#! /usr/bin/env python3
#
def wathen_order ( nx, ny ):

#*****************************************************************************80
#
## WATHEN_ORDER returns the order of the WATHEN matrix.
#
#  Discussion:
#
#    N = 3 * 3 * 2 + 2 * 2 + 2 * 3 + 1 = 29
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    31 August 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Nicholas Higham,
#    Algorithm 694: A Collection of Test Matrices in MATLAB,
#    ACM Transactions on Mathematical Software,
#    Volume 17, Number 3, September 1991, pages 289-305.
#
#    Andrew Wathen,
#    Realistic eigenvalue bounds for the Galerkin mass matrix,
#    IMA Journal of Numerical Analysis,
#    Volume 7, 1987, pages 449-457.
#
#  Parameters:
#
#    Input, integer NX, NY, values which determine the size of A.
#
#    Output, integer N, the order of the matrix,
#    as determined by NX and NY.
#
  n = 3 * nx * ny + 2 * nx + 2 * ny + 1

  return n

def wathen_order_test ( ):

#*****************************************************************************80
#
## WATHEN_ORDER_TEST tests WATHEN_ORDER.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    30 November 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Nicholas Higham,
#    Algorithm 694: A Collection of Test Matrices in MATLAB,
#    ACM Transactions on Mathematical Software,
#    Volume 17, Number 3, September 1991, pages 289-305.
#
#    Andrew Wathen,
#    Realistic eigenvalue bounds for the Galerkin mass matrix,
#    IMA Journal of Numerical Analysis,
#    Volume 7, 1987, pages 449-457.
#
  import platform

  print ( '' )
  print ( 'WATHEN_ORDER_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  WATHEN_ORDER returns N, the order of a Wathen finite element' )
  print ( '  matrix given NX and NY, the number of rows and columns of' )
  print ( '  nodes in the underlying grid.' )
  print ( '' )
  print ( '       NX / NY: 1       2       3       4       5       6' )
  print ( '' )

  for ny in range ( 1, 11 ):
    print ( '       %2d' % ( ny ), end = '' )
    for nx in range ( 1, 7 ):
      n = wathen_order ( nx, ny )
      print ( '  %5d' % ( n ), end = '' )
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'WATHEN_ORDER_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  wathen_order_test ( )
  timestamp ( )