Thinking in arrays#
Originally presented as part of HSF-India training on December 18, 2023.
So far, all the arrays we’ve dealt with have been rectangular (in $n$ dimensions; “rectilinear”).
What if we had data like this?
[
[[1.84, 0.324]],
[[-1.609, -0.713, 0.005], [0.953, -0.993, 0.011, 0.718]],
[[0.459, -1.517, 1.545], [0.33, 0.292]],
[[-0.376, -1.46, -0.206], [0.65, 1.278]],
[[], [], [1.617]],
[]
]
[
[[-0.106, 0.611]],
[[0.118, -1.788, 0.794, 0.658], [-0.105]]
]
[
[[-0.384], [0.697, -0.856]],
[[0.778, 0.023, -1.455, -2.289], [-0.67], [1.153, -1.669, 0.305, 1.517, -0.292]]
]
[
[[0.205, -0.355], [-0.265], [1.042]],
[[-0.004], [-1.167, -0.054, 0.726, 0.213]],
[[1.741, -0.199, 0.827]]
]
What if we had data like this?
[
{"fill": "#b1b1b1", "stroke": "none", "points": [{"x": 5.27453, "y": 1.03276},
{"x": -3.51280, "y": 1.74849}]},
{"fill": "#b1b1b1", "stroke": "none", "points": [{"x": 8.21630, "y": 4.07844},
{"x": -0.79157, "y": 3.49478}, {"x": 16.38932, "y": 5.29399},
{"x": 10.38641, "y": 0.10832}, {"x": -2.07070, "y": 14.07140},
{"x": 9.57021, "y": -0.94823}, {"x": 1.97332, "y": 3.62380},
{"x": 5.66760, "y": 11.38001}, {"x": 0.25497, "y": 3.39276},
{"x": 3.86585, "y": 6.22051}, {"x": -0.67393, "y": 2.20572}]},
{"fill": "#d0d0ff", "stroke": "none", "points": [{"x": 3.59528, "y": 7.37191},
{"x": 0.59192, "y": 2.91503}, {"x": 4.02932, "y": -1.13601},
{"x": -1.01593, "y": 1.95894}, {"x": 1.03666, "y": 0.05251}]},
{"fill": "#d0d0ff", "stroke": "none", "points": [{"x": -8.78510, "y": -0.00497},
{"x": -15.22688, "y": 3.90244}, {"x": 5.74593, "y": 4.12718}]},
{"fill": "none", "stroke": "#000000", "points": [{"x": 4.40625, "y": -6.953125},
{"x": 4.34375, "y": -7.09375}, {"x": 4.3125, "y": -7.140625},
{"x": 4.140625, "y": -7.140625}]},
{"fill": "none", "stroke": "#808080", "points": [{"x": 0.46875, "y": -0.09375},
{"x": 0.46875, "y": -0.078125}, {"x": 0.46875, "y": 0.53125}]}
]
What if we had data like this?
[
{"movie": "Evil Dead", "year": 1981, "actors":
["Bruce Campbell", "Ellen Sandweiss", "Richard DeManincor", "Betsy Baker"]
},
{"movie": "Darkman", "year": 1900, "actors":
["Liam Neeson", "Frances McDormand", "Larry Drake", "Bruce Campbell"]
},
{"movie": "Army of Darkness", "year": 1992, "actors":
["Bruce Campbell", "Embeth Davidtz", "Marcus Gilbert", "Bridget Fonda",
"Ted Raimi", "Patricia Tallman"]
},
{"movie": "A Simple Plan", "year": 1998, "actors":
["Bill Paxton", "Billy Bob Thornton", "Bridget Fonda", "Brent Briscoe"]
},
{"movie": "Spider-Man 2", "year": 2004, "actors":
["Tobey Maguire", "Kristen Dunst", "Alfred Molina", "James Franco",
"Rosemary Harris", "J.K. Simmons", "Stan Lee", "Bruce Campbell"]
},
{"movie": "Drag Me to Hell", "year": 2009, "actors":
["Alison Lohman", "Justin Long", "Lorna Raver", "Dileep Rao", "David Paymer"]
}
]
What if we had data like this?
