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

#*****************************************************************************80
#
## sphere_euler() solves the sphere ODE using euler_system().
#
  from euler_system import euler_system
  from sphere_conserved import sphere_conserved
  from sphere_dydt import sphere_dydt
  import matplotlib.pyplot as plt
  import numpy as np

  print ( '' )
  print ( 'sphere_euler:' )
  print ( '  Solve the sphere ODE using euler_system()' )

  t0 = 0.0
  tstop = 45.0
  tspan = np.array ( [ t0, tstop ] )
  y0 = np.array ( [ np.cos ( 0.9 ), 0.0, np.sin ( 0.9 ) ] )
  n = 201

  t, y = euler_system ( sphere_dydt, tspan, y0, n )
#
#  Time plot.
#
  plt.clf ( )
  plt.plot ( t, y, linewidth = 3 )
  plt.grid ( True );
  plt.xlabel ( '<-- Time -->' )
  plt.ylabel ( '<-- Position -->' )
  plt.legend ( [ 'P', 'Q', 'R' ] )
  plt.title ( 'sphere, euler, time plot' )
  filename = 'sphere_euler_time.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )
  plt.close ( )
#
#  Conservation plot.
#
  P = sphere_conserved ( t, y )

  plt.clf ( )
  plt.plot ( t, P, 'c-', lineWidth = 3 )
  plt.plot ( [ t0, tstop ], [ 0.0, 0.0 ], 'k-', linewidth = 3 )
  plt.grid ( 'on' )
  plt.xlabel ( '<-- Time -->' )
  plt.ylabel ( '<-- P(t) -->' )
  plt.title ( 'sphere, euler, conservation plot' )
  filename = 'sphere_euler_conservation.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "' + filename + '"' )
  plt.show ( )
  plt.close ( )

  return

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