A data structure is defined both in terms of the information it encodes and in how it can be used. For example, a hash-table is not just a buffer, it’s also the “get” and “set” operations that make the buffer usable as a key-value store. Awkward Arrays have a suite of operations for transforming tree structures into new tree structures, but an application of these structures to a data analysis problem should be able to interpret them as objects in the analysis domain, such as latitude-longitude coordinates in geographical studies or Lorentz vectors in particle physics.

Object-oriented programming unites data with its operations. This is a conceptual improvement for data analysts because functions like “distance between this latitude-longitude point and another on a spherical globe” can be bound to the objects that represent latitude-longitude points. It matches the way that data analysts usually think about their data.

However, if these methods are saved in the data, or are written in a way that will only work for one version of the data structures, then it becomes difficult to work with large datasets. Old data that do not “fit” the new methods would have to be converted, or the analysis would have to be broken into different cases for each data generation. This problem is known as schema evolution, and there are many solutions to it.

The approach taken by the Awkward Array library is to encode very little interpretation into the data themselves and apply an interpretation as late as possible. Thus, a latitude-longitude record might be stamped with the name "latlon", but the operations on it are added immediately before the user wants them. These operations can be written in such a way that they only require the "latlon" to have lat and lon fields, so different versions of the data can have additional fields or even be embedded in different structures.

Parameters and behaviors

In Awkward Array, metadata are embedded in data using an array node’s parameters, and parameter-dependent operations can be defined using behavior. A global mapping from parameters to behavior is in a dict called ak.behavior:

>>> import awkward as ak
>>> ak.behavior

but behavior dicts can also be loaded into ak.Array, ak.Record, and ak.ArrayBuilder objects as a constructor argument. See ak.Array.behavior.

The general flow is

  • parameters link data objects to names;

  • behavior links names to code.

In large datasets, parameters may be hard to change (permanently, at least: on-the-fly parameter changes are easier), but behavior is easy to change (it is always assigned on-the-fly).

In the following example, we create two nested arrays of records with fields "x" and "y" and the records are named "point".

one = ak.Array([[{"x": 1, "y": 1.1}, {"x": 2, "y": 2.2}, {"x": 3, "y": 3.3}],
                [{"x": 4, "y": 4.4}, {"x": 5, "y": 5.5}],
                [{"x": 6, "y": 6.6}],
                [{"x": 7, "y": 7.7}, {"x": 8, "y": 8.8}, {"x": 9, "y": 9.9}]],
two = ak.Array([[{"x": 0.9, "y": 1}, {"x": 2, "y": 2.2}, {"x": 2.9, "y": 3}],
                [{"x": 3.9, "y": 4}, {"x": 5, "y": 5.5}],
                [{"x": 5.9, "y": 6}],
                [{"x": 6.9, "y": 7}, {"x": 8, "y": 8.8}, {"x": 8.9, "y": 9}]],

The name appears in the way the type is presented as a string (a departure from Datashape notation):

>>> ak.type(one)
5 * var * point["x": int64, "y": float64]

and it may be accessed as the "__record__" property, through the ak.Array.layout:

>>> one.layout
    <offsets><Index64 i="[0 3 3 5 6 9]" offset="0" length="6"/></offsets>
            <param key="__record__">"point"</param>
        <field index="0" key="x">
            <NumpyArray format="l" shape="9" data="1 2 3 4 5 6 7 8 9"/>
        <field index="1" key="y">
            <NumpyArray format="d" shape="9" data="1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9"/>
>>> one.layout.content.parameters
{'__record__': 'point'}

We have to dig into the layout’s content because the "__record__" parameter is set on the ak.layout.RecordArray, which is buried inside of a ak.layout.ListOffsetArray.