[
{"run": 1, "luminosityBlock": 156, "event": 46501,
"PV": {"x": 0.243, "y": 0.393, "z": 1.451},
"electron": [],
"muon": [
{"pt": 63.043, "eta": -0.718, "phi": 2.968, "mass": 0.105, "charge": 1},
{"pt": 38.120, "eta": -0.879, "phi": -1.032, "mass": 0.105, "charge": -1},
{"pt": 4.048, "eta": -0.320, "phi": 1.038, "mass": 0.105, "charge": 1}
],
"MET": {"pt": 21.929, "phi": -2.730}
},
{"run": 1, "luminosityBlock": 156, "event": 46502,
"PV": {"x": 0.244, "y": 0.395, "z": -2.879},
"electron": [
{"pt": 21.902, "eta": -0.702, "phi": 0.133, "mass": 0.005, "charge": 1},
{"pt": 42.632, "eta": -0.979, "phi": -1.863, "mass": 0.008, "charge": 1},
{"pt": 78.012, "eta": -0.933, "phi": -2.207, "mass": 0.018, "charge": -1},
{"pt": 23.835, "eta": -1.362, "phi": -0.621, "mass": 0.008, "charge": -1}
],
"muon": [],
"MET": {"pt": 16.972, "phi": 2.866}},
...
]
It might be possible to turn these datasets into tabular form using surrogate keys and database normalization, but
they could be inconvenient or less efficient in that form, depending on what we want to do,
they were very likely given in a ragged/untidy form. You can’t ignore the data-cleaning step!
Dealing with these datasets as JSON or Python objects is inefficient for the same reason as for lists of numbers.
We want arbitrary data structure with array-oriented interface and performance…
Libraries for irregular arrays#
import pyarrow as pa
arrow_array = pa.array([
[{"x": 1.1, "y": [1]}, {"x": 2.2, "y": [1, 2]}, {"x": 3.3, "y": [1, 2, 3]}],
[],
[{"x": 4.4, "y": [1, 2, 3, 4]}, {"x": 5.5, "y": [1, 2, 3, 4, 5]}]
])
arrow_array.type
ListType(list<item: struct<x: double, y: list<item: int64>>>)
arrow_array
<pyarrow.lib.ListArray object at 0x7f8d30e74880>
[
-- is_valid: all not null
-- child 0 type: double
[
1.1,
2.2,
3.3
]
-- child 1 type: list<item: int64>
[
[
1
],
[
1,
2
],
[
1,
2,
3
]
],
-- is_valid: all not null
-- child 0 type: double
[]
-- child 1 type: list<item: int64>
[],
-- is_valid: all not null
-- child 0 type: double
[
4.4,
5.5
]
-- child 1 type: list<item: int64>
[
[
1,
2,
3,
4
],
[
1,
2,
3,
4,
5
]
]
]
import awkward as ak
awkward_array = ak.from_arrow(arrow_array)
awkward_array
[[{x: 1.1, y: [1]}, {x: 2.2, y: [...]}, {x: 3.3, y: [1, 2, 3]}],
[],
[{x: 4.4, y: [1, 2, 3, 4]}, {x: 5.5, y: [1, ..., 5]}]]
----------------------------------------------------------------
type: 3 * var * ?{
x: ?float64,
y: option[var * ?int64]
}
ak.to_parquet(awkward_array, "/tmp/file.parquet")
<pyarrow._parquet.FileMetaData object at 0x7f8d30447420>
created_by: parquet-cpp-arrow version 18.1.0
num_columns: 2
num_rows: 3
num_row_groups: 1
format_version: 2.6
serialized_size: 0
ak.from_parquet("/tmp/file.parquet")
[[{x: 1.1, y: [1]}, {x: 2.2, y: [...]}, {x: 3.3, y: [1, 2, 3]}],
[],
[{x: 4.4, y: [1, 2, 3, 4]}, {x: 5.5, y: [1, ..., 5]}]]
