In [24]:
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 [25]:
def np_fact(n):
"""Compute n! = n*(n-1)*...*1 using Numpy."""
if n==0:
return 1
else:
a=np.arange(1.0, (n+1), 1.0)
b= a.cumprod()
c=max(b)
return c
print(np_fact(10))
In [14]:
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 [43]:
def loop_fact(n):
"""Compute n! using a Python for loop."""
a=[]
c=1
if n>0:
b= list(range(1,n+1)) # so b is [ 1,2,3,4,...n]
for x in b:
c=c*x
return c
else:
return 1
print(loop_fact(5))
In [44]:
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 [55]:
%timeit -n1 -r1 np_fact(50)
%timeit -n1 -r1 loop_fact(50)
In the cell below, summarize your timing tests. Which version is faster? Why do you think that version is faster?
loop_fact is faster. Probably because my loop_fact only has one actual computation, c=c*x. Whereas np_fact has to arrange and aray and THEN cumprod().