How to flatten arrays, especially for plotting#

In a data analysis, it is important to plot your data frequently, and the interactive nature of array-at-a-time functions facilitate that.

However, plotting views your data as a generic set or sequence—the structure of nested lists and records can’t be captured by standard plots. Histograms (including 2-dimensional heatmaps) take input data to be an unordered set, as do scatter plots. Connected-line plots, such as time-series, use the sequential order of the data, but there aren’t many visualizations that show nestedness. (Maybe there will be, in the future.)

As such, these standard plotting routines expect simple structures, either a single flat array (in which the order may be relevant or irrelevant) or several same-length arrays (in which the relative or absolute order is relevant). Encountering an Awkward Array, they may try to call np.asarray on it, which only works if the array can be made rectilinear or they may try to iterate over it in Python, which can be prohibitively slow if the dataset is large.

Scope of destructuring#

To destructure an array for plotting, you’ll want to

  • remove nested lists, definitely for variable-length ones (”var *” in the type string) and possibly for regular ones as well (”N *” in the type string, where N is an integer),

  • remove record structures,

  • remove missing data

There are two functions that are responsible for flattening arrays: ak.flatten() with axis=None; and ak.ravel(); but you don’t want to apply them without thinking, because structure is important to the meaning of your data and you want to be able to interpret the plot. Destructuring is an information-losing operation, so your guidance is required to eliminate exactly the structure you want to eliminate, and there are several ways to do that, depending on what you want to do.

After destructuring, you might still need to call np.asarray on the output because the plotting library might not recognize an ak.Array as an array. You’ll probably also want to develop your destructuring on a commandline or a different Jupyter cell from the plotting library function call, to understand what structure the output has without the added complication of the plotting library’s error messages.

import awkward as ak
import numpy as np

ak.ravel#

First, let’s create an array with some interesting structure.

array = ak.Array(
    [[{"x": 1.1, "y": [1]}, {"x": None, "y": [1, 2]}], [], [{"x": 3.3, "y": [1, 2, 3]}]]
)
array
[[{x: 1.1, y: [1]}, {x: None, y: [1, 2]}],
 [],
 [{x: 3.3, y: [1, 2, 3]}]]
------------------------------------------
type: 3 * var * {
    x: ?float64,
    y: var * int64
}

As mentioned above, ak.ravel() is one of two functions that turns any array into a 1-dimensional array with no nested lists, no nested records.

ak.ravel(array)
[1.1,
 None,
 3.3,
 1,
 1,
 2,
 1,
 2,
 3]
------------------
type: 9 * ?float64

Calling this function on an already flat array does nothing, so you don’t have to worry about what state your array had been in before you called it.

ak.ravel(ak.ravel(array))
[1.1,
 None,
 3.3,
 1,
 1,
 2,
 1,
 2,
 3]
------------------
type: 9 * ?float64

Unlike ak.flatten(..., axis=None), ak.ravel() preserves None values at the leaves, meaning that functions which expect a simple array of numbers will usually raise an exception.

However, there are a few questions you should be asking yourself:

  • Did the nested lists have special meaning? What does the plot represent if I just concatenate them all?

  • Did the record fields have distinct meanings? In this example, what does it mean to put floating-point x values and nested-list y values in the same bucket of numbers to plot? Does it matter that there are more y values than x values? In most circumstances, you do not want to mix record fields in a plot.

ak.flatten with axis=None#

If ak.ravel() is a sledgehammer, then ak.flatten() with axis=None is a pile driver that turns any array into a 1-dimensional array with no nested lists, no nested records, and no missing data.

array = ak.Array(
    [[{"x": 1.1, "y": [1]}, {"x": None, "y": [1, 2]}], [], [{"x": 3.3, "y": [1, 2, 3]}]]
)
array
[[{x: 1.1, y: [1]}, {x: None, y: [1, 2]}],
 [],
 [{x: 3.3, y: [1, 2, 3]}]]
------------------------------------------
type: 3 * var * {
    x: ?float64,
    y: var * int64
}
ak.flatten(array, axis=None)
[1.1,
 3.3,
 1,
 1,
 2,
 1,
 2,
 3]
-----------------
type: 8 * float64

Like ak.ravel(), Calling this function on an already flat array does nothing, so you don’t have to worry about what state your array had been in before you called it.

ak.flatten(ak.flatten(array, axis=None), axis=None)
[1.1,
 3.3,
 1,
 1,
 2,
 1,
 2,
 3]
-----------------
type: 8 * float64

