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Polarized NNLO anomalous dimensions #195

Merged
merged 76 commits into from
Feb 22, 2023
Merged

Polarized NNLO anomalous dimensions #195

merged 76 commits into from
Feb 22, 2023

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giacomomagni
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This PR is for the polarized LO implementation

@giacomomagni giacomomagni mentioned this pull request Jan 16, 2023
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@felixhekhorn felixhekhorn added enhancement New feature or request physics new physics features labels Jan 16, 2023
@felixhekhorn felixhekhorn mentioned this pull request Jan 17, 2023
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@giacomomagni giacomomagni changed the title Polarized LO implementation Polarized NLO implementation Jan 25, 2023
@giacomomagni giacomomagni changed the title Polarized NLO implementation Polarized NNLO anomalous dimensions Jan 25, 2023
@felixhekhorn
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If you can complete the unit tests:

  • a bunch of lines in init
  • one line in as3 (that maybe is crucial)
  • two lines in ev_op/init:quad_ker - just check that you can indeed run and everything is correctly joint together ...

@giacomomagni
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Hi Felix,
okay sure next week we'll try to complete the unit tests as well.

Concerning LHA:

  • what we would need is to change T3 without touching anything else, right? so can we tweak the L+- definition? remember that also in the unpolarized case we found an error there

At LO we can change the tables just setting L_{-}=0 in all the cases.
Since T3 and V3 evolve with the same splitting function they will remain the same at all scales.
For the NLO there is not much we can do, since T3 != V3 (will double check that we see a discrepancy here as well...).

  • please add any remaining bugs to the list with corrected numbers if you can

Good point I totally forgot.

giacomomagni and others added 3 commits February 16, 2023 08:55
@giacomomagni @alecandido
Update src/eko/evolution_operator/grid.py
0027f26 
Co-authored-by: Alessandro Candido <candido.ale@gmail.com>
@giacomomagni @alecandido
Update src/ekomark/benchmark/external/LHA_utils.py
b0f9469 
Co-authored-by: Alessandro Candido <candido.ale@gmail.com>
@felixhekhorn
Add NNPDFpol bench
4343e3b
@felixhekhorn
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felixhekhorn commented Feb 16, 2023 •
edited
Loading

4343e3b adds the benchmark to NNPDFpol11 (so FK generator behind the scenes) - however, there are some hickups ...

I wonder whether @enocera can tell us they are intentional ...

  • most of the distributions are ok
  • the ones failing are those involving a $s$ or $c$ or $b$ valence distribution, so $V, V_8,V_{15},V_{24}$
  • in fact, in the LHAPDF file it seems $s=\bar s$, $c=\bar c$, $b = \bar b$
  • however, this seems unphysical to me: first of all we match $V_3$ and there should be no special case for $V_8$ (everything is light!); and starting from NLO (the PTO here) singlet-like and valence-like non-singlet distributions differ
  • finally, there is a small hickup in $S$ for small x, which I don't know if it is related to the former, but we're getting the gluon correct, so we can't be terribly off gone with updated settings

I attach the full output of the benchmark together with its generating command here below.

EDIT: I fixed the settings (do forward evolution)

Full benchmark output 
$ python benchmarks/NNPDF_bench.py 
 ─────────────────────────────────────────── 
  Theories: 1 OCards: 1 PDFs: 1 ext: LHAPDF  
 ─────────────────────────────────────────── 
Computing for theory=f4a4b02, ocard=6c2c5c4 and pdf=NNPDFpol11_100 ...
LHAPDF 6.4.0 loading /home/felix/local/share/LHAPDF/NNPDFpol11_100/NNPDFpol11_100_0000.dat
NNPDFpol11_100 PDF set, member #0, version 1; LHAPDF ID = 251000
Interpolation: number of points = 50, polynomial degree = 4, logarithmic = True
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.26e+01 - 3.06e+04 - inf], ref=25.0 @ None
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.26e+01 - 3.06e+04 - inf], ref=8317.44 @ None
Strong Coupling: a_s(µ_R^2=8317.440000)=0.009470=0.119002/(4π)
Electromagnetic Coupling: a_em(µ_R^2=8317.440000)=0.000597=0.007496/(4π)
{'polarized': True}
Evolution: computing operators 2.500000e+01 -> 9.000000e+02, nf=5
Evolution: µ_R^2 distance: 2.500000e+01 -> 9.000000e+02
Evolution: a_s distance: 1.711336e-02 -> 1.140638e-02
Evolution: order: (2, 0), solution strategy: truncated
Evolution: computing operators - 15/50 took: 2.916153 s
Evolution: computing operators - 13/50 took: 3.150790 s
Evolution: computing operators - 11/50 took: 3.361710 s
Evolution: computing operators - 9/50 took: 3.536423 s
Evolution: computing operators - 7/50 took: 3.628635 s
Evolution: computing operators - 5/50 took: 4.055255 s
Evolution: computing operators - 3/50 took: 4.125364 s
Evolution: computing operators - 1/50 took: 4.200988 s
Evolution: computing operators - 16/50 took: 2.470672 s
Evolution: computing operators - 14/50 took: 2.824491 s
Evolution: computing operators - 12/50 took: 3.022644 s
Evolution: computing operators - 10/50 took: 3.234079 s
Evolution: computing operators - 8/50 took: 3.194990 s
Evolution: computing operators - 6/50 took: 3.689936 s
Evolution: computing operators - 17/50 took: 2.462244 s
Evolution: computing operators - 4/50 took: 3.855829 s
Evolution: computing operators - 2/50 took: 3.947057 s
Evolution: computing operators - 19/50 took: 2.402124 s
Evolution: computing operators - 21/50 took: 2.267344 s
Evolution: computing operators - 25/50 took: 1.976294 s
Evolution: computing operators - 23/50 took: 2.181073 s
Evolution: computing operators - 31/50 took: 1.481846 s
Evolution: computing operators - 27/50 took: 1.893933 s
Evolution: computing operators - 29/50 took: 1.701414 s
Evolution: computing operators - 18/50 took: 2.513582 s
Evolution: computing operators - 26/50 took: 1.887885 s
Evolution: computing operators - 20/50 took: 2.422162 s
Evolution: computing operators - 22/50 took: 2.254575 s
Evolution: computing operators - 24/50 took: 2.096153 s
Evolution: computing operators - 32/50 took: 1.473290 s
Evolution: computing operators - 30/50 took: 1.694563 s
Evolution: computing operators - 28/50 took: 1.864304 s
Evolution: computing operators - 33/50 took: 1.465991 s
Evolution: computing operators - 39/50 took: 1.029645 s
Evolution: computing operators - 37/50 took: 1.116508 s
Evolution: computing operators - 35/50 took: 1.287192 s
Evolution: computing operators - 43/50 took: 0.899435 s
Evolution: computing operators - 41/50 took: 0.996422 s
Evolution: computing operators - 45/50 took: 0.904219 s
Evolution: computing operators - 47/50 took: 0.882766 s
Evolution: computing operators - 44/50 took: 0.899733 s
Evolution: computing operators - 40/50 took: 0.995518 s
Evolution: computing operators - 38/50 took: 1.058954 s
Evolution: computing operators - 42/50 took: 0.957238 s
Evolution: computing operators - 36/50 took: 1.162672 s
Evolution: computing operators - 48/50 took: 0.765260 s
Evolution: computing operators - 46/50 took: 0.869886 s
Evolution: computing operators - 34/50 took: 1.354787 s
Evolution: computing operators - 49/50 took: 0.507490 s
Evolution: computing operators - 50/50 took: 0.248615 s
Evolution: Total time 13.787233 s
Cache contains the external result
Interpolation: number of points = 50, polynomial degree = 4, logarithmic = True

