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

#*****************************************************************************80
#
## flow_vector() draws a vector field (U,V)(X,Y).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    28 February 2023
#
#  Author:
#
#    John Burkardt
#
  import matplotlib.pyplot as plt
  import numpy as np
  from matplotlib import cm

  print ( '' )
  print ( 'flow_vector():' )
  print ( '  Plot a vector field (U,V)(X,Y).' )

  m = 16
  n = 16

  xvec = np.linspace ( 0, 1.0, n )
  yvec = np.linspace ( 0, 1.0, m )
  X, Y = np.meshgrid ( xvec, yvec ) 

  U = - (     X**4 - 2 * X**3 + X**2 ) * ( 2 * Y**3 - 3 * Y**2 + Y )
  V =   ( 2 * X**3 - 3 * X**2 + X    ) * (     Y**4 - 2 * Y**3 + Y**2 ) 
#
#  Form the figure.
#
  plt.quiver ( X, Y, U, V, color = 'c' )
  plt.axis ( 'equal' )
  plt.title ( 'Vector field', fontsize = 16 )
  plt.xlabel ( '<--- X --->', fontsize = 16 )
  plt.ylabel ( '<--- Y --->', fontsize = 16 )
  filename = 'flow_vector.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )
  plt.close ( )

  return

if ( __name__ == '__main__' ):
  flow_vector ( )