Numpy Exercise 2

Imports



In [1]:

    
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 [2]:

    
def np_fact(n):
    """Compute n! = n*(n-1)*...*1 using Numpy."""
    if n > 1:
        nums = np.arange(1, n+1, 1)
        return nums.cumprod()[-1]
    else:
        return 1
    #raise NotImplementedError()



In [3]:

    
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 [4]:

    
def loop_fact(n):
    """Compute n! using a Python for loop."""
    fact = 1
    for i in range(1, n+1):
        fact *= i
    return fact
    #raise NotImplementedError()



In [5]:

    
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 [15]:

    
%timeit -n1 -r1 np_fact(50)
%timeit -n1 -r1 loop_fact(50)
#raise NotImplementedError()









    



1 loops, best of 1: 121 µs per loop
1 loops, best of 1: 24.1 µs per loop

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

The for loop version is faster than using numpy. The structure in memory and creation/manipulation of the objects with numpy is excessive and slowing it down (?).