Alternatively, we can navigate to a single ak.Record first:

>>> one[0, 0]
<Record {x: 1, y: 1.1} type='point["x": int64, "y": float64]'>
>>> one[0, 0].layout.parameters
{'__record__': 'point'}

Adding behavior to records

Suppose we want the points in the above example to be able to calculate distances to other points. We can do this by creating a subclass of ak.Record that has the new methods and associating it with the "__record__" name.

class Point(ak.Record):
    def distance(self, other):
        return np.sqrt((self.x - other.x)**2 + (self.y - other.y)**2)

ak.behavior["point"] = Point

Now one[0, 0] is instantiated as a Point, rather than a Record,

>>> one[0, 0]
<Point {x: 1, y: 1.1} type='point["x": int64, "y": float64]'>

and it has the distance method.

>>> for xs, ys in zip(one, two):
...     for x, y in zip(xs, ys):
...         print(x.distance(y))

Looping over data in Python is inconvenient and slow; we want to compute quantities like this with array-at-a-time methods, but distance is bound to a ak.Record, not an ak.Array of records.

>>> one.distance(two)
AttributeError: no field named 'distance'

To add distance as a method on arrays of points, create a subclass of ak.Array and attach that as ak.behavior[".", "point"] for “array of points.”

class PointArray(ak.Array):
    def distance(self, other):
        return np.sqrt((self.x - other.x)**2 + (self.y - other.y)**2)

ak.behavior[".", "point"] = PointArray

Now one[0] is a PointArray and can compute distance on arrays at a time. Thanks to NumPy’s universal function (ufunc) syntax, the expression is the same (and could perhaps be implemented once and used by both Point and PointArray).

>>> one[0]
<PointArray [{x: 1, y: 1.1}, ... {x: 3, y: 3.3}] type='3 * point["x": int64, "y"...'>
>>> one[0].distance(two[0])
<Array [0.141, 0, 0.316] type='3 * float64'>

But one itself is an Array of PointArrays, and does not apply.

>>> one
<Array [[{x: 1, y: 1.1}, ... x: 9, y: 9.9}]] type='5 * var * point["x": int64, "...'>
>>> one.distance(two)
AttributeError: no field named 'distance'

We can make the assignment work at all levels of list-depth by using a "*" instead of a ".".

ak.behavior["*", "point"] = PointArray

One last caveat: our one array was created before this behavior was assigned, so it needs to be recreated to be a member of the new class. The normal ak.Array constructor is sufficient for this. This is only an issue if you’re working interactively (but something to think about when debugging!).

>>> one = ak.Array(one)
>>> two = ak.Array(two)

Now it works, and again we’re taking advantage of the fact that the expression for distance based on ufuncs works equally well on Awkward Arrays.

>>> one
<PointArray [[{x: 1, y: 1.1}, ... x: 9, y: 9.9}]] type='5 * var * point["x": int...'>
>>> one.distance(two)
<Array [[0.141, 0, 0.316, ... 0.707, 0, 0.906]] type='5 * var * float64'>

In most cases, you want to apply array-of-records for all levels of list-depth: use ak.behavior["*", record_name].

Overriding NumPy ufuncs and binary operators

The ak.Array class overrides Python’s binary operators with the equivalent ufuncs, so __eq__ actually calls np.equal, for instance. This is also true of other basic functions, like __abs__ for overriding abs with np.absolute. Each ufunc is then passed down to the leaves (deepest sub-elements) of an Awkward data structure.

For example,

>>> ak.Array([[1, 2, 3], [], [4]]) == ak.Array([[3, 2, 1], [], [4]])
<Array [[False, True, False], [], [True]] type='3 * var * bool'>

However, this does not apply to records or named types until they are explicitly overridden:

>>> one == two
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: no overloads for custom types: equal(point, point)

We might want to take an object-oriented view in which the == operation applies to points, regardless of how deeply they are nested. If we try to do it by adding __eq__ as a method on PointArray, it would work if the PointArray is the top of the data structure, but not if it’s nested within another structure.

