def california_migration_backwards ( ):

#*****************************************************************************80
#
## california_migration_backwards() goes "backward" in time.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    19 January 2025
#
#  Author:
#
#    John Burkardt
#
  import numpy as np

  print ( '' )
  print ( 'california_migration_backwards():' )
  print ( '  Go "backwards" in time using np.linalg.solve()' )

  A = np.array ( [ \
    [ 0.70, 0.10 ], \
    [ 0.30, 0.90 ] ] )

  m = 21
  pop = np.zeros ( [ m, 2 ] )
  year = np.linspace ( 1980, 1960, m )

  print ( '' )
  print ( '  Year  California    US:' )
  print ( '' )

  for i in range ( 0, m ):
    if ( i == 0 ):
      pop[i,:] = np.array ( [ 44998940, 135001060 ] )
    else:
      pop[i,:] = np.linalg.solve ( A, pop[i-1,:] )


    print ( '  %4d  %9.0f  %9.0f  %9.0f' \
      % ( year[i], pop[i,0], pop[i,1], pop[i,0] + pop[i,1] ) )

  return

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