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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
      0.72, 0.49, ..., 0.86, 1.0
      σ = 0.28, 0.29, ..., 0.02, 0.3
      Values:
      array([[[7.24146216e-01, 4.93815839e-01, 2.30143223e-01, 6.99332580e-01, 6.37899617e-01, 1.35403766e-01, 1.00274990e-01, 5.48075243e-01, 3.27524746e-01, 6.48472733e-01], [8.63223132e-01, 2.78619539e-01, 7.31140498e-01, 9.85530091e-01, 2.93541270e-02, 6.07050666e-01, 4.21388626e-01, 5.76077210e-01, 4.21503336e-02, 8.20309504e-01], [1.30294690e-01, 3.10127680e-01, 4.55002586e-02, 2.22151166e-01, 7.29624630e-01, 6.96704823e-01, 7.04756639e-01, 2.98651415e-01, 9.18017872e-01, 2.60145020e-01], [8.83852585e-01, 3.79835797e-01, 6.48029722e-01, 6.80503166e-01, 8.57062266e-01, 5.49674173e-01, 8.96537087e-01, 7.34907039e-01, 9.16556641e-01, 1.92196947e-01], [5.73553684e-01, 2.66401460e-01, 6.98661813e-01, 4.30351056e-01, 8.46830274e-01, 8.93088270e-01, 7.70369133e-01, 4.09291245e-01, 7.83982797e-01, 5.69672125e-01], [7.89334157e-01, 8.08612906e-03, 2.99801464e-01, 8.13482699e-01, 6.60615813e-01, 7.21838711e-01, 6.89334292e-01, 6.99148513e-01, 6.87106778e-01, 7.70718813e-01], [1.00157273e-02, 4.47628288e-01, 1.97108902e-02, 9.64558085e-03, 9.37628759e-01, 8.11992042e-01, 7.25287196e-01, 3.89607322e-01, 9.44113196e-01, 6.19870486e-01], [2.31222110e-01, 3.58843572e-01, 1.36198904e-01, 7.34063728e-01, 1.89565060e-01, 2.95398092e-02, 3.52294947e-01, 2.51817664e-01, 6.03110802e-01, 4.91320522e-01], [4.91221075e-01, 3.29661232e-01, 7.32223208e-01, 3.12667775e-01, 1.90367055e-01, 3.34528218e-01, 1.77502454e-01, 7.01121644e-01, 4.37407846e-01, 6.04999848e-01], [4.04885681e-01, 5.04714235e-01, 8.48255749e-02, 4.08892672e-01, 1.95818143e-01, 7.97543010e-01, 2.24396252e-01, 7.32784927e-01, 1.65383289e-02, 3.09074365e-01]], [[7.31165512e-01, 5.57007787e-01, 7.17842821e-01, 2.71367058e-01, 7.93224620e-01, 6.34596232e-01, 3.11057328e-01, 9.62166443e-01, 1.53791355e-01, 4.77915312e-01], [8.97458487e-01, 9.16717222e-02, 6.25831717e-01, 2.05571402e-01, 7.83843824e-02, 3.26109183e-01, 3.00338084e-01, 8.54707063e-01, 8.95397835e-01, 2.15405566e-01], [7.44905083e-01, 2.92782440e-01, 3.33324164e-01, 2.45015210e-01, 2.80623563e-01, 5.31067336e-01, 9.25853999e-01, 4.41580448e-01, 4.94905490e-01, 9.96151951e-01], [5.24182824e-01, 3.62462067e-01, 9.05367177e-01, 2.49060557e-01, 3.88265866e-01, 3.46036594e-01, 3.30530051e-01, 6.37784368e-01, 7.62867442e-02, 8.58563365e-02], [3.70748880e-01, 5.20577555e-01, 7.66696539e-01, 4.46322028e-01, 6.07217695e-02, 7.34494650e-01, 5.38828205e-01, 3.90383977e-01, 1.01683103e-01, 6.39174565e-01], [3.25893184e-01, 2.83225516e-01, 1.03494055e-01, 4.10149408e-01, 6.55732640e-01, 2.68225040e-01, 9.98661611e-01, 4.62344571e-01, 6.26595021e-01, 9.69727044e-01], [9.42989672e-01, 2.74292456e-01, 8.78035718e-01, 4.11597429e-01, 8.68449666e-01, 8.88700784e-01, 6.87475160e-01, 7.15372128e-02, 1.82793001e-01, 3.35630958e-01], [6.90720828e-01, 9.24534312e-01, 1.04633353e-01, 2.82804442e-01, 9.59713175e-01, 2.06676116e-01, 1.90998758e-01, 7.06779021e-01, 3.96917632e-01, 5.23164043e-01], [6.84908170e-01, 1.97686639e-01, 6.15142193e-01, 2.85170103e-01, 4.29995801e-01, 4.47309544e-01, 2.14472624e-01, 7.64522431e-01, 4.36219707e-01, 2.23889971e-01], [4.81134444e-01, 8.47618483e-01, 9.05231983e-01, 8.48802865e-01, 3.08181694e-01, 7.01555069e-01, 8.46069219e-01, 6.73653933e-02, 6.83761258e-01, 7.25644826e-01]], [[4.64667349e-01, 1.44846752e-01, 7.42027498e-02, 9.68824046e-01, 9.21478268e-01, 9.83888992e-01, 2.39934399e-01, 2.39005951e-01, 6.30962969e-01, 1.87719109e-01], [6.12778621e-01, 9.46011298e-01, 1.24533619e-01, 8.69343386e-01, 6.11902345e-01, 3.30077596e-01, 2.22897856e-01, 2.65809039e-01, 9.93031101e-01, 6.60043660e-01], [1.80902100e-01, 5.39717073e-01, 6.65780641e-01, 4.41731456e-01, 7.39394738e-02, 8.58495622e-02, 6.39532487e-01, 6.36627669e-01, 1.80681730e-01, 6.13838715e-01], [1.88016179e-01, 6.51776844e-01, 9.11777831e-01, 4.73214397e-01, 3.01006600e-01, 6.95983348e-01, 7.32978189e-01, 8.92983324e-01, 9.16284529e-01, 3.73287894e-01], [6.92479290e-01, 7.64636631e-01, 9.00757866e-01, 7.35940006e-01, 1.07439244e-01, 6.57029145e-01, 7.67921652e-01, 5.02518169e-01, 9.53574248e-01, 8.49351616e-01], [4.20518927e-01, 2.88455148e-01, 6.16671215e-01, 8.68950489e-01, 8.14526208e-01, 4.71809156e-01, 6.67439213e-01, 4.01813752e-01, 9.38478851e-01, 3.36371666e-01], [5.27875696e-01, 3.08750411e-02, 7.73506066e-01, 2.91990075e-01, 9.29462576e-01, 6.57088233e-01, 1.28412107e-01, 6.91753866e-01, 1.60948378e-02, 1.19916598e-01], [9.51705147e-01, 9.13995136e-01, 5.77305683e-02, 1.24617650e-01, 8.38788113e-01, 4.32138050e-01, 7.89130005e-02, 1.15769226e-01, 4.96917754e-01, 5.04260182e-01], [4.67220108e-01, 7.84198735e-01, 8.94285581e-01, 1.54648712e-01, 3.58538840e-01, 3.60135383e-01, 5.98323051e-01, 6.78811365e-01, 1.80369833e-02, 7.62863192e-01], [8.65319497e-01, 6.25656374e-01, 3.24679787e-01, 4.82933723e-01, 4.30429262e-01, 7.88847013e-01, 5.76914455e-01, 7.49364715e-01, 8.19179376e-01, 8.30985384e-01]], [[5.49492638e-01, 4.66831219e-01, 4.00322889e-01, 5.07059447e-01, 5.78844328e-01, 4.55240612e-01, 2.78346109e-01, 3.71289046e-01, 8.72503574e-01, 8.83838227e-01], [5.05611645e-01, 7.24468732e-01, 6.52117204e-01, 3.61754574e-01, 6.63907723e-01, 5.98156262e-01, 6.25313774e-01, 5.79451690e-01, 9.12883234e-01, 4.80440181e-01], [6.24910268e-02, 9.88357411e-01, 2.86888817e-01, 5.36856068e-01, 2.11969922e-01, 4.33287608e-01, 2.40949430e-01, 6.98845975e-02, 3.16191117e-01, 3.65353720e-01], [2.95908847e-01, 9.34237228e-01, 7.69714635e-01, 6.19410982e-01, 3.89787552e-01, 7.45039118e-01, 3.13038057e-01, 9.50755115e-01, 4.25796274e-01, 1.75720256e-01], [9.39016945e-01, 1.48723080e-01, 7.97416832e-01, 8.52926288e-01, 9.52187723e-01, 6.30270166e-01, 7.53779955e-01, 5.65664503e-01, 6.08115183e-01, 5.93290764e-01], [7.95148117e-01, 2.69467210e-01, 9.56667188e-01, 2.86621609e-01, 6.48797080e-01, 2.50298220e-01, 7.00372564e-01, 7.88634407e-02, 9.77675733e-01, 6.66634601e-01], [9.17720226e-01, 5.23704599e-01, 7.25115009e-01, 9.75081358e-01, 1.53561750e-01, 7.71575618e-01, 1.96318630e-01, 7.57860704e-01, 5.17830985e-01, 6.64698444e-01], [9.03313182e-01, 2.20721239e-01, 1.12129276e-01, 5.78866814e-01, 2.28044411e-01, 1.35792584e-01, 6.48394933e-01, 1.89077747e-02, 7.56300299e-01, 2.60221346e-01], [4.67010919e-01, 9.00610769e-01, 5.66530584e-01, 9.13786920e-01, 4.59654451e-01, 4.15336935e-01, 8.32967352e-01, 6.89941582e-01, 7.49370702e-01, 1.12511075e-01], [2.41046773e-01, 8.62847941e-01, 3.67531580e-01, 6.64543291e-01, 7.26830083e-01, 5.81168551e-01, 2.92554116e-01, 9.40925231e-01, 2.70652627e-01, 3.81245834e-01]], [[3.65558718e-01, 4.54833641e-01, 8.74644027e-01, 5.48846147e-01, 7.60505211e-01, 9.01107865e-03, 9.44422327e-01, 8.96005340e-02, 3.43104705e-01, 6.21249812e-01], [9.50505951e-02, 1.45485240e-01, 1.33800646e-01, 3.98175210e-01, 9.34036964e-01, 7.39044833e-01, 2.25793537e-01, 9.81075049e-02, 6.09715030e-01, 4.11589032e-01], [1.44225054e-01, 5.33341775e-01, 6.43242232e-02, 6.61486081e-01, 6.85699539e-01, 9.99674198e-01, 8.91669325e-02, 4.24960853e-01, 1.02727433e-01, 3.64784252e-01], [6.80618157e-01, 2.12886785e-01, 8.56662299e-01, 7.72732551e-01, 9.42153572e-01, 9.02264506e-01, 6.85257476e-01, 9.15035360e-01, 8.23654311e-01, 4.06372217e-01], [6.18357595e-01, 2.61655497e-01, 8.69846632e-01, 3.73757370e-02, 5.39659104e-01, 2.93796004e-01, 1.90833651e-01, 3.31580543e-01, 9.77430912e-01, 9.85869640e-01], [5.00820764e-01, 9.64309651e-01, 4.74796358e-01, 9.61802135e-01, 4.48310845e-02, 6.70619316e-01, 6.17780159e-01, 5.77604120e-01, 9.97644398e-01, 2.58345544e-01], [5.03733475e-02, 2.39437407e-01, 7.56335984e-01, 7.09798530e-01, 2.57535054e-02, 5.04665541e-02, 5.39146392e-01, 3.28954565e-01, 2.81302800e-01, 4.84838171e-02], [6.08525721e-01, 4.65820093e-01, 5.54493450e-01, 8.97172453e-01, 2.41930536e-01, 7.07926657e-01, 7.79819402e-01, 7.43528187e-02, 9.96396806e-01, 6.08536084e-01], [7.04073075e-01, 2.93441019e-01, 9.11012414e-02, 1.76278373e-01, 5.00530100e-01, 9.74563172e-01, 6.35700794e-01, 4.05208938e-02, 7.53831212e-01, 6.67429916e-01], [4.55109161e-01, 4.02268897e-01, 3.38594011e-01, 4.65299390e-01, 3.40329512e-01, 6.18528686e-01, 6.69039883e-01, 8.45157854e-01, 5.84956024e-01, 4.42055048e-01]], [[8.05392358e-01, 2.68434201e-01, 8.13355475e-01, 8.81717827e-01, 2.41935252e-01, 8.84638003e-01, 9.09743987e-01, 9.03367367e-01, 8.70201621e-01, 3.48478621e-01], [7.33602516e-01, 5.60872915e-01, 7.50070442e-01, 7.08106695e-01, 2.02715364e-01, 8.89616322e-01, 8.79002871e-01, 4.27415347e-01, 9.93462612e-01, 5.30554598e-01], [7.82157105e-01, 3.03520001e-01, 1.14743601e-01, 6.04418461e-01, 4.05476482e-01, 3.56882108e-01, 6.79046648e-01, 2.80709268e-01, 4.95400433e-01, 6.42769398e-01], [7.06961251e-02, 2.87451741e-01, 3.66722417e-01, 5.57862255e-01, 4.87487639e-01, 7.02751959e-01, 3.88756241e-01, 6.38456087e-01, 3.55233016e-01, 4.10483412e-01], [4.17620880e-01, 1.20389052e-01, 7.96076163e-01, 3.11283009e-01, 9.25175794e-01, 6.33682373e-01, 4.84205656e-01, 6.31144552e-01, 7.77062558e-01, 3.56486863e-01], [7.77574559e-01, 9.04820812e-01, 1.16353971e-01, 8.58575478e-01, 7.32702787e-01, 1.93669805e-01, 2.65199635e-01, 6.07915909e-01, 4.92213525e-01, 7.56037985e-01], [3.73452083e-01, 4.07355410e-02, 3.94799635e-01, 8.54011704e-01, 9.46386033e-01, 7.08223254e-01, 6.92522431e-01, 7.92240463e-01, 2.95093293e-01, 8.84047525e-01], [2.11975379e-01, 7.23087437e-02, 7.09792389e-01, 5.69477901e-01, 3.48998678e-02, 2.79074264e-01, 3.50148247e-01, 6.64816886e-02, 8.96202669e-01, 9.71780365e-01], [1.69349727e-01, 2.71053055e-01, 3.88492310e-01, 4.19907823e-02, 1.30065956e-01, 6.72013394e-01, 8.38980040e-01, 4.59776583e-01, 1.69703819e-01, 1.44345166e-01], [7.58685249e-01, 4.95929125e-01, 5.15812547e-01, 6.24111709e-02, 2.69110667e-01, 4.24442280e-01, 3.22027434e-01, 8.78023346e-01, 1.00234784e-01, 3.63024032e-01]], [[4.03809575e-01, 9.82705701e-01, 5.52213606e-01, 5.98616636e-01, 6.17943021e-01, 7.00969914e-01, 8.64327302e-01, 5.73492741e-01, 8.95543408e-01, 2.07216668e-01], [4.16590397e-01, 5.48054405e-01, 1.01346224e-01, 9.73749912e-02, 4.65976323e-01, 8.03097703e-01, 8.02620050e-01, 6.05442393e-01, 6.24588005e-01, 5.79394222e-01], [1.99603062e-01, 6.95978340e-01, 4.16252695e-01, 9.13535033e-02, 6.55579053e-01, 5.09254433e-01, 5.25912437e-01, 9.21986465e-02, 1.94771185e-01, 9.64196304e-01], [1.84084263e-01, 6.25272156e-01, 8.65245277e-01, 2.33856945e-01, 3.52110485e-01, 2.94829677e-01, 9.86608115e-01, 3.23414873e-01, 1.59365829e-01, 9.34287963e-01], [3.06925078e-01, 7.67926335e-02, 2.51142360e-01, 5.90617601e-02, 3.91685361e-01, 8.02821060e-02, 2.14788243e-01, 5.56734404e-01, 7.11563392e-01, 7.10583457e-01], [5.85116678e-01, 8.47031045e-01, 5.69592819e-01, 7.12018096e-01, 3.43015066e-01, 7.85959426e-01, 5.42472847e-03, 9.43472383e-01, 2.86138556e-01, 2.76437089e-01], [9.41603843e-01, 7.34275399e-01, 2.27913043e-01, 1.30103524e-02, 3.11498212e-01, 8.65538212e-01, 9.65390211e-02, 6.04196151e-01, 6.75651255e-01, 4.74739250e-01], [4.09335520e-01, 3.49852180e-01, 3.32716123e-01, 1.05703004e-01, 6.36775144e-01, 6.38187972e-01, 5.91635452e-01, 9.50227052e-01, 3.65968653e-01, 3.73307115e-01], [3.09883204e-01, 3.27561440e-01, 3.32793984e-01, 8.53203997e-01, 4.80382912e-01, 6.10498552e-01, 9.60531319e-02, 8.09904684e-01, 1.03271019e-01, 2.34756783e-01], [2.12622414e-01, 9.73528029e-01, 3.47196493e-01, 1.08239449e-01, 8.33361256e-01, 7.40192392e-01, 3.74326019e-01, 6.08253541e-01, 8.00947600e-01, 9.31146307e-01]], [[5.83161081e-01, 3.77414664e-01, 5.60515836e-01, 9.77066623e-01, 7.03262761e-02, 8.10598701e-01, 2.87601885e-01, 4.14446827e-01, 6.70280336e-01, 6.09633331e-01], [4.90221651e-01, 5.62202220e-02, 4.96536298e-01, 3.16606230e-01, 8.76497127e-01, 9.56884310e-01, 9.48492482e-01, 7.49610846e-01, 7.57619216e-01, 3.36387727e-01], [5.09305677e-01, 1.24267558e-01, 2.73568317e-01, 1.09336074e-01, 6.63437686e-01, 5.54196906e-01, 2.73579035e-01, 4.17117893e-01, 9.92985228e-01, 4.64697114e-01], [2.50588087e-01, 5.10188215e-03, 1.83008527e-01, 4.55599314e-01, 1.40717923e-01, 6.52056256e-01, 1.58289900e-01, 7.29453475e-03, 5.72420831e-01, 4.84624712e-01], [7.22967405e-01, 4.83089818e-01, 2.29930676e-01, 3.16820996e-01, 9.74740827e-01, 6.11106397e-01, 5.33019352e-01, 9.44035558e-01, 5.02461134e-01, 2.92116462e-01], [1.79727235e-01, 5.86192907e-01, 1.74432751e-01, 4.73011286e-01, 2.61475393e-01, 5.43589823e-01, 1.39517331e-01, 4.19271637e-02, 6.70725451e-01, 3.82769065e-01], [1.79245925e-01, 1.32218373e-01, 9.34844607e-02, 4.31607022e-01, 5.84402903e-01, 2.78061474e-01, 3.75311210e-01, 7.30709959e-01, 2.72235505e-01, 9.64741755e-01], [7.70317923e-01, 8.86805268e-01, 8.95563795e-01, 3.95700396e-01, 3.55645137e-01, 4.11988012e-01, 6.45712792e-01, 5.22616200e-02, 6.52360445e-01, 3.69120437e-02], [7.63290436e-01, 9.38382906e-01, 4.84738454e-01, 3.24607681e-01, 3.00877303e-01, 4.76326975e-01, 1.00705654e-01, 5.77318098e-01, 6.80988049e-01, 2.61262316e-01], [4.63797845e-01, 8.34925254e-01, 7.85571847e-01, 8.29481571e-01, 4.47730771e-01, 9.38299119e-02, 1.56238373e-01, 8.18780401e-01, 8.91072120e-01, 1.87009277e-01]], [[2.96489242e-01, 6.09219146e-01, 1.79754720e-01, 1.25115238e-01, 2.60251549e-01, 4.87767822e-01, 1.29674872e-01, 1.80871165e-01, 2.77317756e-01, 7.42125672e-01], [4.12846152e-01, 5.37840238e-01, 8.99656426e-01, 4.33603944e-01, 5.93032012e-01, 4.01909850e-02, 9.30400453e-01, 8.92860681e-02, 3.71246215e-01, 8.05126094e-01], [8.69491122e-01, 6.37641653e-01, 2.11602019e-01, 9.50798368e-01, 1.08054000e-01, 7.61477742e-01, 9.67901981e-01, 7.68055676e-01, 6.67114557e-01, 5.44994971e-01], [2.78215718e-02, 2.02416624e-01, 5.02480271e-01, 2.52826237e-01, 3.15004964e-01, 4.66936679e-01, 6.74569281e-01, 4.92787897e-01, 4.72196221e-01, 3.39190335e-01], [1.63585446e-02, 5.11678310e-01, 9.04215157e-01, 4.77055566e-01, 6.52441808e-01, 2.22163894e-02, 1.68289730e-01, 8.67880077e-01, 5.80284110e-01, 5.66505426e-01], [2.07827756e-01, 2.76395957e-01, 9.63158124e-01, 1.03658895e-01, 3.69536397e-01, 4.79485103e-01, 1.48621703e-01, 5.58329839e-01, 1.50945030e-01, 6.28981318e-01], [3.34456930e-01, 7.66299009e-01, 6.36908921e-01, 7.09759679e-01, 7.44975870e-01, 5.63125648e-01, 5.48119182e-01, 7.56485808e-01, 9.06041791e-01, 5.51079736e-01], [1.49646024e-01, 2.51429098e-01, 6.99842829e-01, 3.51376227e-01, 4.73312847e-01, 7.48334721e-01, 2.65593703e-03, 1.08344829e-01, 3.71776376e-01, 4.53234614e-01], [6.60356119e-01, 3.62043266e-01, 9.89542070e-01, 2.29963661e-01, 6.17514809e-01, 3.69239554e-01, 5.86552317e-01, 5.01887385e-01, 1.57892453e-01, 8.52165905e-01], [8.87938514e-01, 7.32795804e-01, 3.39537662e-01, 3.78187456e-01, 1.95926694e-01, 5.55079155e-01, 3.78360129e-01, 4.48563768e-01, 3.12443708e-01, 8.42375377e-01]], [[4.07409922e-01, 3.59447867e-01, 2.19595549e-01, 5.29534455e-01, 3.52996047e-01, 7.61657875e-01, 6.69051968e-01, 6.87739195e-01, 9.06517350e-02, 7.51500329e-02], [3.67939661e-01, 8.47586729e-01, 3.78726050e-04, 8.97998091e-01, 4.84596350e-01, 2.97422660e-01, 4.93380091e-01, 3.20108027e-01, 4.61051640e-01, 2.82943041e-01], [6.62998206e-02, 8.41153322e-01, 4.97547443e-01, 7.51186414e-01, 8.05252260e-01, 7.90452619e-01, 1.66142654e-02, 3.75575043e-01, 4.96722115e-02, 6.73261371e-01], [8.26467576e-01, 8.55369796e-01, 5.03936493e-01, 4.28946422e-01, 7.32450555e-01, 4.29879860e-01, 6.88602895e-01, 1.63633050e-01, 5.46527651e-01, 3.92359949e-01], [9.79760931e-01, 6.72415609e-01, 9.39507563e-01, 7.24761617e-01, 8.46978159e-01, 9.16548728e-01, 3.46394659e-01, 3.96244478e-01, 4.23790439e-01, 4.15727794e-01], [2.30806245e-01, 6.26537147e-01, 5.39454541e-01, 2.78007421e-01, 8.33630493e-01, 5.76702673e-01, 6.95566960e-01, 8.06686220e-01, 3.19751631e-01, 5.66060205e-01], [6.01583661e-01, 3.81304909e-01, 1.70102179e-01, 3.99484951e-01, 2.14515167e-01, 5.16133835e-01, 2.29890161e-01, 5.82990423e-01, 4.36410679e-01, 3.06508461e-01], [8.14279434e-01, 2.27762469e-01, 3.83823019e-01, 6.91018520e-01, 2.75268624e-02, 9.16242225e-01, 8.99755244e-01, 4.84328046e-01, 1.39227458e-03, 3.36574166e-01], [9.70992103e-01, 2.31779948e-01, 2.47047234e-01, 8.47090684e-01, 5.56886869e-01, 8.93545313e-01, 6.89405560e-02, 4.47856652e-01, 9.49051043e-01, 5.55843563e-01], [3.71042248e-01, 5.12085423e-01, 8.88489553e-04, 2.83650703e-01, 1.51534050e-01, 7.56232935e-01, 1.57917639e-01, 6.93957503e-02, 8.60880045e-01, 9.98213381e-01]]])

