# Histogramming, grouping, and binning#

## Overview#

Histogramming (see sc.hist), grouping (using sc.groupby), and binning (see Binned data) all serve similar but slightly different purposes. Picking the optimal one of the three for a particular application may yield more natural code and better performance. Let us start by an example. Consider a table of scattered measurements:

[1]:

import numpy as np
import scipp as sc
N = 5000
values = 10*np.random.rand(N)
table = sc.DataArray(
data=sc.array(dims=['position'], unit=sc.units.counts, values=values, variances=values),
coords={
'x':sc.array(dims=['position'], unit='m', values=np.random.rand(N)),
'y':sc.array(dims=['position'], unit='m', values=np.random.rand(N))
})
table.values *= 1.0/np.exp(5.0*table.coords['x'].values)
sc.table(table['position', :5])

[1]:

CoordinatesData
x [m]y [m] [counts]
0.3490.4830.170±0.987
0.2140.3090.774±1.501
0.1660.5681.438±1.817
0.0690.2986.198±2.960
0.5050.7100.798±3.158

We may now be interested in the total intensity (counts) as a function of 'x'. There are three ways to do this:

[2]:

xbins = sc.linspace('x', 0, 1, num=40, unit='m')
ds = sc.Dataset()
ds['histogram'] = table.hist(x=xbins)
ds['groupby'] = table.groupby('x', bins=xbins).sum('position')
ds['bin'] = table.bin(x=xbins).bins.sum()
ds.plot()

[2]:


In the above plot we can only see a single line, since the three solutions yield exactly the same result (neglecting floating-point rounding errors):

• hist sorts data points into ‘x’ bins, summing immediately.

• groupby groups by ‘x’ and then sums (on-the-fly) all data points falling in the same ‘x’ bin.

• bin sorts data points into ‘x’ bins. Summing all rows in a bin yields the same result as grouping and summing directly.

So in this case we get equivalent results, but the application areas differ, as described in more detail in the following sections.

## Histogramming#

scipp.hist directly sums the data and is efficient. Limitations are:

• When histogramming in more than one dimension, the implementation uses sc.bin internally, which may be less efficient and uses more memory.

• Can only apply “sum” or “nansum” to accumulate into a bin. scipp.nanhist is currently implemented differently and uses sc.bin internally. It therefore uses more memory and may be less efficient.

We can also histogram binned data (since binning preserves the 'y' coord), to create 2-D (or N-D) histograms:

[3]:

binned = table.bin(x=xbins)
hist = binned.hist(y=30)
hist.plot()

[3]:

[4]:

hist

[4]:

scipp.DataArray (20.09 KB)
• x: 39
• y: 30
• x
(x [bin-edge])
float64
m
0.0, 0.026, ..., 0.974, 1.0
Values:array([0.        , 0.02564103, 0.05128205, 0.07692308, 0.1025641 ,
0.12820513, 0.15384615, 0.17948718, 0.20512821, 0.23076923,
0.25641026, 0.28205128, 0.30769231, 0.33333333, 0.35897436,
0.38461538, 0.41025641, 0.43589744, 0.46153846, 0.48717949,
0.51282051, 0.53846154, 0.56410256, 0.58974359, 0.61538462,
0.64102564, 0.66666667, 0.69230769, 0.71794872, 0.74358974,
0.76923077, 0.79487179, 0.82051282, 0.84615385, 0.87179487,
0.8974359 , 0.92307692, 0.94871795, 0.97435897, 1.        ])
• y
(y [bin-edge])
float64
m
0.000, 0.033, ..., 0.967, 1.000
Values:array([1.66752674e-04, 3.34919054e-02, 6.68170580e-02, 1.00142211e-01,
1.33467363e-01, 1.66792516e-01, 2.00117669e-01, 2.33442821e-01,
2.66767974e-01, 3.00093127e-01, 3.33418279e-01, 3.66743432e-01,
4.00068585e-01, 4.33393738e-01, 4.66718890e-01, 5.00044043e-01,
5.33369196e-01, 5.66694348e-01, 6.00019501e-01, 6.33344654e-01,
6.66669806e-01, 6.99994959e-01, 7.33320112e-01, 7.66645264e-01,
7.99970417e-01, 8.33295570e-01, 8.66620722e-01, 8.99945875e-01,
9.33271028e-01, 9.66596180e-01, 9.99921333e-01])
• (x, y)
float64
counts
8.843, 23.819, ..., 0.176, 0.210
σ = 3.120, 4.994, ..., 4.944, 5.411
Values:array([[ 8.84325644, 23.81860976, 49.4976635 , ...,  3.2135056 ,
13.45829025, 14.04592603],
[42.74222002, 18.39388409, 12.75192563, ..., 46.46322584,
6.52778616, 11.79280919],
[21.48789334, 16.11954921,  0.        , ...,  9.82269106,
21.96689844, 14.04321256],
...,
[ 0.21908713,  0.22260487,  0.1974337 , ...,  0.09024851,
0.20105889,  0.41550927],
[ 0.41132585,  0.23171099,  0.18533479, ...,  0.20527199,
0.19933816,  0.15076266],
[ 0.22117646,  0.07388296,  0.28080816, ...,  0.07041057,
0.17599879,  0.21047286]])Variances (σ²):array([[ 9.73612674, 24.93789928, 52.11755855, ...,  3.48638267,
14.41914251, 14.28772168],
[52.80128181, 22.22555888, 15.56847396, ..., 56.13397291,
8.0005368 , 14.04364146],
[29.35380961, 21.40488388,  0.        , ..., 13.16919082,
31.65339085, 19.48055248],
...,
[23.6604271 , 23.07548767, 22.12024326, ...,  9.40524155,
21.65074116, 44.6613208 ],
[51.31806853, 27.95875222, 22.98567965, ..., 24.56105537,
24.81783993, 18.35878785],
[31.40714635, 10.82869794, 38.38862395, ..., 10.09899177,
24.44543063, 29.28121435]])