In addition to the concerns raised above, it is also important to consider whether the None values in your array are meaningful. For example, consider an array of x-axis and y-axis values. If only the y-axis contains None values, ak.flatten(y_values, axis=None) would produce an array that does not align with the flattened x-axis values.

x = ak.Array([[1, 2, 3], [4, 5, 6, 7]])
y = ak.Array([[8, None, 6], [5, None, None, 4]])

z = 2 * np.ravel(x) + np.ravel(y)

Selecting record fields#

A more controlled way to extract fields from a record is to project them by name.

array = ak.Array(
    [
        [{"x": 1.1, "y": [1], "z": "one"}, {"x": None, "y": [1, 2], "z": "two"}],
        [],
        [{"x": 3.3, "y": [1, 2, 3], "z": "three"}],
    ]
)
array
[[{x: 1.1, y: [1], z: 'one'}, {x: None, y: [1, 2], z: 'two'}],
 [],
 [{x: 3.3, y: [1, 2, 3], z: 'three'}]]
--------------------------------------------------------------
type: 3 * var * {
    x: ?float64,
    y: var * int64,
    z: string
}

If we want only the x field, we can ask for it as an attribute (because it’s a valid Python name) or with a string-valued slice:

array.x
[[1.1, None],
 [],
 [3.3]]
------------------------
type: 3 * var * ?float64
array["x"]
[[1.1, None],
 [],
 [3.3]]
------------------------
type: 3 * var * ?float64

This controls the biggest deficiency of ak.flatten() with axis=None, the mixing of data with different meanings.

ak.flatten(array.x, axis=None)
[1.1,
 3.3]
-----------------
type: 2 * float64
ak.flatten(array.y, axis=None)
[1,
 1,
 2,
 1,
 2,
 3]
---------------
type: 6 * int64

If some of your fields can be safely flattened—together into one set—and others can’t, you can use a list of strings to pick just the fields you want.

ak.flatten(array[["x", "y"]], axis=None)
[1.1,
 3.3,
 1,
 1,
 2,
 1,
 2,
 3]
-----------------
type: 8 * float64

(Careful! A tuple has a special meaning in slices, which doesn’t apply here.)

array[("x", "y")]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[15], line 1
----> 1 array[("x", "y")]

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/highlevel.py:951, in Array.__getitem__(self, where)
    522 """
    523 Args:
    524     where (many types supported; see below): Index of positions to
   (...)
    948 have the same dimension as the array being indexed.
    949 """
    950 with ak._errors.SlicingErrorContext(self, where):
--> 951     out = self._layout[where]
    952     if isinstance(out, ak.contents.NumpyArray):
    953         array_param = out.parameter("__array__")

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:514, in Content.__getitem__(self, where)
    513 def __getitem__(self, where):
--> 514     return self._getitem(where)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:551, in Content._getitem(self, where)
    542 nextwhere = ak._slicing.prepare_advanced_indexing(items)
    544 next = ak.contents.RegularArray(
    545     self,
    546     self.length,
    547     1,
    548     parameters=None,
    549 )
--> 551 out = next._getitem_next(nextwhere[0], nextwhere[1:], None)
    553 if out.length is not None and out.length == 0:
    554     return out._getitem_nothing()

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/regulararray.py:465, in RegularArray._getitem_next(self, head, tail, advanced)
    457         return RegularArray(
    458             nextcontent._getitem_next(nexthead, nexttail, nextadvanced),
    459             nextsize,
    460             self._length,
    461             parameters=self._parameters,
    462         )
    464 elif isinstance(head, str):
--> 465     return self._getitem_next_field(head, tail, advanced)
    467 elif isinstance(head, list):
    468     return self._getitem_next_fields(head, tail, advanced)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:306, in Content._getitem_next_field(self, head, tail, advanced)
    304 def _getitem_next_field(self, head, tail, advanced: ak.index.Index | None):
    305     nexthead, nexttail = ak._slicing.headtail(tail)
--> 306     return self._getitem_field(head)._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/regulararray.py:465, in RegularArray._getitem_next(self, head, tail, advanced)
    457         return RegularArray(
    458             nextcontent._getitem_next(nexthead, nexttail, nextadvanced),
    459             nextsize,
    460             self._length,
    461             parameters=self._parameters,
    462         )
    464 elif isinstance(head, str):
--> 465     return self._getitem_next_field(head, tail, advanced)
    467 elif isinstance(head, list):
    468     return self._getitem_next_fields(head, tail, advanced)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:306, in Content._getitem_next_field(self, head, tail, advanced)
    304 def _getitem_next_field(self, head, tail, advanced: ak.index.Index | None):
    305     nexthead, nexttail = ak._slicing.headtail(tail)
--> 306     return self._getitem_field(head)._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/regulararray.py:227, in RegularArray._getitem_field(self, where, only_fields)
    225 def _getitem_field(self, where, only_fields=()):
    226     return RegularArray(
--> 227         self._content._getitem_field(where, only_fields),
    228         self._size,
    229         self._length,
    230         parameters=None,
    231     )