      Variances (σ²):
      array([[[8.01207301e-02, 8.63378264e-02, 9.38591580e-02, 3.69835074e-02, 2.14089142e-02, 9.80798157e-02, 5.31857834e-02, 3.11624377e-02, 9.29542424e-02, 8.19041531e-02], [3.83395722e-02, 9.58576498e-02, 3.35100988e-02, 4.52191878e-02, 3.47955545e-02, 3.91611184e-02, 5.38114186e-02, 9.67475781e-02, 2.79199095e-02, 1.48608461e-02], [9.48935698e-02, 7.78691619e-02, 6.80584183e-02, 9.43161698e-02, 7.55934256e-02, 6.31720503e-02, 4.66870184e-02, 2.13604181e-03, 9.89581946e-02, 9.38158125e-02], [3.93624386e-02, 6.16264734e-02, 3.49923650e-02, 2.86202182e-02, 9.41585928e-02, 1.18163067e-02, 6.30849535e-02, 6.92828252e-02, 7.78842075e-02, 8.26528381e-02], [8.25526762e-02, 1.68686270e-02, 5.68080622e-02, 4.51747837e-02, 6.21739525e-02, 6.67643326e-02, 1.09478258e-02, 4.65664673e-02, 7.94259097e-02, 2.00880614e-02], [2.31494066e-02, 6.13908498e-02, 5.93857101e-02, 5.55261536e-02, 9.46974335e-02, 7.36959207e-02, 3.21595185e-02, 6.88523756e-02, 5.85584512e-02, 8.25982100e-02], [9.47161099e-03, 9.07174918e-02, 3.17598895e-03, 9.74531663e-02, 3.73148775e-02, 1.70094082e-02, 9.58745387e-02, 8.56658051e-02, 4.14679715e-02, 3.70412437e-02], [1.11539813e-02, 9.94206747e-02, 9.39391843e-02, 1.52431312e-02, 8.94142526e-02, 9.16682153e-02, 8.45863687e-02, 5.99723956e-02, 4.33643384e-02, 5.74679779e-02], [6.74361317e-02, 8.50302161e-02, 6.04485483e-02, 3.97499781e-02, 7.64766798e-02, 8.57234854e-02, 9.97615497e-02, 5.43009174e-02, 5.42785316e-02, 6.10655613e-02], [9.59381275e-02, 8.06891760e-02, 3.55841247e-02, 1.69832619e-02, 4.83524052e-03, 3.17209432e-02, 2.91042027e-02, 8.03769612e-02, 6.92007096e-02, 3.48614239e-02]], [[3.11022370e-02, 8.01613874e-02, 9.70592872e-02, 7.48603509e-02, 1.23230935e-03, 3.46239474e-02, 1.06999586e-02, 8.69200542e-02, 9.39033841e-02, 3.33182641e-03], [5.36426115e-02, 8.57200453e-02, 9.15523028e-02, 6.37120912e-02, 6.47094107e-02, 8.87945111e-02, 4.47765784e-02, 7.71615167e-02, 4.16330180e-02, 6.86535264e-02], [6.47942737e-02, 9.46451920e-03, 1.99064413e-02, 1.58911322e-02, 3.22049584e-02, 1.47528659e-03, 2.63050525e-02, 9.05206355e-03, 5.16629851e-02, 7.30592880e-02], [1.32160064e-02, 5.83018670e-02, 5.77909955e-02, 9.08624304e-03, 9.00939082e-02, 3.34337067e-02, 6.89622883e-02, 8.68041055e-03, 7.68861085e-02, 6.99415790e-02], [5.06784825e-02, 5.33475241e-02, 6.44952309e-02, 1.52659763e-02, 8.21761595e-02, 7.30785238e-02, 9.80996474e-02, 5.00616816e-02, 9.28348326e-02, 6.17693881e-02], [9.88229778e-02, 1.09674144e-02, 2.40739519e-02, 3.19890867e-02, 1.38293640e-02, 5.71934782e-02, 9.59985719e-02, 1.21353018e-02, 9.92558500e-03, 6.04726195e-02], [6.94464707e-02, 9.93805726e-02, 1.48090618e-02, 5.28569868e-02, 8.27398223e-02, 7.51950308e-02, 5.09152409e-02, 1.69184918e-02, 8.13528836e-02, 1.20271222e-02], [3.04140840e-02, 3.66697249e-02, 5.08206031e-02, 4.53472537e-02, 7.95740200e-02, 8.91734852e-02, 1.49380666e-02, 3.50595147e-02, 3.94482952e-02, 4.62139882e-02], [2.04748692e-02, 5.48445070e-03, 6.82075313e-02, 2.43662985e-02, 7.05914192e-02, 5.25916209e-02, 2.40968381e-02, 3.09464760e-02, 3.62074940e-02, 8.14136254e-02], [3.40045451e-02, 5.17117041e-02, 4.58451748e-02, 2.06384398e-02, 6.77324683e-02, 5.45087625e-02, 3.34617884e-02, 1.50851525e-02, 3.02278933e-02, 6.99902766e-02]], [[8.48944835e-02, 4.39942451e-03, 2.15519531e-02, 4.82226205e-03, 8.76539995e-02, 2.09666116e-02, 2.72575898e-02, 5.80073463e-02, 7.78210267e-02, 1.26981887e-02], [1.51259823e-02, 6.77488532e-03, 5.37473461e-02, 5.62574400e-02, 2.05954466e-02, 4.65583304e-03, 2.12394524e-02, 5.16679860e-02, 1.44630225e-02, 6.66566191e-02], [5.97320443e-02, 8.41533360e-02, 3.48673849e-03, 7.31412909e-02, 4.71772902e-02, 2.58246729e-02, 6.54214084e-02, 4.76462234e-02, 1.46531341e-02, 5.49628645e-02], [9.58318712e-02, 8.88063708e-02, 4.15648951e-02, 9.14855586e-02, 7.66044459e-02, 9.37729782e-02, 3.17886231e-02, 2.47793659e-02, 2.85477582e-02, 3.31784762e-02], [2.72102429e-02, 9.19973331e-03, 1.48048363e-02, 1.62569791e-02, 8.29915699e-02, 3.72916807e-02, 8.42406074e-02, 1.96220817e-02, 1.10011547e-02, 1.94899835e-02], [6.78848713e-02, 6.36605267e-02, 5.48252263e-02, 3.32841228e-02, 1.19554168e-02, 3.37550004e-02, 4.49662588e-02, 3.41062567e-02, 4.63353336e-02, 2.03518067e-02], [1.49407753e-02, 6.90400085e-02, 1.89883141e-02, 3.27572111e-02, 8.34903879e-02, 7.17296965e-02, 8.43767269e-02, 8.11855078e-02, 1.79917472e-02, 6.97696567e-02], [4.47894233e-02, 2.41148401e-02, 4.78384202e-02, 9.72755031e-02, 9.61713954e-02, 4.75430990e-02, 9.58945313e-02, 9.86045636e-02, 5.47916024e-02, 9.85887820e-02], [1.80763242e-03, 8.38400378e-02, 2.05983856e-02, 2.90510407e-02, 5.22359179e-02, 2.15234512e-02, 8.34239529e-02, 2.87472725e-02, 8.18910915e-02, 1.96674583e-02], [6.16978332e-02, 6.91563922e-02, 3.62193214e-02, 2.15990894e-02, 1.95227949e-02, 9.98667918e-02, 9.39947416e-02, 4.64857838e-02, 3.84005775e-02, 1.25828914e-02]], [[8.73138975e-02, 1.47093650e-02, 3.62551621e-03, 2.25254178e-02, 4.44583279e-02, 8.29499488e-02, 2.12699437e-02, 8.61662258e-02, 6.62347191e-02, 6.44270899e-02], [6.95404366e-02, 4.56939390e-03, 2.02568403e-02, 3.61103447e-02, 6.77023234e-02, 1.38686675e-03, 2.79512947e-02, 1.35141960e-02, 6.10514363e-02, 5.58235009e-04], [9.08083490e-02, 8.43068124e-02, 2.33234861e-02, 1.50328673e-02, 9.50798444e-02, 1.06810121e-02, 7.99876174e-02, 3.83876862e-02, 5.29816874e-02, 3.41436584e-02], [4.50235215e-02, 1.67520479e-02, 6.16740973e-02, 3.39951907e-02, 3.51629256e-02, 5.98382544e-02, 1.78825558e-02, 6.46415397e-02, 8.92882525e-02, 7.01067682e-03], [5.13783020e-02, 1.29884276e-02, 9.78629119e-02, 4.52154340e-02, 1.86447860e-02, 8.55782041e-02, 2.15788168e-02, 5.22465435e-02, 9.31940523e-02, 7.74025891e-03], [4.43996008e-02, 1.93966262e-02, 2.27543142e-02, 2.24615702e-02, 8.11460762e-02, 2.19126606e-03, 5.14209458e-02, 3.35136222e-02, 3.31039800e-02, 3.53320926e-02], [1.69719891e-02, 6.15560666e-02, 8.02225625e-02, 2.37538442e-02, 6.07300341e-02, 8.56253240e-02, 6.06737196e-02, 5.54952121e-02, 9.43464088e-02, 1.79889729e-02], [3.05610103e-02, 4.44130601e-02, 2.89872849e-02, 1.90953902e-02, 8.70996474e-02, 4.59715434e-02, 8.29189286e-02, 7.05215078e-02, 5.23030206e-02, 3.12334025e-02], [1.74208497e-02, 6.42538071e-02, 2.44872634e-02, 1.68532584e-02, 1.76845029e-02, 1.28852721e-02, 6.36279390e-02, 6.94510701e-02, 3.86214159e-02, 6.95189698e-02], [4.03504747e-02, 6.35704354e-02, 9.46312215e-02, 9.36549078e-02, 8.89030858e-03, 5.60555624e-02, 3.91608241e-02, 1.76691015e-02, 3.19812792e-02, 9.97326189e-02]], [[1.84269449e-02, 2.30206498e-02, 8.47586580e-02, 7.72511688e-04, 3.93264505e-02, 1.18643754e-02, 8.98504715e-02, 2.38596971e-02, 7.82212047e-02, 4.25052392e-02], [7.89745333e-02, 8.35450077e-02, 9.06005083e-02, 1.38027505e-02, 8.45509995e-02, 2.43116793e-02, 4.99393243e-02, 4.11161467e-02, 5.81208682e-02, 6.61581810e-02], [8.58120602e-02, 8.00566639e-02, 9.40802094e-04, 2.63243823e-02, 4.99502104e-03, 3.66061192e-02, 7.47668370e-02, 8.86231765e-02, 4.48850135e-04, 4.13258245e-02], [5.67312050e-02, 7.92887400e-02, 5.49456441e-02, 6.37148894e-02, 5.91543349e-03, 7.31226172e-02, 1.14949018e-02, 8.08279875e-02, 6.87845607e-02, 2.90715571e-02], [4.17817652e-02, 7.97365522e-02, 4.62697680e-02, 1.26781712e-02, 8.93800793e-02, 5.91754841e-02, 3.57812654e-02, 1.74863614e-02, 7.62267251e-02, 9.88235227e-02], [6.98599410e-03, 7.02762141e-02, 9.27389608e-02, 5.65720713e-02, 4.04713427e-02, 3.71580772e-02, 4.21780074e-02, 5.60600137e-02, 4.04598060e-03, 3.94149940e-02], [8.91051367e-02, 9.37710535e-02, 3.91761026e-02, 9.59160286e-02, 1.95150589e-02, 1.27752689e-02, 1.14842357e-02, 9.77263190e-02, 3.43434739e-02, 5.56836833e-02], [7.55963199e-02, 3.40166158e-02, 8.48107991e-02, 4.69273207e-02, 5.01350412e-02, 6.09729248e-02, 5.36565279e-02, 9.90412610e-02, 3.83938193e-02, 2.41823682e-02], [3.45354489e-02, 1.79708175e-02, 2.30480481e-02, 4.15077095e-03, 3.35634754e-02, 5.15627720e-02, 8.57326614e-02, 8.64028987e-02, 2.59238223e-02, 3.77762969e-02], [3.92422540e-03, 5.98607970e-02, 5.40296749e-02, 6.14607252e-02, 6.25035474e-02, 1.44614540e-02, 8.61989921e-02, 6.93283546e-02, 3.11027977e-03, 1.46143044e-02]], [[4.21990894e-02, 4.95124590e-02, 7.56605220e-02, 4.43448178e-02, 7.70310698e-02, 9.60996044e-02, 9.58496480e-02, 2.99693801e-02, 9.36411967e-02, 7.74513425e-04], [7.45932942e-02, 8.54539187e-03, 9.07926587e-03, 6.12111780e-02, 2.66933799e-03, 8.87247028e-02, 5.74433992e-02, 6.48850973e-02, 3.34000352e-02, 9.72630020e-04], [6.77849849e-02, 2.76183321e-02, 5.85316686e-02, 5.27822757e-02, 1.98865660e-02, 9.49037009e-02, 5.20783384e-02, 2.16667783e-02, 3.30798361e-02, 2.35785634e-02], [9.41899456e-02, 5.15117151e-02, 1.45351184e-02, 4.58403282e-02, 4.29031590e-02, 4.90464756e-02, 3.39351748e-02, 8.27686164e-03, 9.01867616e-02, 9.75486379e-02], [5.05401902e-02, 2.31979588e-03, 7.43080013e-02, 8.49854360e-02, 4.91804075e-02, 1.41959176e-03, 9.94499967e-02, 6.61386599e-02, 3.84127422e-02, 1.34875120e-02], [9.06625945e-02, 7.94171083e-04, 6.66733118e-03, 6.61814995e-02, 7.10191137e-02, 9.00415500e-02, 3.43423356e-03, 7.69880044e-02, 1.74227005e-02, 7.65658566e-02], [7.48597003e-02, 6.99953836e-02, 9.67795077e-02, 8.64029783e-02, 8.87927571e-02, 1.63008264e-02, 3.74788463e-02, 9.05006405e-02, 4.37796522e-02, 6.54105720e-02], [7.33967364e-02, 1.38102246e-02, 4.65594796e-02, 7.16859417e-02, 4.25481242e-04, 5.24526213e-02, 8.39325685e-02, 1.68899962e-06, 5.90070410e-02, 3.60164446e-02], [4.79500294e-02, 9.77504062e-02, 5.14895981e-02, 2.64229723e-02, 2.81290430e-02, 8.94066444e-02, 3.37254242e-02, 4.48201323e-02, 6.47475262e-02, 2.22809545e-02], [8.79159226e-02, 1.73546280e-03, 2.17319595e-02, 8.02021442e-02, 4.60752024e-02, 9.36207198e-02, 9.70960107e-02, 3.37043044e-02, 3.52953134e-02, 1.04077919e-02]], [[4.63817326e-02, 6.81108061e-02, 1.55510055e-02, 7.26919990e-03, 3.36726033e-02, 1.50969417e-03, 6.33416256e-02, 6.90994830e-02, 5.74432088e-02, 7.76836610e-02], [9.99352566e-03, 9.87148473e-02, 7.29034042e-02, 8.78609232e-02, 4.03957872e-02, 2.03001377e-03, 3.81688102e-02, 4.32234616e-02, 6.71447974e-02, 5.78217478e-03], [9.67110285e-02, 2.11595556e-02, 5.67880804e-02, 5.25453382e-03, 7.47839180e-03, 6.75053623e-02, 8.51557378e-02, 6.88768498e-03, 3.34684705e-03, 9.47888881e-02], [4.47248653e-02, 2.93528811e-02, 9.04467306e-02, 5.19910825e-02, 7.10931201e-02, 6.97312491e-02, 8.61002374e-02, 3.70252550e-02, 7.04534577e-02, 7.03183875e-02], [2.98120203e-02, 5.73419975e-02, 1.93624971e-02, 4.69949835e-02, 3.76811465e-02, 2.13200717e-02, 4.69894591e-02, 1.70613845e-02, 3.59406836e-02, 1.41390054e-02], [2.16411670e-02, 8.25316172e-02, 9.16592798e-02, 2.08644791e-02, 2.93847755e-02, 8.45644397e-02, 9.93752145e-02, 7.81001762e-02, 3.16882100e-03, 6.01485913e-02], [1.93474914e-02, 8.98282083e-03, 7.42503109e-02, 8.03399491e-02, 5.85031623e-02, 3.63410524e-02, 7.07623269e-02, 6.92607121e-02, 5.13764728e-02, 3.34930068e-02], [2.47050685e-02, 1.19643824e-02, 3.81450149e-02, 3.00782582e-02, 4.43756662e-02, 8.26376659e-02, 3.73985134e-02, 9.21124482e-02, 8.97890771e-02, 3.86154233e-02], [4.64399831e-02, 3.85630832e-02, 2.41075244e-02, 2.58800080e-03, 9.79897668e-02, 7.67690878e-02, 3.68868648e-02, 9.12255348e-02, 8.00947023e-02, 8.90084307e-02], [8.50851591e-02, 9.10121989e-02, 7.50901209e-02, 3.43192180e-02, 1.47339731e-03, 9.13106048e-02, 1.02993501e-02, 6.04194248e-02, 6.45644755e-02, 5.35017779e-02]], [[3.76948517e-02, 7.08172724e-02, 8.68639129e-02, 8.87477496e-02, 6.94320522e-02, 8.38033402e-02, 1.04920452e-02, 8.34929334e-03, 4.20572977e-02, 2.17806868e-02], [6.65237155e-02, 6.69276057e-02, 7.36291118e-02, 6.71974786e-02, 3.05124342e-02, 6.81676068e-02, 2.52010890e-02, 6.56272941e-02, 6.82021861e-02, 9.81206095e-03], [3.61241789e-03, 5.22843581e-02, 7.48480867e-02, 5.66827482e-02, 3.12180025e-02, 1.42157850e-03, 6.87974808e-02, 6.09120185e-02, 5.15605980e-02, 4.46155750e-02], [1.84882334e-02, 7.77403740e-02, 5.72271465e-02, 2.08555769e-02, 3.23859915e-02, 4.94353063e-02, 4.51733428e-02, 3.92400793e-02, 2.41231077e-02, 3.03006992e-02], [8.60725025e-02, 3.64232549e-02, 9.68591846e-03, 1.64704705e-02, 2.28222673e-02, 6.99540027e-02, 3.70047963e-02, 8.54652369e-02, 2.76710759e-02, 9.64622949e-02], [3.72194218e-02, 6.95800886e-02, 3.45642058e-02, 3.16106799e-02, 3.97254286e-02, 4.12088017e-02, 8.15595841e-02, 8.63164651e-03, 1.17207029e-02, 8.86376961e-02], [5.57810282e-02, 8.78610852e-02, 7.10527146e-02, 6.80905503e-02, 2.47168658e-02, 9.12151190e-02, 2.82237056e-03, 7.45901114e-02, 6.79605199e-02, 3.54549078e-02], [9.75544739e-02, 9.70698050e-02, 4.80924468e-02, 8.94525651e-02, 1.20551950e-02, 7.45377557e-02, 6.26868983e-03, 5.17859349e-02, 7.01238456e-02, 4.27211113e-02], [6.12900196e-02, 7.25001688e-02, 9.13564964e-02, 6.14144901e-02, 2.29350167e-02, 8.73865709e-03, 5.19068453e-02, 8.14378213e-02, 5.46544447e-02, 8.98544487e-02], [8.93420707e-02, 4.18771100e-02, 5.61504693e-02, 4.07977922e-03, 5.94591072e-02, 9.21125967e-02, 3.31214183e-02, 3.23693549e-02, 7.85507158e-02, 9.26195885e-02]], [[9.77512268e-02, 6.25581321e-02, 5.34835339e-02, 9.04234526e-03, 5.18557043e-02, 9.76632424e-02, 2.53858284e-02, 5.33589324e-02, 3.19080812e-02, 1.12994772e-03], [7.69664367e-02, 8.48312115e-02, 1.24488548e-02, 4.75662570e-02, 4.20715530e-04, 8.98843814e-02, 9.23695961e-02, 6.43359152e-04, 4.84893292e-02, 3.03626488e-04], [6.55686447e-02, 8.00506031e-02, 6.10312158e-02, 6.62087022e-02, 7.74587083e-02, 3.02869938e-02, 7.84316426e-02, 5.04001450e-02, 7.09928676e-02, 5.29477376e-02], [3.70338969e-02, 4.50254497e-03, 2.74136883e-02, 8.43775447e-02, 2.45999592e-02, 9.48772800e-02, 7.88164556e-02, 2.55619214e-02, 2.67821743e-02, 2.14444263e-02], [7.45499203e-02, 7.75343796e-03, 1.20405707e-02, 6.70487116e-02, 2.82258136e-02, 7.97883850e-02, 3.80605334e-02, 3.43378946e-02, 7.41529101e-02, 8.22564889e-02], [7.89691858e-02, 2.58645717e-02, 2.31417434e-02, 8.56483399e-02, 8.60871074e-02, 1.13381482e-02, 5.64371363e-02, 4.96761241e-02, 1.35840906e-02, 6.72807023e-02], [9.00458995e-02, 3.33380808e-02, 6.74128121e-02, 7.88804977e-02, 1.00224248e-02, 6.45719586e-02, 4.95184343e-03, 1.90647642e-02, 5.67034356e-02, 5.79515531e-02], [1.40850145e-02, 4.11717683e-02, 2.67581787e-02, 9.21229239e-02, 6.41175236e-02, 4.48174629e-02, 6.72562539e-02, 1.31974566e-02, 7.29135160e-03, 7.24087182e-02], [5.01486756e-02, 5.85344600e-02, 9.97303324e-02, 8.83453237e-02, 5.46893818e-02, 5.54424838e-02, 8.15079346e-02, 6.59224043e-03, 4.03829447e-02, 4.53081714e-03], [1.76499778e-02, 1.12477335e-02, 4.43385779e-02, 1.83661327e-02, 2.66597062e-02, 3.19628438e-02, 7.72133014e-02, 1.05627004e-02, 6.54894323e-02, 4.25261311e-03]], [[1.11767268e-02, 2.44176632e-02, 6.33177057e-02, 9.43568269e-02, 3.39186704e-02, 9.34158351e-03, 5.05291695e-02, 6.33874380e-02, 2.57973207e-02, 1.60139623e-02], [8.09410909e-02, 8.32188262e-02, 8.24531054e-02, 8.94986445e-02, 2.08032638e-02, 5.65424137e-02, 4.72964385e-02, 8.93984777e-02, 8.93454522e-02, 8.52783867e-02], [1.22581822e-03, 9.00637764e-02, 9.59610776e-02, 5.69090214e-02, 8.78018465e-02, 2.59880231e-02, 2.91592578e-02, 8.74837165e-02, 2.72059309e-02, 3.57498767e-02], [2.73707528e-04, 4.04516646e-02, 1.02096939e-03, 5.55187127e-02, 9.22867850e-02, 1.48984256e-02, 5.89898081e-02, 1.91941884e-02, 5.22095889e-02, 5.79594484e-02], [9.28015016e-02, 4.47635150e-03, 8.36359158e-02, 3.45879290e-02, 8.77376804e-02, 7.36387638e-02, 3.52204852e-02, 3.81623229e-03, 1.67145580e-02, 5.42799064e-04], [1.56719212e-02, 4.85459065e-02, 1.59975498e-02, 8.01253799e-02, 9.76982024e-02, 9.31288243e-02, 6.75986820e-02, 6.96468912e-02, 1.19455375e-02, 5.55283210e-02], [4.00569364e-03, 8.06842329e-02, 4.51335250e-03, 2.59937399e-02, 5.70870234e-02, 8.74914295e-02, 4.58260309e-02, 8.63302289e-02, 2.89481927e-02, 8.23246511e-02], [7.96926686e-02, 3.31291083e-02, 7.56623487e-03, 5.91245281e-03, 1.93948836e-02, 8.93906476e-03, 9.10140076e-03, 1.76959578e-02, 8.75058373e-02, 5.84698749e-02], [2.43056265e-02, 9.27404199e-02, 8.67533693e-02, 1.00650386e-02, 8.39217087e-02, 4.19145935e-02, 2.58681374e-02, 6.42950675e-02, 3.80570506e-02, 2.39680820e-02], [1.92659672e-02, 4.30961990e-02, 7.17466483e-02, 8.63362529e-02, 3.13948079e-02, 8.72052296e-02, 9.86149974e-02, 5.01077739e-02, 3.74478016e-04, 8.93097729e-02]]])
    • bob
      (x, z)
      float64
      0.0, 0.1, ..., 9.8, 9.9
      σ = 0.27, 0.22, ..., 0.14, 0.31
      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([[0.07273377, 0.04989699, 0.06445848, 0.05642493, 0.00490842, 0.09408408, 0.06094089, 0.01940279, 0.04121442, 0.07359646], [0.0320617 , 0.05037877, 0.09247093, 0.05387947, 0.04058386, 0.06378661, 0.0086305 , 0.05223879, 0.02351903, 0.06851242], [0.00372053, 0.04242474, 0.00050031, 0.01351683, 0.00975447, 0.03302091, 0.07919148, 0.05392051, 0.06757294, 0.05636131], [0.00485702, 0.03105401, 0.09113896, 0.09416773, 0.09207814, 0.07902188, 0.03382482, 0.01480256, 0.04314213, 0.04878144], [0.05749054, 0.06941926, 0.08119641, 0.02715996, 0.09890429, 0.092456 , 0.03769801, 0.06793582, 0.07270839, 0.06428407], [0.05978408, 0.09369024, 0.04861367, 0.08889728, 0.06205336, 0.05967507, 0.00872669, 0.06267435, 0.06854531, 0.0363729 ], [0.04311726, 0.00057827, 0.08897441, 0.07851432, 0.06037546, 0.02624816, 0.0867688 , 0.00209828, 0.07878133, 0.00961017], [0.0815546 , 0.07548409, 0.06810872, 0.05723724, 0.05567111, 0.08875519, 0.0001808 , 0.03286223, 0.05769091, 0.04123132], [0.07812832, 0.01428348, 0.08723245, 0.07545137, 0.09522267, 0.05876783, 0.01941469, 0.09641863, 0.04411309, 0.0348458 ], [0.03413437, 0.07558359, 0.06137484, 0.09937847, 0.09384991, 0.03867708, 0.05866082, 0.01063345, 0.02028928, 0.09552854]])