Log already present, hash=789b3e8921e153dc18052d70b0bc9ba0cc8c2dc321a04f6eeb8aeb8f8e040ffe


 ─── 
  S  
 ─── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900 -1.803379e-02 -6.790094e-08 -1.804135e-02      -0.041919
1   0.000014  900 -2.224870e-02 -7.693297e-08 -2.225579e-02      -0.031871
2   0.000020  900 -2.659829e-02 -8.930419e-08 -2.660442e-02      -0.023058
3   0.000027  900 -3.090914e-02 -8.250721e-08 -3.091379e-02      -0.015039
4   0.000038  900 -3.492654e-02 -3.045056e-08 -3.492955e-02      -0.008600
5   0.000054  900 -3.832328e-02 -6.572576e-09 -3.832446e-02      -0.003102
6   0.000076  900 -4.076653e-02 -9.435386e-09 -4.076631e-02       0.000556
7   0.000106  900 -4.199373e-02 -5.260666e-09 -4.199286e-02       0.002095
8   0.000148  900 -4.188877e-02  5.951582e-09 -4.188690e-02       0.004467
9   0.000207  900 -4.063978e-02  3.800183e-09 -4.063585e-02       0.009671
10  0.000290  900 -3.883650e-02 -4.815656e-08 -3.883101e-02       0.014142
11  0.000406  900 -3.717125e-02 -5.034675e-08 -3.716696e-02       0.011541
12  0.000569  900 -3.593632e-02 -1.029515e-07 -3.593633e-02      -0.000011
13  0.000796  900 -3.498792e-02 -3.778104e-08 -3.498762e-02       0.000863
14  0.001113  900 -3.408642e-02 -1.609175e-08 -3.408463e-02       0.005271
15  0.001556  900 -3.296817e-02  2.192265e-08 -3.296611e-02       0.006237
16  0.002173  900 -3.134003e-02  2.209928e-08 -3.133651e-02       0.011254
17  0.003030  900 -2.899291e-02  1.313374e-08 -2.898799e-02       0.016999
18  0.004220  900 -2.580370e-02  2.852192e-08 -2.579976e-02       0.015247
19  0.005862  900 -2.160593e-02  4.271877e-08 -2.160300e-02       0.013546
20  0.008119  900 -1.614502e-02  4.775399e-08 -1.614318e-02       0.011411
21  0.011199  900 -9.090765e-03  2.928493e-08 -9.089262e-03       0.016533
22  0.015364  900 -2.243038e-05  1.116350e-08 -2.267508e-05      -1.079176
23  0.020930  900  1.154040e-02  2.071837e-08  1.154173e-02      -0.011498
24  0.028262  900  2.600469e-02  9.854985e-09  2.600632e-02      -0.006256
25  0.037753  900  4.355522e-02  2.010641e-08  4.355321e-02       0.004619
26  0.049792  900  6.395525e-02  1.188171e-08  6.395152e-02       0.005824
27  0.064727  900  8.636623e-02  4.422277e-08  8.637804e-02      -0.013667
28  0.082822  900  1.094025e-01  3.852958e-08  1.094147e-01      -0.011210
29  0.104234  900  1.312003e-01  3.166801e-08  1.312021e-01      -0.001383
30  0.128999  900  1.498613e-01  5.623392e-07  1.498753e-01      -0.009381
31  0.157049  900  1.634721e-01  4.536958e-07  1.634948e-01      -0.013916
32  0.188228  900  1.707916e-01  2.767004e-08  1.708131e-01      -0.012592
33  0.222328  900  1.712997e-01  2.389363e-07  1.713210e-01      -0.012427
34  0.259109  900  1.652738e-01  2.772209e-07  1.652930e-01      -0.011576
35  0.298323  900  1.536139e-01  2.881340e-07  1.536269e-01      -0.008485
36  0.339728  900  1.376398e-01  2.437106e-07  1.376485e-01      -0.006346
37  0.383099  900  1.188647e-01  2.322872e-07  1.188672e-01      -0.002137
38  0.428226  900  9.880884e-02  1.647372e-07  9.880343e-02       0.005476
39  0.474925  900  7.885145e-02  9.847267e-08  7.883998e-02       0.014542
40  0.523028  900  6.013461e-02  5.421349e-08  6.011830e-02       0.027136
41  0.572391  900  4.352773e-02  2.733706e-08  4.350850e-02       0.044204
42  0.622883  900  2.960448e-02  1.247831e-08  2.958371e-02       0.070210
43  0.674392  900  1.863080e-02  5.129925e-09  1.861087e-02       0.107079
44  0.726818  900  1.059111e-02  1.861258e-09  1.057381e-02       0.163602
45  0.780075  900  5.224453e-03  5.720992e-10  5.210924e-03       0.259628
46  0.834085  900  2.075114e-03  1.401018e-10  2.066254e-03       0.428757
47  0.888782  900  5.634316e-04  7.998779e-11  5.591008e-04       0.774593
48  0.944104  900  6.537898e-05  4.918731e-11  6.391218e-05       2.295023
49  1.000000  900 -2.433074e-21  0.000000e+00 -8.276695e-22     193.966798

