Multi-dimensional datasets#

This is the continuation of 1-D datasets and tables.

Creation, slicing, and visualization#

[1]:

import numpy as np
import scipp as sc

To create variables with more than one dimension we specify a list of dimension labels and provide data with a corresponding shape. When inserted into a dataset it is important to note that while the dimensions extents have to match, individual variables may have transposed memory layout.

[2]:

d = sc.Dataset(
    data={
        'alice': sc.Variable(dims=['z', 'y', 'x'], values=np.random.rand(10, 10, 10),
                             variances=0.1*np.random.rand(10, 10, 10)),
        'bob': sc.Variable(dims=['x', 'z'], values=np.arange(0.0, 10.0, 0.1).reshape(10, 10),
                           variances=0.1*np.random.rand(10, 10))
    },
    coords={
        'x': sc.arange('x', 11.0, unit=sc.units.m),
        'y': sc.arange('y', 11.0, unit=sc.units.m),
        'z': sc.arange('z', 11.0, unit=sc.units.m)})

Note that in this example the coordinates are exceeding the shape of the data by 1. This means that the coordinates represent bin edges:

[3]:

sc.show(d)
d
bobbob(dims=['x', 'z'], shape=[10, 10], unit=dimensionless, variances=True)variances x zvalues x z alicealice(dims=['z', 'y', 'x'], shape=[10, 10, 10], unit=dimensionless, variances=True)variances z yxvalues z yx zz(dims=['z'], shape=[11], unit=m, variances=False)values z yy(dims=['y'], shape=[11], unit=m, variances=False)values y xx(dims=['x'], shape=[11], unit=m, variances=False)values x
[3]:
Show/Hide data repr Show/Hide attributes
scipp.Dataset (17.45 KB)
    • z: 10
    • y: 10
    • x: 10
    • x
      (x [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • y
      (y [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • z
      (z [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • alice
      (z, y, x)
      float64
      𝟙
      0.661, 0.283, ..., 0.315, 0.245
      σ = 0.236, 0.279, ..., 0.206, 0.112
      Values:
      array([[[6.60733411e-01, 2.83127437e-01, 2.26107658e-01, 6.25184508e-01,
         2.10889089e-01, 5.22092080e-01, 8.93873265e-01, 9.46680313e-01,
         5.36980099e-01, 7.12326304e-01],
        [4.84345565e-01, 9.50951550e-01, 5.65664546e-01, 4.75192394e-01,
         8.72793432e-01, 1.78462591e-01, 1.87316791e-01, 6.26219505e-02,
         4.14408381e-02, 1.07608761e-01],
        [9.48740362e-02, 7.86244188e-01, 7.69327547e-01, 6.41964178e-01,
         5.66784587e-01, 3.81105263e-01, 2.31866704e-01, 1.43538205e-02,
         7.20532534e-01, 4.69413123e-01],
        [7.54280999e-01, 8.59835366e-01, 6.07909991e-01, 7.24012788e-01,
         1.19041720e-01, 8.71049938e-01, 3.18678213e-01, 2.17120148e-01,
         6.15908280e-01, 8.06649682e-01],
        [4.92931220e-01, 2.78527615e-01, 6.37630458e-01, 8.23890662e-03,
         6.22050609e-01, 5.68098832e-01, 8.19564698e-01, 3.69210045e-01,
         3.21197615e-01, 3.63577958e-01],
        [6.75089196e-01, 4.01041252e-01, 5.89316678e-01, 4.29742076e-01,
         5.90445130e-01, 9.28946609e-01, 2.32476120e-01, 2.18918446e-01,
         5.43089967e-01, 3.68579868e-01],
        [1.08434207e-01, 3.82166176e-01, 7.66499433e-01, 5.06945074e-01,
         2.98206392e-01, 2.33811527e-01, 3.34118562e-01, 9.24563810e-01,
         4.45758789e-01, 8.18958015e-01],
        [6.98749688e-01, 8.60749563e-01, 4.49228458e-01, 8.69613894e-02,
         8.85576264e-02, 7.93615942e-01, 1.48601998e-04, 8.66817520e-01,
         8.24038818e-01, 6.40288483e-01],
        [9.10225132e-01, 1.38566288e-01, 9.34230437e-01, 4.46419557e-01,
         4.75773401e-01, 1.03995149e-01, 9.39206806e-02, 2.72656558e-01,
         8.88882918e-01, 2.81019535e-01],
        [3.89749893e-01, 6.66991778e-01, 4.85491289e-01, 7.33274492e-01,
         4.69766411e-01, 7.16378996e-01, 7.08484943e-01, 8.88306039e-02,
         2.01950931e-01, 5.49597580e-01]],

       [[2.30227804e-01, 2.05980193e-01, 5.09394105e-01, 5.07359302e-01,
         6.51685185e-01, 1.76784507e-01, 4.38954023e-01, 3.83195575e-01,
         3.14818868e-01, 7.75912646e-01],
        [5.41603082e-01, 1.80912640e-01, 4.16227770e-01, 8.16646452e-01,
         9.10656518e-01, 8.64559173e-01, 9.63992895e-01, 3.26638560e-01,
         1.86235033e-01, 1.97065188e-01],
        [7.89366091e-01, 6.84143218e-01, 8.78877756e-01, 3.00987822e-01,
         1.19769027e-01, 6.35899274e-02, 6.94571803e-01, 5.61781636e-01,
         5.45117974e-01, 4.52334278e-01],
        [8.06125555e-01, 1.10989330e-01, 3.84788363e-01, 9.68177103e-01,
         4.93324417e-01, 3.72217788e-01, 4.33781766e-01, 3.03034770e-01,
         9.69421499e-01, 3.06300459e-01],
        [3.20201687e-01, 5.78031997e-01, 2.86741356e-01, 9.23112648e-01,
         8.69672681e-01, 3.56953800e-01, 5.17948686e-01, 9.25810005e-01,
         6.40536617e-01, 3.18826354e-01],
        [6.68768466e-01, 4.85089466e-01, 3.97567577e-01, 2.94990867e-01,
         4.33424569e-01, 3.15043331e-01, 9.75080473e-01, 3.02113424e-01,
         5.49907898e-01, 1.87606188e-01],
        [6.71436014e-01, 9.91588736e-01, 1.85694925e-01, 4.89462962e-01,
         2.20642120e-01, 7.84953000e-01, 1.81119064e-01, 8.58149786e-01,
         9.16790795e-01, 4.23550819e-01],
        [8.48971327e-01, 7.68392613e-01, 9.85319588e-02, 2.45123974e-01,
         4.70740848e-01, 7.42559371e-01, 8.71591062e-01, 4.25895270e-01,
         4.12323391e-01, 1.38275052e-01],
        [9.41230767e-01, 5.40173746e-01, 6.69391450e-02, 5.46992055e-01,
         6.73230527e-01, 1.78568077e-01, 2.83071196e-01, 1.29406564e-01,
         3.31431855e-01, 4.42851327e-01],
        [9.99799273e-01, 7.27421469e-01, 9.89431022e-01, 3.48628798e-01,
         6.97381456e-01, 4.63429207e-01, 8.64485253e-01, 5.41176178e-01,
         2.55746711e-01, 2.54730849e-01]],

       [[7.32368137e-01, 2.45551828e-01, 1.89809884e-01, 6.91786674e-01,
         5.73239205e-01, 4.65429416e-01, 4.14737651e-01, 6.33535628e-01,
         9.28708091e-01, 7.51098639e-01],
        [6.55114307e-01, 9.81604094e-01, 1.84413454e-01, 1.54574943e-01,
         2.84670981e-01, 6.36626398e-01, 2.32686467e-01, 6.29636551e-01,
         4.67118801e-01, 3.01970683e-01],
        [9.28323456e-01, 3.66923365e-01, 3.97442100e-01, 5.61014312e-01,
         1.66772279e-01, 6.93533358e-01, 6.11054650e-01, 5.19657089e-01,
         4.54894430e-01, 6.13758031e-01],
        [6.34809190e-01, 3.91204818e-01, 5.25245578e-01, 5.10405949e-01,
         2.53679614e-02, 4.05852532e-01, 7.73494218e-01, 9.72936299e-01,
         9.72558390e-02, 1.59409206e-01],
        [1.37433491e-01, 9.86227574e-01, 1.67306639e-01, 2.49255966e-01,
         6.61076387e-01, 6.55603048e-01, 9.93717050e-03, 5.76866154e-01,
         4.20417533e-01, 1.50741706e-01],
        [5.05880476e-01, 5.45627484e-01, 9.95464265e-01, 3.46440411e-03,
         6.59329445e-02, 4.53617720e-01, 5.31163150e-01, 6.42635580e-02,
         6.21866955e-01, 9.70024483e-01],
        [5.28427735e-01, 8.84135995e-01, 7.92734278e-01, 5.75946543e-02,
         8.52555097e-01, 9.79032622e-01, 8.30197985e-01, 8.36923307e-01,
         4.90050556e-01, 5.24762220e-01],
        [7.41879784e-01, 4.91954624e-01, 6.15224741e-01, 1.31307100e-01,
         3.09205232e-01, 3.29931512e-01, 6.97242875e-01, 7.93677511e-01,
         2.42668716e-01, 9.14511037e-02],
        [8.79914463e-01, 7.93543091e-01, 7.24855056e-01, 1.38503919e-01,
         6.65634284e-01, 4.73151341e-02, 8.48826248e-01, 1.67326498e-01,
         5.54849125e-01, 4.72661942e-01],
        [8.79010011e-01, 5.41129420e-01, 8.99077610e-01, 6.05001319e-01,
         4.89411381e-01, 6.07068726e-01, 6.78537980e-01, 8.68502925e-01,
         8.26585082e-01, 2.33006177e-01]],

       [[7.82521464e-01, 9.93403398e-01, 2.75048041e-01, 1.56999073e-01,
         3.73491904e-01, 5.77015735e-01, 9.61407923e-01, 2.17767315e-01,
         1.02461255e-01, 4.67444333e-01],
        [2.81349585e-01, 8.53126709e-01, 7.99980568e-01, 9.50075411e-01,
         9.46554906e-01, 5.95706372e-01, 9.69935483e-01, 9.02301122e-01,
         6.39160338e-01, 8.24618942e-01],
        [4.99790246e-02, 7.43599259e-01, 9.28024236e-03, 7.22395404e-01,
         4.54131354e-01, 8.29586027e-01, 7.18250569e-01, 9.12126780e-01,
         2.90173223e-01, 1.39555745e-01],
        [8.05727054e-01, 6.64392642e-01, 8.07058595e-01, 9.46344189e-01,
         5.44179111e-01, 7.17610673e-01, 2.01044602e-01, 3.39013543e-01,
         7.94099456e-01, 4.85349335e-01],
        [3.94063081e-01, 1.57357306e-01, 9.16763072e-01, 8.28799732e-01,
         8.83992395e-02, 4.38483549e-01, 1.82643085e-01, 8.09191699e-01,
         5.72423125e-01, 7.20158768e-02],
        [3.41191859e-01, 9.18713898e-01, 3.46435371e-01, 7.18969708e-02,
         3.82554276e-01, 4.79213420e-01, 2.02801825e-01, 2.57480079e-01,
         9.53773631e-01, 9.09141924e-01],
        [3.96910399e-01, 6.95976443e-01, 5.98910839e-01, 1.07149036e-01,
         1.26276562e-01, 4.41422126e-01, 1.70664917e-01, 6.52002636e-01,
         8.12032201e-01, 6.68197084e-01],
        [9.85708553e-01, 9.28868033e-01, 9.14728970e-02, 5.73121074e-01,
         3.71843166e-01, 6.80300676e-01, 4.73290501e-01, 8.09315141e-01,
         9.76908417e-01, 9.02602758e-02],
        [8.77421213e-01, 8.95875866e-01, 4.31857012e-01, 3.56236751e-01,
         1.26581095e-01, 4.18100075e-01, 4.11983691e-01, 1.71928198e-01,
         1.28757397e-01, 2.82272896e-01],
        [1.36639502e-01, 1.88980768e-01, 1.55382055e-01, 7.05974018e-01,
         1.07744536e-01, 4.07937717e-01, 5.93799388e-01, 9.54754065e-01,
         5.02011362e-01, 8.99016675e-01]],

       [[7.23034591e-01, 4.07457169e-01, 5.04763494e-02, 1.24566489e-01,
         1.47377444e-01, 2.22313900e-02, 2.52591770e-01, 9.80875344e-01,
         4.14036398e-01, 1.01258256e-01],
        [5.15790798e-01, 9.10357054e-02, 5.26692474e-01, 3.12034276e-03,
         4.89136123e-01, 8.95724844e-01, 7.83056906e-01, 1.23765277e-01,
         5.07471157e-01, 4.48185533e-01],
        [8.90848537e-01, 6.99950538e-01, 1.43067232e-01, 2.60406616e-01,
         6.92120537e-01, 4.93989419e-01, 4.68659039e-02, 6.31515501e-01,
         4.96619775e-01, 5.42001551e-01],
        [6.08843472e-01, 4.26326706e-01, 7.69755923e-02, 2.38787367e-01,
         2.91465253e-01, 5.65850273e-01, 8.07411522e-01, 5.66270761e-01,
         8.80304898e-02, 9.34206669e-01],
        [9.26768669e-01, 9.28810570e-01, 9.30102292e-01, 8.43521861e-01,
         4.48646477e-01, 1.75645408e-01, 9.40930618e-01, 9.96954911e-01,
         6.92840509e-01, 5.76272459e-02],
        [9.08827096e-01, 5.15936904e-01, 9.73584142e-01, 9.49479048e-01,
         9.69175794e-01, 4.54340470e-01, 6.25223812e-01, 6.38654494e-01,
         8.06366124e-01, 8.26828490e-01],
        [1.70458553e-01, 9.72553272e-01, 8.44349087e-01, 6.54877468e-01,
         3.01643915e-01, 3.06849821e-01, 8.76968091e-01, 2.96767740e-01,
         5.57893219e-02, 3.42345796e-01],
        [6.78792263e-01, 6.92609545e-01, 1.55710504e-01, 2.41104117e-01,
         2.24988062e-01, 8.34572887e-01, 3.09217040e-01, 3.98421567e-01,
         2.32122227e-01, 2.99322888e-01],
        [5.57242273e-01, 1.47933097e-01, 5.20086619e-01, 3.37880331e-01,
         2.80100989e-01, 2.26980252e-01, 5.11442147e-01, 2.12886965e-01,
         4.55564961e-01, 1.38251092e-01],
        [9.38416997e-02, 3.27794233e-01, 3.55382368e-01, 7.40603544e-01,
         1.57075494e-01, 5.06566146e-01, 5.43284374e-01, 3.02918288e-01,
         7.38022678e-01, 5.53029915e-01]],

       [[9.45786163e-01, 3.08914612e-01, 1.85128840e-01, 8.39413183e-01,
         9.43786639e-01, 7.48639900e-03, 8.34897963e-01, 2.76903902e-01,
         7.76749732e-01, 8.21837426e-01],
        [6.96833138e-01, 8.51458099e-01, 5.63630918e-01, 7.53857052e-01,
         6.24264616e-01, 9.68822608e-01, 7.87859224e-01, 9.09315860e-01,
         9.11297994e-01, 1.45422576e-01],
        [6.08285166e-01, 8.13274119e-01, 1.63560971e-01, 1.58909376e-01,
         6.16676354e-01, 8.91532375e-01, 6.60090908e-01, 6.46841049e-01,
         1.34077103e-01, 6.00168301e-01],
        [9.07707411e-01, 3.31380488e-01, 5.17369174e-01, 8.69697850e-01,
         9.12231991e-01, 8.43455591e-02, 8.25988305e-02, 5.56898816e-01,
         8.49873252e-02, 6.01644232e-01],
        [7.00019662e-01, 3.91243097e-01, 4.85616291e-01, 7.12800652e-01,
         3.84551822e-01, 3.64726920e-01, 6.13574066e-01, 4.13124651e-01,
         4.57514784e-01, 4.52182553e-02],
        [3.67810437e-01, 4.42110860e-01, 6.37112505e-01, 4.26532646e-01,
         9.62390428e-01, 2.84092355e-01, 1.41891104e-01, 5.60998381e-01,
         2.76770415e-01, 6.18966779e-01],
        [1.01442169e-01, 3.21961729e-02, 7.30015167e-01, 3.18018804e-01,
         7.74329499e-03, 2.32593796e-01, 8.31081356e-01, 1.84065493e-01,
         3.95531875e-01, 2.58753526e-01],
        [2.88237054e-01, 8.93902410e-01, 9.39156453e-01, 7.46179015e-01,
         1.05972298e-01, 6.68783666e-01, 8.00491824e-01, 2.53222020e-01,
         4.75074419e-02, 6.33943075e-01],
        [9.55808991e-01, 2.65060493e-01, 6.75589064e-01, 7.83537391e-01,
         5.74125352e-01, 6.11217888e-02, 6.22072238e-01, 5.33998341e-01,
         9.65610058e-01, 2.52232628e-01],
        [3.01707410e-02, 5.39665611e-01, 6.85382488e-01, 4.60092219e-01,
         1.52410373e-02, 5.42155840e-01, 2.62197475e-01, 4.53606066e-01,
         2.50152438e-01, 6.98303215e-03]],