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]:
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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
      0.27, 0.61, ..., -0.11, 0.16
      σ = 0.44, 0.45, ..., 0.42, 0.41
      Values:
      array([[[ 2.73782270e-01, 6.14348766e-01, -1.38782351e-01, 1.37491980e-01, 3.66371192e-01, -6.87604284e-01, 4.99821872e-01, -4.72803666e-01], [-1.91553794e-01, 5.22337662e-01, -2.04578007e-01, -5.77348257e-01, 5.78841428e-02, -6.98323527e-01, 3.92362492e-01, 2.68802815e-01], [ 9.55692366e-03, 2.29830109e-01, -1.65134199e-01, -3.75109077e-01, 2.62842296e-01, -7.28076120e-02, -2.07641233e-02, -1.31689531e-01], [ 7.92365510e-02, 8.01873122e-01, -1.61088851e-01, -2.67466774e-01, 7.78115533e-02, -6.68131560e-01, 1.75439796e-01, -5.50308276e-01], [ 2.37352039e-01, 6.63202484e-01, 3.61726196e-02, -5.95010870e-01, 4.66269610e-01, -4.59833406e-01, -7.19605945e-02, -5.24911918e-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], [-8.93306061e-03, 7.74541663e-01, 1.44802070e-03, 2.12717027e-01, 6.20475743e-01, -3.11186451e-01, -3.90807358e-01, -4.43802019e-01], [ 6.41308796e-01, 1.13929780e-03, -1.27344967e-01, 3.03980535e-01, -6.15489242e-02, -8.07662853e-01, 2.44434450e-01, -2.29677388e-01], [-8.55388776e-02, 5.11648138e-01, -1.24979306e-01, -2.25736838e-01, 1.79084503e-01, -7.84188987e-01, 3.02177860e-01, -1.90375314e-01], [ 5.64392967e-01, 8.01737928e-01, 4.38653456e-01, -3.47550946e-01, 4.33330028e-01, -1.52592392e-01, -3.94979178e-01, 5.71662379e-02]], [[-1.43608396e-01, -5.42468465e-01, 9.98735573e-02, 1.06952060e-01, 5.12079836e-01, -4.27504814e-01, -1.62807801e-01, -3.07515883e-01], [ 6.57556150e-01, -4.92137597e-01, 3.92896803e-04, -2.02623863e-01, -1.41731560e-01, -4.44541357e-01, -1.36004713e-01, 5.45522499e-02], [ 2.51261925e-01, 4.91094261e-02, -4.27219033e-01, -7.40586734e-01, -3.85959594e-01, -2.79067259e-02, 2.34813917e-01, -7.57797122e-01], [ 3.63321696e-01, 2.95106616e-01, -3.95736092e-01, -5.13519607e-01, 2.24174193e-01, 6.55389758e-02, 4.91169572e-01, -2.21943225e-02], [ 4.76181483e-01, 2.84086651e-01, -1.33010483e-01, -7.07086964e-01, 1.85219989e-01, 1.00482439e-01, 1.00704416e-01, 1.50953971e-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], [-2.57580107e-01, 1.56834851e-01, -5.76960414e-01, 1.14936369e-01, 1.85279077e-01, -5.39027106e-01, 2.89940114e-01, -9.22384014e-01], [ 6.25539987e-01, -5.58940647e-01, -7.44332839e-01, 2.42619050e-02, -3.96711057e-02, -5.88526212e-01, -2.86044526e-01, -4.41561098e-01], [ 4.95743587e-01, 2.77614366e-01, -7.14301777e-01, -4.55987367e-01, -1.11673773e-01, -6.91161614e-02, 2.76997613e-01, -9.20441868e-01], [ 3.37201225e-01, -2.91991428e-01, -3.86016766e-01, -3.84096946e-01, 3.17037857e-01, -9.05247575e-02, 3.47550963e-01, -1.19299476e-01]], [[ 1.97364009e-01, -5.56344298e-01, 2.20437838e-01, -6.99527519e-02, 2.04942392e-01, -4.22026455e-01, 2.92425605e-01, -1.05172159e-01], [ 4.55001522e-01, -3.04549984e-01, 7.51329655e-02, 1.51106436e-02, 3.47858041e-01, -7.50587900e-02, 5.00588249e-01, -6.47924987e-02], [ 7.18890201e-01, -6.69778371e-01, 2.50234459e-01, -4.36827157e-01, 1.82989388e-01, -4.59423134e-01, -8.97884321e-03, -6.61484616e-01], [ 6.64770018e-01, -1.86952553e-01, 3.32789373e-01, -2.59009528e-01, 4.94740898e-01, -3.87334508e-01, 8.71891674e-01, -5.51879459e-01], [-1.20744130e-01, -1.59250356e-01, 5.66304680e-01, 3.03390643e-01, 3.79971946e-01, 5.34073909e-02, 4.86801063e-01, -3.69560550e-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], [ 2.54237389e-01, -2.31552179e-01, 6.88459749e-01, -4.95235329e-01, 5.21277398e-01, -5.04053934e-01, 6.78997263e-01, -4.59844748e-01], [-4.87459706e-02, -8.44537912e-01, 2.92245205e-01, -4.20752669e-01, -1.14505636e-01, -5.19776316e-02, -5.99556660e-02, -2.21375434e-01], [ 6.31143559e-01, -3.90136604e-01, 6.27165311e-01, -1.89142629e-01, 1.65038714e-01, 1.32594788e-01, 6.11078141e-01, -2.28305031e-01], [ 5.93380731e-01, -5.89135608e-01, 3.77921682e-01, 7.80330033e-02, 3.30870331e-01, -4.07818448e-01, 8.62061791e-01, -7.07023106e-01]], [[-5.09476010e-01, 3.99847670e-01, -4.12955988e-01, 7.15674126e-01, -6.61608237e-01, 3.26642168e-01, -4.88003586e-01, -6.54539693e-01], [-8.18824411e-01, -3.40995712e-01, -5.63626924e-01, 8.89205880e-01, 6.84255171e-02, -3.91986622e-01, -4.79496615e-01, -3.87929367e-01], [-4.30967877e-01, -4.10472134e-01, -3.00316054e-01, 6.40868454e-01, 3.29054883e-01, -5.28613226e-01, -1.52643267e-01, -8.94916965e-01], [-7.51422866e-01, 3.81865942e-01, -1.89069584e-01, 8.97322488e-01, 2.31645191e-01, 6.74773169e-02, 3.37431240e-01, -1.73990086e-01], [-7.02654155e-01, 3.95050274e-01, -9.24426398e-01, 4.94828020e-01, -3.76823312e-01, -4.26946508e-01, -2.46023578e-01, -2.02134859e-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], [-7.24872245e-01, 2.81539627e-01, -2.52003605e-01, -1.90775792e-02, -6.20152762e-01, -7.86337672e-02, -2.48649556e-01, -7.16341597e-01], [-4.98489558e-01, 7.96970920e-02, -6.46296817e-02, 1.97099452e-01, 3.73073413e-02, 1.62039243e-01, -5.03251302e-01, -1.24759125e-03], [-6.70868633e-01, -3.83695116e-01, -7.85523762e-01, 4.55699015e-01, 3.03943856e-01, 1.79206349e-02, -5.37083226e-01, -2.43813186e-01], [-5.62040754e-01, -1.36202347e-01, -4.96502744e-01, 2.95498428e-01, -5.20906300e-02, 5.12597238e-02, 2.67553734e-01, -4.12688373e-01]], [[-6.36386611e-01, 6.97001503e-01, 2.31423488e-02, -4.90767536e-01, 6.90968199e-01, 6.44544352e-01, 2.95451458e-01, 3.77988096e-01], [-3.43947897e-01, 6.33716470e-01, -1.50468784e-01, -5.29987423e-01, 6.95946517e-01, 6.13803236e-01, -1.80500561e-01, 5.01249087e-01], [-6.01300811e-01, -1.61037042e-03, -2.54157018e-01, -3.27226306e-01, 1.63212303e-01, 4.13847013e-01, -3.27206640e-01, 3.18690780e-03], [-6.17369071e-01, 2.50368445e-01, -3.00713223e-01, -2.45215148e-01, 5.09082154e-01, 1.23556607e-01, 3.05401779e-02, -1.36980509e-01], [-7.84431760e-01, 6.79722192e-01, -5.47292470e-01, 1.92473006e-01, 4.40012568e-01, 2.19006021e-01, 2.32286434e-02, 2.84849033e-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], [-8.64085271e-01, 2.78445664e-01, -4.56377453e-03, 2.13683246e-01, 5.14553449e-01, 4.27322796e-01, 1.84324555e-01, -1.97120232e-01], [-8.32512068e-01, 5.93438418e-01, -2.89097577e-01, -6.97802920e-01, 8.54044588e-02, 8.49486123e-02, -5.41434220e-01, 4.03989144e-01], [-6.33767757e-01, 2.72138338e-01, -8.16584696e-01, -6.02636832e-01, 4.78343589e-01, 5.73780405e-01, -1.48139326e-01, -3.22509706e-01], [-4.08891687e-01, 3.99458576e-01, -7.96164307e-01, -4.63592121e-01, 2.30772475e-01, 5.68277994e-02, 2.70107437e-01, -3.91978741e-01]], [[ 1.35674657e-01, -1.73792135e-02, -1.13401460e-01, 2.74927955e-01, -8.49895118e-02, 8.58902573e-01, -3.69979642e-01, 6.09404852e-01], [-2.98976639e-01, -4.68246596e-01, -6.14643104e-01, 1.22961257e-01, 1.71382772e-02, 7.97195321e-01, -3.38029991e-01, 3.38449449e-01], [-1.51052704e-01, -1.53340124e-01, -6.20664592e-01, 3.12563987e-01, -2.76704992e-01, 5.20487709e-01, -8.51273737e-01, -9.13673707e-02], [-2.21758889e-01, 2.95652458e-01, -4.78161151e-01, 9.09541881e-03, -4.91129748e-01, 9.81183386e-01, -6.20057511e-01, -1.26772727e-01], [-7.70238411e-01, -3.18450460e-01, -6.52956336e-01, 4.86702948e-02, -7.05677320e-01, 2.09363514e-01, -3.86737979e-01, 4.25424836e-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], [-1.12755645e-01, -3.41679776e-01, -6.99007743e-01, -3.15168539e-02, 7.95787867e-02, 9.11142927e-02, -3.39276233e-01, 3.89512699e-01], [-4.97178865e-01, -2.36876696e-01, -6.06315091e-01, 2.93760078e-01, -1.47771454e-01, 5.86210723e-01, 6.75466814e-03, 7.98300973e-02], [-5.19469604e-01, -2.36798835e-01, 1.41185901e-01, 1.37367846e-01, -1.75460873e-01, 9.06284034e-02, -1.33567699e-01, -1.82867537e-01], [ 1.26496985e-01, -2.22396326e-01, -6.03778647e-01, 4.90346190e-01, -4.57670334e-02, 3.68901291e-01, -3.35218842e-01, 5.14809044e-01]], [[-2.08778243e-01, 3.86083085e-01, 5.04055336e-01, -1.91149117e-01, 2.67008878e-01, 1.48084554e-01, 3.72519663e-01, -4.45114995e-04], [-5.29972685e-01, 3.22103548e-01, -1.56405056e-01, 6.15021734e-01, 4.13294487e-01, 8.08975151e-01, 7.07683682e-01, 8.68937648e-02], [-4.61925349e-01, 9.91355659e-02, -3.63675213e-01, 4.01962293e-01, 1.06070832e-02, 1.34061704e-01, 3.75190729e-01, 3.22259777e-01], [-5.81091025e-01, 8.57577607e-03, -1.74119728e-02, -1.20757470e-01, 1.08466432e-01, 1.87725694e-02, -3.46326290e-02, -9.83046195e-02], [-1.03103089e-01, 5.54979256e-02, -1.56190290e-01, 7.13265435e-01, 6.75165742e-02, 3.93502021e-01, 9.02108394e-01, -1.68264317e-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], [-4.53974534e-01, -8.09482899e-02, -4.14042640e-02, 3.22927511e-01, -2.65528350e-01, 2.35793879e-01, 6.88782796e-01, -3.98489946e-01], [ 3.00612361e-01, 7.21131044e-01, -7.73108903e-02, 9.41697444e-02, -1.31601812e-01, 5.06195461e-01, 1.03344563e-02, -1.83650061e-02], [ 3.52189999e-01, 3.10305703e-01, -1.48403605e-01, 3.94019100e-02, -6.72628482e-02, -3.88116763e-02, 5.35390934e-01, 1.02625984e-02], [ 2.48732347e-01, 6.11139096e-01, 3.56470284e-01, 1.86255379e-01, -4.49759911e-01, 1.67210423e-02, 7.76853237e-01, 2.20346669e-01]], [[ 3.32823189e-01, -7.83403404e-01, 2.14563435e-02, -1.09284848e-01, 8.28271879e-03, -1.89468315e-02, -3.77458674e-01, 1.26372726e-01], [ 2.61444281e-01, -6.35016977e-02, 3.29945049e-01, 2.23495615e-01, -4.39294118e-01, 7.81778749e-01, -4.69043771e-01, 2.20301185e-01], [ 3.61245695e-01, -7.51556105e-01, 8.47139473e-01, -2.61482397e-01, 2.81992639e-01, 8.19280277e-01, 2.09725837e-01, 5.16169528e-01], [-7.39793333e-02, -4.60677853e-01, 1.49167342e-01, -5.45314327e-02, -1.25484243e-02, 5.25947578e-01, -6.55419415e-02, 3.21251191e-01], [ 2.35282352e-01, -5.89429671e-02, 3.73396671e-01, 2.82905411e-01, -4.57268714e-01, 1.96680267e-02, 3.09550238e-01, 4.29339080e-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], [ 4.89903052e-01, -3.26249203e-01, 6.06100784e-01, 3.75439473e-01, 8.36405453e-02, 3.99497478e-01, 1.98155969e-01, 7.55096761e-01], [-2.49668591e-02, -2.63315295e-01, 2.47717332e-01, 1.03776450e-01, 2.68849618e-01, -1.45965766e-01, -4.49985010e-01, 2.20831347e-01], [ 8.56473086e-02, 2.63839454e-02, 1.26304766e-01, 2.47978412e-01, -1.10245549e-01, 4.37930613e-01, -5.64424539e-02, 6.94742287e-03], [ 4.56399847e-01, -6.23620462e-01, 2.74528561e-01, -1.73609702e-01, 7.55940525e-02, 2.29738425e-01, -1.09766071e-01, 1.61498679e-01]]])

