Computational Statistics in Python: Exercises

I worked through Exercises section of the Computational Statistics in Python tutorial.

Below are the results, with some variations i generated to get a better understanding of the solutions:

 # Exercises  
 """http://people.duke.edu/~ccc14/sta-663/FunctionsSolutions.html#exercises"""  
   
 """1. Rewrite the following nested loop as a list comprehension  
   ans = []  
   for i in range(3):  
     for j in range(4):  
       ans.append((i, j))  
   print ans"""  
   
 arr = [(i,j) for i in range(3) for j in range(4)]  
 arr  
   
   
 """2. Rewrite the following as a list comprehension  
     ans = map(lambda x: x*x, filter(lambda x: x%2 == 0, range(5)))  
     print ans"""  
   
 arr = [x**2 for x in range(5) if x%2 == 0]  
   
   
 """3. Convert the function below into a pure function with no global variables or side effects  
   x = 5  
   def f(alist):  
     for i in range(x):  
       alist.append(i)  
     return alist  
     
   alist = [1,2,3]  
   ans = f(alist)  
   print ans  
   print alist # alist has been changed!"""  
   
 def f(alist, x):  
   newList = alist.copy()  
   for i in range(x):  
     newList.append(i)  
   return newList  
     
 alist = [1,2,3]  
 ans = f(alist, 5)  
 print(ans)  
 print(alist) # alist has been changed!"""  
     
 # better example  
 def f2(alist, x):  
   return alist + [n for n in range(x)]  
   
 alist2 = [1,2,3]  
 ans2 = f2(alist2, 5)  
 print(ans2)  
 print(alist2) # alist has been changed!"""  
   
 # even better example  
 def f3(alist, x):  
   return alist + range(x)  

   
 """4. Write a decorator hello that makes every wrapped function print “Hello!”  
   For example:  
     @hello  
     def square(x):  
       return x*x"""  
   
 #import datetime  
 def TimeThis(func):  
   def timer(*arg1, **arg2):  
     start = datetime.datetime.now()  
     func(*arg1, **arg2)  
     end = datetime.datetime.now()  
     return print(end - start)  
   return timer  
   
 @TimeThis  
 def readfile(str):  
   return [line for line in open(str)]  
   
 readfile("requirements.txt")  
   
   
 """5. Rewrite the factorial function so that it does not use recursion.  
   def fact(n):  
     # base case  
     if n==0:  
       return 1  
     # recursive case  
     else:  
       return n * fact(n-1)"""  
   
 # still uses recursion  
 def factCached(n, cache={0:1, 1:1}):  
   try:  
     return cache[n]  
   except:  
     cache[n] = n * factCached(n-1)  
     return cache[n]  
   
 # assignment  
 def factAssignment(n):  
   x = 1  
   if n == 0 or n == 1:    
     return x  
   else:  
     for i in range(1, n+1):  
       x *= i  
     return x  
   
 arr1 = [factCached(x) for x in range(10)]  
 arr2 = [factAssignment(x) for x in range(10)]  
   
   
 """Exercise 6. Rewrite the same factorail funciotn so that it uses a cache to speed up calculations"""  
   
 # still uses recursion  
 def factCached(n, cache={0:1, 1:1}):  
   try:  
     return cache[n]  
   except:  
     cache[n] = n * factCached(n-1)  
     return cache[n]  
   
 arrEx6 = [factCached(x) for x in range(10)]  

   
 """7. Rewrite the following anonymous functiona as a regular named fucntion: lambda x, y: x**2 + y**2"""  
   
 @TimeThis  
 def hypotSquared(x, y):  
   return x**2 + y**2  
   
 import math  
 @TimeThis  
 def hypotSquaredAlt(x, y):  
   return math.hypot(x, y)**2  
   
 hypotSquared(3,6)  
 hypotSquaredAlt(3,6)  
   
   
 """8. Find an efficient way to extrac a subset of dict1 into a a new dictionary dict2   
 that only contains entrires with the keys given in the set good_keys. Note that good_keys   
 may include keys not found in dict1 - these must be excluded when building dict2.  
   
   import numpy as np  
   import cPickle  
   
   try:  
     dict1 = cPickle.load(open('dict1.pic'))  
   except:  
     numbers = np.arange(1e6).astype('int') # 1 million entries  
     dict1 = dict(zip(numbers, numbers))  
     cPickle.dump(dict1, open('dict1.pic', 'w'), protocol=2)  
   
   good_keys = set(np.random.randint(1, 1e7, 1000)"""  
   
 dict1 = {str(x): x**2 for x in range(1, 100)}  
 good_keys = set(str(x) for x in range(30, 70))  
 dict2 = {x: dict1[x] for x in dict1.keys() if x in good_keys}