#! /usr/bin/env python # def r8_choose ( n, k ): #*****************************************************************************80 # ## R8_CHOOSE computes the binomial coefficient C(N,K) as an R8. # # Discussion: # # The value is calculated in such a way as to avoid overflow and # roundoff. The calculation is done in R8 arithmetic. # # The formula used is: # # C(N,K) = N! / ( K! * (N-K)! ) # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 24 March 2015 # # Author: # # John Burkardt # # Parameters: # # Input, integer N, K, are the values of N and K. # # Output, real VALUE, the number of combinations of N # things taken K at a time. # import numpy as np from r8_gamma_log import r8_gamma_log if ( n < 0 ): value = 0.0 elif ( k == 0 ): value = 1.0 elif ( k == 1 ): value = float ( n ) elif ( 1 < k and k < n - 1 ): facn = r8_gamma_log ( float ( n + 1 ) ) fack = r8_gamma_log ( float ( k + 1 ) ) facnmk = r8_gamma_log ( float ( n - k + 1 ) ) value = round ( np.exp ( facn - fack - facnmk ) ) elif ( k == n - 1 ): value = float ( n ) elif ( k == n ): value = 1.0 else: value = 0.0 return value def r8_choose_test ( ): #*****************************************************************************80 # ## R8_CHOOSE_TEST tests R8_CHOOSE. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 26 July 2014 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'R8_CHOOSE_TEST' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' R8_CHOOSE evaluates C(N,K).' ) print ( '' ) print ( ' N K CNK' ) for n in range ( 0, 6 ): print ( '' ) for k in range ( 0, n + 1 ): cnk = r8_choose ( n, k ) print ( ' %8d %8d %14.6g' % ( n, k, cnk ) ) # # Terminate. # print ( '' ) print ( 'R8_CHOOSE_TEST' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) r8_choose_test ( ) timestamp ( )