Data Science from Scratch

Getting Python

You can download Python from python.org. But if you don’t already have Python, I recommend instead installing the Anaconda distribution, which already includes most of the libraries that you need to do data science.

As I write this, the latest version of Python is 3.4. At DataSciencester, however, we use old, reliable Python 2.7. Python 3 is not backward-compatible with Python 2, and many important libraries only work well with 2.7. The data science community is still firmly stuck on 2.7, which means we will be, too. Make sure to get that version.

If you don’t get Anaconda, make sure to install pip, which is a Python package manager that allows you to easily install third-party packages (some of which we’ll need). It’s also worth getting IPython, which is a much nicer Python shell to work with.

(If you installed Anaconda then it should have come with pip and IPython.)

Just run:

pip install ipython

and then search the Internet for solutions to whatever cryptic error messages that causes.

The Zen of Python

Python has a somewhat Zen description of its design principles, which you can also find inside the Python interpreter itself by typing import this.

One of the most discussed of these is:

There should be one—​and preferably only one—​obvious way to do it.

Code written in accordance with this “obvious” way (which may not be obvious at all to a newcomer) is often described as “Pythonic.” Although this is not a book about Python, we will occasionally contrast Pythonic and non-Pythonic ways of accomplishing the same things, and we will generally favor Pythonic solutions to our problems.

Whitespace Formatting

Many languages use curly braces to delimit blocks of code. Python uses indentation:

for i in [1, 2, 3, 4, 5]:
    print i                     # first line in "for i" block
    for j in [1, 2, 3, 4, 5]:
        print j                 # first line in "for j" block
        print i + j             # last line in "for j" block
    print i                     # last line in "for i" block
print "done looping"

This makes Python code very readable, but it also means that you have to be very careful with your formatting. Whitespace is ignored inside parentheses and brackets, which can be helpful for long-winded computations:

long_winded_computation = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 +
                           13 + 14 + 15 + 16 + 17 + 18 + 19 + 20)

and for making code easier to read:

list_of_lists = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

easier_to_read_list_of_lists = [ [1, 2, 3],
                                 [4, 5, 6],
                                 [7, 8, 9] ]

You can also use a backslash to indicate that a statement continues onto the next line, although we’ll rarely do this:

two_plus_three = 2 + \
                 3

One consequence of whitespace formatting is that it can be hard to copy and paste code into the Python shell. For example, if you tried to paste the code:

for i in [1, 2, 3, 4, 5]:

    # notice the blank line
    print i

into the ordinary Python shell, you would get a:

IndentationError: expected an indented block

because the interpreter thinks the blank line signals the end of the for loop’s block.

IPython has a magic function %paste, which correctly pastes whatever is on your clipboard, whitespace and all. This alone is a good reason to use IPython.

Modules

Certain features of Python are not loaded by default. These include both features included as part of the language as well as third-party features that you download yourself. In order to use these features, you’ll need to import the modules that contain them.

One approach is to simply import the module itself:

import re
my_regex = re.compile("[0-9]+", re.I)

Here re is the module containing functions and constants for working with regular expressions. After this type of import you can only access those functions by prefixing them with re..

If you already had a different re in your code you could use an alias:

import re as regex
my_regex = regex.compile("[0-9]+", regex.I)

You might also do this if your module has an unwieldy name or if you’re going to be typing it a lot. For example, when visualizing data with matplotlib, a standard convention is:

import matplotlib.pyplot as plt

If you need a few specific values from a module, you can import them explicitly and use them without qualification:

from collections import defaultdict, Counter
lookup = defaultdict(int)
my_counter = Counter()

If you were a bad person, you could import the entire contents of a module into your namespace, which might inadvertently overwrite variables you’ve already defined:

match = 10
from re import *    # uh oh, re has a match function
print match         # "<function re.match>"

However, since you are not a bad person, you won’t ever do this.

Arithmetic

Python 2.7 uses integer division by default, so that 5 / 2 equals 2. Almost always this is not what we want, so we will always start our files with:

from __future__ import division

after which 5 / 2 equals 2.5. Every code example in this book uses this new-style division. In the handful of cases where we need integer division, we can get it with a double slash: 5 // 2.

