function tet_mesh_tet_neighbors ( prefix )

%*****************************************************************************80
%
%% tet_mesh_tet_neighbors() manages the tet mesh neighbor calculation.
%
%  Discussion:
%
%    A tet mesh of order 4 or order 10 may be used.
%
%  Usage:
%
%    tet_mesh_tet_neighbors ( 'prefix' )
%
%    where
%
%    * 'prefix'_nodes.txt contains nodal coordinates (not used by this function);
%    * 'prefix'_elements.txt the element definitions;
%    * 'prefix'_element_neighbors.txt contains the element neigbhbors.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    character PREFIX, the common filename prefix.
%
  fprintf ( 1, '\n' );
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'TET_MESH_TET_NEIGHBORS:\n' );
  fprintf ( 1, '  MATLAB/Octave version %s\n', version ( ) );
  fprintf ( 1, '  Read a tet mesh dataset of TETRA_NUM\n' );
  fprintf ( 1, '  tetrahedrons, u sing 4 or 10 nodes.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Compute tet mesh neighbors and write this\n' );
  fprintf ( 1, '  information to a file.\n' );
%
%  Argument 1 is the common file prefix.
%
  if ( 1 <= nargin )

  else

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

  end
%
%  Create the filenames.
%
  element_filename = strcat ( prefix, '_elements.txt' );
  neighbor_filename = strcat ( prefix, '_element_neighbors.txt' );
%
%  Read the tetra data.
%
  [ tetra_order, tetra_num ] = i4mat_header_read ( element_filename );

  if ( tetra_order ~= 4 && tetra_order ~= 10 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'TET_MESH_TET_NEIGHBORS - Fatal error!\n' );
    fprintf ( 1, '  Data is not for a 4 or 10 node tet mesh.\n' );
    error ( 'TET_MESH_TET_NEIGHBORS - Fatal error!' );
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of "%s".\n', element_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Tetrahedron order = %d\n', tetra_order );
  fprintf ( 1, '  Number of tetras  = %d\n', tetra_num );

  tetra_node = i4mat_data_read ( element_filename, tetra_order, ...
    tetra_num );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the data in "%s".\n', element_filename );
%
%  Detect and correct 0-based indexing.
%
  tetra_node = mesh_base_one ( tetra_order, tetra_num, tetra_node );
%
%  Print first 5.
%
  i4mat_transpose_print_some ( tetra_order, tetra_num, ...
    tetra_node, 1, 1, tetra_order, 5, '  First 5 tetrahedrons:' );
%
%  Compute the neighbor information.
%
  tetra_neighbor = tet_mesh_neighbor_tets ( tetra_order, tetra_num, ...
    tetra_node );

  i4mat_transpose_print_some ( 4, tetra_num, ...
    tetra_neighbor, 1, 1, 4, 5, '  First 5 neighbors:' );
%
%  Write the neighbor information to a file.
%  Create the output file name from the input file name.
%
  i4mat_write ( neighbor_filename, 4, tetra_num, tetra_neighbor );

  fprintf ( 1, '  Wrote the tetrahedron neighbor information to "%s".\n', ...
    neighbor_filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'TET_MESH_TET_NEIGHBORS:\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 isgn = i4col_compare ( m, n, a, i, j )

%*****************************************************************************80
%
%% i4col_compare() compares columns I and J of a integer array.
%
%  Example:
%
%    Input:
%
%      M = 3, N = 4, I = 2, J = 4
%
%      A = (
%        1  2  3  4
%        5  6  7  8
%        9 10 11 12 )
%
%    Output:
%
%      ISGN = -1
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    12 June 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    integer A(M,N), an array of N columns of vectors of length M.
%
%    integer I, J, the columns to be compared.
%    I and J must be between 1 and N.
%
%  Output:
%
%    integer ISGN, the results of the comparison:
%    -1, column I < column J,
%     0, column I = column J,
%    +1, column J < column I.
%

%
%  Check.
%
  if ( i < 1)
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4COL_COMPARE - Fatal error!\n' );
    fprintf ( 1, '  Column index I = %d < 1.\n', i );
    error ( 'I4COL_COMPARE - Fatal error!' );
  end

  if ( n < i )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4COL_COMPARE - Fatal error!\n' );
    fprintf ( 1, '  N = %d < column index I = %d.\n', n, i );
    error ( 'I4COL_COMPARE - Fatal error!' );
  end

  if ( j < 1 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4COL_COMPARE - Fatal error!\n' );
    fprintf ( 1, '  Column index J = %d < 1.\n', j );
    error ( 'I4COL_COMPARE - Fatal error!' );
  end

  if ( n < j )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4COL_COMPARE - Fatal error!\n' );
    fprintf ( 1, '  N = %d < column index J = %d.\n', n, j );
    error ( 'I4COL_COMPARE - Fatal error!' );
  end

  isgn = 0;

  if ( i == j )
    return
  end

  k = 1;

  while ( k <= m )

    if ( a(k,i) < a(k,j) )
      isgn = -1;
      return
    elseif ( a(k,j) < a(k,i) )
      isgn = +1;
      return
    end

    k = k + 1;

  end

  return
end
function a = i4col_sort_a ( m, n, a )