----------------------------------------------------------------
type: 3 * var * ?{
x: ?float64,
y: option[var * ?int64]
}Awkward Array#
ragged = ak.Array([
[
[[1.84, 0.324]],
[[-1.609, -0.713, 0.005], [0.953, -0.993, 0.011, 0.718]],
[[0.459, -1.517, 1.545], [0.33, 0.292]],
[[-0.376, -1.46, -0.206], [0.65, 1.278]],
[[], [], [1.617]],
[]
],
[
[[-0.106, 0.611]],
[[0.118, -1.788, 0.794, 0.658], [-0.105]]
],
[
[[-0.384], [0.697, -0.856]],
[[0.778, 0.023, -1.455, -2.289], [-0.67], [1.153, -1.669, 0.305, 1.517, -0.292]]
],
[
[[0.205, -0.355], [-0.265], [1.042]],
[[-0.004], [-1.167, -0.054, 0.726, 0.213]],
[[1.741, -0.199, 0.827]]
]
])
Multidimensional indexing
ragged[3, 1, -1, 2]
np.float64(0.726)
Basic slicing
ragged[3, 1:, -1, 1:3]
[[-0.054, 0.726], [-0.199, 0.827]] ----------------------- type: 2 * var * float64
Advanced slicing
ragged[[False, False, True, True], [0, -1, 0, -1], 0, -1]
[-0.384, 0.827] ----------------- type: 2 * float64
Awkward slicing
ragged > 0
[[[[True, True]], [[False, False, True], [True, ..., True]], ..., [...], []], [[[False, True]], [[True, False, True, True], [False]]], [[[False], [True, False]], [[True, True, False, False], ..., [...]]], [[[True, False], [False], [True]], [[False], ...], [[True, False, True]]]] ----------------------------------------------------------------------------- type: 4 * var * var * var * bool
ragged[ragged > 0]
[[[[1.84, 0.324]], [[0.005], [0.953, 0.011, 0.718]], [...], ..., [[], ...], []], [[[0.611]], [[0.118, 0.794, 0.658], []]], [[[], [0.697]], [[0.778, 0.023], [], [1.15, 0.305, 1.52]]], [[[0.205], [], [1.04]], [[], [0.726, 0.213]], [[1.74, 0.827]]]] -------------------------------------------------------------------------------- type: 4 * var * var * var * float64
Reductions
ak.sum(ragged)
np.float64(2.8980000000000006)
ak.sum(ragged, axis=-1)
[[[2.16], [-2.32, 0.689], [0.487, 0.622], [-2.04, ...], [0, 0, 1.62], []], [[0.505], [-0.218, -0.105]], [[-0.384, -0.159], [-2.94, -0.67, 1.01]], [[-0.15, -0.265, 1.04], [-0.004, -0.282], [2.37]]] -------------------------------------------------------------------------- type: 4 * var * var * float64
ak.sum(ragged, axis=0)
[[[1.56, 0.58], [0.432, -0.856], [1.04]], [[-0.717, -2.48, -0.656, -1.63], ..., [1.15, -1.67, 0.305, 1.52, -0.292]], [[2.2, -1.72, 2.37], [0.33, 0.292]], [[-0.376, -1.46, -0.206], [0.65, 1.28]], [[], [], [1.62]], []] --------------------------------------------------------------------------- type: 6 * var * var * float64
How do we even define reductions on an array with variable length lists?
How do we even define reductions on an array with variable length lists?
array = ak.Array([[ 1, 2, 3, 4],
[ 10, None, 30 ],
[ 100, 200 ]])
ak.sum(array, axis=0).tolist()
[111, 202, 33, 4]
ak.sum(array, axis=1).tolist()
[10, 40, 300]
(You almost always want the deepest/maximum axis, which you can get with axis=-1.)