Another capability of hist is to histogram a dimension that has previously been binned with a different or higher resolution, i.e. different bin edges. Compare to the plot of the initial example:

[5]:

binned = table.bin(x=xbins)
binned.hist(x=100).plot()

[5]:


## Grouping#

groupby is more flexible in terms of operations than can be applied and may be the go-to solution when a quick one-liner is required. Limitations are:

• Can only group along a single dimension.

• Works best for small to medium-sized data, or if data is already mostly sorted along the grouping dimension. Slow if millions of small input slices contribute to each group.

groupby can also operate on binned data, combining bin contents by concatenation:

[6]:

binned = table.bin(x=xbins)
binned.coords['param'] = sc.array(dims=['x'], values=(np.random.random(39)*4).astype(np.int32))
grouped = binned.groupby('param').bins.concat('x')
grouped

/home/runner/work/scipp/scipp/.tox/docs/lib/python3.8/site-packages/scipp/core/bins.py:465: UserWarning: groupby(...).bins.concat(dim) is deprecated. Use group or bin instead
warnings.warn(

[6]:

scipp.DataArray (158.70 KB)
• param: 4
• param
(param)
int32
𝟙
0, 1, 2, 3
Values:array([0, 1, 2, 3], dtype=int32)
• (param)
DataArrayView
binned data [len=611, len=1431, len=1569, len=1389]
dim='position',
content=DataArray(
dims=(position: 5000),
data=float64[counts],
coords={'x':float64[m], 'y':float64[m]})

Each output bin is a combination of multiple input bins:

[7]:

grouped.values[0]

[7]:

scipp.DataArray (20.35 KB out of 157.50 KB)
• position: 611
• x
(position)
float64
m
0.166, 0.170, ..., 0.946, 0.924
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0.17783141, 0.17168246, 0.16902034, 0.17226067, 0.1749174 ,
0.15817696, 0.1544267 , 0.17866485, 0.16599251, 0.17258198,
0.16761383, 0.1654829 , 0.15988281, 0.171422  , 0.17751625,
0.15717724, 0.15620496, 0.16016751, 0.17198831, 0.15598394,
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0.88473846, 0.88270976, 0.89228737, 0.87733648, 0.895093  ,
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0.87608179, 0.87258422, 0.87710094, 0.87727844, 0.89140608,
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0.89495109, 0.89431718, 0.89017405, 0.88669638, 0.89449641,
0.87341469, 0.8838654 , 0.88838185, 0.88805504, 0.89311528,
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0.92398253])
• y
(position)
float64
m
0.568, 0.292, ..., 0.355, 0.893
Values:array([5.68093248e-01, 2.92396230e-01, 3.33223977e-01, 7.03073265e-01,
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2.69648938e-01, 5.47781157e-01, 7.78183557e-02, 4.34863202e-01,
1.03702524e-01, 7.46370120e-01, 5.49891961e-01, 9.37403693e-01,
2.71406077e-01, 9.49703318e-01, 9.51374654e-01, 8.70674104e-01,
6.45655289e-01, 9.23154281e-01, 3.04774776e-01, 9.14193482e-01,
3.90187395e-01, 3.23001972e-01, 7.78646527e-01, 9.76028454e-01,
1.87615801e-01, 9.60590244e-01, 4.03669819e-01, 9.70187524e-01,
7.67912274e-01, 8.01291289e-01, 6.07130723e-01, 7.36235780e-01,
4.61961942e-01, 3.16992755e-01, 8.24573240e-01, 6.59745956e-01,
1.23995067e-01, 4.81041164e-01, 3.04606466e-02, 2.12985046e-01,
3.16212109e-02, 7.96368129e-01, 6.86765634e-01, 9.93441203e-01,
2.78748376e-01, 8.87423644e-01, 3.02603889e-01, 8.38575318e-01,
3.00790743e-01, 1.74310849e-01, 5.71914205e-01, 3.39481419e-01,
9.29939584e-01, 7.02790469e-01, 3.97426272e-02, 3.61110802e-01,
2.89427219e-01, 4.50203069e-01, 1.43300696e-01, 4.23033592e-01,
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• (position)
float64
counts
1.438, 2.850, ..., 0.039, 0.086
σ = 1.817, 2.580, ..., 2.094, 2.959
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2.31990009e-01, 9.06703873e-02, 2.24363653e-01, 6.29753909e-01,
8.13983203e-02, 5.42294401e-01, 2.18797797e-01, 3.18223890e-01,
5.67890825e-01, 2.20956980e-01, 2.74690806e-02, 1.22812318e-01,
5.48186760e-01, 3.52303833e-01, 4.20836770e-01, 3.34513310e-02,
8.53865260e-02, 5.83594078e-01, 2.18469783e-01, 3.43483192e-01,
2.42533057e-01, 3.33873532e-02, 5.22512849e-02, 4.01384066e-01,
3.52554730e-01, 1.11387776e-02, 7.58756752e-02, 4.09163057e-02,
5.20558978e-01, 4.44935903e-01, 3.49377527e-01, 2.96955242e-01,
4.74756287e-02, 9.70689619e-02, 2.71416304e-01, 5.52440112e-01,
2.93842440e-02, 2.53012055e-01, 5.56547635e-01, 2.10516147e-01,
5.86233099e-01, 5.94716593e-01, 1.90052108e-01, 2.50478578e-01,
1.37832566e-01, 3.29794934e-01, 2.59900480e-01, 2.75347612e-01,
2.35471815e-01, 7.78899989e-02, 3.29524057e-01, 5.30966405e-01,
4.41696766e-01, 8.29187389e-02, 5.24615958e-02, 8.43084781e-02,
1.16246002e-01, 7.50298270e-02, 3.45114522e-02, 7.53256532e-02,
1.60645490e-02, 3.23454174e-02, 1.54598957e-02, 6.61248826e-03,
3.07075510e-02, 4.53068923e-02, 2.39332773e-02, 9.26032584e-02,
5.86834448e-02, 9.76661587e-02, 9.76670248e-02, 5.86934823e-02,
2.59019133e-02, 2.99833967e-02, 5.85658812e-02, 8.85923910e-02,
4.87078324e-03, 2.11790997e-02, 6.28670753e-02, 5.81487243e-02,
8.82553047e-02, 5.33392823e-02, 8.63361754e-02, 1.22930813e-02,
2.08672960e-02, 5.00826395e-04, 3.22401955e-02, 1.11946625e-01,
