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/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1102, in Array.__getitem__(self, where)
def __getitem__(self, where):
   """
   Args:
       where (many types supported; see below): Index of positions to
   (...)
   have the same dimension as the array being indexed.
   """
-> 1102     with ak._errors.SlicingErrorContext(self, where):
       # Handle named axis
       (_, ndim) = self._layout.minmax_depth
       named_axis = _get_named_axis(self)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_errors.py:80, in ErrorContext.__exit__(self, exception_type, exception_value, traceback)
   self._slate.__dict__.clear()
   # Handle caught exception
---> 80     raise self.decorate_exception(exception_type, exception_value)
else:
   # Step out of the way so that another ErrorContext can become primary.
   if self.primary() is self:

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1110, in Array.__getitem__(self, where)
where = _normalize_named_slice(named_axis, where, ndim)
NamedAxis.mapping = named_axis
-> 1110 indexed_layout = prepare_layout(self._layout._getitem(where, NamedAxis))
if NamedAxis.mapping:
   return ak.operations.ak_with_named_axis._impl(
       indexed_layout,
       named_axis=NamedAxis.mapping,
   (...)
       attrs=self._attrs,
   )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:649, in Content._getitem(self, where, named_axis)
named_axis.mapping = _named_axis
next = ak.contents.RegularArray(
   this,
   this.length,
   1,
   parameters=None,
)
--> 649 out = next._getitem_next(nextwhere[0], nextwhere[1:], None)
if out.length is not unknown_length and out.length == 0:
   return out._getitem_nothing()

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/regulararray.py:559, in RegularArray._getitem_next(self, head, tail, advanced)
       return RegularArray(
           nextcontent._getitem_next(nexthead, nexttail, nextadvanced),
           nextsize,
           self._length,
           parameters=self._parameters,
       )
elif isinstance(head, str):
--> 559     return self._getitem_next_field(head, tail, advanced)
elif isinstance(head, list):
   return self._getitem_next_fields(head, tail, advanced)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:326, in Content._getitem_next_field(self, head, tail, advanced)
def _getitem_next_field(
   self,
   head: SliceItem | tuple,
   tail: tuple[SliceItem, ...],
   advanced: Index | None,
):
   nexthead, nexttail = ak._slicing.head_tail(tail)
--> 326     return self._getitem_field(head)._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/regulararray.py:559, in RegularArray._getitem_next(self, head, tail, advanced)
       return RegularArray(
           nextcontent._getitem_next(nexthead, nexttail, nextadvanced),
           nextsize,
           self._length,
           parameters=self._parameters,
       )
elif isinstance(head, str):
--> 559     return self._getitem_next_field(head, tail, advanced)
elif isinstance(head, list):
   return self._getitem_next_fields(head, tail, advanced)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:326, in Content._getitem_next_field(self, head, tail, advanced)
def _getitem_next_field(
   self,
   head: SliceItem | tuple,
   tail: tuple[SliceItem, ...],
   advanced: Index | None,
):
   nexthead, nexttail = ak._slicing.head_tail(tail)
--> 326     return self._getitem_field(head)._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/regulararray.py:324, in RegularArray._getitem_field(self, where, only_fields)
def _getitem_field(
   self, where: str | SupportsIndex, only_fields: tuple[str, ...] = ()
) -> Content:
   return RegularArray(
--> 324         self._content._getitem_field(where, only_fields),
       self._size,
       self._length,
       parameters=None,
   )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/listoffsetarray.py:348, in ListOffsetArray._getitem_field(self, where, only_fields)
def _getitem_field(
   self, where: str | SupportsIndex, only_fields: tuple[str, ...] = ()
) -> Content:
   return ListOffsetArray(
       self._offsets,
--> 348         self._content._getitem_field(where, only_fields),
       parameters=None,
   )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/indexedoptionarray.py:345, in IndexedOptionArray._getitem_field(self, where, only_fields)
def _getitem_field(
   self, where: str | SupportsIndex, only_fields: tuple[str, ...] = ()
) -> Content:
   return IndexedOptionArray.simplified(
       self._index,
--> 345         self._content._getitem_field(where, only_fields),
       parameters=None,
   )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/numpyarray.py:346, in NumpyArray._getitem_field(self, where, only_fields)
def _getitem_field(
   self, where: str | SupportsIndex, only_fields: tuple[str, ...] = ()
) -> Content:
--> 346     raise ak._errors.index_error(self, where, "not an array of records")

IndexError: cannot slice NumpyArray (of length 2) with 'y': not an array of records

This error occurred while attempting to slice

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

with

    ('x', 'y')

