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 document we'll use this simple dataset of accounts
>>> accounts = [(1, 'Alice', 100, 'F'), # id, name, balance, gender ... (2, 'Bob', 200, 'M'), ... (3, 'Charlie', 150, 'M'), ... (4, 'Dennis', 50, 'M'), ... (5, 'Edith', 300, 'F')]
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 acc: acc[2] > 150), ... map(get([1, 2])), ... list)
Note: this uses the curried` versions of map and filter.
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]
We separate split-apply-combine operations into the following two concepts
- Split the dataset into groups by some property
- Reduce each of the groups with some synopsis function
Toolz supports this common workflow with
- a simple in-memory solution
- a more sophisticated streaming solution.
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 these two functions piece by piece to show the intermediate groups.
>>> from toolz import compose
>>> from toolz.curried import get, pluck, groupby, valmap
>>> 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)),
... _) # The underscore captures results from the previous prompt
{'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}
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 applies the key function to each item in succession,
accumulating running totals for each key by combining each new
value with the previous 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
>>> def add(x, y):
... 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, account: total + account[2]
>>> reduceby(get(3), binop, accounts, 0)
{'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.
We register multiple datasets together with join. Consider a second dataset storing addresses by ID
>>> addresses = [(1, '123 Main Street'), # id, address ... (2, '5 Adams Way'), ... (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 FROM accounts JOIN addresses ON accounts.id = addresses.id;
>>> from toolz import join, first
>>> result = join(first, accounts,
... first, addresses)
>>> for ((id, name, bal, gender), (id, address)) in result:
... print((name, address))
('Alice', '123 Main Street')
('Bob', '5 Adams Way')
('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.
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(x): ... return x % 2 == 0 >>> def isodd(x): ... return x % 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)]
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.
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.)
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
Toolz is a general purpose functional standard library, not a library specifically for data analytics. While there are obvious benefits (streaming, composition, ...) users interested in data analytics might be better served by using projects specific to data analytics like Pandas or SQLAlchemy.