Functions

Leverage the power of code recycling with functions. For interactive reading and executing code blocks Binder and find pyfun.ipynb, or install Python and JupyterLab locally.

What are functions?

Functions are a convenient way to divide code into handy, reusable and better readable blocks, which help structuring code. Blocks can accept parametric arguments and can be reused. Thus, functions are a key element for sharing code.

  • The def keyword followed by a function name with arguments in parentheses and a code block is what defines a function.

  • The type of arguments that a functions can receive are:

    • Required arguments: arg

    • Default keyword arguments (with default values): arg=value

    • Optional arguments: *args

    • Optional keyword arguments: **kwargs

Using optional (keyword) arguments makes functions more robust and flexible. The code block of a function is indented, similar to loops:

def my_function(argument1, *args, **kwargs):
    something = f(arguments)
    return something

A Basic Example

Three countries on earth use imperial units, while most other countries use the Système International (French: International System) of units (SI units). Let’s write a simple function to help imperial unit users converting feet (imperial) to meters (SI).

In the following example, the function name is feet_to_meter and the function accepts one argument, which is feet. The function returns the feet argument multiplied with a conversion_factor of 0.3048, which corresponds to the conversion factor from feet to meters. In this simple example the definition of the conversion_factor variable is not explicitly required.

Note

Internal variables (i.e., variables defined within a function), such as conversion_factor, are not accessible outside of the function.

def feet_to_meter(feet):
    conversion_factor = 0.3048
    return conversion_factor * feet

Function Calls

In order to call a function, it must be defined before the call. The function may be defined in the same script or in another script, which can than be imported as module (read more about modules and packages). Then we can call, for example, the above-defined feet_to_meter function as follows:

feet_value = 10
print("{0} feet are {1} meters.".format(feet_value, feet_to_meter(feet_value)))
10 feet are 3.048 meters.

Optional Arguments *args

Let’s replace the non-optional feet argument in the above function with an optional argument *args to enable the conversion of as many length values as the function receives. The following lines explain step by step how that works.

  1. We want to ensure that anyone understands the input and output parameters of the function. This is why we defined within a pair of triple double-apostrophes (""") input parameters (:params parameter_name: definition) and the function return (:output: definition).

  2. By default, we will assume that multiple values are provided. Therefore, a list called value_list in intantiated at the beginning of the function, while conversion_factor remains the same as before.

  3. A for-loop over *args identifies and processes the arguments provided. Why a for-loop? Well, Python recognizes *args automatically as a list, and therefore, we can iterate over *args, even though the provided range of values was not a list type.

  4. The for-loop in the try code block includes a try - except statement in order to verify if the provided values (arguments) are numeric and can be converted to meters. If the try block runs successfully, the expression arg * conversion_factor appends the converted argument arg to value_list.

  5. Eventually, the return keyword returns the value list.

def feet_to_meter(*args):
    """ 
    :param *args: numeric values in feet
    :output: returns list of values in meter
    """
    value_list = []
    conversion_factor = 0.3048
    for arg in args:
        try:
            value_list.append(arg * conversion_factor)
        except TypeError:
            print(str(arg) + " is not a number.")
    return value_list

With the newly defined and more flexible function, we can now call feet_to_meter with as many arguments as needed:

print("Function call with 3 values: ")
print(feet_to_meter(3, 1, 10))

print("Function call with no value: ")
print(feet_to_meter())

print("Function call with non-numeric values:")
print(feet_to_meter("just", "words"))

print("Function call with mixed numeric and non-numeric values:")
print(feet_to_meter("just", "words", 2))
Function call with 3 values: 
[0.9144000000000001, 0.3048, 3.048]
Function call with no value: 
[]
Function call with non-numeric values:
just is not a number.
words is not a number.
[]
Function call with mixed numeric and non-numeric values:
just is not a number.
words is not a number.
[0.6096]