       [[5.90147277e-01, 7.82216721e-01, 3.19210888e-02, 7.12821129e-01,
         8.35315201e-01, 9.53033924e-01, 5.59928302e-01, 2.07328209e-01,
         4.97492536e-01, 8.49811398e-01],
        [8.16319399e-01, 2.12644011e-02, 2.19821479e-01, 4.76860309e-02,
         5.75615836e-01, 9.21125771e-01, 6.31569464e-01, 5.05429725e-02,
         3.98016046e-01, 9.56664942e-01],
        [2.95519668e-01, 6.31300397e-01, 2.43878576e-01, 4.22686724e-01,
         8.04482551e-01, 4.85553071e-01, 2.85783725e-01, 4.46759645e-01,
         4.92842342e-01, 2.70110549e-02],
        [4.41992912e-01, 3.01924507e-01, 7.48360325e-01, 6.73864582e-01,
         5.91175508e-01, 4.43848373e-02, 5.96079504e-01, 1.80968555e-02,
         5.10139526e-01, 6.03915326e-01],
        [8.03992364e-01, 8.39943785e-01, 5.56059753e-01, 8.21889794e-01,
         4.64256720e-01, 6.86421237e-01, 2.11963031e-01, 7.62284664e-01,
         9.51456591e-01, 6.05157135e-01],
        [4.82860253e-01, 1.33760170e-01, 4.39771095e-01, 2.74922697e-01,
         1.09690136e-02, 9.83483069e-02, 7.83984306e-01, 3.36028692e-01,
         7.03915851e-01, 8.05697057e-01],
        [9.85336699e-01, 1.96821489e-01, 4.88369925e-01, 7.61008548e-01,
         2.75750944e-01, 6.53743113e-01, 9.27304671e-01, 3.11701551e-01,
         8.45931695e-01, 4.31957031e-01],
        [4.57486745e-01, 9.44242019e-01, 4.62549327e-02, 5.62481034e-02,
         4.87357495e-01, 6.12826119e-01, 1.42173902e-01, 5.83773271e-03,
         4.19895199e-01, 3.77357874e-01],
        [3.87777778e-01, 8.79932549e-01, 5.81567653e-01, 6.75067178e-01,
         4.43387927e-01, 4.81654974e-01, 7.33349448e-01, 7.14733233e-01,
         6.18195742e-01, 5.75545444e-01],
        [9.12747030e-01, 5.45012097e-01, 6.96075946e-01, 1.51281211e-01,
         4.66863878e-01, 9.50972373e-02, 8.66543922e-01, 6.00856727e-02,
         5.85045857e-01, 3.48153627e-01]],

       [[7.70156060e-01, 5.44391489e-01, 9.69260125e-01, 4.76526387e-01,
         4.89215381e-01, 1.83413795e-01, 4.09253179e-02, 6.54304373e-01,
         2.14713631e-01, 7.29873348e-01],
        [3.65290927e-01, 7.45570028e-01, 1.75649300e-01, 3.93872985e-01,
         1.11285230e-01, 1.97387320e-01, 6.83767564e-01, 2.11524041e-01,
         1.65643745e-01, 4.82494903e-01],
        [7.23583295e-01, 5.16937161e-01, 5.58457156e-01, 8.20125261e-01,
         3.87256741e-01, 4.98188720e-01, 8.99560043e-01, 1.53874717e-01,
         2.94187818e-01, 1.14247941e-01],
        [4.88624136e-02, 1.01170356e-01, 2.62400141e-01, 5.43620158e-02,
         1.30732092e-01, 2.11086027e-02, 5.85614493e-01, 4.23545515e-01,
         9.76327516e-01, 3.61461006e-01],
        [8.84143335e-01, 1.61531771e-01, 9.24106531e-01, 9.41482923e-01,
         8.39854290e-01, 1.61085637e-01, 5.83815388e-01, 2.49587951e-02,
         2.30156789e-01, 4.26921729e-01],
        [8.97770443e-01, 7.96312930e-01, 5.67462732e-01, 9.96039386e-01,
         7.86729847e-01, 4.09487183e-01, 1.00445045e-01, 4.68179356e-01,
         7.21305896e-01, 2.39433235e-02],
        [3.90465069e-01, 6.36476398e-02, 5.56262814e-01, 4.89048956e-01,
         4.31521842e-01, 5.26893218e-01, 3.72339461e-01, 6.50300472e-01,
         3.76607738e-01, 9.48324423e-01],
        [7.87386609e-01, 9.11065724e-01, 9.70422064e-02, 3.72140712e-02,
         5.16202261e-01, 9.78366792e-01, 1.06916058e-01, 8.06457179e-02,
         7.66798767e-01, 3.89390871e-01],
        [4.76858214e-01, 6.70520908e-01, 8.87853320e-02, 4.60494990e-01,
         4.17492437e-01, 5.92023981e-01, 5.03376268e-01, 6.92317342e-01,
         3.09447971e-01, 3.10487032e-01],
        [1.87581564e-01, 9.93124158e-01, 4.34340724e-01, 9.91659681e-01,
         4.08575436e-02, 2.73515011e-01, 3.33578662e-01, 5.60315039e-01,
         7.20193473e-01, 8.86018945e-02]],

       [[3.87431549e-01, 8.89285426e-01, 4.49008466e-01, 6.60538623e-01,
         8.35859712e-01, 7.18974853e-01, 1.01548806e-01, 3.28887851e-02,
         5.66933208e-01, 2.38205461e-01],
        [8.24021012e-01, 6.21807472e-01, 8.95857449e-02, 5.53021148e-01,
         9.86436414e-01, 4.49799522e-01, 5.89302297e-01, 7.76475802e-02,
         5.25566814e-01, 5.90882283e-01],
        [7.59411183e-01, 1.64801688e-01, 2.79576903e-01, 3.07957411e-01,
         1.32951308e-01, 8.33951301e-01, 9.77153268e-01, 6.28284938e-01,
         4.40787328e-01, 3.10325226e-01],
        [4.83185580e-02, 2.26557998e-01, 3.29462809e-01, 1.00334126e-01,
         5.34614599e-01, 7.44334638e-01, 5.55658613e-01, 9.66660847e-01,
         2.62816115e-01, 2.34683501e-01],
        [9.33314323e-01, 3.18949062e-01, 9.96647617e-01, 4.96156093e-01,
         3.11916508e-01, 9.07886051e-01, 6.95343028e-01, 3.44097199e-01,
         2.92470520e-01, 9.00801063e-01],
        [5.73846652e-01, 8.55536710e-01, 3.44409559e-01, 3.95178802e-01,
         1.59975973e-01, 5.06237167e-01, 4.86806263e-01, 8.18873189e-01,
         8.62734931e-01, 8.77066616e-01],
        [4.36405534e-01, 5.97372961e-01, 5.80817405e-01, 8.62454695e-01,
         6.87248957e-01, 6.75764228e-01, 2.52388534e-01, 2.03465281e-01,
         1.70556238e-01, 3.04658786e-01],
        [7.54024377e-01, 9.23331842e-01, 5.90660930e-01, 5.95018078e-01,
         4.76036067e-01, 5.70976822e-01, 9.10367641e-01, 5.95106759e-01,
         7.93433475e-01, 1.17387107e-01],
        [1.43652975e-01, 3.16458109e-01, 2.75630259e-01, 1.09738717e-01,
         4.19522823e-01, 3.25187266e-03, 5.58723482e-01, 9.96571689e-01,
         2.61676965e-01, 6.87142827e-01],
        [7.75815807e-01, 7.84157507e-01, 6.80351711e-01, 6.70194818e-01,
         3.59803502e-01, 3.95497510e-01, 3.39789498e-01, 2.00661832e-01,
         9.82460298e-01, 9.33239025e-01]],

       [[2.48135387e-01, 4.82227504e-02, 9.78091670e-01, 8.93031696e-01,
         2.88817809e-01, 4.14189709e-01, 2.72676779e-01, 9.62747550e-01,
         4.81836170e-01, 9.15346520e-01],
        [7.75749616e-02, 1.03906462e-02, 7.08237143e-01, 3.91458013e-01,
         2.37468216e-01, 2.65691391e-01, 9.48575089e-02, 9.31603489e-01,
         5.08793921e-02, 8.35676463e-01],
        [5.48544036e-01, 1.36291019e-01, 2.23699402e-01, 5.30873413e-01,
         4.97362683e-01, 1.24313488e-01, 8.75640138e-01, 7.24456321e-01,
         5.90857291e-01, 3.33040840e-01],
        [5.04184166e-01, 9.13513002e-01, 4.26825851e-01, 7.72553970e-01,
         4.56739869e-01, 4.39812065e-01, 5.08701270e-02, 7.75070432e-01,
         8.20388726e-01, 1.84235360e-02],
        [4.11049383e-01, 5.10689339e-01, 9.61647433e-01, 9.26302753e-01,
         6.05820226e-02, 6.53760276e-01, 1.08279163e-01, 2.90158400e-01,
         2.36826273e-01, 1.57953530e-01],
        [8.81475768e-01, 5.71518251e-01, 4.59212385e-01, 4.51856909e-01,
         1.02228343e-01, 5.91169153e-01, 2.80539553e-01, 5.80418229e-01,
         5.45309816e-01, 8.14452823e-02],
        [9.53454106e-02, 5.92541648e-01, 3.06284444e-01, 5.79389476e-01,
         6.50603288e-01, 2.16740966e-01, 6.36150725e-01, 8.81823469e-01,
         6.72422195e-01, 3.23035968e-01],
        [2.83569201e-02, 7.10128330e-01, 1.06416235e-01, 1.68469628e-01,
         1.44478665e-01, 1.30947763e-02, 6.60711482e-01, 2.39740641e-01,
         3.25575408e-01, 3.66373164e-01],
        [2.34143067e-01, 3.30653242e-01, 9.32658912e-01, 2.39920066e-01,
         1.59487801e-01, 2.67661436e-02, 3.40957317e-01, 2.43143830e-01,
         7.80661175e-02, 8.17890767e-01],
        [8.34453253e-02, 2.28476308e-01, 1.52750582e-01, 8.05405698e-01,
         5.74749686e-01, 2.01686165e-01, 6.59160207e-01, 4.09210432e-02,
         3.15389714e-01, 2.44795332e-01]]])

      Variances (σ²):
      array([[[5.55814752e-02, 7.75641765e-02, 3.93143246e-02, 9.41883446e-02,
         9.78630230e-02, 7.07754701e-03, 6.97009582e-02, 5.84867976e-02,
         4.86252572e-02, 3.98545269e-02],
        [3.51264918e-02, 7.07217312e-02, 3.46001936e-02, 6.94503254e-02,
         4.76883481e-02, 7.38519033e-02, 2.39886070e-02, 6.14162023e-02,
         1.56436408e-02, 7.54512837e-02],
        [4.69481380e-02, 4.48338739e-04, 4.67406387e-05, 7.08800421e-02,
         2.04462235e-02, 6.06808681e-02, 7.84043563e-02, 4.07742404e-02,
         7.34642497e-02, 8.11155791e-02],
        [3.13832125e-02, 3.93115513e-03, 5.04714964e-02, 9.98383703e-02,
         1.26261743e-02, 6.52382107e-02, 7.12972297e-03, 1.25636986e-02,
         9.19216198e-02, 2.65309703e-02],
        [3.09934909e-02, 2.48123640e-02, 1.25249201e-02, 1.68229321e-02,
         8.41742601e-02, 5.34753753e-02, 2.53645457e-02, 5.95362106e-02,
         4.69315405e-03, 7.37986262e-02],
        [3.82299645e-02, 4.33160659e-02, 9.04604893e-02, 5.69646899e-02,
         8.31073016e-02, 2.24390066e-03, 3.71214038e-02, 7.03615941e-02,
         1.72737806e-02, 1.22194255e-02],
        [1.64615525e-02, 1.61529232e-02, 1.95381546e-02, 8.45257378e-02,
         6.61895192e-02, 5.76921078e-02, 8.32032165e-02, 4.68324635e-02,
         2.38972360e-03, 5.79124144e-02],
        [7.77373134e-02, 9.14658081e-02, 7.60105495e-03, 4.52977218e-02,
         8.66466087e-02, 3.39731356e-02, 8.76970906e-02, 8.59618450e-02,
         7.95171644e-02, 9.62526729e-02],
        [1.03630606e-02, 7.59292745e-02, 4.12173657e-02, 1.99974803e-02,
         5.59226105e-02, 6.09274209e-02, 4.12712328e-02, 9.16406384e-02,
         1.88453367e-02, 6.53073816e-02],
        [5.49070533e-02, 7.29981514e-02, 7.89326636e-02, 4.69235872e-02,
         1.11167612e-02, 7.65324879e-02, 8.26008527e-02, 2.24314564e-02,
         2.94287975e-02, 3.44781380e-02]],

       [[8.39766084e-02, 2.55621492e-02, 6.61988753e-02, 6.47294376e-02,
         4.10280553e-02, 8.64123336e-02, 6.58206165e-02, 8.99039462e-02,
         5.13080934e-02, 3.51036450e-03],
        [8.55210278e-02, 3.50844490e-02, 1.57574554e-02, 2.99326639e-02,
         9.26610114e-02, 4.26993409e-03, 5.00524009e-02, 7.54998619e-02,
         1.42630902e-02, 9.73852542e-02],
        [1.47114101e-02, 5.98173229e-02, 3.69767079e-02, 3.22481637e-02,
         3.07247671e-02, 6.12562290e-02, 5.56734382e-02, 6.64347186e-02,
         1.62860024e-02, 4.68635302e-02],
        [7.26095239e-02, 7.66922537e-02, 6.88286113e-02, 9.72185633e-02,
         8.92479467e-02, 6.89370717e-03, 2.80319097e-02, 5.06789101e-02,
         3.40775192e-02, 7.95269549e-02],
        [1.08332112e-02, 4.29939368e-02, 1.12939447e-02, 7.88151729e-02,
         8.13548833e-02, 7.55944233e-02, 5.97189473e-02, 3.12746340e-02,
         7.40754752e-02, 1.07294483e-02],
        [5.66701120e-02, 5.48480341e-02, 9.67480926e-02, 8.30513480e-02,
         6.51472870e-02, 1.98285240e-02, 6.74185567e-02, 1.20443256e-02,
         9.94704937e-03, 2.52561501e-03],
        [5.07024835e-02, 7.31391422e-02, 5.40148246e-02, 1.04867542e-02,
         7.75239955e-02, 2.61189552e-02, 5.03057247e-02, 7.10915313e-02,
         1.08623822e-02, 6.93874825e-02],
        [2.80326594e-02, 1.85514480e-02, 9.98622959e-02, 6.93038419e-02,
         8.85402041e-02, 9.34946710e-02, 6.30539863e-02, 5.63297173e-03,
         7.52106191e-02, 7.05511652e-02],
        [7.43095073e-02, 2.37040492e-02, 9.88372704e-02, 7.89723387e-02,
         4.39806997e-02, 6.64195145e-02, 3.83074203e-02, 8.08123083e-02,
         6.21941323e-02, 4.13117389e-02],
        [9.64893718e-03, 8.34237825e-02, 2.42758625e-02, 9.62278535e-02,
         1.19140014e-02, 1.28006647e-02, 7.39630727e-02, 4.07713332e-02,
         6.67586829e-02, 7.44536091e-02]],

       [[1.71928844e-02, 2.31469079e-02, 1.57169325e-02, 1.00889442e-02,
         9.41530198e-02, 7.90372708e-02, 7.17670725e-03, 9.08567200e-03,
         7.57422179e-02, 8.50218847e-02],
        [3.35425130e-02, 5.28203725e-02, 9.21520343e-02, 3.36173925e-02,
         7.18321347e-02, 5.85121059e-03, 9.00858558e-02, 5.64399470e-02,
         8.79148876e-02, 8.96881751e-02],
        [4.73592424e-02, 4.87774230e-02, 4.04862428e-02, 2.73562021e-02,
         5.52202262e-02, 1.58245841e-02, 7.50993463e-02, 4.11773716e-02,
         5.41014020e-02, 3.12404857e-02],
        [4.34335988e-02, 6.46048324e-02, 3.52764739e-02, 3.29286535e-02,
         9.53529378e-02, 7.25651623e-04, 6.47184683e-02, 2.42722410e-02,
         6.82801940e-02, 2.42701070e-02],
        [8.51481361e-02, 3.70243359e-02, 9.90656809e-02, 6.39421342e-02,
         3.61922033e-02, 7.46845092e-02, 8.27526128e-02, 3.02270094e-02,
         2.94540917e-02, 2.63949474e-02],
        [7.91368419e-02, 1.42376211e-03, 5.22476988e-02, 8.84594944e-02,
         3.67746829e-02, 1.31321546e-02, 8.98581201e-02, 1.75835026e-02,
         8.72940955e-02, 4.48065677e-02],
        [3.85483488e-02, 7.26737935e-02, 1.35299502e-02, 3.22004219e-03,
         1.33823865e-02, 2.40036545e-02, 1.20545916e-02, 5.43180712e-02,
         6.89021114e-02, 5.00063430e-02],
        [7.12543391e-02, 9.07123654e-02, 9.66181734e-02, 1.54819374e-03,
         6.69799114e-02, 3.78060438e-02, 4.24336739e-02, 5.31183360e-02,
         8.57470623e-02, 3.46833601e-02],
        [9.40242971e-02, 4.81075215e-02, 6.19822582e-02, 1.85994984e-03,
         4.78727854e-02, 8.15255095e-02, 5.41236726e-02, 7.05077743e-02,
         7.26706336e-03, 5.51903898e-02],
        [3.91540990e-02, 7.84913263e-02, 8.24865488e-02, 9.46551222e-02,
         8.96668780e-03, 8.71762878e-02, 4.37897106e-03, 4.25882276e-02,
         1.18684872e-02, 3.02213172e-02]],

