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])
[1,
 2,
 3,
 None,
 4,
 5]
----------------
type: 6 * ?int64

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

ak.Array([[[[], [1, 2, None]]], [[[3]]], []])
[[[[], [1, 2, None]]],
 [[[3]]],
 []]
----------------------------------
type: 3 * var * var * var * ?int64

They can be shallow (missing lists):

ak.Array([[[[], [1, 2]]], None, [[[3]]], []])
[[[[], [1, 2]]],
 None,
 [[[3]]],
 []]
-----------------------------------------
type: 4 * option[var * var * var * int64]

Or both:

ak.Array([[[[], [3]]], None, [[[None]]], []])
[[[[], [3]]],
 None,
 [[[None]]],
 []]
------------------------------------------
type: 4 * option[var * var * var * ?int64]

Records can also be missing:

ak.Array([{"x": 1, "y": 1}, None, {"x": 2, "y": 2}])
[{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
[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)
Cell In[12], line 1
----> 1 np.asarray(awkward_array)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1439, in Array.__array__(self, dtype)
   1434 with ak._errors.OperationErrorContext(
   1435     "numpy.asarray", (self,), {"dtype": dtype}
   1436 ):
   1437     from awkward._connect.numpy import convert_to_array
-> 1439     return convert_to_array(self._layout, dtype=dtype)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:481, in convert_to_array(layout, dtype)
    480 def convert_to_array(layout, dtype=None):
--> 481     out = ak.operations.to_numpy(layout, allow_missing=False)
    482     if dtype is None:
    483         return out

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_to_numpy.py:48, in to_numpy(array, allow_missing)
     45 yield (array,)
     47 # Implementation
---> 48 return _impl(array, allow_missing)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/operations/ak_to_numpy.py:60, in _impl(array, allow_missing)
     57 backend = NumpyBackend.instance()
     58 numpy_layout = layout.to_backend(backend)
---> 60 return numpy_layout.to_backend_array(allow_missing=allow_missing)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/content.py:1020, in Content.to_backend_array(self, allow_missing, backend)
   1018 else:
   1019     backend = regularize_backend(backend)
-> 1020 return self._to_backend_array(allow_missing, backend)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/bytemaskedarray.py:1055, in ByteMaskedArray._to_backend_array(self, allow_missing, backend)
   1054 def _to_backend_array(self, allow_missing, backend):
-> 1055     return self.to_IndexedOptionArray64()._to_backend_array(allow_missing, backend)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/indexedoptionarray.py:1611, in IndexedOptionArray._to_backend_array(self, allow_missing, backend)
   1609         return nplike.ma.MaskedArray(data, mask)
   1610     else:
-> 1611         raise ValueError(
   1612             "Content.to_nplike cannot convert 'None' values to "
   1613             "np.ma.MaskedArray unless the "
   1614             "'allow_missing' parameter is set to True"
   1615         )
   1616 else:
   1617     if allow_missing:

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

This error occurred while calling

    numpy.asarray(
        <Array [1, 2, None, None, 5] type='5 * ?int64'>
        dtype = None
    )

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
[[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
[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
[1,
 2,
 3,
 None,
 None,
 5]
----------------
type: 6 * ?int64
lists_form = ak.singletons(none_form)
lists_form
[[1],
 [2],
 [3],
 [],
 [],
 [5]]
---------------------
type: 6 * var * int64
ak.firsts(lists_form)
[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
[1,
 2,
 3,
 4,
 5]
---------------
type: 5 * int64
booleans = ak.Array([True, True, False, False, True])
booleans
[True,
 True,
 False,
 False,
 True]
--------------
type: 5 * bool
array[booleans]
[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]
[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]
[2,
 4,
 None,
 None,
 10]
----------------
type: 5 * ?int64

whereas

array + array[booleans]
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[25], line 1
----> 1 array + array[booleans]

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_operators.py:53, in _binary_method.<locals>.func(self, other)
     51 if _disables_array_ufunc(other):
     52     return NotImplemented
---> 53 return ufunc(self, other)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1516, in Array.__array_ufunc__(self, ufunc, method, *inputs, **kwargs)
   1514 name = f"{type(ufunc).__module__}.{ufunc.__name__}.{method!s}"
   1515 with ak._errors.OperationErrorContext(name, inputs, kwargs):
-> 1516     return ak._connect.numpy.array_ufunc(ufunc, method, inputs, kwargs)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:466, in array_ufunc(ufunc, method, inputs, kwargs)
    458         raise TypeError(
    459             "no {}.{} overloads for custom types: {}".format(
    460                 type(ufunc).__module__, ufunc.__name__, ", ".join(error_message)
    461             )
    462         )
    464     return None
--> 466 out = ak._broadcasting.broadcast_and_apply(
    467     inputs, action, allow_records=False, function_name=ufunc.__name__
    468 )
    470 if len(out) == 1:
    471     return wrap_layout(out[0], behavior=behavior, attrs=attrs)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:968, in broadcast_and_apply(inputs, action, depth_context, lateral_context, allow_records, left_broadcast, right_broadcast, numpy_to_regular, regular_to_jagged, function_name, broadcast_parameters_rule)
    966 backend = backend_of(*inputs, coerce_to_common=False)
    967 isscalar = []
--> 968 out = apply_step(
    969     backend,
    970     broadcast_pack(inputs, isscalar),
    971     action,
    972     0,
    973     depth_context,
    974     lateral_context,
    975     {
    976         "allow_records": allow_records,
    977         "left_broadcast": left_broadcast,
    978         "right_broadcast": right_broadcast,
    979         "numpy_to_regular": numpy_to_regular,
    980         "regular_to_jagged": regular_to_jagged,
    981         "function_name": function_name,
    982         "broadcast_parameters_rule": broadcast_parameters_rule,
    983     },
    984 )
    985 assert isinstance(out, tuple)
    986 return tuple(broadcast_unpack(x, isscalar) for x in out)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:946, in apply_step(backend, inputs, action, depth, depth_context, lateral_context, options)
    944     return result
    945 elif result is None:
--> 946     return continuation()
    947 else:
    948     raise AssertionError(result)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:915, in apply_step.<locals>.continuation()
    913 # Any non-string list-types?
    914 elif any(x.is_list and not is_string_like(x) for x in contents):
--> 915     return broadcast_any_list()
    917 # Any RecordArrays?
    918 elif any(x.is_record for x in contents):

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:614, in apply_step.<locals>.broadcast_any_list()
    612         nextparameters.append(x._parameters)
    613     else:
--> 614         raise ValueError(
    615             "cannot broadcast RegularArray of size "
    616             f"{x.size} with RegularArray of size {dim_size}{in_function(options)}"
    617         )
    618 else:
    619     nextinputs.append(x)

ValueError: cannot broadcast RegularArray of size 3 with RegularArray of size 5 in add

This error occurred while calling

    numpy.add.__call__(
        <Array [1, 2, 3, 4, 5] type='5 * int64'>
        <Array [1, 2, 5] type='3 * int64'>
    )

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
[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
@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
[1,
 2,
 None,
 None,
 3]
----------------
type: 5 * ?int64
@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
[1,
 2,
 None,
 None,
 5]
----------------
type: 5 * ?int64