Numpy Exercise 2

Imports



In [3]:

    
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns

Factorial

Write a function that computes the factorial of small numbers using np.arange and np.cumprod.



In [10]:

    
def np_fact(n):
    """Compute n! = n*(n-1)*...*1 using Numpy."""
    if n == 0:
        return 1
    else:
        a = np.arange(1,float(n)+1,1)
        return a.cumprod()[n-1]



In [11]:

    
assert np_fact(0)==1
assert np_fact(1)==1
assert np_fact(10)==3628800
assert [np_fact(i) for i in range(0,11)]==[1,1,2,6,24,120,720,5040,40320,362880,3628800]

Write a function that computes the factorial of small numbers using a Python loop.



In [13]:

    
def loop_fact(n):
    """Compute n! using a Python for loop."""
    if n == 0:
        return 1
    else:
        prod = 1
        for i in range(1, n+1):
            prod = prod * i
        return prod



In [14]:

    
assert loop_fact(0)==1
assert loop_fact(1)==1
assert loop_fact(10)==3628800
assert [loop_fact(i) for i in range(0,11)]==[1,1,2,6,24,120,720,5040,40320,362880,3628800]

Use the %timeit magic to time both versions of this function for an argument of 50. The syntax for %timeit is:

%timeit -n1 -r1 function_to_time()



In [22]:

    
%timeit -n1 -r1 np_fact(50)
%timeit -n1 -r1 loop_fact(50)









    



1 loops, best of 1: 62.9 µs per loop
1 loops, best of 1: 28.8 µs per loop

In the cell below, summarize your timing tests. Which version is faster? Why do you think that version is faster?

It seems after a couple runs, the loop_fact function is consistently faster than np_fact. This could be because the methods used in loop_fact are part of Python, while np_fact has code that comes from another source.