#! /usr/bin/env python # def r8_factorial2_values ( n_data ): #*****************************************************************************80 # ## R8_FACTORIAL2_VALUES returns values of the double factorial function. # # Formula: # # FACTORIAL2( N ) = Product ( N * (N-2) * (N-4) * ... * 2 ) (N even) # = Product ( N * (N-2) * (N-4) * ... * 1 ) (N odd) # # In Mathematica, the function can be evaluated by: # # n!! # # Example: # # N N!! # # 0 1 # 1 1 # 2 2 # 3 3 # 4 8 # 5 15 # 6 48 # 7 105 # 8 384 # 9 945 # 10 3840 # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 07 February 2015 # # 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. # # Daniel Zwillinger, # CRC Standard Mathematical Tables and Formulae, # 30th Edition, # CRC Press, 1996, page 16. # # 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 N, the argument of the function. # # Output, real F, the value of the function. # import numpy as np n_max = 16 f_vec = np.array ( ( 1.0, \ 1.0, \ 2.0, \ 3.0, \ 8.0, \ 15.0, \ 48.0, \ 105.0, \ 384.0, \ 945.0, \ 3840.0, \ 10395.0, \ 46080.0, \ 135135.0, \ 645120.0, \ 2027025.0 ) ) n_vec = np.array ( ( 0, \ 1, 2, 3, 4, 5, \ 6, 7, 8, 9, 10, \ 11, 12, 13, 14, 15 ) ) if ( n_data < 0 ): n_data = 0 if ( n_max <= n_data ): n_data = 0 n = 0 f = 0.0 else: n = n_vec[n_data] f = f_vec[n_data] n_data = n_data + 1 return n_data, n, f def r8_factorial2_values_test ( ): #*****************************************************************************80 # ## R8_FACTORIAL2_VALUES_TEST demonstrates the use of R8_FACTORIAL2_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 07 February 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'R8_FACTORIAL2_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' R8_FACTORIAL2_VALUES returns values of the double factorial function.' ) print ( '' ) print ( ' N N!!' ) print ( '' ) n_data = 0 while ( True ): n_data, n, f = r8_factorial2_values ( n_data ) if ( n_data == 0 ): break print ( '%6d %14.6g' % ( n, f ) ) # # Terminate. # print ( '' ) print ( 'R8_FACTORIAL2_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) r8_factorial2_values_test ( ) timestamp ( )