       [[9.97289308e-02, 4.98612055e-02, 5.21689604e-02, 7.31989680e-02,
         5.52015626e-02, 9.63987723e-02, 2.92996783e-02, 3.36493251e-02,
         4.58459710e-02, 8.95504925e-03],
        [4.39105953e-02, 6.57790470e-02, 8.04649600e-02, 3.02522876e-02,
         7.61329080e-02, 9.13456572e-02, 3.60419430e-02, 9.64395580e-03,
         6.44467432e-02, 9.40608395e-02],
        [4.82223448e-02, 6.76611185e-02, 2.86507430e-02, 9.18600942e-02,
         8.96740243e-02, 1.79725059e-02, 5.34546711e-02, 9.78426521e-02,
         6.17543962e-02, 3.70894806e-02],
        [2.51411199e-03, 8.31075364e-02, 6.38154038e-02, 7.21844691e-02,
         3.15317638e-02, 5.97074253e-02, 6.92720352e-02, 2.48632198e-03,
         1.25324794e-02, 9.92350294e-02],
        [1.86858733e-02, 5.03238065e-02, 7.17358936e-02, 5.49434152e-02,
         3.30086771e-02, 6.41716317e-02, 8.14539099e-03, 5.73019623e-02,
         6.97990335e-02, 3.26376343e-02],
        [4.94868206e-02, 6.18169148e-02, 2.01233455e-02, 2.75693316e-02,
         1.53352169e-02, 2.79892627e-02, 4.89422799e-02, 7.74651793e-02,
         3.76250044e-02, 1.28395458e-02],
        [7.15570619e-02, 9.50220789e-02, 5.98542695e-02, 6.28410761e-02,
         1.64502636e-02, 9.76609678e-04, 8.42168364e-02, 6.68295403e-02,
         9.79718987e-02, 8.95295728e-02],
        [3.49695070e-02, 3.77883735e-02, 6.99218394e-02, 1.16096596e-02,
         5.41213996e-02, 7.76681240e-02, 6.06033823e-02, 5.09736149e-02,
         7.31809714e-02, 4.24100188e-02],
        [8.76558978e-02, 3.80244515e-02, 4.21746554e-02, 7.49638913e-02,
         2.12495391e-02, 1.08774230e-02, 4.66831163e-02, 5.99772404e-02,
         8.13692946e-02, 7.61529615e-02],
        [5.57836816e-02, 4.69147877e-02, 9.04780159e-03, 1.86998844e-02,
         4.70535904e-02, 5.42524090e-03, 1.32558463e-02, 1.65001223e-02,
         4.99251224e-02, 5.33401267e-02]],

       [[3.64681458e-02, 4.62497588e-02, 2.39391965e-02, 6.03050773e-02,
         5.98006897e-02, 2.02659950e-02, 1.78957841e-02, 5.12766970e-03,
         1.47222102e-02, 7.24258181e-02],
        [4.64562644e-02, 5.09242649e-02, 2.91096890e-02, 6.91964219e-02,
         1.00377111e-02, 4.46710447e-03, 4.36520429e-02, 2.09194122e-02,
         3.48834770e-02, 1.12834266e-02],
        [6.78376864e-02, 5.23215312e-02, 9.61045695e-02, 6.94183419e-02,
         3.29978110e-02, 7.56033454e-02, 9.02189988e-02, 4.16629365e-02,
         9.98990506e-02, 8.50742524e-03],
        [2.86535411e-02, 3.36472633e-02, 9.35235324e-02, 9.72746250e-02,
         3.65154927e-02, 5.40922725e-02, 2.82889697e-03, 4.90005462e-02,
         6.10006494e-03, 3.67825062e-02],
        [6.63848611e-02, 7.15549522e-02, 2.41076782e-02, 3.37343340e-02,
         6.73621355e-02, 7.57331120e-02, 7.18033243e-02, 4.33308845e-02,
         4.87169529e-03, 7.84519257e-03],
        [4.34740852e-02, 8.06807066e-02, 1.55583946e-02, 4.92479196e-02,
         6.72241486e-02, 7.75132065e-02, 9.26615582e-02, 1.91048946e-02,
         5.99316358e-02, 2.55286719e-02],
        [3.51104880e-02, 2.61536073e-02, 7.52582044e-02, 3.43620275e-02,
         5.00920881e-02, 4.27546950e-02, 9.99772003e-02, 6.75074449e-03,
         1.98773100e-02, 8.47281929e-02],
        [5.78105801e-02, 7.16286795e-02, 7.25716649e-02, 7.35872470e-02,
         6.75803586e-02, 2.32960344e-02, 6.65776274e-02, 9.30347827e-02,
         7.47536737e-02, 2.46585832e-02],
        [8.21611616e-02, 8.46318269e-02, 5.35605487e-02, 4.39702476e-02,
         4.70303980e-02, 1.99847214e-02, 5.55235381e-02, 1.15044573e-03,
         5.45166041e-02, 2.73945771e-02],
        [6.26421297e-02, 3.00876201e-02, 8.94206808e-02, 3.99626058e-02,
         9.26643096e-02, 9.83811488e-02, 2.12061635e-03, 9.37937010e-02,
         8.53987409e-02, 1.94358752e-02]],

       [[3.37481668e-03, 8.78614502e-02, 3.41518489e-02, 1.07361073e-02,
         4.28769330e-02, 4.11201217e-02, 7.34993076e-02, 6.70371985e-02,
         2.09941088e-02, 1.54029312e-03],
        [1.03069099e-02, 5.67505610e-03, 4.27597236e-02, 9.56491162e-02,
         3.61018060e-02, 9.00753246e-03, 9.50831813e-03, 9.30834433e-02,
         8.23152346e-02, 2.24378289e-02],
        [6.04333783e-02, 3.42990949e-02, 1.54881279e-02, 5.82648119e-03,
         9.11746028e-02, 9.31634152e-02, 4.95786876e-02, 5.38618468e-02,
         4.65005316e-02, 1.96896000e-02],
        [9.71593183e-02, 7.39487204e-02, 3.15223945e-02, 6.20641025e-03,
         2.02567687e-03, 7.22988115e-02, 7.98630670e-03, 9.84118185e-02,
         4.60411625e-02, 1.47664492e-02],
        [9.70445939e-02, 9.91065682e-02, 9.11997120e-02, 1.28401977e-02,
         5.49012697e-02, 2.13903496e-02, 9.10083222e-02, 9.75312977e-02,
         5.47358262e-02, 9.72271524e-02],
        [1.06878746e-02, 5.80071146e-02, 2.74225347e-02, 9.71954363e-02,
         1.34170020e-02, 2.81794173e-02, 4.35446826e-02, 3.01414737e-02,
         5.83810966e-02, 8.33713112e-03],
        [7.21394062e-02, 4.32174712e-02, 2.88999714e-03, 1.00083429e-02,
         3.61023648e-02, 8.34226840e-04, 3.70987421e-02, 8.44124722e-02,
         3.00967154e-04, 1.37258714e-02],
        [8.29567262e-02, 4.13295356e-02, 5.38183876e-02, 4.27531839e-02,
         3.59901808e-02, 9.36631376e-02, 7.90641560e-02, 8.42261957e-02,
         4.19931167e-02, 4.09563027e-02],
        [5.29184836e-02, 1.63346423e-02, 8.37514713e-02, 6.53786589e-03,
         2.84612104e-02, 6.98592067e-02, 6.82149472e-02, 4.82467393e-02,
         6.58720690e-02, 4.46048952e-02],
        [9.81023137e-03, 1.08946172e-02, 9.63542316e-02, 6.54119452e-02,
         7.72404195e-02, 2.99491623e-02, 5.12698603e-02, 5.75917077e-02,
         6.05053905e-02, 3.01735719e-02]],

       [[8.11077693e-02, 8.58023037e-02, 5.60237793e-02, 3.73467074e-02,
         9.16055741e-02, 5.47938496e-03, 9.50064725e-02, 7.33459347e-02,
         7.87164263e-02, 6.64025354e-02],
        [7.99201294e-02, 9.99869158e-02, 1.23095806e-03, 3.89191053e-02,
         3.15462055e-02, 4.30518134e-03, 7.80624763e-02, 6.92674585e-02,
         7.78108366e-02, 6.69067569e-02],
        [6.66956884e-02, 9.59158126e-02, 6.43659799e-02, 5.99419676e-02,
         5.22966747e-02, 8.04581323e-02, 3.00203232e-02, 2.38841543e-02,
         9.63459288e-02, 7.05253014e-02],
        [6.99184347e-02, 4.91929886e-02, 8.43669752e-02, 9.49758258e-02,
         2.98712690e-02, 6.25291569e-02, 6.98402480e-02, 9.25979579e-02,
         7.58873511e-02, 7.61260391e-02],
        [1.12713181e-02, 8.44267004e-02, 9.74660528e-02, 2.12401431e-02,
         5.31696306e-02, 6.98565736e-02, 3.61713745e-02, 1.44646034e-02,
         9.58294977e-02, 4.62016979e-02],
        [1.73753614e-02, 9.93421851e-02, 7.99668450e-02, 7.88111331e-02,
         2.81709249e-03, 8.09974257e-02, 9.58305705e-02, 4.28753856e-02,
         1.84806712e-02, 6.83120602e-02],
        [6.60423621e-02, 2.60612368e-02, 9.53188649e-02, 3.97889670e-02,
         2.80672560e-02, 7.85732466e-02, 1.36239163e-02, 3.58273818e-02,
         4.24793458e-02, 4.48747127e-02],
        [6.27226313e-02, 6.49091701e-02, 1.08478543e-02, 3.38465678e-02,
         7.61830531e-02, 4.73272473e-02, 4.77096547e-02, 4.19608489e-02,
         8.44392022e-02, 6.34053291e-02],
        [3.06271766e-02, 8.31420520e-02, 8.80986700e-02, 5.44593356e-02,
         4.89639266e-03, 3.01193512e-02, 9.22385853e-02, 4.93536703e-02,
         5.79473346e-04, 9.35916867e-02],
        [8.41408065e-02, 9.18065297e-02, 2.49394683e-03, 4.57227028e-02,
         1.53628541e-02, 6.24964564e-02, 3.68093284e-02, 6.75878470e-02,
         8.19807294e-02, 9.16268759e-02]],

       [[6.83834954e-02, 1.44925555e-02, 1.05279705e-02, 3.93838283e-03,
         4.80536257e-02, 8.19749420e-02, 8.42906100e-02, 2.38861904e-02,
         6.34625655e-02, 8.08262136e-02],
        [3.64108465e-02, 2.45384426e-02, 8.02892900e-02, 9.33311527e-02,
         3.92099541e-02, 7.74960974e-02, 2.01013703e-02, 3.27350164e-03,
         7.57314375e-02, 4.70528630e-02],
        [7.16201280e-02, 5.64604180e-02, 5.51222629e-02, 5.42733239e-02,
         7.23716365e-02, 1.17783450e-02, 6.13778374e-02, 6.55800322e-02,
         2.61268642e-02, 8.66911211e-02],
        [4.56338822e-02, 7.20376303e-03, 6.89848725e-02, 9.48135590e-03,
         4.68058366e-03, 8.97696382e-02, 7.23173624e-02, 3.41528678e-02,
         2.20244369e-02, 6.35351391e-02],
        [3.13459118e-02, 1.42191819e-02, 6.23750063e-02, 6.29798630e-02,
         5.52886990e-02, 6.62327118e-02, 9.35381721e-02, 3.51014693e-02,
         9.08077850e-02, 6.20005990e-02],
        [6.41707835e-02, 8.25304283e-02, 3.21608699e-02, 9.76949554e-02,
         5.35243935e-02, 3.80296754e-02, 9.59417832e-02, 3.86177392e-02,
         7.19286216e-02, 8.22939483e-03],
        [4.64619440e-02, 6.45064179e-02, 3.40525606e-02, 7.56049870e-03,
         4.22304483e-02, 6.24184984e-02, 2.82960754e-02, 9.87945980e-02,
         6.86806932e-02, 4.80881361e-02],
        [3.93924408e-02, 8.62275024e-02, 3.13164053e-02, 8.92310943e-02,
         8.39245920e-02, 4.09418735e-02, 8.91448398e-02, 8.43040347e-02,
         6.51016018e-02, 1.37370152e-02],
        [3.11980687e-02, 6.38987848e-02, 7.41329856e-02, 2.73623498e-02,
         7.96377637e-02, 4.56125987e-03, 8.72574553e-02, 3.97334594e-02,
         4.44726278e-02, 3.70997348e-02],
        [3.22612047e-02, 8.29009002e-03, 2.83241575e-02, 7.16906555e-02,
         2.89085853e-02, 3.57597877e-03, 9.82679632e-03, 5.61031294e-02,
         5.11241115e-02, 6.12190030e-02]],

       [[7.13125943e-02, 8.60983944e-02, 6.17783308e-03, 8.24747931e-02,
         5.64626382e-02, 7.00635249e-03, 5.80248503e-02, 2.51080120e-02,
         8.10276833e-02, 4.85113183e-03],
        [1.43823705e-02, 3.84948347e-02, 5.74363215e-02, 2.57614912e-02,
         3.84648993e-02, 1.24283362e-03, 6.03798028e-02, 1.47687195e-02,
         1.56853908e-03, 8.51186995e-02],
        [3.31601272e-02, 2.06212500e-02, 5.71106205e-03, 6.15456187e-02,
         3.70193967e-02, 5.85499830e-02, 6.01438150e-02, 2.23959536e-02,
         4.05035975e-02, 5.70265542e-02],
        [8.48144414e-02, 9.52616901e-02, 2.13814910e-02, 4.19092106e-02,
         2.60666940e-02, 3.06072592e-02, 9.64055147e-02, 5.85896643e-02,
         3.34659129e-02, 1.77403698e-02],
        [2.91001642e-02, 8.15281435e-02, 2.74126266e-02, 7.28478146e-02,
         9.67471078e-02, 9.12995960e-02, 8.25470930e-02, 6.41292314e-02,
         7.10511488e-03, 1.44715001e-02],
        [4.76161634e-02, 1.47631122e-02, 9.19729317e-02, 5.44575944e-02,
         8.01239881e-02, 1.67423726e-02, 1.75107046e-02, 3.00578468e-02,
         7.82928702e-02, 6.05888810e-02],
        [8.71137537e-02, 5.21406039e-02, 9.89206895e-02, 1.48477241e-02,
         1.61187045e-02, 4.79679224e-02, 5.49963585e-02, 7.71649928e-02,
         3.63214464e-02, 4.88388761e-02],
        [2.67381162e-02, 5.92008915e-02, 2.81482863e-02, 7.78465155e-02,
         5.04477089e-02, 8.01991871e-02, 8.99412882e-02, 8.28843634e-02,
         2.64931477e-02, 2.71796943e-02],
        [1.10186607e-02, 6.88450062e-02, 2.46796420e-02, 4.51365307e-02,
         3.68107998e-02, 4.03992664e-02, 3.54988803e-02, 4.72173692e-02,
         3.70595982e-02, 5.10931486e-02],
        [7.69890594e-02, 6.63072645e-02, 9.06765650e-02, 1.18358722e-02,
         3.14532342e-03, 8.39341193e-03, 7.14989558e-02, 3.61109732e-02,
         6.58052415e-03, 9.35055148e-02]],

       [[5.29856615e-02, 1.94480419e-02, 3.03247633e-02, 5.63682237e-02,
         7.44487612e-02, 8.36703275e-02, 7.59157739e-02, 9.18728831e-02,
         1.85687188e-02, 6.74805489e-03],
        [6.24830040e-03, 8.08619431e-02, 9.44405593e-02, 7.51604098e-02,
         5.98603605e-02, 7.25790084e-02, 4.58290378e-02, 1.50981410e-02,
         5.41553336e-02, 5.67584419e-02],
        [1.15825218e-02, 4.52560063e-02, 2.71021152e-02, 3.35912635e-02,
         7.42933244e-02, 1.30249958e-02, 9.91358357e-02, 5.37148057e-03,
         7.89022012e-02, 6.89495491e-02],
        [3.92724794e-02, 3.15105875e-02, 8.85611547e-02, 8.39152994e-02,
         1.49085915e-02, 8.33281984e-02, 8.91896036e-02, 8.52577184e-04,
         1.31242274e-02, 6.81345169e-02],
        [5.83776113e-02, 2.39456621e-02, 5.33384923e-02, 8.23930745e-02,
         2.99137811e-02, 9.06129889e-02, 6.67639258e-02, 8.10913175e-02,
         1.52722181e-02, 9.22176153e-02],
        [8.45429187e-02, 8.53747101e-02, 2.48680024e-02, 2.65938411e-02,
         4.09929409e-02, 8.42670228e-02, 3.97462932e-02, 9.92506695e-03,
         5.96916574e-02, 7.70708777e-02],
        [2.16109936e-02, 4.33302457e-02, 4.00648764e-02, 4.39115995e-02,
         6.81886311e-02, 5.43799468e-02, 7.55016728e-02, 2.43239857e-02,
         4.18098589e-02, 4.52086091e-02],
        [8.45823343e-02, 4.59597715e-02, 1.17847198e-02, 1.85338480e-03,
         3.91235772e-02, 4.52432755e-02, 5.63537955e-02, 9.69374010e-02,
         2.32372420e-02, 6.07734658e-02],
        [1.84959446e-02, 2.93944517e-02, 3.03079023e-03, 4.84785657e-02,
         4.81725939e-02, 9.68529825e-03, 7.23083139e-02, 8.83497060e-02,
         8.97493674e-02, 1.03430918e-02],
        [4.64882396e-02, 8.86077807e-02, 3.40367763e-03, 3.66175935e-02,
         9.65036779e-02, 6.30763766e-02, 6.59950873e-02, 1.27783770e-02,
         4.25266604e-02, 1.25623694e-02]]])
    • bob
      (x, z)
      float64
      𝟙
      0.0, 0.1, ..., 9.8, 9.9
      σ = 0.231, 0.232, ..., 0.218, 0.198
      Values:
      array([[0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9],
       [1. , 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9],
       [2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9],
       [3. , 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9],
       [4. , 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9],
       [5. , 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9],
       [6. , 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9],
       [7. , 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9],
       [8. , 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9],
       [9. , 9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9]])

      Variances (σ²):
      array([[0.05341706, 0.05364781, 0.06082259, 0.08952127, 0.04400558,
        0.07902606, 0.01893112, 0.08880097, 0.08097018, 0.08868005],
       [0.09532432, 0.09453228, 0.01823721, 0.0335211 , 0.07134438,
        0.01729049, 0.03081114, 0.0024635 , 0.07447827, 0.03907167],
       [0.08397303, 0.09743895, 0.08202897, 0.02379371, 0.02422616,
        0.07979023, 0.08751186, 0.03352043, 0.01747812, 0.09389281],
       [0.07483366, 0.00702779, 0.00012289, 0.0521478 , 0.04551805,
        0.00465947, 0.04788339, 0.0415599 , 0.0071038 , 0.09588559],
       [0.04334168, 0.04042072, 0.04553209, 0.06061073, 0.08188847,
        0.05607157, 0.03228922, 0.02484937, 0.08888189, 0.03919254],
       [0.00890728, 0.04741125, 0.09664958, 0.08518083, 0.0811361 ,
        0.09279934, 0.01358403, 0.09163447, 0.01753268, 0.02217555],
       [0.02031463, 0.00847511, 0.03489222, 0.08343603, 0.03227952,
        0.00868752, 0.07043597, 0.09257888, 0.02286138, 0.08959809],
       [0.05071653, 0.05515376, 0.08413628, 0.00870838, 0.04334792,
        0.07028481, 0.08652677, 0.02026737, 0.09993673, 0.09441159],
       [0.01247763, 0.00550021, 0.0558913 , 0.09911113, 0.02710745,
        0.01826467, 0.09547214, 0.06046085, 0.05373682, 0.09103262],
       [0.01330423, 0.01669914, 0.01719492, 0.0216747 , 0.09179748,
        0.04633023, 0.01446615, 0.05909261, 0.04772873, 0.03911943]])

To slice in multiple dimensions, we can simply chain the slicing notation used previously for 1D data. This gives us a number of different options for visualizing our data:

[4]:

sc.table(d['x', 5]['z', 2])

We can plot and item of a Dataset using:

[5]:

sc.plot(d['bob'])

Plotting a 3-dimensional data cube will show a 2D image with a slider to navigate through the third dimension (note that interactive sliders will only appear in a Jupyter notebook and not in the documentation pages):

[6]:

sc.plot(d['alice'])

Finally, by extracting a 1D variable, we obtain a 1D plot:

[7]:

sc.plot(d['x', 8]['y', 2])

Note that this is now plotted as a histogram since the coordinate in the dataset represents bin edges, in contrast to the 1D data plotted in 1-D datasets and tables.

