In [1]:
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
Write a function that computes the factorial of small numbers using np.arange and np.cumprod.
In [20]:
def np_fact(n):
"""Compute n! = n*(n-1)*...*1 using Numpy."""
if n>0:
array = np.arange(1,n+1) #The arrange function counts by 1 for the range of the array. With a factorial that range is 1 to n
x = np.cumprod(array) #This multiplies the values of the array
y = x[n-1]
else:
y = 1 #I couldn't get a function to work with the factorial of 0, so I made it a special case
return y
#print np_fact(6)
#raise NotImplementedError()
In [21]:
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 [27]:
def loop_fact(n):
"""Compute n! using a Python for loop."""
if n > 0:
n = n+1 #To offset the first step of the while loop
x = 1
while n > 1:
n = n - 1
x = n*x #Multiply n and subtract 1 from n
else: #Special case for 0!
x = 1
return x
print loop_fact(5)
#raise NotImplementedError()
In [28]:
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 [58]:
%timeit -n1 -r1 np_fact(100000) #I didn't get the expected result until I called larger numbers
%timeit -n1 -r1 loop_fact(100000)
#raise NotImplementedError()
In the cell below, summarize your timing tests. Which version is faster? Why do you think that version is faster?
With an argument of 50, the python function was faster. This makes sense because for such a low number, the time to call the np function takes up the largest amount of time. On the other hand, with arguments around 100,000, the np function was nearly 5000 times faster. This makes sense beause the np function uses a more efficient language, C.