Keyword Arguments **kwargs

In the last section, we made the feet_to_meter more flexible so that it can now receive as many arguments as needed. Since the first definition of the function, there is this internal conversion_factor variable, which was essentially useless because we could have directly used the value 0.3048 instead. Until now. Imagine we are writing this function for a historian. So in the past imperial units were wide spread in many cultures (e.g., Greek, Roman or Chinese) with varying length definitions between 0.250 m and 0.335 m. That means our historian will need flexibility regarding the conversion factor, while we still want to use 0.3048 m as default value. This job can be done with optional keyword arguments **kwargs an this is how we implement them:

  1. Add **kwargs after *args in the function def parentheses (the order of *args, **kwargs is important).

  2. Keep conversion_factor = 0.3048 as default value (we want the function to be functional also without any keyword argument provided).

  3. Similar to the *args statement, Python automatically identifies variables beginning with ** as optional keyword arguments (actually, the name args and kwargs does not matter - the * sign are important). The difference to *args is that Python identifies **kwargs as a dictionary.

  4. A for-loop iterates over the kwargs-dictionary and the if statement will identify any keyword argument that contains the string "conv" as conversion_factor.

  5. A try- except statement tests if the provided value for the keyword argument is numeric by attempting a conversion to float().

The remaining function is unchanged from above.

def feet_to_meter(*args, **kwargs):
    """ 
    :param *args: numeric values in feet
    :output: returns list of values in meter
    """
    value_list = []
    conversion_factor = 0.3048
    for k in kwargs.items():
            if "conv" in k[0]:
                try:
                    conversion_factor = float(k[1])
                    print("Using conversion factor = " + str(k[1]))
                except:
                    print(str(k[1]) + " is not a number (using default value 0.3048).")  
    
    for arg in args:
        try:
            value_list.append(arg * conversion_factor)
        except TypeError:
            print(str(arg) + " is not a number.")
    return value_list

With the newly defined flexibility of the feet_to_meter let’s test some different conversion factors:

print("Function call with 3 values and a conversion factor of 0.25: ")
print(feet_to_meter(3, 1, 10, conv_factor=0.25))

print("Function call with 3 values and a conversion factor of 1/7 with slightly different name: ")
print(feet_to_meter(3, 1, 10, conversion_factor=1/7))

print("Function call with 2 values with default conversion factor: ")
print(feet_to_meter(25, 10))
Function call with 3 values and a conversion factor of 0.25: 
Using conversion factor = 0.25
[0.75, 0.25, 2.5]
Function call with 3 values and a conversion factor of 1/7 with slightly different name: 
Using conversion factor = 0.14285714285714285
[0.42857142857142855, 0.14285714285714285, 1.4285714285714284]
Function call with 2 values with default conversion factor: 
[7.62, 3.048]

Default Keyword Arguments

Keyword arguments can also be defined by default. The below example shows how the conversion_factor can be defaulted in the def function parentheses. Note that conversion_factor must be defined after any optional arguments *args.

def feet_to_meter(*args, conversion_factor=0.3048):
    """ 
    :param *args: numeric values in feet
    :output: returns list of values in meter
    """
    value_list = []
   
    for arg in args:
        try:
            value_list.append(arg * conversion_factor)
        except TypeError:
            print(str(arg) + " is not a number.")
    return value_list

Now we can use feet_to_meter with or without or with a conversion factor and after the value list:

print("Function call with a conversion factor of 0.313 and two values: ")
print(feet_to_meter(1, 10, conversion_factor=0.313))
                    
print("Function call with 3 values without any conversion factor: ")
print(feet_to_meter(3, 1, 10))
Function call with a conversion factor of 0.313 and two values: 
[0.313, 3.13]
Function call with 3 values without any conversion factor: 
[0.9144000000000001, 0.3048, 3.048]

Function Wrappers and Decorators

If multiple functions contain similar lines, chances are that those functions can be further factorized by using function wrappers and decorators. A typical example is for example if a license checkout is needed in order to use a commercial Python module/package (e.g., Esri’s arcpy) or if we want to use a recurring error statement with try - except statements.

