#! /usr/bin/env python
#
def fem1d_bvp_linear_test08 ( ):

#*****************************************************************************80
#
## FEM1D_BVP_LINEAR_TEST08 carries out test case #8.
#
#  Location:
#
#    http://people.sc.fsu.edu/~jburkardt/py_src/fem1d_bvp_linear/fem1d_bvp_linear_test08.py
#
#  Discussion:
#
#    Use A8, C8, F8, EXACT8, EXACT_UX8.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Dianne O'Leary,
#    Scientific Computing with Case Studies,
#    SIAM, 2008,
#    ISBN13: 978-0-898716-66-5,
#    LC: QA401.O44.
#
  import numpy as np
  import platform
  from fem1d_bvp_linear import fem1d_bvp_linear
  from h1s_error_linear import h1s_error_linear
  from l1_error import l1_error
  from l2_error_linear import l2_error_linear
  from max_error_linear import max_error_linear

  n = 11

  print ( '' )
  print ( 'FEM1D_BVP_LINEAR_TEST08' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Solve -( A(x) U\'(x) )\' + C(x) U(x) = F(x)' )
  print ( '  for 0 < x < 1, with U(0) = U(1) = 0.' )
  print ( '  A8(X)  = 1.0' )
  print ( '  C8(X)  = 0.0' )
  print ( '  F8(X)  = X * ( X + 3 ) * exp ( X ),   X <= 2/3' )
  print ( '         = 2 * exp ( 2/3),                   2/3 < X' )
  print ( '  U8(X)  = X * ( 1 - X ) * exp ( X ),   X <= 2/3' )
  print ( '         = X * ( 1 - X ) * exp ( 2/3 ),      2/3 < X' )
  print ( '' )
  print ( '  Number of nodes = %d' % ( n ) )
#
#  Geometry definitions.
#
  x_first = 0.0
  x_last = 1.0
  x = np.linspace ( x_first, x_last, n )

  u = fem1d_bvp_linear ( n, a8, c8, f8, x )

  g = np.zeros ( n )
  for i in range ( 0, n ):
    g[i] = exact8 ( x[i] )

  print ( '' )
  print ( '     I    X         U         Uexact    Error' )
  print ( '' )

  for i in range ( 0, n ):
    print ( '  %4d  %8f  %8f  %8f  %8e' \
      % ( i, x[i], u[i], g[i], abs ( u[i] - g[i] ) ) )

  e1 = l1_error ( n, x, u, exact8 )
  e2 = l2_error_linear ( n, x, u, exact8 )
  h1s = h1s_error_linear ( n, x, u, exactp8 )
  mx = max_error_linear ( n, x, u, exact8 )

  print ( '' )
  print ( '  l1 norm of error  = %g' % ( e1 ) )
  print ( '  L2 norm of error  = %g' % ( e2 ) )
  print ( '  Seminorm of error = %g' % ( h1s ) )
  print ( '  Max norm of error = %g' % ( mx ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'FEM1D_BVP_LINEAR_TEST08' )
  print ( '  Normal end of execution.' )
  return

def a8 ( x ):
  value = 1.0
  return value

def c8 ( x ):
  value = 0.0
  return value

def exact8 ( x ):
  from math import exp
  if ( x <= 2.0 / 3.0 ):
    value = x * ( 1.0 - x ) * exp ( x )
  else:
    value = x * ( 1.0 - x ) * exp ( 2.0 / 3.0 )
  return value

def exactp8 ( x ):
  from math import exp
  if ( x <= 2.0 / 3.0 ):
    value = ( 1.0 - x - x * x ) * exp ( x )
  else:
    value = ( 1.0 - 2.0 * x ) * exp ( 2.0 / 3.0 )
  return value

def f8 ( x ):
  from math import exp
  if ( x <= 2.0 / 3.0 ):
    value = x * ( x + 3.0 ) * exp ( x )
  else:
    value = 2.0 * exp ( 2.0 / 3.0 )
  return value

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  fem1d_bvp_linear_test08 ( )
  timestamp ( )