Numpy Exercise 2

Imports



In [4]:

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



In [5]:

    
import antipackage
import github.ellisonbg.misc.vizarray as va









    



Downloading:  https://raw.githubusercontent.com/ellisonbg/misc/master/vizarray.py
Using existing version:  github.ellisonbg.misc.vizarray

Factorial

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



In [26]:

    
def np_fact(n):
    if n == 0:
        return 1
    elif n == 1:
        return 1
    else:
        a = np.arange(1,n+1,1)
        b = a.cumprod()
    return b[-1]



In [27]:

    
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 [40]:

    
def loop_fact(n):
    if n == 0:
        return 1
    elif n == 1:
        return 1
    else:
        a = 1
        while n >= 1:
            a = n * a
            n = n - 1
        return a



In [41]:

    
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 [43]:

    
# YOUR CODE HERE
%timeit -n1 -r1 (loop_fact)

%timeit -n1 -r1 (np_fact)









    



1 loops, best of 1: 3.1 µs per loop
1 loops, best of 1: 2.86 µs per loop

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

np_fact is faster, but by a very small amount of time. np_fact is faster because it does not loop through each iteration of the loop like np_loop does. Instead, I called the cumprod function, which acts on the entire array at the same time.