 ─── 
  g  
 ─── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900 -2.016532e-01 -1.857725e-07 -2.016573e-01      -0.002033
1   0.000014  900 -1.964721e-01 -3.454973e-07 -1.964790e-01      -0.003536
2   0.000020  900 -1.892968e-01 -8.827220e-08 -1.893027e-01      -0.003155
3   0.000027  900 -1.798943e-01 -2.052311e-07 -1.798989e-01      -0.002566
4   0.000038  900 -1.680161e-01 -1.518882e-07 -1.680203e-01      -0.002508
5   0.000054  900 -1.533962e-01 -7.161902e-08 -1.533989e-01      -0.001810
6   0.000076  900 -1.358375e-01 -9.330615e-08 -1.358382e-01      -0.000497
7   0.000106  900 -1.153636e-01 -2.317679e-08 -1.153603e-01       0.002877
8   0.000148  900 -9.225753e-02 -2.055659e-09 -9.225476e-02       0.003005
9   0.000207  900 -6.713161e-02 -5.855427e-09 -6.713330e-02      -0.002512
10  0.000290  900 -4.123243e-02  1.334393e-08 -4.121947e-02       0.031438
11  0.000406  900 -1.629884e-02  1.962551e-08 -1.628051e-02       0.112583
12  0.000569  900  6.452622e-03  6.406517e-08  6.446474e-03       0.095365
13  0.000796  900  2.693294e-02  7.363069e-09  2.692623e-02       0.024915
14  0.001113  900  4.559867e-02  6.481323e-08  4.559722e-02       0.003168
15  0.001556  900  6.283092e-02  5.805873e-08  6.282969e-02       0.001964
16  0.002173  900  7.895331e-02  7.349356e-08  7.895381e-02      -0.000641
17  0.003030  900  9.412516e-02  1.805913e-07  9.412812e-02      -0.003137
18  0.004220  900  1.081262e-01  1.081274e-07  1.081339e-01      -0.007077
19  0.005862  900  1.205844e-01  4.789393e-07  1.205918e-01      -0.006115
20  0.008119  900  1.312089e-01  1.674867e-07  1.312180e-01      -0.006958
21  0.011199  900  1.397324e-01  2.315436e-07  1.397440e-01      -0.008254
22  0.015364  900  1.459394e-01  3.452038e-07  1.459531e-01      -0.009409
23  0.020930  900  1.497075e-01  2.652356e-07  1.497225e-01      -0.010025
24  0.028262  900  1.509881e-01  1.548447e-07  1.510038e-01      -0.010446
25  0.037753  900  1.497586e-01  1.034076e-07  1.497779e-01      -0.012905
26  0.049792  900  1.460115e-01  1.512598e-07  1.460270e-01      -0.010610
27  0.064727  900  1.397827e-01  3.221123e-07  1.398030e-01      -0.014522
28  0.082822  900  1.312012e-01  1.717989e-07  1.312198e-01      -0.014220
29  0.104234  900  1.205259e-01  4.330442e-07  1.205426e-01      -0.013846
30  0.128999  900  1.081349e-01  1.080213e-07  1.081459e-01      -0.010112
31  0.157049  900  9.451124e-02  4.349545e-08  9.452264e-02      -0.012058
32  0.188228  900  8.020581e-02  1.077737e-08  8.021201e-02      -0.007731
33  0.222328  900  6.585766e-02  2.697473e-07  6.586284e-02      -0.007861
34  0.259109  900  5.217436e-02  4.513074e-08  5.217734e-02      -0.005702
35  0.298323  900  3.979873e-02  3.933708e-08  3.979952e-02      -0.001987
36  0.339728  900  2.918341e-02  6.520350e-08  2.918296e-02       0.001541
37  0.383099  900  2.053448e-02  5.781148e-08  2.053334e-02       0.005596
38  0.428226  900  1.382830e-02  4.211532e-08  1.382679e-02       0.010945
39  0.474925  900  8.875785e-03  2.272244e-08  8.873976e-03       0.020385
40  0.523028  900  5.395935e-03  1.357812e-08  5.394300e-03       0.030305
41  0.572391  900  3.077520e-03  8.195721e-09  3.076373e-03       0.037292
42  0.622883  900  1.623063e-03  3.450451e-09  1.622061e-03       0.061746
43  0.674392  900  7.745119e-04  1.009014e-09  7.737201e-04       0.102342
44  0.726818  900  3.234788e-04  2.597210e-10  3.229453e-04       0.165199
45  0.780075  900  1.120529e-04  4.719112e-11  1.117687e-04       0.254232
46  0.834085  900  2.917567e-05  5.625176e-12  2.906330e-05       0.386643
47  0.888782  900  4.605332e-06  3.005225e-12  4.570616e-06       0.759547
48  0.944104  900  2.321023e-07  3.300460e-12  2.354458e-07      -1.420067
49  1.000000  900  1.150418e-23  0.000000e+00 -4.892839e-24    -335.122742

 ─── 
  V  
 ─── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  8.109616e-04 -3.797320e-11 -2.295977e-03    -135.320981
1   0.000014  900  1.738229e-04  2.919727e-09 -3.532416e-03    -104.920792
2   0.000020  900 -5.663469e-04 -5.023609e-10 -4.864025e-03     -88.356413
3   0.000027  900 -1.387607e-03 -3.458236e-09 -6.238173e-03     -77.756192
4   0.000038  900 -2.228183e-03 -8.649411e-09 -7.547741e-03     -70.478806
5   0.000054  900 -2.983244e-03 -1.441468e-09 -8.633486e-03     -65.445663
6   0.000076  900 -3.531174e-03 -1.108370e-08 -9.325684e-03     -62.134960
7   0.000106  900 -3.769229e-03 -1.486762e-08 -9.493609e-03     -60.297199
8   0.000148  900 -3.638767e-03 -1.012076e-08 -9.081208e-03     -59.930804
9   0.000207  900 -3.179348e-03 -2.371254e-09 -8.180173e-03     -61.133488
10  0.000290  900 -2.578161e-03 -1.837705e-09 -7.080657e-03     -63.588672
11  0.000406  900 -2.073902e-03 -2.835148e-09 -6.124973e-03     -66.140231
12  0.000569  900 -1.725399e-03 -1.363435e-09 -5.413532e-03     -68.128033
13  0.000796  900 -1.350146e-03 -1.154993e-09 -4.746802e-03     -71.556714
14  0.001113  900 -7.487213e-04 -7.269132e-09 -3.902768e-03     -80.815634
15  0.001556  900  1.677649e-04 -1.072725e-08 -2.762603e-03    -106.072710
16  0.002173  900  1.546228e-03 -4.668453e-09 -1.148170e-03    -234.668872
17  0.003030  900  3.634876e-03  1.227699e-09  1.214082e-03     199.392952
18  0.004220  900  6.664861e-03  6.522911e-09  4.568609e-03      45.883816
19  0.005862  900  1.087867e-02  1.719458e-08  9.169147e-03      18.644307
20  0.008119  900  1.660104e-02  3.415144e-08  1.535056e-02       8.146103
21  0.011199  900  2.420098e-02  5.113058e-08  2.347883e-02       3.075760
22  0.015364  900  3.403762e-02  2.736984e-08  3.390087e-02       0.403373
23  0.020930  900  4.640383e-02  1.094015e-08  4.689290e-02      -1.042939
24  0.028262  900  6.141286e-02  2.966377e-08  6.253439e-02      -1.793454
25  0.037753  900  7.889484e-02  3.683233e-08  8.061647e-02      -2.135586
26  0.049792  900  9.827919e-02  2.269692e-08  1.005104e-01      -2.219847
27  0.064727  900  1.185182e-01  1.313459e-08  1.211287e-01      -2.155144
28  0.082822  900  1.381371e-01  1.976067e-08  1.409376e-01      -1.987083
29  0.104234  900  1.554056e-01  2.295791e-08  1.581777e-01      -1.752500
30  0.128999  900  1.688372e-01  1.473714e-08  1.714189e-01      -1.506074
31  0.157049  900  1.770679e-01  1.083426e-08  1.793170e-01      -1.254246
32  0.188228  900  1.793380e-01  9.462018e-09  1.811717e-01      -1.012108
33  0.222328  900  1.755173e-01  7.111382e-09  1.769242e-01      -0.795192
34  0.259109  900  1.661575e-01  5.335433e-09  1.671748e-01      -0.608519
35  0.298323  900  1.523036e-01  3.323815e-09  1.529971e-01      -0.453245
36  0.339728  900  1.352276e-01  2.623324e-09  1.356760e-01      -0.330485
37  0.383099  900  1.162227e-01  1.821572e-09  1.164950e-01      -0.233698
38  0.428226  900  9.650900e-02  1.424955e-09  9.665995e-02      -0.156173
39  0.474925  900  7.717897e-02  9.322632e-10  7.725251e-02      -0.095196
40  0.523028  900  5.914947e-02  6.175052e-10  5.917624e-02      -0.045246
41  0.572391  900  4.313552e-02  3.275868e-10  4.313636e-02      -0.001946
42  0.622883  900  2.962931e-02  8.835994e-11  2.961715e-02       0.041030
43  0.674392  900  1.888192e-02  1.034670e-11  1.886525e-02       0.088353
44  0.726818  900  1.090705e-02  9.481897e-13  1.089077e-02       0.149499
45  0.780075  900  5.493901e-03  2.149276e-14  5.480583e-03       0.243010
46  0.834085  900  2.244284e-03  1.984260e-14  2.235325e-03       0.400791
47  0.888782  900  6.343017e-04  1.605858e-14  6.296471e-04       0.739240
48  0.944104  900  7.786885e-05  2.558545e-14  7.675814e-05       1.447023
49  1.000000  900 -3.066612e-21  0.000000e+00 -4.560172e-22     572.477212

