How to restructure arrays with zip/unzip and project#
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%config InteractiveShell.ast_node_interactivity = "last_expr_or_assign"
Unzipping an array of records#
As discussed in How to create arrays of records, in addition to primitive types like numpy.float64 and numpy.datetime64, Awkward Arrays can also contain records. These records are formed from a fixed number of optionally named fields.
import awkward as ak
import numpy as np
records = ak.Array(
[
{"x": 1, "y": 1.1, "z": "one"},
{"x": 2, "y": 2.2, "z": "two"},
{"x": 3, "y": 3.3, "z": "three"},
{"x": 4, "y": 4.4, "z": "four"},
{"x": 5, "y": 5.5, "z": "five"},
]
)
[{x: 1, y: 1.1, z: 'one'},
{x: 2, y: 2.2, z: 'two'},
{x: 3, y: 3.3, z: 'three'},
{x: 4, y: 4.4, z: 'four'},
{x: 5, y: 5.5, z: 'five'}]
----------------------------
type: 5 * {
x: int64,
y: float64,
z: string
}Although it is useful to be able to create arrays from a sequence of records (as arrays of structures), Awkward Array implements arrays as structures of arrays. It is therefore more natural to think about arrays in terms of their fields.
In the above example, we have created an array of records from a list of dictionaries. We can see that the x field of records contains five numpy.int64 values:
records.x
[1, 2, 3, 4, 5] --------------- type: 5 * int64
If we wanted to look at each of the fields of records, we could pull them out individually from the array:
records.y
[1.1, 2.2, 3.3, 4.4, 5.5] ----------------- type: 5 * float64
records.z
['one', 'two', 'three', 'four', 'five'] ---------------- type: 5 * string
Clearly, for arrays with a large number of fields, retrieving each field in this manner would become tedious rather quickly. ak.unzip() can be used to directly build a tuple of the field arrays:
ak.unzip(records)
(<Array [1, 2, 3, 4, 5] type='5 * int64'>,
<Array [1.1, 2.2, 3.3, 4.4, 5.5] type='5 * float64'>,
<Array ['one', 'two', 'three', 'four', 'five'] type='5 * string'>)
Records are not required to have field names. A record without field names is known as a “tuple”, e.g.
tuples = ak.Array(
[
(1, 1.1, "one"),
(2, 2.2, "two"),
(3, 3.3, "three"),
(4, 4.4, "four"),
(5, 5.5, "five"),
]
)
[(1, 1.1, 'one'),
(2, 2.2, 'two'),
(3, 3.3, 'three'),
(4, 4.4, 'four'),
(5, 5.5, 'five')]
-------------------
type: 5 * (
int64,
float64,
string
)If we unzip an array of tuples, we obtain the same result as for records:
ak.unzip(tuples)
(<Array [1, 2, 3, 4, 5] type='5 * int64'>,
<Array [1.1, 2.2, 3.3, 4.4, 5.5] type='5 * float64'>,
<Array ['one', 'two', 'three', 'four', 'five'] type='5 * string'>)
ak.unzip() can be combined with ak.fields() to build a mapping from field name to field array:
dict(zip(ak.fields(records), ak.unzip(records)))
{'x': <Array [1, 2, 3, 4, 5] type='5 * int64'>,
'y': <Array [1.1, 2.2, 3.3, 4.4, 5.5] type='5 * float64'>,
'z': <Array ['one', 'two', 'three', 'four', 'five'] type='5 * string'>}
For tuples, the field names will be strings corresponding to the field index:
dict(zip(ak.fields(tuples), ak.unzip(tuples)))
{'0': <Array [1, 2, 3, 4, 5] type='5 * int64'>,
'1': <Array [1.1, 2.2, 3.3, 4.4, 5.5] type='5 * float64'>,
'2': <Array ['one', 'two', 'three', 'four', 'five'] type='5 * string'>}
Zipping together arrays#
Because Awkward Arrays unzip into distinct arrays, it is reasonable to ask whether the reverse is possible, i.e. given the following arrays
age = ak.Array([18, 32, 87, 55])
name = ak.Array(["Dorit", "Caitlin", "Theodor", "Albano"]);
can we form an array of records? The ak.zip() function provides a way to join compatible arrays into a single array of records:
people = ak.zip({"age": age, "name": name})
[{age: 18, name: 'Dorit'},
{age: 32, name: 'Caitlin'},
{age: 87, name: 'Theodor'},
{age: 55, name: 'Albano'}]
----------------------------
type: 4 * {
age: int64,
name: string
}Similarly, we could also build an array of tuples by passing a sequence of arrays:
ak.zip([age, name])
[(18, 'Dorit'),
(32, 'Caitlin'),
(87, 'Theodor'),
(55, 'Albano')]
-----------------
type: 4 * (
int64,
string
)Zipping and unzipping arrays is a lightweight operation, and so you should not hesitate to zip together arrays if it makes sense for the problem at hand. One of the benefits of combining arrays into an array of records is that slicing and masking operations are applied to all fields, e.g.