%*****************************************************************************80
%
%% i4col_sort_a() ascending sorts an I4COL.
%
%  Discussion:
%
%    In lexicographic order, the statement "X < Y", applied to two real
%    vectors X and Y of length M, means that there is some index I, with
%    1 <= I <= M, with the property that
%
%      X(J) = Y(J) for J < I,
%    and
%      X(I) < Y(I).
%
%    In other words, the first time they differ, X is smaller.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    20 February 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, the number of rows of A, and the length of
%    a vector of data.
%
%    integer N, the number of columns of A.
%
%    integer A(M,N), the array of N columns of M-vectors.
%
%  Output:
%
%    integer A(M,N), the columns of A have been sorted in ascending
%    lexicographic order.
%
  if ( m <= 0 )
    return
  end

  if ( n <= 1 )
    return
  end
%
%  Initialize.
%
  indx = 0;
  isgn = 0;
%
%  Call the external heap sorter.
%
  while ( true )

    [ indx, i, j ] = sort_heap_external ( n, indx, isgn );
%
%  Interchange the I and J objects.
%
    if ( 0 < indx )

      a = i4col_swap ( m, n, a, i, j );
%
%  Compare the I and J objects.
%
    elseif ( indx < 0 )

      isgn = i4col_compare ( m, n, a, i, j );

    elseif ( indx == 0 )

      break

    end

  end

  return
end
function a = i4col_swap ( m, n, a, i, j )

%*****************************************************************************80
%
%% i4col_swap() swaps columns I and J of a integer array of column data.
%
%  Example:
%
%    Input:
%
%      M = 3, N = 4, I = 2, J = 4
%
%      A = (
%        1  2  3  4
%        5  6  7  8
%        9 10 11 12 )
%
%    Output:
%
%      A = (
%        1  4  3  2
%        5  8  7  6
%        9 12 11 10 )
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    19 February 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns in the array.
%
%    integer A(M,N), an array of N columns of length M.
%
%    integer I, J, the columns to be swapped.
%
%  Output:
%
%    integer A(M,N), the array, with columns I and J swapped.
%
  if ( i < 1 || n < i || j < 1 || n < j )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4COL_SWAP - Fatal error!\n' );
    fprintf ( 1, '  I or J is out of bounds.\n' );
    fprintf ( 1, '  I =    %d\n', i );
    fprintf ( 1, '  J =    %d\n', j );
    fprintf ( 1, '  N =    %d\n', n );
    error ( 'I4COL_SWAP - Fatal error!' );
  end

  if ( i == j )
    return
  end

  col(1:m) = a(1:m,i)';
  a(1:m,i) = a(1:m,j);
  a(1:m,j) = col(1:m)';

  return
end
function [ j1, j2, j3 ] = i4i4i4_sort_a ( i1, i2, i3 )

%*****************************************************************************80
%
%% i4i4i4_sort_a() ascending sorts a triple of integers.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    12 October 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer I1, I2, I3, the values to sort.
%
%  Output:
%
%    integer J1, J2, J3, the sorted values.
%
  j1 = min ( min ( i1, i2 ), min ( i2, i3 ) );
  j2 = min ( max ( i1, i2 ), ...
       min ( max ( i2, i3 ), max ( i3, i1 ) ) );
  j3 = max ( max ( i1, i2 ), max ( i2, i3 ) );

  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 i4mat_write ( output_filename, m, n, table )

%*****************************************************************************80
%
%% i4mat_write() writes an I4MAT file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    20 July 2005
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string OUTPUT_FILENAME, the output filename.
%
%    integer M, the spatial dimension.
%
%    integer N, the number of points.
%
%    integer TABLE(M,N), the points.
%
%    logical HEADER, is TRUE if the header is to be included.
%

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

  if ( output_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4MAT_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'I4MAT_WRITE - Error!' );
  end
%
%  Write the data.
%
  for j = 1 : n
    for i = 1 : m
      fprintf ( output_unit, '  %12d', round ( table(i,j) ) );
    end
    fprintf ( output_unit, '\n' );
  end
%
%  Close the file.
%
  fclose ( output_unit );

  return
end
function element_node = mesh_base_one ( 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 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 updated element definitions.
%
  node_min = min ( min ( element_node(1:element_order,1:element_num) ) );

  if ( node_min == 0 )
    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;
  else
    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' );
  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 [ indx, i, j ] = sort_heap_external ( n, indx, isgn )