Operations automatically broadcast based on dimension labels. That is, if one of the operands lacks one (or multiple) dimensions that the other operands have, the operand is considered constant along those dimensions. Its values are implicitly “duplicated” so the shape matches. In contrast to numpy or MATLAB there is no need to keep track of dimension order:

[8]:

d['alice'] -= d['bob']
d['alice'] -= d['alice']['y', 5]
sc.plot(d['alice']['x', 4])

Exercise 1#

Remove the X and Z surface layer of the volume, i.e., remove the first and last slice in each of the dimensions 'x' and 'z'.

Solution 1#

[9]:

d = d['x', 1:-1]['z', 1:-1].copy()
d

[9]:
Show/Hide data repr Show/Hide attributes
scipp.Dataset (11.23 KB)
    • z: 8
    • y: 10
    • x: 8
    • x
      (x [bin-edge])
      float64
      m
      1.0, 2.0, ..., 8.0, 9.0
      Values:
      array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
    • y
      (y [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • z
      (z [bin-edge])
      float64
      m
      1.0, 2.0, ..., 8.0, 9.0
      Values:
      array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
    • alice
      (z, y, x)
      float64
      𝟙
      -0.279, 0.112, ..., -0.618, 0.120
      σ = 0.519, 0.598, ..., 0.516, 0.439
      Values:
      array([[[-2.79109272e-01,  1.11826528e-01,  2.12368435e-01,
          2.18260616e-01, -1.38258825e-01, -5.36126450e-01,
          8.10821516e-02, -2.35089030e-01],
        [-3.04176825e-01,  1.86601936e-02,  5.21655584e-01,
          4.77231948e-01,  5.49515841e-01, -1.10875774e-02,
          2.45251358e-02, -3.63672865e-01],
        [ 1.99053753e-01,  4.81310180e-01,  5.99695465e-03,
         -3.13655542e-01, -2.51453404e-01, -2.80508670e-01,
          2.59668212e-01, -4.78992435e-03],
        [-3.74100136e-01, -1.27792140e-02,  6.73186236e-01,
          5.98998479e-02,  5.71744569e-02, -5.41298707e-01,
          9.21346140e-04,  4.19513601e-01],
        [ 9.29425310e-02, -1.10826220e-01,  6.28121781e-01,
          4.36248112e-01,  4.19104683e-02, -4.57131787e-01,
          6.23696582e-01,  9.06287184e-02],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 5.06499271e-01, -2.11872651e-01,  1.94472095e-01,
         -2.12782449e-01,  4.69909668e-01, -7.93961409e-01,
          5.56036362e-01,  3.66882896e-01],
        [ 2.83303147e-01, -2.99035618e-01, -4.98668935e-02,
          3.73162786e-02,  4.27516039e-01, -1.03489411e-01,
          1.23781846e-01, -1.37584507e-01],
        [ 5.50842801e-02, -3.30628432e-01,  2.52001188e-01,
          2.39805958e-01, -1.36475254e-01, -6.92009277e-01,
         -1.72706860e-01, -2.18476044e-01],
        [ 2.42332003e-01,  5.91863445e-01,  5.36379311e-02,
          2.63956887e-01,  1.48385875e-01, -1.10595219e-01,
          2.39062754e-01, -2.94161187e-01]],

       [[-3.00075655e-01, -8.05654381e-01,  6.88322270e-01,
          5.07306260e-01,  1.18116961e-02, -1.16425499e-01,
          5.69272070e-01,  3.06841136e-01],
        [ 4.35976611e-01, -8.11050811e-01,  1.51110538e-01,
          2.18738036e-01,  1.83008678e-01, -2.98476682e-01,
          5.65372993e-01, -1.54748155e-01],
        [-1.78704119e-01, -5.98022165e-01,  5.57549908e-01,
          1.00839335e-01,  2.39915638e-01,  7.98915003e-02,
          4.55393531e-01, -1.66972526e-01],
        [-1.54422665e-01, -4.70218686e-01,  5.06941545e-01,
         -4.05649831e-02, -4.77651882e-02,  2.42331069e-01,
          9.08672741e-01, -5.24611116e-01],
        [ 4.40600091e-01, -8.28157626e-01,  2.45791562e-01,
          5.95143443e-01,  2.01985329e-01, -5.21225979e-01,
          5.12602596e-01, -2.01449422e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 3.38508512e-01, -2.02729987e-01,  5.41302502e-02,
          7.86622152e-01,  5.25414902e-01,  2.99034835e-01,
          7.72659749e-01, -1.31816399e-01],
        [-5.36728593e-02, -3.80239524e-01,  1.27842696e-01,
          2.43272287e-01, -1.23686207e-01,  1.66079726e-01,
          7.29413953e-01, -3.79198240e-01],
        [ 2.47915608e-01, -2.70609209e-01,  1.35039514e-01,
          5.99701340e-01, -4.06302586e-01,  3.17663098e-01,
          1.03062940e-01, -6.70178306e-02],
        [-4.49806381e-03, -9.63866554e-02,  6.01536915e-01,
          4.23478437e-01,  1.53451006e-01,  1.47374830e-01,
          8.04239367e-01,  2.04718126e-01]],

       [[ 7.46895005e-02, -7.13873301e-02,  8.51021026e-02,
         -9.06237277e-03,  9.78023153e-02,  7.58606099e-01,
         -3.97127636e-02, -8.51312377e-01],
        [-6.55871887e-02,  4.53545197e-01,  8.78178440e-01,
          5.64000630e-01,  1.16492952e-01,  7.67133658e-01,
          6.44821043e-01, -3.14613293e-01],
        [-1.75114639e-01, -3.37155128e-01,  6.50498433e-01,
          7.15770779e-02,  3.50372607e-01,  5.15448744e-01,
          6.54646701e-01, -6.63600408e-01],
        [-2.54321256e-01,  4.60623224e-01,  8.74447218e-01,
          1.61624834e-01,  2.38397253e-01, -1.75722326e-03,
          8.15334642e-02, -1.59674176e-01],
        [-7.61356592e-01,  5.70327701e-01,  7.56902761e-01,
         -2.94155037e-01, -4.07298708e-02, -2.01587396e-02,
          5.51711620e-01, -3.81350507e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-2.22737455e-01,  2.52475468e-01,  3.52520649e-02,
         -2.56277715e-01, -3.77912943e-02, -3.21369082e-02,
          3.94522557e-01, -1.41741430e-01],
        [ 1.01541348e-02, -2.54962474e-01,  5.01224103e-01,
         -1.07111106e-02,  2.01087256e-01,  2.70488676e-01,
          5.51835062e-01,  2.31347857e-02],
        [-2.28380321e-02,  8.54216415e-02,  2.84339780e-01,
         -2.55973182e-01, -6.11133451e-02,  2.09181867e-01,
         -8.55518810e-02, -8.25016235e-01],
        [-7.29733130e-01, -1.91053316e-01,  6.34077047e-01,
         -2.74809740e-01, -7.12757028e-02,  3.90997563e-01,
          6.97273986e-01, -4.51762269e-01]],

       [[-1.08479735e-01, -9.23107793e-01, -8.24912559e-01,
         -8.21798350e-01, -4.32109080e-01, -3.72632042e-01,
          3.42220850e-01, -3.92329726e-01],
        [-4.24901199e-01, -4.46891668e-01, -9.46358705e-01,
         -4.80039672e-01,  4.41384374e-01,  1.57833094e-01,
         -5.14889217e-01, -2.98894967e-01],
        [ 1.84013633e-01, -8.30516910e-01, -6.89072432e-01,
         -2.77055257e-01,  3.96489489e-02, -5.78357908e-01,
         -7.13899342e-03, -3.09746349e-01],
        [-8.96101986e-02, -8.96608550e-01, -7.10691680e-01,
         -6.77710542e-01,  1.11509803e-01,  1.82187710e-01,
         -7.23837331e-02, -7.18335634e-01],
        [ 4.12873665e-01, -4.34818504e-02, -1.05957187e-01,
         -5.20529317e-01, -2.78695062e-01,  3.15706806e-01,
          3.58300417e-01, -1.13525614e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 4.56616368e-01, -1.29235056e-01, -2.94601579e-01,
         -6.67531879e-01, -1.47490649e-01,  2.51744279e-01,
         -3.41886754e-01, -7.50576802e-01],
        [ 1.76672641e-01, -8.17873639e-01, -7.08374931e-01,
         -7.44187732e-01,  3.80232417e-01, -3.16006772e-01,
         -2.40232927e-01, -5.74243896e-01],
        [-3.68003807e-01, -4.53497523e-01, -6.11598717e-01,
         -6.89074806e-01, -2.27360218e-01, -1.13781665e-01,
         -4.25767530e-01, -3.50801162e-01],
        [-1.88142671e-01, -6.18201775e-01, -2.08875503e-01,
         -8.12100300e-01,  5.22256758e-02, -8.19394381e-02,
         -3.35736206e-01, -6.83434452e-02]],

       [[-1.33196248e-01, -4.51983665e-01,  4.12880537e-01,
         -1.86037887e-02, -2.76605956e-01,  6.93006859e-01,
         -2.84094479e-01,  4.99979317e-01],
        [ 4.09347239e-01, -7.34815870e-02,  3.27324406e-01,
         -3.38125812e-01,  6.84730253e-01,  6.45968120e-01,
          3.48317480e-01,  6.34527579e-01],
        [ 3.71163260e-01, -4.73551534e-01, -2.67623270e-01,
         -3.45714074e-01,  6.07440020e-01,  5.18199804e-01,
          8.58426681e-02, -1.42693313e-01],
        [-1.10730372e-01, -1.19743331e-01,  4.43165204e-01,
         -5.01584369e-02, -1.99746796e-01, -5.92922737e-02,
         -4.09956502e-03, -1.91783090e-01],
        [-5.08677631e-02, -1.51496215e-01,  2.86268006e-01,
         -5.77838606e-01,  8.06345647e-02,  4.71682961e-01,
         -1.47873730e-01,  1.80744369e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-4.09914687e-01,  9.29026616e-02, -1.08513842e-01,
         -9.54647133e-01, -5.14985594e-02,  6.89190252e-01,
         -3.76932887e-01,  1.18761460e-01],
        [ 4.51791551e-01,  3.02043947e-01,  3.19646369e-01,
         -8.56418130e-01,  3.84691310e-01,  6.58600720e-01,
         -3.07776360e-01, -2.29262973e-01],
        [-1.77050367e-01,  3.84765591e-02,  3.57004745e-01,
         -3.88265076e-01, -2.22970567e-01,  4.80181134e-01,
         -2.70000395e-02,  6.88839643e-01],
        [ 9.75547518e-02,  4.82699826e-02,  3.35595729e-02,
         -9.47149391e-01,  2.58063485e-01,  1.20306371e-01,
         -1.07392314e-01, -2.66179769e-02]],

       [[ 6.48456551e-01, -4.07850006e-01,  4.37898432e-01,
          8.24346188e-01,  8.54685617e-01, -2.24056005e-01,
         -1.28700483e-01, -2.06423315e-01],
        [-1.12495769e-01, -2.19949616e-01, -2.27236666e-01,
          5.64646822e-01,  8.22777465e-01, -1.52414842e-01,
         -2.85485719e-01, -3.05899805e-01],
        [ 4.97540228e-01, -1.95892519e-01,  1.47764027e-01,
          7.93513537e-01,  3.87204764e-01, -4.98200582e-01,
          1.10730954e-01, -2.11073509e-01],
        [ 1.68164337e-01,  3.08589230e-01,  3.98941886e-01,
          5.80206494e-01, -5.39634696e-02, -1.87904802e-01,
         -3.17931836e-01, -1.93776325e-01],
        [ 7.06183616e-01,  1.16288659e-01,  5.46967098e-01,
          4.53287707e-01,  5.88072930e-01, -5.72021275e-01,
          4.26255972e-01,  2.47540740e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 6.30613194e-02,  4.85988298e-02,  4.86085851e-01,
          2.64781930e-01,  5.55394806e-01,  1.43320364e-01,
         -2.43271404e-02,  1.42015844e-01],
        [ 8.10481849e-01, -3.93516162e-01, -2.18674593e-01,
          4.76388481e-01,  5.14477812e-01, -6.41810404e-01,
         -3.30190959e-01, -2.84020652e-01],
        [ 7.46172380e-01,  1.41796559e-01,  4.00144481e-01,
          4.32418914e-01,  3.83306667e-01, -5.06348587e-02,
          3.78704541e-01, -8.57201091e-02],
        [ 4.11251927e-01,  2.56304851e-01, -1.23641486e-01,
          4.55894864e-01, -3.25106958e-03,  8.25596159e-02,
         -2.75943019e-01, -1.18869994e-01]],

       [[-2.51921441e-01,  4.01797393e-01, -5.19512999e-01,
         -2.97514467e-01, -2.26073387e-01, -5.95197268e-02,
          1.86125017e-01, -5.06592264e-01],
        [-5.07429013e-02, -3.91813432e-01, -6.02166401e-01,
         -6.75444617e-01, -2.12099862e-01,  5.83322519e-01,
         -2.56655315e-01, -5.55662151e-01],
        [-2.79375769e-01, -9.00557536e-03, -1.75914125e-01,
         -3.99473107e-01,  8.87015373e-02,  7.99114998e-01,
         -3.14304639e-01, -4.27118078e-01],
        [-6.95142574e-01, -3.05062590e-01, -9.41677370e-01,
         -6.55997756e-01, -3.88378580e-01,  4.85169448e-01,
         -4.46338416e-02,  2.55021621e-01],
        [-6.34781159e-01,  3.56643799e-01, -5.45564627e-02,
          5.31244421e-02, -2.48401545e-01,  4.83370343e-01,
         -4.43220561e-01, -4.91149107e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-7.32665290e-01, -1.11999180e-02, -5.06990430e-01,
         -3.55208006e-01,  1.17406035e-01,  2.71894416e-01,
          1.82121115e-01, -3.44698158e-01],
        [ 1.14752794e-01, -4.70420525e-01, -9.58825315e-01,
         -2.70527586e-01,  5.68879609e-01,  6.47101359e-03,
         -3.87533638e-01,  4.54928717e-02],
        [-1.25792022e-01, -4.78677400e-01, -5.35544396e-01,
         -3.69237410e-01,  1.82536798e-01,  4.02931224e-01,
          2.24137985e-01, -4.11857924e-01],
        [ 1.96811228e-01, -1.33122008e-01, -4.37970523e-03,
         -7.45872304e-01, -1.35972171e-01,  2.33133617e-01,
          9.21356827e-02, -1.11242220e-03]],

       [[ 3.37487157e-02,  1.04598908e-01,  2.65359821e-01,
          6.75883739e-01,  2.12737686e-01, -3.85257458e-01,
         -7.85984403e-01, -2.95801723e-01],
        [-2.33729238e-01, -2.54823814e-01,  1.57842347e-01,
          8.26460442e-01, -5.64376446e-02,  1.02496034e-01,
         -7.41225608e-01, -3.37168117e-01],
        [-6.90735022e-01, -6.48326553e-02, -8.72213911e-02,
         -2.70246647e-02,  3.27714134e-01,  4.90347005e-01,
         -1.90588250e-01, -4.21947603e-01],
        [-6.28978712e-01, -1.49467498e-02, -2.94844676e-01,
          3.74638627e-01,  2.38097471e-01,  6.88523494e-02,
          1.47787658e-01, -5.99918816e-01],
        [-5.36587648e-01,  6.52238059e-01,  1.00977292e-01,
          1.51940536e-01,  4.01648884e-01,  2.08536765e-01,
         -4.74775990e-01, -5.70264411e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-2.58163749e-01,  2.36407847e-01,  4.67275894e-01,
          5.27272984e-01,  1.69527061e-01, -2.34417729e-01,
         -6.15407907e-01, -6.92178693e-01],
        [ 6.77951314e-02,  2.46251371e-01,  1.99839277e-01,
          3.16060094e-01,  6.47396554e-02,  4.23561377e-01,
         -2.23766429e-01, -6.93014555e-02],
        [-5.39078602e-01, -6.87792992e-02, -2.85440085e-01,
          2.59546851e-01, -5.02985294e-01,  7.19172186e-02,
          1.77698500e-01, -6.01057966e-01],
        [-7.13792027e-02,  3.35942152e-01,  2.75016016e-01,
          1.99827530e-01, -1.10739657e-01, -1.47016765e-01,
         -6.18211356e-01,  1.19725367e-01]]])

      Variances (σ²):
      array([[[0.26947474, 0.35782486, 0.16183636, 0.18701678, 0.20106336,
         0.15018938, 0.2122558 , 0.07225557],
        [0.27899704, 0.30738344, 0.12703958, 0.23864974, 0.11892096,
         0.13442117, 0.19785171, 0.03521057],
        [0.30372991, 0.3286027 , 0.12935508, 0.17671349, 0.17590725,
         0.14004221, 0.18878657, 0.03723348],
        [0.32060484, 0.3604546 , 0.19432548, 0.23523667, 0.12154473,
         0.11240068, 0.17303076, 0.055025  ],
        [0.28690653, 0.30291993, 0.17592209, 0.22734361, 0.19024545,
         0.14408771, 0.15362649, 0.09502295],
        [0.29876062, 0.38837408, 0.18015827, 0.21113601, 0.13447955,
         0.15178732, 0.13439618, 0.03089453],
        [0.31705173, 0.34564081, 0.10759367, 0.22351272, 0.14076998,
         0.13467449, 0.19344338, 0.03180986],
        [0.26246404, 0.39148828, 0.16641076, 0.23452893, 0.20814569,
         0.14742275, 0.12798482, 0.0961581 ],
        [0.26761664, 0.39046326, 0.17607926, 0.18996943, 0.18107054,
         0.12267619, 0.20316416, 0.08314161],
        [0.32733637, 0.31590185, 0.19333477, 0.15790273, 0.12745169,
         0.15833184, 0.16312319, 0.08770616]],

       [[0.0610451 , 0.23202256, 0.09879421, 0.22199188, 0.28546859,
         0.16681926, 0.19494173, 0.27481891],
        [0.09071856, 0.30845766, 0.12232266, 0.199671  , 0.21228253,
         0.24972841, 0.242296  , 0.28699158],
        [0.08667561, 0.25679187, 0.11606147, 0.18305909, 0.2222559 ,
         0.2347419 , 0.22703343, 0.2531781 ],
        [0.10250302, 0.2515821 , 0.12163392, 0.2231918 , 0.20715697,
         0.22436103, 0.2101283 , 0.26735689],
        [0.07492253, 0.31537131, 0.1526474 , 0.16403107, 0.28111583,
         0.24239517, 0.21608306, 0.22853079],
        [0.03932195, 0.26855333, 0.17716476, 0.16461355, 0.21956347,
         0.24950068, 0.20343956, 0.28637079],
        [0.11057199, 0.22983558, 0.09192531, 0.14122125, 0.23043497,
         0.17169715, 0.24017413, 0.26797881],
        [0.12861056, 0.3129238 , 0.09025346, 0.19481878, 0.24423736,
         0.20207623, 0.23897439, 0.28482376],
        [0.08600571, 0.27828789, 0.09056521, 0.17571165, 0.28795683,
         0.21376623, 0.25636383, 0.20634376],
        [0.11638952, 0.29879218, 0.18336039, 0.13680555, 0.2936076 ,
         0.16402153, 0.22844428, 0.21094518]],

       [[0.17872032, 0.11987973, 0.20506389, 0.19175824, 0.29474969,
         0.24511401, 0.12853127, 0.28169323],
        [0.19463816, 0.14817573, 0.16211721, 0.21268958, 0.28969658,
         0.25185628, 0.1045259 , 0.300294  ],
        [0.19652023, 0.09636151, 0.22372502, 0.2262307 , 0.21632343,
         0.269269  , 0.1927246 , 0.29760165],
        [0.21196665, 0.13152617, 0.20404939, 0.16808844, 0.25805834,
         0.28508637, 0.09736827, 0.24837973],
        [0.17918292, 0.13944666, 0.18680834, 0.16956535, 0.26252255,
         0.22395972, 0.15218391, 0.30564629],
        [0.19067603, 0.08783411, 0.15943425, 0.15189189, 0.22634018,
         0.26475661, 0.17234713, 0.27347226],
        [0.22388119, 0.12756504, 0.194706  , 0.15300694, 0.19932753,
         0.30003117, 0.16171149, 0.33381915],
        [0.16664749, 0.13763261, 0.14347458, 0.19067807, 0.27601904,
         0.27641771, 0.14585556, 0.30902823],
        [0.16688356, 0.10988542, 0.20682881, 0.15780621, 0.20922834,
         0.26249745, 0.15485919, 0.31721655],
        [0.1757739 , 0.07675857, 0.15056481, 0.18361026, 0.20377616,
         0.22907018, 0.11138207, 0.28577238]],

       [[0.26961922, 0.08794991, 0.20058911, 0.29080177, 0.2600514 ,
         0.17511638, 0.1109284 , 0.12886875],
        [0.27429373, 0.09312041, 0.20948045, 0.24103879, 0.24425251,
         0.20087264, 0.12672014, 0.14903002],
        [0.27569099, 0.16011529, 0.20970237, 0.26399889, 0.31538875,
         0.2474396 , 0.14746367, 0.21404559],
        [0.25701673, 0.15753425, 0.23755865, 0.26751657, 0.29387767,
         0.16004949, 0.15480128, 0.12024661],
        [0.29492442, 0.0881184 , 0.17401836, 0.29836322, 0.31551851,
         0.22902392, 0.14913162, 0.11901824],
        [0.30405017, 0.07956911, 0.18953195, 0.29822523, 0.31729861,
         0.24988215, 0.12490563, 0.17407818],
        [0.24952307, 0.13926892, 0.17464606, 0.28109317, 0.2825401 ,
         0.2571978 , 0.11255148, 0.13402385],
        [0.29499814, 0.13658238, 0.21387128, 0.29858144, 0.26308144,
         0.22379822, 0.19883551, 0.18890022],
        [0.30800129, 0.11757127, 0.18425428, 0.27803148, 0.25977012,
         0.21274413, 0.10695118, 0.16866315],
        [0.25345708, 0.1534314 , 0.18024663, 0.32366539, 0.33816655,
         0.15934121, 0.19959443, 0.19954528]],

       [[0.18044955, 0.22115484, 0.11725049, 0.16843708, 0.25489822,
         0.13441902, 0.23774828, 0.11590454],
        [0.09826316, 0.22976272, 0.20216349, 0.16166195, 0.22278563,
         0.07042803, 0.26379453, 0.17722567],
        [0.1268872 , 0.20249112, 0.11234086, 0.21673475, 0.30694152,
         0.1104984 , 0.22457293, 0.14141096],
        [0.16653682, 0.21852539, 0.11272079, 0.12758583, 0.28607691,
         0.06890602, 0.2691229 , 0.1409516 ],
        [0.19169467, 0.27820271, 0.11935458, 0.18046142, 0.23516845,
         0.15192804, 0.26824238, 0.14964626],
        [0.15059522, 0.21442553, 0.20370981, 0.13897715, 0.24195752,
         0.1044644 , 0.20085256, 0.15329153],
        [0.13580557, 0.18989299, 0.11652272, 0.16166251, 0.21461233,
         0.09801846, 0.25512356, 0.0952114 ],
        [0.13391764, 0.24082138, 0.14926756, 0.16155033, 0.30744124,
         0.13998387, 0.25493728, 0.13690355],
        [0.10892274, 0.27075447, 0.11305224, 0.15402136, 0.28363731,
         0.12913466, 0.21895783, 0.1607825 ],
        [0.10348272, 0.28335723, 0.17192632, 0.20280057, 0.24372726,
         0.11218958, 0.22830279, 0.15541582]],

       [[0.24676676, 0.31101434, 0.21192461, 0.1590011 , 0.11364487,
         0.33170898, 0.28927487, 0.28814138],
        [0.26095137, 0.25622152, 0.21349701, 0.09894173, 0.11247066,
         0.31476499, 0.28519639, 0.28723579],
        [0.25688027, 0.31935654, 0.23451987, 0.1196922 , 0.18862362,
         0.26672283, 0.23981309, 0.30577088],
        [0.21015744, 0.33935753, 0.26955373, 0.0972668 , 0.17069464,
         0.30654276, 0.30852689, 0.2853123 ],
        [0.24539116, 0.35245661, 0.19581805, 0.12056516, 0.17802206,
         0.27287389, 0.23039354, 0.30525445],
        [0.26030664, 0.3349574 , 0.25338904, 0.07021262, 0.18916291,
         0.33253308, 0.25880432, 0.22790562],
        [0.18702569, 0.35030942, 0.21436687, 0.09546278, 0.18673873,
         0.25032643, 0.25175631, 0.25190429],
        [0.22587363, 0.26583841, 0.20842447, 0.14357858, 0.15549273,
         0.28441217, 0.25788978, 0.29386415],
        [0.24410651, 0.34308923, 0.22903724, 0.07229192, 0.13828483,
         0.3289411 , 0.2652826 , 0.21000442],
        [0.25277099, 0.2574845 , 0.22030061, 0.08275838, 0.17066194,
         0.27351184, 0.28351678, 0.29140568]],

       [[0.10194999, 0.10972969, 0.18475314, 0.15127676, 0.30327355,
         0.36539015, 0.10303867, 0.25631288],
        [0.11199588, 0.17949101, 0.27414591, 0.14243309, 0.29879471,
         0.30120091, 0.08242598, 0.26858176],
        [0.14391785, 0.15432398, 0.23508808, 0.17559477, 0.23307696,
         0.34247738, 0.14473251, 0.21897718],
        [0.0946612 , 0.16818659, 0.19029611, 0.10790372, 0.31106825,
         0.35341691, 0.11330535, 0.21487476],
        [0.10167662, 0.16157673, 0.24379462, 0.15851184, 0.28753132,
         0.37463772, 0.11425395, 0.2836581 ],
        [0.16998786, 0.13136259, 0.27850971, 0.15674753, 0.25932829,
         0.37704133, 0.11777022, 0.26477894],
        [0.15196385, 0.13325428, 0.18837525, 0.14545359, 0.28371711,
         0.30939562, 0.17794708, 0.26153101],
        [0.17368494, 0.13051813, 0.27004585, 0.18714773, 0.26224049,
         0.37024438, 0.16345651, 0.25795192],
        [0.15135622, 0.17333471, 0.2081771 , 0.1828609 , 0.22585987,
         0.368357  , 0.11888594, 0.23732295],
        [0.09574752, 0.12752588, 0.25250541, 0.13213172, 0.22487459,
         0.29092634, 0.13525561, 0.24397443]],

       [[0.24981804, 0.13310701, 0.15113998, 0.3143504 , 0.05881409,
         0.12125832, 0.25503932, 0.2667942 ],
        [0.20221448, 0.1843655 , 0.09442668, 0.29635266, 0.05305057,
         0.12361327, 0.24470003, 0.18733505],
        [0.1843409 , 0.13264024, 0.13021081, 0.29490716, 0.11035772,
         0.12337728, 0.25232726, 0.22627011],
        [0.25898134, 0.14831067, 0.1105744 , 0.28395445, 0.082415  ,
         0.15963898, 0.28852097, 0.21923243],
        [0.24524779, 0.1543418 , 0.141513  , 0.35463487, 0.14310733,
         0.14578056, 0.29406054, 0.19287163],
        [0.17848276, 0.21890211, 0.12312278, 0.33801175, 0.06855011,
         0.08074417, 0.25998915, 0.26405938],
        [0.21586025, 0.22584986, 0.08351291, 0.27400646, 0.09977566,
         0.11822983, 0.3070963 , 0.22208796],
        [0.22292054, 0.15507746, 0.14651171, 0.30833547, 0.13200692,
         0.15317476, 0.31281567, 0.21225966],
        [0.23256465, 0.15160882, 0.11380172, 0.29469856, 0.092207  ,
         0.09873235, 0.27714868, 0.22282611],
        [0.23002691, 0.21760574, 0.08050106, 0.26103308, 0.06020115,
         0.13473242, 0.26604228, 0.19234704]]])
    • bob
      (x, z)
      float64
      𝟙
      1.1, 1.200, ..., 8.700, 8.8
      σ = 0.307, 0.135, ..., 0.246, 0.232
      Values:
      array([[1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8],
       [2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8],
       [3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8],
       [4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8],
       [5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8],
       [6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8],
       [7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8],
       [8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8]])

      Variances (σ²):
      array([[0.09453228, 0.01823721, 0.0335211 , 0.07134438, 0.01729049,
        0.03081114, 0.0024635 , 0.07447827],
       [0.09743895, 0.08202897, 0.02379371, 0.02422616, 0.07979023,
        0.08751186, 0.03352043, 0.01747812],
       [0.00702779, 0.00012289, 0.0521478 , 0.04551805, 0.00465947,
        0.04788339, 0.0415599 , 0.0071038 ],
       [0.04042072, 0.04553209, 0.06061073, 0.08188847, 0.05607157,
        0.03228922, 0.02484937, 0.08888189],
       [0.04741125, 0.09664958, 0.08518083, 0.0811361 , 0.09279934,
        0.01358403, 0.09163447, 0.01753268],
       [0.00847511, 0.03489222, 0.08343603, 0.03227952, 0.00868752,
        0.07043597, 0.09257888, 0.02286138],
       [0.05515376, 0.08413628, 0.00870838, 0.04334792, 0.07028481,
        0.08652677, 0.02026737, 0.09993673],
       [0.00550021, 0.0558913 , 0.09911113, 0.02710745, 0.01826467,
        0.09547214, 0.06046085, 0.05373682]])

Note the important call to copy(). If we omit it, d will just be a multi-dimensional slice of the larger volume (which is kept alive), wasting memory and preventing further modification, such as insertion of other variables.

Note also that if we had also sliced 'y' the result would not contain the data for 'bob' since this item does not depend on Y.

More advanced operations with multi-dimensional datasets#

Operations like concat and merge work just like with one-dimensional datasets.

Exercise 2#

  • Try to concatenate the dataset with itself along the X dimensions. Why does this fail?

  • Make a copy of the dataset, add an offset to the X coordinate to fix the issue, and try to concatenate again.

Solution 2#

[10]:

try:
    d = sc.concat([d, d], 'x')
except RuntimeError:
    print("Failed as expected!")

Failed as expected!

With a data extent of, e.g. 8 in this case, bin edges have extent 9. Naive concatenation would thus lead a new data extent of 16 and a coordinate extent of 18, which is meaningless and thus prevented. In this concat merges the last edge of the first input with the first edge of the second input, if compatible.

[11]:

offset = d.copy()
offset.coords['x'] += sc.scalar(8.0, unit=sc.units.m)
combined = sc.concat([d, offset], 'x')
sc.plot(combined['alice'])

Another available operation is rebin. This is only for count-data or count-density-data, so we have to set an appropriate unit first:

[12]:

d['alice'].unit = sc.units.counts
d['bob'].unit = sc.units.counts

Before rebin we have the following:

[13]:

sc.to_html(d)
sc.plot(d['z', 0])
Show/Hide data repr Show/Hide attributes
scipp.Dataset (11.23 KB)
    • z: 8
    • y: 10
    • x: 8
    • x
      (x [bin-edge])
      float64
      m
      1.0, 2.0, ..., 8.0, 9.0
      Values:
      array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
    • y
      (y [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • z
      (z [bin-edge])
      float64
      m
      1.0, 2.0, ..., 8.0, 9.0
      Values:
      array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
    • alice
      (z, y, x)
      float64
      counts
      -0.279, 0.112, ..., -0.618, 0.120
      σ = 0.519, 0.598, ..., 0.516, 0.439
      Values:
      array([[[-2.79109272e-01,  1.11826528e-01,  2.12368435e-01,
          2.18260616e-01, -1.38258825e-01, -5.36126450e-01,
          8.10821516e-02, -2.35089030e-01],
        [-3.04176825e-01,  1.86601936e-02,  5.21655584e-01,
          4.77231948e-01,  5.49515841e-01, -1.10875774e-02,
          2.45251358e-02, -3.63672865e-01],
        [ 1.99053753e-01,  4.81310180e-01,  5.99695465e-03,
         -3.13655542e-01, -2.51453404e-01, -2.80508670e-01,
          2.59668212e-01, -4.78992435e-03],
        [-3.74100136e-01, -1.27792140e-02,  6.73186236e-01,
          5.98998479e-02,  5.71744569e-02, -5.41298707e-01,
          9.21346140e-04,  4.19513601e-01],
        [ 9.29425310e-02, -1.10826220e-01,  6.28121781e-01,
          4.36248112e-01,  4.19104683e-02, -4.57131787e-01,
          6.23696582e-01,  9.06287184e-02],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 5.06499271e-01, -2.11872651e-01,  1.94472095e-01,
         -2.12782449e-01,  4.69909668e-01, -7.93961409e-01,
          5.56036362e-01,  3.66882896e-01],
        [ 2.83303147e-01, -2.99035618e-01, -4.98668935e-02,
          3.73162786e-02,  4.27516039e-01, -1.03489411e-01,
          1.23781846e-01, -1.37584507e-01],
        [ 5.50842801e-02, -3.30628432e-01,  2.52001188e-01,
          2.39805958e-01, -1.36475254e-01, -6.92009277e-01,
         -1.72706860e-01, -2.18476044e-01],
        [ 2.42332003e-01,  5.91863445e-01,  5.36379311e-02,
          2.63956887e-01,  1.48385875e-01, -1.10595219e-01,
          2.39062754e-01, -2.94161187e-01]],

       [[-3.00075655e-01, -8.05654381e-01,  6.88322270e-01,
          5.07306260e-01,  1.18116961e-02, -1.16425499e-01,
          5.69272070e-01,  3.06841136e-01],
        [ 4.35976611e-01, -8.11050811e-01,  1.51110538e-01,
          2.18738036e-01,  1.83008678e-01, -2.98476682e-01,
          5.65372993e-01, -1.54748155e-01],
        [-1.78704119e-01, -5.98022165e-01,  5.57549908e-01,
          1.00839335e-01,  2.39915638e-01,  7.98915003e-02,
          4.55393531e-01, -1.66972526e-01],
        [-1.54422665e-01, -4.70218686e-01,  5.06941545e-01,
         -4.05649831e-02, -4.77651882e-02,  2.42331069e-01,
          9.08672741e-01, -5.24611116e-01],
        [ 4.40600091e-01, -8.28157626e-01,  2.45791562e-01,
          5.95143443e-01,  2.01985329e-01, -5.21225979e-01,
          5.12602596e-01, -2.01449422e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 3.38508512e-01, -2.02729987e-01,  5.41302502e-02,
          7.86622152e-01,  5.25414902e-01,  2.99034835e-01,
          7.72659749e-01, -1.31816399e-01],
        [-5.36728593e-02, -3.80239524e-01,  1.27842696e-01,
          2.43272287e-01, -1.23686207e-01,  1.66079726e-01,
          7.29413953e-01, -3.79198240e-01],
        [ 2.47915608e-01, -2.70609209e-01,  1.35039514e-01,
          5.99701340e-01, -4.06302586e-01,  3.17663098e-01,
          1.03062940e-01, -6.70178306e-02],
        [-4.49806381e-03, -9.63866554e-02,  6.01536915e-01,
          4.23478437e-01,  1.53451006e-01,  1.47374830e-01,
          8.04239367e-01,  2.04718126e-01]],

       [[ 7.46895005e-02, -7.13873301e-02,  8.51021026e-02,
         -9.06237277e-03,  9.78023153e-02,  7.58606099e-01,
         -3.97127636e-02, -8.51312377e-01],
        [-6.55871887e-02,  4.53545197e-01,  8.78178440e-01,
          5.64000630e-01,  1.16492952e-01,  7.67133658e-01,
          6.44821043e-01, -3.14613293e-01],
        [-1.75114639e-01, -3.37155128e-01,  6.50498433e-01,
          7.15770779e-02,  3.50372607e-01,  5.15448744e-01,
          6.54646701e-01, -6.63600408e-01],
        [-2.54321256e-01,  4.60623224e-01,  8.74447218e-01,
          1.61624834e-01,  2.38397253e-01, -1.75722326e-03,
          8.15334642e-02, -1.59674176e-01],
        [-7.61356592e-01,  5.70327701e-01,  7.56902761e-01,
         -2.94155037e-01, -4.07298708e-02, -2.01587396e-02,
          5.51711620e-01, -3.81350507e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-2.22737455e-01,  2.52475468e-01,  3.52520649e-02,
         -2.56277715e-01, -3.77912943e-02, -3.21369082e-02,
          3.94522557e-01, -1.41741430e-01],
        [ 1.01541348e-02, -2.54962474e-01,  5.01224103e-01,
         -1.07111106e-02,  2.01087256e-01,  2.70488676e-01,
          5.51835062e-01,  2.31347857e-02],
        [-2.28380321e-02,  8.54216415e-02,  2.84339780e-01,
         -2.55973182e-01, -6.11133451e-02,  2.09181867e-01,
         -8.55518810e-02, -8.25016235e-01],
        [-7.29733130e-01, -1.91053316e-01,  6.34077047e-01,
         -2.74809740e-01, -7.12757028e-02,  3.90997563e-01,
          6.97273986e-01, -4.51762269e-01]],

       [[-1.08479735e-01, -9.23107793e-01, -8.24912559e-01,
         -8.21798350e-01, -4.32109080e-01, -3.72632042e-01,
          3.42220850e-01, -3.92329726e-01],
        [-4.24901199e-01, -4.46891668e-01, -9.46358705e-01,
         -4.80039672e-01,  4.41384374e-01,  1.57833094e-01,
         -5.14889217e-01, -2.98894967e-01],
        [ 1.84013633e-01, -8.30516910e-01, -6.89072432e-01,
         -2.77055257e-01,  3.96489489e-02, -5.78357908e-01,
         -7.13899342e-03, -3.09746349e-01],
        [-8.96101986e-02, -8.96608550e-01, -7.10691680e-01,
         -6.77710542e-01,  1.11509803e-01,  1.82187710e-01,
         -7.23837331e-02, -7.18335634e-01],
        [ 4.12873665e-01, -4.34818504e-02, -1.05957187e-01,
         -5.20529317e-01, -2.78695062e-01,  3.15706806e-01,
          3.58300417e-01, -1.13525614e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 4.56616368e-01, -1.29235056e-01, -2.94601579e-01,
         -6.67531879e-01, -1.47490649e-01,  2.51744279e-01,
         -3.41886754e-01, -7.50576802e-01],
        [ 1.76672641e-01, -8.17873639e-01, -7.08374931e-01,
         -7.44187732e-01,  3.80232417e-01, -3.16006772e-01,
         -2.40232927e-01, -5.74243896e-01],
        [-3.68003807e-01, -4.53497523e-01, -6.11598717e-01,
         -6.89074806e-01, -2.27360218e-01, -1.13781665e-01,
         -4.25767530e-01, -3.50801162e-01],
        [-1.88142671e-01, -6.18201775e-01, -2.08875503e-01,
         -8.12100300e-01,  5.22256758e-02, -8.19394381e-02,
         -3.35736206e-01, -6.83434452e-02]],

       [[-1.33196248e-01, -4.51983665e-01,  4.12880537e-01,
         -1.86037887e-02, -2.76605956e-01,  6.93006859e-01,
         -2.84094479e-01,  4.99979317e-01],
        [ 4.09347239e-01, -7.34815870e-02,  3.27324406e-01,
         -3.38125812e-01,  6.84730253e-01,  6.45968120e-01,
          3.48317480e-01,  6.34527579e-01],
        [ 3.71163260e-01, -4.73551534e-01, -2.67623270e-01,
         -3.45714074e-01,  6.07440020e-01,  5.18199804e-01,
          8.58426681e-02, -1.42693313e-01],
        [-1.10730372e-01, -1.19743331e-01,  4.43165204e-01,
         -5.01584369e-02, -1.99746796e-01, -5.92922737e-02,
         -4.09956502e-03, -1.91783090e-01],
        [-5.08677631e-02, -1.51496215e-01,  2.86268006e-01,
         -5.77838606e-01,  8.06345647e-02,  4.71682961e-01,
         -1.47873730e-01,  1.80744369e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-4.09914687e-01,  9.29026616e-02, -1.08513842e-01,
         -9.54647133e-01, -5.14985594e-02,  6.89190252e-01,
         -3.76932887e-01,  1.18761460e-01],
        [ 4.51791551e-01,  3.02043947e-01,  3.19646369e-01,
         -8.56418130e-01,  3.84691310e-01,  6.58600720e-01,
         -3.07776360e-01, -2.29262973e-01],
        [-1.77050367e-01,  3.84765591e-02,  3.57004745e-01,
         -3.88265076e-01, -2.22970567e-01,  4.80181134e-01,
         -2.70000395e-02,  6.88839643e-01],
        [ 9.75547518e-02,  4.82699826e-02,  3.35595729e-02,
         -9.47149391e-01,  2.58063485e-01,  1.20306371e-01,
         -1.07392314e-01, -2.66179769e-02]],

       [[ 6.48456551e-01, -4.07850006e-01,  4.37898432e-01,
          8.24346188e-01,  8.54685617e-01, -2.24056005e-01,
         -1.28700483e-01, -2.06423315e-01],
        [-1.12495769e-01, -2.19949616e-01, -2.27236666e-01,
          5.64646822e-01,  8.22777465e-01, -1.52414842e-01,
         -2.85485719e-01, -3.05899805e-01],
        [ 4.97540228e-01, -1.95892519e-01,  1.47764027e-01,
          7.93513537e-01,  3.87204764e-01, -4.98200582e-01,
          1.10730954e-01, -2.11073509e-01],
        [ 1.68164337e-01,  3.08589230e-01,  3.98941886e-01,
          5.80206494e-01, -5.39634696e-02, -1.87904802e-01,
         -3.17931836e-01, -1.93776325e-01],
        [ 7.06183616e-01,  1.16288659e-01,  5.46967098e-01,
          4.53287707e-01,  5.88072930e-01, -5.72021275e-01,
          4.26255972e-01,  2.47540740e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [ 6.30613194e-02,  4.85988298e-02,  4.86085851e-01,
          2.64781930e-01,  5.55394806e-01,  1.43320364e-01,
         -2.43271404e-02,  1.42015844e-01],
        [ 8.10481849e-01, -3.93516162e-01, -2.18674593e-01,
          4.76388481e-01,  5.14477812e-01, -6.41810404e-01,
         -3.30190959e-01, -2.84020652e-01],
        [ 7.46172380e-01,  1.41796559e-01,  4.00144481e-01,
          4.32418914e-01,  3.83306667e-01, -5.06348587e-02,
          3.78704541e-01, -8.57201091e-02],
        [ 4.11251927e-01,  2.56304851e-01, -1.23641486e-01,
          4.55894864e-01, -3.25106958e-03,  8.25596159e-02,
         -2.75943019e-01, -1.18869994e-01]],

       [[-2.51921441e-01,  4.01797393e-01, -5.19512999e-01,
         -2.97514467e-01, -2.26073387e-01, -5.95197268e-02,
          1.86125017e-01, -5.06592264e-01],
        [-5.07429013e-02, -3.91813432e-01, -6.02166401e-01,
         -6.75444617e-01, -2.12099862e-01,  5.83322519e-01,
         -2.56655315e-01, -5.55662151e-01],
        [-2.79375769e-01, -9.00557536e-03, -1.75914125e-01,
         -3.99473107e-01,  8.87015373e-02,  7.99114998e-01,
         -3.14304639e-01, -4.27118078e-01],
        [-6.95142574e-01, -3.05062590e-01, -9.41677370e-01,
         -6.55997756e-01, -3.88378580e-01,  4.85169448e-01,
         -4.46338416e-02,  2.55021621e-01],
        [-6.34781159e-01,  3.56643799e-01, -5.45564627e-02,
          5.31244421e-02, -2.48401545e-01,  4.83370343e-01,
         -4.43220561e-01, -4.91149107e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-7.32665290e-01, -1.11999180e-02, -5.06990430e-01,
         -3.55208006e-01,  1.17406035e-01,  2.71894416e-01,
          1.82121115e-01, -3.44698158e-01],
        [ 1.14752794e-01, -4.70420525e-01, -9.58825315e-01,
         -2.70527586e-01,  5.68879609e-01,  6.47101359e-03,
         -3.87533638e-01,  4.54928717e-02],
        [-1.25792022e-01, -4.78677400e-01, -5.35544396e-01,
         -3.69237410e-01,  1.82536798e-01,  4.02931224e-01,
          2.24137985e-01, -4.11857924e-01],
        [ 1.96811228e-01, -1.33122008e-01, -4.37970523e-03,
         -7.45872304e-01, -1.35972171e-01,  2.33133617e-01,
          9.21356827e-02, -1.11242220e-03]],

       [[ 3.37487157e-02,  1.04598908e-01,  2.65359821e-01,
          6.75883739e-01,  2.12737686e-01, -3.85257458e-01,
         -7.85984403e-01, -2.95801723e-01],
        [-2.33729238e-01, -2.54823814e-01,  1.57842347e-01,
          8.26460442e-01, -5.64376446e-02,  1.02496034e-01,
         -7.41225608e-01, -3.37168117e-01],
        [-6.90735022e-01, -6.48326553e-02, -8.72213911e-02,
         -2.70246647e-02,  3.27714134e-01,  4.90347005e-01,
         -1.90588250e-01, -4.21947603e-01],
        [-6.28978712e-01, -1.49467498e-02, -2.94844676e-01,
          3.74638627e-01,  2.38097471e-01,  6.88523494e-02,
          1.47787658e-01, -5.99918816e-01],
        [-5.36587648e-01,  6.52238059e-01,  1.00977292e-01,
          1.51940536e-01,  4.01648884e-01,  2.08536765e-01,
         -4.74775990e-01, -5.70264411e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00,  0.00000000e+00],
        [-2.58163749e-01,  2.36407847e-01,  4.67275894e-01,
          5.27272984e-01,  1.69527061e-01, -2.34417729e-01,
         -6.15407907e-01, -6.92178693e-01],
        [ 6.77951314e-02,  2.46251371e-01,  1.99839277e-01,
          3.16060094e-01,  6.47396554e-02,  4.23561377e-01,
         -2.23766429e-01, -6.93014555e-02],
        [-5.39078602e-01, -6.87792992e-02, -2.85440085e-01,
          2.59546851e-01, -5.02985294e-01,  7.19172186e-02,
          1.77698500e-01, -6.01057966e-01],
        [-7.13792027e-02,  3.35942152e-01,  2.75016016e-01,
          1.99827530e-01, -1.10739657e-01, -1.47016765e-01,
         -6.18211356e-01,  1.19725367e-01]]])

      Variances (σ²):
      array([[[0.26947474, 0.35782486, 0.16183636, 0.18701678, 0.20106336,
         0.15018938, 0.2122558 , 0.07225557],
        [0.27899704, 0.30738344, 0.12703958, 0.23864974, 0.11892096,
         0.13442117, 0.19785171, 0.03521057],
        [0.30372991, 0.3286027 , 0.12935508, 0.17671349, 0.17590725,
         0.14004221, 0.18878657, 0.03723348],
        [0.32060484, 0.3604546 , 0.19432548, 0.23523667, 0.12154473,
         0.11240068, 0.17303076, 0.055025  ],
        [0.28690653, 0.30291993, 0.17592209, 0.22734361, 0.19024545,
         0.14408771, 0.15362649, 0.09502295],
        [0.29876062, 0.38837408, 0.18015827, 0.21113601, 0.13447955,
         0.15178732, 0.13439618, 0.03089453],
        [0.31705173, 0.34564081, 0.10759367, 0.22351272, 0.14076998,
         0.13467449, 0.19344338, 0.03180986],
        [0.26246404, 0.39148828, 0.16641076, 0.23452893, 0.20814569,
         0.14742275, 0.12798482, 0.0961581 ],
        [0.26761664, 0.39046326, 0.17607926, 0.18996943, 0.18107054,
         0.12267619, 0.20316416, 0.08314161],
        [0.32733637, 0.31590185, 0.19333477, 0.15790273, 0.12745169,
         0.15833184, 0.16312319, 0.08770616]],

       [[0.0610451 , 0.23202256, 0.09879421, 0.22199188, 0.28546859,
         0.16681926, 0.19494173, 0.27481891],
        [0.09071856, 0.30845766, 0.12232266, 0.199671  , 0.21228253,
         0.24972841, 0.242296  , 0.28699158],
        [0.08667561, 0.25679187, 0.11606147, 0.18305909, 0.2222559 ,
         0.2347419 , 0.22703343, 0.2531781 ],
        [0.10250302, 0.2515821 , 0.12163392, 0.2231918 , 0.20715697,
         0.22436103, 0.2101283 , 0.26735689],
        [0.07492253, 0.31537131, 0.1526474 , 0.16403107, 0.28111583,
         0.24239517, 0.21608306, 0.22853079],
        [0.03932195, 0.26855333, 0.17716476, 0.16461355, 0.21956347,
         0.24950068, 0.20343956, 0.28637079],
        [0.11057199, 0.22983558, 0.09192531, 0.14122125, 0.23043497,
         0.17169715, 0.24017413, 0.26797881],
        [0.12861056, 0.3129238 , 0.09025346, 0.19481878, 0.24423736,
         0.20207623, 0.23897439, 0.28482376],
        [0.08600571, 0.27828789, 0.09056521, 0.17571165, 0.28795683,
         0.21376623, 0.25636383, 0.20634376],
        [0.11638952, 0.29879218, 0.18336039, 0.13680555, 0.2936076 ,
         0.16402153, 0.22844428, 0.21094518]],

       [[0.17872032, 0.11987973, 0.20506389, 0.19175824, 0.29474969,
         0.24511401, 0.12853127, 0.28169323],
        [0.19463816, 0.14817573, 0.16211721, 0.21268958, 0.28969658,
         0.25185628, 0.1045259 , 0.300294  ],
        [0.19652023, 0.09636151, 0.22372502, 0.2262307 , 0.21632343,
         0.269269  , 0.1927246 , 0.29760165],
        [0.21196665, 0.13152617, 0.20404939, 0.16808844, 0.25805834,
         0.28508637, 0.09736827, 0.24837973],
        [0.17918292, 0.13944666, 0.18680834, 0.16956535, 0.26252255,
         0.22395972, 0.15218391, 0.30564629],
        [0.19067603, 0.08783411, 0.15943425, 0.15189189, 0.22634018,
         0.26475661, 0.17234713, 0.27347226],
        [0.22388119, 0.12756504, 0.194706  , 0.15300694, 0.19932753,
         0.30003117, 0.16171149, 0.33381915],
        [0.16664749, 0.13763261, 0.14347458, 0.19067807, 0.27601904,
         0.27641771, 0.14585556, 0.30902823],
        [0.16688356, 0.10988542, 0.20682881, 0.15780621, 0.20922834,
         0.26249745, 0.15485919, 0.31721655],
        [0.1757739 , 0.07675857, 0.15056481, 0.18361026, 0.20377616,
         0.22907018, 0.11138207, 0.28577238]],