Instead, we should override np.equal itself. Custom ufunc overrides are checked at every step in broadcasting, so the override would be applied if point objects are discovered at any level.

def point_equal(left, right):
    return np.logical_and(left.x == right.x, left.y == right.y)

ak.behavior[np.equal, "point", "point"] = point_equal

The above should be read as “override np.equal for cases in which both arguments are "point".”

>>> ak.to_list(one == two)
[[False, True, False], [], [False, True], [False], [False, True, False]]

Similarly for overriding abs

>>> def point_abs(point):
...     return np.sqrt(point.x**2 + point.y**2)
>>> ak.behavior[np.absolute, "point"] = point_abs
>>> ak.to_list(abs(one))
[[1.4866068747318506, 2.973213749463701, 4.459820624195552],
 [5.946427498927402, 7.433034373659253],
 [10.406248123122953, 11.892854997854805, 13.379461872586655]]

and all other ufuncs.

If you need a placeholder for “any number,” use numbers.Real, numbers.Integral, etc. Non-arrays are resolved by type; builtin Python numbers and NumPy numbers are subclasses of the generic number types in the numbers library.

Also, for commutative operations, be sure to override both operator orders. (Function signatures are matched to ak.behavior using multiple dispatch.)

>>> import numbers
>>> def point_lmult(point, scalar):
...     return ak.Array({"x": point.x * scalar, "y": point.y * scalar})
>>> def point_rmult(scalar, point):
...     return point_lmult(point, scalar)
>>> ak.behavior[np.multiply, "point", numbers.Real] = point_lmult
>>> ak.behavior[np.multiply, numbers.Real, "point"] = point_rmult
>>> ak.to_list(one * 10)
[[{'x': 10, 'y': 11.0}, {'x': 20, 'y': 22.0}, {'x': 30, 'y': 33.0}],
 [{'x': 40, 'y': 44.0}, {'x': 50, 'y': 55.0}],
 [{'x': 60, 'y': 66.0}],
 [{'x': 70, 'y': 77.0}, {'x': 80, 'y': 88.0}, {'x': 90, 'y': 99.0}]]

If you need to override ufuncs in more generality, you can use the “apply_ufunc” interface:

>>> def apply_ufunc(ufunc, method, args, kwargs):
...     if ufunc in (np.sin, np.cos, np.tan):
...         x = ufunc(args[0].x)
...         y = ufunc(args[0].y)
...         return ak.Array({"x": x, "y": y})
...     else:
...         return NotImplemented
>>> ak.behavior[np.ufunc, "point"] = apply_ufunc
>>> ak.to_list(np.sin(one))
[[{'x': 0.8414709848078965, 'y': 0.8912073600614354},
  {'x': 0.9092974268256817, 'y': 0.8084964038195901},
  {'x': 0.1411200080598672, 'y': -0.1577456941432482}],
 [{'x': -0.7568024953079282, 'y': -0.951602073889516},
  {'x': -0.9589242746631385, 'y': -0.7055403255703919}],
 [{'x': -0.27941549819892586, 'y': 0.31154136351337786}],
 [{'x': 0.6569865987187891, 'y': 0.9881682338770004},
  {'x': 0.9893582466233818, 'y': 0.5849171928917617},
  {'x': 0.4121184852417566, 'y': -0.45753589377532133}]]
>>> np.sqrt(one)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: no overloads for custom types: sqrt(point)

But be forewarned: the ak.behavior[np.ufunc, name] syntax will match any ufunc that has an array containing an array with type name anywhere in the argument list. The first array in the argument list with type name will be matched instead of more detailed argument lists with type name at a later spot in the list. The “apply_ufunc” interface is greedy.

