Pythonic way to iterate through multidimensional space?

[Peter Otten]

Frank Miles wrote:

> I need to evaluate a complicated function over a multidimensional space
> as part of an optimization problem.  This is a somewhat general problem
> in which the number of dimensions and the function being evaluated can
> vary from problem to problem.
> 
> I've got a working version (with loads of conditionals, and it only works
> to #dimensions <= 10), but I'd like something simpler and clearer and
> less hard-coded.
> 
> I've web-searched for some plausible method, but haven't found anything
> "nice".  Any recommendations where I should look, or what technique should
> be used?

Not sure this is what you want, but if you have nested for loops -- these 
can be replaced with itertools.product():

>>> a = [1, 2]
>>> b = [10, 20, 30]
>>> c = [100]
>>> for x in a:
...     for y in b:
...         for z in c:
...             print(x, y, z)
... 
1 10 100
1 20 100
1 30 100
2 10 100
2 20 100
2 30 100
>>> for xyz in product(a, b, c):
...     print(*xyz)
... 
1 10 100
1 20 100
1 30 100
2 10 100
2 20 100
2 30 100