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/listoffsetarray.py:260, in ListOffsetArray._getitem_field(self, where, only_fields)
    257 def _getitem_field(self, where, only_fields=()):
    258     return ListOffsetArray(
    259         self._offsets,
--> 260         self._content._getitem_field(where, only_fields),
    261         parameters=None,
    262     )

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/indexedoptionarray.py:263, in IndexedOptionArray._getitem_field(self, where, only_fields)
    260 def _getitem_field(self, where, only_fields=()):
    261     return IndexedOptionArray.simplified(
    262         self._index,
--> 263         self._content._getitem_field(where, only_fields),
    264         parameters=None,
    265     )

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/numpyarray.py:248, in NumpyArray._getitem_field(self, where, only_fields)
    247 def _getitem_field(self, where, only_fields=()):
--> 248     raise ak._errors.index_error(self, where, "not an array of records")

IndexError: while attempting to slice

    <Array [[{x: 1.1, y: [1], ...}, ...], ...] type='3 * var * {x: ?float64...'>

with

    ('x', 'y')

at inner NumpyArray of length 2, using sub-slice 'y'.

Error details: not an array of records.

If you have records inside of records, you can extract them with nested projection if they have common names.

array = ak.Array(
    [
        {"x": {"up": 1, "down": -1}, "y": {"up": 1.1, "down": -1.1}},
        {"x": {"up": 2, "down": -2}, "y": {"up": 2.2, "down": -2.2}},
        {"x": {"up": 3, "down": -3}, "y": {"up": 3.3, "down": -3.3}},
        {"x": {"up": 4, "down": -4}, "y": {"up": 4.4, "down": -4.4}},
    ]
)
array
[{x: {up: 1, down: -1}, y: {up: 1.1, ...}},
 {x: {up: 2, down: -2}, y: {up: 2.2, ...}},
 {x: {up: 3, down: -3}, y: {up: 3.3, ...}},
 {x: {up: 4, down: -4}, y: {up: 4.4, ...}}]
-------------------------------------------
type: 4 * {
    x: {
        up: int64,
        down: int64
    },
    y: {
        up: float64,
        down: float64
    }
}
ak.flatten(array[["x", "y"], "up"], axis=None)
[1,
 2,
 3,
 4,
 1.1,
 2.2,
 3.3,
 4.4]
-----------------
type: 8 * float64

ak.flatten for one axis#

Since axis=None is so dangerous, the default value of ak.flatten() is axis=1. This flattens only the first nested dimension.

ak.flatten(ak.Array([[0, 1, 2], [], [3, 4], [5], [6, 7, 8, 9]]))
[0,
 1,
 2,
 3,
 4,
 5,
 6,
 7,
 8,
 9]
----------------
type: 10 * int64

It also removes missing values in the axis that is being flattened because flattening considers a missing list like an empty list.

ak.flatten(ak.Array([[0, 1, 2], None, [3, 4], [5], [6, 7, 8, 9]]))
[0,
 1,
 2,
 3,
 4,
 5,
 6,
 7,
 8,
 9]
----------------
type: 10 * int64

It does not flatten or remove missing values from any other axis.

ak.flatten(ak.Array([[[0, 1, 2, 3, 4]], [], [[5], [6, 7, 8, 9]]]))
[[0, 1, 2, 3, 4],
 [5],
 [6, 7, 8, 9]]
---------------------
type: 3 * var * int64
ak.flatten(ak.Array([[[0, 1, 2, None]], [], [[5], [6, 7, 8, 9]]]))
[[0, 1, 2, None],
 [5],
 [6, 7, 8, 9]]
----------------------
type: 3 * var * ?int64

Moreover, you can’t flatten already-flat data because a 1-dimensional array does not have an axis=1. (axis starts counting at 0.)

ak.flatten(ak.Array([1, 2, 3, 4, 5]))
---------------------------------------------------------------------------
AxisError                                 Traceback (most recent call last)
Cell In[22], line 1
----> 1 ak.flatten(ak.Array([1, 2, 3, 4, 5]))