Mixin decorators

The pattern of adding additional properties and function overrides to records and arrays of records is quite common, and can be nicely described by the “mixin” idiom: a class with no constructor that is mixed with both the ak.Array and ak.Record class as to create new derived classes. The _auto/ak.behaviors.mixins.mixin_class and _auto/ak.behaviors.mixins.mixin_class_method python decorators assist with some of this boilerplate. Consider the Point class from above; we can implement all the functionality so far described as follows:

class Point:
    def distance(self, other):
        return np.sqrt((self.x - other.x) ** 2 + (self.y - other.y) ** 2)

    @ak.mixin_class_method(np.equal, {"Point"})
    def point_equal(self, other):
        return np.logical_and(self.x == other.x, self.y == other.y)

    def point_abs(self):
        return np.sqrt(self.x ** 2 + self.y ** 2)

The behavior name is taken as the mixin class name, e.g. here it is Point (as opposed to lowercase point previously). We can extend our implementation to allow Point types to be added by overriding the np.add ufunc (appending to our class definition):

class Point:
    # ...

    @ak.mixin_class_method(np.add, {"Point"})
    def point_add(self, other):
        return ak.zip(
            {"x": self.x + other.x, "y": self.y + other.y}, with_name="Point",

The real power of using mixin classes comes from the ability to inherit behaviors. Consider a Point-like record that also has a weight field. Suppose that we want these WeightedPoint types to have the same distance and magnitude functionality, but only be considered equal when they have the same weight. Also, suppose we want the addition of two weighted points to give their weighted mean rather than a sum. We could implement such a class as follows:

class WeightedPoint(Point):
    @ak.mixin_class_method(np.equal, {"WeightedPoint"})
    def weighted_equal(self, other):
        return np.logical_and(self.point_equal(other), self.weight == other.weight)

    @ak.mixin_class_method(np.add, {"WeightedPoint"})
    def weighted_add(self, other):
        sumw = self.weight + other.weight
        return ak.zip(
                "x": (self.x * self.weight + other.x * other.weight) / sumw,
                "y": (self.y * self.weight + other.y * other.weight) / sumw,
                "weight": sumw,

A footnote: in this implementation, adding a WeightedPoint and a Point returns a Point. One may wish to disable this by type-checking, since the functionalities are rather different.

Adding behavior to arrays

Occasionally, you may want to add behavior to an array that does not contain records. A good example of this is to implement strings: strings are not a special data type in Awkward Array as they are in many other libraries, they are a behavior overlaid on arrays.

There are four predefined string behaviors:

All four override the string representations (__str__ and __repr__), but the string behaviors additionally override equality:

>>> ak.Array(["one", "two", "three"]) == ak.Array(["1", "TWO", "three"])
<Array [False, False, True] type='3 * bool'>

The only difference here is the parameter: instead of setting "__record__", we set "__array__".

>>> ak.Array(["one", "two", "three"]).layout
        <param key="__array__">"string"</param>
    <offsets><Index64 i="[0 3 6 11]" offset="0" length="4""/></offsets>
    <content><NumpyArray format="B" shape="11" data="0x 6f6e6574 776f7468 726565">
            <param key="__array__">"char"</param>

In ak.behaviors.string, string behaviors are assigned with lines like

ak.behavior["string"] = StringBehavior
ak.behavior[np.equal, "string", "string"] = _string_equal

Custom type names

To make the string type appear as string in type representations, a "__typestr__" behavior is overriden (in ak.behaviors.string):

ak.behavior["__typestr__", "string"] = "string"

so that

>>> ak.type(ak.Array(["one", "two", "three"]))
3 * string

Custom broadcasting

In situations where we want to think about lists as objects, such as strings, we may even need to override the broadcasting rules. For instance, given

ak.Array(["HAL"]) + ak.Array([[1, 1, 1, 1, 1]])

we might expect "HAL" to broadcast to each 1, like

[[[73, 66, 77], [73, 66, 77], [73, 66, 77], [73, 66, 77], [73, 66, 77]]]

but (without custom broadcasting) instead it raises a broadcasting for any length of 1 list other than 3:

>>> # without custom broadcasting
>>> print(ak.Array(["HAL"]) + ak.Array([[1, 1, 1, 1, 1]]))
ValueError: in ListOffsetArray64, cannot broadcast nested list
>>> print(ak.Array(["HAL"]) + ak.Array([[1, 1, 1]]))
[[73, 66, 77]]

It’s matching each character of "HAL" with a number from the list, but we want the string to be taken as an object. That is fixed (in ak.behaviors.string) with a custom broadcasting rule:

def _string_broadcast(layout, offsets):
    # layout:  an ak.layout.Content object
    # offsets: an ak.layout.Index of offsets to match
    # should return: an ak.layout.Content object of the broadcasted result

awkward.behavior["__broadcast__", "string"] = _string_broadcast

Very few applications would need to do this, but the ak.behavior object provides a lot of room for customization hooks like this.