people[age > 35]
[{age: 87, name: 'Theodor'},
{age: 55, name: 'Albano'}]
----------------------------
type: 2 * {
age: int64,
name: string
}Arrays with different dimensions#
So far, we’ve looked at simple arrays with the same dimension in each field. It is actually possible to build arrays with fields of different dimensions, e.g.
x = ak.Array(
[
103,
450,
33,
4,
]
)
digits_of_x = ak.Array(
[
[1, 0, 3],
[4, 5, 0],
[3, 3],
[4],
]
)
x_and_digits = ak.zip({"x": x, "digits": digits_of_x})
[[{x: 103, digits: 1}, {x: 103, digits: 0}, {x: 103, digits: 3}],
[{x: 450, digits: 4}, {x: 450, digits: 5}, {x: 450, digits: 0}],
[{x: 33, digits: 3}, {x: 33, digits: 3}],
[{x: 4, digits: 4}]]
-----------------------------------------------------------------
type: 4 * var * {
x: int64,
digits: int64
}The type of this array is
x_and_digits.type
ArrayType(ListType(RecordType([NumpyType('int64'), NumpyType('int64')], ['x', 'digits'])), 4, None)
Note that the x field has changed type:
x.type
ArrayType(NumpyType('int64'), 4, None)
x_and_digits.x.type
ArrayType(ListType(NumpyType('int64')), 4, None)
In zipping the two arrays together, the x has been broadcast against digits_of_x. Sometimes you might want to limit the broadcasting to a particular depth (dimension). This can be done by passing the depth_limit parameter:
x_and_digits = ak.zip({"x": x, "digits": digits_of_x}, depth_limit=1)
[{x: 103, digits: [1, 0, 3]},
{x: 450, digits: [4, 5, 0]},
{x: 33, digits: [3, 3]},
{x: 4, digits: [4]}]
-----------------------------
type: 4 * {
x: int64,
digits: var * int64
}Now the x field has a single dimension
x_and_digits.x.type
ArrayType(NumpyType('int64'), 4, None)
Arrays with different dimension lengths#
What happens if we zip together arrays with the same dimensions, but different lengths in each dimensions?
x_and_y = ak.Array(
[
[103, 903],
[450, 83],
[33, 8],
[4, 109],
]
)
digits_of_x_and_y = ak.Array(
[
[1, 0, 3, 9, 0, 3],
[4, 5, 0, 8, 3],
[3, 3, 8],
[4, 1, 0, 9],
]
)
ak.zip({"x_and_y": x_and_y, "digits": digits_of_x_and_y})
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In[21], line 19
1 x_and_y = ak.Array(
2 [
3 [103, 903],
(...)
7 ]
8 )
10 digits_of_x_and_y = ak.Array(
11 [
12 [1, 0, 3, 9, 0, 3],
(...)
16 ]
17 )
---> 19 ak.zip({"x_and_y": x_and_y, "digits": digits_of_x_and_y})
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_zip.py:153, in zip(arrays, depth_limit, parameters, with_name, right_broadcast, optiontype_outside_record, highlevel, behavior, attrs)
150 yield arrays
152 # Implementation
--> 153 return _impl(
154 arrays,
155 depth_limit,
156 parameters,
157 with_name,
158 right_broadcast,
159 optiontype_outside_record,
160 highlevel,
161 behavior,
162 attrs,
163 )
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/operations/ak_zip.py:247, in _impl(arrays, depth_limit, parameters, with_name, right_broadcast, optiontype_outside_record, highlevel, behavior, attrs)
242 return None
244 depth_context, lateral_context = NamedAxesWithDims.prepare_contexts(
245 list(arrays.values()) if isinstance(arrays, Mapping) else list(arrays)
246 )
--> 247 out = ak._broadcasting.broadcast_and_apply(
248 layouts,
249 action,
250 depth_context=depth_context,
251 lateral_context=lateral_context,
252 right_broadcast=right_broadcast,
253 )
254 assert isinstance(out, tuple) and len(out) == 1
255 out = out[0]
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:1200, 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)
1198 backend = backend_of(*inputs, coerce_to_common=False)
1199 isscalar = []
-> 1200 out = apply_step(
1201 backend,
1202 broadcast_pack(inputs, isscalar),
1203 action,
1204 0,
1205 depth_context,
1206 lateral_context,
1207 {
1208 "allow_records": allow_records,
1209 "left_broadcast": left_broadcast,
1210 "right_broadcast": right_broadcast,
1211 "numpy_to_regular": numpy_to_regular,
1212 "regular_to_jagged": regular_to_jagged,
1213 "function_name": function_name,
1214 "broadcast_parameters_rule": broadcast_parameters_rule,
1215 },
1216 )
1217 assert isinstance(out, tuple)
1218 return tuple(broadcast_unpack(x, isscalar) for x in out)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:1178, in apply_step(backend, inputs, action, depth, depth_context, lateral_context, options)
1176 return result
1177 elif result is None:
-> 1178 return continuation()
1179 else:
1180 raise AssertionError(result)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:1147, in apply_step.<locals>.continuation()
1145 # Any non-string list-types?
1146 elif any(x.is_list and not is_string_like(x) for x in contents):
-> 1147 return broadcast_any_list()
1149 # Any RecordArrays?
1150 elif any(x.is_record for x in contents):
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:671, in apply_step.<locals>.broadcast_any_list()
668 nextinputs.append(x)
669 nextparameters.append(NO_PARAMETERS)
--> 671 outcontent = apply_step(
672 backend,
673 nextinputs,
674 action,
675 depth + 1,
676 copy.copy(depth_context),
677 lateral_context,
678 options,
679 )
680 assert isinstance(outcontent, tuple)
681 parameters = parameters_factory(nextparameters, len(outcontent))
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:1178, in apply_step(backend, inputs, action, depth, depth_context, lateral_context, options)
1176 return result
1177 elif result is None:
-> 1178 return continuation()
1179 else:
1180 raise AssertionError(result)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:1147, in apply_step.<locals>.continuation()
1145 # Any non-string list-types?
1146 elif any(x.is_list and not is_string_like(x) for x in contents):
-> 1147 return broadcast_any_list()
1149 # Any RecordArrays?
1150 elif any(x.is_record for x in contents):
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:722, in apply_step.<locals>.broadcast_any_list()
718 for i, ((named_axis, ndim), x, x_is_string) in enumerate(
719 zip(named_axes_with_ndims, inputs, input_is_string)
720 ):
721 if isinstance(x, listtypes) and not x_is_string:
--> 722 next_content = broadcast_to_offsets_avoiding_carry(x, offsets)
723 nextinputs.append(next_content)
724 nextparameters.append(x._parameters)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_broadcasting.py:385, in broadcast_to_offsets_avoiding_carry(list_content, offsets)
383 return list_content.content[:next_length]
384 else:
--> 385 return list_content._broadcast_tooffsets64(offsets).content
386 elif isinstance(list_content, ListArray):
387 # Is this list contiguous?
388 if index_nplike.array_equal(
389 list_content.starts.data[1:], list_content.stops.data[:-1]
390 ):
391 # Does this list match the offsets?
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/contents/listoffsetarray.py:420, in ListOffsetArray._broadcast_tooffsets64(self, offsets)
415 next_content = self._content[this_start:]
417 if index_nplike.known_data and not index_nplike.array_equal(
418 this_zero_offsets, offsets.data
419 ):
--> 420 raise ValueError("cannot broadcast nested list")
422 return ListOffsetArray(
423 offsets, next_content[: offsets[-1]], parameters=self._parameters
424 )
ValueError: cannot broadcast nested list
This error occurred while calling
ak.zip(
{'x_and_y': <Array [[103, 903], [450, 83], [33, ...], [4, 109]] type=...
)
Arrays which cannot be broadcast against each other will raise a ValueError. In this case, we want to stop broadcasting at the first dimension (depth_limit=1)
ak.zip({"x_and_y": x_and_y, "digits": digits_of_x_and_y}, depth_limit=1)
[{x_and_y: [103, 903], digits: [1, 0, 3, ..., 0, 3]},
{x_and_y: [450, 83], digits: [4, 5, 0, 8, 3]},
{x_and_y: [33, 8], digits: [3, 3, 8]},
{x_and_y: [4, 109], digits: [4, 1, 0, 9]}]
-----------------------------------------------------
type: 4 * {
x_and_y: var * int64,
digits: var * int64
}Projecting arrays#
Sometimes we are interested only in a subset of the fields of an array. For example, imagine that we have an array of coordinates on the \(\hat{x}\hat{y}\) plane:
triangle = ak.Array(
[
{"x": 1, "y": 6, "z": 0},
{"x": 2, "y": 7, "z": 0},
{"x": 3, "y": 8, "z": 0},
]
)
[{x: 1, y: 6, z: 0},
{x: 2, y: 7, z: 0},
{x: 3, y: 8, z: 0}]
--------------------
type: 3 * {
x: int64,
y: int64,
z: int64
}If we know that these points should lie on a plane, then we might wish to discard the \(\hat{z}\) coordinate. We can do this by slicing only the \(\hat{x}\) and \(\hat{y}\) fields:
triangle_2d = triangle[["x", "y"]]
[{x: 1, y: 6},
{x: 2, y: 7},
{x: 3, y: 8}]
--------------
type: 3 * {
x: int64,
y: int64
}Note that the key passed to the subscript operator is a list ["x", "y"], not a tuple. Awkward Array recognises the list to mean “take both the "x" and "y" fields”.
Projections can be combined with array slicing and masking, e.g.
triangle_2d_first_2 = triangle[:2, ["x", "y"]]
[{x: 1, y: 6},
{x: 2, y: 7}]
--------------
type: 2 * {
x: int64,
y: int64
}Let’s now consider an array of triangles, i.e. a polygon:
triangles = ak.Array(
[
[
{"x": 1, "y": 6, "z": 0},
{"x": 2, "y": 7, "z": 0},
{"x": 3, "y": 8, "z": 0},
],
[
{"x": 4, "y": 9, "z": 0},
{"x": 5, "y": 10, "z": 0},
{"x": 6, "y": 11, "z": 0},
],
]
)
[[{x: 1, y: 6, z: 0}, {x: 2, y: 7, z: 0}, {x: 3, y: 8, z: 0}],
[{x: 4, y: 9, z: 0}, {x: 5, y: 10, z: 0}, {x: 6, y: 11, z: 0}]]
----------------------------------------------------------------
type: 2 * var * {
x: int64,
y: int64,
z: int64
}We can combine an int index 0 with a str projection to view the "x" coordinates of the first triangle vertices
triangles[0, "x"]
[1, 2, 3] --------------- type: 3 * int64
We could even ignore the first vertex of each triangle
triangles[0, 1:, "x"]
[2, 3] --------------- type: 2 * int64
Projections commute (to the left) with other indices to produce the same result as their “natural” position. This means that the above projection could also be written as
triangles[0, "x", 1:]
[2, 3] --------------- type: 2 * int64
or even
triangles["x", 0, 1:]
[2, 3] --------------- type: 2 * int64
For columnar Awkward Arrays, there is no performance difference between any of these approaches; projecting the records of an array just changes its metadata, rather than invoking any loops over the data.
Projecting records-of-records#
The records of an array can themselves contain records
polygon = ak.Array(
[
{
"vertex": [
{"x": 1, "y": 6, "z": 0},
{"x": 2, "y": 7, "z": 0},
{"x": 3, "y": 8, "z": 0},
],
"normal": [
{"x": 0.164, "y": 0.986, "z": 0.0},
{"x": 0.275, "y": 0.962, "z": 0.0},
{"x": 0.351, "y": 0.936, "z": 0.0},
],
"n_vertex": 3,
},
{
"vertex": [
{"x": 4, "y": 9, "z": 0},
{"x": 5, "y": 10, "z": 0},
{"x": 6, "y": 11, "z": 0},
{"x": 7, "y": 12, "z": 0},
],
"normal": [
{"x": 0.406, "y": 0.914, "z": 0.0},
{"x": 0.447, "y": 0.894, "z": 0.0},
{"x": 0.470, "y": 0.878, "z": 0.0},
{"x": 0.504, "y": 0.864, "z": 0.0},
],
"n_vertex": 4,
},
]
)
[{vertex: [{x: 1, y: 6, z: 0}, ..., {...}], normal: [...], n_vertex: 3},
{vertex: [{x: 4, y: 9, z: 0}, ..., {...}], normal: [...], n_vertex: 4}]
------------------------------------------------------------------------
type: 2 * {
vertex: var * {
x: int64,
y: int64,
z: int64
},
normal: var * {
x: float64,
y: float64,
z: float64
},
n_vertex: int64
}Naturally we can access the "vertex" field with the . operator:
polygon.vertex
[[{x: 1, y: 6, z: 0}, {x: 2, y: 7, z: 0}, {x: 3, y: 8, z: 0}],
[{x: 4, y: 9, z: 0}, {x: 5, y: 10, z: 0}, {...}, {x: 7, y: 12, z: 0}]]
-----------------------------------------------------------------------
type: 2 * var * {
x: int64,
y: int64,
z: int64
}We can view the "x" field of the vertex array with an additional lookup
polygon.vertex.x
[[1, 2, 3], [4, 5, 6, 7]] --------------------- type: 2 * var * int64
The . operator represents the simplest slice of a single string, i.e.
polygon["vertex"]
[[{x: 1, y: 6, z: 0}, {x: 2, y: 7, z: 0}, {x: 3, y: 8, z: 0}],
[{x: 4, y: 9, z: 0}, {x: 5, y: 10, z: 0}, {...}, {x: 7, y: 12, z: 0}]]
-----------------------------------------------------------------------
type: 2 * var * {
x: int64,
y: int64,
z: int64
}The slice corresponding to the nested lookup .vertex.x is given by a tuple of str:
polygon[("vertex", "x")]
[[1, 2, 3], [4, 5, 6, 7]] --------------------- type: 2 * var * int64
It is even possible to combine multiple and single projections. Let’s project the "x" field of the "vertex" and "normal" fields:
polygon[["vertex", "normal"], "x"]
[{vertex: [1, 2, 3], normal: [0.164, ..., 0.351]},
{vertex: [4, 5, 6, 7], normal: [0.406, ..., 0.504]}]
-----------------------------------------------------
type: 2 * {
vertex: var * int64,
normal: var * float64
}