Consider two or more functions that should receive, process and produce numerical output from user input. These functions could look like this:

def multiply_arguments(*args):
    result = 1.0
    try:
        for arg in args:
            result *= arg
        print("The result is: " + str(result))
    except TypeError:
        print("ERROR: The calculation could not be performed failed (input arguments: %s)" % ", ".join(args))
    except ValueError:
        print("ERROR: The calculation could not be performed failed (input arguments: %s)" % ", ".join(args))
    return result

def sum_up_arguments(*args):
    result = 0.0
    try:
        for arg in args:
            result += arg
    except TypeError:
        print("ERROR: The calculation could not be performed failed (input arguments: %s)" % ", ".join(args))
    except ValueError:
        print("ERROR: The calculation could not be performed failed (input arguments: %s)" % ", ".join(args))   
    return result

Both functions involve the statement print("The result is: " + str(result)) to print the results to the Python console (e.g., to ensure get some intermediate information) and to run only on valid (i.e., numeric) input with the help of exception (try - except) statements. However, we want our functions to focus on the calculation only and this is where a wrapper function helps.

A wrapper function can be defined by first defining a normal function (e.g., def verify_result) and passing a function (func) as argument. In that function, we can then place a nested def wrapper() function that will embrace func. It is important to use both optional *args and optional keyword **kwargs in the wrapper and the call to func in order to make the wrapper as flexible as possible.

def verify_result(func):
    def wrapper(*args, **kwargs):
        try:
            result = func(*args, **kwargs)
            print("Success. The result is %1.3f." % float(result))
            return result
        except TypeError:
            print("ERROR: The calculation could not be performed because of at least one non-numeric input (input arguments: %s)" % str(args))
            return 0.0
        except ValueError:
            print("ERROR: The calculation could not be performed because of non-nmumeric input (input arguments: %s)" % str(args))
            return 0.0
    return wrapper

Now, we can use an @-decorator to wrap the above function in the verify_result(fun) function. When Python reads the beautiful, code-decorating @ sign, it will look for the wrapper function defined after the @ sign to wrap the following function.

@verify_result
def multiply_arguments(*args):
    result = 1.0
    for arg in args:
        result *= arg
    return result

@verify_result
def sum_up_arguments(*args):
    result = 0.0
    for arg in args:
        result += arg
    return result

The two functions (multiply_arguments and sum_up_arguments) can be called as usually, for example:

multiply_arguments(3, 4)
multiply_arguments(3, 4, "not a number")
sum_up_arguments(3, 4)
sum_up_arguments("absolutely", "no", "valid", "input")
Success. The result is 12.000.
ERROR: The calculation could not be performed because of at least one non-numeric input (input arguments: (3, 4, 'not a number'))
Success. The result is 7.000.
ERROR: The calculation could not be performed because of at least one non-numeric input (input arguments: ('absolutely', 'no', 'valid', 'input'))
0.0

The above wrapper function returns the wrapped function results, too. However, in order to use built-in function attributes (e.g., the function’s name with __name__, the function’s docstring with __doc__, or the module in which the function is defined with __module__) outside of the wrapper, we need the wrapper function to return the wrapped (decorated) function itself. This can be done as follows:

def error_func(*args, **kwargs):
    return 0.0

def verify_result(func):
    def wrapper(*args, **kwargs):
        try:
            return func(*args, **kwargs)
        except TypeError:
            print("ERROR: The calculation could not be performed because of at least one non-numeric input (input arguments: %s)" % str(args))
            return error_func(*args, **kwargs)
        except ValueError:
            print("ERROR: The calculation could not be performed because of non-nmumeric input (input arguments: %s)" % str(args))
            return error_func(*args, **kwargs)
    return wrapper

Note the difference: the wrapper function now returns func(*arg, **kwargs) instead of the numeric variable results. If the function can not be executed because of invalid input, the wrapper will return an error function (error_func), which ensures the consistency of the wrapper function. One may think that the error function returning 0.0 is obsolete, because the exception statements could directly return 0.0. However, 0.0 is a float variable, while error_func is a function and it is important that the function wrapper always returns the same data type, regardless of the an exception raise or successful execution. This is what makes code consistent.