3.29236258e-02, 1.07347426e-01, 3.11973008e-02, 5.10147367e-02,
1.13154836e-01, 9.05505423e-02, 2.76909055e-02, 5.51918900e-02,
1.18284446e-01, 6.77136451e-02, 7.11776489e-02, 8.79947389e-02,
7.06192385e-02, 4.84644678e-02, 9.42524268e-02, 8.76893604e-02,
1.06731675e-01, 8.07883621e-02, 1.07449272e-01, 2.04517605e-02,
1.10744022e-01, 8.10336409e-02, 1.18368144e-01, 5.10898847e-02,
4.97157314e-02, 6.78983317e-02, 6.36769915e-02, 1.06278860e-01,
5.56780815e-02, 6.18674523e-02, 2.06585225e-02, 1.23777821e-01,
1.04649297e-01, 9.40597464e-02, 8.76590608e-02, 9.92750602e-02,
6.06657593e-02, 7.93371995e-04, 1.01886678e-01, 1.01846654e-01,
7.52980435e-02, 2.16629346e-02, 1.07211523e-01, 7.80252455e-02,
1.15130762e-01, 1.03027163e-02, 1.02784607e-01, 3.41904710e-03,
9.29304750e-03, 9.74945643e-02, 5.51936949e-02, 5.28097808e-02,
7.05159500e-02, 1.75321775e-02, 7.57275753e-02, 2.81233394e-02,
4.15933259e-02, 1.07502698e-02, 3.49383323e-02, 3.32534733e-02,
4.07426350e-02, 9.06016099e-02, 4.09834364e-02, 7.52890402e-02,
4.17394313e-02, 7.44990266e-02, 1.28700103e-02, 2.25413728e-02,
6.04438607e-02, 2.35158675e-02, 7.49930030e-02, 3.81763738e-02,
6.35592406e-02, 8.34920594e-02, 1.02658492e-01, 9.33532592e-03,
2.26093836e-02, 2.01441841e-03, 1.41182468e-02, 8.89456298e-02,
5.27597538e-03, 1.12700509e-02, 4.35329092e-02, 8.98903287e-02,
1.11652612e-01, 7.65313625e-02, 1.37459236e-02, 1.16211616e-02,
7.71983048e-02, 4.46776879e-04, 8.34021029e-02, 5.46513146e-03,
6.84259900e-02, 3.16508581e-02, 5.76401149e-02, 3.03963975e-02,
6.33586063e-02, 5.43249067e-02, 5.90028616e-02, 3.31427164e-02,
8.31712962e-02, 1.99549923e-02, 7.69206062e-02, 6.32520036e-02,
2.91173607e-02, 2.68773026e-03, 5.81963716e-02, 5.64686969e-02,
7.27539780e-02, 6.07135737e-02, 9.46481594e-03, 2.93777874e-02,
1.83615587e-02, 6.89172269e-02, 8.80426287e-02, 6.73877372e-02,
7.86476262e-02, 3.64549596e-03, 6.50586899e-02, 8.71564863e-02,
1.89854733e-02, 9.02485102e-02, 4.68330011e-02, 7.35335198e-02,
3.74233129e-02, 1.58808715e-03, 5.10960272e-02, 3.04834587e-02,
3.67434584e-02, 8.83689631e-02, 1.25767638e-02, 1.06390214e-02,
1.10652819e-02, 7.26251385e-02, 8.84023467e-02, 3.43825824e-02,
5.62414268e-02, 1.31881568e-03, 2.15861991e-02, 3.42414333e-04,
5.92656890e-03, 9.03681564e-02, 7.39966288e-02, 4.12860482e-02,
8.10407681e-02, 5.20766254e-02, 5.03669728e-02, 9.16542074e-02,
1.33642581e-02, 1.33539563e-02, 7.88851516e-02, 2.09202755e-02,
1.07576311e-02, 8.00587847e-02, 6.11859571e-02, 8.48838888e-02,
1.50662815e-02, 6.30255622e-03, 7.00408200e-02, 6.07891400e-02,
2.96008620e-02, 3.47793882e-02, 2.44991887e-02, 9.26026575e-02,
2.32751083e-02, 4.56714261e-02, 5.88580186e-02, 5.67523883e-02,
6.08648427e-02, 9.10707535e-02, 9.67425920e-03, 6.75276731e-02,
3.08398443e-02, 3.56310598e-03, 7.87967163e-02, 8.70078418e-02,
4.08318249e-03, 8.01675958e-02, 2.96749210e-02, 1.21782273e-02,
8.59695261e-02, 6.01380936e-02, 5.94470744e-02, 2.30306226e-02,
7.73651261e-02, 3.59978882e-02, 4.41019845e-02, 4.21564751e-02,
6.31772369e-04, 9.03051523e-02, 1.18872662e-02, 4.89348115e-02,
3.81867280e-02, 8.62325233e-02, 3.58795275e-03, 2.12119770e-02,
4.28315653e-03, 4.10713321e-02, 1.01283914e-02, 7.22546041e-02,
9.45078143e-02, 5.62602855e-02, 8.10826743e-02, 8.03167418e-02,
6.69254413e-02, 6.64546315e-03, 2.06148426e-02, 6.95893661e-02,
7.48601544e-03, 3.86615712e-02, 8.62764884e-02])Variances (σ²):array([3.30262262, 6.65522802, 8.01266494, 7.77267295, 8.28175707,
4.52386799, 5.22224176, 6.63697722, 9.5062045 , 9.2434808 ,
2.89528257, 7.305406  , 9.40899597, 3.80218957, 9.12674176,