 ──── 
  V3  
 ──── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900 -5.233937e-04 -5.527363e-10 -5.246026e-04      -0.230447
1   0.000014  900 -2.132286e-04 -2.911234e-09 -2.147721e-04      -0.718676
2   0.000020  900  1.875122e-04 -1.689289e-09  1.858791e-04       0.878572
3   0.000027  900  6.921986e-04  4.518556e-10  6.904661e-04       0.250918
4   0.000038  900  1.319192e-03  4.070311e-09  1.317367e-03       0.138585
5   0.000054  900  2.090744e-03  2.536897e-09  2.088751e-03       0.095411
6   0.000076  900  3.030184e-03  8.119106e-09  3.027728e-03       0.081113
7   0.000106  900  4.152534e-03  1.243548e-08  4.150204e-03       0.056149
8   0.000148  900  5.451000e-03  1.302430e-08  5.449161e-03       0.033750
9   0.000207  900  6.922302e-03  6.502530e-09  6.919952e-03       0.033964
10  0.000290  900  8.620505e-03  9.892138e-09  8.617911e-03       0.030091
11  0.000406  900  1.066873e-02  1.584944e-08  1.066683e-02       0.017813
12  0.000569  900  1.320063e-02  9.311088e-09  1.320057e-02       0.000506
13  0.000796  900  1.626598e-02  1.769068e-08  1.626694e-02      -0.005884
14  0.001113  900  1.980482e-02  5.688440e-08  1.980678e-02      -0.009897
15  0.001556  900  2.386747e-02  1.087639e-07  2.386979e-02      -0.009744
16  0.002173  900  2.883250e-02  1.076863e-07  2.883683e-02      -0.015017
17  0.003030  900  3.505177e-02  6.380504e-08  3.506037e-02      -0.024518
18  0.004220  900  4.282113e-02  4.530501e-08  4.283148e-02      -0.024175
19  0.005862  900  5.251424e-02  7.356720e-08  5.252578e-02      -0.021956
20  0.008119  900  6.461886e-02  1.300571e-07  6.463241e-02      -0.020956
21  0.011199  900  7.967495e-02  1.631700e-07  7.969277e-02      -0.022354
22  0.015364  900  9.817155e-02  7.317037e-08  9.819303e-02      -0.021876
23  0.020930  900  1.204499e-01  2.186133e-08  1.204738e-01      -0.019882
24  0.028262  900  1.464939e-01  6.527517e-08  1.465295e-01      -0.024252
25  0.037753  900  1.757352e-01  7.771962e-08  1.757643e-01      -0.016550
26  0.049792  900  2.075513e-01  4.577201e-08  2.075788e-01      -0.013257
27  0.064727  900  2.408297e-01  2.576123e-08  2.408804e-01      -0.021056
28  0.082822  900  2.738351e-01  3.874400e-08  2.738835e-01      -0.017695
29  0.104234  900  3.041898e-01  4.357114e-08  3.042236e-01      -0.011100
30  0.128999  900  3.292033e-01  2.718172e-08  3.292471e-01      -0.013314
31  0.157049  900  3.457394e-01  1.924436e-08  3.457913e-01      -0.015006
32  0.188228  900  3.509437e-01  1.637970e-08  3.510004e-01      -0.016168
33  0.222328  900  3.432701e-01  1.170308e-08  3.433104e-01      -0.011743
34  0.259109  900  3.232004e-01  7.764285e-09  3.232318e-01      -0.009704
35  0.298323  900  2.927140e-01  4.621987e-09  2.927301e-01      -0.005509
36  0.339728  900  2.545903e-01  3.272834e-09  2.545953e-01      -0.001964
37  0.383099  900  2.120905e-01  2.184101e-09  2.120824e-01       0.003805
38  0.428226  900  1.685906e-01  1.535318e-09  1.685669e-01       0.014030
39  0.474925  900  1.272282e-01  9.287782e-10  1.271932e-01       0.027578
40  0.523028  900  9.056489e-02  5.247922e-10  9.052216e-02       0.047205
41  0.572391  900  6.030483e-02  2.357784e-10  6.026177e-02       0.071463
42  0.622883  900  3.713591e-02  5.525362e-11  3.709506e-02       0.110112
43  0.674392  900  2.079153e-02  4.443621e-12  2.075687e-02       0.166984
44  0.726818  900  1.030338e-02  1.607373e-13  1.027817e-02       0.245272
45  0.780075  900  4.305307e-03  1.624967e-14  4.289345e-03       0.372126
46  0.834085  900  1.369806e-03  1.282816e-14  1.361277e-03       0.626572
47  0.888782  900  2.522490e-04  1.005191e-14  2.492026e-04       1.222422
48  0.944104  900  5.834768e-06  1.637439e-14  4.127631e-06      41.358741
49  1.000000  900 -8.005978e-21  0.000000e+00  4.484752e-22   -1885.155001

