#! /usr/bin/env python3
#
def exercise10 ( ):

#*****************************************************************************80
#
## exercise10() applies the midpoint method to stiff_ode.
#
  from midpoint import midpoint
  from stiff_ode import stiff_ode, stiff_lambda, stiff_solution
  import matplotlib.pyplot as plt
  import numpy as np

  print ( "exercise10:" )

  LAMBDA = 55.0
  stiff_lambda ( LAMBDA )

  y_exact = stiff_solution ( 2.0 * np.pi )

  numSteps = np.array ( [ 40, 80, 160, 320, 640, 1280, 2560 ] )
  e = np.zeros ( 7 )

  print ( '' )
  print ( '  e[k]' )
  print ( '' )
  for k in range ( 0, 7 ):
    f = stiff_ode
    xRange = np.array ( [ 0.0, 2.0 * np.pi ] )
    yInit = 0.0
    x, y = midpoint ( f, xRange, yInit, numSteps[k] )
    e[k] = np.abs ( y_exact - y[numSteps[k]] )
    print ( k, e[k] )

  print ( '' )
  print ( '  r[k] = e[k] / e[k+1]' )
  print ( '' )
  r = np.zeros ( 6 )
  for k in range ( 0, 6 ):
    r[k] = e[k] / e[k+1]
    print ( k, r[k] )

  return

if ( __name__ == "__main__" ):
  exercise10 ( )