#! /usr/bin/env python
#
def fem1d_bvp_linear_test00 ( ):

#*****************************************************************************80
#
## FEM1D_BVP_LINEAR_TEST00 tests FEM1D_BVP_LINEAR.
#
#  Discussion:
#
#    - uxx + u = x  for 0 < x < 1
#    u(0) = u(1) = 0
#
#    exact  = x - sinh(x) / sinh(1)
#    exact' = 1 - cosh(x) / sinh(1)
#
#  Location:
#
#    http://people.sc.fsu.edu/~jburkardt/m_src/fem1d_bvp_linear/fem1d_bvp_linear_test00.py
#
#  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 matplotlib.pyplot as plt
  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_TEST00' )
  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 ( '  A(X)  = 1.0' )
  print ( '  C(X)  = 1.0' )
  print ( '  F(X)  = X' )
  print ( '  U(X)  = X - SINH(X) / SINH(1)' )
  print ( '' )
  print ( '  Number of nodes = %d' % ( n ) )
#
#  Geometry definitions.
#
  x_lo = 0.0
  x_hi = 1.0
  x = np.linspace ( x_lo, x_hi, n )

  u = fem1d_bvp_linear ( n, a00, c00, f00, x )

  g = np.zeros ( n )
  for i in range ( 0, n ):
    g[i] = exact00 ( x[i] )
#
#  Print a table.
#
  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] ) ) )
#
#  Compute error norms.
#
  e1 = l1_error ( n, x, u, exact00 )
  e2 = l2_error_linear ( n, x, u, exact00 )
  h1s = h1s_error_linear ( n, x, u, exactp00 )
  mx = max_error_linear ( n, x, u, exact00 )

  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 ) )
#
#  Plot the computed solution.
#
  fig = plt.figure ( )
  plt.plot ( x, u, 'bo-' )
  plt.xlabel ( '<---X--->' )
  plt.ylabel ( '<---U(X)--->' )
  plt.title ( 'FEM1D_BVP_LINEAR_TEST00 Solution' )
  plt.savefig ( 'fem1d_bvp_linear_test00.png' )
# plt.show ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'FEM1D_BVP_LINEAR_TEST00' )
  print ( '  Normal end of execution.' )
  return

def a00 ( x ):
  value = 1.0
  return value

def c00 ( x ):
  value = 1.0
  return value

def exact00 ( x ):
  from math import sinh
  value = x - sinh ( x ) / sinh ( 1.0 )
  return value

def exactp00 ( x ):
  from math import cosh
  from math import sinh
  value = 1.0 - cosh ( x ) / sinh ( 1.0 )
  return value

def f00 ( x ):
  value = x
  return value

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  fem1d_bvp_linear_test00 ( )
  timestamp ( )