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:2074, in ListOffsetArray._to_backend_array(self, allow_missing, backend)
2072 return buffer.view(np.dtype(("S", max_count)))
2073 else:
-> 2074 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-32/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