Functions

A function is a rule for taking zero or more inputs and returning a corresponding output. In Python, we typically define functions using def:

def double(x):
    """this is where you put an optional docstring
    that explains what the function does.
    for example, this function multiplies its input by 2"""
    return x * 2

Python functions are first-class, which means that we can assign them to variables and pass them into functions just like any other arguments:

def apply_to_one(f):
    """calls the function f with 1 as its argument"""
    return f(1)

my_double = double             # refers to the previously defined function
x = apply_to_one(my_double)    # equals 2

It is also easy to create short anonymous functions, or lambdas:

y = apply_to_one(lambda x: x + 4)      # equals 5

You can assign lambdas to variables, although most people will tell you that you should just use def instead:

another_double = lambda x: 2 * x       # don't do this
def another_double(x): return 2 * x    # do this instead

Function parameters can also be given default arguments, which only need to be specified when you want a value other than the default:

def my_print(message="my default message"):
    print message

my_print("hello")   # prints 'hello'
my_print()          # prints 'my default message'

It is sometimes useful to specify arguments by name:

def subtract(a=0, b=0):
    return a - b

subtract(10, 5) # returns 5
subtract(0, 5)  # returns -5
subtract(b=5)   # same as previous

We will be creating many, many functions.

Strings

Strings can be delimited by single or double quotation marks (but the quotes have to match):

single_quoted_string = 'data science'
double_quoted_string = "data science"

Python uses backslashes to encode special characters. For example:

tab_string = "\t"       # represents the tab character
len(tab_string)         # is 1

If you want backslashes as backslashes (which you might in Windows directory names or in regular expressions), you can create raw strings using r””:

not_tab_string = r"\t"  # represents the characters '\' and 't'
len(not_tab_string)     # is 2

You can create multiline strings using triple-[double-]-quotes:

multi_line_string = """This is the first line.
and this is the second line
and this is the third line"""

Exceptions

When something goes wrong, Python raises an exception. Unhandled, these will cause your program to crash. You can handle them using try and except:

try:
    print 0 / 0
except ZeroDivisionError:
    print "cannot divide by zero"

Although in many languages exceptions are considered bad, in Python there is no shame in using them to make your code cleaner, and we will occasionally do so.

Lists

Probably the most fundamental data structure in Python is the list. A list is simply an ordered collection. (It is similar to what in other languages might be called an array, but with some added functionality.)

integer_list = [1, 2, 3]
heterogeneous_list = ["string", 0.1, True]
list_of_lists = [ integer_list, heterogeneous_list, [] ]

list_length = len(integer_list)     # equals 3
list_sum    = sum(integer_list)     # equals 6

You can get or set the nth element of a list with square brackets:

x = range(10)   # is the list [0, 1, ..., 9]
zero = x[0]     # equals 0, lists are 0-indexed
one = x[1]      # equals 1
nine = x[-1]    # equals 9, 'Pythonic' for last element
eight = x[-2]   # equals 8, 'Pythonic' for next-to-last element
x[0] = -1       # now x is [-1, 1, 2, 3, ..., 9]

You can also use square brackets to “slice” lists:

first_three   = x[:3]               # [-1, 1, 2]
three_to_end = x[3:]                # [3, 4, ..., 9]
one_to_four = x[1:5]                # [1, 2, 3, 4]
last_three = x[-3:]                 # [7, 8, 9]
without_first_and_last = x[1:-1]    # [1, 2, ..., 8]
copy_of_x = x[:]                    # [-1, 1, 2, ..., 9]

Python has an in operator to check for list membership:

1 in [1, 2, 3]    # True
0 in [1, 2, 3]    # False

This check involves examining the elements of the list one at a time, which means that you probably shouldn’t use it unless you know your list is pretty small (or unless you don’t care how long the check takes).

It is easy to concatenate lists together:

x = [1, 2, 3]
x.extend([4, 5, 6])     # x is now [1,2,3,4,5,6]

If you don’t want to modify x you can use list addition:

x = [1, 2, 3]
y = x + [4, 5, 6]       # y is [1, 2, 3, 4, 5, 6]; x is unchanged

More frequently we will append to lists one item at a time:

x = [1, 2, 3]
x.append(0)      # x is now [1, 2, 3, 0]
y = x[-1]        # equals 0
z = len(x)       # equals 4

It is often convenient to unpack lists if you know how many elements they contain:

x, y = [1, 2]    # now x is 1, y is 2

although you will get a ValueError if you don’t have the same numbers of elements on both sides.