This page shows examples for using the decorators in the shape of an @ sign to wrap (embrace) a function. Decorators are also a useful feature in classes, for example when a class function returns static values. Read more about decorators in classes later in the chapter about object orientation and classes.

Iterators and Generators

A characteristic of list, tuple, and dictionary data types is their iterability, which is provided by their __iter__ built-in method. For example, iterability is the for why we can write:

for e in [1, 2, 3]: print(e)
1
2
3

Besides iterations, Python also enables to create generators (i.e., generator functions). Instead of using a return statement, a generator function ends with a yield statement, that returns data as long as a next() function (inherent step in iterations) is called. An application of a generator is for example the flattening of nested lists (i.e., remove sub-lists and write all variables directly into a non-nested list):

from collections.abc import Iterable

def flatten(nested_list):
    for e in nested_list:
        if isinstance(e, Iterable) and not isinstance(e, str):
            for x in flatten(e):
                yield x
        else:
            yield e
            
a_nested_list = [[1, 2, 3], ["a", "b", "c"]]
flattened_list = list(flatten(a_nested_list))
print(flattened_list)
[1, 2, 3, 'a', 'b', 'c']

Note

The above example uses Iterable from the standard module collections.abc. More about importing packages and modules is discussed in the Modules & Packages section.

Lambda Functions

Lambda (λ) calculus is a formal language for expressing computation-based on function abstraction and was introduced in the 1930s by Alonzo Church and Stephen Cole Kleene. Lambda functions originate from functional programming and represent short, anonymous (i.e, without name) functions. Although Python is not inherently a functional programming language, functional concepts were implemented early in Python, for example with the map(), filter(), and deprecated reduce() functions and also the lambda operator.

In Python, an anonymous (nameless) lambda function can take any number of arguments, but can only have one expression. The list of arguments consists of a comma-separated list of variables and the expression uses these arguments. The syntax of lambda functions is:

lambda arguments : expression

The following example illustrates a lambda function with one argument and adds 1 to the argument:

add_one = lambda number : number + 1
print(add_one(1))
2

That was nice, but pretty useless. So here is an example of a lambda function that sums up two input arguments:

sum_up = lambda x, y : x + y
print(sum_up(1, 5))
6

The above-shown function for converting feet to meters can also be written as a lambda function:

feet_to_meter = lambda ft_value : ft_value * 0.3048
print(feet_to_meter(10))
3.048

Using a lambda function made the code here shorter and more efficient. In order to evaluate the feet_to_meter lambda function for multiple values, we can use the map() function. The syntax of a map() function is:

result = map(function, sequence)

where sequence can be a list or a tuple. Thus, to evaluate a tuple of four values, we can write:

four_ft_values = (4, 9.7, 7, 2)
print(list(map(feet_to_meter, four_ft_values)))
[1.2192, 2.95656, 2.1336, 0.6096]

The print statement converts the map() object into a list to evaluate the map() object (otherwise, the result would be somethine like <map object at ...>).

If the feet_to_meter function is not needed at another place in the code, one can also write:

print(list(map(lambda x : x * 0.3048, (4, 9.7, 7, 2))))
[1.2192, 2.95656, 2.1336, 0.6096]

Another feature are filter(function, list) objects which provide an elegant solution to filter out those elements from a list for which the function returns True. The following code block illustrates a filter that eliminates all numbers from the some_numbers list, which can be divided by three.

some_numbers = list(range(1, 10))
print(list(filter(lambda x: x % 3, some_numbers)))
[1, 2, 4, 5, 7, 8]

Formerly, the reduce() function to merge down list input into one value was implemented in Python. However, the Python developer Guido van Rossum successfully banned it from Python3 (read his post), which is why it is not used here.

Exercise

Get familiar with functions in the Hydraulics (1d) exercise.