#! /usr/bin/env python # def i4_fall_values ( n_data ): #*****************************************************************************80 # ## I4_FALL_VALUES returns values of the integer falling factorial function. # # Discussion: # # The definition of the falling factorial function is # # (m)_n = (m)! / (m-n)! # = ( m ) * ( m - 1 ) * ( m - 2 ) ... * ( m - n + 1 ) # = Gamma ( m + 1 ) / Gamma ( m - n + 1 ) # # We assume 0 <= N <= M. # # In Mathematica, the function can be evaluated by: # # FactorialPower[m,n] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 December 2014 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz and Irene Stegun, # Handbook of Mathematical Functions, # US Department of Commerce, 1964. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Wolfram Media / Cambridge University Press, 1999. # # Parameters: # # Input/output, integer N_DATA. The user sets N_DATA to 0 before the # first call. On each call, the routine increments N_DATA by 1, and # returns the corresponding data; when there is no more data, the # output value of N_DATA will be 0 again. # # Output, integer M, N, the arguments of the function. # # Output, integer FMN, the value of the function. # import numpy as np n_max = 15 fmn_vec = np.array ( [ 1, 5, 20, 60, 120, \ 120, 0, 1, 10, 4000, \ 90, 4896, 24, 912576, 0 ] ) m_vec = np.array ( [ 5, 5, 5, 5, 5, \ 5, 5, 50, 10, 4000, \ 10, 18, 4, 98, 1 ] ) n_vec = np.array ( [ 0, 1, 2, 3, 4, \ 5, 6, 0, 1, 1, \ 2, 3, 4, 3, 7 ] ) if ( n_data < 0 ): n_data = 0 if ( n_max <= n_data ): n_data = 0 m = 0 n = 0 fmn = 0 else: m = m_vec[n_data] n = n_vec[n_data] fmn = fmn_vec[n_data] n_data = n_data + 1 return n_data, m, n, fmn def i4_fall_values_test ( ): #*****************************************************************************80 # ## I4_FALL_VALUES_TEST tests I4_FALL_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 December 2014 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'I4_FALL_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' I4_FALL_VALUES returns values of the integer falling factorial.' ) print ( '' ) print ( ' M N I4_FALL(M,N)' ) print ( '' ) n_data = 0 while ( True ): n_data, m, n, fmn = i4_fall_values ( n_data ) if ( n_data == 0 ): break print ( ' %8d %8d %8d' % ( m, n, fmn ) ) # # Terminate. # print ( '' ) print ( 'I4_FALL_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) i4_fall_values_test ( ) timestamp ( )