lab6¶
New topic: passing functions to functions
positive_places(f, xs)¶
Write 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) returns
a value 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]
eval_f_0123(f)¶
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[ ]: ['', '*', '**', '***']
eval_f(f, xs)¶
Write 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 call 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]
sum_f(f, xs)¶
Implement 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
Please submit your file lab6.py for this assignment.
End of lab6.