 ──── 
  V8  
 ──── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  8.109616e-04 -3.797320e-11 -2.295977e-03    -135.320981
1   0.000014  900  1.738229e-04  2.919727e-09 -3.532416e-03    -104.920792
2   0.000020  900 -5.663469e-04 -5.023609e-10 -4.864025e-03     -88.356413
3   0.000027  900 -1.387607e-03 -3.458236e-09 -6.238173e-03     -77.756192
4   0.000038  900 -2.228183e-03 -8.649411e-09 -7.547741e-03     -70.478806
5   0.000054  900 -2.983244e-03 -1.441468e-09 -8.633486e-03     -65.445663
6   0.000076  900 -3.531174e-03 -1.108370e-08 -9.325684e-03     -62.134960
7   0.000106  900 -3.769229e-03 -1.486762e-08 -9.493609e-03     -60.297199
8   0.000148  900 -3.638767e-03 -1.012076e-08 -9.081208e-03     -59.930804
9   0.000207  900 -3.179348e-03 -2.371254e-09 -8.180173e-03     -61.133488
10  0.000290  900 -2.578161e-03 -1.837705e-09 -7.080657e-03     -63.588672
11  0.000406  900 -2.073902e-03 -2.835148e-09 -6.124973e-03     -66.140231
12  0.000569  900 -1.725399e-03 -1.363435e-09 -5.413532e-03     -68.128033
13  0.000796  900 -1.350146e-03 -1.154993e-09 -4.746802e-03     -71.556714
14  0.001113  900 -7.487213e-04 -7.269132e-09 -3.902768e-03     -80.815634
15  0.001556  900  1.677649e-04 -1.072725e-08 -2.762603e-03    -106.072710
16  0.002173  900  1.546228e-03 -4.668453e-09 -1.148170e-03    -234.668872
17  0.003030  900  3.634876e-03  1.227699e-09  1.214082e-03     199.392952
18  0.004220  900  6.664861e-03  6.522911e-09  4.568609e-03      45.883816
19  0.005862  900  1.087867e-02  1.719458e-08  9.169147e-03      18.644307
20  0.008119  900  1.660104e-02  3.415144e-08  1.535056e-02       8.146103
21  0.011199  900  2.420098e-02  5.113058e-08  2.347883e-02       3.075760
22  0.015364  900  3.403762e-02  2.736984e-08  3.390087e-02       0.403373
23  0.020930  900  4.640383e-02  1.094015e-08  4.689290e-02      -1.042939
24  0.028262  900  6.141286e-02  2.966377e-08  6.253439e-02      -1.793454
25  0.037753  900  7.889484e-02  3.683233e-08  8.061647e-02      -2.135586
26  0.049792  900  9.827919e-02  2.269692e-08  1.005104e-01      -2.219847
27  0.064727  900  1.185182e-01  1.313459e-08  1.211287e-01      -2.155144
28  0.082822  900  1.381371e-01  1.976067e-08  1.409376e-01      -1.987083
29  0.104234  900  1.554056e-01  2.295791e-08  1.581777e-01      -1.752500
30  0.128999  900  1.688372e-01  1.473714e-08  1.714189e-01      -1.506074
31  0.157049  900  1.770679e-01  1.083426e-08  1.793170e-01      -1.254246
32  0.188228  900  1.793380e-01  9.462018e-09  1.811717e-01      -1.012108
33  0.222328  900  1.755173e-01  7.111382e-09  1.769242e-01      -0.795192
34  0.259109  900  1.661575e-01  5.335433e-09  1.671748e-01      -0.608519
35  0.298323  900  1.523036e-01  3.323815e-09  1.529971e-01      -0.453245
36  0.339728  900  1.352276e-01  2.623324e-09  1.356760e-01      -0.330485
37  0.383099  900  1.162227e-01  1.821572e-09  1.164950e-01      -0.233698
38  0.428226  900  9.650900e-02  1.424955e-09  9.665995e-02      -0.156173
39  0.474925  900  7.717897e-02  9.322632e-10  7.725251e-02      -0.095196
40  0.523028  900  5.914947e-02  6.175052e-10  5.917624e-02      -0.045246
41  0.572391  900  4.313552e-02  3.275868e-10  4.313636e-02      -0.001946
42  0.622883  900  2.962931e-02  8.835994e-11  2.961715e-02       0.041030
43  0.674392  900  1.888192e-02  1.034670e-11  1.886525e-02       0.088353
44  0.726818  900  1.090705e-02  9.481897e-13  1.089077e-02       0.149499
45  0.780075  900  5.493901e-03  2.149276e-14  5.480583e-03       0.243010
46  0.834085  900  2.244284e-03  1.984260e-14  2.235325e-03       0.400791
47  0.888782  900  6.343017e-04  1.605858e-14  6.296471e-04       0.739240
48  0.944104  900  7.786885e-05  2.558545e-14  7.675814e-05       1.447023
49  1.000000  900 -3.066612e-21  0.000000e+00 -4.560172e-22     572.477212

 ───── 
  V15  
 ───── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  8.109616e-04 -3.797320e-11 -2.295977e-03    -135.320981
1   0.000014  900  1.738229e-04  2.919727e-09 -3.532416e-03    -104.920792
2   0.000020  900 -5.663469e-04 -5.023609e-10 -4.864025e-03     -88.356413
3   0.000027  900 -1.387607e-03 -3.458236e-09 -6.238173e-03     -77.756192
4   0.000038  900 -2.228183e-03 -8.649411e-09 -7.547741e-03     -70.478806
5   0.000054  900 -2.983244e-03 -1.441468e-09 -8.633486e-03     -65.445663
6   0.000076  900 -3.531174e-03 -1.108370e-08 -9.325684e-03     -62.134960
7   0.000106  900 -3.769229e-03 -1.486762e-08 -9.493609e-03     -60.297199
8   0.000148  900 -3.638767e-03 -1.012076e-08 -9.081208e-03     -59.930804
9   0.000207  900 -3.179348e-03 -2.371254e-09 -8.180173e-03     -61.133488
10  0.000290  900 -2.578161e-03 -1.837705e-09 -7.080657e-03     -63.588672
11  0.000406  900 -2.073902e-03 -2.835148e-09 -6.124973e-03     -66.140231
12  0.000569  900 -1.725399e-03 -1.363435e-09 -5.413532e-03     -68.128033
13  0.000796  900 -1.350146e-03 -1.154993e-09 -4.746802e-03     -71.556714
14  0.001113  900 -7.487213e-04 -7.269132e-09 -3.902768e-03     -80.815634
15  0.001556  900  1.677649e-04 -1.072725e-08 -2.762603e-03    -106.072710
16  0.002173  900  1.546228e-03 -4.668453e-09 -1.148170e-03    -234.668872
17  0.003030  900  3.634876e-03  1.227699e-09  1.214082e-03     199.392952
18  0.004220  900  6.664861e-03  6.522911e-09  4.568609e-03      45.883816
19  0.005862  900  1.087867e-02  1.719458e-08  9.169147e-03      18.644307
20  0.008119  900  1.660104e-02  3.415144e-08  1.535056e-02       8.146103
21  0.011199  900  2.420098e-02  5.113058e-08  2.347883e-02       3.075760
22  0.015364  900  3.403762e-02  2.736984e-08  3.390087e-02       0.403373
23  0.020930  900  4.640383e-02  1.094015e-08  4.689290e-02      -1.042939
24  0.028262  900  6.141286e-02  2.966377e-08  6.253439e-02      -1.793454
25  0.037753  900  7.889484e-02  3.683233e-08  8.061647e-02      -2.135586
26  0.049792  900  9.827919e-02  2.269692e-08  1.005104e-01      -2.219847
27  0.064727  900  1.185182e-01  1.313459e-08  1.211287e-01      -2.155144
28  0.082822  900  1.381371e-01  1.976067e-08  1.409376e-01      -1.987083
29  0.104234  900  1.554056e-01  2.295791e-08  1.581777e-01      -1.752500
30  0.128999  900  1.688372e-01  1.473714e-08  1.714189e-01      -1.506074
31  0.157049  900  1.770679e-01  1.083426e-08  1.793170e-01      -1.254246
32  0.188228  900  1.793380e-01  9.462018e-09  1.811717e-01      -1.012108
33  0.222328  900  1.755173e-01  7.111382e-09  1.769242e-01      -0.795192
34  0.259109  900  1.661575e-01  5.335433e-09  1.671748e-01      -0.608519
35  0.298323  900  1.523036e-01  3.323815e-09  1.529971e-01      -0.453245
36  0.339728  900  1.352276e-01  2.623324e-09  1.356760e-01      -0.330485
37  0.383099  900  1.162227e-01  1.821572e-09  1.164950e-01      -0.233698
38  0.428226  900  9.650900e-02  1.424955e-09  9.665995e-02      -0.156173
39  0.474925  900  7.717897e-02  9.322632e-10  7.725251e-02      -0.095196
40  0.523028  900  5.914947e-02  6.175052e-10  5.917624e-02      -0.045246
41  0.572391  900  4.313552e-02  3.275868e-10  4.313636e-02      -0.001946
42  0.622883  900  2.962931e-02  8.835994e-11  2.961715e-02       0.041030
43  0.674392  900  1.888192e-02  1.034670e-11  1.886525e-02       0.088353
44  0.726818  900  1.090705e-02  9.481897e-13  1.089077e-02       0.149499
45  0.780075  900  5.493901e-03  2.149276e-14  5.480583e-03       0.243010
46  0.834085  900  2.244284e-03  1.984260e-14  2.235325e-03       0.400791
47  0.888782  900  6.343017e-04  1.605858e-14  6.296471e-04       0.739240
48  0.944104  900  7.786885e-05  2.558545e-14  7.675814e-05       1.447023
49  1.000000  900 -3.066612e-21  0.000000e+00 -4.560172e-22     572.477212