1.57605545, 5.24734738, 4.7706545 , 3.95653183, 9.14575595,
2.97291337, 1.57450156, 7.07784007, 3.26433946, 8.14113019,
7.82036507, 4.98456708, 6.4440704 , 3.0228115 , 5.23333701,
3.30420684, 0.98067535, 0.42948852, 0.08353648, 2.17008665,
5.76890075, 9.40962856, 6.0147479 , 0.78849923, 5.71388317,
3.42004652, 3.12718545, 2.98544299, 3.37283945, 4.62374153,
2.61679088, 4.13881604, 4.03530364, 9.38475237, 2.61149938,
4.62341291, 7.64334777, 1.35196407, 4.22835542, 1.77620037,
6.47913173, 6.80866633, 3.30532827, 5.73506576, 8.10561598,
1.8883395 , 1.34693041, 2.35648822, 6.40622815, 2.69961755,
7.48611118, 4.88122956, 5.67718879, 0.02493251, 7.128154  ,
0.97306386, 5.93304751, 7.82077658, 2.80580661, 5.54360282,
9.99517543, 7.93746033, 6.00182426, 7.62699182, 5.27944968,
2.73620894, 4.80630555, 2.48039083, 9.08006725, 2.28953181,
7.18854662, 5.41172438, 2.83462   , 7.7811284 , 5.69955387,
8.78130321, 3.78465241, 4.17414043, 8.80644055, 1.34853847,
3.14913882, 6.07316939, 7.09458921, 5.85865614, 9.58952314,
6.26926405, 8.05251862, 1.83330265, 0.15522957, 7.81225417,
1.29306093, 7.15997911, 6.83062279, 5.19290323, 1.43331442,
3.19051595, 0.91697987, 6.96645394, 1.347575  , 6.16961071,
4.77792257, 3.79654508, 6.86434155, 0.56261938, 2.09986239,
4.16980297, 7.08836156, 2.77102617, 4.81266751, 7.32675533,
0.37043898, 8.45686475, 3.25781693, 3.64760937, 9.11931629,
8.86476758, 2.26735043, 0.34905232, 8.28314938, 2.05458868,
7.64801648, 4.53831129, 3.53664092, 7.15892311, 3.04654524,
8.12637799, 9.30483793, 2.97373192, 6.23677623, 2.9826347 ,
8.51146378, 3.70290938, 7.36032491, 1.65910479, 0.80087496,
9.86656238, 8.93064495, 5.32456723, 8.75767761, 7.02411744,
6.47622297, 4.07221025, 7.49902623, 5.04254516, 2.37584119,
8.84277267, 5.08860084, 7.59701032, 8.3293101 , 8.77198657,
1.6219669 , 6.83192652, 7.64777817, 7.74101713, 0.03824569,
3.12635353, 9.40487769, 0.08709328, 9.84774338, 3.71348858,
7.32126146, 5.37905926, 9.347311  , 7.93088227, 1.83367837,
6.36084899, 2.94280402, 6.49964546, 9.44546187, 5.55159855,
4.94394653, 1.51370414, 2.39883558, 4.51152454, 8.03151757,
7.34226645, 1.14978585, 1.60931279, 3.31804145, 5.61874893,
7.57085746, 4.36317792, 6.36758475, 5.29948311, 7.85082507,
0.33450535, 7.21643395, 3.67744981, 2.35793808, 5.94211476,
4.14140736, 5.43214577, 9.89031738, 1.58905883, 8.80587132,
9.36972743, 4.68622848, 6.8114246 , 7.07982283, 2.34706112,
1.87281516, 4.48722539, 6.4045007 , 4.61677814, 5.00959841,
8.04138583, 8.6213699 , 8.99265849, 3.33723024, 9.57843646,
7.9211029 , 3.33378674, 5.76493602, 8.05403987, 2.80594122,
5.985466  , 2.81558683, 3.41169957, 1.49518292, 2.17206628,
0.83836185, 6.69719937, 4.49632109, 3.76540583, 1.05815246,
1.55440559, 1.02971303, 6.12911508, 7.72059576, 5.14505418,
3.03555791, 8.305308  , 5.02537359, 3.32052819, 5.93584632,
5.64471956, 9.27416406, 9.73991012, 1.08441433, 3.34458335,
1.04683229, 9.77874439, 8.49696755, 4.36887898, 9.1227968 ,
3.1896419 , 9.01635246, 5.09312079, 9.39687005, 4.76680717,
9.22398624, 8.65453016, 2.85026867, 4.61843757, 7.48290036,
4.71939608, 5.22327544, 2.15439207, 2.00247063, 0.68522163,
7.91843299, 5.39479573, 1.44240174, 5.52992422, 0.56178401,
4.4712712 , 8.92857173, 3.69416815, 3.41459144, 4.6982063 ,
9.11988289, 7.90180308, 6.73680329, 0.91610428, 4.05016781,
1.14185204, 3.18776198, 8.63491783, 6.35109682, 2.86457659,
2.13502421, 2.88788392, 9.94725158, 1.39971396, 6.42868334,
3.51866786, 0.41383885, 8.59707197, 7.39272554, 3.24018366,
0.30235453, 3.44900946, 1.77140601, 3.46704568, 9.14466179,
3.05757288, 1.6632739 , 3.49471576, 1.35896527, 3.66422346,