It’s common to use an underscore for a value you’re going to throw away:

_, y = [1, 2]    # now y == 2, didn't care about the first element

Tuples

Tuples are lists’ immutable cousins. Pretty much anything you can do to a list that doesn’t involve modifying it, you can do to a tuple. You specify a tuple by using parentheses (or nothing) instead of square brackets:

my_list = [1, 2]
my_tuple = (1, 2)
other_tuple = 3, 4
my_list[1] = 3      # my_list is now [1, 3]

try:
    my_tuple[1] = 3
except TypeError:
    print "cannot modify a tuple"

Tuples are a convenient way to return multiple values from functions:

def sum_and_product(x, y):
    return (x + y),(x * y)

sp = sum_and_product(2, 3)    # equals (5, 6)
s, p = sum_and_product(5, 10) # s is 15, p is 50

Tuples (and lists) can also be used for multiple assignment:

x, y = 1, 2     # now x is 1, y is 2
x, y = y, x     # Pythonic way to swap variables; now x is 2, y is 1

Dictionaries

Another fundamental data structure is a dictionary, which associates values with keys and allows you to quickly retrieve the value corresponding to a given key:

empty_dict = {}                         # Pythonic
empty_dict2 = dict()                    # less Pythonic
grades = { "Joel" : 80, "Tim" : 95 }    # dictionary literal

You can look up the value for a key using square brackets:

joels_grade = grades["Joel"]            # equals 80

But you’ll get a KeyError if you ask for a key that’s not in the dictionary:

try:
    kates_grade = grades["Kate"]
except KeyError:
    print "no grade for Kate!"

You can check for the existence of a key using in:

joel_has_grade = "Joel" in grades     # True
kate_has_grade = "Kate" in grades     # False

Dictionaries have a get method that returns a default value (instead of raising an exception) when you look up a key that’s not in the dictionary:

joels_grade = grades.get("Joel", 0)   # equals 80
kates_grade = grades.get("Kate", 0)   # equals 0
no_ones_grade = grades.get("No One")  # default default is None

You assign key-value pairs using the same square brackets:

grades["Tim"] = 99                    # replaces the old value
grades["Kate"] = 100                  # adds a third entry
num_students = len(grades)            # equals 3

We will frequently use dictionaries as a simple way to represent structured data:

tweet = {
    "user" : "joelgrus",
    "text" : "Data Science is Awesome",
    "retweet_count" : 100,
    "hashtags" : ["#data", "#science", "#datascience", "#awesome", "#yolo"]
}

Besides looking for specific keys we can look at all of them:

tweet_keys   = tweet.keys()     # list of keys
tweet_values = tweet.values()   # list of values
tweet_items  = tweet.items()    # list of (key, value) tuples

"user" in tweet_keys            # True, but uses a slow list in
"user" in tweet                 # more Pythonic, uses faster dict in
"joelgrus" in tweet_values      # True

Dictionary keys must be immutable; in particular, you cannot use lists as keys. If you need a multipart key, you should use a tuple or figure out a way to turn the key into a string.

word_counts = {}
for word in document:
    if word in word_counts:
        word_counts[word] += 1
    else:
        word_counts[word] = 1

word_counts = {}
for word in document:
    try:
        word_counts[word] += 1
    except KeyError:
        word_counts[word] = 1

word_counts = {}
for word in document:
    previous_count = word_counts.get(word, 0)
    word_counts[word] = previous_count + 1

from collections import defaultdict

word_counts = defaultdict(int)          # int() produces 0
for word in document:
    word_counts[word] += 1

dd_list = defaultdict(list)             # list() produces an empty list
dd_list[2].append(1)                    # now dd_list contains {2: [1]}

dd_dict = defaultdict(dict)             # dict() produces an empty dict
dd_dict["Joel"]["City"] = "Seattle"     # { "Joel" : { "City" : Seattle"}}

dd_pair = defaultdict(lambda: [0, 0])
dd_pair[2][1] = 1                       # now dd_pair contains {2: [0,1]}

from collections import Counter
c = Counter([0, 1, 2, 0])          # c is (basically) { 0 : 2, 1 : 1, 2 : 1 }

word_counts = Counter(document)