 ───── 
  V24  
 ───── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  8.109616e-04 -3.797320e-11 -2.295977e-03    -135.320981
1   0.000014  900  1.738229e-04  2.919727e-09 -3.532416e-03    -104.920792
2   0.000020  900 -5.663469e-04 -5.023609e-10 -4.864025e-03     -88.356413
3   0.000027  900 -1.387607e-03 -3.458236e-09 -6.238173e-03     -77.756192
4   0.000038  900 -2.228183e-03 -8.649411e-09 -7.547741e-03     -70.478806
5   0.000054  900 -2.983244e-03 -1.441468e-09 -8.633486e-03     -65.445663
6   0.000076  900 -3.531174e-03 -1.108370e-08 -9.325684e-03     -62.134960
7   0.000106  900 -3.769229e-03 -1.486762e-08 -9.493609e-03     -60.297199
8   0.000148  900 -3.638767e-03 -1.012076e-08 -9.081208e-03     -59.930804
9   0.000207  900 -3.179348e-03 -2.371254e-09 -8.180173e-03     -61.133488
10  0.000290  900 -2.578161e-03 -1.837705e-09 -7.080657e-03     -63.588672
11  0.000406  900 -2.073902e-03 -2.835148e-09 -6.124973e-03     -66.140231
12  0.000569  900 -1.725399e-03 -1.363435e-09 -5.413532e-03     -68.128033
13  0.000796  900 -1.350146e-03 -1.154993e-09 -4.746802e-03     -71.556714
14  0.001113  900 -7.487213e-04 -7.269132e-09 -3.902768e-03     -80.815634
15  0.001556  900  1.677649e-04 -1.072725e-08 -2.762603e-03    -106.072710
16  0.002173  900  1.546228e-03 -4.668453e-09 -1.148170e-03    -234.668872
17  0.003030  900  3.634876e-03  1.227699e-09  1.214082e-03     199.392952
18  0.004220  900  6.664861e-03  6.522911e-09  4.568609e-03      45.883816
19  0.005862  900  1.087867e-02  1.719458e-08  9.169147e-03      18.644307
20  0.008119  900  1.660104e-02  3.415144e-08  1.535056e-02       8.146103
21  0.011199  900  2.420098e-02  5.113058e-08  2.347883e-02       3.075760
22  0.015364  900  3.403762e-02  2.736984e-08  3.390087e-02       0.403373
23  0.020930  900  4.640383e-02  1.094015e-08  4.689290e-02      -1.042939
24  0.028262  900  6.141286e-02  2.966377e-08  6.253439e-02      -1.793454
25  0.037753  900  7.889484e-02  3.683233e-08  8.061647e-02      -2.135586
26  0.049792  900  9.827919e-02  2.269692e-08  1.005104e-01      -2.219847
27  0.064727  900  1.185182e-01  1.313459e-08  1.211287e-01      -2.155144
28  0.082822  900  1.381371e-01  1.976067e-08  1.409376e-01      -1.987083
29  0.104234  900  1.554056e-01  2.295791e-08  1.581777e-01      -1.752500
30  0.128999  900  1.688372e-01  1.473714e-08  1.714189e-01      -1.506074
31  0.157049  900  1.770679e-01  1.083426e-08  1.793170e-01      -1.254246
32  0.188228  900  1.793380e-01  9.462018e-09  1.811717e-01      -1.012108
33  0.222328  900  1.755173e-01  7.111382e-09  1.769242e-01      -0.795192
34  0.259109  900  1.661575e-01  5.335433e-09  1.671748e-01      -0.608519
35  0.298323  900  1.523036e-01  3.323815e-09  1.529971e-01      -0.453245
36  0.339728  900  1.352276e-01  2.623324e-09  1.356760e-01      -0.330485
37  0.383099  900  1.162227e-01  1.821572e-09  1.164950e-01      -0.233698
38  0.428226  900  9.650900e-02  1.424955e-09  9.665995e-02      -0.156173
39  0.474925  900  7.717897e-02  9.322632e-10  7.725251e-02      -0.095196
40  0.523028  900  5.914947e-02  6.175052e-10  5.917624e-02      -0.045246
41  0.572391  900  4.313552e-02  3.275868e-10  4.313636e-02      -0.001946
42  0.622883  900  2.962931e-02  8.835994e-11  2.961715e-02       0.041030
43  0.674392  900  1.888192e-02  1.034670e-11  1.886525e-02       0.088353
44  0.726818  900  1.090705e-02  9.481897e-13  1.089077e-02       0.149499
45  0.780075  900  5.493901e-03  2.149276e-14  5.480583e-03       0.243010
46  0.834085  900  2.244284e-03  1.984260e-14  2.235325e-03       0.400791
47  0.888782  900  6.343017e-04  1.605858e-14  6.296471e-04       0.739240
48  0.944104  900  7.786885e-05  2.558545e-14  7.675814e-05       1.447023
49  1.000000  900 -3.066612e-21  0.000000e+00 -4.560172e-22     572.477212