%*****************************************************************************80
%
%% sort_heap_external() externally sorts a list of items into ascending order.
%
%  Discussion:
%
%    The actual list of data is not passed to the routine.  Hence this
%    routine may be used to sort integers, reals, numbers, names,
%    dates, shoe sizes, and so on.  After each call, the routine asks
%    the user to compare or interchange two items, until a special
%    return value signals that the sorting is completed.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    05 February 2004
%
%  Author:
%
%    Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf.
%    MATLAB version by John Burkardt
%
%  Reference:
%
%    Albert Nijenhuis, Herbert Wilf.
%    Combinatorial Algorithms,
%    Academic Press, 1978, second edition,
%    ISBN 0-12-519260-6.
%
%  Input:
%
%    integer N, the number of items to be sorted.
%
%    integer INDX, the main communication signal.
%    The user must set INDX to 0 before the first call.
%    Thereafter, the user should set the input value of INDX
%    to the output value from the previous call.
%
%    integer ISGN, results of comparison of elements I and J.
%    (Used only when the previous call returned INDX less than 0).
%    ISGN <= 0 means I is less than or equal to J;
%    0 <= ISGN means I is greater than or equal to J.
%
%  Output:
%
%    integer INDX, the main communication signal.
%    If INDX is
%
%      greater than 0, the user should:
%      * interchange items I and J;
%      * call again.
%
%      less than 0, the user should:
%      * compare items I and J;
%      * set ISGN = -1 if I < J, ISGN = +1 if J < I;
%      * call again.
%
%      equal to 0, the sorting is done.
%
%    integer I, J, the indices of two items.
%    On return with INDX positive, elements I and J should be interchanged.
%    On return with INDX negative, elements I and J should be compared, and
%    the result reported in ISGN on the next call.
%
  persistent i_save;
  persistent j_save;
  persistent k;
  persistent k1;
  persistent n1;
%
%  INDX = 0: This is the first call.
%
  if ( indx == 0 )
      
    i_save = -1;
    j_save = -1;
    k = floor ( n / 2 );
    k1 = k;
    n1 = n;
%
%  INDX < 0: The user is returning the results of a comparison.
%
  elseif ( indx < 0 )

    if ( indx == -2 )

      if ( isgn < 0 )
        i_save = i_save + 1;
      end

      j_save = k1;
      k1 = i_save;
      indx = -1;
      i = i_save;
      j = j_save;
      return;
    end

    if ( 0 < isgn )
      indx = 2;
      i = i_save;
      j = j_save;
      return;
    end

    if ( k <= 1 )

      if ( n1 == 1 )
        i_save = 0;
        j_save = 0;
        indx = 0;
      else
        i_save = n1;
        n1 = n1 - 1;
        j_save = 1;
        indx = 1;
      end

      i = i_save;
      j = j_save;
      return;

    end

    k = k - 1;
    k1 = k;
%
%  0 < INDX, the user was asked to make an interchange.
%
  elseif ( indx == 1 )

    k1 = k;

  end

  while ( true )

    i_save = 2 * k1;

    if ( i_save == n1 )
      j_save = k1;
      k1 = i_save;
      indx = -1;
      i = i_save;
      j = j_save;
      return;
    elseif ( i_save <= n1 )
      j_save = i_save + 1;
      indx = -2;
      i = i_save;
      j = j_save;
      return;
    end

    if ( k <= 1 )
      break;
    end

    k = k - 1;
    k1 = k;

  end

  if ( n1 == 1 )
    i_save = 0;
    j_save = 0;
    indx = 0;
    i = i_save;
    j = j_save;
  else
    i_save = n1;
    n1 = n1 - 1;
    j_save = 1;
    indx = 1;
    i = i_save;
    j = j_save;
  end

  return
end
function tetra_neighbor = tet_mesh_neighbor_tets ( tetra_order, tetra_num, ...
  tetra_node )

