Functional programming

Of course, at some point, we are going to want to define our ownfunctions rather than just use the ones provided by Python and its various modules.

The general syntax for defining a function is as follows:

def function(arg1):
    # do stuff with arg1
    return ans

So, an example function that adds two numbers together might look a little like this:

def adder(x, y):
	return x + y

adder(1, 2)

3

We can also add a default argument (say if we wanted y to be equal to 10 unless we otherwise specified), by using an equals sign and a default value in our function definition:

def adder(x, y=10):
    return x + y

adder(5)

15

Conditional statements

We may also need to have our functions do specific things in some conditions, but not in others. This relies upon comparisons between items:

In python, comparison is done using the == operator:

True == True
True == False
'words' == 'words'

True
False

not indicates the opposite of True or False, and != means not equal to.

not True == False
True != False

True
True

As with other programming languages, we can make the usual comparisons with the > and < operators. Adding an equals sign (>=, <=) indicates less than or equal to or greater than or equal to.

5 < 10
5 > 10
-4 >= -4
1 <= 2

True
False
True
False

These statements can be combined with the if statement to produce code that executes at various times.

number = 5
if number <= 10:
	print('number was less than 10')

number was less than 10

If the if statement is not equal to True, the statement does not execute:

number = 11
if number <= 10:
	print('number was less than 10')

However, we can add code to execute when the if condition is not met by adding an else statement.

number = 11
if number <= 10:
	print('number was less than 10')
else:
	print('number was greater than 10')

number was greater than 10

And if we want to check an additional statement, we can use the elif keyword (else-if):

number = 10
if number <= 10:
	print('number was less than 10')
elif number == 10:
	print('number was equal to 10')
else:
	print('number was greater than 10')

One final note, to check if a value is equal to None in Python we must use is None and is not None. Normal == operators will not work.

None is None
5 is not None

True
True

Additionally, we can check if one value is in another set of values with the in operator:

5 in [4, 5, 6]
43 in [4, 5, 6]

True
False

map(), filter(), and anonymous (lambda) functions

Python has good support for functional programming, and has its own equivalents for map/reduce-style functionality. To “map” a function means to apply it to a set of elements. To “reduce” means to collapse a set of values to a single value. Finally, “filtering” means returning only a set of elements where a certain value is true.

Let’s explore what that means with our own functions. The syntax of map/reduce/filter is identical:

map(function, thing_to_iterate_over, next_thing_to_iterate_over)

Let’s apply this to a few test cases using map. Note that when selecting which function we are going to “map” with,

import math
values = [0, 1, 2, 3, 4, 5, 6]
map(math.sin, values)

<map at 0x7f31c246cba8>

To retrieve the actual values, we typically need to make the resulting output a list.

list(map(math.sin, values))

[0.0,
 0.8414709848078965,
 0.9092974268256817,
 0.1411200080598672,
 -0.7568024953079282,
 -0.9589242746631385,
 -0.27941549819892586]

filter() applies a similar operation, but instead of applying a function to every piece, it only returns points where a function returns true.

def less_than_3(val):
	return val < 3

list(filter(less_than_3, values))

[0, 1, 2]

That was very inconvenient. We had to define an entire function just to only use it once. The solution for this is to write a one-time use function that has no name. Such functions are called either anonymous functions or lamdba ufunctions (both mean the same thing).

To define a lambda function in python, the general syntax is as follows:

lambda x: x + 54

In this case, lambda x: indicates we are defining a lambda function with a single argument, x. Everything following the : is our function. Whatever value this evaluates to is automatically returned. So lambda x: x + 54 equates to:

def some_func(x):
	return x + 54

Rewriting our filter statement to use a lambda function:

list(filter(lambda x: x < 3, values))

[0, 1, 2]

map/filter style functionality with Numpy arrays

Although you could use a for-loop to apply a custom function to a numpy array in a single go, there is a handy np.vectorize() function you can use to convert your functions to a vectorized numpy equivalent. Note that this is purely for convenience - this uses a for-loop internally.

# create a function to perform cubes of a number
vector_cube = np.vectorize(lambda x: x ** 3)

vector_cube(np.array([1, 2, 3, 4, 5]))

array([  1,   8,  27,  64, 125])

To perform a similar option to filter(), you can actually specify a conditional statement inside the [] when indexing a Numpy array.

arr = np.array([1, 2, 3, 4, 5])
arr[arr >= 3]

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