# print the 10 most common words and their counts
for word, count in word_counts.most_common(10):
    print word, count

Sets

Another data structure is set, which represents a collection of distinct elements:

s = set()
s.add(1)       # s is now { 1 }
s.add(2)       # s is now { 1, 2 }
s.add(2)       # s is still { 1, 2 }
x = len(s)     # equals 2
y = 2 in s     # equals True
z = 3 in s     # equals False

We’ll use sets for two main reasons. The first is that in is a very fast operation on sets. If we have a large collection of items that we want to use for a membership test, a set is more appropriate than a list:

stopwords_list = ["a","an","at"] + hundreds_of_other_words + ["yet", "you"]

"zip" in stopwords_list     # False, but have to check every element

stopwords_set = set(stopwords_list)
"zip" in stopwords_set      # very fast to check

The second reason is to find the distinct items in a collection:

item_list = [1, 2, 3, 1, 2, 3]
num_items = len(item_list)                # 6
item_set = set(item_list)                 # {1, 2, 3}
num_distinct_items = len(item_set)        # 3
distinct_item_list = list(item_set)       # [1, 2, 3]

We’ll use sets much less frequently than dicts and lists.

Control Flow

As in most programming languages, you can perform an action conditionally using if:

if 1 > 2:
    message = "if only 1 were greater than two..."
elif 1 > 3:
    message = "elif stands for 'else if'"
else:
    message = "when all else fails use else (if you want to)"

You can also write a ternary if-then-else on one line, which we will do occasionally:

parity = "even" if x % 2 == 0 else "odd"

Python has a while loop:

x = 0
while x < 10:
    print x, "is less than 10"
    x += 1

although more often we’ll use for and in:

for x in range(10):
    print x, "is less than 10"

If you need more-complex logic, you can use continue and break:

for x in range(10):
    if x == 3:
        continue  # go immediately to the next iteration
    if x == 5:
        break     # quit the loop entirely
    print x

This will print 0, 1, 2, and 4.

Truthiness

Booleans in Python work as in most other languages, except that they’re capitalized:

one_is_less_than_two = 1 < 2          # equals True
true_equals_false = True == False     # equals False

Python uses the value None to indicate a nonexistent value. It is similar to other languages’ null:

x = None
print x == None    # prints True, but is not Pythonic
print x is None    # prints True, and is Pythonic

Python lets you use any value where it expects a Boolean. The following are all “Falsy”:

• False
• None
• [] (an empty list)
• {} (an empty dict)
• “”
• set()
• 0
• 0.0

Pretty much anything else gets treated as True. This allows you to easily use if statements to test for empty lists or empty strings or empty dictionaries or so on. It also sometimes causes tricky bugs if you’re not expecting this behavior:

s = some_function_that_returns_a_string()
if s:
    first_char = s[0]
else:
    first_char = ""

A simpler way of doing the same is:

first_char = s and s[0]

since and returns its second value when the first is “truthy,” the first value when it’s not. Similarly, if x is either a number or possibly None:

safe_x = x or 0

is definitely a number.

Python has an all function, which takes a list and returns True precisely when every element is truthy, and an any function, which returns True when at least one element is truthy:

all([True, 1, { 3 }])   # True
all([True, 1, {}])      # False, {} is falsy
any([True, 1, {}])      # True, True is truthy
all([])                 # True, no falsy elements in the list
any([])                 # False, no truthy elements in the list

Sorting

Every Python list has a sort method that sorts it in place. If you don’t want to mess up your list, you can use the sorted function, which returns a new list:

x = [4,1,2,3]
y = sorted(x)     # is [1,2,3,4], x is unchanged
x.sort()          # now x is [1,2,3,4]

By default, sort (and sorted) sort a list from smallest to largest based on naively comparing the elements to one another.