Overriding behavior in Numba

Awkward Arrays can be arguments and return values of functions compiled with Numba. Since these functions run on low-level objects, most functionality must be reimplemented, including behavioral overrides.

The documentation on Extending Numba introduces typing, lowering, and models, which are necessary for reimplementing the behavior of a Python object in the compiled environment. To apply the same to records and arrays from an Awkward data structure, we use ak.behavior hooks that start with "__numba_typer__" and "__numba_lower__".

Case 1: Adding a property, such as rec.property_name.

ak.behavior["__numba_typer__", record_name, property_name] = typer
ak.behavior["__numba_lower__", record_name, property_name] = lower

The typer function takes an ak._connect._numba.arrayview.ArrayViewType as its only argument and returns the property’s type.

The lower function takes the standard context, builder, sig, args arguments and returns the lowered value. Given a Python function that takes one record and returns the property, the lower can be

def lower(context, builder, sig, args):
    return context.compile_internal(builder, function, sig, args)

Case 2: Adding a method, such as rec.method_name(arg0, arg1).

ak.behavior["__numba_typer__", record_name, method_name, ()] = typer
ak.behavior["__numba_lower__", record_name, method_name, ()] = lower

The last item is an empty tuple, () (regardless of whether the method takes any arguments).

In this case, the typer takes an ak._connect._numba.arrayview.ArrayViewType as well as any arguments and returns the property’s type, and the sig and args in lower include these arguments.

Case 3: Unary and binary operations, like -rec1 and rec1 + rec2.

ak.behavior["__numba_typer__", operator.neg, "rec1"] = typer
ak.behavior["__numba_lower__", operator.neg, "rec1"] = lower

ak.behavior["__numba_typer__", "rec1", operator.add, "rec2"] = typer
ak.behavior["__numba_lower__", "rec1", operator.add, "rec2"] = lower

Case 4: Completely replacing the Awkward record with an object in Numba.

If a fully defined model for the object already exists and Numba, we can have references to Awkward records or arrays simply become these objects, which implies some overhead from copying data and a loss of the functionality that Awkward would bring.

Strings, for instance, are replaced by Numba’s built-in string model so that all string operations will work, but Awkward operations like broadcasting characters will not.

For this case, the signatures are

# parameters["__record__"] = record_name
ak.behavior["__numba_typer__", record_name] = typer
ak.behavior["__numba_lower__", record_name] = lower

# for an array one-level deep
ak.behavior["__numba_typer__", ".", record_name] = typer
ak.behavior["__numba_lower__", ".", record_name] = lower

# for an array any number of levels deep
ak.behavior["__numba_typer__", "*", record_name] = typer
ak.behavior["__numba_lower__", "*", record_name] = lower

# parameters["__array__"] = array_name
ak.behavior["__numba_typer__", array_name] = typer
ak.behavior["__numba_lower__", array_name] = lower

The typer function takes an ak._connect._numba.arrayview.ArrayViewType as its only argument and returns the Numba type of its replacement, while the lower function takes

  • context: Numba context

  • builder: Numba builder

  • rettype: the Numba type of its replacement

  • viewtype: an ak._connect._numba.arrayview.ArrayViewType

  • viewval: a Numba value of the view

  • viewproxy: a Numba proxy (context.make_helper) of the view

  • attype: the Numba integer type of the index position

  • atval: the Numba value of the index position

Complete example

The Vector design prototype has a complete example, including Numba.