# 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);
```

(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.)