9.33935046, 1.22453001, 9.01630149, 3.40426841, 4.80072146,
9.35845928, 3.43112577, 0.43239481, 2.05223842, 8.61643947,
5.45037588, 6.30053023, 0.56007483, 1.26409779, 9.36280096,
3.64103638, 5.28768751, 3.75377696, 0.53121696, 0.80662855,
6.68954392, 5.66896144, 0.18410822, 1.20858302, 0.65653921,
8.08962987, 6.68542281, 5.59681523, 4.94582806, 0.77284848,
1.55381162, 4.25060989, 8.48222664, 0.44212691, 3.85455382,
9.15680365, 3.24317723, 9.47753559, 9.4250678 , 2.92597252,
3.94165762, 2.25161699, 5.09016916, 4.08812632, 4.38408653,
3.51220958, 1.25336886, 5.47239283, 8.10775164, 6.63606624,
1.37824054, 4.12741601, 7.33930554, 9.09163662, 6.64096316,
2.94342337, 5.97027457, 1.34462225, 2.75770119, 1.31461562,
0.53639439, 2.53830758, 3.93127136, 2.04452569, 7.8284935 ,
4.83647406, 8.54592643, 8.25630246, 4.65860132, 2.18368452,
2.34519037, 5.12495036, 7.79024655, 0.40185359, 1.68829801,
5.04577451, 5.03854491, 7.45769257, 4.24339536, 7.41102339,
1.05983804, 1.77156194, 0.04266995, 2.79411161, 9.89906114,
2.91365812, 9.01286222, 2.543372  , 4.33005477, 9.55835834,
7.69306571, 2.45357493, 4.52411793, 9.88519655, 5.84882216,
6.28504486, 6.95158928, 5.71113755, 3.81518994, 7.78365427,
7.31174442, 8.6102676 , 6.93950821, 9.02936372, 1.77587068,
9.71822088, 6.5164521 , 9.47548822, 4.37168979, 4.1743776 ,
5.32117988, 5.06231193, 9.15107558, 4.46755825, 4.89913405,
1.66103808, 9.90741106, 8.84810058, 7.56015036, 7.18924244,
8.32162125, 5.20089193, 0.06396207, 9.03192322, 8.42997923,
6.04216809, 1.74854662, 9.04522136, 6.75840492, 9.52610011,
0.85235032, 8.88649646, 0.29339273, 0.81590654, 8.27163718,
4.6033567 , 4.36007787, 6.10751818, 1.40911948, 6.65156449,
2.22804869, 3.38116378, 0.85094379, 2.93251354, 2.9539143 ,
3.25414229, 7.11096388, 3.29009823, 6.04947501, 3.59923533,
5.9796213 , 1.01511874, 1.91514795, 4.7459582 , 1.95861497,
6.62330326, 2.99017981, 5.08586766, 7.3725722 , 8.81058907,
0.81939082, 1.97821647, 0.17263867, 1.18909758, 7.78930837,
0.41581357, 0.9358693 , 3.69755262, 7.62254464, 9.71055559,
6.34762808, 1.51295348, 1.27473373, 8.81214148, 0.04935683,
8.69988912, 0.62493069, 7.81066617, 3.20806523, 6.19981923,
3.23872558, 7.08827524, 5.85965492, 6.33963674, 3.7283044 ,
9.17023875, 2.23996475, 8.68321012, 7.02464559, 3.2856178 ,
0.29366421, 6.1194618 , 5.87475323, 7.75860042, 6.74317855,
1.04167075, 3.17404941, 2.10689124, 7.55540717, 9.00005955,
7.1838389 , 8.27316745, 0.40584458, 6.96899217, 9.15144212,
1.98855487, 9.40524155, 5.2601642 , 7.53581793, 4.22603017,
0.17841183, 5.47213528, 3.1344879 , 3.90490358, 9.297212  ,
1.35594565, 1.13570206, 1.14780726, 8.04589157, 9.36147286,
3.52297082, 5.95662034, 0.14972975, 2.27174623, 0.03659098,
0.62496809, 9.96130659, 7.98425745, 4.58240351, 8.67219084,
5.51927162, 5.74540674, 9.90888547, 1.49925307, 1.37900571,
8.32237382, 2.32207477, 1.2174691 , 8.57720326, 6.8844385 ,
9.03323254, 1.53978672, 0.68842164, 7.86970477, 6.83950091,
3.05447102, 3.71922609, 2.58071903, 9.66491651, 2.44128884,
4.67261954, 6.65933325, 6.40802521, 6.40898645, 9.28650523,
1.07012772, 7.16210568, 3.29971624, 0.38311398, 8.85165897,
9.5891067 , 0.42991174, 9.17134334, 3.34581219, 1.31150489,
9.35910023, 6.85848138, 6.04027746, 2.34971268, 8.56213665,
3.68401086, 4.92603248, 4.789074  , 0.06875273, 9.67327012,
1.36443178, 5.16419258, 4.34520859, 9.28616807, 0.36861229,
2.35487992, 0.43884908, 4.64737965, 1.05527191, 8.11319014,
9.99201117, 6.08412878, 8.82753635, 8.41809173, 6.78423584,
0.69144464, 2.09445342, 7.35078956, 0.83643766, 4.3866077 ,
8.75578401])

