Numpy Exercise 2

Imports



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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 [58]:

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



In [59]:

    
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 [45]:

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



In [46]:

    
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()



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%timeit -n1 -r1 np_fact(100)









    



1 loops, best of 1: 61 µs per loop



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%timeit -n1 -r1 loop_fact(100)









    



1 loops, best of 1: 26 µs per loop

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

I would have guessed that np_fact was going to be faster, but it turned out loop_fact was faster. I think np_fact was slower because it creates a whole array and then finds the product of all of the values in that array. loop_fact is faster because it iterates over a range and multiplies those numbers together as one step.



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