      Variances (σ²):
      array([[[0.19188634, 0.20598272, 0.16895745, 0.1539002 , 0.2791979 , 0.10785508, 0.25002353, 0.13239592], [0.19744499, 0.20047573, 0.15780919, 0.2173773 , 0.33336846, 0.1419317 , 0.24026499, 0.08012556], [0.12118947, 0.12882987, 0.10998823, 0.18487285, 0.24604924, 0.12346017, 0.17215554, 0.09015553], [0.17002682, 0.16671443, 0.10318334, 0.2427618 , 0.27800766, 0.16611741, 0.17178389, 0.11537865], [0.16507247, 0.17341866, 0.10936307, 0.23484405, 0.31765248, 0.19525476, 0.21316516, 0.13132737], [0.12269236, 0.13299738, 0.12608618, 0.16649726, 0.30176743, 0.19315369, 0.17523878, 0.04841813], [0.21110552, 0.12373249, 0.14695408, 0.23540771, 0.31976898, 0.14807036, 0.18002197, 0.11984542], [0.14839467, 0.15974404, 0.13944435, 0.23224191, 0.33374744, 0.11209318, 0.19816299, 0.07794084], [0.1172094 , 0.17713096, 0.1184634 , 0.22325931, 0.29716557, 0.12125195, 0.19404995, 0.07470003], [0.16343665, 0.15476861, 0.11473554, 0.22040036, 0.29908272, 0.13061691, 0.17818863, 0.06872043]], [[0.2530018 , 0.07737781, 0.22038431, 0.26200225, 0.15194895, 0.25017267, 0.22833105, 0.29862126], [0.25537726, 0.1095732 , 0.27181948, 0.19494369, 0.13563817, 0.24415453, 0.22199169, 0.23526325], [0.33275572, 0.05931259, 0.28870334, 0.22152554, 0.15680701, 0.28833649, 0.21796993, 0.23545336], [0.33740875, 0.09739075, 0.3070476 , 0.25095269, 0.22475532, 0.2547037 , 0.19510307, 0.24934799], [0.25780211, 0.07063069, 0.23181902, 0.25733982, 0.16827402, 0.30715568, 0.18994578, 0.23180139], [0.31226291, 0.11065108, 0.24884617, 0.18630366, 0.16473734, 0.26788134, 0.20442996, 0.26713556], [0.31764239, 0.07481417, 0.24831926, 0.25783863, 0.20271204, 0.3072918 , 0.25150921, 0.23879198], [0.27271722, 0.10366427, 0.31283755, 0.27051964, 0.17852544, 0.31880961, 0.26892827, 0.27559183], [0.33244242, 0.07642424, 0.24461309, 0.22658416, 0.15250579, 0.30633903, 0.19907098, 0.30269132], [0.31775877, 0.09204518, 0.23716113, 0.19387104, 0.23084913, 0.31690982, 0.21680949, 0.25920081]], [[0.14186494, 0.0534135 , 0.23332246, 0.17992431, 0.26293578, 0.22971953, 0.23415433, 0.25024144], [0.13172497, 0.07004482, 0.24690738, 0.20316831, 0.1813727 , 0.23640088, 0.1615023 , 0.24505816], [0.21146239, 0.07311147, 0.22582991, 0.23054583, 0.19066684, 0.2884372 , 0.18637579, 0.23698841], [0.14390762, 0.11146208, 0.24479223, 0.17062891, 0.23982409, 0.22633214, 0.21262964, 0.27329498], [0.140144 , 0.14765089, 0.25601247, 0.15411077, 0.26556404, 0.2300284 , 0.20023465, 0.27720078], [0.1465522 , 0.0725423 , 0.23325861, 0.21661206, 0.1821771 , 0.25987053, 0.18150172, 0.21711071], [0.18871164, 0.13001054, 0.23455088, 0.19619602, 0.26561116, 0.2691233 , 0.20348331, 0.27835313], [0.17156864, 0.07877527, 0.22989243, 0.22256563, 0.22595738, 0.29136851, 0.21850961, 0.23630975], [0.19140938, 0.07427525, 0.2276503 , 0.15315049, 0.1928711 , 0.27207752, 0.21743917, 0.22262814], [0.19072601, 0.1444192 , 0.30445195, 0.1443563 , 0.23604139, 0.24761041, 0.1656572 , 0.215988 ]], [[0.17446459, 0.19700656, 0.24150087, 0.27760638, 0.17312918, 0.2527794 , 0.19126193, 0.27271252], [0.23498895, 0.20284841, 0.25453111, 0.32283093, 0.18557648, 0.21286825, 0.20851838, 0.25261218], [0.23150061, 0.1131887 , 0.26705274, 0.24327495, 0.19787092, 0.23769577, 0.25602541, 0.19494017], [0.23073268, 0.16719355, 0.30444324, 0.24419536, 0.23438742, 0.17442383, 0.24823022, 0.26327588], [0.23118049, 0.15851767, 0.25340653, 0.32766001, 0.22044029, 0.19871019, 0.1848886 , 0.27071804], [0.22172016, 0.20498686, 0.29730043, 0.27875127, 0.19842288, 0.20510694, 0.22346225, 0.1985373 ], [0.245215 , 0.151424 , 0.33664438, 0.25779499, 0.17404007, 0.17441316, 0.26512856, 0.22883479], [0.18546056, 0.1970587 , 0.28765568, 0.28841497, 0.22223773, 0.21658546, 0.2664435 , 0.23288513], [0.16941476, 0.13529595, 0.24487913, 0.27184341, 0.21282758, 0.24866159, 0.25380514, 0.22041514], [0.21130474, 0.16627758, 0.30218908, 0.30078348, 0.17572626, 0.24912792, 0.23673059, 0.19760159]], [[0.17787986, 0.14836966, 0.26857008, 0.33296219, 0.3054913 , 0.15178021, 0.28446777, 0.22859955], [0.13691279, 0.08178841, 0.28543644, 0.25860046, 0.2981164 , 0.11337396, 0.31938349, 0.16835839], [0.15598573, 0.13124081, 0.27700754, 0.27581769, 0.3042954 , 0.1080089 , 0.27616517, 0.16803819], [0.17987912, 0.08724426, 0.27006559, 0.29883428, 0.25843817, 0.08986573, 0.26277525, 0.22514512], [0.1306872 , 0.14701714, 0.3092107 , 0.30511153, 0.21081129, 0.15538056, 0.32063705, 0.1733711 ], [0.12916157, 0.07937647, 0.29040676, 0.32695024, 0.29943325, 0.05936479, 0.33148639, 0.15238106], [0.19836278, 0.16948865, 0.31062824, 0.34472388, 0.22569252, 0.09340941, 0.34499903, 0.17873801], [0.14217762, 0.11926862, 0.29591121, 0.2563566 , 0.26184432, 0.13986313, 0.25450008, 0.1939654 ], [0.22611781, 0.12419874, 0.25064824, 0.28406016, 0.29879834, 0.08965598, 0.29931852, 0.19970588], [0.13010286, 0.0944411 , 0.30442741, 0.30200632, 0.30301242, 0.15302657, 0.28820269, 0.17025367]], [[0.16790342, 0.26559325, 0.09578332, 0.1384534 , 0.10352752, 0.33625445, 0.14756126, 0.09944141], [0.19850746, 0.32294565, 0.17637504, 0.14517658, 0.10404784, 0.31108163, 0.12168524, 0.109143 ], [0.12095217, 0.30683033, 0.09376865, 0.11225919, 0.16952319, 0.35806856, 0.08534946, 0.04534505], [0.12914549, 0.34048898, 0.1405052 , 0.17587391, 0.17174908, 0.35901306, 0.11548703, 0.11245166], [0.15713461, 0.26940474, 0.1355091 , 0.14246194, 0.1233379 , 0.31990228, 0.09552316, 0.07793888], [0.18232423, 0.34170153, 0.1093786 , 0.13416557, 0.18658227, 0.37228804, 0.15656195, 0.04516702], [0.10877543, 0.32429256, 0.16885407, 0.16328396, 0.13835888, 0.34367515, 0.14772249, 0.09337467], [0.11175699, 0.28818726, 0.11859238, 0.14915646, 0.18465549, 0.31031134, 0.17057422, 0.13178728], [0.13835569, 0.27414977, 0.09110212, 0.20277056, 0.17878692, 0.30979969, 0.16968731, 0.1220929 ], [0.19080481, 0.32513237, 0.12283334, 0.10625419, 0.19332843, 0.28321217, 0.1388812 , 0.10656268]], [[0.24487494, 0.22926915, 0.14996355, 0.24502912, 0.25036084, 0.09624818, 0.08270539, 0.24661525], [0.24098527, 0.21603434, 0.12841328, 0.2061095 , 0.23472511, 0.11095723, 0.1399834 , 0.27276014], [0.22634203, 0.21725332, 0.11789855, 0.20681507, 0.16797908, 0.15455362, 0.13526812, 0.25611855], [0.25179804, 0.19963238, 0.08207138, 0.20798306, 0.21599281, 0.13092948, 0.11359618, 0.22868106], [0.21048092, 0.15209115, 0.07768627, 0.19841933, 0.23651151, 0.12276094, 0.15982134, 0.23222903], [0.24363776, 0.17696944, 0.09282648, 0.21532249, 0.2077663 , 0.16731572, 0.08298775, 0.21627866], [0.26191875, 0.21345795, 0.12930635, 0.20031393, 0.25777262, 0.08857851, 0.14894621, 0.27251848], [0.27112747, 0.19049768, 0.15066837, 0.18765226, 0.24109526, 0.09202483, 0.12614204, 0.2746818 ], [0.24655784, 0.23376173, 0.12263029, 0.19853208, 0.17529616, 0.13766298, 0.15579392, 0.2592124 ], [0.21593478, 0.1985557 , 0.06529558, 0.23505617, 0.2586701 , 0.11887756, 0.10672546, 0.28310867]], [[0.13546075, 0.21177116, 0.18097495, 0.28335959, 0.246092 , 0.23938562, 0.21841687, 0.13371835], [0.15773383, 0.17073648, 0.21949886, 0.2319246 , 0.23831314, 0.30636939, 0.1657013 , 0.1502996 ], [0.15295323, 0.21931884, 0.23814131, 0.30896259, 0.17871576, 0.29243144, 0.21545808, 0.17280314], [0.07740517, 0.18570131, 0.25631015, 0.25610385, 0.24330604, 0.29281625, 0.19061986, 0.12859244], [0.08065606, 0.17032819, 0.23898132, 0.2597297 , 0.22821715, 0.25206033, 0.19939583, 0.17596318], [0.09876719, 0.18142937, 0.25758094, 0.31759099, 0.15976691, 0.27043693, 0.21473406, 0.11539436], [0.1062407 , 0.22570043, 0.2508131 , 0.24152631, 0.21300072, 0.21895164, 0.1841227 , 0.1585137 ], [0.11407439, 0.1850458 , 0.26405553, 0.29562141, 0.19324622, 0.28125605, 0.17825539, 0.10910162], [0.13143708, 0.25801795, 0.26027793, 0.28619327, 0.20387125, 0.29550773, 0.17165018, 0.14219321], [0.08415036, 0.2026262 , 0.19029874, 0.25816359, 0.18039161, 0.29121309, 0.17562064, 0.1672997 ]]])
    • bob
      (x, z)
      float64
      1.1, 1.2, ..., 8.7, 8.8
      σ = 0.22, 0.3, ..., 0.31, 0.21
      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([[0.05037877, 0.09247093, 0.05387947, 0.04058386, 0.06378661, 0.0086305 , 0.05223879, 0.02351903], [0.04242474, 0.00050031, 0.01351683, 0.00975447, 0.03302091, 0.07919148, 0.05392051, 0.06757294], [0.03105401, 0.09113896, 0.09416773, 0.09207814, 0.07902188, 0.03382482, 0.01480256, 0.04314213], [0.06941926, 0.08119641, 0.02715996, 0.09890429, 0.092456 , 0.03769801, 0.06793582, 0.07270839], [0.09369024, 0.04861367, 0.08889728, 0.06205336, 0.05967507, 0.00872669, 0.06267435, 0.06854531], [0.00057827, 0.08897441, 0.07851432, 0.06037546, 0.02624816, 0.0867688 , 0.00209828, 0.07878133], [0.07548409, 0.06810872, 0.05723724, 0.05567111, 0.08875519, 0.0001808 , 0.03286223, 0.05769091], [0.01428348, 0.08723245, 0.07545137, 0.09522267, 0.05876783, 0.01941469, 0.09641863, 0.04411309]])