Awkward Arrays in particle physics#
import uproot
file = uproot.open("https://github.com/jpivarski-talks/2023-12-18-hsf-india-tutorial-bhubaneswar/raw/main/data/SMHiggsToZZTo4L.root")
file
<ReadOnlyDirectory '/' at 0x7f8d8c7d4810>
tree = file["Events"]
tree
<TTree 'Events' (32 branches) at 0x7f8d2edcbfd0>
tree.arrays(entry_stop=100)
[{run: 1, luminosityBlock: 156, event: 46501, PV_npvs: 15, PV_x: 0.244, ...},
{run: 1, luminosityBlock: 156, event: 46502, PV_npvs: 13, PV_x: 0.244, ...},
{run: 1, luminosityBlock: 156, event: 46503, PV_npvs: 11, PV_x: 0.242, ...},
{run: 1, luminosityBlock: 156, event: 46504, PV_npvs: 22, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46505, PV_npvs: 18, PV_x: 0.24, ...},
{run: 1, luminosityBlock: 156, event: 46506, PV_npvs: 5, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46507, PV_npvs: 11, PV_x: 0.242, ...},
{run: 1, luminosityBlock: 156, event: 46508, PV_npvs: 25, PV_x: 0.245, ...},
{run: 1, luminosityBlock: 156, event: 46509, PV_npvs: 12, PV_x: 0.246, ...},
{run: 1, luminosityBlock: 156, event: 46510, PV_npvs: 18, PV_x: 0.244, ...},
...,
{run: 1, luminosityBlock: 156, event: 46592, PV_npvs: 26, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46593, PV_npvs: 12, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46594, PV_npvs: 8, PV_x: 0.246, ...},
{run: 1, luminosityBlock: 156, event: 46595, PV_npvs: 17, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46596, PV_npvs: 17, PV_x: 0.245, ...},
{run: 1, luminosityBlock: 156, event: 46597, PV_npvs: 14, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46598, PV_npvs: 22, PV_x: 0.243, ...},
{run: 1, luminosityBlock: 156, event: 46599, PV_npvs: 13, PV_x: 0.245, ...},
{run: 1, luminosityBlock: 156, event: 46600, PV_npvs: 21, PV_x: 0.246, ...}]
-----------------------------------------------------------------------------
type: 100 * {
run: int32,
luminosityBlock: uint32,
event: uint64,
PV_npvs: int32,
PV_x: float32,
PV_y: float32,
PV_z: float32,
nMuon: uint32,
Muon_pt: var * float32,
Muon_eta: var * float32,
Muon_phi: var * float32,
Muon_mass: var * float32,
Muon_charge: var * int32,
Muon_pfRelIso03_all: var * float32,
Muon_pfRelIso04_all: var * float32,
Muon_dxy: var * float32,
Muon_dxyErr: var * float32,
Muon_dz: var * float32,
Muon_dzErr: var * float32,
nElectron: uint32,
Electron_pt: var * float32,
Electron_eta: var * float32,
Electron_phi: var * float32,
Electron_mass: var * float32,
Electron_charge: var * int32,
Electron_pfRelIso03_all: var * float32,
Electron_dxy: var * float32,
Electron_dxyErr: var * float32,
Electron_dz: var * float32,
Electron_dzErr: var * float32,
MET_pt: float32,
MET_phi: float32
}The same data fits into Parquet files (a little more easily).
events = ak.from_parquet("https://github.com/jpivarski-talks/2023-12-18-hsf-india-tutorial-bhubaneswar/raw/main/data/SMHiggsToZZTo4L.parquet")
events
[{run: 1, luminosityBlock: 156, event: 46501, PV: {...}, electron: [], ...},
{run: 1, luminosityBlock: 156, event: 46502, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 156, event: 46503, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 156, event: 46504, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 156, event: 46505, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 156, event: 46506, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 156, event: 46507, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 156, event: 46508, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 156, event: 46509, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 156, event: 46510, PV: {...}, electron: [], ...},
...,
{run: 1, luminosityBlock: 996, event: 298792, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 996, event: 298793, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 996, event: 298794, PV: {...}, electron: [], ...},
{run: 1, luminosityBlock: 996, event: 298795, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 996, event: 298796, PV: {...}, electron: [], ...},
{run: 1, luminosityBlock: 996, event: 298797, PV: {...}, electron: ..., ...},
{run: 1, luminosityBlock: 996, event: 298798, PV: {...}, electron: [], ...},
{run: 1, luminosityBlock: 996, event: 298799, PV: {...}, electron: [...], ...},
{run: 1, luminosityBlock: 996, event: 298800, PV: {...}, electron: [...], ...}]
--------------------------------------------------------------------------------
type: 299973 * {
run: int32,
luminosityBlock: int64,
event: uint64,
PV: Vector3D[
x: float32,
y: float32,
z: float32
],
electron: var * Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
],
muon: var * Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
pfRelIso04_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
],
MET: Momentum2D[
pt: float32,
phi: float32
]
}View the first event as Python lists and dicts (like JSON).
