04 Python III — Functions

We are continuing from the previous lesson in the "work directory" ~/PHY494/04_python. We will use ipython and your text editor.

Functions

Functions package re-useable code and generalize code by allowing variable inputs. Writing code with functions is essential for debugging and reusability. If you have, say, 10 lines of code (or even less) that do something specific, consider making it a function.

Basic structure a of a python function

def func_name(arg1, arg2, ...):
    """documentation string (optional)"""
    # body
    ...
    return results

Repackage our step function:

# Heaviside step function

def heaviside(x):
   """Heaviside step function"""

   theta = None
   if x < 0:
      theta = 0.
   elif x == 0:
      theta = 0.5
   else:
      theta = 1.

   return theta

When you run it… then nothing happens: The function was defined but not called.

Now add at the end of heaviside.py

x = 3
theta = heaviside(x)

print("Theta({0}) = {1}".format(x, theta))

and run it. Now the function is being called (theta = heaviside(x)) and its return value assigned to the variable theta.

Activity: create functions

1. create a file myfuncs.py
2. add heaviside() to the file
3. add a function fahrenheit2kelvin() to convert from Fahrenheit to Kelvin ¹
4. add a function kelvin2celsius() to convert from Kelvin to Celsius (subtract 273.15).

Try out your functions (in ipython):

%run myfuncs.py

heaviside(5)
fahrenheit2kelvin(100)
kelvin2celsius(300)

kelvin2celsius(fahrenheit2kelvin(100))

should give ²

1.0
310.92777777777775
26.850000000000023
37.77777777777777

Activity: Plotting the step function

Perform this activity using pair programming³.

Use what you learnt about loops and functions to plot the Heaviside step function. Create a program step_plot.py that

1. defines the Heaviside step function \(\Theta(x)\) (use heaviside(x) from above);
2. generates a list of \(x\) values x_values = [-4, -3.5, -3, ..., 0, 0.5, 1, 1.5, ... 4];
3. evaluates \(\Theta(x)\) for all \(x\) values and stores the results in a list y_values;
4. prints the lists of \(x\) and \(y = \Theta(x)\) values; it should look like

    -4.0 0.0
    -3.5 0.0
    ...
    3.5 1.0
    4.0 1.0 
   

5. BONUS: plots \(\Theta(x)\) against \(x\); see the Basic Plotting example, namely you can use code like

   import matplotlib.pyplot as plt
   plt.plot(x_values, y_values, '-o', color="red", linewidth=2)
   plt.show()
   

Does your graph look the way that you expect it? ⁴

Advanced: Optional keyword arguments

Functions have arguments in their "call signature", e.g., the x in def heaviside(x) or x and y in a function area()

def area(x, y):
   """Calculate area of rectangle with lengths x and y"""
   return x*y

Let's assume that you might also want to be able to calculate the area when you scale the rectangle with a factor scale. Obviously you can do scale * area(x, y). You could also add a third argument

def area(x, y, scale):
   """Calculate scaled area of rectangle with lengths x and y and scale factor scale"""
   return scale*x*y

But this means that even for unscaled rectangles you will have to provide scale=1, i.e., area(x, y, 1).

With an optional argument you can set a default value that is used if the argument is not provided:

def area(x, y, scale=1):
   """Calculate scaled area of rectangle with lengths `x` and `y`.
   
   scale factor `scale` defaults to 1
   """
   return scale*x*y

which can be used as

x, y = 2, 10.5
area(x, y)             # uses scale=1
area(x, y, scale=0.5)
area(x, y, scale=2)
area(x, y, 2)          # DISCOURAGED, use scale=2

For further details see More on Defining Functions.

Footnotes