       [[0.26961922, 0.08794991, 0.20058911, 0.29080177, 0.2600514 ,
         0.17511638, 0.1109284 , 0.12886875],
        [0.27429373, 0.09312041, 0.20948045, 0.24103879, 0.24425251,
         0.20087264, 0.12672014, 0.14903002],
        [0.27569099, 0.16011529, 0.20970237, 0.26399889, 0.31538875,
         0.2474396 , 0.14746367, 0.21404559],
        [0.25701673, 0.15753425, 0.23755865, 0.26751657, 0.29387767,
         0.16004949, 0.15480128, 0.12024661],
        [0.29492442, 0.0881184 , 0.17401836, 0.29836322, 0.31551851,
         0.22902392, 0.14913162, 0.11901824],
        [0.30405017, 0.07956911, 0.18953195, 0.29822523, 0.31729861,
         0.24988215, 0.12490563, 0.17407818],
        [0.24952307, 0.13926892, 0.17464606, 0.28109317, 0.2825401 ,
         0.2571978 , 0.11255148, 0.13402385],
        [0.29499814, 0.13658238, 0.21387128, 0.29858144, 0.26308144,
         0.22379822, 0.19883551, 0.18890022],
        [0.30800129, 0.11757127, 0.18425428, 0.27803148, 0.25977012,
         0.21274413, 0.10695118, 0.16866315],
        [0.25345708, 0.1534314 , 0.18024663, 0.32366539, 0.33816655,
         0.15934121, 0.19959443, 0.19954528]],

       [[0.18044955, 0.22115484, 0.11725049, 0.16843708, 0.25489822,
         0.13441902, 0.23774828, 0.11590454],
        [0.09826316, 0.22976272, 0.20216349, 0.16166195, 0.22278563,
         0.07042803, 0.26379453, 0.17722567],
        [0.1268872 , 0.20249112, 0.11234086, 0.21673475, 0.30694152,
         0.1104984 , 0.22457293, 0.14141096],
        [0.16653682, 0.21852539, 0.11272079, 0.12758583, 0.28607691,
         0.06890602, 0.2691229 , 0.1409516 ],
        [0.19169467, 0.27820271, 0.11935458, 0.18046142, 0.23516845,
         0.15192804, 0.26824238, 0.14964626],
        [0.15059522, 0.21442553, 0.20370981, 0.13897715, 0.24195752,
         0.1044644 , 0.20085256, 0.15329153],
        [0.13580557, 0.18989299, 0.11652272, 0.16166251, 0.21461233,
         0.09801846, 0.25512356, 0.0952114 ],
        [0.13391764, 0.24082138, 0.14926756, 0.16155033, 0.30744124,
         0.13998387, 0.25493728, 0.13690355],
        [0.10892274, 0.27075447, 0.11305224, 0.15402136, 0.28363731,
         0.12913466, 0.21895783, 0.1607825 ],
        [0.10348272, 0.28335723, 0.17192632, 0.20280057, 0.24372726,
         0.11218958, 0.22830279, 0.15541582]],

       [[0.24676676, 0.31101434, 0.21192461, 0.1590011 , 0.11364487,
         0.33170898, 0.28927487, 0.28814138],
        [0.26095137, 0.25622152, 0.21349701, 0.09894173, 0.11247066,
         0.31476499, 0.28519639, 0.28723579],
        [0.25688027, 0.31935654, 0.23451987, 0.1196922 , 0.18862362,
         0.26672283, 0.23981309, 0.30577088],
        [0.21015744, 0.33935753, 0.26955373, 0.0972668 , 0.17069464,
         0.30654276, 0.30852689, 0.2853123 ],
        [0.24539116, 0.35245661, 0.19581805, 0.12056516, 0.17802206,
         0.27287389, 0.23039354, 0.30525445],
        [0.26030664, 0.3349574 , 0.25338904, 0.07021262, 0.18916291,
         0.33253308, 0.25880432, 0.22790562],
        [0.18702569, 0.35030942, 0.21436687, 0.09546278, 0.18673873,
         0.25032643, 0.25175631, 0.25190429],
        [0.22587363, 0.26583841, 0.20842447, 0.14357858, 0.15549273,
         0.28441217, 0.25788978, 0.29386415],
        [0.24410651, 0.34308923, 0.22903724, 0.07229192, 0.13828483,
         0.3289411 , 0.2652826 , 0.21000442],
        [0.25277099, 0.2574845 , 0.22030061, 0.08275838, 0.17066194,
         0.27351184, 0.28351678, 0.29140568]],

       [[0.10194999, 0.10972969, 0.18475314, 0.15127676, 0.30327355,
         0.36539015, 0.10303867, 0.25631288],
        [0.11199588, 0.17949101, 0.27414591, 0.14243309, 0.29879471,
         0.30120091, 0.08242598, 0.26858176],
        [0.14391785, 0.15432398, 0.23508808, 0.17559477, 0.23307696,
         0.34247738, 0.14473251, 0.21897718],
        [0.0946612 , 0.16818659, 0.19029611, 0.10790372, 0.31106825,
         0.35341691, 0.11330535, 0.21487476],
        [0.10167662, 0.16157673, 0.24379462, 0.15851184, 0.28753132,
         0.37463772, 0.11425395, 0.2836581 ],
        [0.16998786, 0.13136259, 0.27850971, 0.15674753, 0.25932829,
         0.37704133, 0.11777022, 0.26477894],
        [0.15196385, 0.13325428, 0.18837525, 0.14545359, 0.28371711,
         0.30939562, 0.17794708, 0.26153101],
        [0.17368494, 0.13051813, 0.27004585, 0.18714773, 0.26224049,
         0.37024438, 0.16345651, 0.25795192],
        [0.15135622, 0.17333471, 0.2081771 , 0.1828609 , 0.22585987,
         0.368357  , 0.11888594, 0.23732295],
        [0.09574752, 0.12752588, 0.25250541, 0.13213172, 0.22487459,
         0.29092634, 0.13525561, 0.24397443]],

       [[0.24981804, 0.13310701, 0.15113998, 0.3143504 , 0.05881409,
         0.12125832, 0.25503932, 0.2667942 ],
        [0.20221448, 0.1843655 , 0.09442668, 0.29635266, 0.05305057,
         0.12361327, 0.24470003, 0.18733505],
        [0.1843409 , 0.13264024, 0.13021081, 0.29490716, 0.11035772,
         0.12337728, 0.25232726, 0.22627011],
        [0.25898134, 0.14831067, 0.1105744 , 0.28395445, 0.082415  ,
         0.15963898, 0.28852097, 0.21923243],
        [0.24524779, 0.1543418 , 0.141513  , 0.35463487, 0.14310733,
         0.14578056, 0.29406054, 0.19287163],
        [0.17848276, 0.21890211, 0.12312278, 0.33801175, 0.06855011,
         0.08074417, 0.25998915, 0.26405938],
        [0.21586025, 0.22584986, 0.08351291, 0.27400646, 0.09977566,
         0.11822983, 0.3070963 , 0.22208796],
        [0.22292054, 0.15507746, 0.14651171, 0.30833547, 0.13200692,
         0.15317476, 0.31281567, 0.21225966],
        [0.23256465, 0.15160882, 0.11380172, 0.29469856, 0.092207  ,
         0.09873235, 0.27714868, 0.22282611],
        [0.23002691, 0.21760574, 0.08050106, 0.26103308, 0.06020115,
         0.13473242, 0.26604228, 0.19234704]]])
    • bob
      (x, z)
      float64
      counts
      1.1, 1.200, ..., 8.700, 8.8
      σ = 0.307, 0.135, ..., 0.246, 0.232
      Values:
      array([[1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8],
       [2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8],
       [3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8],
       [4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8],
       [5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8],
       [6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8],
       [7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8],
       [8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8]])

      Variances (σ²):
      array([[0.09453228, 0.01823721, 0.0335211 , 0.07134438, 0.01729049,
        0.03081114, 0.0024635 , 0.07447827],
       [0.09743895, 0.08202897, 0.02379371, 0.02422616, 0.07979023,
        0.08751186, 0.03352043, 0.01747812],
       [0.00702779, 0.00012289, 0.0521478 , 0.04551805, 0.00465947,
        0.04788339, 0.0415599 , 0.0071038 ],
       [0.04042072, 0.04553209, 0.06061073, 0.08188847, 0.05607157,
        0.03228922, 0.02484937, 0.08888189],
       [0.04741125, 0.09664958, 0.08518083, 0.0811361 , 0.09279934,
        0.01358403, 0.09163447, 0.01753268],
       [0.00847511, 0.03489222, 0.08343603, 0.03227952, 0.00868752,
        0.07043597, 0.09257888, 0.02286138],
       [0.05515376, 0.08413628, 0.00870838, 0.04334792, 0.07028481,
        0.08652677, 0.02026737, 0.09993673],
       [0.00550021, 0.0558913 , 0.09911113, 0.02710745, 0.01826467,
        0.09547214, 0.06046085, 0.05373682]])

We rebin onto a coarser grid, in this case combining two neightboring bins:

[14]:

new_x = sc.array(dims=['x'], unit=sc.units.m, values=d.coords['x'].values[::2])
d = sc.rebin(d, 'x', new_x)

The result looks as follows:

[15]:

sc.to_html(d)
sc.plot(d['z', 0])
Show/Hide data repr Show/Hide attributes
scipp.Dataset (5.70 KB)
    • z: 8
    • y: 10
    • x: 4
    • x
      (x [bin-edge])
      float64
      m
      1.0, 3.0, 5.0, 7.0, 9.0
      Values:
      array([1., 3., 5., 7., 9.])
    • y
      (y [bin-edge])
      float64
      m
      0.0, 1.0, ..., 9.0, 10.0
      Values:
      array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
    • z
      (z [bin-edge])
      float64
      m
      1.0, 2.0, ..., 8.0, 9.0
      Values:
      array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
    • alice
      (z, y, x)
      float64
      counts
      -0.167, 0.431, ..., -0.258, -0.498
      σ = 0.792, 0.591, ..., 0.442, 0.677
      Values:
      array([[[-1.67282744e-01,  4.30629051e-01, -6.74385275e-01,
         -1.54006878e-01],
        [-2.85516632e-01,  9.98887533e-01,  5.38428264e-01,
         -3.39147730e-01],
        [ 6.80363933e-01, -3.07658588e-01, -5.31962074e-01,
          2.54878288e-01],
        [-3.86879350e-01,  7.33086084e-01, -4.84124250e-01,
          4.20434947e-01],
        [-1.78836892e-02,  1.06436989e+00, -4.15221318e-01,
          7.14325300e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 2.94626619e-01, -1.83103541e-02, -3.24051740e-01,
          9.22919259e-01],
        [-1.57324708e-02, -1.25506149e-02,  3.24026629e-01,
         -1.38026609e-02],
        [-2.75544151e-01,  4.91807145e-01, -8.28484531e-01,
         -3.91182904e-01],
        [ 8.34195448e-01,  3.17594818e-01,  3.77906558e-02,
         -5.50984325e-02]],

       [[-1.10573004e+00,  1.19562853e+00, -1.04613803e-01,
          8.76113206e-01],
        [-3.75074201e-01,  3.69848575e-01, -1.15468004e-01,
          4.10624839e-01],
        [-7.76726284e-01,  6.58389243e-01,  3.19807138e-01,
          2.88421005e-01],
        [-6.24641352e-01,  4.66376562e-01,  1.94565880e-01,
          3.84061625e-01],
        [-3.87557535e-01,  8.40935005e-01, -3.19240651e-01,
          3.11153174e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 1.35778525e-01,  8.40752402e-01,  8.24449737e-01,
          6.40843350e-01],
        [-4.33912383e-01,  3.71114983e-01,  4.23935182e-02,
          3.50215713e-01],
        [-2.26936015e-02,  7.34740854e-01, -8.86394874e-02,
          3.60451092e-02],
        [-1.00884719e-01,  1.02501535e+00,  3.00825836e-01,
          1.00895749e+00]],

       [[ 3.30217040e-03,  7.60397298e-02,  8.56408414e-01,
         -8.91025140e-01],
        [ 3.87958009e-01,  1.44217907e+00,  8.83626610e-01,
          3.30207750e-01],
        [-5.12269767e-01,  7.22075511e-01,  8.65821351e-01,
         -8.95370642e-03],
        [ 2.06301968e-01,  1.03607205e+00,  2.36640030e-01,
         -7.81407114e-02],
        [-1.91028891e-01,  4.62747724e-01, -6.08886104e-02,
          1.70361114e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 2.97380131e-02, -2.21025650e-01, -6.99282025e-02,
          2.52781126e-01],
        [-2.44808339e-01,  4.90512993e-01,  4.71575932e-01,
          5.74969847e-01],
        [ 6.25836094e-02,  2.83665981e-02,  1.48068522e-01,
         -9.10568116e-01],
        [-9.20786446e-01,  3.59267307e-01,  3.19721860e-01,
          2.45511717e-01]],

       [[-1.03158753e+00, -1.64671091e+00, -8.04741122e-01,
         -5.01088756e-02],
        [-8.71792867e-01, -1.42639838e+00,  5.99217468e-01,
         -8.13784184e-01],
        [-6.46503277e-01, -9.66127689e-01, -5.38708959e-01,
         -3.16885342e-01],
        [-9.86218749e-01, -1.38840222e+00,  2.93697513e-01,
         -7.90719367e-01],
        [ 3.69391815e-01, -6.26486504e-01,  3.70117445e-02,
          2.44774803e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 3.27381312e-01, -9.62133458e-01,  1.04253630e-01,
         -1.09246356e+00],
        [-6.41200998e-01, -1.45256266e+00,  6.42256453e-02,
         -8.14476823e-01],
        [-8.21501331e-01, -1.30067352e+00, -3.41141883e-01,
         -7.76568692e-01],
        [-8.06344446e-01, -1.02097580e+00, -2.97137623e-02,
         -4.04079651e-01]],

       [[-5.85179913e-01,  3.94276748e-01,  4.16400902e-01,
          2.15884838e-01],
        [ 3.35865652e-01, -1.08014061e-02,  1.33069837e+00,
          9.82845059e-01],
        [-1.02388274e-01, -6.13337344e-01,  1.12563982e+00,
         -5.68506445e-02],
        [-2.30473703e-01,  3.93006767e-01, -2.59039070e-01,
         -1.95882655e-01],
        [-2.02363978e-01, -2.91570601e-01,  5.52317526e-01,
          3.28706391e-02],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-3.17012025e-01, -1.06316098e+00,  6.37691693e-01,
         -2.58171427e-01],
        [ 7.53835498e-01, -5.36771761e-01,  1.04329203e+00,
         -5.37039334e-01],
        [-1.38573808e-01, -3.12603311e-02,  2.57210568e-01,
          6.61839603e-01],
        [ 1.45824734e-01, -9.13589818e-01,  3.78369855e-01,
         -1.34010291e-01]],

       [[ 2.40606545e-01,  1.26224462e+00,  6.30629612e-01,
         -3.35123798e-01],
        [-3.32445384e-01,  3.37410156e-01,  6.70362623e-01,
         -5.91385524e-01],
        [ 3.01647709e-01,  9.41277564e-01, -1.10995818e-01,
         -1.00342555e-01],
        [ 4.76753567e-01,  9.79148380e-01, -2.41868272e-01,
         -5.11708162e-01],
        [ 8.22472274e-01,  1.00025480e+00,  1.60516550e-02,
          6.73796712e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 1.11660149e-01,  7.50867781e-01,  6.98715170e-01,
          1.17688703e-01],
        [ 4.16965687e-01,  2.57713888e-01, -1.27332592e-01,
         -6.14211612e-01],
        [ 8.87968938e-01,  8.32563394e-01,  3.32671808e-01,
          2.92984432e-01],
        [ 6.67556778e-01,  3.32253379e-01,  7.93085463e-02,
         -3.94813013e-01]],

       [[ 1.49875952e-01, -8.17027466e-01, -2.85593114e-01,
         -3.20467247e-01],
        [-4.42556333e-01, -1.27761102e+00,  3.71222657e-01,
         -8.12317466e-01],
        [-2.88381344e-01, -5.75387232e-01,  8.87816535e-01,
         -7.41422717e-01],
        [-1.00020516e+00, -1.59767513e+00,  9.67908680e-02,
          2.10387779e-01],
        [-2.78137359e-01, -1.43202058e-03,  2.34968798e-01,
         -9.34369668e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-7.43865208e-01, -8.62198436e-01,  3.89300451e-01,
         -1.62577043e-01],
        [-3.55667731e-01, -1.22935290e+00,  5.75350623e-01,
         -3.42040767e-01],
        [-6.04469421e-01, -9.04781806e-01,  5.85468022e-01,
         -1.87719939e-01],
        [ 6.36892197e-02, -7.50252009e-01,  9.71614456e-02,
          9.10232605e-02]],

       [[ 1.38347624e-01,  9.41243561e-01, -1.72519772e-01,
         -1.08178613e+00],
        [-4.88553052e-01,  9.84302788e-01,  4.60583894e-02,
         -1.07839373e+00],
        [-7.55567677e-01, -1.14246056e-01,  8.18061138e-01,
         -6.12535853e-01],
        [-6.43925462e-01,  7.97939513e-02,  3.06949820e-01,
         -4.52131158e-01],
        [ 1.15650411e-01,  2.52917827e-01,  6.10185649e-01,
         -1.04504040e+00],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-2.17559026e-02,  9.94548878e-01, -6.48906683e-02,
         -1.30758660e+00],
        [ 3.14046503e-01,  5.15899371e-01,  4.88301033e-01,
         -2.93067885e-01],
        [-6.07857901e-01, -2.58932341e-02, -4.31068076e-01,
         -4.23359466e-01],
        [ 2.64562949e-01,  4.74843546e-01, -2.57756423e-01,
         -4.98485989e-01]]])

      Variances (σ²):
      array([[[0.6272996 , 0.34885314, 0.35125274, 0.28451137],
        [0.58638048, 0.36568932, 0.25334213, 0.23306228],
        [0.63233261, 0.30606858, 0.31594946, 0.22602005],
        [0.68105944, 0.42956216, 0.23394541, 0.22805576],
        [0.58982646, 0.4032657 , 0.33433316, 0.24864944],
        [0.6871347 , 0.39129428, 0.28626687, 0.16529071],
        [0.66269254, 0.3311064 , 0.27544447, 0.22525324],
        [0.65395232, 0.40093969, 0.35556845, 0.22414292],
        [0.6580799 , 0.36604868, 0.30374673, 0.28630577],
        [0.64323822, 0.3512375 , 0.28578353, 0.25082935]],

       [[0.29306766, 0.32078609, 0.45228785, 0.46976064],
        [0.39917623, 0.32199366, 0.46201094, 0.52928758],
        [0.34346749, 0.29912056, 0.4569978 , 0.48021152],
        [0.35408513, 0.34482572, 0.43151799, 0.47748519],
        [0.39029384, 0.31667847, 0.523511  , 0.44461385],
        [0.30787528, 0.34177831, 0.46906415, 0.48981035],
        [0.34040757, 0.23314656, 0.40213212, 0.50815293],
        [0.44153436, 0.28507223, 0.44631359, 0.52379815],
        [0.3642936 , 0.26627686, 0.50172306, 0.46270759],
        [0.4151817 , 0.32016594, 0.45762913, 0.43938946]],

       [[0.29860005, 0.39682213, 0.5398637 , 0.4102245 ],
        [0.34281389, 0.37480679, 0.54155285, 0.4048199 ],
        [0.29288174, 0.44995571, 0.48559243, 0.49032625],
        [0.34349282, 0.37213783, 0.54314471, 0.345748  ],
        [0.31862958, 0.35637369, 0.48648227, 0.4578302 ],
        [0.27851014, 0.31132614, 0.49109679, 0.44581939],
        [0.35144623, 0.34771294, 0.4993587 , 0.49553064],
        [0.30428009, 0.33415265, 0.55243676, 0.45488379],
        [0.27676899, 0.36463503, 0.47172579, 0.47207574],
        [0.25253247, 0.33417507, 0.43284634, 0.39715445]],

       [[0.35756914, 0.49139088, 0.43516778, 0.23979716],
        [0.36741413, 0.45051924, 0.44512515, 0.27575016],
        [0.43580628, 0.47370126, 0.56282834, 0.36150926],
        [0.41455098, 0.50507523, 0.45392717, 0.27504789],
        [0.38304281, 0.47238158, 0.54454244, 0.26814986],
        [0.38361928, 0.48775718, 0.56718076, 0.29898381],
        [0.38879199, 0.45573922, 0.53973789, 0.24657533],
        [0.43158052, 0.51245271, 0.48687966, 0.38773573],
        [0.42557256, 0.46228575, 0.47251426, 0.27561433],
        [0.40688848, 0.50391202, 0.49750776, 0.39913972]],

       [[0.4016044 , 0.28568757, 0.38931725, 0.35365283],
        [0.32802588, 0.36382545, 0.29321367, 0.4410202 ],
        [0.32937832, 0.32907561, 0.41743992, 0.3659839 ],
        [0.38506221, 0.24030661, 0.35498294, 0.4100745 ],
        [0.46989738, 0.29981599, 0.38709649, 0.41788864],
        [0.36502075, 0.34268697, 0.34642192, 0.35414409],
        [0.32569857, 0.27818523, 0.31263079, 0.35033496],
        [0.37473902, 0.31081789, 0.44742511, 0.39184083],
        [0.37967721, 0.2670736 , 0.41277197, 0.37974033],
        [0.38683995, 0.37472689, 0.35591684, 0.38371862]],

       [[0.5577811 , 0.37092572, 0.44535385, 0.57741624],
        [0.51717289, 0.31243875, 0.42723565, 0.57243218],
        [0.57623681, 0.35421208, 0.45534645, 0.54558396],
        [0.54951498, 0.36682053, 0.4772374 , 0.59383919],
        [0.59784777, 0.31638321, 0.45089594, 0.53564798],
        [0.59526404, 0.32360166, 0.52169599, 0.48670994],
        [0.53733512, 0.30982966, 0.43706516, 0.50366061],
        [0.49171204, 0.35200306, 0.4399049 , 0.55175393],
        [0.58719574, 0.30132916, 0.46722593, 0.47528703],
        [0.51025549, 0.30305899, 0.44417378, 0.57492246]],

       [[0.21167968, 0.3360299 , 0.66866371, 0.35935155],
        [0.29148689, 0.416579  , 0.59999562, 0.35100774],
        [0.29824184, 0.41068285, 0.57555434, 0.36370969],
        [0.26284779, 0.29819983, 0.66448516, 0.3281801 ],
        [0.26325334, 0.40230645, 0.66216904, 0.39791205],
        [0.30135045, 0.43525724, 0.63636961, 0.38254916],
        [0.28521813, 0.33382884, 0.59311273, 0.43947809],
        [0.30420306, 0.45719358, 0.63248487, 0.42140843],
        [0.32469093, 0.39103801, 0.59421687, 0.35620889],
        [0.2232734 , 0.38463713, 0.51580093, 0.37923004]],

       [[0.38292505, 0.46549038, 0.18007241, 0.52183352],
        [0.38657998, 0.39077934, 0.17666384, 0.43203508],
        [0.31698113, 0.42511797, 0.233735  , 0.47859737],
        [0.407292  , 0.39452885, 0.24205398, 0.5077534 ],
        [0.39958959, 0.49614787, 0.28888789, 0.48693217],
        [0.39738487, 0.46113453, 0.14929428, 0.52404854],
        [0.44171011, 0.35751938, 0.21800549, 0.52918426],
        [0.377998  , 0.45484717, 0.28518168, 0.52507533],
        [0.38417347, 0.40850028, 0.19093935, 0.49997479],
        [0.44763265, 0.34153415, 0.19493357, 0.45838932]]])
    • bob
      (x, z)
      float64
      counts
      3.2, 3.400, ..., 16.400, 16.6
      σ = 0.438, 0.317, ..., 0.284, 0.392
      Values:
      array([[ 3.2,  3.4,  3.6,  3.8,  4. ,  4.2,  4.4,  4.6],
       [ 7.2,  7.4,  7.6,  7.8,  8. ,  8.2,  8.4,  8.6],
       [11.2, 11.4, 11.6, 11.8, 12. , 12.2, 12.4, 12.6],
       [15.2, 15.4, 15.6, 15.8, 16. , 16.2, 16.4, 16.6]])

      Variances (σ²):
      array([[0.19197122, 0.10026618, 0.05731481, 0.09557054, 0.09708072,
        0.11832299, 0.03598393, 0.09195639],
       [0.04744851, 0.04565498, 0.11275852, 0.12740652, 0.06073104,
        0.0801726 , 0.06640927, 0.09598568],
       [0.05588635, 0.1315418 , 0.16861685, 0.11341562, 0.10148686,
        0.08402   , 0.18421335, 0.04039406],
       [0.06065398, 0.14002758, 0.10781951, 0.07045537, 0.08854947,
        0.18199891, 0.08072822, 0.15367355]])

Interaction with numpy#

Variable in a dataset are exposed in a numpy-compatible buffer format, so we can directly hand them to numpy functions:

[16]:

d['alice'].values = np.sin(d['alice'].values)

In contrast to the 1-D case considered earlier, the values are now a multi-dimensional array:

[17]:

d['alice'].values

[17]:

array([[[-0.16650364,  0.41744251, -0.62441728, -0.15339881],
        [-0.28165321,  0.8408694 ,  0.51278727, -0.33268349],
        [ 0.62907597, -0.302828  , -0.50722526,  0.25212763],
        [-0.37730025,  0.66916613, -0.46543343,  0.40815756],
        [-0.01788274,  0.87448346, -0.40339245,  0.65510781],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 0.29038258, -0.01830933, -0.31841002,  0.79736677],
        [-0.01573182, -0.01255029,  0.31838622, -0.01380222],
        [-0.2720706 ,  0.47221962, -0.73690777, -0.38128223],
        [ 0.74075627,  0.31228257,  0.03778166, -0.05507056]],

       [[-0.89379184,  0.93044615, -0.10442309,  0.76825659],
        [-0.36634157,  0.36147425, -0.11521159,  0.3991823 ],
        [-0.70094833,  0.61184357,  0.31438348,  0.28443881],
        [-0.58480638,  0.44965278,  0.19334062,  0.37468929],
        [-0.37792823,  0.74526688, -0.31384567,  0.30615664],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 0.13536171,  0.74514511,  0.73417429,  0.59787168],
        [-0.42042382,  0.36265474,  0.04238082,  0.34310043],
        [-0.02269165,  0.67039489, -0.08852346,  0.0360373 ],
        [-0.10071368,  0.85472216,  0.29630906,  0.84627692]],

       [[ 0.00330216,  0.07596647,  0.75549439, -0.77771657],
        [ 0.37829897,  0.9917402 ,  0.7730445 ,  0.32423956],
        [-0.49015691,  0.66094363,  0.76162777, -0.00895359],
        [ 0.20484169,  0.86040917,  0.23443762, -0.07806121],
        [-0.18986917,  0.44640853, -0.06085099,  0.16953825],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 0.02973363, -0.21923044, -0.06987123,  0.25009767],
        [-0.24237038,  0.47107846,  0.45429077,  0.54380949],
        [ 0.06254276,  0.02836279,  0.14752806, -0.78985229],
        [-0.79607782,  0.35158841,  0.31430253,  0.24305273]],

       [[-0.8581152 , -0.99711987, -0.72065119, -0.05008791],
        [-0.7654838 , -0.98959272,  0.56399645, -0.72689117],
        [-0.60239903, -0.82269052, -0.51302823, -0.3116085 ],
        [-0.83394527, -0.98341226,  0.28949338, -0.71085941],
        [ 0.36104834, -0.58630213,  0.03700329,  0.24233785],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 0.32156453, -0.82041328,  0.10406488, -0.88776358],
        [-0.59815833, -0.99301854,  0.0641815 , -0.72736667],
        [-0.73216924, -0.96373813, -0.33456339, -0.70083592],
        [-0.72176184, -0.85261832, -0.02970939, -0.3931727 ]],

       [[-0.55234937,  0.38414053,  0.40447152,  0.21421181],
        [ 0.32958658, -0.0108012 ,  0.97131469,  0.83207877],
        [-0.10220947, -0.57559971,  0.90254329, -0.05682003],
        [-0.22843873,  0.38296768, -0.2561518 , -0.19463239],
        [-0.20098563, -0.28745689,  0.52466157,  0.03286472],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [-0.31172887, -0.87389643,  0.59534237, -0.25531301],
        [ 0.68444013, -0.51136443,  0.86406604, -0.51159435],
        [-0.13813073, -0.03125524,  0.25438388,  0.61456909],
        [ 0.14530846, -0.79170188,  0.36940612, -0.13360954]],

       [[ 0.23829174,  0.95277439,  0.58965338, -0.32888608],
        [-0.32635549,  0.33104439,  0.62127018, -0.55751178],
        [ 0.29709392,  0.80831093, -0.11076805, -0.10017425],
        [ 0.45889718,  0.8300227 , -0.23951693, -0.48966732],
        [ 0.73283023,  0.84160863,  0.01605097,  0.62395745],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [ 0.11142826,  0.68227345,  0.64323446,  0.11741721],
        [ 0.40498798,  0.25487061, -0.12698878, -0.57631441],
        [ 0.77579177,  0.73965892,  0.32656951,  0.28881076],
        [ 0.61906909,  0.326174  ,  0.07922543, -0.38463559]],

       [[ 0.14931548, -0.72911468, -0.28172659, -0.31501005],
        [-0.42825092, -0.95732817,  0.36275508, -0.72588312],
        [-0.28440078, -0.54415971,  0.7756956 , -0.67533786],
        [-0.84158182, -0.99963879,  0.09663981,  0.20883914],
        [-0.27456507, -0.00143202,  0.23281264, -0.80422462],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [-0.6771372 , -0.75927507,  0.3795413 , -0.1618618 ],
        [-0.34821638, -0.94227232,  0.544129  , -0.33541034],
        [-0.56832559, -0.78629036,  0.55258952, -0.18661938],
        [ 0.06364617, -0.68182313,  0.09700864,  0.09089762]],

       [[ 0.13790672,  0.80829091, -0.17166526, -0.88279825],
        [-0.46934871,  0.83288643,  0.04604211, -0.88119959],
        [-0.68570198, -0.11399769,  0.72982172, -0.57494412],
        [-0.60033943,  0.0797093 ,  0.30215243, -0.43688354],
        [ 0.11539278,  0.25023002,  0.57301962, -0.86494481],
        [ 0.        ,  0.        ,  0.        ,  0.        ],
        [-0.02175419,  0.83851324, -0.06484514, -0.96555984],
        [ 0.30890975,  0.49331737,  0.46912615, -0.28889066],
        [-0.57111038, -0.02589034, -0.41784141, -0.41082564],
        [ 0.26148745,  0.45719931, -0.25491174, -0.47809632]]])

Exercise 3#

  1. Use sc.mean to compute the mean of the data for Alice along the Z dimension.

  2. Do the same with numpy, what are the complications you encounter, that are not present when using the dataset?

Solution 3#

[18]:

help(sc.mean)

Help on function mean in module scipp.core.reduction:

mean(x: 'VariableLike', dim: 'Optional[str]' = None, *, out: 'Optional[VariableLike]' = None) -> 'VariableLike'
    Element-wise mean over the specified dimension.

    If the input has variances, the variances stored in the output are based on
    the "standard deviation of the mean", i.e.,
    :math:`\sigma_{mean} = \sigma / \sqrt{N}`.
    :math:`N` is the length of the input dimension.
    :math:`\sigma` is estimated as the average of the standard deviations of
    the input elements along that dimension.

    See :py:func:`scipp.sum` on how rounding errors for float32 inputs are handled.

    :param x: Input data.
    :param dim: Dimension along which to calculate the mean. If not
                given, the mean over all dimensions is calculated.
    :param out: Optional output buffer.
    :raises: If the dimension does not exist, or the dtype cannot be summed,
             e.g., if it is a string.
    :return: The mean of the input values.
    :seealso: :py:func:`scipp.nanmean`.


[19]:

mean = sc.mean(d['alice'], 'z')

When using numpy to compute the mean: - We must remember (or lookup) which dimension corresponds to the Z dimensions. - We need a separate call for values and variances. - We need to manually scale the variance with the inverse of the number of data points to get the variance of the mean (standard deviation of the mean scales with 1/sqrt(N)).

[20]:

np_values = np.mean(d['alice'].values, axis=0)
np_variances = np.mean(d['alice'].variances, axis=0)
np_variances /= d['alice'].shape[0]

[21]:

print(mean.values)
print(mean.variances)
print(np_values)
print(np_variances)

[[-0.24274299  0.2303533  -0.01915801 -0.19067866]
 [-0.24119352  0.17503657  0.46699983 -0.20858356]
 [-0.24245583 -0.03477219  0.29413129 -0.14890899]
 [-0.35033413  0.16110959  0.01937021 -0.11480224]
 [ 0.01850506  0.28535081  0.07568237  0.04509916]
 [ 0.          0.          0.          0.        ]
 [-0.01526869 -0.05314909  0.25040386 -0.06346811]
 [-0.02832036 -0.10966055  0.32869647 -0.19580859]
 [-0.18327046  0.01293277 -0.03709563 -0.19124979]
 [ 0.02646426 -0.00302211  0.11367654 -0.03304468]]
[[0.04891448 0.04712478 0.05409343 0.05025856]
 [0.05029766 0.04682237 0.04998656 0.05061586]
 [0.05039572 0.04762398 0.05474131 0.05174909]
 [0.05309227 0.04611651 0.05314523 0.04947163]
 [0.05331845 0.04786489 0.05746747 0.05090038]
 [0.05181499 0.04835682 0.05417797 0.04917744]
 [0.05208282 0.04136044 0.05121074 0.05153391]
 [0.05281249 0.04855436 0.0569718  0.05438499]
 [0.05313207 0.0441748  0.05335725 0.05012366]
 [0.05134129 0.04552262 0.04975925 0.05129333]]
[[-0.24274299  0.2303533  -0.01915801 -0.19067866]
 [-0.24119352  0.17503657  0.46699983 -0.20858356]
 [-0.24245583 -0.03477219  0.29413129 -0.14890899]
 [-0.35033413  0.16110959  0.01937021 -0.11480224]
 [ 0.01850506  0.28535081  0.07568237  0.04509916]
 [ 0.          0.          0.          0.        ]
 [-0.01526869 -0.05314909  0.25040386 -0.06346811]
 [-0.02832036 -0.10966055  0.32869647 -0.19580859]
 [-0.18327046  0.01293277 -0.03709563 -0.19124979]
 [ 0.02646426 -0.00302211  0.11367654 -0.03304468]]
[[0.04891448 0.04712478 0.05409343 0.05025856]
 [0.05029766 0.04682237 0.04998656 0.05061586]
 [0.05039572 0.04762398 0.05474131 0.05174909]
 [0.05309227 0.04611651 0.05314523 0.04947163]
 [0.05331845 0.04786489 0.05746747 0.05090038]
 [0.05181499 0.04835682 0.05417797 0.04917744]
 [0.05208282 0.04136044 0.05121074 0.05153391]
 [0.05281249 0.04855436 0.0569718  0.05438499]
 [0.05313207 0.0441748  0.05335725 0.05012366]
 [0.05134129 0.04552262 0.04975925 0.05129333]]