 ──── 
  T3  
 ──── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  8.858955e-03  1.979166e-08  8.860386e-03      -0.016146
1   0.000014  900  1.000349e-02  5.365305e-08  1.000443e-02      -0.009302
2   0.000020  900  1.126343e-02  5.145031e-08  1.126445e-02      -0.009089
3   0.000027  900  1.263499e-02  3.469715e-08  1.263611e-02      -0.008896
4   0.000038  900  1.411985e-02  2.723844e-08  1.412109e-02      -0.008793
5   0.000054  900  1.572410e-02  2.101703e-08  1.572548e-02      -0.008729
6   0.000076  900  1.745610e-02  5.914873e-08  1.745755e-02      -0.008347
7   0.000106  900  1.932648e-02  1.466758e-07  1.932812e-02      -0.008474
8   0.000148  900  2.135020e-02  5.372773e-08  2.135214e-02      -0.009095
9   0.000207  900  2.355642e-02  1.951740e-08  2.355837e-02      -0.008297
10  0.000290  900  2.600601e-02  2.115630e-08  2.600809e-02      -0.007997
11  0.000406  900  2.879476e-02  3.710794e-08  2.879742e-02      -0.009227
12  0.000569  900  3.203337e-02  2.576670e-08  3.203645e-02      -0.009613
13  0.000796  900  3.582847e-02  1.106238e-08  3.583184e-02      -0.009417
14  0.001113  900  4.029500e-02  1.529633e-07  4.029893e-02      -0.009734
15  0.001556  900  4.558979e-02  2.431994e-08  4.559467e-02      -0.010712
16  0.002173  900  5.193685e-02  7.506809e-08  5.194296e-02      -0.011756
17  0.003030  900  5.961926e-02  1.104165e-07  5.962651e-02      -0.012153
18  0.004220  900  6.897094e-02  1.525013e-07  6.897850e-02      -0.010959
19  0.005862  900  8.037900e-02  1.645138e-07  8.038727e-02      -0.010278
20  0.008119  900  9.427899e-02  1.873157e-07  9.428864e-02      -0.010235
21  0.011199  900  1.111358e-01  1.245491e-07  1.111485e-01      -0.011453
22  0.015364  900  1.314026e-01  3.234054e-08  1.314188e-01      -0.012393
23  0.020930  900  1.554478e-01  6.605133e-08  1.554710e-01      -0.014971
24  0.028262  900  1.834109e-01  1.154673e-07  1.834374e-01      -0.014454
25  0.037753  900  2.150491e-01  1.121958e-07  2.150787e-01      -0.013754
26  0.049792  900  2.495038e-01  6.287901e-08  2.495326e-01      -0.011539
27  0.064727  900  2.851177e-01  3.856411e-08  2.851694e-01      -0.018125
28  0.082822  900  3.194429e-01  6.304120e-08  3.195016e-01      -0.018349
29  0.104234  900  3.493587e-01  5.210661e-08  3.493935e-01      -0.009970
30  0.128999  900  3.718037e-01  3.207575e-08  3.718562e-01      -0.014103
31  0.157049  900  3.836693e-01  1.962794e-08  3.837280e-01      -0.015290
32  0.188228  900  3.830579e-01  1.505282e-08  3.831066e-01      -0.012708
33  0.222328  900  3.693589e-01  1.023398e-08  3.693999e-01      -0.011105
34  0.259109  900  3.434488e-01  6.864244e-09  3.434788e-01      -0.008730
35  0.298323  900  3.074871e-01  4.473324e-09  3.075003e-01      -0.004300
36  0.339728  900  2.645603e-01  3.425473e-09  2.645616e-01      -0.000463
37  0.383099  900  2.181946e-01  2.303236e-09  2.181826e-01       0.005503
38  0.428226  900  1.718940e-01  1.574939e-09  1.718667e-01       0.015834
39  0.474925  900  1.287423e-01  9.308248e-10  1.287040e-01       0.029695
40  0.523028  900  9.109757e-02  5.155383e-10  9.105279e-02       0.049186
41  0.572391  900  6.039424e-02  2.285401e-10  6.035017e-02       0.073026
42  0.622883  900  3.706628e-02  5.272396e-11  3.702538e-02       0.110450
43  0.674392  900  2.067637e-02  4.021193e-12  2.064179e-02       0.167513
44  0.726818  900  1.018615e-02  1.342143e-13  1.016084e-02       0.249121
45  0.780075  900  4.214506e-03  1.604341e-14  4.198437e-03       0.382738
46  0.834085  900  1.320811e-03  9.566276e-15  1.312271e-03       0.650790
47  0.888782  900  2.385066e-04  4.713230e-15  2.356462e-04       1.213883
48  0.944104  900  6.414889e-06  7.639009e-15  4.501338e-06      42.510716
49  1.000000  900 -8.058597e-21  0.000000e+00  4.033789e-22   -2097.773492

 ──── 
  T8  
 ──── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900  1.613146e-03  3.420385e-09  1.613284e-03      -0.008544
1   0.000014  900  1.874144e-03  9.276445e-09  1.874191e-03      -0.002515
2   0.000020  900  2.182758e-03  9.269577e-09  2.182826e-03      -0.003123
3   0.000027  900  2.548460e-03  6.652940e-09  2.548570e-03      -0.004281
4   0.000038  900  2.983061e-03  5.633533e-09  2.983218e-03      -0.005264
5   0.000054  900  3.500748e-03  5.115785e-09  3.500954e-03      -0.005892
6   0.000076  900  4.118622e-03  1.352812e-08  4.118866e-03      -0.005941
7   0.000106  900  4.857541e-03  3.322651e-08  4.857800e-03      -0.005324
8   0.000148  900  5.742962e-03  1.417971e-08  5.743293e-03      -0.005767
9   0.000207  900  6.805914e-03  6.341534e-09  6.806386e-03      -0.006937
10  0.000290  900  8.084226e-03  7.420612e-09  8.084851e-03      -0.007740
11  0.000406  900  9.623712e-03  1.255057e-08  9.624589e-03      -0.009112
12  0.000569  900  1.147960e-02  9.347756e-09  1.148061e-02      -0.008853
13  0.000796  900  1.371790e-02  5.136666e-09  1.371912e-02      -0.008925
14  0.001113  900  1.641627e-02  6.076620e-08  1.641790e-02      -0.009972
15  0.001556  900  1.966500e-02  1.191789e-08  1.966721e-02      -0.011227
16  0.002173  900  2.356731e-02  3.427936e-08  2.357030e-02      -0.012679
17  0.003030  900  2.823861e-02  5.252044e-08  2.824222e-02      -0.012803
18  0.004220  900  3.380559e-02  7.555889e-08  3.380960e-02      -0.011864
19  0.005862  900  4.040335e-02  8.352701e-08  4.040792e-02      -0.011304
20  0.008119  900  4.816684e-02  9.614941e-08  4.817222e-02      -0.011152
21  0.011199  900  5.721661e-02  6.359649e-08  5.722350e-02      -0.012030
22  0.015364  900  6.763642e-02  1.553395e-08  6.764526e-02      -0.013075
23  0.020930  900  7.944026e-02  3.296211e-08  7.945174e-02      -0.014452
24  0.028262  900  9.252238e-02  5.691745e-08  9.253454e-02      -0.013143
25  0.037753  900  1.066141e-01  5.388114e-08  1.066293e-01      -0.014313
26  0.049792  900  1.212408e-01  2.924201e-08  1.212554e-01      -0.012033
27  0.064727  900  1.357241e-01  1.772148e-08  1.357462e-01      -0.016265
28  0.082822  900  1.492115e-01  3.017648e-08  1.492360e-01      -0.016414
29  0.104234  900  1.607492e-01  2.526172e-08  1.607667e-01      -0.010839
30  0.128999  900  1.694563e-01  1.626983e-08  1.694799e-01      -0.013942
31  0.157049  900  1.744625e-01  1.074130e-08  1.744859e-01      -0.013423
32  0.188228  900  1.751775e-01  8.622205e-09  1.751991e-01      -0.012315
33  0.222328  900  1.712907e-01  6.305530e-09  1.713105e-01      -0.011562
34  0.259109  900  1.628568e-01  4.919543e-09  1.628734e-01      -0.010175
35  0.298323  900  1.503185e-01  3.294730e-09  1.503295e-01      -0.007324
36  0.339728  900  1.344792e-01  2.769750e-09  1.344858e-01      -0.004853
37  0.383099  900  1.163917e-01  1.938815e-09  1.163924e-01      -0.000590
38  0.428226  900  9.721974e-02  1.499271e-09  9.721326e-02       0.006665
39  0.474925  900  7.810743e-02  9.705660e-10  7.809554e-02       0.015234
40  0.523028  900  6.007026e-02  6.439555e-10  6.005401e-02       0.027060
41  0.572391  900  4.392804e-02  3.448473e-10  4.390893e-02       0.043522
42  0.622883  900  3.025616e-02  9.368251e-11  3.023562e-02       0.067920
43  0.674392  900  1.935401e-02  1.126451e-11  1.933415e-02       0.102728
44  0.726818  900  1.125175e-02  1.091269e-12  1.123442e-02       0.154284
45  0.780075  900  5.733168e-03  2.271904e-14  5.719545e-03       0.238189
46  0.834085  900  2.390766e-03  1.602689e-14  2.381682e-03       0.381406
47  0.888782  900  7.020527e-04  8.140597e-15  6.972474e-04       0.689194
48  0.944104  900  9.309433e-05  1.290596e-14  9.223973e-05       0.926500
49  1.000000  900 -4.491546e-21  0.000000e+00  4.678281e-22   -1060.084729