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 concatenate 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.concatenate(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 concatenate 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.concatenate(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
      0.27, 0.61, ..., -0.11, 0.16
      σ = 0.44, 0.45, ..., 0.42, 0.41
      Values:
      array([[[ 2.73782270e-01, 6.14348766e-01, -1.38782351e-01, 1.37491980e-01, 3.66371192e-01, -6.87604284e-01, 4.99821872e-01, -4.72803666e-01], [-1.91553794e-01, 5.22337662e-01, -2.04578007e-01, -5.77348257e-01, 5.78841428e-02, -6.98323527e-01, 3.92362492e-01, 2.68802815e-01], [ 9.55692366e-03, 2.29830109e-01, -1.65134199e-01, -3.75109077e-01, 2.62842296e-01, -7.28076120e-02, -2.07641233e-02, -1.31689531e-01], [ 7.92365510e-02, 8.01873122e-01, -1.61088851e-01, -2.67466774e-01, 7.78115533e-02, -6.68131560e-01, 1.75439796e-01, -5.50308276e-01], [ 2.37352039e-01, 6.63202484e-01, 3.61726196e-02, -5.95010870e-01, 4.66269610e-01, -4.59833406e-01, -7.19605945e-02, -5.24911918e-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], [-8.93306061e-03, 7.74541663e-01, 1.44802070e-03, 2.12717027e-01, 6.20475743e-01, -3.11186451e-01, -3.90807358e-01, -4.43802019e-01], [ 6.41308796e-01, 1.13929780e-03, -1.27344967e-01, 3.03980535e-01, -6.15489242e-02, -8.07662853e-01, 2.44434450e-01, -2.29677388e-01], [-8.55388776e-02, 5.11648138e-01, -1.24979306e-01, -2.25736838e-01, 1.79084503e-01, -7.84188987e-01, 3.02177860e-01, -1.90375314e-01], [ 5.64392967e-01, 8.01737928e-01, 4.38653456e-01, -3.47550946e-01, 4.33330028e-01, -1.52592392e-01, -3.94979178e-01, 5.71662379e-02]], [[-1.43608396e-01, -5.42468465e-01, 9.98735573e-02, 1.06952060e-01, 5.12079836e-01, -4.27504814e-01, -1.62807801e-01, -3.07515883e-01], [ 6.57556150e-01, -4.92137597e-01, 3.92896803e-04, -2.02623863e-01, -1.41731560e-01, -4.44541357e-01, -1.36004713e-01, 5.45522499e-02], [ 2.51261925e-01, 4.91094261e-02, -4.27219033e-01, -7.40586734e-01, -3.85959594e-01, -2.79067259e-02, 2.34813917e-01, -7.57797122e-01], [ 3.63321696e-01, 2.95106616e-01, -3.95736092e-01, -5.13519607e-01, 2.24174193e-01, 6.55389758e-02, 4.91169572e-01, -2.21943225e-02], [ 4.76181483e-01, 2.84086651e-01, -1.33010483e-01, -7.07086964e-01, 1.85219989e-01, 1.00482439e-01, 1.00704416e-01, 1.50953971e-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], [-2.57580107e-01, 1.56834851e-01, -5.76960414e-01, 1.14936369e-01, 1.85279077e-01, -5.39027106e-01, 2.89940114e-01, -9.22384014e-01], [ 6.25539987e-01, -5.58940647e-01, -7.44332839e-01, 2.42619050e-02, -3.96711057e-02, -5.88526212e-01, -2.86044526e-01, -4.41561098e-01], [ 4.95743587e-01, 2.77614366e-01, -7.14301777e-01, -4.55987367e-01, -1.11673773e-01, -6.91161614e-02, 2.76997613e-01, -9.20441868e-01], [ 3.37201225e-01, -2.91991428e-01, -3.86016766e-01, -3.84096946e-01, 3.17037857e-01, -9.05247575e-02, 3.47550963e-01, -1.19299476e-01]], [[ 1.97364009e-01, -5.56344298e-01, 2.20437838e-01, -6.99527519e-02, 2.04942392e-01, -4.22026455e-01, 2.92425605e-01, -1.05172159e-01], [ 4.55001522e-01, -3.04549984e-01, 7.51329655e-02, 1.51106436e-02, 3.47858041e-01, -7.50587900e-02, 5.00588249e-01, -6.47924987e-02], [ 7.18890201e-01, -6.69778371e-01, 2.50234459e-01, -4.36827157e-01, 1.82989388e-01, -4.59423134e-01, -8.97884321e-03, -6.61484616e-01], [ 6.64770018e-01, -1.86952553e-01, 3.32789373e-01, -2.59009528e-01, 4.94740898e-01, -3.87334508e-01, 8.71891674e-01, -5.51879459e-01], [-1.20744130e-01, -1.59250356e-01, 5.66304680e-01, 3.03390643e-01, 3.79971946e-01, 5.34073909e-02, 4.86801063e-01, -3.69560550e-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], [ 2.54237389e-01, -2.31552179e-01, 6.88459749e-01, -4.95235329e-01, 5.21277398e-01, -5.04053934e-01, 6.78997263e-01, -4.59844748e-01], [-4.87459706e-02, -8.44537912e-01, 2.92245205e-01, -4.20752669e-01, -1.14505636e-01, -5.19776316e-02, -5.99556660e-02, -2.21375434e-01], [ 6.31143559e-01, -3.90136604e-01, 6.27165311e-01, -1.89142629e-01, 1.65038714e-01, 1.32594788e-01, 6.11078141e-01, -2.28305031e-01], [ 5.93380731e-01, -5.89135608e-01, 3.77921682e-01, 7.80330033e-02, 3.30870331e-01, -4.07818448e-01, 8.62061791e-01, -7.07023106e-01]], [[-5.09476010e-01, 3.99847670e-01, -4.12955988e-01, 7.15674126e-01, -6.61608237e-01, 3.26642168e-01, -4.88003586e-01, -6.54539693e-01], [-8.18824411e-01, -3.40995712e-01, -5.63626924e-01, 8.89205880e-01, 6.84255171e-02, -3.91986622e-01, -4.79496615e-01, -3.87929367e-01], [-4.30967877e-01, -4.10472134e-01, -3.00316054e-01, 6.40868454e-01, 3.29054883e-01, -5.28613226e-01, -1.52643267e-01, -8.94916965e-01], [-7.51422866e-01, 3.81865942e-01, -1.89069584e-01, 8.97322488e-01, 2.31645191e-01, 6.74773169e-02, 3.37431240e-01, -1.73990086e-01], [-7.02654155e-01, 3.95050274e-01, -9.24426398e-01, 4.94828020e-01, -3.76823312e-01, -4.26946508e-01, -2.46023578e-01, -2.02134859e-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], [-7.24872245e-01, 2.81539627e-01, -2.52003605e-01, -1.90775792e-02, -6.20152762e-01, -7.86337672e-02, -2.48649556e-01, -7.16341597e-01], [-4.98489558e-01, 7.96970920e-02, -6.46296817e-02, 1.97099452e-01, 3.73073413e-02, 1.62039243e-01, -5.03251302e-01, -1.24759125e-03], [-6.70868633e-01, -3.83695116e-01, -7.85523762e-01, 4.55699015e-01, 3.03943856e-01, 1.79206349e-02, -5.37083226e-01, -2.43813186e-01], [-5.62040754e-01, -1.36202347e-01, -4.96502744e-01, 2.95498428e-01, -5.20906300e-02, 5.12597238e-02, 2.67553734e-01, -4.12688373e-01]], [[-6.36386611e-01, 6.97001503e-01, 2.31423488e-02, -4.90767536e-01, 6.90968199e-01, 6.44544352e-01, 2.95451458e-01, 3.77988096e-01], [-3.43947897e-01, 6.33716470e-01, -1.50468784e-01, -5.29987423e-01, 6.95946517e-01, 6.13803236e-01, -1.80500561e-01, 5.01249087e-01], [-6.01300811e-01, -1.61037042e-03, -2.54157018e-01, -3.27226306e-01, 1.63212303e-01, 4.13847013e-01, -3.27206640e-01, 3.18690780e-03], [-6.17369071e-01, 2.50368445e-01, -3.00713223e-01, -2.45215148e-01, 5.09082154e-01, 1.23556607e-01, 3.05401779e-02, -1.36980509e-01], [-7.84431760e-01, 6.79722192e-01, -5.47292470e-01, 1.92473006e-01, 4.40012568e-01, 2.19006021e-01, 2.32286434e-02, 2.84849033e-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], [-8.64085271e-01, 2.78445664e-01, -4.56377453e-03, 2.13683246e-01, 5.14553449e-01, 4.27322796e-01, 1.84324555e-01, -1.97120232e-01], [-8.32512068e-01, 5.93438418e-01, -2.89097577e-01, -6.97802920e-01, 8.54044588e-02, 8.49486123e-02, -5.41434220e-01, 4.03989144e-01], [-6.33767757e-01, 2.72138338e-01, -8.16584696e-01, -6.02636832e-01, 4.78343589e-01, 5.73780405e-01, -1.48139326e-01, -3.22509706e-01], [-4.08891687e-01, 3.99458576e-01, -7.96164307e-01, -4.63592121e-01, 2.30772475e-01, 5.68277994e-02, 2.70107437e-01, -3.91978741e-01]], [[ 1.35674657e-01, -1.73792135e-02, -1.13401460e-01, 2.74927955e-01, -8.49895118e-02, 8.58902573e-01, -3.69979642e-01, 6.09404852e-01], [-2.98976639e-01, -4.68246596e-01, -6.14643104e-01, 1.22961257e-01, 1.71382772e-02, 7.97195321e-01, -3.38029991e-01, 3.38449449e-01], [-1.51052704e-01, -1.53340124e-01, -6.20664592e-01, 3.12563987e-01, -2.76704992e-01, 5.20487709e-01, -8.51273737e-01, -9.13673707e-02], [-2.21758889e-01, 2.95652458e-01, -4.78161151e-01, 9.09541881e-03, -4.91129748e-01, 9.81183386e-01, -6.20057511e-01, -1.26772727e-01], [-7.70238411e-01, -3.18450460e-01, -6.52956336e-01, 4.86702948e-02, -7.05677320e-01, 2.09363514e-01, -3.86737979e-01, 4.25424836e-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], [-1.12755645e-01, -3.41679776e-01, -6.99007743e-01, -3.15168539e-02, 7.95787867e-02, 9.11142927e-02, -3.39276233e-01, 3.89512699e-01], [-4.97178865e-01, -2.36876696e-01, -6.06315091e-01, 2.93760078e-01, -1.47771454e-01, 5.86210723e-01, 6.75466814e-03, 7.98300973e-02], [-5.19469604e-01, -2.36798835e-01, 1.41185901e-01, 1.37367846e-01, -1.75460873e-01, 9.06284034e-02, -1.33567699e-01, -1.82867537e-01], [ 1.26496985e-01, -2.22396326e-01, -6.03778647e-01, 4.90346190e-01, -4.57670334e-02, 3.68901291e-01, -3.35218842e-01, 5.14809044e-01]], [[-2.08778243e-01, 3.86083085e-01, 5.04055336e-01, -1.91149117e-01, 2.67008878e-01, 1.48084554e-01, 3.72519663e-01, -4.45114995e-04], [-5.29972685e-01, 3.22103548e-01, -1.56405056e-01, 6.15021734e-01, 4.13294487e-01, 8.08975151e-01, 7.07683682e-01, 8.68937648e-02], [-4.61925349e-01, 9.91355659e-02, -3.63675213e-01, 4.01962293e-01, 1.06070832e-02, 1.34061704e-01, 3.75190729e-01, 3.22259777e-01], [-5.81091025e-01, 8.57577607e-03, -1.74119728e-02, -1.20757470e-01, 1.08466432e-01, 1.87725694e-02, -3.46326290e-02, -9.83046195e-02], [-1.03103089e-01, 5.54979256e-02, -1.56190290e-01, 7.13265435e-01, 6.75165742e-02, 3.93502021e-01, 9.02108394e-01, -1.68264317e-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], [-4.53974534e-01, -8.09482899e-02, -4.14042640e-02, 3.22927511e-01, -2.65528350e-01, 2.35793879e-01, 6.88782796e-01, -3.98489946e-01], [ 3.00612361e-01, 7.21131044e-01, -7.73108903e-02, 9.41697444e-02, -1.31601812e-01, 5.06195461e-01, 1.03344563e-02, -1.83650061e-02], [ 3.52189999e-01, 3.10305703e-01, -1.48403605e-01, 3.94019100e-02, -6.72628482e-02, -3.88116763e-02, 5.35390934e-01, 1.02625984e-02], [ 2.48732347e-01, 6.11139096e-01, 3.56470284e-01, 1.86255379e-01, -4.49759911e-01, 1.67210423e-02, 7.76853237e-01, 2.20346669e-01]], [[ 3.32823189e-01, -7.83403404e-01, 2.14563435e-02, -1.09284848e-01, 8.28271879e-03, -1.89468315e-02, -3.77458674e-01, 1.26372726e-01], [ 2.61444281e-01, -6.35016977e-02, 3.29945049e-01, 2.23495615e-01, -4.39294118e-01, 7.81778749e-01, -4.69043771e-01, 2.20301185e-01], [ 3.61245695e-01, -7.51556105e-01, 8.47139473e-01, -2.61482397e-01, 2.81992639e-01, 8.19280277e-01, 2.09725837e-01, 5.16169528e-01], [-7.39793333e-02, -4.60677853e-01, 1.49167342e-01, -5.45314327e-02, -1.25484243e-02, 5.25947578e-01, -6.55419415e-02, 3.21251191e-01], [ 2.35282352e-01, -5.89429671e-02, 3.73396671e-01, 2.82905411e-01, -4.57268714e-01, 1.96680267e-02, 3.09550238e-01, 4.29339080e-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], [ 4.89903052e-01, -3.26249203e-01, 6.06100784e-01, 3.75439473e-01, 8.36405453e-02, 3.99497478e-01, 1.98155969e-01, 7.55096761e-01], [-2.49668591e-02, -2.63315295e-01, 2.47717332e-01, 1.03776450e-01, 2.68849618e-01, -1.45965766e-01, -4.49985010e-01, 2.20831347e-01], [ 8.56473086e-02, 2.63839454e-02, 1.26304766e-01, 2.47978412e-01, -1.10245549e-01, 4.37930613e-01, -5.64424539e-02, 6.94742287e-03], [ 4.56399847e-01, -6.23620462e-01, 2.74528561e-01, -1.73609702e-01, 7.55940525e-02, 2.29738425e-01, -1.09766071e-01, 1.61498679e-01]]])

