#! /usr/bin/env python
#
def power_series2 ( n, a ):

#*****************************************************************************80
#
## POWER_SERIES2 computes the power series for G(Z) = exp(F(Z)) - 1.
#
#  Discussion:
#
#    The power series for F(Z) is given.
#
#    The power series have the form:
#
#      F(Z) = A1*Z + A2*Z^2 + A3*Z^3 + ... + AN*Z^N
#
#      G(Z) = B1*Z + B2*Z^2 + B3*Z^3 + ... + BN*Z^N
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    09 June 2015
#
#  Author:
#
#    John Burkardt.
#
#  Reference:
#
#    Albert Nijenhuis, Herbert Wilf,
#    Combinatorial Algorithms,
#    Academic Press, 1978, second edition,
#    ISBN 0-12-519260-6.
#
#  Parameters:
#
#    Input, integer N, the number of terms in the power series.
#
#    Input, real A(N), the power series coefficients for F(Z).
#
#    Output, real B(N), the power series coefficients for G(Z).
#
  import numpy as np

  b = np.zeros ( n )

  for j in range ( 1, n + 1 ):

    v = 0.0

    for i in range ( 1, j ):
      v = v + b[i-1] * a[j-i-1] * float ( j - i )

    b[j-1] = a[j-1] + v / float ( j )

  return b

def power_series2_test ( ):

#*****************************************************************************80
#
## POWER_SERIES2_TEST tests POWER_SERIES2
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 June 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_print import r8vec_print

  n = 4
  a = np.zeros ( n )
  a[0] = -4.0

  print ( '' )
  print ( 'POWER_SERIES2_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  POWER_SERIES2 composes a power series' )
  print ( '  Here we compute the power series of G(x) = exp(F(x))-1' )
  print ( '  The number of terms is N = %d' % ( n ) )

  r8vec_print ( n, a, '  Series for F(x):' )
 
  b = power_series2 ( n, a )
 
  r8vec_print ( n, b, '  Series for G(x):' )
#
#  Terminate.
#
  print ( '' )
  print ( 'POWER_SERIES2_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  power_series2_test ( )
  timestamp ( )