Training

Create a file training6.py and populate with the following functions:

1. A function positive_places(f, xs) that takes as arguments some function f and a list of numbers xs and returns a list of those-and-only-those elements x of xs for which f(x) is strictly greater than zero.

   Example 1:

   In [ ]: def my_f(x):
      ...:     return x ** 3
      ...:
   
   In [ ]: positive_places(my_f, [1, 2, -1, -2, 3, 42, -9])
   Out[ ]: [1, 2, 3, 42]
   
   In [ ]: positive_places(my_f, [1, 2, 3, 4, 5])
   Out[ ]: [1, 2, 3, 4, 5]
   
   In [ ]: positive_places(my_f, [])
   Out[ ]: []
   
   In [ ]: positive_places(my_f, [-1, -2, -3, -4, -5])
   Out[ ]: []
   

   Example 2:

   In [ ]: def f(x):
      ...:     return 2 * x + 4
      ...:
   
   In [ ]: positive_places(f, [10, 1, -3, -1.5, 0, 0.5])
   Out[ ]: [10, 1, -1.5, 0, 0.5]
   

2. Write a function eval_f_0123(f) that evaluates the function f=f(x) at positions x=0, x=1, x=2 and x=3. The function should return the list [f(0), f(1), f(2), f(3)].

   Example 1:

   In [ ]: def square(x):
      ...:     return x * x
      ...:
   
   In [ ]: eval_f_0123(square)
   Out[ ]: [0, 1, 4, 9]
   

   Example 2:

   In [ ]: def cubic(x):
      ...:     return x ** 3
      ...:
   
   In [ ]: eval_f_0123(cubic)
   Out[ ]: [0, 1, 8, 27]
   

   Example 3:

   In [ ]: def stars(x):
      ...:     return "*" * x
      ...:
   
   In [ ]: eval_f_0123(stars)
   Out[ ]: ['', '*', '**', '***']
   

Submit your file training6.py with subject line training6 to get your code tested and obtain some feedback.

Assessed part

Create a file lab6.py and populate with the following functions:

1. A function eval_f(f, xs) which takes a function f = f(x) and a list xs of values that should be used as arguments for f. The function eval_f should apply the function f subsequently to every value x in xs, and return a list fs of function values. I.e. for an input argument xs=[x0, x1, x2,..., xn] the function eval_f(f, xs) should return [f(x0), f(x1), f(x2), ..., f(xn)].

   Example 1:

   In [ ]: def square(x):
      ...:     return x * x
      ...:
   
   In [ ]: eval_f(square, [-1, 10, 20, 42])
   Out[ ]: [1, 100, 400, 1764]
   

   Example 2:

   In [ ]: import math
   
   In [ ]: eval_f(math.sqrt, [1, 2, 4, 9])
   Out[ ]: [1.0, 1.4142135623730951, 2.0, 3.0]
   

   Example 3:

   In [ ]: def sign(x):
       ...:     if x > 0:
       ...:         return 1
       ...:     elif x < 0:
       ...:         return -1
       ...:     else:
       ...:         return 0
       ...:
   
   In [ ]: sign(-1.1)
   Out[ ]: -1
   
   In [ ]: sign(0.1)
   Out[ ]: 1
   
   In [ ]: sign(0.0)
   Out[ ]: 0
   
   In [ ]: eval_f(sign, [-0.2, -0.1, 0, 0.1, 0.2, 0.3])
   Out[ ]: [-1, -1, 0, 1, 1, 1]
   

2. A function sum_f(f, xs) that returns the sum of the function values of f evaluated at values x0, x1, x2, ..., xn where xs=[x0,x1,x2,...,xn].

   Example 1:

   In [ ]: def f(x):
      ...:     return x
      ...:
   
   In [ ]: sum_f(f, [1, 2, 3, 10])
   Out[ ]: 16
   

   Example 2:

   In [ ]: def square(x):
      ...:     return x * x
      ...:
   
   In [ ]: sum_f(square, [1, 2, 3, 10])
   Out[ ]: 114
   

3. A function box_volume_UPS(a,b,c) that returns the volume of a box with edge lengths a, b and c. Inputs should be provided in inch, and the output should be expressed in inch^3.

   The standard dimensions of the UPS express box (small) are a=13 inch, b=11 inch and c=2 inch.

   Your function should use these values for a, b and c unless others are provided.

   Examples:

   In [ ]: box_volume_UPS()
   Out[ ]: 286
   
   In [ ]: box_volume_UPS(a=10, b=10, c=10)
   Out[ ]: 1000
   
   In [ ]: box_volume_UPS(c=5)
   Out[ ]: 715
   

This submission is assessed: the first submission (with subject line lab6 and file lab6.py attached) will be used for this assessment.

Last updated: 2016-10-30 at 12:17