If you want elements sorted from largest to smallest, you can specify a reverse=True parameter. And instead of comparing the elements themselves, you can compare the results of a function that you specify with key:

# sort the list by absolute value from largest to smallest
x = sorted([-4,1,-2,3], key=abs, reverse=True)  # is [-4,3,-2,1]

# sort the words and counts from highest count to lowest
wc = sorted(word_counts.items(),
            key=lambda (word, count): count,
            reverse=True)

List Comprehensions

Frequently, you’ll want to transform a list into another list, by choosing only certain elements, or by transforming elements, or both. The Pythonic way of doing this is list comprehensions:

even_numbers = [x for x in range(5) if x % 2 == 0]  # [0, 2, 4]
squares      = [x * x for x in range(5)]            # [0, 1, 4, 9, 16]
even_squares = [x * x for x in even_numbers]        # [0, 4, 16]

You can similarly turn lists into dictionaries or sets:

square_dict = { x : x * x for x in range(5) }  # { 0:0, 1:1, 2:4, 3:9, 4:16 }
square_set  = { x * x for x in [1, -1] }       # { 1 }

If you don’t need the value from the list, it’s conventional to use an underscore as the variable:

zeroes = [0 for _ in even_numbers]      # has the same length as even_numbers

A list comprehension can include multiple fors:

pairs = [(x, y)
         for x in range(10)
         for y in range(10)]   # 100 pairs (0,0) (0,1) ... (9,8), (9,9)

and later fors can use the results of earlier ones:

increasing_pairs = [(x, y)                       # only pairs with x < y,
                    for x in range(10)           # range(lo, hi) equals
                    for y in range(x + 1, 10)]   # [lo, lo + 1, ..., hi - 1]

We will use list comprehensions a lot.

Generators and Iterators

A problem with lists is that they can easily grow very big. range(1000000) creates an actual list of 1 million elements. If you only need to deal with them one at a time, this can be a huge source of inefficiency (or of running out of memory). If you potentially only need the first few values, then calculating them all is a waste.

A generator is something that you can iterate over (for us, usually using for) but whose values are produced only as needed (lazily).

One way to create generators is with functions and the yield operator:

def lazy_range(n):
    """a lazy version of range"""
    i = 0
    while i < n:
        yield i
        i += 1

The following loop will consume the yielded values one at a time until none are left:

for i in lazy_range(10):
    do_something_with(i)

(Python actually comes with a lazy_range function called xrange, and in Python 3, range itself is lazy.) This means you could even create an infinite sequence:

def natural_numbers():
    """returns 1, 2, 3, ..."""
    n = 1
    while True:
        yield n
        n += 1

although you probably shouldn’t iterate over it without using some kind of break logic.

A second way to create generators is by using for comprehensions wrapped in parentheses:

lazy_evens_below_20 = (i for i in lazy_range(20) if i % 2 == 0)

Recall also that every dict has an items() method that returns a list of its key-value pairs. More frequently we’ll use the iteritems() method, which lazily yields the key-value pairs one at a time as we iterate over it.

Randomness

As we learn data science, we will frequently need to generate random numbers, which we can do with the random module:

import random

four_uniform_randoms = [random.random() for _ in range(4)]

#  [0.8444218515250481,      # random.random() produces numbers
#   0.7579544029403025,      # uniformly between 0 and 1
#   0.420571580830845,       # it's the random function we'll use
#   0.25891675029296335]     # most often

The random module actually produces pseudorandom (that is, deterministic) numbers based on an internal state that you can set with random.seed if you want to get reproducible results:

random.seed(10)         # set the seed to 10
print random.random()   # 0.57140259469
random.seed(10)         # reset the seed to 10
print random.random()   # 0.57140259469 again

We’ll sometimes use random.randrange, which takes either 1 or 2 arguments and returns an element chosen randomly from the corresponding range():

random.randrange(10)    # choose randomly from range(10) = [0, 1, ..., 9]
random.randrange(3, 6)  # choose randomly from range(3, 6) = [3, 4, 5]

There are a few more methods that we’ll sometimes find convenient. random.shuffle randomly reorders the elements of a list:

up_to_ten = range(10)
random.shuffle(up_to_ten)
print up_to_ten
# [2, 5, 1, 9, 7, 3, 8, 6, 4, 0]   (your results will probably be different)

