## Overview

Teaching:15 min

Exercises:15 minQuestions

How do I write functions?

Objectives

Be able to write our own functions and use basic functional programming constructs like

`map()`

and`filter()`

.

Of course, at some point, we are going to want to define our own functions 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
```

## Practice defining functions

Define a function that converts from temperatures in fahrenheit to temperatures in kelvin, and another function that converts back again.

The general formula for the conversion from fahrenheit to kelvin is:

`kelvin = (fahr - 32) * 5 / 9 + 273.15`

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
True
```

`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
True
```

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
```

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 object 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 functions (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]
```

And a side-by-side example that demonstrates the difference between `map()`

and `filter()`

.

```
list(map(lambda x: x+100, [1,2,3,4,5]))
list(filter(lambda x: x<3, [1,2,3,4,5]))
```

```
[101, 102, 103, 104, 105] # map()
[1, 2] # filter()
```

## Using lambdas in practice

Add

`'-cheesecake'`

to every word in the following list using`map()`

.

`['new york', 'chocalate', 'new york', 'ketchup', 'mayo']`

Using

`filter()`

, remove the items which would be absolutely terrible to eat.

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.

```
import numpy as np
# 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]
```

## Removing np.nan values

Remove all of the

`np.nan`

values from the following sequence using logical indexing.

`np.array([np.nan, np.nan, 2, 3, 4, np.nan])`

## Key Points

`map()`

applies a function to every object in a data structure.

`filter()`

returns only the data objects for which some condition is true.