#! /usr/bin/env python
#
def rhs_vortex ( nu, rho, n, x, y, t ):

#*****************************************************************************80
#
## RHS_VORTEX returns the Vortex right hand side.
#
#  Location:
#
#    http://people.sc.fsu.edu/~jburkardt/py_src/navier_stokes_2d_exact/rhs_vortex.py
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real NU, the kinematic viscosity.
#
#    Input, real RHO, the density.
#
#    Input, integer N, the number of points at which the solution is to
#    be evaluated.
#
#    Input, real X(N), Y(N), the coordinates of the points.
#
#    Input, real T(N), the time coordinate or coordinates.
#
#    Output, real F(N), G(N), H(N), the residuals in the U, V and P equations.
#
  import numpy as np

  f = - 2.0 * nu * ( np.pi ) ** 2 * ( np.cos ( np.pi * x ) * np.sin ( np.pi * y ) )
  g =   2.0 * nu * ( np.pi ) ** 2 * ( np.sin ( np.pi * x ) * np.cos ( np.pi * y ) )
  h = np.zeros ( n )

  return f, g, h

def rhs_vortex_test ( ):

#*****************************************************************************80
#
## RHS_VORTEX_TEST samples the Vortex right hand side.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ( '' )
  print ( 'RHS_VORTEX_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Sample the Vortex right hand sides' )
  print ( '  at the initial time T = 0, using a region that is' )
  print ( '  the square centered at (1.5,1.5) with "radius" 1.0,' )
  print ( '  Kinematic viscosity NU = %g' % ( nu ) )
  print ( '  Fluid density RHO = %g' % ( rho ) )

  n = 1000
  x_lo = 0.5
  x_hi = +2.5
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  f, g, h = rhs_vortex ( nu, rho, n, x, y, t )

  print ( '' )
  print ( '           Minimum       Maximum' )
  print ( '' )
  print ( '  Ur:  %14.6g  %14.6g' % ( np.min ( f ), np.max ( f ) ) )
  print ( '  Vr:  %14.6g  %14.6g' % ( np.min ( g ), np.max ( g ) ) )
  print ( '  Pr:  %14.6g  %14.6g' % ( np.min ( h ), np.max ( h ) ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'RHS_VORTEX_TEST:' )
  print ( '  Normal end of execution.' )
  return

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