If you need to randomly pick one element from a list you can use random.choice:

my_best_friend = random.choice(["Alice", "Bob", "Charlie"])     # "Bob" for me

And if you need to randomly choose a sample of elements without replacement (i.e., with no duplicates), you can use random.sample:

lottery_numbers = range(60)
winning_numbers = random.sample(lottery_numbers, 6)  # [16, 36, 10, 6, 25, 9]

To choose a sample of elements with replacement (i.e., allowing duplicates), you can just make multiple calls to random.choice:

four_with_replacement = [random.choice(range(10))
                         for _ in range(4)]
# [9, 4, 4, 2]

Regular Expressions

Regular expressions provide a way of searching text. They are incredibly useful but also fairly complicated, so much so that there are entire books written about them. We will explain their details the few times we encounter them; here are a few examples of how to use them in Python:

import re

print all([                                # all of these are true, because
    not re.match("a", "cat"),              # * 'cat' doesn't start with 'a'
    re.search("a", "cat"),                 # * 'cat' has an 'a' in it
    not re.search("c", "dog"),             # * 'dog' doesn't have a 'c' in it
    3 == len(re.split("[ab]", "carbs")),   # * split on a or b to ['c','r','s']
    "R-D-" == re.sub("[0-9]", "-", "R2D2") # * replace digits with dashes
    ])  # prints True

Object-Oriented Programming

Like many languages, Python allows you to define classes that encapsulate data and the functions that operate on them. We’ll use them sometimes to make our code cleaner and simpler. It’s probably simplest to explain them by constructing a heavily annotated example.

Imagine we didn’t have the built-in Python set. Then we might want to create our own Set class.

What behavior should our class have? Given an instance of Set, we’ll need to be able to add items to it, remove items from it, and check whether it contains a certain value. We’ll create all of these as member functions, which means we’ll access them with a dot after a Set object:

# by convention, we give classes PascalCase names
class Set:

    # these are the member functions
    # every one takes a first parameter "self" (another convention)
    # that refers to the particular Set object being used

    def __init__(self, values=None):
        """This is the constructor.
        It gets called when you create a new Set.
        You would use it like
        s1 = Set()          # empty set
        s2 = Set([1,2,2,3]) # initialize with values"""

        self.dict = {} # each instance of Set has its own dict property
                       # which is what we'll use to track memberships
        if values is not None:
            for value in values:
                self.add(value)

    def __repr__(self):
        """this is the string representation of a Set object
        if you type it at the Python prompt or pass it to str()"""
        return "Set: " + str(self.dict.keys())

    # we'll represent membership by being a key in self.dict with value True
    def add(self, value):
        self.dict[value] = True

    # value is in the Set if it's a key in the dictionary
    def contains(self, value):
        return value in self.dict

    def remove(self, value):
        del self.dict[value]

Which we could then use like:

s = Set([1,2,3])
s.add(4)
print s.contains(4)     # True
s.remove(3)
print s.contains(3)     # False

Functional Tools

When passing functions around, sometimes we’ll want to partially apply (or curry) functions to create new functions. As a simple example, imagine that we have a function of two variables:

def exp(base, power):
    return base ** power

and we want to use it to create a function of one variable two_to_the whose input is a power and whose output is the result of exp(2, power).

We can, of course, do this with def, but this can sometimes get unwieldy:

def two_to_the(power):
    return exp(2, power)

A different approach is to use functools.partial:

from functools import partial
two_to_the = partial(exp, 2)     # is now a function of one variable
print two_to_the(3)              # 8

You can also use partial to fill in later arguments if you specify their names:

square_of = partial(exp, power=2)
print square_of(3)                  # 9

It starts to get messy if you curry arguments in the middle of the function, so we’ll try to avoid doing that.