## Binning#

scipp.bin actually reorders data and meta data such that all data contributing to a bin is in a contiguous block. Binning along multiple dimensions is supported. Of the three options it is the only solution that supports modifying data in the grouped/binned layout. A variety of operations on such binned data is available. Limitations are:

• Requires copying and reordering the input data and can thus become expensive.

In the above example the 'y' information is dropped by hist and groupby, but bin preserves it:

[8]:

binned = table.bin(x=xbins)
binned.values[0]

[8]:

scipp.DataArray (4.88 KB out of 157.50 KB)
• position: 116
• x
(position)
float64
m
0.013, 0.007, ..., 0.019, 0.007
Values:array([0.01341082, 0.00674854, 0.00124212, 0.01605677, 0.0076007 ,
0.00012884, 0.02074027, 0.01252309, 0.01388511, 0.02380089,
0.00323959, 0.02441797, 0.0104041 , 0.00486334, 0.00155994,
0.01850965, 0.00224517, 0.00858542, 0.00706852, 0.01666857,
0.01511133, 0.01507182, 0.0043397 , 0.00127773, 0.01982551,
0.00241375, 0.02369028, 0.0055294 , 0.01103775, 0.0199403 ,
0.01862933, 0.0050892 , 0.02333499, 0.02308278, 0.01282285,
0.00924493, 0.010898  , 0.02150245, 0.01847693, 0.02186651,
0.01770097, 0.02196477, 0.0186333 , 0.00529771, 0.00454003,
0.01319337, 0.01711278, 0.01244405, 0.02197087, 0.02140273,
0.00236163, 0.02475197, 0.00075598, 0.01406825, 0.01782322,
0.00539831, 0.01350491, 0.00065497, 0.00488585, 0.00461248,
0.00937401, 0.00018565, 0.01206347, 0.02266198, 0.01184596,
0.00739731, 0.015748  , 0.02086287, 0.00563051, 0.00840498,
0.02204037, 0.00900532, 0.0110072 , 0.02150124, 0.02105368,
0.02058015, 0.00620351, 0.00747785, 0.01630046, 0.0216419 ,
0.00020191, 0.00666018, 0.02280237, 0.01717417, 0.01844675,
0.01905506, 0.00673875, 0.02500152, 0.0086278 , 0.02042661,
0.00654179, 0.00832215, 0.01044455, 0.01814629, 0.01923764,
0.00550433, 0.00162677, 0.00172054, 0.000244  , 0.02156317,
0.01760236, 0.01799563, 0.02516493, 0.00034955, 0.00613472,
0.02302928, 0.00187485, 0.0108025 , 0.02110716, 0.01602091,
0.0038261 , 0.01239692, 0.0224797 , 0.00344897, 0.01927919,
0.00656931])
• y
(position)
float64
m
0.413, 0.829, ..., 0.469, 0.290
Values:array([0.41345108, 0.82897621, 0.46554662, 0.07455039, 0.98275361,
0.74464154, 0.48513071, 0.20889904, 0.33747454, 0.63364914,
0.4229297 , 0.85925963, 0.52753899, 0.44873265, 0.15440453,
0.93773643, 0.08830422, 0.30301302, 0.83609062, 0.76597774,
0.48266168, 0.44067943, 0.06925309, 0.7343824 , 0.36587507,
0.05865598, 0.69993495, 0.20074869, 0.21094638, 0.42018179,
0.16155301, 0.77697431, 0.60252769, 0.44565102, 0.17597423,
0.66174335, 0.77067752, 0.50200245, 0.37615778, 0.78620166,
0.8652417 , 0.056556  , 0.79807656, 0.4297381 , 0.86076864,
0.73706236, 0.42526774, 0.21733209, 0.4932889 , 0.30234911,
0.94537933, 0.36665451, 0.60643431, 0.47230535, 0.41791087,
0.57016903, 0.31357162, 0.48247112, 0.09334738, 0.62063553,
0.79493813, 0.72510023, 0.11778181, 0.63999281, 0.94680245,
0.68774379, 0.75831833, 0.47189809, 0.82405599, 0.17731012,
0.13946922, 0.41721169, 0.04435025, 0.20632256, 0.06783375,
0.46350104, 0.08642263, 0.04414839, 0.92570305, 0.4470891 ,
0.08991347, 0.37321106, 0.64695499, 0.24679294, 0.61616705,
0.15716846, 0.39417621, 0.24161846, 0.35488123, 0.2632197 ,
0.41949406, 0.37163684, 0.61183995, 0.1713582 , 0.01715131,
0.29006211, 0.9945185 , 0.08634312, 0.5459315 , 0.08618554,
0.60988714, 0.30221768, 0.96177201, 0.05721328, 0.1767491 ,
0.08918606, 0.25157565, 0.29989562, 0.84681572, 0.08214064,
0.9745338 , 0.33464195, 0.11677853, 0.12732173, 0.46932359,
0.28966363])
• (position)
float64
counts
2.446, 1.161, ..., 0.630, 1.976
σ = 1.617, 1.096, ..., 0.833, 1.429
Values:array([2.44570777, 1.16090923, 0.06266408, 5.95115874, 3.64890119,
3.09007708, 7.5612098 , 7.69820324, 6.5318802 , 0.15862316,
6.73251861, 2.81059989, 6.42011369, 5.6297167 , 1.13321561,
5.28190475, 1.16651046, 7.79700216, 5.96095298, 1.97504934,
4.65909924, 5.07132831, 6.49572719, 5.05803414, 2.00173158,
0.83290239, 4.43485253, 3.74768444, 1.52384465, 2.12462201,
9.09020427, 8.68390065, 7.59934939, 1.94707225, 6.08550154,
6.54187096, 1.26421859, 4.5928975 , 6.53765871, 7.57110238,
2.66686656, 5.29084415, 3.80995808, 7.97762007, 1.52305233,
5.99746519, 4.78067259, 4.19722666, 6.52367316, 6.93345817,
4.18850991, 4.80848198, 7.27470487, 3.40009851, 2.12580659,
3.92787072, 6.09239805, 7.69166445, 7.68611104, 4.41537743,
7.94531387, 1.10516574, 5.92863204, 4.83610691, 1.85826085,
2.88009334, 8.67373583, 0.88732713, 8.23256253, 3.4045493 ,
6.45460458, 7.72748629, 6.13380891, 8.44275556, 0.77032232,
8.01049228, 8.23500921, 3.51442435, 3.2135056 , 8.48296103,
1.20877359, 6.24293864, 6.7540939 , 6.2174331 , 7.72676727,
8.34134053, 9.09641432, 2.92274492, 7.11842399, 5.35840189,
7.3790111 , 4.92356456, 1.24822991, 3.56965792, 8.84325644,
9.42293369, 9.00271566, 3.63143893, 4.26712386, 6.03682125,
6.54720111, 7.86788312, 2.12961473, 8.04662996, 3.04697145,
0.47486339, 5.47751514, 5.41326396, 2.43979608, 7.84092736,
1.39430917, 2.33612359, 8.13459031, 0.92209768, 0.62979233,
1.97577272])Variances (σ²):array([2.61532575, 1.2007498 , 0.06305447, 6.44864334, 3.79024091,
3.09206832, 8.38741636, 8.19564069, 7.00147183, 0.17866915,
6.84245948, 3.17557212, 6.76293055, 5.76829087, 1.14208894,
5.7940702 , 1.17967934, 8.13899249, 6.1753957 , 2.14670952,
5.02476548, 5.46826779, 6.63821495, 5.09045161, 2.21032629,
0.84301538, 4.99254471, 3.85274228, 1.61030766, 2.34736963,
9.97761428, 8.9077064 , 8.53979984, 2.18527296, 6.48844806,
6.85136482, 1.33501726, 5.11421205, 7.17041643, 8.44581646,
2.91365722, 5.90501315, 4.18197944, 8.19175934, 1.55802121,
6.40644013, 5.20773569, 4.46667479, 7.2811728 , 7.71658842,
4.23826168, 5.44197086, 7.30225468, 3.64787801, 2.32394781,
4.03533385, 6.51799187, 7.71689487, 7.87618911, 4.51838985,
8.32657615, 1.1061921 , 6.29723619, 5.41633789, 1.97165016,
2.9886126 , 9.38431405, 0.98488817, 8.46762341, 3.55067403,
7.206588  , 8.0833809 , 6.48085149, 9.40098928, 0.85583486,
8.87868073, 8.49444166, 3.64831339, 3.48638267, 9.45240379,
1.20999453, 6.45433428, 7.5697549 , 6.77492294, 8.47333605,
9.17515449, 9.40812867, 3.31192908, 7.43222538, 5.93459521,
7.62436159, 5.13275991, 1.31514802, 3.90868595, 9.73612674,
9.68587014, 9.07624102, 3.66281396, 4.27233303, 6.72406889,
7.14955028, 8.60864713, 2.41516047, 8.06070586, 3.1418812 ,
0.53281461, 5.52910424, 5.71368816, 2.71135972, 8.4948633 ,
1.42123976, 2.48550925, 9.10227059, 0.93813703, 0.69352416,
2.04174759])

