How to create arrays of missing data

Data at any level of an Awkward Array can be “missing,” represented by None in Python.

This functionality is somewhat like NumPy’s masked arrays, but masked arrays can only declare numerical values to be missing (not, for instance, a row of a 2-dimensional array) and they represent missing data with an np.ma.masked object instead of None.

Pandas also handles missing data, but in several different ways. For floating point columns, NaN (not a number) is used to mean “missing,” and as of version 1.0, Pandas has a pd.NA object for missing data in other data types.

In Awkward Array, floating point NaN and a missing value are clearly distinct. Missing data, like all data in Awkward Arrays, are also not represented by any Python object; they are converted to and from None by ak.to_list and ak.from_iter.

import awkward as ak
import numpy as np

From Python None

The ak.Array constructor and ak.from_iter interpret None as a missing value, and ak.to_list converts them back into None.

ak.Array([1, 2, 3, None, 4, 5])
<Array [1, 2, 3, None, 4, 5] type='6 * ?int64'>

The missing values can be deeply nested (missing integers):

ak.Array([[[[], [1, 2, None]]], [[[3]]], []])
<Array [[[[], [1, 2, None]]], [[[3]]], []] type='3 * var * var * var * ?int64'>

They can be shallow (missing lists):

ak.Array([[[[], [1, 2]]], None, [[[3]]], []])
<Array [[[[], [1, 2]]], None, [[[3]]], []] type='4 * option[var * var * var * in...'>

Or both:

ak.Array([[[[], [3]]], None, [[[None]]], []])
<Array [[[[], [3]]], None, [[[None]]], []] type='4 * option[var * var * var * ?i...'>

Records can also be missing:

ak.Array([{"x": 1, "y": 1}, None, {"x": 2, "y": 2}])
<Array [{x: 1, y: 1}, None, {x: 2, y: 2}] type='3 * ?{"x": int64, "y": int64}'>

Potentially missing values are represented in the type string as “?” or “option[...]” (if the nested type is a list, which needs to be bracketed for clarity).

From NumPy arrays

Normal NumPy arrays can’t represent missing data, but masked arrays can. Here is how one is constructed in NumPy:

numpy_array = np.ma.MaskedArray([1, 2, 3, 4, 5], [False, False, True, True, False])
numpy_array
masked_array(data=[1, 2, --, --, 5],
             mask=[False, False,  True,  True, False],
       fill_value=999999)

It returns np.ma.masked objects if you try to access missing values:

numpy_array[0], numpy_array[1], numpy_array[2], numpy_array[3], numpy_array[4]
(1, 2, masked, masked, 5)

But it uses None for missing values in tolist:

numpy_array.tolist()
[1, 2, None, None, 5]

The ak.from_numpy function converts masked arrays into Awkward Arrays with missing values, as does the ak.Array constructor.

awkward_array = ak.Array(numpy_array)
awkward_array
<Array [1, 2, None, None, 5] type='5 * ?int64'>

The reverse, ak.to_numpy, returns masked arrays if the Awkward Array has missing data.

ak.to_numpy(awkward_array)
masked_array(data=[1, 2, --, --, 5],
             mask=[False, False,  True,  True, False],
       fill_value=999999)

But np.asarray, the usual way of casting data as NumPy arrays, does not. (np.asarray is supposed to return a plain np.ndarray, which np.ma.masked_array is not.)

np.asarray(awkward_array)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
/tmp/ipykernel_1904/3831085602.py in <module>
----> 1 np.asarray(awkward_array)

~/python3.8/lib/python3.8/site-packages/awkward/highlevel.py in __array__(self, *args, **kwargs)
   1355         cannot be sliced as dimensions.
   1356         """
-> 1357         return ak._connect._numpy.convert_to_array(self.layout, args, kwargs)
   1358 
   1359     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):

~/python3.8/lib/python3.8/site-packages/awkward/_connect/_numpy.py in convert_to_array(layout, args, kwargs)
     11 
     12 def convert_to_array(layout, args, kwargs):
---> 13     out = ak.operations.convert.to_numpy(layout, allow_missing=False)
     14     if args == () and kwargs == {}:
     15         return out

~/python3.8/lib/python3.8/site-packages/awkward/operations/convert.py in to_numpy(array, allow_missing)
    308                 return numpy.ma.MaskedArray(data, mask)
    309             else:
--> 310                 raise ValueError(
    311                     "ak.to_numpy cannot convert 'None' values to "
    312                     "np.ma.MaskedArray unless the "

ValueError: ak.to_numpy cannot convert 'None' values to np.ma.MaskedArray unless the 'allow_missing' parameter is set to True

(https://github.com/scikit-hep/awkward-1.0/blob/1.5.0/src/awkward/operations/convert.py#L314)

Missing rows vs missing numbers

In Awkward Array, a missing list is a different thing from a list whose values are missing. However, ak.to_numpy converts it for you.

missing_row = ak.Array([[1, 2, 3], None, [4, 5, 6]])
missing_row
<Array [[1, 2, 3], None, [4, 5, 6]] type='3 * option[var * int64]'>
ak.to_numpy(missing_row)
masked_array(
  data=[[1, 2, 3],
        [--, --, --],
        [4, 5, 6]],
  mask=[[False, False, False],
        [ True,  True,  True],
        [False, False, False]],
  fill_value=999999)

NaN is not missing

Floating point NaN values are simply unrelated to missing values, in both Awkward Array and NumPy.

missing_with_nan = ak.Array([1.1, 2.2, np.nan, None, 3.3])
missing_with_nan
<Array [1.1, 2.2, nan, None, 3.3] type='5 * ?float64'>
ak.to_numpy(missing_with_nan)
masked_array(data=[1.1, 2.2, nan, --, 3.3],
             mask=[False, False, False,  True, False],
       fill_value=1e+20)

Missing values as empty lists

Sometimes, it’s useful to think about a potentially missing value as a length-1 list if it is not missing and a length-0 list if it is. (Some languages define the option type as a kind of list.)

The Awkward functions ak.singletons and ak.firsts convert from “None form” to and from “lists form.”

none_form = ak.Array([1, 2, 3, None, None, 5])
none_form
<Array [1, 2, 3, None, None, 5] type='6 * ?int64'>
lists_form = ak.singletons(none_form)
lists_form
<Array [[1], [2], [3], [], [], [5]] type='6 * var * int64'>
ak.firsts(lists_form)
<Array [1, 2, 3, None, None, 5] type='6 * ?int64'>

Masking instead of slicing

The most common way of filtering data is to slice it with an array of booleans (usually the result of a calculation).

array = ak.Array([1, 2, 3, 4, 5])
array
<Array [1, 2, 3, 4, 5] type='5 * int64'>
booleans = ak.Array([True, True, False, False, True])
booleans
<Array [True, True, False, False, True] type='5 * bool'>
array[booleans]
<Array [1, 2, 5] type='3 * int64'>

The data can also be effectively filtered by replacing values with None. The following syntax does that:

array.mask[booleans]
<Array [1, 2, None, None, 5] type='5 * ?int64'>

(Or use the ak.mask function.)

An advantage of masking is that the length and nesting structure of the masked array is the same as the original array, so anything that broadcasts with one broadcasts with the other (so that unfiltered data can be used interchangeably with filtered data).

array + array.mask[booleans]
<Array [2, 4, None, None, 10] type='5 * ?int64'>

whereas

array + array[booleans]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
/tmp/ipykernel_1904/4053498700.py in <module>
----> 1 array + array[booleans]

~/python3.8/lib/python3.8/site-packages/numpy/lib/mixins.py in func(self, other)
     19         if _disables_array_ufunc(other):
     20             return NotImplemented
---> 21         return ufunc(self, other)
     22     func.__name__ = '__{}__'.format(name)
     23     return func

~/python3.8/lib/python3.8/site-packages/awkward/highlevel.py in __array_ufunc__(self, ufunc, method, *inputs, **kwargs)
   1415         """
   1416         if not hasattr(self, "_tracers"):
-> 1417             return ak._connect._numpy.array_ufunc(ufunc, method, inputs, kwargs)
   1418         else:
   1419             return ak._connect._jax.jax_utils.array_ufunc(

~/python3.8/lib/python3.8/site-packages/awkward/_connect/_numpy.py in array_ufunc(ufunc, method, inputs, kwargs)
    260         return None
    261 
--> 262     out = ak._util.broadcast_and_apply(
    263         inputs, getfunction, behavior, allow_records=False, pass_depth=False
    264     )

~/python3.8/lib/python3.8/site-packages/awkward/_util.py in broadcast_and_apply(inputs, getfunction, behavior, allow_records, pass_depth, pass_user, user, left_broadcast, right_broadcast, numpy_to_regular, regular_to_jagged)
   1153     else:
   1154         isscalar = []
-> 1155         out = apply(broadcast_pack(inputs, isscalar), 0, user)
   1156         assert isinstance(out, tuple)
   1157         return tuple(broadcast_unpack(x, isscalar) for x in out)

~/python3.8/lib/python3.8/site-packages/awkward/_util.py in apply(inputs, depth, user)
    726             args = args + (user,)
    727 
--> 728         custom = getfunction(inputs, *args)
    729         if callable(custom):
    730             return custom()

~/python3.8/lib/python3.8/site-packages/awkward/_connect/_numpy.py in getfunction(inputs)
    205         ):
    206             nplike = ak.nplike.of(*inputs)
--> 207             result = getattr(ufunc, method)(
    208                 *[nplike.asarray(x) for x in inputs], **kwargs
    209             )

ValueError: operands could not be broadcast together with shapes (1,5) (1,3) 

With ArrayBuilder

ak.ArrayBuilder is described in more detail in this tutorial, but you can add missing values to an array using the null method or appending None.

(This is what ak.from_iter uses internally to accumulate data.)

builder = ak.ArrayBuilder()

builder.append(1)
builder.append(2)
builder.null()
builder.append(None)
builder.append(3)

array = builder.snapshot()
array
<Array [1, 2, None, None, 3] type='5 * ?int64'>

In Numba

Functions that Numba Just-In-Time (JIT) compiles can use ak.ArrayBuilder or construct a boolean array for ak.mask.

(ak.ArrayBuilder can’t be constructed or converted to an array using snapshot inside a JIT-compiled function, but can be outside the compiled context.)

import numba as nb
---------------------------------------------------------------------------
ImportError                               Traceback (most recent call last)
/tmp/ipykernel_1904/977659880.py in <module>
----> 1 import numba as nb

~/python3.8/lib/python3.8/site-packages/numba/__init__.py in <module>
    196 
    197 _ensure_llvm()
--> 198 _ensure_critical_deps()
    199 
    200 # we know llvmlite is working as the above tests passed, import it now as SVML

~/python3.8/lib/python3.8/site-packages/numba/__init__.py in _ensure_critical_deps()
    136         raise ImportError("Numba needs NumPy 1.17 or greater")
    137     elif numpy_version > (1, 20):
--> 138         raise ImportError("Numba needs NumPy 1.20 or less")
    139 
    140     try:

ImportError: Numba needs NumPy 1.20 or less
@nb.jit
def example(builder):
    builder.append(1)
    builder.append(2)
    builder.null()
    builder.append(None)
    builder.append(3)
    return builder

builder = example(ak.ArrayBuilder())

array = builder.snapshot()
array
@nb.jit
def faster_example():
    data = np.empty(5, np.int64)
    mask = np.empty(5, np.bool_)
    data[0] = 1
    mask[0] = True
    data[1] = 2
    mask[1] = True
    mask[2] = False
    mask[3] = False
    data[4] = 5
    mask[4] = True
    return data, mask

data, mask = faster_example()

array = ak.Array(data).mask[mask]
array