We will also occasionally use map, reduce, and filter, which provide functional alternatives to list comprehensions:

def double(x):
    return 2 * x

xs = [1, 2, 3, 4]
twice_xs = [double(x) for x in xs]        # [2, 4, 6, 8]
twice_xs = map(double, xs)                # same as above
list_doubler = partial(map, double)       # *function* that doubles a list
twice_xs = list_doubler(xs)               # again [2, 4, 6, 8]

You can use map with multiple-argument functions if you provide multiple lists:

def multiply(x, y): return x * y

products = map(multiply, [1, 2], [4, 5]) # [1 * 4, 2 * 5] = [4, 10]

Similarly, filter does the work of a list-comprehension if:

def is_even(x):
    """True if x is even, False if x is odd"""
    return x % 2 == 0

x_evens = [x for x in xs if is_even(x)]    # [2, 4]
x_evens = filter(is_even, xs)              # same as above
list_evener = partial(filter, is_even)     # *function* that filters a list
x_evens = list_evener(xs)                  # again [2, 4]

And reduce combines the first two elements of a list, then that result with the third, that result with the fourth, and so on, producing a single result:

x_product = reduce(multiply, xs)           # = 1 * 2 * 3 * 4 = 24
list_product = partial(reduce, multiply)   # *function* that reduces a list
x_product = list_product(xs)               # again = 24

enumerate

Not infrequently, you’ll want to iterate over a list and use both its elements and their indexes:

# not Pythonic
for i in range(len(documents)):
    document = documents[i]
    do_something(i, document)

# also not Pythonic
i = 0
for document in documents:
    do_something(i, document)
    i += 1

The Pythonic solution is enumerate, which produces tuples (index, element):

for i, document in enumerate(documents):
    do_something(i, document)

Similarly, if we just want the indexes:

for i in range(len(documents)): do_something(i)     # not Pythonic
for i, _ in enumerate(documents): do_something(i)   # Pythonic

We’ll use this a lot.

zip and Argument Unpacking

Often we will need to zip two or more lists together. zip transforms multiple lists into a single list of tuples of corresponding elements:

list1 = ['a', 'b', 'c']
list2 = [1, 2, 3]
zip(list1, list2)        # is [('a', 1), ('b', 2), ('c', 3)]

If the lists are different lengths, zip stops as soon as the first list ends.

You can also “unzip” a list using a strange trick:

pairs = [('a', 1), ('b', 2), ('c', 3)]
letters, numbers = zip(*pairs)

The asterisk performs argument unpacking, which uses the elements of pairs as individual arguments to zip. It ends up the same as if you’d called:

zip(('a', 1), ('b', 2), ('c', 3))

which returns [('a','b','c'), ('1','2','3')].

You can use argument unpacking with any function:

def add(a, b): return a + b

add(1, 2)      # returns 3
add([1, 2])    # TypeError!
add(*[1, 2])   # returns 3

It is rare that we’ll find this useful, but when we do it’s a neat trick.

args and kwargs

Let’s say we want to create a higher-order function that takes as input some function f and returns a new function that for any input returns twice the value of f:

def doubler(f):
    def g(x):
        return 2 * f(x)
    return g

This works in some cases:

def f1(x):
    return x + 1

g = doubler(f1)
print g(3)          # 8 (== ( 3 + 1) * 2)
print g(-1)         # 0 (== (-1 + 1) * 2)

However, it breaks down with functions that take more than a single argument:

def f2(x, y):
    return x + y

g = doubler(f2)
print g(1, 2)    # TypeError: g() takes exactly 1 argument (2 given)

What we need is a way to specify a function that takes arbitrary arguments. We can do this with argument unpacking and a little bit of magic:

def magic(*args, **kwargs):
    print "unnamed args:", args
    print "keyword args:", kwargs

magic(1, 2, key="word", key2="word2")

# prints
#  unnamed args: (1, 2)
#  keyword args: {'key2': 'word2', 'key': 'word'}

That is, when we define a function like this, args is a tuple of its unnamed arguments and kwargs is a dict of its named arguments. It works the other way too, if you want to use a list (or tuple) and dict to supply arguments to a function:

def other_way_magic(x, y, z):
    return x + y + z

x_y_list = [1, 2]
z_dict = { "z" : 3 }
print other_way_magic(*x_y_list, **z_dict)   # 6

You could do all sorts of strange tricks with this; we will only use it to produce higher-order functions whose inputs can accept arbitrary arguments:

def doubler_correct(f):
    """works no matter what kind of inputs f expects"""
    def g(*args, **kwargs):
        """whatever arguments g is supplied, pass them through to f"""
        return 2 * f(*args, **kwargs)
    return g

g = doubler_correct(f2)
print g(1, 2) # 6

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