 ───── 
  T15  
 ───── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900 -1.146229e-03 -2.597079e-09 -1.146518e-03      -0.025245
1   0.000014  900 -1.882191e-03 -7.412973e-09 -1.882368e-03      -0.009364
2   0.000020  900 -2.728868e-03 -1.071684e-08 -2.729075e-03      -0.007567
3   0.000027  900 -3.675846e-03 -9.380428e-09 -3.676090e-03      -0.006649
4   0.000038  900 -4.698915e-03 -9.553317e-09 -4.699312e-03      -0.008448
5   0.000054  900 -5.756861e-03 -8.274695e-09 -5.757313e-03      -0.007843
6   0.000076  900 -6.801176e-03 -2.416863e-08 -6.801607e-03      -0.006342
7   0.000106  900 -7.787911e-03 -6.115661e-08 -7.788591e-03      -0.008731
8   0.000148  900 -8.687508e-03 -2.261477e-08 -8.688230e-03      -0.008303
9   0.000207  900 -9.513941e-03 -7.962608e-09 -9.514422e-03      -0.005055
10  0.000290  900 -1.035246e-02 -8.700996e-09 -1.035327e-02      -0.007798
11  0.000406  900 -1.130972e-02 -1.528452e-08 -1.131077e-02      -0.009334
12  0.000569  900 -1.240892e-02 -1.064896e-08 -1.241052e-02      -0.012902
13  0.000796  900 -1.358984e-02 -2.997392e-09 -1.359173e-02      -0.013873
14  0.001113  900 -1.478826e-02 -6.451060e-08 -1.479022e-02      -0.013235
15  0.001556  900 -1.592297e-02 -6.308752e-09 -1.592524e-02      -0.014252
16  0.002173  900 -1.687018e-02 -2.620779e-08 -1.687216e-02      -0.011727
17  0.003030  900 -1.747977e-02 -3.814569e-08 -1.748150e-02      -0.009883
18  0.004220  900 -1.757000e-02 -4.431443e-08 -1.757260e-02      -0.014798
19  0.005862  900 -1.688951e-02 -3.582343e-08 -1.689250e-02      -0.017703
20  0.008119  900 -1.509819e-02 -2.598234e-08 -1.510114e-02      -0.019523
21  0.011199  900 -1.176894e-02 -2.017378e-09 -1.177063e-02      -0.014361
22  0.015364  900 -6.390137e-03  6.167688e-09 -6.391830e-03      -0.026480
23  0.020930  900  1.603497e-03  6.846988e-09  1.605844e-03      -0.146149
24  0.028262  900  1.272381e-02  1.468720e-08  1.272970e-02      -0.046276
25  0.037753  900  2.730243e-02  2.267856e-08  2.730513e-02      -0.009878
26  0.049792  900  4.529096e-02  1.921437e-08  4.529605e-02      -0.011243
27  0.064727  900  6.605285e-02  1.519063e-08  6.607249e-02      -0.029730
28  0.082822  900  8.837747e-02  2.531445e-08  8.839820e-02      -0.023453
29  0.104234  900  1.104928e-01  2.212048e-08  1.105035e-01      -0.009689
30  0.128999  900  1.304757e-01  1.540006e-08  1.304987e-01      -0.017599
31  0.157049  900  1.462602e-01  1.065045e-08  1.462880e-01      -0.018989
32  0.188228  900  1.563300e-01  8.533157e-09  1.563566e-01      -0.016994
33  0.222328  900  1.598133e-01  6.242550e-09  1.598377e-01      -0.015308
34  0.259109  900  1.566493e-01  4.827487e-09  1.566702e-01      -0.013341
35  0.298323  900  1.474901e-01  3.236772e-09  1.475045e-01      -0.009774
36  0.339728  900  1.335286e-01  2.688545e-09  1.335379e-01      -0.006960
37  0.383099  900  1.162597e-01  1.876775e-09  1.162622e-01      -0.002199
38  0.428226  900  9.725699e-02  1.426671e-09  9.725122e-02       0.005931
39  0.474925  900  7.798859e-02  9.150410e-10  7.797671e-02       0.015237
40  0.523028  900  5.969217e-02  5.908610e-10  5.967541e-02       0.028083
41  0.572391  900  4.332256e-02  3.070200e-10  4.330287e-02       0.045475
42  0.622883  900  2.952119e-02  8.143861e-11  2.950007e-02       0.071597
43  0.674392  900  1.860282e-02  9.096424e-12  1.858265e-02       0.108574
44  0.726818  900  1.058420e-02  7.845123e-13  1.056673e-02       0.165350
45  0.780075  900  5.223633e-03  2.041646e-14  5.209998e-03       0.261694
46  0.834085  900  2.075278e-03  1.404766e-14  2.066360e-03       0.431546
47  0.888782  900  5.635043e-04  7.087255e-15  5.591581e-04       0.777276
48  0.944104  900  6.538270e-05  1.129375e-14  6.391234e-05       2.300583
49  1.000000  900 -2.433074e-21  0.000000e+00 -8.276695e-22     193.966798

 ───── 
  T24  
 ───── 
           x   Q2           eko     eko_error        LHAPDF  percent_error
0   0.000010  900 -6.183490e-03 -1.459294e-08 -6.205640e-03      -0.356943
1   0.000014  900 -8.535154e-03 -4.072096e-08 -8.561513e-03      -0.307877
2   0.000020  900 -1.109053e-02 -4.781495e-08 -1.112140e-02      -0.277519
3   0.000027  900 -1.377249e-02 -3.673349e-08 -1.380761e-02      -0.254333
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49  1.000000  900 -2.433074e-21  0.000000e+00 -8.276695e-22     193.966798

felixhekhorn
felixhekhorn approved these changes Feb 16, 2023
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As already said, the only two points remaining are

  • complete docs
  • complete unit tests

else the code is good and doing what it is supposed to do

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enocera commented Feb 16, 2023

I wonder whether @enocera can tell us they are intentional ...

  • most of the distributions are ok
  • the ones failing are those involving a s or c or b valence distribution, so V,V8,V15,V24
  • in fact, in the LHAPDF file it seems s=s¯, c=c¯, b=b¯

That was intentional. And hard-coded in the FK generator.

@felixhekhorn felixhekhorn mentioned this pull request Feb 16, 2023
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giacomomagni and others added 16 commits February 17, 2023 14:47
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giacomomagni commented Feb 21, 2023 •
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@adrianneschauss, okay we tick all the missing pieces.
So I think we can merge. Just press the green button :)

@adrianneschauss adrianneschauss merged commit daed096 into master Feb 22, 2023
@adrianneschauss adrianneschauss deleted the polarized_implementation branch February 22, 2023 13:39
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polarized setup
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@giacomomagni @alecandido @felixhekhorn @enocera @adrianneschauss