      Variances (σ²):
      array([[[0.19188634, 0.20598272, 0.16895745, 0.1539002 , 0.2791979 , 0.10785508, 0.25002353, 0.13239592], [0.19744499, 0.20047573, 0.15780919, 0.2173773 , 0.33336846, 0.1419317 , 0.24026499, 0.08012556], [0.12118947, 0.12882987, 0.10998823, 0.18487285, 0.24604924, 0.12346017, 0.17215554, 0.09015553], [0.17002682, 0.16671443, 0.10318334, 0.2427618 , 0.27800766, 0.16611741, 0.17178389, 0.11537865], [0.16507247, 0.17341866, 0.10936307, 0.23484405, 0.31765248, 0.19525476, 0.21316516, 0.13132737], [0.12269236, 0.13299738, 0.12608618, 0.16649726, 0.30176743, 0.19315369, 0.17523878, 0.04841813], [0.21110552, 0.12373249, 0.14695408, 0.23540771, 0.31976898, 0.14807036, 0.18002197, 0.11984542], [0.14839467, 0.15974404, 0.13944435, 0.23224191, 0.33374744, 0.11209318, 0.19816299, 0.07794084], [0.1172094 , 0.17713096, 0.1184634 , 0.22325931, 0.29716557, 0.12125195, 0.19404995, 0.07470003], [0.16343665, 0.15476861, 0.11473554, 0.22040036, 0.29908272, 0.13061691, 0.17818863, 0.06872043]], [[0.2530018 , 0.07737781, 0.22038431, 0.26200225, 0.15194895, 0.25017267, 0.22833105, 0.29862126], [0.25537726, 0.1095732 , 0.27181948, 0.19494369, 0.13563817, 0.24415453, 0.22199169, 0.23526325], [0.33275572, 0.05931259, 0.28870334, 0.22152554, 0.15680701, 0.28833649, 0.21796993, 0.23545336], [0.33740875, 0.09739075, 0.3070476 , 0.25095269, 0.22475532, 0.2547037 , 0.19510307, 0.24934799], [0.25780211, 0.07063069, 0.23181902, 0.25733982, 0.16827402, 0.30715568, 0.18994578, 0.23180139], [0.31226291, 0.11065108, 0.24884617, 0.18630366, 0.16473734, 0.26788134, 0.20442996, 0.26713556], [0.31764239, 0.07481417, 0.24831926, 0.25783863, 0.20271204, 0.3072918 , 0.25150921, 0.23879198], [0.27271722, 0.10366427, 0.31283755, 0.27051964, 0.17852544, 0.31880961, 0.26892827, 0.27559183], [0.33244242, 0.07642424, 0.24461309, 0.22658416, 0.15250579, 0.30633903, 0.19907098, 0.30269132], [0.31775877, 0.09204518, 0.23716113, 0.19387104, 0.23084913, 0.31690982, 0.21680949, 0.25920081]], [[0.14186494, 0.0534135 , 0.23332246, 0.17992431, 0.26293578, 0.22971953, 0.23415433, 0.25024144], [0.13172497, 0.07004482, 0.24690738, 0.20316831, 0.1813727 , 0.23640088, 0.1615023 , 0.24505816], [0.21146239, 0.07311147, 0.22582991, 0.23054583, 0.19066684, 0.2884372 , 0.18637579, 0.23698841], [0.14390762, 0.11146208, 0.24479223, 0.17062891, 0.23982409, 0.22633214, 0.21262964, 0.27329498], [0.140144 , 0.14765089, 0.25601247, 0.15411077, 0.26556404, 0.2300284 , 0.20023465, 0.27720078], [0.1465522 , 0.0725423 , 0.23325861, 0.21661206, 0.1821771 , 0.25987053, 0.18150172, 0.21711071], [0.18871164, 0.13001054, 0.23455088, 0.19619602, 0.26561116, 0.2691233 , 0.20348331, 0.27835313], [0.17156864, 0.07877527, 0.22989243, 0.22256563, 0.22595738, 0.29136851, 0.21850961, 0.23630975], [0.19140938, 0.07427525, 0.2276503 , 0.15315049, 0.1928711 , 0.27207752, 0.21743917, 0.22262814], [0.19072601, 0.1444192 , 0.30445195, 0.1443563 , 0.23604139, 0.24761041, 0.1656572 , 0.215988 ]], [[0.17446459, 0.19700656, 0.24150087, 0.27760638, 0.17312918, 0.2527794 , 0.19126193, 0.27271252], [0.23498895, 0.20284841, 0.25453111, 0.32283093, 0.18557648, 0.21286825, 0.20851838, 0.25261218], [0.23150061, 0.1131887 , 0.26705274, 0.24327495, 0.19787092, 0.23769577, 0.25602541, 0.19494017], [0.23073268, 0.16719355, 0.30444324, 0.24419536, 0.23438742, 0.17442383, 0.24823022, 0.26327588], [0.23118049, 0.15851767, 0.25340653, 0.32766001, 0.22044029, 0.19871019, 0.1848886 , 0.27071804], [0.22172016, 0.20498686, 0.29730043, 0.27875127, 0.19842288, 0.20510694, 0.22346225, 0.1985373 ], [0.245215 , 0.151424 , 0.33664438, 0.25779499, 0.17404007, 0.17441316, 0.26512856, 0.22883479], [0.18546056, 0.1970587 , 0.28765568, 0.28841497, 0.22223773, 0.21658546, 0.2664435 , 0.23288513], [0.16941476, 0.13529595, 0.24487913, 0.27184341, 0.21282758, 0.24866159, 0.25380514, 0.22041514], [0.21130474, 0.16627758, 0.30218908, 0.30078348, 0.17572626, 0.24912792, 0.23673059, 0.19760159]], [[0.17787986, 0.14836966, 0.26857008, 0.33296219, 0.3054913 , 0.15178021, 0.28446777, 0.22859955], [0.13691279, 0.08178841, 0.28543644, 0.25860046, 0.2981164 , 0.11337396, 0.31938349, 0.16835839], [0.15598573, 0.13124081, 0.27700754, 0.27581769, 0.3042954 , 0.1080089 , 0.27616517, 0.16803819], [0.17987912, 0.08724426, 0.27006559, 0.29883428, 0.25843817, 0.08986573, 0.26277525, 0.22514512], [0.1306872 , 0.14701714, 0.3092107 , 0.30511153, 0.21081129, 0.15538056, 0.32063705, 0.1733711 ], [0.12916157, 0.07937647, 0.29040676, 0.32695024, 0.29943325, 0.05936479, 0.33148639, 0.15238106], [0.19836278, 0.16948865, 0.31062824, 0.34472388, 0.22569252, 0.09340941, 0.34499903, 0.17873801], [0.14217762, 0.11926862, 0.29591121, 0.2563566 , 0.26184432, 0.13986313, 0.25450008, 0.1939654 ], [0.22611781, 0.12419874, 0.25064824, 0.28406016, 0.29879834, 0.08965598, 0.29931852, 0.19970588], [0.13010286, 0.0944411 , 0.30442741, 0.30200632, 0.30301242, 0.15302657, 0.28820269, 0.17025367]], [[0.16790342, 0.26559325, 0.09578332, 0.1384534 , 0.10352752, 0.33625445, 0.14756126, 0.09944141], [0.19850746, 0.32294565, 0.17637504, 0.14517658, 0.10404784, 0.31108163, 0.12168524, 0.109143 ], [0.12095217, 0.30683033, 0.09376865, 0.11225919, 0.16952319, 0.35806856, 0.08534946, 0.04534505], [0.12914549, 0.34048898, 0.1405052 , 0.17587391, 0.17174908, 0.35901306, 0.11548703, 0.11245166], [0.15713461, 0.26940474, 0.1355091 , 0.14246194, 0.1233379 , 0.31990228, 0.09552316, 0.07793888], [0.18232423, 0.34170153, 0.1093786 , 0.13416557, 0.18658227, 0.37228804, 0.15656195, 0.04516702], [0.10877543, 0.32429256, 0.16885407, 0.16328396, 0.13835888, 0.34367515, 0.14772249, 0.09337467], [0.11175699, 0.28818726, 0.11859238, 0.14915646, 0.18465549, 0.31031134, 0.17057422, 0.13178728], [0.13835569, 0.27414977, 0.09110212, 0.20277056, 0.17878692, 0.30979969, 0.16968731, 0.1220929 ], [0.19080481, 0.32513237, 0.12283334, 0.10625419, 0.19332843, 0.28321217, 0.1388812 , 0.10656268]], [[0.24487494, 0.22926915, 0.14996355, 0.24502912, 0.25036084, 0.09624818, 0.08270539, 0.24661525], [0.24098527, 0.21603434, 0.12841328, 0.2061095 , 0.23472511, 0.11095723, 0.1399834 , 0.27276014], [0.22634203, 0.21725332, 0.11789855, 0.20681507, 0.16797908, 0.15455362, 0.13526812, 0.25611855], [0.25179804, 0.19963238, 0.08207138, 0.20798306, 0.21599281, 0.13092948, 0.11359618, 0.22868106], [0.21048092, 0.15209115, 0.07768627, 0.19841933, 0.23651151, 0.12276094, 0.15982134, 0.23222903], [0.24363776, 0.17696944, 0.09282648, 0.21532249, 0.2077663 , 0.16731572, 0.08298775, 0.21627866], [0.26191875, 0.21345795, 0.12930635, 0.20031393, 0.25777262, 0.08857851, 0.14894621, 0.27251848], [0.27112747, 0.19049768, 0.15066837, 0.18765226, 0.24109526, 0.09202483, 0.12614204, 0.2746818 ], [0.24655784, 0.23376173, 0.12263029, 0.19853208, 0.17529616, 0.13766298, 0.15579392, 0.2592124 ], [0.21593478, 0.1985557 , 0.06529558, 0.23505617, 0.2586701 , 0.11887756, 0.10672546, 0.28310867]], [[0.13546075, 0.21177116, 0.18097495, 0.28335959, 0.246092 , 0.23938562, 0.21841687, 0.13371835], [0.15773383, 0.17073648, 0.21949886, 0.2319246 , 0.23831314, 0.30636939, 0.1657013 , 0.1502996 ], [0.15295323, 0.21931884, 0.23814131, 0.30896259, 0.17871576, 0.29243144, 0.21545808, 0.17280314], [0.07740517, 0.18570131, 0.25631015, 0.25610385, 0.24330604, 0.29281625, 0.19061986, 0.12859244], [0.08065606, 0.17032819, 0.23898132, 0.2597297 , 0.22821715, 0.25206033, 0.19939583, 0.17596318], [0.09876719, 0.18142937, 0.25758094, 0.31759099, 0.15976691, 0.27043693, 0.21473406, 0.11539436], [0.1062407 , 0.22570043, 0.2508131 , 0.24152631, 0.21300072, 0.21895164, 0.1841227 , 0.1585137 ], [0.11407439, 0.1850458 , 0.26405553, 0.29562141, 0.19324622, 0.28125605, 0.17825539, 0.10910162], [0.13143708, 0.25801795, 0.26027793, 0.28619327, 0.20387125, 0.29550773, 0.17165018, 0.14219321], [0.08415036, 0.2026262 , 0.19029874, 0.25816359, 0.18039161, 0.29121309, 0.17562064, 0.1672997 ]]])
    • bob
      (x, z)
      float64
      counts
      1.1, 1.2, ..., 8.7, 8.8
      σ = 0.22, 0.3, ..., 0.31, 0.21
      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([[0.05037877, 0.09247093, 0.05387947, 0.04058386, 0.06378661, 0.0086305 , 0.05223879, 0.02351903], [0.04242474, 0.00050031, 0.01351683, 0.00975447, 0.03302091, 0.07919148, 0.05392051, 0.06757294], [0.03105401, 0.09113896, 0.09416773, 0.09207814, 0.07902188, 0.03382482, 0.01480256, 0.04314213], [0.06941926, 0.08119641, 0.02715996, 0.09890429, 0.092456 , 0.03769801, 0.06793582, 0.07270839], [0.09369024, 0.04861367, 0.08889728, 0.06205336, 0.05967507, 0.00872669, 0.06267435, 0.06854531], [0.00057827, 0.08897441, 0.07851432, 0.06037546, 0.02624816, 0.0867688 , 0.00209828, 0.07878133], [0.07548409, 0.06810872, 0.05723724, 0.05567111, 0.08875519, 0.0001808 , 0.03286223, 0.05769091], [0.01428348, 0.08723245, 0.07545137, 0.09522267, 0.05876783, 0.01941469, 0.09641863, 0.04411309]])

