ak.broadcast_arrays — Awkward Array documentation

# ak.broadcast_arrays

Defined in awkward.operations.structure on line 1321.

ak.broadcast_arrays()
  Parameters:

    - arrays – Arrays to broadcast into the same structure.

    - left_broadcast (bool) – If True, follow rules for implicit left-broadcasting, as described below.

    - right_broadcast (bool) – If True, follow rules for implicit right-broadcasting, as described below.

    - highlevel (bool, default is True) – If True, return an `ak.Array`; otherwise, return a low-level `ak.layout.Content` subclass.

    - depth_limit (None or int, default is None) – If None, attempt to fully broadcast the `arrays` to all levels. If an int, limit the number of dimensions that get broadcasted. The minimum value is `1`, for no broadcasting.

Like NumPy’s broadcast_arrays function, this function returns the input `arrays` with enough elements duplicated that they can be combined element-by-element.

For NumPy arrays, this means that scalars are replaced with arrays with the same scalar value repeated at every element of the array, and regular dimensions are created to increase low-dimensional data into high-dimensional data.

For example,

    >>> ak.broadcast_arrays(5,
    ...                     [1, 2, 3, 4, 5])
    [<Array [5, 5, 5, 5, 5] type='5 * int64'>,
     <Array [1, 2, 3, 4, 5] type='5 * int64'>]

and

    >>> ak.broadcast_arrays(np.array([1, 2, 3]),
    ...                     np.array([[0.1, 0.2, 0.3], [10, 20, 30]]))
    [<Array [[  1,   2,   3], [ 1,  2,  3]] type='2 * 3 * int64'>,
     <Array [[0.1, 0.2, 0.3], [10, 20, 30]] type='2 * 3 * float64'>]

Note that in the second example, when the `3 * int64` array is expanded to match the `2 * 3 * float64` array, it is the deepest dimension that is aligned. If we try to match a `2 * int64` with the `2 * 3 * float64`,

    >>> ak.broadcast_arrays(np.array([1, 2]),
    ...                     np.array([[0.1, 0.2, 0.3], [10, 20, 30]]))
    ValueError: cannot broadcast RegularArray of size 2 with RegularArray of size 3

NumPy has the same behavior: arrays with different numbers of dimensions are aligned to the right before expansion. One can control this by explicitly adding a new axis (reshape to add a dimension of length 1) where the expansion is supposed to take place because a dimension of length 1 can be expanded like a scalar.

    >>> ak.broadcast_arrays(np.array([1, 2])[:, np.newaxis],
    ...                     np.array([[0.1, 0.2, 0.3], [10, 20, 30]]))
    [<Array [[  1,   1,   1], [ 2,  2,  2]] type='2 * 3 * int64'>,
     <Array [[0.1, 0.2, 0.3], [10, 20, 30]] type='2 * 3 * float64'>]

Again, NumPy does the same thing (`np.newaxis` is equal to None, so this trick is often shown with None in the slice-tuple). Where the broadcasting happens can be controlled, but numbers of dimensions that don’t match are implicitly aligned to the right (fitting innermost structure, not outermost).

While that might be an arbitrary decision for rectilinear arrays, it is much more natural for implicit broadcasting to align left for tree-like structures. That is, the root of each data structure should agree and leaves may be duplicated to match. For example,

    >>> ak.broadcast_arrays([            100,   200,        300],
    ...                     [[1.1, 2.2, 3.3],    [], [4.4, 5.5]])
    [<Array [[100, 100, 100], [], [300, 300]] type='3 * var * int64'>,
     <Array [[1.1, 2.2, 3.3], [], [4.4, 5.5]] type='3 * var * float64'>]

One typically wants single-item-per-element data to be duplicated to match multiple-items-per-element data. Operations on the broadcasted arrays like

    one_dimensional + nested_lists

would then have the same effect as the procedural code

    for x, outer in zip(one_dimensional, nested_lists):
        output = []
        for inner in outer:
            output.append(x + inner)
        yield output

where `x` has the same value for each `inner` in the inner loop.

Awkward Array’s broadcasting manages to have it both ways by applying the following rules:

> - If all dimensions are regular (i.e. `ak.types.RegularType`), like NumPy, implicit broadcasting aligns to the right, like NumPy.

> - If any dimension is variable (i.e. `ak.types.ListType`), which can never be true of NumPy, implicit broadcasting aligns to the left.

> - Explicit broadcasting with a length-1 regular dimension always broadcasts, like NumPy.

Thus, it is important to be aware of the distinction between a dimension that is declared to be regular in the type specification and a dimension that is allowed to be variable (even if it happens to have the same length for all elements). This distinction is can be accessed through the `ak.Array.type`, but it is lost when converting an array into JSON or Python objects.

If arrays have the same depth but different lengths of nested lists, attempting to broadcast them together is a broadcasting error.

    >>> one = ak.Array([[[1, 2, 3], [], [4, 5], [6]], [], [[7, 8]]])
    >>> two = ak.Array([[[1.1, 2.2], [3.3], [4.4], [5.5]], [], [[6.6]]])
    >>> ak.broadcast_arrays(one, two)
    ValueError: in ListArray64, cannot broadcast nested list

For this, one can set the `depth_limit` to prevent the operation from attempting to broadcast what can’t be broadcasted.

    >>> this, that = ak.broadcast_arrays(one, two, depth_limit=1)
    >>> ak.to_list(this)
    [[[1, 2, 3], [], [4, 5], [6]], [], [[7, 8]]]
    >>> ak.to_list(that)
    [[[1.1, 2.2], [3.3], [4.4], [5.5]], [], [[6.6]]]