tl;dr: We demonstrate data workflows with Python data structures and PyToolz. We also introduce join, a new operation in toolz.

## Prelude

In my last two posts I show that Python data structures are fast and that CyToolz, an implementation of toolz in Cython, achieves Java speeds on standard Python core data structures like dicts, lists, and tuples. As a reminder, toolz provides functions like groupby

>>> from toolz import groupby

>>> names = ['Alice', 'Bob', 'Charlie', 'Dan', 'Edith', 'Frank']
>>> groupby(len, names)
{3: ['Bob', 'Dan'],
5: ['Alice', 'Edith', 'Frank'],
7: ['Charlie']}

I always give this example when talking about toolz. It often spurs the following question:

That looks like GROUP BY from SQL. In what other ways does toolz let me do SQL-like operations in Python?

My answer for this is to go look at Pandas which really does a wonderful job at in-memory data analytics. Toolz targets functional programming more than it targets data analytics. Still this question is common enough to warrant a blogpost. The following is my stock answer on how to use pure Python and toolz (or cytoolz) for streaming data analytic workflows like selections, split-apply-combine, and joins. I’ll note throughout when operations are streaming (can support datasets bigger than memory) or not. This is one of the few ways in which analysis with toolz might be preferred over pandas.

# Streaming Analytics

The toolz functions can be composed to analyze large streaming datasets. Toolz supports common analytics patterns like the selection, grouping, reduction, and joining of data through pure composable functions. These functions often have analogs to familiar operations in other data analytics platforms like SQL or Pandas.

Throughout this post we’ll use this simple dataset of accounts.

>>> #           id, name, balance, gender
>>> accounts = [(1, 'Alice', 100, 'F'),
...             (2, 'Bob', 200, 'M'),
...             (3, 'Charlie', 150, 'M'),
...             (4, 'Dennis', 50, 'M'),
...             (5, 'Edith', 300, 'F')]

## Selecting with map and filter

Simple projection and linear selection from a sequence is achieved through the standard functions map and filter.

SELECT name, balance
FROM accounts
WHERE balance > 150;

These functions correspond to the SQL commands SELECT and WHERE.

>>> from toolz.curried import pipe, map, filter, get

>>> pipe(accounts, filter(lambda (id, name, balance, gender): balance > 150),
...                map(get([1, 2])),
...                list)

note: this uses the curried versions of map and reduce.

Of course, these operations are also well supported with standard list/generator comprehension syntax. This syntax is more often used and generally considered to be more Pythonic.

>>> [(name, balance) for (id, name, balance, gender) in accounts
...                  if balance > 150]

## Split-apply-combine with groupby and reduceby

We separate split-apply-combine operations into the following two concepts

1. Split the dataset into groups by some property
2. Reduce each of the groups with some aggregation function

Toolz supports this common workflow with

1. a simple in-memory solution
2. a more sophisticated streaming solution.

### In Memory Split-Apply-Combine

The in-memory solution depends on the functions groupby to split, and valmap to apply/combine.

SELECT gender, SUM(balance)
FROM accounts
GROUP BY gender;

We first show groupby and valmap separately to show the intermediate groups.

>>> from toolz import groupby, valmap, compose
>>> from toolz.curried import get, pluck

>>> groupby(get(3), accounts)
{'F': [(1, 'Alice', 100, 'F'), (5, 'Edith', 300, 'F')],
'M': [(2, 'Bob', 200, 'M'), (3, 'Charlie', 150, 'M'), (4, 'Dennis', 50, 'M')]}

>>> valmap(compose(sum, pluck(2)),
...        _)
{'F': 400, 'M': 400}

Then we chain them together into a single computation

>>> pipe(accounts, groupby(get(3)),
...                valmap(compose(sum, pluck(2))))
{'F': 400, 'M': 400}

### Streaming Split-Apply-Combine

The groupby function collects the entire dataset in memory into a dictionary. While convenient, the groupby operation is not streaming and so this approach is limited to datasets that can fit comfortably into memory.

Toolz achieves streaming split-apply-combine with reduceby, a function that performs a simultaneous reduction on each group as the elements stream in. To understand this section you should first be familiar with the builtin function reduce.

The reduceby operation takes a key function, like get(3) or lambda x: x[3], and a binary operator like add or lesser = lambda acc, x: acc if acc < x else x. It successively applies the key function to each item in succession, accumulating running totals for each key by combining each new value with the previous total using the binary operator. It can’t accept full reduction operations like sum or min as these require access to the entire group at once. Here is a simple example:

>>> from toolz import reduceby

>>> def iseven(n):
...     return n % 2 == 0

...     return x + y

>>> reduceby(iseven, add, [1, 2, 3, 4])
{True: 6, False: 4}

The even numbers are added together (2 + 4 = 6) into group True, and the odd numbers are added together (1 + 3 = 4) into group False.