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/operations/ak_flatten.py:162, in flatten(array, axis, highlevel, behavior)
     10 """
     11 Args:
     12     array: Array-like data (anything #ak.to_layout recognizes).
   (...)
    156      999]
    157 """
    158 with ak._errors.OperationErrorContext(
    159     "ak.flatten",
    160     {"array": array, "axis": axis, "highlevel": highlevel, "behavior": behavior},
    161 ):
--> 162     return _impl(array, axis, highlevel, behavior)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/operations/ak_flatten.py:229, in _impl(array, axis, highlevel, behavior)
    226     return ak._util.wrap(out, behavior, highlevel, like=array)
    228 else:
--> 229     out = ak._do.flatten(layout, axis)
    230     return ak._util.wrap(out, behavior, highlevel, like=array)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/_do.py:254, in flatten(layout, axis)
    253 def flatten(layout: Content, axis: int = 1) -> Content:
--> 254     offsets, flattened = layout._offsets_and_flattened(axis, 1)
    255     return flattened

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/numpyarray.py:351, in NumpyArray._offsets_and_flattened(self, axis, depth)
    348     return self.to_RegularArray()._offsets_and_flattened(axis, depth)
    350 else:
--> 351     raise ak._errors.wrap_error(
    352         np.AxisError(f"axis={axis} exceeds the depth of this array ({depth})")
    353     )

AxisError: while calling

    ak.flatten(
        array = <Array [1, 2, 3, 4, 5] type='5 * int64'>
        axis = 1
        highlevel = True
        behavior = None
    )

Error details: axis=1 exceeds the depth of this array (1)

axis=0 is a valid option for ak.flatten(), but since there can’t be any lists at this level, it only removes missing values.

ak.flatten(ak.Array([1, 2, 3, None, None, 4, 5]), axis=0)
[1,
 2,
 3,
 4,
 5]
---------------
type: 5 * int64

Selecting one element from each list#

Flattening removes list structure without removing values. Often, you want to do the opposite of that: you want to plot one element from each list. This makes the plot “aware” of your list structure.

This kind of operation is usually just a slice.

array = ak.Array([[0, 1, 2], [3, 4], [5], [6, 7, 8, 9]])
array
[[0, 1, 2],
 [3, 4],
 [5],
 [6, 7, 8, 9]]
---------------------
type: 4 * var * int64
array[:, 0]
[0,
 3,
 5,
 6]
---------------
type: 4 * int64

The above syntax selects all lists from the array (axis=0) and the first element from each list (axis=1). We could have as easily selected the last:

array[:, -1]
[2,
 4,
 5,
 9]
---------------
type: 4 * int64

A plot made from ak.flatten(array) would be a plot of all numbers with no knowledge of lists; a plot made from array[:, 0] would be a plot of lists, as represented by the first element in each. It depends on what you want to plot.

What if you get this error?

array = ak.Array([[0, 1, 2], [], [3, 4], [5], [6, 7, 8, 9]])
array
[[0, 1, 2],
 [],
 [3, 4],
 [5],
 [6, 7, 8, 9]]
---------------------
type: 5 * var * int64
array[:, 0]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[28], line 1
----> 1 array[:, 0]

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/highlevel.py:951, in Array.__getitem__(self, where)
    522 """
    523 Args:
    524     where (many types supported; see below): Index of positions to
   (...)
    948 have the same dimension as the array being indexed.
    949 """
    950 with ak._errors.SlicingErrorContext(self, where):
--> 951     out = self._layout[where]
    952     if isinstance(out, ak.contents.NumpyArray):
    953         array_param = out.parameter("__array__")

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:514, in Content.__getitem__(self, where)
    513 def __getitem__(self, where):
--> 514     return self._getitem(where)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:551, in Content._getitem(self, where)
    542 nextwhere = ak._slicing.prepare_advanced_indexing(items)
    544 next = ak.contents.RegularArray(
    545     self,
    546     self.length,
    547     1,
    548     parameters=None,
    549 )
--> 551 out = next._getitem_next(nextwhere[0], nextwhere[1:], None)
    553 if out.length is not None and out.length == 0:
    554     return out._getitem_nothing()

