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4 Functions and the Writing of Code
Alternatively, with default values for all the parameters, and again aiming for the
same printout, our program (ball_position_xy.py) appears as
def xy(v0x=2.0, v0y=5.0, t=0.6):
"""Computes horizontal and vertical positions at time t"""
g = 9.81
# acceleration of gravity
return v0x*t, v0y*t - 0.5*g*t**2
x, y = xy()
print(’Horizontal position: {:g} , Vertical position: {:g}’.format(x, y))
Running the code, we get the printout
Horizontal position: 1.2 , Vertical position: 1.2342
Some, or all, of the default values may also be overridden, e.g., like
x, y = xy(v0y=6.0)
# override default value for v0y only
which means that xy will run with default values for v0x and t, while v0y will have
the value 6.0, as specified in the function call. The output then, becomes
Horizontal position: 1.2 , Vertical position: 1.8342
which is reasonable, since the initial velocity for the vertical direction was higher
than in the previous case.
4.1.8 A Function with Another Function as Input Argument
Functions are straightforwardly passed as arguments to other functions. This is
illustrated by the following script function_as_argument.py, where a function
sums up function values of another function:
def f(x):
return x
def g(x):
return x**2
def sum_function_values(f, start, stop):
"""Sum up function values for integer arguments as
f(start) + f(start+1) + f(start+2) + ... + f(stop)"""
S = 0
for i in range(start, stop+1, 1):
S = S + f(i)
return S
print(’Sum with f becomes {:g}’.format(sum_function_values(f, 1, 3)))
print(’Sum with g becomes {:g}’.format(sum_function_values(g, 1, 3)))
We note that the function sum_function_values takes a function as its first
argument and repeatedly calls that function without (of course) knowing what that
function does, it just gets the function values back and sums them up!
Remember that the argument f in the function header sum_funcion_values
(f, start, stop) and the function defined by the name f, is not the same. The