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/envs/awkward-docs/lib/python3.11/site-packages/awkward/_dispatch.py:38, in named_high_level_function.<locals>.dispatch(*args, **kwargs)
     35 @wraps(func)
     36 def dispatch(*args, **kwargs):
     37     # NOTE: this decorator assumes that the operation is exposed under `ak.`
---> 38     with OperationErrorContext(name, args, kwargs):
     39         gen_or_result = func(*args, **kwargs)
     40         if isgenerator(gen_or_result):

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_errors.py:80, in ErrorContext.__exit__(self, exception_type, exception_value, traceback)
     78     self._slate.__dict__.clear()
     79     # Handle caught exception
---> 80     raise self.decorate_exception(exception_type, exception_value)
     81 else:
     82     # Step out of the way so that another ErrorContext can become primary.
     83     if self.primary() is self:

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_dispatch.py:64, in named_high_level_function.<locals>.dispatch(*args, **kwargs)
     62 # Failed to find a custom overload, so resume the original function
     63 try:
---> 64     next(gen_or_result)
     65 except StopIteration as err:
     66     return err.value

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/operations/ak_flatten.py:178, in flatten(array, axis, highlevel, behavior, attrs)
    175 yield (array,)
    177 # Implementation
--> 178 return _impl(array, axis, highlevel, behavior, attrs)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/operations/ak_flatten.py:257, in _impl(array, axis, highlevel, behavior, attrs)
    255     out = apply(layout)
    256 else:
--> 257     out = ak._do.flatten(layout, axis)
    259 wrapped_out = ctx.wrap(
    260     out,
    261     highlevel=highlevel,
    262 )
    264 # propagate named axis to output
    265 #   if axis == None: use strategy "remove all" (see: awkward._namedaxis)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_do.py:196, in flatten(layout, axis)
    195 def flatten(layout: Content, axis: int = 1) -> Content:
--> 196     offsets, flattened = layout._offsets_and_flattened(axis, 1)
    197     return flattened

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/numpyarray.py:459, in NumpyArray._offsets_and_flattened(self, axis, depth)
    456     return self.to_RegularArray()._offsets_and_flattened(axis, depth)
    458 else:
--> 459     raise AxisError(f"axis={axis} exceeds the depth of this array ({depth})")

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

This error occurred while calling

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

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/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1102, in Array.__getitem__(self, where)
def __getitem__(self, where):
   """
   Args:
       where (many types supported; see below): Index of positions to
   (...)
   have the same dimension as the array being indexed.
   """
-> 1102     with ak._errors.SlicingErrorContext(self, where):
       # Handle named axis
       (_, ndim) = self._layout.minmax_depth
       named_axis = _get_named_axis(self)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_errors.py:80, in ErrorContext.__exit__(self, exception_type, exception_value, traceback)
   self._slate.__dict__.clear()
   # Handle caught exception
---> 80     raise self.decorate_exception(exception_type, exception_value)
else:
   # Step out of the way so that another ErrorContext can become primary.
   if self.primary() is self:

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1110, in Array.__getitem__(self, where)
where = _normalize_named_slice(named_axis, where, ndim)
NamedAxis.mapping = named_axis
-> 1110 indexed_layout = prepare_layout(self._layout._getitem(where, NamedAxis))
if NamedAxis.mapping:
   return ak.operations.ak_with_named_axis._impl(
       indexed_layout,
       named_axis=NamedAxis.mapping,
   (...)
       attrs=self._attrs,
   )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:649, in Content._getitem(self, where, named_axis)
named_axis.mapping = _named_axis
next = ak.contents.RegularArray(
   this,
   this.length,
   1,
   parameters=None,
)
--> 649 out = next._getitem_next(nextwhere[0], nextwhere[1:], None)
if out.length is not unknown_length and out.length == 0:
   return out._getitem_nothing()

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/regulararray.py:526, in RegularArray._getitem_next(self, head, tail, advanced)
nextcontent = self._content._carry(nextcarry, True)
if advanced is None or (
   advanced.length is not unknown_length and advanced.length == 0
):
   return RegularArray(
--> 526         nextcontent._getitem_next(nexthead, nexttail, advanced),
       nextsize,
       self._length,
       parameters=self._parameters,
   )
else:
   nextadvanced = ak.index.Index64.empty(nextcarry.length, index_nplike)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/listarray.py:730, in ListArray._getitem_next(self, head, tail, advanced)
head = ak._slicing.normalize_integer_like(head)
assert (
   nextcarry.nplike is self._backend.index_nplike
   and self._starts.nplike is self._backend.index_nplike
   and self._stops.nplike is self._backend.index_nplike
)
--> 730 self._maybe_index_error(
   self._backend[
       "awkward_ListArray_getitem_next_at",
       nextcarry.dtype.type,
       self._starts.dtype.type,
       self._stops.dtype.type,
   ](
       nextcarry.data,
       self._starts.data,
       self._stops.data,
       lenstarts,
       head,
   ),
   slicer=head,
)
nextcontent = self._content._carry(nextcarry, True)
return nextcontent._getitem_next(nexthead, nexttail, advanced)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:295, in Content._maybe_index_error(self, error, slicer)
else:
   message = self._backend.format_kernel_error(error)
--> 295     raise ak._errors.index_error(self, slicer, message)

IndexError: cannot slice ListArray (of length 5) with array(0): index out of range while attempting to get index 0 (in compiled code: https://github.com/scikit-hep/awkward/blob/awkward-cpp-43/awkward-cpp/src/cpu-kernels/awkward_ListArray_getitem_next_at.cpp#L21)

This error occurred while attempting to slice

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

with

    (:, 0)

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/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1102, in Array.__getitem__(self, where)
    673 def __getitem__(self, where):
    674     """
    675     Args:
    676         where (many types supported; see below): Index of positions to
   (...)
   1100     have the same dimension as the array being indexed.
   1101     """
-> 1102     with ak._errors.SlicingErrorContext(self, where):
   1103         # Handle named axis
   1104         (_, ndim) = self._layout.minmax_depth
   1105         named_axis = _get_named_axis(self)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_errors.py:80, in ErrorContext.__exit__(self, exception_type, exception_value, traceback)
     78     self._slate.__dict__.clear()
     79     # Handle caught exception
---> 80     raise self.decorate_exception(exception_type, exception_value)
     81 else:
     82     # Step out of the way so that another ErrorContext can become primary.
     83     if self.primary() is self:

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1110, in Array.__getitem__(self, where)
   1106 where = _normalize_named_slice(named_axis, where, ndim)
   1108 NamedAxis.mapping = named_axis
-> 1110 indexed_layout = prepare_layout(self._layout._getitem(where, NamedAxis))
   1112 if NamedAxis.mapping:
   1113     return ak.operations.ak_with_named_axis._impl(
   1114         indexed_layout,
   1115         named_axis=NamedAxis.mapping,
   (...)
   1118         attrs=self._attrs,
   1119     )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:584, in Content._getitem(self, where, named_axis)
    582 items = ak._slicing.normalise_items(where, backend)
    583 # Prepare items for advanced indexing (e.g. via broadcasting)
--> 584 nextwhere = ak._slicing.prepare_advanced_indexing(items, backend)
    586 # Handle named axis
    587 # first expand the ellipsis to colons in nextwhere,
    588 # copy nextwhere to not pollute the original
    589 _nextwhere = tuple(nextwhere)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_slicing.py:118, in prepare_advanced_indexing(items, backend)
    116 # Then broadcast the index items
    117 nplike = backend.index_nplike
--> 118 broadcasted = nplike.broadcast_arrays(*[nplike.asarray(x) for x in broadcastable])
    120 # And re-assemble the index with the broadcasted items
    121 prepared = []

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_nplikes/array_module.py:281, in ArrayModuleNumpyLike.broadcast_arrays(self, *arrays)
    279 def broadcast_arrays(self, *arrays: ArrayLikeT) -> list[ArrayLikeT]:
    280     assert not any(isinstance(x, PlaceholderArray) for x in arrays)
--> 281     return self._module.broadcast_arrays(*arrays)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/numpy/lib/_stride_tricks_impl.py:551, in broadcast_arrays(subok, *args)
    544 # nditer is not used here to avoid the limit of 32 arrays.
    545 # Otherwise, something like the following one-liner would suffice:
    546 # return np.nditer(args, flags=['multi_index', 'zerosize_ok'],
    547 #                  order='C').itviews
    549 args = tuple(np.array(_m, copy=None, subok=subok) for _m in args)
--> 551 shape = _broadcast_shape(*args)
    553 if all(array.shape == shape for array in args):
    554     # Common case where nothing needs to be broadcasted.
    555     return args

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/numpy/lib/_stride_tricks_impl.py:431, in _broadcast_shape(*args)
    426 """Returns the shape of the arrays that would result from broadcasting the
    427 supplied arrays against each other.
    428 """
    429 # use the old-iterator because np.nditer does not handle size 0 arrays
    430 # consistently
--> 431 b = np.broadcast(*args[:32])
    432 # unfortunately, it cannot handle 32 or more arguments directly
    433 for pos in range(32, len(args), 31):
    434     # ironically, np.broadcast does not properly handle np.broadcast
    435     # objects (it treats them as scalars)
    436     # 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,).

This error occurred while attempting to slice

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

with

    (<Array [True, False, True, True, True] type='5 * bool'>, [0, -1])

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/17a1ade794ecb17feb6065363ba8286d4eff9cf8cfe27fb44325332d4a77f548.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.)