Note that we have to replace the reduction sum with the binary operator add. The incremental nature of add allows us to do the summation work as new data comes in. The use of binary operators like add over full reductions like sum enables computation on very large streaming datasets.

The challenge to using reduceby often lies in the construction of a suitable binary operator. Here is the solution for our accounts example that adds up the balances for each group:

>>> binop = lambda total, (id, name, bal, gend): total + bal

>>> reduceby(get(3), binop, accounts)
{'F': 400, 'M': 400}

This construction supports datasets that are much larger than available memory. Only the output must be able to fit comfortably in memory and this is rarely an issue, even for very large split-apply-combine computations.

## Semi-Streaming join

We register multiple datasets together with join. Consider a second dataset that stores addresses by ID:

>>> addresses = [(1, '123 Main Street'),  # id, address
...              (5, '34 Rue St Michel')]

We can join this dataset against our accounts dataset by specifying attributes which register different elements with each other; in this case they share a common first column, id.

SELECT accounts.name, addresses.address
WHERE accounts.id = addresses.id;
>>> from toolz import join, first, second

>>> result = join(first, accounts,

>>> for ((id, name, bal, gender), (id, address)) in result:
('Alice', '123 Main Street')
('Edith', '34 Rue St Michel')

Join takes four main arguments, a left and right key function and a left and right sequence. It returns a sequence of pairs of matching items. In our case the return value of join is a sequence of pairs of tuples such that the first element of each tuple (the ID) is the same. In the example above we unpack this pair of tuples to get the fields that we want (name and address) from the result.

### Join on arbitrary functions / data

Those familiar with SQL are accustomed to this kind of join on columns. However a functional join is more general than this; it doesn’t need to operate on tuples, and key functions do not need to get particular columns. In the example below we match numbers from two collections so that exactly one is even and one is odd.

>>> def iseven(n):
...     return n % 2 == 0
>>> def isodd(n):
...     return n % 2 == 1

>>> list(join(iseven, [1, 2, 3, 4],
...           isodd, [7, 8, 9]))
[(2, 7), (4, 7), (1, 8), (3, 8), (2, 9), (4, 9)]

### Semi-Streaming Join

The Toolz Join operation fully evaluates the left sequence and streams the right sequence through memory. Thus, if streaming support is desired the larger of the two sequences should always occupy the right side of the join.

### Algorithmic Details

The semi-streaming join operation in toolz is asymptotically optimal. Computationally it is linear in the size of the input + output. In terms of storage the left sequence must fit in memory but the right sequence is free to stream.

The results are not normalized, as in SQL, in that they permit repeated values. If normalization is desired, consider composing with the function unique (note that unique is not fully streaming.)

### More Complex Example

The accounts example above connects two one-to-one relationships, accounts and addresses; there was exactly one name per ID and one address per ID. This need not be the case. The join abstraction is sufficiently flexible to join one-to-many or even many-to-many relationships. The following example finds city/person pairs where that person has a friend who has a residence in that city. This is an example of joining two many-to-many relationships because a person may have many friends and because a friend may have many residences.

>>> friends = [('Alice', 'Edith'),
...            ('Alice', 'Zhao'),
...            ('Edith', 'Alice'),
...            ('Zhao', 'Alice'),
...            ('Zhao', 'Edith')]

>>> cities = [('Alice', 'NYC'),
...           ('Alice', 'Chicago'),
...           ('Dan', 'Syndey'),
...           ('Edith', 'Paris'),
...           ('Edith', 'Berlin'),
...           ('Zhao', 'Shanghai')]

>>> # Vacation opportunities
>>> # In what cities do people have friends?
>>> result = join(second, friends,
...               first, cities)
>>> for ((name, friend), (friend, city)) in sorted(unique(result)):
...     print((name, city))
('Alice', 'Berlin')
('Alice', 'Paris')
('Alice', 'Shanghai')
('Edith', 'Chicago')
('Edith', 'NYC')
('Zhao', 'Chicago')
('Zhao', 'NYC')
('Zhao', 'Berlin')
('Zhao', 'Paris')

Join is computationally powerful:

• It is expressive enough to cover a wide set of analytics operations
• It runs in linear time relative to the size of the input and output
• Only the left sequence must fit in memory

## Conclusion

Toolz gives a compact set of primitives for data analysis on plain Python data structures. CyToolz accelerates those workflows through Cython. This approach is both low-tech and supports uncomfortably big data through streaming.

At the same time, Toolz is a general purpose functional standard library, and is not specifically dedicated to data analysis. While there are obvious benefits (streaming, composition, etc.) users interested in data analysis might be better served by using projects dedicated projects like Pandas or SQLAlchemy.

This post is also part of the toolz docs. Thanks to John Jacobsen, Clark Fitzgerald, and Erik Welch for their help with this post.