What is an “Awkward” Array?#

import numpy as np
import awkward as ak

Versatile Arrays#

Awkward Arrays are general tree-like data structures, like JSON, but contiguous in memory and operated upon with compiled, vectorized code like NumPy.

They look like NumPy arrays:

ak.Array([1, 2, 3])
[1,
 2,
 3]
---------------
type: 3 * int64

Like NumPy, they can have multiple dimensions:

ak.Array([
    [1, 2, 3],
    [4, 5, 6]
])
[[1, 2, 3],
 [4, 5, 6]]
---------------------
type: 2 * var * int64

These dimensions can have varying lengths; arrays can be ragged:

ak.Array([
    [1, 2, 3],
    [4],
    [5, 6]
])
[[1, 2, 3],
 [4],
 [5, 6]]
---------------------
type: 3 * var * int64

Each dimension can contain missing values:

ak.Array([
    [1, 2, 3],
    [4],
    [5, 6, None]
])
[[1, 2, 3],
 [4],
 [5, 6, None]]
----------------------
type: 3 * var * ?int64

Awkward Arrays can store numbers:

ak.Array([
    [3, 141], 
    [59, 26, 535], 
    [8]
])
[[3, 141],
 [59, 26, 535],
 [8]]
---------------------
type: 3 * var * int64

They can also work with dates:

ak.Array(
    [
        [np.datetime64("1815-12-10"), np.datetime64("1969-07-16")],
        [np.datetime64("1564-04-26")],
    ]
)
[[1815-12-10, 1969-07-16],
 [1564-04-26]]
-----------------------------
type: 2 * var * datetime64[D]

They can even work with strings:

ak.Array(
    [
        [
            "Benjamin List",
            "David MacMillan",
        ],
        [
            "Emmanuelle Charpentier",
            "Jennifer A. Doudna",
        ],
    ]
)
[['Benjamin List', 'David MacMillan'],
 ['Emmanuelle Charpentier', 'Jennifer A. Doudna']]
--------------------------------------------------
type: 2 * var * string

Awkward Arrays can have structure through records:

ak.Array(
    [
        [
            {"name": "Benjamin List", "age": 53},
            {"name": "David MacMillan", "age": 53},
        ],
        [
            {"name": "Emmanuelle Charpentier", "age": 52},
            {"name": "Jennifer A. Doudna", "age": 57},
        ],
        [
            {"name": "Akira Yoshino", "age": 73},
            {"name": "M. Stanley Whittingham", "age": 79},
            {"name": "John B. Goodenough", "age": 98},
        ],
    ]
)
[[{name: 'Benjamin List', age: 53}, {name: 'David MacMillan', ...}],
 [{name: 'Emmanuelle Charpentier', age: 52}, {name: ..., ...}],
 [{name: 'Akira Yoshino', age: 73}, ..., {name: 'John B. Goodenough', ...}]]
----------------------------------------------------------------------------
type: 3 * var * {
    name: string,
    age: int64
}

In fact, Awkward Arrays can represent many kinds of jagged data. They can possess complex structures that mix records, and primitive types.

ak.Array(
    [
        [
            {
                "name": "Benjamin List",
                "age": 53,
                "institutions": [
                    "University of Cologne",
                    "Max Planck Institute for Coal Research",
                    "Hokkaido University",
                ],
            },
            {
                "name": "David MacMillan",
                "age": 53,
                "institutions": None,
            },
        ]
    ]
)
[[{name: 'Benjamin List', age: 53, institutions: [...]}, {name: ..., ...}]]
---------------------------------------------------------------------------
type: 1 * var * {
    name: string,
    age: int64,
    institutions: option[var * string]
}

They can even contain unions!

ak.Array(
    [
        [np.datetime64("1815-12-10"), "Cassini"],
        [np.datetime64("1564-04-26")],
    ]
)
[[1815-12-10, 'Cassini'],
 [1564-04-26]]
-------------------------
type: 2 * var * union[
    datetime64[D],
    string
]

NumPy-like interface#

Awkward Array looks like NumPy. It behaves identically to NumPy for regular arrays

x = ak.Array([
    [1, 2, 3],
    [4, 5, 6]
]);
ak.sum(x, axis=-1)
[6,
 15]
---------------
type: 2 * int64

providing a similar high-level API, and implementing the ufunc mechanism:

powers_of_two = ak.Array(
    [
        [1, 2, 4],
        [None, 8],
        [16],
    ]
);
ak.sum(powers_of_two)
np.int64(31)

But generalises to the tricky kinds of data that NumPy struggles to work with. It can perform reductions through varying length lists:

ak.sum(powers_of_two, axis=0)
[17,
 10,
 4]
---------------
type: 3 * int64

Lightweight structures#

Awkward makes it east to pull apart record structures:

nobel_prize_winner = ak.Array(
    [
        [
            {"name": "Benjamin List", "age": 53},
            {"name": "David MacMillan", "age": 53},
        ],
        [
            {"name": "Emmanuelle Charpentier", "age": 52},
            {"name": "Jennifer A. Doudna", "age": 57},
        ],
        [
            {"name": "Akira Yoshino", "age": 73},
            {"name": "M. Stanley Whittingham", "age": 79},
            {"name": "John B. Goodenough", "age": 98},
        ],
    ]
);
nobel_prize_winner.name
[['Benjamin List', 'David MacMillan'],
 ['Emmanuelle Charpentier', 'Jennifer A. Doudna'],
 ['Akira Yoshino', 'M. Stanley Whittingham', 'John B. Goodenough']]
-------------------------------------------------------------------
type: 3 * var * string
nobel_prize_winner.age
[[53, 53],
 [52, 57],
 [73, 79, 98]]
---------------------
type: 3 * var * int64

These records are lightweight, and simple to compose:

nobel_prize_winner_with_birth_year = ak.zip({
    "name": nobel_prize_winner.name,
    "age": nobel_prize_winner.age,
    "birth_year": 2021 - nobel_prize_winner.age
});
nobel_prize_winner_with_birth_year.show()
[[{name: 'Benjamin List', age: 53, birth_year: 1968}, {name: ..., ...}],
 [{name: 'Emmanuelle Charpentier', age: 52, birth_year: 1969}, {...}],
 [{name: 'Akira Yoshino', age: 73, birth_year: 1948}, ..., {name: ..., ...}]]

High performance#

Like NumPy, Awkward Array performs computations in fast, optimised kernels.

large_array = ak.Array([[1, 2, 3], [], [4, 5]] * 1_000_000)

We can compute the sum in 3.37 ms ± 107 µs on a reference CPU:

ak.sum(large_array)
np.int64(15000000)

The same sum can be computed with pure-Python over the flattened array in 369 ms ± 8.07 ms:

large_flat_array = ak.ravel(large_array)

sum(large_flat_array)
np.int64(15000000)

These performance values are not benchmarks; they are only an indication of the speed of Awkward Array.

Some problems are hard to solve with array-oriented programming. Awkward Array supports Numba out of the box:

import numba as nb

@nb.njit
def cumulative_sum(arr):
    result = 0
    for x in arr:
        for y in x:
            result += y
    return result
    
cumulative_sum(large_array)
15000000