Python exponentiation of two lists performance

Question

Is there a way to compute the Cobb-Douglas utility function faster in Python. I run it millions of time, so a speed increase would help. The function raises elements of quantities_list to power of corresponding elements of exponents list, and then multiplies all the resulting elements.

n = 10

quantities = range(n)
exponents = range(n)

def Cobb_Douglas(quantities_list, exponents_list):
    number_of_variables = len(quantities_list)
    value = 1
    for variable in xrange(number_of_variables):
        value *= quantities_list[variable] ** exponents_list[variable]
    return value

t0 = time.time()
for i in xrange(100000):
    Cobb_Douglas(quantities, exponents)
t1 = time.time()
print t1-t0

Answer 1

Iterators are your friend. I got a 28% speedup on my computer by switching your loop to this:

for q, e in itertools.izip(quantities_list, exponents_list):
    value *= q ** e

I also got similar results when switching your loop to a functools.reduce call, so it's not worth providing a code sample.

---

In general, numpy is the right choice for fast arithmetic operations, but numpy's largest integer type is 64 bits, which won't hold the result for your example. If you're using a different numeric range or arithmetic type, numpy is king:

quantities = np.array(quantities, dtype=np.int64)
exponents = np.array(exponents, dtype=np.int64)

def Cobb_Douglas(quantities_list, exponents_list):
    return np.product(np.power(quantities_list, exponents_list))
# result: 2649120435010011136
# actual: 21577941222941856209168026828800000