%*****************************************************************************80
%
% TET_MESH_NEIGHBOR_TETS determines tetrahedron neighbors.
%
%  Discussion:
%
%    A tet mesh of a set of nodes can be completely described by
%    the coordinates of the nodes, and the list of nodes that make up
%    each tetrahedron.  In the most common case, four nodes are used.
%    There is also a 10 node case, where nodes are also placed on
%    the midsides of the tetrahedral edges.
%
%    This routine can handle 4 or 10-node tetrahedral meshes.  The
%    10-node case is handled simply by ignoring the six midside nodes,
%    which are presumed to be listed after the vertices.
%
%    The tetrahedron adjacency information records which tetrahedron
%    is adjacent to a given tetrahedron on a particular face.
%
%    This routine creates a data structure recording this information.
%
%    The primary amount of work occurs in sorting a list of 4 * TETRA_NUM
%    data items.
%
%    The neighbor tetrahedrons are indexed by the face they share with
%    the tetrahedron.
%
%    Each face of the tetrahedron is indexed by the node which is NOT
%    part of the face.  That is:
%
%    * Neighbor 1 shares face 1 defined by nodes 2, 3, 4.
%    * Neighbor 2 shares face 2 defined by nodes 1, 3, 4;
%    * Neighbor 3 shares face 3 defined by nodes 1, 2, 4;
%    * Neighbor 4 shares face 4 defined by nodes 1, 2, 3.
%
%    For instance, if the (transposed) TETRA_NODE array was:
%
%    Row       1      2      3      4
%    Col
%
%      1       4      3      5      1
%      2       4      2      5      1
%      3       4      7      3      5
%      4       4      7      8      5
%      5       4      6      2      5
%      6       4      6      8      5
%
%    then the (transposed) TETRA_NEIGHBOR array should be:
%
%    Row       1      2      3      4
%    Col
%
%      1      -1      2     -1      3
%      2      -1      1     -1      5
%      3      -1      1      4     -1
%      4      -1      6      3     -1
%      5      -1      2      6     -1
%      6      -1      4      5     -1
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    16 January 2007
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer TETRA_ORDER, the order of the tetrahedrons.
%
%    integer TETRA_NUM, the number of tetrahedrons.
%
%    integer TETRA_NODE(TETRA_ORDER,TETRA_NUM), the nodes that make up
%    each tetrahedron.
%
%  Output:
%
%    integer TETRA_NEIGHBOR(4,TETRA_NUM), the four tetrahedrons that
%    are direct neighbors of a given tetrahedron.  If there is no neighbor
%    sharing a given face, the index is set to -1.
%

%
%  Step 1.
%  From the list of nodes for tetrahedron T, of the form: (I,J,K,L)
%  construct the four face relations:
%
%    (J,K,L,1,T)
%    (I,K,L,2,T)
%    (I,J,L,3,T)
%    (I,J,K,4,T)
%
%  In order to make matching easier, we reorder each triple of nodes
%  into ascending order.
%
  faces = zeros ( 5, 4 * tetra_num );
  for tetra = 1 : tetra_num

    i = tetra_node(1,tetra);
    j = tetra_node(2,tetra);
    k = tetra_node(3,tetra);
    l = tetra_node(4,tetra);

    [ a, b, c ] = i4i4i4_sort_a ( j, k, l );

    faces(1:5,4*(tetra-1)+1) = [ a, b, c, 1, tetra ]';

    [ a, b, c ] = i4i4i4_sort_a ( i, k, l );

    faces(1:5,4*(tetra-1)+2) = [ a, b, c, 2, tetra ]';

    [ a, b, c ] = i4i4i4_sort_a ( i, j, l );

    faces(1:5,4*(tetra-1)+3) = [ a, b, c, 3, tetra ]';

    [ a, b, c ] = i4i4i4_sort_a ( i, j, k );

    faces(1:5,4*(tetra-1)+4) = [ a, b, c, 4, tetra ]';

  end
%
%  Step 2. Perform an ascending dictionary sort on the neighbor relations.
%  We only intend to sort on rows 1:3; the routine we call here
%  sorts on rows 1 through 5 but that won't hurt us.
%
%  What we need is to find cases where two tetrahedrons share a face.
%  By sorting the columns of the FACES array, we will put shared faces
%  next to each other.
%
  faces = i4col_sort_a ( 5, 4*tetra_num, faces );
%
%  Step 3. Neighboring tetrahedrons show up as consecutive columns with
%  identical first three entries.  Whenever you spot this happening,
%  make the appropriate entries in TETRA_NEIGHBOR.
%
  tetra_neighbor(1:4,1:tetra_num) = -1;

  face = 1;

  while ( true )

    if ( 4 * tetra_num <= face )
      break
    end

    if ( faces(1:3,face) == faces(1:3,face+1) )
      face1 = faces(4,face);
      tetra1 = faces(5,face);
      face2 = faces(4,face+1);
      tetra2 = faces(5,face+1);
      tetra_neighbor(face1,tetra1) = tetra2;
      tetra_neighbor(face2,tetra2) = tetra1;
      face = face + 2;
    else
      face = face + 1;
    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
 