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/regulararray.py:432, in RegularArray._getitem_next(self, head, tail, advanced)
    426 nextcontent = self._content._carry(nextcarry, True)
    428 if advanced is None or (
    429     advanced.length is not None and advanced.length == 0
    430 ):
    431     return RegularArray(
--> 432         nextcontent._getitem_next(nexthead, nexttail, advanced),
    433         nextsize,
    434         self._length,
    435         parameters=self._parameters,
    436     )
    437 else:
    438     nextadvanced = ak.index.Index64.empty(nextcarry.length, index_nplike)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/listarray.py:599, in ListArray._getitem_next(self, head, tail, advanced)
    593 nextcarry = ak.index.Index64.empty(lenstarts, self._backend.index_nplike)
    594 assert (
    595     nextcarry.nplike is self._backend.index_nplike
    596     and self._starts.nplike is self._backend.index_nplike
    597     and self._stops.nplike is self._backend.index_nplike
    598 )
--> 599 self._handle_error(
    600     self._backend[
    601         "awkward_ListArray_getitem_next_at",
    602         nextcarry.dtype.type,
    603         self._starts.dtype.type,
    604         self._stops.dtype.type,
    605     ](
    606         nextcarry.data,
    607         self._starts.data,
    608         self._stops.data,
    609         lenstarts,
    610         head,
    611     ),
    612     slicer=head,
    613 )
    614 nextcontent = self._content._carry(nextcarry, True)
    615 return nextcontent._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:249, in Content._handle_error(self, error, slicer)
    247     raise ak._errors.wrap_error(ValueError(message))
    248 else:
--> 249     raise ak._errors.index_error(self, slicer, message)

IndexError: while attempting to slice

    <Array [[0, 1, 2], [], ..., [5], [6, 7, 8, 9]] type='5 * var * int64'>

with

    (:, 0)

at inner ListArray of length 5, using sub-slice 0.

Error details: index out of range while attempting to get index 0 (in compiled code: https://github.com/scikit-hep/awkward/blob/awkward-cpp-8/awkward-cpp/src/cpu-kernels/awkward_NumpyArray_getitem_next_at.cpp#L21).

It says that it can’t get element 0 of one of the lists, and that’s because this array contains an empty list.

One way to deal with that is to take a range-slice, rather than ask for an individual element from each list.

array[:, :1]
[[0],
 [],
 [3],
 [5],
 [6]]
---------------------
type: 5 * var * int64

But this array still has structure, so you can flatten it as an additional step.

ak.flatten(array[:, :1])
[0,
 3,
 5,
 6]
---------------
type: 4 * int64

Alternatively, you may want to attack the problem head-on: the issue is that some lists have too few elements, so why not remove those lists with an explicit slice? The ak.num() function tells us the length of each nested list.

ak.num(array)
[3,
 0,
 2,
 1,
 4]
---------------
type: 5 * int64
ak.num(array) > 0
[True,
 False,
 True,
 True,
 True]
--------------
type: 5 * bool

Slicing the first dimension with this would ensure that the second dimension always has the element we seek.

array[ak.num(array) > 0, 0]
[0,
 3,
 5,
 6]
---------------
type: 4 * int64

The same applies if we’re taking the last element:

array[ak.num(array) > 0, -1]
[2,
 4,
 5,
 9]
---------------
type: 4 * int64

You can also do fancy things, requesting both the first and last element of each list, as long as it doesn’t run afoul of slicing rules (which were constrained to match NumPy’s in cases that overlap).

array[
    ak.num(array) > 0, [0, -1]
]  # these two arrays have different lengths, can't be broadcasted as in NumPy advanced slicing
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[35], line 1
----> 1 array[
      2     ak.num(array) > 0, [0, -1]
      3 ]  # these two arrays have different lengths, can't be broadcasted as in NumPy advanced slicing

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/highlevel.py:951, in Array.__getitem__(self, where)
    522 """
    523 Args:
    524     where (many types supported; see below): Index of positions to
   (...)
    948 have the same dimension as the array being indexed.
    949 """
    950 with ak._errors.SlicingErrorContext(self, where):
--> 951     out = self._layout[where]
    952     if isinstance(out, ak.contents.NumpyArray):
    953         array_param = out.parameter("__array__")

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:514, in Content.__getitem__(self, where)
    513 def __getitem__(self, where):
--> 514     return self._getitem(where)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/contents/content.py:542, in Content._getitem(self, where)
    540 items = ak._slicing.normalise_items(where, self._backend)
    541 # Prepare items for advanced indexing (e.g. via broadcasting)
--> 542 nextwhere = ak._slicing.prepare_advanced_indexing(items)
    544 next = ak.contents.RegularArray(
    545     self,
    546     self.length,
    547     1,
    548     parameters=None,
    549 )
    551 out = next._getitem_next(nextwhere[0], nextwhere[1:], None)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/_slicing.py:82, in prepare_advanced_indexing(items)
     80 # Then broadcast the index items
     81 nplike = nplike_of(*broadcastable)
---> 82 broadcasted = nplike.broadcast_arrays(*broadcastable)
     84 # And re-assemble the index with the broadcasted items
     85 prepared = []

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/awkward/_nplikes/array_module.py:116, in ArrayModuleNumpyLike.broadcast_arrays(self, *arrays)
    115 def broadcast_arrays(self, *arrays: ArrayLike) -> list[ArrayLike]:
--> 116     return self._module.broadcast_arrays(*arrays)

File <__array_function__ internals>:180, in broadcast_arrays(*args, **kwargs)

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/numpy/lib/stride_tricks.py:540, in broadcast_arrays(subok, *args)
    533 # nditer is not used here to avoid the limit of 32 arrays.
    534 # Otherwise, something like the following one-liner would suffice:
    535 # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],
    536 #                  order='C').itviews
    538 args = [np.array(_m, copy=False, subok=subok) for _m in args]
--> 540 shape = _broadcast_shape(*args)
    542 if all(array.shape == shape for array in args):
    543     # Common case where nothing needs to be broadcasted.
    544     return args

File ~/micromamba-root/envs/awkward-docs/lib/python3.10/site-packages/numpy/lib/stride_tricks.py:422, in _broadcast_shape(*args)
    417 """Returns the shape of the arrays that would result from broadcasting the
    418 supplied arrays against each other.
    419 """
    420 # use the old-iterator because np.nditer does not handle size 0 arrays
    421 # consistently
--> 422 b = np.broadcast(*args[:32])
    423 # unfortunately, it cannot handle 32 or more arguments directly
    424 for pos in range(32, len(args), 31):
    425     # ironically, np.broadcast does not properly handle np.broadcast
    426     # objects (it treats them as scalars)
    427     # use broadcasting to avoid allocating the full array

ValueError: shape mismatch: objects cannot be broadcast to a single shape.  Mismatch is between arg 0 with shape (5,) and arg 1 with shape (2,).
array[ak.num(array) > 0][:, [0, -1]]  # so just put them in different slices
[[0, 2],
 [3, 4],
 [5, 5],
 [6, 9]]
-------------------
type: 4 * 2 * int64

And then flatten the result (if necessary—the shape is regular; some plotting libraries would interpret it as a single set of numbers).

ak.flatten(array[ak.num(array) > 0][:, [0, -1]])
[0,
 2,
 3,
 4,
 5,
 5,
 6,
 9]
---------------
type: 8 * int64

Aggregating each list#

Reductions should be familiar to users of SQL and Pandas; after grouping data by some quantity, one must apply some aggregating operation on each group to get one number for each group. The one-element slices of the previous section are like SQL’s FIRST_VALUE and LAST_VALUE, which is a special case of reducing.

The architypical aggregation function is “sum,” which reduces a list by adding up its values. ak.sum() and its relatives, ak.prod() (product/multiplication), ak.mean(), etc., are all reducers in Awkward Array.

Following NumPy, their default axis is None, but for this application, you’ll need to specify an explicit axis.

array = ak.Array([[0, 1, 2], [], [3, 4], [5], [6, 7, 8, 9]])
array
[[0, 1, 2],
 [],
 [3, 4],
 [5],
 [6, 7, 8, 9]]
---------------------
type: 5 * var * int64
ak.sum(array, axis=1)
[3,
 0,
 7,
 5,
 30]
---------------
type: 5 * int64

Some of these are not defined for empty lists, so you’ll need to either replace the missing values with ak.fill_none() or flatten them.

ak.mean(array, axis=1)
[1,
 nan,
 3.5,
 5,
 7.5]
-----------------
type: 5 * float64
ak.fill_none(ak.mean(array, axis=1), 0)  # fill with zero
[1,
 nan,
 3.5,
 5,
 7.5]
-----------------
type: 5 * float64
ak.fill_none(ak.mean(array, axis=1), ak.mean(array))  # fill with the mean of all
[1,
 nan,
 3.5,
 5,
 7.5]
-----------------
type: 5 * float64
ak.flatten(ak.mean(array, axis=1), axis=0)
[1,
 nan,
 3.5,
 5,
 7.5]
-----------------
type: 5 * float64

Each of these has a different effect: filling with 0 puts an identifiable value in the plot (a peak at 0 if it’s a histogram), filling with the overall mean imputes a value in missing cases, flattening away the missing values reduces the number of entries in the plot. Each of these has a different meaning when interpreting your plot!

Minimizing/maximizing over each list#

Minimizing and maximizing are also reducers, ak.min() and ak.max() (and ak.ptp() for the peak-to-peak difference between the minimum and maximum).

They deserve their own section because they are an important case.

array = ak.Array([[0, 2, 1], [], [4, 3], [5], [8, 6, 7, 9]])
array
[[0, 2, 1],
 [],
 [4, 3],
 [5],
 [8, 6, 7, 9]]
---------------------
type: 5 * var * int64
ak.min(array, axis=1)
[0,
 None,
 3,
 5,
 6]
----------------
type: 5 * ?int64
ak.max(array, axis=1)
[2,
 None,
 4,
 5,
 9]
----------------
type: 5 * ?int64

As before, they aren’t defined for empty lists, so you’ll have to choose a method to eliminate the missing values.

Sometimes, you want the “top N” elements from each list, rather than the “top 1.” Awkward Array doesn’t (yet) have a function for the “top N” elements, but it can be done with ak.sort() and a slice.

ak.sort(array, axis=1)
[[0, 1, 2],
 [],
 [3, 4],
 [5],
 [6, 7, 8, 9]]
---------------------
type: 5 * var * int64
ak.sort(array, axis=1)[:, -2:]
[[1, 2],
 [],
 [3, 4],
 [5],
 [8, 9]]
---------------------
type: 5 * var * int64

We still have work to do: some of these lists are shorter than the 2 elements we asked for. What should be done with them? Eliminate all lists with fewer than two elements?

ak.sort(array[ak.num(array) >= 2], axis=1)[:, -2:]
[[1, 2],
 [3, 4],
 [8, 9]]
---------------------
type: 3 * var * int64

Or just concatenate everything so that we don’t lose the lists with only one value (5 in this example)?

ak.flatten(ak.sort(array, axis=1)[:, -2:])
[1,
 2,
 3,
 4,
 5,
 8,
 9]
---------------
type: 7 * int64

Minimizing/maximizing lists of records#

Unlike numbers, records do not have an ordering: you cannot call ak.min() on an array of records. But usually, what you want to do instead is to find the minimum or maximum of some quantity calculated from the records and pick records (or record fields) from that.

array = ak.Array(
    [
        [
            {"x": 2, "y": 2, "z": 2.2},
            {"x": 1, "y": 1, "z": 1.1},
            {"x": 3, "y": 3, "z": 3.3},
        ],
        [],
        [{"x": 5, "y": 5, "z": 5.5}, {"x": 4, "y": 4, "z": 4.4}],
        [
            {"x": 7, "y": 7, "z": 7.7},
            {"x": 9, "y": 9, "z": 9.9},
            {"x": 8, "y": 8, "z": 8.8},
            {"x": 6, "y": 6, "z": 6.6},
        ],
    ]
)
array
[[{x: 2, y: 2, z: 2.2}, {x: 1, y: 1, z: 1.1}, {x: 3, y: 3, z: 3.3}],
 [],
 [{x: 5, y: 5, z: 5.5}, {x: 4, y: 4, z: 4.4}],
 [{x: 7, y: 7, z: 7.7}, {x: 9, y: 9, z: 9.9}, {...}, {x: 6, y: 6, z: 6.6}]]
---------------------------------------------------------------------------
type: 4 * var * {
    x: int64,
    y: int64,
    z: float64
}

The ak.argmin() and ak.argmax() functions return the integer index where the minimum or maximum of some numeric formula can be found.

np.sqrt(array.x**2 + array.y**2)
[[2.83, 1.41, 4.24],
 [],
 [7.07, 5.66],
 [9.9, 12.7, 11.3, 8.49]]
-------------------------
type: 4 * var * float64
ak.argmax(np.sqrt(array.x**2 + array.y**2), axis=1)
[2,
 None,
 0,
 1]
----------------
type: 4 * ?int64

These integer indexes can be used as slices if they don’t eliminate a dimension, which can be requested via keepdims=True. This makes a length-1 list for each reduced output.

maximize_by = ak.argmax(np.sqrt(array.x**2 + array.y**2), axis=1, keepdims=True)
maximize_by
[[2],
 [None],
 [0],
 [1]]
--------------------
type: 4 * 1 * ?int64

Applying this to the original array, we get the “best” record in each list, according to maximize_by.

array[maximize_by]
[[{x: 3, y: 3, z: 3.3}],
 [None],
 [{x: 5, y: 5, z: 5.5}],
 [{x: 9, y: 9, z: 9.9}]]
------------------------
type: 4 * var * ?{
    x: int64,
    y: int64,
    z: float64
}
array[maximize_by].to_list()
[[{'x': 3, 'y': 3, 'z': 3.3}],
 [None],
 [{'x': 5, 'y': 5, 'z': 5.5}],
 [{'x': 9, 'y': 9, 'z': 9.9}]]

This still has list structures and missing values, so it’s ready for ak.flatten(), assuming that we extract the appropriate record field to plot.

ak.flatten(array[maximize_by].z, axis=None)
[3.3,
 5.5,
 9.9]
-----------------
type: 3 * float64

