Clarity vs. code reuse/generality

[Alan G Isaac]

On 7/3/2009 10:05 AM kj apparently wrote:
> The context is the concept of a binary search.  In one of their
> homeworks, my students will have two occasions to use a binary
> search.  This seemed like a perfect opportunity to illustrate the
> idea of abstracting commonalities of code into a re-usable function.
> So I thought that I'd code a helper function, called _binary_search,
> that took five parameters: a lower limit, an upper limit, a
> one-parameter function, a target value, and a tolerance (epsilon).
> It returns the value of the parameter for which the value of the
> passed function is within the tolerance of the target value.
> 
> This seemed straightforward enough, until I realized that, to be
> useful to my students in their homework, this _binary_search function
> had to handle the case in which the passed function was monotonically
> decreasing in the specified interval...
> 
> The implementation is still very simple, but maybe not very clear,
> particularly to programming novices (docstring omitted):
> 
> def _binary_search(lo, hi, func, target, epsilon):
>     assert lo < hi
>     assert epsilon > 0
>     sense = cmp(func(hi), func(lo))
>     if sense == 0:
>         return None
>     target_plus = sense * target + epsilon
>     target_minus = sense * target - epsilon
>     while True:
>         param = (lo + hi) * 0.5
>         value = sense * func(param)
>         if value > target_plus:
>             hi = param
>         elif value < target_minus:
>             lo = param
>         else:
>             return param
> 
> 	if lo == hi:
> 	    return None



1. Don't use assertions to test argument values!

2.
from scipy.optimize import bisect
def _binary_search(lo, hi, func, target, epsilon):
    def f(x): return func(x) - target
    return bisect(f, lo, high, xtol=epsilon)

3. If you don't want to use SciPy (why?), have them
implement http://en.wikipedia.org/wiki/Bisection_method#Pseudo-code
to produce their own `bisect` function.

hth,
Alan Isaac