* wpylib.math: added choose() function.

master
Wirawan Purwanto 12 years ago
parent b58ea30ba8
commit 332d9ae240
  1. 36
      math/__init__.py

@ -49,3 +49,39 @@ def roundup(value, unit):
return numpy.ceil(float(value) / float(unit)) * unit return numpy.ceil(float(value) / float(unit)) * unit
def choose(n,r):
"""Computes n! / {r! (n-r)!} . Note that the following condition must
always be fulfilled:
1 <= n
1 <= r <= n
Otherwise the result is not predictable!
Optimization: To minimize the # of multiplications and divisions, we
rewrite the expression as
n! n(n-1)...(n-r+1)
--------- = ----------------
r!(n-r)! r!
To avoid multiplication overflow as much as possible, we will evaluate
in the following STRICT order, from left to right:
n / 1 * (n-1) / 2 * (n-2) / 3 * ... * (n-r+1) / r
We can show that integer arithmatic operated in this order is exact
(i.e. no roundoff error).
Note: this implementation is based on my C++ cp.inc library.
For other implementations, see:
http://stackoverflow.com/questions/3025162/statistics-combinations-in-python
Published in stack overflow, see URL above.
"""
assert n >= 0
assert 0 <= r <= n
c = 1L
denom = 1
for (num,denom) in zip(xrange(n,n-r,-1), xrange(1,r+1,1)):
c = (c * num) // denom
return c

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