Concatenating independently restructured arrays#

Sometimes, what you want to do can’t be a single expression. Suppose we have this data:

array = ak.Array(
    [[{"x": 1.1, "y": [1]}, {"x": 2.2, "y": [1, 2]}], [], [{"x": 3.3, "y": [1, 2, 3]}]]
)
array
[[{x: 1.1, y: [1]}, {x: 2.2, y: [1, 2]}],
 [],
 [{x: 3.3, y: [1, 2, 3]}]]
-----------------------------------------
type: 3 * var * {
    x: float64,
    y: var * int64
}

and we want to combine all x values and the maximum y value in a plot. This requires a different expression on array.x from array.y.

ak.flatten(array.x)
[1.1,
 2.2,
 3.3]
-----------------
type: 3 * float64
ak.flatten(ak.max(array.y, axis=2), axis=None)
[1,
 2,
 3]
---------------
type: 3 * int64

To get all of these into one array (because the plotting function only accepts one argument), you’ll need to ak.concatenate() them.

ak.concatenate(
    [
        ak.flatten(array.x),
        ak.flatten(ak.max(array.y, axis=2), axis=None),
    ]
)
[1.1,
 2.2,
 3.3,
 1,
 2,
 3]
-----------------
type: 6 * float64

Maintaining alignment between arrays with missing values#

Dropping missing values with ak.flatten() doesn’t keep track of where they were removed. This is a problem if the plotting library takes separate sequences for the x-axis and y-axis, and these must be aligned.

Instead of ak.flatten(), you can use ak.is_none().

array = ak.Array(
    [
        {"x": 1, "y": 5.5},
        {"x": 2, "y": 3.3},
        {"x": None, "y": 2.2},
        {"x": 4, "y": None},
        {"x": 5, "y": 1.1},
    ]
)
array
[{x: 1, y: 5.5},
 {x: 2, y: 3.3},
 {x: None, y: 2.2},
 {x: 4, y: None},
 {x: 5, y: 1.1}]
-------------------
type: 5 * {
    x: ?int64,
    y: ?float64
}
ak.is_none(array.x)
[False,
 False,
 True,
 False,
 False]
--------------
type: 5 * bool
ak.is_none(array.y)
[False,
 False,
 False,
 True,
 False]
--------------
type: 5 * bool
to_keep = ~(ak.is_none(array.x) | ak.is_none(array.y))
to_keep
[True,
 True,
 False,
 False,
 True]
--------------
type: 5 * bool
array.x[to_keep], array.y[to_keep]
(<Array [1, 2, 5] type='3 * ?int64'>,
 <Array [5.5, 3.3, 1.1] type='3 * ?float64'>)

Actually drawing structure#

If need be, you can change the plotter to match the data.

array = ak.Array(
    [
        [{"x": 1, "y": 3.3}, {"x": 2, "y": 1.1}, {"x": 3, "y": 2.2}],
        [],
        [{"x": 4, "y": 5.5}, {"x": 5, "y": 4.4}],
        [
            {"x": 5, "y": 1.1},
            {"x": 4, "y": 3.3},
            {"x": 2, "y": 5.5},
            {"x": 1, "y": 4.4},
        ],
    ]
)
array
[[{x: 1, y: 3.3}, {x: 2, y: 1.1}, {x: 3, y: 2.2}],
 [],
 [{x: 4, y: 5.5}, {x: 5, y: 4.4}],
 [{x: 5, y: 1.1}, {x: 4, y: 3.3}, {x: 2, y: 5.5}, {x: 1, y: 4.4}]]
------------------------------------------------------------------
type: 4 * var * {
    x: int64,
    y: float64
}
import matplotlib.pyplot as plt
import matplotlib.path
import matplotlib.patches

fig, ax = plt.subplots()

for line in array:
    if len(line) > 0:
        vertices = np.dstack([np.asarray(line.x), np.asarray(line.y)])[0]
        codes = [matplotlib.path.Path.MOVETO] + [matplotlib.path.Path.LINETO] * (
            len(line) - 1
        )
        path = matplotlib.path.Path(vertices, codes)
        ax.add_patch(matplotlib.patches.PathPatch(path, facecolor="none"))

ax.set_xlim(0, 6)
ax.set_ylim(0, 6);
../_images/5ab1a1868a44e37a002e5b30d9581d2b3163d0872e6cd3e4b5dfe616aaab29a0.png

(The above example assumes that len(array) is small enough to iterate over in Python, but vectorizes over each list in the array. It was adapted from the Matplotlib path tutorial.)