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
      0.89, -0.0, ..., 0.31, 0.05
      σ = 0.63, 0.57, ..., 0.69, 0.59
      Values:
      array([[[ 8.88131036e-01, -1.29037090e-03, -3.21233092e-01, 2.70182065e-02], [ 3.30783868e-01, -7.81926264e-01, -6.40439385e-01, 6.61165306e-01], [ 2.39387033e-01, -5.40243275e-01, 1.90034684e-01, -1.52453654e-01], [ 8.81109673e-01, -4.28555625e-01, -5.90320007e-01, -3.74868480e-01], [ 9.00554522e-01, -5.58838250e-01, 6.43620414e-03, -5.96872512e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [ 7.65608602e-01, 2.14165048e-01, 3.09289292e-01, -8.34609378e-01], [ 6.42448094e-01, 1.76635569e-01, -8.69211777e-01, 1.47570617e-02], [ 4.26109261e-01, -3.50716144e-01, -6.05104484e-01, 1.11802546e-01], [ 1.36613090e+00, 9.11025104e-02, 2.80737636e-01, -3.37812940e-01]], [[-6.86076862e-01, 2.06825618e-01, 8.45750216e-02, -4.70323684e-01], [ 1.65418553e-01, -2.02230966e-01, -5.86272916e-01, -8.14524628e-02], [ 3.00371351e-01, -1.16780577e+00, -4.13866319e-01, -5.22983205e-01], [ 6.58428312e-01, -9.09255699e-01, 2.89713168e-01, 4.68975250e-01], [ 7.60268134e-01, -8.40097447e-01, 2.85702428e-01, 1.15799813e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [-1.00745256e-01, -4.62024045e-01, -3.53748029e-01, -6.32443899e-01], [ 6.65993404e-02, -7.20070934e-01, -6.28197318e-01, -7.27605624e-01], [ 7.73357953e-01, -1.17028914e+00, -1.80789935e-01, -6.43444255e-01], [ 4.52097970e-02, -7.70113711e-01, 2.26513099e-01, 2.28251487e-01]], [[-3.58980290e-01, 1.50485086e-01, -2.17084063e-01, 1.87253447e-01], [ 1.50451538e-01, 9.02436091e-02, 2.72799251e-01, 4.35795750e-01], [ 4.91118304e-02, -1.86592698e-01, -2.76433746e-01, -6.70463459e-01], [ 4.77817465e-01, 7.37798449e-02, 1.07406390e-01, 3.20012215e-01], [-2.79994487e-01, 8.69695323e-01, 4.33379337e-01, 1.17240512e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [ 2.26852099e-02, 1.93224420e-01, 1.72234637e-02, 2.19152515e-01], [-8.93283883e-01, -1.28507464e-01, -1.66483268e-01, -2.81331100e-01], [ 2.41006955e-01, 4.38022682e-01, 2.97633502e-01, 3.82773111e-01], [ 4.24512292e-03, 4.55954686e-01, -7.69481171e-02, 1.55038684e-01]], [[-1.09628340e-01, 3.02718138e-01, -3.34966069e-01, -1.14254328e+00], [-1.15982012e+00, 3.25578955e-01, -3.23561105e-01, -8.67425983e-01], [-8.41440011e-01, 3.40552400e-01, -1.99558344e-01, -1.04756023e+00], [-3.69556924e-01, 7.08252904e-01, 2.99122507e-01, 1.63441154e-01], [-3.07603880e-01, -4.29598378e-01, -8.03769820e-01, -2.66237064e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [-4.43332618e-01, -2.71081184e-01, -6.98786529e-01, -9.64991153e-01], [-4.18792466e-01, 1.32469770e-01, 1.99346584e-01, -5.04498893e-01], [-1.05456375e+00, -3.29824747e-01, 3.21864491e-01, -7.80896412e-01], [-6.98243100e-01, -2.01004317e-01, -8.30906168e-04, -1.45134640e-01]], [[ 6.06148926e-02, -4.67625187e-01, 1.33551255e+00, 6.73439554e-01], [ 2.89768573e-01, -6.80456206e-01, 1.30974975e+00, 3.20748526e-01], [-6.02911181e-01, -5.81383323e-01, 5.77059316e-01, -3.24019732e-01], [-3.67000625e-01, -5.45928371e-01, 6.32638761e-01, -1.06440331e-01], [-1.04709568e-01, -3.54819463e-01, 6.59018590e-01, 3.08077676e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [-5.85639607e-01, 2.09119471e-01, 9.41876245e-01, -1.27956774e-02], [-2.39073651e-01, -9.86900497e-01, 1.70353071e-01, -1.37445076e-01], [-3.61629419e-01, -1.41922153e+00, 1.05212399e+00, -4.70649032e-01], [-9.43311161e-03, -1.25975643e+00, 2.87600274e-01, -1.21871303e-01]], [[ 1.18295443e-01, 1.61526496e-01, 7.73913062e-01, 2.39425209e-01], [-7.67223235e-01, -4.91681847e-01, 8.14333599e-01, 4.19458094e-04], [-3.04392828e-01, -3.08100606e-01, 2.43782717e-01, -9.42641108e-01], [ 7.38935691e-02, -4.69065732e-01, 4.90053638e-01, -7.46830238e-01], [-1.08868887e+00, -6.04286041e-01, -4.96313805e-01, 3.86868567e-02], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [-4.54435422e-01, -7.30524597e-01, 1.70693079e-01, 5.02364666e-02], [-7.34055561e-01, -3.12555014e-01, 4.38439269e-01, 8.65847655e-02], [-7.56268440e-01, 2.78553747e-01, -8.48324698e-02, -3.16435236e-01], [-9.58993412e-02, -1.13432456e-01, 3.23134257e-01, 1.79590202e-01]], [[ 1.77304842e-01, 3.12906220e-01, 4.15093432e-01, 3.72074548e-01], [-2.07869137e-01, 4.58616678e-01, 1.22226964e+00, 7.94577447e-01], [-3.62789784e-01, 3.82870806e-02, 1.44668788e-01, 6.97450506e-01], [-5.72515249e-01, -1.38169443e-01, 1.27239002e-01, -1.32937248e-01], [-4.76051637e-02, 5.57075144e-01, 4.61018595e-01, 7.33844077e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [-5.34922824e-01, 2.81523247e-01, -2.97344703e-02, 2.90292850e-01], [ 1.02174341e+00, 1.68588540e-02, 3.74593650e-01, -8.03054979e-03], [ 6.62495702e-01, -1.09001695e-01, -1.06074524e-01, 5.45653532e-01], [ 8.59871443e-01, 5.42725663e-01, -4.33038869e-01, 9.97199906e-01]], [[-4.50580215e-01, -8.78285041e-02, -1.06641127e-02, -2.51085948e-01], [ 1.97942583e-01, 5.53440665e-01, 3.42484631e-01, -2.48742586e-01], [-3.90310410e-01, 5.85657076e-01, 1.10127292e+00, 7.25895365e-01], [-5.34657186e-01, 9.46359095e-02, 5.13399153e-01, 2.55709250e-01], [ 1.76339385e-01, 6.56302082e-01, -4.37600687e-01, 7.38889318e-01], [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00], [ 1.63653849e-01, 9.81540257e-01, 4.83138024e-01, 9.53252729e-01], [-2.88282154e-01, 3.51493782e-01, 1.22883852e-01, -2.29153663e-01], [ 1.12031254e-01, 3.74283178e-01, 3.27685065e-01, -4.94950310e-02], [-1.67220615e-01, 1.00918859e-01, 3.05332478e-01, 5.17326072e-02]]])

