How to perform computations with NumPy#

Awkward Array’s integration with NumPy allows you to use NumPy’s array functions on data with complex structures, including ragged and heterogeneous arrays.

import awkward as ak
import numpy as np

Universal functions (ufuncs)#

NumPy’s universal functions (ufuncs) are functions that operate elementwise on arrays. They are broadcasting-aware, so they can naturally handle data structures like ragged arrays that are common in Awkward Arrays.

Here’s an example of applying np.sqrt, a NumPy ufunc, to an Awkward Array:

data = ak.Array([[1, 4, 9], [], [16, 25]])

np.sqrt(data)
[[1, 2, 3],
 [],
 [4, 5]]
-----------------------
type: 3 * var * float64

Notice that the ufunc applies to the numeric data, passing through all dimensions of nested lists, even if those lists have variable length. This also applies to heterogeneous data, in which the data are not all of the same type.

data = ak.Array([[1, 4, 9], [], 16, [[[25]]]])

np.sqrt(data)
[[1, 2, 3],
 [],
 4,
 [[[5]]]]
---------------------------
type: 4 * union[
    var * union[
        float64,
        var * var * float64
    ],
    float64
]

Unary and binary operations on Awkward Arrays, such as +, -, >, and ==, are actually calling NumPy ufuncs. For instance, +:

array1 = ak.Array([[1, 2, 3], [], [4, 5]])
array2 = ak.Array([[10, 20, 30], [], [40, 50]])

array1 + array2
[[11, 22, 33],
 [],
 [44, 55]]
---------------------
type: 3 * var * int64

is actually np.add:

np.add(array1, array2)
[[11, 22, 33],
 [],
 [44, 55]]
---------------------
type: 3 * var * int64

Arrays with record fields#

Ufuncs can only be applied to numerical data in lists, not records.

records = ak.Array([{"x": 4, "y": 9}, {"x": 16, "y": 25}])
np.sqrt(records)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[7], line 1
----> 1 np.sqrt(records)

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:622, in apply_step.<locals>.broadcast_any_list()
    619         nextinputs.append(x)
    620         nextparameters.append(NO_PARAMETERS)
--> 622 outcontent = apply_step(
    623     backend,
    624     nextinputs,
    625     action,
    626     depth + 1,
    627     copy.copy(depth_context),
    628     lateral_context,
    629     options,
    630 )
    631 assert isinstance(outcontent, tuple)
    632 parameters = parameters_factory(nextparameters, len(outcontent))

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:919, in apply_step.<locals>.continuation()
    917 # Any RecordArrays?
    918 elif any(x.is_record for x in contents):
--> 919     return broadcast_any_record()
    921 else:
    922     raise ValueError(
    923         "cannot broadcast: {}{}".format(
    924             ", ".join(repr(type(x)) for x in inputs), in_function(options)
    925         )
    926     )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:467, in apply_step.<locals>.broadcast_any_record()
    465 def broadcast_any_record():
    466     if not options["allow_records"]:
--> 467         raise ValueError(f"cannot broadcast records{in_function(options)}")
    469     frozen_record_fields: frozenset[str] | None = UNSET
    470     first_record = next(c for c in contents if c.is_record)

ValueError: cannot broadcast records in sqrt

This error occurred while calling

    numpy.sqrt.__call__(
        <Array [{x: 4, y: 9}, {x: 16, ...}] type='2 * {x: int64, y: int64}'>
    )

However, you can pull each field out of a record and apply the ufunc to it.

np.sqrt(records.x)
[2,
 4]
-----------------
type: 2 * float64
np.sqrt(records.y)
[3,
 5]
-----------------
type: 2 * float64

If you want the result wrapped up in a new array of records, you can use ak.zip() to do that.

ak.zip({"x": np.sqrt(records.x), "y": np.sqrt(records.y)})
[{x: 2, y: 3},
 {x: 4, y: 5}]
---------------
type: 2 * {
    x: float64,
    y: float64
}

Here’s an idiom that would apply a ufunc to every field individually, and then wrap up the result as a new record with the same fields (using ak.fields(), ak.unzip(), and ak.zip()):

ak.zip({key: np.sqrt(value) for key, value in zip(ak.fields(records), ak.unzip(records))})
[{x: 2, y: 3},
 {x: 4, y: 5}]
---------------
type: 2 * {
    x: float64,
    y: float64
}

The reaons that Awkward Array does not do this automatically is to prevent mistakes: it’s common for records to represent coordinates of data points, and if the coordinates are not Cartesian, the one-to-one application is not correct.

Using non-NumPy ufuncs#

NumPy-compatible ufuncs exist in other libraries, like SciPy, and can be applied in the same way. Here’s how you can apply scipy.special.gamma and scipy.special.erf:

import scipy.special

data = ak.Array([[0.1, 0.2, 0.3], [], [0.4, 0.5]])
scipy.special.gamma(data)
[[9.51, 4.59, 2.99],
 [],
 [2.22, 1.77]]
-----------------------
type: 3 * var * float64
scipy.special.erf(data)
[[0.112, 0.223, 0.329],
 [],
 [0.428, 0.52]]
-----------------------
type: 3 * var * float64

You can even create your own ufuncs using Numba’s @nb.vectorize:

import numba as nb

@nb.vectorize
def gcd_euclid(x, y):
    # computation that is more complex than a formula
    while y != 0:
        x, y = y, x % y
    return x
x = ak.Array([[10, 20, 30], [], [40, 50]])
y = ak.Array([[5, 40, 15], [], [24, 255]])
gcd_euclid(x, y)
[[5, 20, 15],
 [],
 [8, 5]]
---------------------
type: 3 * var * int64

Since Numba has JIT-compiled this function, it would run much faster on large arrays than custom Python code.

Non-ufunc NumPy functions#

Some NumPy functions don’t satisfy the ufunc protocol, but have been implemented for Awkward Arrays because they are useful. You can tell when a NumPy function has an Awkward Array implementation when a function with the same name and signature exists in both libraries.

For instance, np.where works on Awkward Arrays because ak.where() exists:

np.where(y % 2 == 0, x, y) 
[[5, 20, 15],
 [],
 [40, 255]]
---------------------
type: 3 * var * int64

(The above selects elements from x when y is even and elements from y when y is odd.)

Similarly, np.concatenate works on Awkward Arrays because ak.concatenate() exists:

np.concatenate([x, y])
[[10, 20, 30],
 [],
 [40, 50],
 [5, 40, 15],
 [],
 [24, 255]]
---------------------
type: 6 * var * int64
np.concatenate([x, y], axis=1)
[[10, 20, 30, 5, 40, 15],
 [],
 [40, 50, 24, 255]]
-------------------------
type: 3 * var * int64

Other NumPy functions, without an equivalent in the Awkward Array library, will work only if the Awkward Array can be converted into a NumPy array.

Ragged arrays can’t be converted to NumPy:

np.fft.fft(ak.Array([[1.1, 2.2, 3.3], [], [7.7, 8.8, 9.9]]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[21], line 1
----> 1 np.fft.fft(ak.Array([[1.1, 2.2, 3.3], [], [7.7, 8.8, 9.9]]))

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1532, in Array.__array_function__(self, func, types, args, kwargs)
   1518 def __array_function__(self, func, types, args, kwargs):
   1519     """
   1520     Intercepts attempts to pass this Array to those NumPy functions other
   1521     than universal functions that have an Awkward equivalent.
   (...)
   1530     See also #__array_ufunc__.
   1531     """
-> 1532     return ak._connect.numpy.array_function(
   1533         func, types, args, kwargs, behavior=self._behavior, attrs=self._attrs
   1534     )

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:109, in array_function(func, types, args, kwargs, behavior, attrs)
    106 unique_backends = frozenset(_find_backends(all_arguments))
    107 backend = common_backend(unique_backends)
--> 109 rectilinear_args = tuple(_to_rectilinear(x, backend) for x in args)
    110 rectilinear_kwargs = {k: _to_rectilinear(v, backend) for k, v in kwargs.items()}
    111 result = func(*rectilinear_args, **rectilinear_kwargs)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:109, in <genexpr>(.0)
    106 unique_backends = frozenset(_find_backends(all_arguments))
    107 backend = common_backend(unique_backends)
--> 109 rectilinear_args = tuple(_to_rectilinear(x, backend) for x in args)
    110 rectilinear_kwargs = {k: _to_rectilinear(v, backend) for k, v in kwargs.items()}
    111 result = func(*rectilinear_args, **rectilinear_kwargs)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:78, in _to_rectilinear(arg, backend)
     69     # Otherwise, cast to layout and convert
     70     else:
     71         layout = ak.to_layout(
     72             arg,
     73             allow_record=False,
   (...)
     76             string_policy="error",
     77         )
---> 78         return layout.to_backend(backend).to_backend_array(allow_missing=True)
     79 elif isinstance(arg, tuple):
     80     return tuple(_to_rectilinear(x, backend) for x in arg)

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/listoffsetarray.py:2072, in ListOffsetArray._to_backend_array(self, allow_missing, backend)
   2070     return buffer.view(np.dtype(("S", max_count)))
   2071 else:
-> 2072     return self.to_RegularArray()._to_backend_array(allow_missing, backend)

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/listoffsetarray.py:283, in ListOffsetArray.to_RegularArray(self)
    278 _size = Index64.empty(1, self._backend.index_nplike)
    279 assert (
    280     _size.nplike is self._backend.index_nplike
    281     and self._offsets.nplike is self._backend.index_nplike
    282 )
--> 283 self._backend.maybe_kernel_error(
    284     self._backend[
    285         "awkward_ListOffsetArray_toRegularArray",
    286         _size.dtype.type,
    287         self._offsets.dtype.type,
    288     ](
    289         _size.data,
    290         self._offsets.data,
    291         self._offsets.length,
    292     )
    293 )
    294 size = self._backend.index_nplike.index_as_shape_item(_size[0])
    295 length = self._offsets.length - 1

File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_backends/backend.py:67, in Backend.maybe_kernel_error(self, error)
     65     return
     66 else:
---> 67     raise ValueError(self.format_kernel_error(error))

ValueError: cannot convert to RegularArray because subarray lengths are not regular (in compiled code: https://github.com/scikit-hep/awkward/blob/awkward-cpp-34/awkward-cpp/src/cpu-kernels/awkward_ListOffsetArray_toRegularArray.cpp#L22)

But arrays with equal-sized lists can:

np.fft.fft(ak.Array([[1.1, 2.2, 3.3], [4.4, 5.5, 6.6], [7.7, 8.8, 9.9]]))
[[6.6+0j, -1.65+0.953j, -1.65+-0.953j],
 [16.5+0j, -1.65+0.953j, -1.65+-0.953j],
 [26.4+0j, -1.65+0.953j, -1.65+-0.953j]]
----------------------------------------
type: 3 * 3 * complex128