events[0].to_list()
{'run': 1,
'luminosityBlock': 156,
'event': 46501,
'PV': {'x': 0.24369880557060242,
'y': 0.3936990201473236,
'z': 1.451307773590088},
'electron': [],
'muon': [{'pt': 63.04386901855469,
'eta': -0.7186822295188904,
'phi': 2.968005895614624,
'mass': 0.10565836727619171,
'charge': 1,
'pfRelIso03_all': 0.0,
'pfRelIso04_all': 0.0,
'dxy': -0.004785160068422556,
'dxyErr': 0.0060764215886592865,
'dz': 0.09005985409021378,
'dzErr': 0.044572051614522934},
{'pt': 38.12034606933594,
'eta': -0.8794569969177246,
'phi': -1.0324749946594238,
'mass': 0.10565836727619171,
'charge': -1,
'pfRelIso03_all': 0.0,
'pfRelIso04_all': 0.0,
'dxy': 0.0005746808601543307,
'dxyErr': 0.0013040687190368772,
'dz': -0.0032290113158524036,
'dzErr': 0.003023269586265087},
{'pt': 4.04868745803833,
'eta': -0.320764422416687,
'phi': 1.0385035276412964,
'mass': 0.10565836727619171,
'charge': 1,
'pfRelIso03_all': 0.0,
'pfRelIso04_all': 0.17997965216636658,
'dxy': -0.00232272082939744,
'dxyErr': 0.004343290813267231,
'dz': -0.005162843037396669,
'dzErr': 0.004190043080598116}],
'MET': {'pt': 21.929929733276367, 'phi': -2.7301223278045654}}
Get one numeric field (also known as “column”).
events.electron.pt
[[], [21.9, 42.6, 78, 23.8], [11.6, 6.69], [10.4], [30.7, 29.2, 6.38, 6.24], [16.1], [5.32], [6.99], [41, 6.5, 13.1, 52.1], [], ..., [19.1, 9.69], [30.2], [], [37, 7.36, 48], [], [12.3], [], [17.9, 23.2], [48.1, 38.7]] ---------------------------- type: 299973 * var * float32
Compute something ($p_z = p_T \sinh\eta$).
import numpy as np
events.electron.pt * np.sinh(events.electron.eta)
[[], [-16.7, -48.8, -83.9, -43.5], [-11.1, 26], [-0.237], [-19.9, 47.5, -18, -15.1], [5.58], [-3.22], [3.88], [-8.92, -10.5, -23.8, -17.3], [], ..., [26.4, 19.1], [92.2], [], [-193, -2.78, -43.4], [], [-3.4], [], [80.1, 99.3], [26.8, 74]] ------------------------------ type: 299973 * var * float32
Note that the Vector library works with Awkward Arrays, if it is imported this way:
import vector
vector.register_awkward()
Records with name="Momentum4D" and fields with coordinate names (px, py, pz, E or pt, phi, eta, m) automatically get Vector properties and methods.
events.electron.type.show()
299973 * var * Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
]
# implicitly computes pz = pt * sinh(eta)
events.electron.pz
[[], [-16.7, -48.8, -83.9, -43.5], [-11.1, 26], [-0.237], [-19.9, 47.5, -18, -15.1], [5.58], [-3.22], [3.88], [-8.92, -10.5, -23.8, -17.3], [], ..., [26.4, 19.1], [92.2], [], [-193, -2.78, -43.4], [], [-3.4], [], [80.1, 99.3], [26.8, 74]] ------------------------------ type: 299973 * var * float32
To make histograms or other plots, we need numbers without structure, so ak.flatten() the array.
from hist import Hist
Hist.new.Regular(100, 0, 100, name=" ").Double().fill(
ak.flatten(events.electron.pt)
).plot();
Each event has a different number of electrons and muons (ak.num() to check).
ak.num(events.electron), ak.num(events.muon)
(<Array [0, 4, 2, 1, 4, 1, 1, 1, ..., 0, 3, 0, 1, 0, 2, 2] type='299973 * int64'>,
<Array [3, 0, 0, 7, 0, 2, 1, 0, ..., 2, 0, 2, 2, 4, 0, 0] type='299973 * int64'>)
So what happens if we try to compute something with the electrons’ $p_T$ and the muons’ $\eta$?
events.electron.pt * np.sinh(events.muon.eta)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In[33], line 1
----> 1 events.electron.pt * np.sinh(events.muon.eta)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_operators.py:54, in _binary_method.<locals>.func(self, other)
51 if _disables_array_ufunc(other):
52 return NotImplemented
---> 54 return ufunc(self, other)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/highlevel.py:1600, in Array.__array_ufunc__(self, ufunc, method, *inputs, **kwargs)
1535 """
1536 Intercepts attempts to pass this Array to a NumPy
1537 [universal functions](https://docs.scipy.org/doc/numpy/reference/ufuncs.html)
(...)
1597 See also #__array_function__.
1598 """
1599 name = f"{type(ufunc).__module__}.{ufunc.__name__}.{method!s}"
-> 1600 with ak._errors.OperationErrorContext(name, inputs, kwargs):
1601 return ak._connect.numpy.array_ufunc(ufunc, method, inputs, kwargs)
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/highlevel.py:1601, in Array.__array_ufunc__(self, ufunc, method, *inputs, **kwargs)
1599 name = f"{type(ufunc).__module__}.{ufunc.__name__}.{method!s}"
1600 with ak._errors.OperationErrorContext(name, inputs, kwargs):
-> 1601 return ak._connect.numpy.array_ufunc(ufunc, method, inputs, kwargs)
File ~/micromamba/envs/awkward-docs/lib/python3.11/site-packages/awkward/_connect/numpy.py:469, in array_ufunc(ufunc, method, inputs, kwargs)
461 raise TypeError(
462 "no {}.{} overloads for custom types: {}".format(
463 type(ufunc).__module__, ufunc.__name__, ", ".join(error_message)
464 )
465 )
467 return None
--> 469 out = ak._broadcasting.broadcast_and_apply(
470 inputs,
471 action,
472 depth_context=depth_context,
473 lateral_context=lateral_context,
474 allow_records=False,
475 function_name=ufunc.__name__,
476 )
478 out_named_axis = functools.reduce(
479 _unify_named_axis, lateral_context[NAMED_AXIS_KEY].named_axis
480 )
481 if len(out) == 1:
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
numpy.multiply.__call__(
<Array [[], [21.9, ...], ..., [48.1, 38.7]] type='299973 * var * fl...'>
<Array [[-0.782, -0.997, -0.326], ..., []] type='299973 * var * flo...'>
)
This is data structure-aware, array-oriented programming.
Application: Filtering events with an array of booleans.
events.MET.pt, events.MET.pt > 20
(<Array [21.9, 17, 19.1, 30.9, ..., 17.7, 24, 12.9] type='299973 * float32'>,
<Array [True, False, False, True, ..., False, True, False] type='299973 * bool'>)
len(events), len(events[events.MET.pt > 20])
(299973, 163222)
Application: Filtering particles with an array of lists of booleans.
events.electron.pt, events.electron.pt > 30
(<Array [[], [21.9, ..., 23.8], ..., [48.1, 38.7]] type='299973 * var * float32'>,
<Array [[], [False, ..., False], ..., [True, True]] type='299973 * var * bool'>)
ak.num(events.electron), ak.num(events.electron[events.electron.pt > 30])
(<Array [0, 4, 2, 1, 4, 1, 1, 1, ..., 0, 3, 0, 1, 0, 2, 2] type='299973 * int64'>,
<Array [0, 2, 0, 0, 1, 0, 0, 0, ..., 0, 2, 0, 0, 0, 0, 2] type='299973 * int64'>)
Quizlet: Using the reducer ak.any(), how would we select events in which any electron has $p_T > 30$ GeV/c$^2$?
events.electron[events.electron.pt > 30]
[[],
[{pt: 42.6, eta: -0.98, phi: -1.86, mass: 0.00867, charge: 1, ...}, ...],
[],
[],
[{pt: 30.7, eta: -0.61, phi: 1.01, mass: 0.0117, charge: -1, ...}],
[],
[],
[],
[{pt: 41, eta: -0.216, phi: 2.79, mass: -0.0128, charge: -1, ...}, {...}],
[],
...,
[],
[{pt: 30.2, eta: 1.84, phi: 1.94, mass: -0.00882, charge: 1, ...}],
[],
[{pt: 37, eta: -2.35, phi: 0.903, mass: -0.0594, charge: 1, ...}, {...}],
[],
[],
[],
[],
[{pt: 48.1, eta: 0.532, phi: -1.61, mass: 0.0127, charge: -1, ...}, ...]]
---------------------------------------------------------------------------
type: 299973 * var * Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
]Awkward Array has two combinatorial primitives:
ak.cartesian() takes a Cartesian product of lists from $N$ different arrays, producing an array of lists of $N$-tuples.
ak.combinations() takes $N$ samples without replacement of lists from a single array, producing an array of lists of $N$-tuples.
numbers = ak.Array([[1, 2, 3], [], [4]])
letters = ak.Array([["a", "b"], ["c"], ["d", "e"]])
ak.cartesian([numbers, letters])
[[(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b'), (3, 'a'), (3, 'b')],
[],
[(4, 'd'), (4, 'e')]]
--------------------------------------------------------------
type: 3 * var * (
int64,
string
)values = ak.Array([[1.1, 2.2, 3.3, 4.4], [], [5.5, 6.6]])
ak.combinations(values, 2)
[[(1.1, 2.2), (1.1, 3.3), (1.1, 4.4), (2.2, ...), (2.2, 4.4), (3.3, 4.4)],
[],
[(5.5, 6.6)]]
--------------------------------------------------------------------------
type: 3 * var * (
float64,
float64
)Often, it’s useful to separate the separate the left-hand sides and right-hand sides of these pairs with ak.unzip(), so they can be used in mathematical expressions.
electron_muon_pairs = ak.cartesian([events.electron, events.muon])
electron_muon_pairs.type.show()
299973 * var * (
Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
],
Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
pfRelIso04_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
]
)
electron_in_pair, muon_in_pair = ak.unzip(electron_muon_pairs)
electron_in_pair.type.show()
299973 * var * Momentum4D[
pt: float32,
eta: float32,
phi: float32,
mass: float32,
charge: int32,
pfRelIso03_all: float32,
dxy: float32,
dxyErr: float32,
dz: float32,
dzErr: float32
]
electron_in_pair.pt, muon_in_pair.pt
(<Array [[], [], [], [10.4, ...], ..., [], [], []] type='299973 * var * float32'>,
<Array [[], [], [], [54.3, ...], ..., [], [], []] type='299973 * var * float32'>)
ak.num(electron_in_pair), ak.num(muon_in_pair)
(<Array [0, 0, 0, 7, 0, 2, 1, 0, ..., 0, 0, 0, 2, 0, 0, 0] type='299973 * int64'>,
<Array [0, 0, 0, 7, 0, 2, 1, 0, ..., 0, 0, 0, 2, 0, 0, 0] type='299973 * int64'>)
To use Vector’s deltaR method ($\Delta R = \sqrt{\Delta\phi^2 + \Delta\eta^2}$), we need to have the electrons and muons in separate arrays.
electron_in_pair, muon_in_pair = ak.unzip(ak.cartesian([events.electron, events.muon]))
electron_in_pair.deltaR(muon_in_pair)
[[], [], [], [1.07, 0.405, 1.97, 2.78, 1.01, 0.906, 2.79], [], [2.55, 0.8], [2.63], [], [], [], ..., [0.44, 3.16, 3.01, 1.05], [3.06, 1.52], [], [], [], [2.54, 0.912], [], [], []] ---------------------------------------------- type: 299973 * var * float32
first_electron_in_pair, second_electron_in_pair = ak.unzip(ak.combinations(events.electron, 2))
first_electron_in_pair.deltaR(second_electron_in_pair)
[[], [2.02, 2.35, 1, 0.347, 1.3, 1.64], [2.96], [], [3.31, 1.23, 2.39, 3.8, 3.19, 2.61], [], [], [], [1.18, 2.05, 2.98, 2.26, 2.59, 1.9], [], ..., [2.87], [], [], [2.05, 2.92, 3.02], [], [], [], [2.96], [2.72]] ------------------------------------- type: 299973 * var * float32
Quizlet: What’s this?
(first_electron_in_pair + second_electron_in_pair).mass
[[], [52.1, 76.8, 22.8, 19.9, 39.1, 64.2], [36], [], [87.3, 18.1, 28.5, 63.9, 56.5, 12.2], [], [], [], [19.8, 44.7, 92.2, 16.7, 38.7, 46.9], [], ..., [27.3], [], [], [39.2, 107, 38.4], [], [], [], [40.6], [91.5]] -------------------------------------- type: 299973 * var * float32
Hist.new.Reg(120, 0, 120, name="mass (GeV)").Double().fill(
ak.flatten((first_electron_in_pair + second_electron_in_pair).mass, axis=-1)
).plot();