If we omit the call to bins.sum in the original example, we can subsequently apply another histogramming or binning operation to the data:

[9]:

binned = binned.bin(y=100)
binned

[9]:

scipp.DataArray (220.91 KB)
• x: 39
• y: 100
• x
(x [bin-edge])
float64
m
0.0, 0.026, ..., 0.974, 1.0
Values:array([0.        , 0.02564103, 0.05128205, 0.07692308, 0.1025641 ,
0.12820513, 0.15384615, 0.17948718, 0.20512821, 0.23076923,
0.25641026, 0.28205128, 0.30769231, 0.33333333, 0.35897436,
0.38461538, 0.41025641, 0.43589744, 0.46153846, 0.48717949,
0.51282051, 0.53846154, 0.56410256, 0.58974359, 0.61538462,
0.64102564, 0.66666667, 0.69230769, 0.71794872, 0.74358974,
0.76923077, 0.79487179, 0.82051282, 0.84615385, 0.87179487,
0.8974359 , 0.92307692, 0.94871795, 0.97435897, 1.        ])
• y
(y [bin-edge])
float64
m
0.000, 0.010, ..., 0.990, 1.000
Values:array([1.66752674e-04, 1.01642985e-02, 2.01618443e-02, 3.01593901e-02,
4.01569359e-02, 5.01544817e-02, 6.01520275e-02, 7.01495733e-02,
8.01471191e-02, 9.01446649e-02, 1.00142211e-01, 1.10139757e-01,
1.20137302e-01, 1.30134848e-01, 1.40132394e-01, 1.50129940e-01,
1.60127486e-01, 1.70125031e-01, 1.80122577e-01, 1.90120123e-01,
2.00117669e-01, 2.10115215e-01, 2.20112760e-01, 2.30110306e-01,
2.40107852e-01, 2.50105398e-01, 2.60102944e-01, 2.70100489e-01,
2.80098035e-01, 2.90095581e-01, 3.00093127e-01, 3.10090673e-01,
3.20088218e-01, 3.30085764e-01, 3.40083310e-01, 3.50080856e-01,
3.60078402e-01, 3.70075947e-01, 3.80073493e-01, 3.90071039e-01,
4.00068585e-01, 4.10066131e-01, 4.20063676e-01, 4.30061222e-01,
4.40058768e-01, 4.50056314e-01, 4.60053860e-01, 4.70051405e-01,
4.80048951e-01, 4.90046497e-01, 5.00044043e-01, 5.10041589e-01,
5.20039134e-01, 5.30036680e-01, 5.40034226e-01, 5.50031772e-01,
5.60029318e-01, 5.70026864e-01, 5.80024409e-01, 5.90021955e-01,
6.00019501e-01, 6.10017047e-01, 6.20014593e-01, 6.30012138e-01,
6.40009684e-01, 6.50007230e-01, 6.60004776e-01, 6.70002322e-01,
6.79999867e-01, 6.89997413e-01, 6.99994959e-01, 7.09992505e-01,
7.19990051e-01, 7.29987596e-01, 7.39985142e-01, 7.49982688e-01,
7.59980234e-01, 7.69977780e-01, 7.79975325e-01, 7.89972871e-01,
7.99970417e-01, 8.09967963e-01, 8.19965509e-01, 8.29963054e-01,
8.39960600e-01, 8.49958146e-01, 8.59955692e-01, 8.69953238e-01,
8.79950783e-01, 8.89948329e-01, 8.99945875e-01, 9.09943421e-01,
9.19940967e-01, 9.29938512e-01, 9.39936058e-01, 9.49933604e-01,
9.59931150e-01, 9.69928696e-01, 9.79926241e-01, 9.89923787e-01,
9.99921333e-01])
• (x, y)
DataArrayView
binned data [len=0, len=1, ..., len=2, len=2]
dim='position',
content=DataArray(
dims=(position: 5000),
data=float64[counts],
coords={'x':float64[m], 'y':float64[m]})

As in the 1-D example above, summing the bins is equivalent to histogramming binned data:

[10]:

binned.bins.sum().plot()

[10]: