#! /usr/bin/env python
#
def fem1d_bvp_linear_test10 ( ):

#*****************************************************************************80
#
## FEM1D_BVP_LINEAR_TEST10 tests FEM1D_BVP_LINEAR.
#
#  Discussion:
#
#    We want to compute errors and do convergence rates for the 
#    following problem:
#
#    - uxx + u = x  for 0 < x < 1
#    u(0) = u(1) = 0
#
#    exact  = x - sinh(x) / sinh(1)
#    exact' = 1 - cosh(x) / sinh(1)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 July 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 l2_error_linear import l2_error_linear
  from max_error_linear import max_error_linear

  print ( '' )
  print ( 'FEM1D_BVP_LINEAR_TEST10' )
  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 ( ' log(E)    E         L2error         H1error        Maxerror' )
  print ( '' )

  e_log_max = 6

  ne_plot = np.zeros ( e_log_max + 1 )
  h_plot = np.zeros ( e_log_max + 1 )
  l2_plot = np.zeros ( e_log_max + 1 )
  h1_plot = np.zeros ( e_log_max + 1 )
  mx_plot = np.zeros ( e_log_max + 1 )

  for e_log in range ( 0, e_log_max + 1 ):

    ne = 2 ** e_log
    n = ne + 1

    x_lo = 0.0
    x_hi = 1.0
    x = np.linspace ( x_lo, x_hi, n )

    u = fem1d_bvp_linear ( n, a10, c10, f10, x )

    ne_plot[e_log] = ne

    h_plot[e_log] = ( x_hi - x_lo ) / float ( ne )

    l2_plot[e_log] = l2_error_linear ( n, x, u, exact10 )

    h1_plot[e_log] = h1s_error_linear ( n, x, u, exactp10 )

    mx_plot[e_log] = max_error_linear ( n, x, u, exact10 )

    print ( '  %4d  %4d  %14g  %14g  %14g' \
      % ( e_log, ne, l2_plot[e_log], h1_plot[e_log], mx_plot[e_log] ) )

  print ( '' )
  print ( ' log(E1)  E1 / E2          L2rate          H1rate         Maxrate' )
  print ( '' )

  for e_log in range ( 0, e_log_max ):
    ne1 = ne_plot[e_log]
    ne2 = ne_plot[e_log+1]
    r = float ( ne2 ) / float ( ne1 )
    l2 = l2_plot[e_log] / l2_plot[e_log+1]
    l2 = np.log ( l2 ) / np.log ( r )
    h1 = h1_plot[e_log] / h1_plot[e_log+1]
    h1 = np.log ( h1 ) / np.log ( r )
    mx = mx_plot[e_log] / mx_plot[e_log+1]
    mx = np.log ( mx ) / np.log ( r )
    print ( '  %4d  %4d/%4d  %14g  %14g  %14g' \
    % ( e_log, ne1, ne2, l2, h1, mx ) )
#
#  Plot the L2 error as a function of NE.
#
  fig = plt.figure ( )
  plt.plot ( ne_plot, l2_plot, 'bo-' )
  plt.xlabel ( '<---NE--->' )
  plt.ylabel ( '<---L2(error)--->' )
  plt.title ( 'L2 error as function of number of elements' )
  plt.xscale ( 'log' )
  plt.yscale ( 'log' )
  plt.grid ( True )
  plt.axis ( 'equal' )
  plt.savefig ( 'l2error_test10.png' )
# plt.show ( )
#
#  Plot the max error as a function of NE.
#
  fig = plt.figure ( )
  plt.plot ( ne_plot, mx_plot, 'bo-' )
  plt.xlabel ( '<---NE--->' )
  plt.ylabel ( '<---Max(error)--->' )
  plt.title ( 'Max error as function of number of elements' )
  plt.xscale ( 'log' )
  plt.yscale ( 'log' )
  plt.grid ( True )
  plt.axis ( 'equal' )
  plt.savefig ( 'maxerror_test10.png' )
# plt.show ( )
#
#  Plot the H1 error as a function of NE.
#
  fig = plt.figure ( )
  plt.plot ( ne_plot, h1_plot, 'bo-' )
  plt.xlabel ( '<---NE--->' )
  plt.ylabel ( '<---H1(error)--->' )
  plt.title ( 'H1 error as function of number of elements' )
  plt.xscale ( 'log' )
  plt.yscale ( 'log' )
  plt.grid ( True )
  plt.axis ( 'equal' )
  plt.savefig ( 'h1error_test10.png' )
# plt.show ( )
#
#  Terminate.
#
  print ( '' )
  print ( 'FEM1D_BVP_LINEAR_TEST10' )
  print ( '  Normal end of execution.' )
  return

def a10 ( x ):
  value = 1.0
  return value

def c10 ( x ):
  value = 1.0
  return value

def exact10 ( x ):
  from math import sinh
  value = x - sinh ( x ) / sinh ( 1.0 )
  return value

def exactp10 ( x ):
  from math import cosh
  from math import sinh
  value = 1.0 - cosh ( x ) / sinh ( 1.0 )
  return value

def f10 ( x ):
  value = x
  return value

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  fem1d_bvp_linear_test10 ( )
  timestamp ( )