      Variances (σ²):
      array([[[0.39786906, 0.32285765, 0.38705298, 0.38241945], [0.39792073, 0.37518649, 0.47530016, 0.32039055], [0.25001934, 0.29486108, 0.36950941, 0.26231107], [0.33674124, 0.34594514, 0.44412507, 0.28716254], [0.33849114, 0.34420713, 0.51290724, 0.34449253], [0.25568975, 0.29258344, 0.49492112, 0.2236569 ], [0.33483802, 0.3823618 , 0.46783934, 0.29986739], [0.30813871, 0.37168626, 0.44584062, 0.27610383], [0.29434036, 0.34172271, 0.41841753, 0.26874999], [0.31820526, 0.3351359 , 0.42969962, 0.24690906]], [[0.33037961, 0.48238655, 0.40212162, 0.52695231], [0.36495046, 0.46676318, 0.3797927 , 0.45725494], [0.39206831, 0.51022887, 0.4451435 , 0.45342329], [0.4347995 , 0.5580003 , 0.47945902, 0.44445106], [0.3284328 , 0.48915884, 0.47542971, 0.42174717], [0.42291399, 0.43514983, 0.43261868, 0.47156552], [0.39245656, 0.50615789, 0.51000384, 0.49030119], [0.37638149, 0.58335719, 0.49733505, 0.5445201 ], [0.40886666, 0.47119725, 0.45884482, 0.5017623 ], [0.40980395, 0.43103218, 0.54775895, 0.47601029]], [[0.19527844, 0.41324677, 0.49265531, 0.48439577], [0.20176979, 0.45007569, 0.41777358, 0.40656046], [0.28457386, 0.45637574, 0.47910405, 0.4233642 ], [0.2553697 , 0.41542114, 0.46615623, 0.48592462], [0.2877949 , 0.41012325, 0.49559244, 0.47743542], [0.2190945 , 0.44987067, 0.44204763, 0.39861243], [0.31872219, 0.4307469 , 0.53473446, 0.48183645], [0.2503439 , 0.45245806, 0.51732589, 0.45481936], [0.26568463, 0.38080079, 0.46494863, 0.44006731], [0.33514521, 0.44880824, 0.4836518 , 0.38164521]], [[0.37147115, 0.51910725, 0.42590858, 0.46397445], [0.43783736, 0.57736203, 0.39844474, 0.46113057], [0.34468931, 0.51032769, 0.43556669, 0.45096558], [0.39792623, 0.54863861, 0.40881125, 0.5115061 ], [0.38969816, 0.58106654, 0.41915048, 0.45560664], [0.42670702, 0.5760517 , 0.40352982, 0.42199955], [0.396639 , 0.59443937, 0.34845324, 0.49396334], [0.38251926, 0.57607065, 0.43882319, 0.49932863], [0.30471071, 0.51672253, 0.46148917, 0.47422027], [0.37758232, 0.60297256, 0.42485418, 0.43433219]], [[0.32624952, 0.60153227, 0.45727151, 0.51306732], [0.2187012 , 0.5440369 , 0.41149036, 0.48774188], [0.28722654, 0.55282523, 0.41230429, 0.44420336], [0.26712338, 0.56889987, 0.3483039 , 0.48792037], [0.27770434, 0.61432223, 0.36619184, 0.49400815], [0.20853804, 0.617357 , 0.35879804, 0.48386745], [0.36785143, 0.65535212, 0.31910193, 0.52373704], [0.26144625, 0.55226781, 0.40170744, 0.44846547], [0.35031655, 0.5347084 , 0.38845432, 0.4990244 ], [0.22454396, 0.60643373, 0.45603899, 0.45845636]], [[0.43349667, 0.23423672, 0.43978197, 0.24700267], [0.52145311, 0.32155162, 0.41512948, 0.23082823], [0.42778249, 0.20602784, 0.52759175, 0.13069451], [0.46963447, 0.31637912, 0.53076214, 0.22793869], [0.42653935, 0.27797104, 0.44324018, 0.17346204], [0.52402575, 0.24354417, 0.55887031, 0.20172897], [0.43306799, 0.33213802, 0.48203403, 0.24109716], [0.39994425, 0.26774884, 0.49496683, 0.3023615 ], [0.41250546, 0.29387268, 0.48858661, 0.29178021], [0.51593718, 0.22908753, 0.47654061, 0.24544387]], [[0.47414409, 0.39499267, 0.34660903, 0.32932065], [0.45701962, 0.33452278, 0.34568234, 0.41274354], [0.44359535, 0.32471362, 0.3225327 , 0.39138667], [0.45143042, 0.29005444, 0.34692229, 0.34227724], [0.36257207, 0.27610561, 0.35927244, 0.39205037], [0.4206072 , 0.30814898, 0.37508203, 0.29926641], [0.4753767 , 0.32962029, 0.34635113, 0.42146469], [0.46162515, 0.33832063, 0.33312009, 0.40082384], [0.48031957, 0.32116238, 0.31295914, 0.41500632], [0.41449048, 0.30035176, 0.37754766, 0.38983413]], [[0.34723191, 0.46433454, 0.48547763, 0.35213522], [0.32847031, 0.45142346, 0.54468253, 0.3160009 ], [0.37227206, 0.5471039 , 0.47114719, 0.38826122], [0.26310648, 0.51241399, 0.53612229, 0.3192123 ], [0.25098425, 0.49871102, 0.48027747, 0.37535901], [0.28019656, 0.57517194, 0.43020384, 0.33012842], [0.33194114, 0.49233941, 0.43195236, 0.34263641], [0.29912019, 0.55967694, 0.47450227, 0.28735702], [0.38945504, 0.5464712 , 0.49937897, 0.31384339], [0.28677656, 0.44846233, 0.4716047 , 0.34292034]]])
    • bob
      (x, z)
      float64
      counts
      3.2, 3.4, ..., 16.4, 16.6
      σ = 0.3, 0.3, ..., 0.36, 0.32
      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([[0.09280351, 0.09297124, 0.06739631, 0.05033833, 0.09680752, 0.08782198, 0.1061593 , 0.09109196], [0.10047327, 0.17233538, 0.12132769, 0.19098244, 0.17147789, 0.07152283, 0.08273838, 0.11585052], [0.09426851, 0.13758808, 0.1674116 , 0.12242882, 0.08592324, 0.0954955 , 0.06477263, 0.14732664], [0.08976756, 0.15534117, 0.13268861, 0.15089378, 0.14752302, 0.01959549, 0.12928085, 0.101804 ]])

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([[[ 7.75894043e-01, -1.29037055e-03, -3.15736816e-01,
          2.70149195e-02],
        [ 3.24784501e-01, -7.04647521e-01, -5.97547812e-01,
          6.14037018e-01],
        [ 2.37107184e-01, -5.14344636e-01,  1.88892955e-01,
         -1.51863782e-01],
        [ 7.71445434e-01, -4.15557481e-01, -5.56626901e-01,
         -3.66150146e-01],
        [ 7.83671486e-01, -5.30201541e-01,  6.43615970e-03,
         -5.62058489e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 6.92975905e-01,  2.12531625e-01,  3.04381728e-01,
         -7.41034278e-01],
        [ 5.99157255e-01,  1.75718492e-01, -7.63820433e-01,
          1.47565261e-02],
        [ 4.13331107e-01, -3.43570446e-01, -5.68848011e-01,
          1.11569773e-01],
        [ 9.79129037e-01,  9.09765426e-02,  2.77064482e-01,
         -3.31424435e-01]],

       [[-6.33506587e-01,  2.05354211e-01,  8.44742311e-02,
         -4.53174848e-01],
        [ 1.64665185e-01, -2.00855330e-01, -5.53260180e-01,
         -8.13624266e-02],
        [ 2.95874952e-01, -9.19892298e-01, -4.02152222e-01,
         -4.99466806e-01],
        [ 6.11874474e-01, -7.89046710e-01,  2.85677359e-01,
          4.51972413e-01],
        [ 6.89115774e-01, -7.44708159e-01,  2.81831475e-01,
          1.15541182e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-1.00574922e-01, -4.45760847e-01, -3.46416186e-01,
         -5.91117735e-01],
        [ 6.65501181e-02, -6.59437999e-01, -5.87687185e-01,
         -6.65083497e-01],
        [ 6.98542019e-01, -9.20863369e-01, -1.79806690e-01,
         -5.99954516e-01],
        [ 4.51943976e-02, -6.96216869e-01,  2.24581066e-01,
          2.26274708e-01]],

       [[-3.51319707e-01,  1.49917754e-01, -2.15383044e-01,
          1.86161059e-01],
        [ 1.49884585e-01,  9.01211697e-02,  2.69428225e-01,
          4.22131910e-01],
        [ 4.90920900e-02, -1.85511821e-01, -2.72926531e-01,
         -6.21349190e-01],
        [ 4.59842180e-01,  7.37129268e-02,  1.07200000e-01,
          3.14578155e-01],
        [-2.76350350e-01,  7.64132437e-01,  4.19940118e-01,
          1.16972112e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 2.26832642e-02,  1.92024302e-01,  1.72226122e-02,
          2.17402487e-01],
        [-7.79134469e-01, -1.28154057e-01, -1.65715273e-01,
         -2.77634664e-01],
        [ 2.38680600e-01,  4.24149652e-01,  2.93258579e-01,
          3.73494330e-01],
        [ 4.24511017e-03,  4.40319670e-01, -7.68722045e-02,
          1.54418320e-01]],

       [[-1.09408880e-01,  2.98115848e-01, -3.28737125e-01,
         -9.09692616e-01],
        [-9.16731262e-01,  3.19857380e-01, -3.17944886e-01,
         -7.62666612e-01],
        [-7.45603501e-01,  3.34007819e-01, -1.98236459e-01,
         -8.66206687e-01],
        [-3.61202305e-01,  6.50507846e-01,  2.94681792e-01,
          1.62714458e-01],
        [-3.02775858e-01, -4.16505708e-01, -7.19977446e-01,
         -2.63102948e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-4.28952286e-01, -2.67773294e-01, -6.43289099e-01,
         -8.22043879e-01],
        [-4.06657570e-01,  1.32082675e-01,  1.98028898e-01,
         -4.83368823e-01],
        [-8.69684974e-01, -3.23877226e-01,  3.16335853e-01,
         -7.03916408e-01],
        [-6.42872943e-01, -1.99653528e-01, -8.30906073e-04,
         -1.44625655e-01]],

       [[ 6.05777812e-02, -4.50767702e-01,  9.72448227e-01,
          6.23678306e-01],
        [ 2.85730454e-01, -6.29147692e-01,  9.66120395e-01,
          3.15276999e-01],
        [-5.67042779e-01, -5.49180510e-01,  5.45561799e-01,
         -3.18379681e-01],
        [-3.58817410e-01, -5.19211743e-01,  5.91274896e-01,
         -1.06239458e-01],
        [-1.04518332e-01, -3.47421080e-01,  6.12341250e-01,
          3.03227380e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-5.52732518e-01,  2.07598635e-01,  8.08663265e-01,
         -1.27953282e-02],
        [-2.36802726e-01, -8.34321300e-01,  1.69530320e-01,
         -1.37012736e-01],
        [-3.53798733e-01, -9.88534517e-01,  8.68478106e-01,
         -4.53464846e-01],
        [-9.43297171e-03, -9.52015825e-01,  2.83651882e-01,
         -1.21569843e-01]],

       [[ 1.18019736e-01,  1.60825018e-01,  6.98939130e-01,
          2.37144271e-01],
        [-6.94139088e-01, -4.72109171e-01,  7.27268373e-01,
          4.19458081e-04],
        [-2.99713971e-01, -3.03249230e-01,  2.41375213e-01,
         -8.09112976e-01],
        [ 7.38263411e-02, -4.52053124e-01,  4.70673214e-01,
         -6.79316060e-01],
        [-8.86019774e-01, -5.68174698e-01, -4.76187349e-01,
          3.86772072e-02],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-4.38955105e-01, -6.67260460e-01,  1.69865397e-01,
          5.02153390e-02],
        [-6.69886243e-01, -3.07490863e-01,  4.24526873e-01,
          8.64766195e-02],
        [-6.86211886e-01,  2.74965431e-01, -8.47307563e-02,
         -3.11180769e-01],
        [-9.57524161e-02, -1.13189358e-01,  3.17540159e-01,
          1.78626382e-01]],

       [[ 1.76377312e-01,  3.07825035e-01,  4.03275430e-01,
          3.63548811e-01],
        [-2.06375379e-01,  4.42708153e-01,  9.39876889e-01,
          7.13567634e-01],
        [-3.54883809e-01,  3.82777271e-02,  1.44164685e-01,
          6.42265635e-01],
        [-5.41747930e-01, -1.37730235e-01,  1.26895951e-01,
         -1.32546043e-01],
        [-4.75871848e-02,  5.28705830e-01,  4.44860591e-01,
          6.69729208e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [-5.09774646e-01,  2.77819252e-01, -2.97300889e-02,
          2.86232834e-01],
        [ 8.53019166e-01,  1.68580554e-02,  3.65894387e-01,
         -8.03046348e-03],
        [ 6.15086526e-01, -1.08785975e-01, -1.05875715e-01,
          5.18976833e-01],
        [ 7.57758681e-01,  5.16471904e-01, -4.19631101e-01,
          8.39954791e-01]],

       [[-4.35487914e-01, -8.77156317e-02, -1.06639106e-02,
         -2.48456001e-01],
        [ 1.96652507e-01,  5.25617380e-01,  3.35828458e-01,
         -2.46185440e-01],
        [-3.80475498e-01,  5.52747075e-01,  8.91784028e-01,
          6.63805357e-01],
        [-5.09546098e-01,  9.44947136e-02,  4.91141013e-01,
          2.52931660e-01],
        [ 1.75426909e-01,  6.10191340e-01, -4.23767459e-01,
          6.73467292e-01],
        [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
          0.00000000e+00],
        [ 1.62924314e-01,  8.31354343e-01,  4.64560309e-01,
          8.15303256e-01],
        [-2.84305689e-01,  3.44300642e-01,  1.22574819e-01,
         -2.27153392e-01],
        [ 1.11797050e-01,  3.65605427e-01,  3.21852135e-01,
         -4.94748250e-02],
        [-1.66442380e-01,  1.00747643e-01,  3.00610291e-01,
          5.17095353e-02]]])

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.

    :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)
[[-0.04985678  0.07278302  0.16107702 -0.02172201]
 [-0.08694106 -0.07855695  0.22122118  0.12190232]
 [-0.22070567 -0.19339323  0.14230793 -0.24503852]
 [ 0.01820934 -0.18686048  0.22636467 -0.01275688]
 [ 0.00387033 -0.0879977   0.01818467  0.13655662]
 [ 0.          0.          0.          0.        ]
 [-0.14405075  0.04256669  0.09315724 -0.09972966]
 [-0.10725752 -0.15755554 -0.02958345 -0.2121313 ]
 [ 0.02096771 -0.20261388  0.10758294 -0.1392438 ]
 [ 0.10897831 -0.10156998  0.11326421  0.10667048]]
[[0.04493938 0.05363585 0.05370123 0.05155106]
 [0.04575192 0.05501441 0.05294212 0.04832267]
 [0.0437848  0.0531635  0.05410781 0.04600953]
 [0.04493955 0.05555863 0.05563535 0.04853739]
 [0.04159714 0.05455728 0.05550097 0.04897127]
 [0.0430902  0.05465434 0.05462612 0.04423165]
 [0.0476702  0.05817431 0.05375735 0.05148287]
 [0.04280499 0.05783729 0.05630658 0.05021531]
 [0.04540936 0.05322903 0.05457936 0.0500696 ]
 [0.04503883 0.05316069 0.05730776 0.04649299]]
[[-0.04985678  0.07278302  0.16107702 -0.02172201]
 [-0.08694106 -0.07855695  0.22122118  0.12190232]
 [-0.22070567 -0.19339323  0.14230793 -0.24503852]
 [ 0.01820934 -0.18686048  0.22636467 -0.01275688]
 [ 0.00387033 -0.0879977   0.01818467  0.13655662]
 [ 0.          0.          0.          0.        ]
 [-0.14405075  0.04256669  0.09315724 -0.09972966]
 [-0.10725752 -0.15755554 -0.02958345 -0.2121313 ]
 [ 0.02096771 -0.20261388  0.10758294 -0.1392438 ]
 [ 0.10897831 -0.10156998  0.11326421  0.10667048]]
[[0.04493938 0.05363585 0.05370123 0.05155106]
 [0.04575192 0.05501441 0.05294212 0.04832267]
 [0.0437848  0.0531635  0.05410781 0.04600953]
 [0.04493955 0.05555863 0.05563535 0.04853739]
 [0.04159714 0.05455728 0.05550097 0.04897127]
 [0.0430902  0.05465434 0.05462612 0.04423165]
 [0.0476702  0.05817431 0.05375735 0.05148287]
 [0.04280499 0.05783729 0.05630658 0.05021531]
 [0.04540936 0.05322903 0.05457936 0.0500696 ]
 [0.04503883 0.05316069 0.05730776 0.04649299]]
[ ]: