1309-1331, 2009.
%
%  Input:
%
%    string GMSH_FILENAME, the name of the Gmsh file.
%
%    integer M, the spatial dimension.
%
%    integer NODE_NUM, the number of nodes.
%
%    real NODE_X(M,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.
%

%
%  Enforce 1-based indexing.
%
  element_node = mesh_base_one ( node_num, element_order, element_num, ...
    element_node );
%
%  Open the file.
%
  gmsh = fopen ( gmsh_filename, 'wt' );

  if ( gmsh < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'GMSH_MESH1D_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'GMSH_MESH1D_WRITE - Error!' );
  end
%
%  Write the data.
%
  fprintf ( gmsh, '$MeshFormat\n' );
  fprintf ( gmsh, '  2.2 0 8\n' );
  fprintf ( gmsh, '$EndMeshFormat\n' );

  fprintf ( gmsh, '$Nodes\n' );
  fprintf ( gmsh, '  %d\n', node_num );
  for node = 1 : node_num
    fprintf ( gmsh, '  %d %g  0.0  0.0\n', node, node_x(1:m,node) );
  end
  fprintf ( gmsh, '$EndNodes\n' );

  element_type = 1;

  tag_num = 2;
  tag1 = 0;
  fprintf ( gmsh, '$Elements\n' );
  fprintf ( gmsh, '  %d\n', element_num );
  for element = 1 : element_num
    fprintf ( gmsh, '  %d  %d  %d  %d  %d', ...
      element, element_type, tag_num, tag1, element );
    for vertex = 1 : element_order
      fprintf ( gmsh, '  %d', element_node(vertex,element) );
    end
    fprintf ( gmsh, '\n' );
  end
  fprintf ( gmsh, '$EndElements\n' );

  fclose ( gmsh );

  return
end
function gmsh_mesh2d_write ( gmsh_filename, m, node_num, node_x, ...
  element_order, element_num, element_node )

%*****************************************************************************80
%
%% gmsh_mesh2d_write() writes 2D mesh data as a Gmsh mesh file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    07 October 2014
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Christophe Geuzaine, Jean-Francois Remacle,
%    Gmsh: a three-dimensional finite element mesh generator with
%    built-in pre- and post-processing facilities,
%    International Journal for Numerical Methods in Engineering,
%    Volume 79, Number 11, pages 1309-1331, 2009.
%
%  Input:
%
%    string GMSH_FILENAME, the name of the Gmsh file.
%
%    integer M, the spatial dimension.
%
%    integer NODE_NUM, the number of nodes.
%
%    real NODE_X(M,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.
%

%
%  Enforce 1-based indexing.
%
  element_node = mesh_base_one ( node_num, element_order, element_num, ...
    element_node );
%
%  Open the file.
%
  gmsh = fopen ( gmsh_filename, 'wt' );

  if ( gmsh < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'GMSH_MESH2D_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'GMSH_MESH2D_WRITE - Error!' );
  end
%
%  Write the data.
%
  fprintf ( gmsh, '$MeshFormat\n' );
  fprintf ( gmsh, '  2.2 0 8\n' );
  fprintf ( gmsh, '$EndMeshFormat\n' );

  fprintf ( gmsh, '$Nodes\n' );
  fprintf ( gmsh, '  %d\n', node_num );
  for node = 1 : node_num
    fprintf ( gmsh, '  %d %g %g 0.0\n', node, node_x(1:m,node) );
  end
  fprintf ( gmsh, '$EndNodes\n' );

  if ( element_order == 3 )
    element_type = 2;
  elseif ( element_order == 6 )
    element_type = 9;
  end

  tag_num = 2;
  tag1 = 0;
  fprintf ( gmsh, '$Elements\n' );
  fprintf ( gmsh, '  %d\n', element_num );
  for element = 1 : element_num
    fprintf ( gmsh, '  %d  %d  %d  %d  %d', ...
      element, element_type, tag_num, tag1, element );
    for vertex = 1 : element_order
      fprintf ( gmsh, '  %d', element_node(vertex,element) );
    end
    fprintf ( gmsh, '\n' );
  end
  fprintf ( gmsh, '$EndElements\n' );

  fclose ( gmsh );

  return
end
function gmsh_mesh3d_write ( gmsh_filename, m, node_num, node_x, ...
  element_order, element_num, element_node )

%*****************************************************************************80
%
%% gmsh_mesh3d_write() writes 3D mesh data as a Gmsh mesh file.
%
%  Discussion:
%
%    The node ordering for the 20 node element is not standard.
%
%    Assuming the vertices are A, B, C and D, Gmsh uses the following ordering:
%
%    1:    a
%    2:        b
%    3:            c
%    4:                d
%    5: (2*a  +b        )/3
%    6: (  a+2*b        )/3
%    7: (    2*b+  c    )/3
%    8: (      b+2*c    )/3
%    9: (  a    +2*c    )/3
%   10: (2*a    +  c    )/3
%   11: (2*a        +  d)/3
%   12: (  a        +2*d)/3
%   13: (     b     +2*d)/3
%   14: (   2*b     +  d)/3
%   15: (       +  c+2*d)/3
%   16: (       +2*c+  d)/3
%   17: (  a+  b+  c    )/3
%   18: (  a+  b    +  d)/3
%   19: (      b+  c+  d)/3
%   20: (  a+      c+  d)/3
%
%    Leo Rebholz used the following ordering:
%
%    1:    a
%    2:        b
%    3:            c
%    4:                d
%    5: (2*a  +b        )/3
%    6: (2*a    +  c    )/3
%    7: (  a+2*b        )/3
%    8: (  a    +2*c    )/3
%    9: (  a+  b+  c    )/3
%   10: (    2*b+  c    )/3
%   11: (      b+2*c    )/3
%   12: (2*a        +  d)/3
%   13: (   2*b     +  d)/3
%   14: (       +2*c+  d)/3
%   15: (  a+  b    +  d)/3
%   16: (      b+  c+  d)/3
%   17: (  a+      c+  d)/3
%   18: (  a        +2*d)/3
%   19: (     b     +2*d)/3
%   20: (       +  c+2*d)/3
%
%    Since the only 20 node data we have is from Leo, we will assume that
%    all 20 node input data is in Leo's format, and needs to be converted
%    to the Gmsh convention.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    07 October 2014
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Christophe Geuzaine, Jean-Francois Remacle,
%    Gmsh: a three-dimensional finite element mesh generator with
%    built-in pre- and post-processing facilities,
%    International Journal for Numerical Methods in Engineering,
%    Volume 79, Number 11, pages 1309-1331, 2009.
%
%  Input:
%
%    string GMSH_FILENAME, the name of the Gmsh file.
%
%    integer M, the spatial dimension.
%
%    integer NODE_NUM, the number of nodes.
%
%    real NODE_X(M,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.
%
  leo_to_gmsh = [...
     1,  2,  3,  4,  5, ...
     7, 10, 11,  8,  6, ...
    12, 18, 19, 13, 20, ...
    14,  9, 15, 16, 17 ];
%
%  Enforce 1-based indexing.
%
  element_node = mesh_base_one ( node_num, element_order, element_num, ...
    element_node );
%
%  Open the file.
%
  gmsh = fopen ( gmsh_filename, 'wt' );

  if ( gmsh < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'GMSH_MESH3D_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'GMSH_MESH3D_WRITE - Error!' );
  end
%
%  Write the data.
%
  fprintf ( gmsh, '$MeshFormat\n' );
  fprintf ( gmsh, '2.2 0 8\n' );
  fprintf ( gmsh, '$EndMeshFormat\n' );

  fprintf ( gmsh, '$Nodes\n' );
  fprintf ( gmsh, '%d\n', node_num );
  for node = 1 : node_num
    fprintf ( gmsh, '%d', node );
    for dim = 1 : 3
      if ( dim <= m )
        fprintf ( gmsh, '  %g', node_x(dim,node) );
      else
        fprintf ( gmsh, '  %g', 0.0 );
      end
    end
    fprintf ( gmsh, '\n' );
  end
  fprintf ( gmsh, '$EndNodes\n' );
%
%  These are the Gmsh codes for 4, 10 and 20 node tetrahedral elements.
%
  if ( element_order == 4 )
    element_type = 4;
  elseif ( element_order == 10 )
    element_type = 11;
  elseif ( element_order == 20 )
    element_type = 29;
  end

  tag_num = 2;
  tag1 = 0;
  fprintf ( gmsh, '$Elements\n' );
  fprintf ( gmsh, '%d\n', element_num );
  for element = 1 : element_num
    fprintf ( gmsh, '%d  %d  %d  %d  %d', ...
      element, element_type, tag_num, tag1, element );
    for vertex = 1 : element_order
      if ( element_order == 20 )
        v = leo_to_gmsh(vertex);
      else
        v = vertex;
      end
      fprintf ( gmsh, '  %d', element_node(v,element) );
    end
    fprintf ( gmsh, '\n' );
  end
  fprintf ( gmsh, '$EndElements\n' );

  fclose ( gmsh );

  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 ( m, n, a, title )

%*****************************************************************************80
%
%% i4mat_transpose_print() prints an I4MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    31 January 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.
%
%    string TITLE, a title.
%
  i4mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

  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, a title.
%
  incx = 10;

  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' );
    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_one ( node_num, element_order, ...
  element_num, element_node )

%*****************************************************************************80
%
%% mesh_base_one() ensures that the element definition is one-based.
%
%  Discussion:
%
%    The ELEMENT_NODE array contains nodes indices that form elements.
%    The convention for node indexing might start at 0 or at 1.
%    Since a MATLAB program will naturally assume a 1-based indexing, it is
%    necessary to check a given element definition and, if it is actually
%    0-based, to convert it.
%
%    This function attempts to detect 0-based node indexing and correct it.
%
%    Thanks to Feifei Xu for pointing out that I was subtracting 1 when I
%    should have been adding 1!  29 November 2012.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    29 November 2012
%
%  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,ELEMEN_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_ONE:\n' );
    fprintf ( 1, '  The element indexing appears to be 0-based!\n' );
    fprintf ( 1, '  This will be converted to 1-based.\n' );
    element_node(1:element_order,1:element_num) = ...
      element_node(1:element_order,1:element_num) + 1;
  elseif ( node_min == 1 && node_max == node_num )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BASE_ONE:\n' );
    fprintf ( 1, '  The element indexing appears to be 1-based!\n' );
    fprintf ( 1, '  No conversion is necessary.\n' );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, 'MESH_BASE_ONE - Warning!\n' );
    fprintf ( 1, '  The element indexing is not of a recognized type.\n' );
    fprintf ( 1, '  NODE_MIN = %d\n', node_min );
    fprintf ( 1, '  NODE_MAX = %d\n', node_max );
    fprintf ( 1, '  NODE_NUM = %d\n', node_num );
  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 ( 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 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

