#! /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 ( )