Allow to easily generate order masks

[scarlehoff]

In order to mask orders in the python interface I need to pass five different booleans

    qcd_result = pine.convolute(xf, xf, a_s,  [True, True, False, False, False])

What is the combination for NLO QCD and NLO EW? (so, LO * as and LO * a)
The closest combination for the he qcd_result I get is [True, False, False, False, True] but would prefer to have the exact definition.

(wasn't sure whether this is a python or internal pineapl thing, so wasn't sure whether to direct the question to @cschwan or @felixhekhorn @alecandido)

[cschwan]

You need to match the ordering returned by grid.orders(). This returns a list of PyOrder objects, which you can query with as_tuple(), which in turn returns the exponents. For Drell-Yan you should get the following tuples:

(0, 2, 0, 0)
(1, 2, 0, 0)
(1, 2, 1, 0)
(1, 2, 0, 1)
(0, 3, 0, 0)
(0, 3, 1, 0)
(0, 3, 0, 1)

The ordering can be different, and some tuples may be missing. The first tuple is the alpha^2 contribution (that's the LO), the next three are the NLO QCD (one power in alphas^1), and the last three are the NLO EW (alpha^3). If you don't need scale variations you can ignore (mask out) all orders that have non-zero power in logxir or logxif.

To calculate NLO QCD, you would therefore have to construct the following mask (no scale variations):

[True, True, False, False, False, False, False]

NLO EW would be

[True, False, False, False, True, False, False]

Note again that the ordering of the tuples given above are arbitrary, and that there can be many NLO contributions depending on the process, jets for instance can have four different NLO (and three LO), each with a renormalization and factorization scale variation grid, yielding in total 12 NLO grids (and three LO grids).

[scarlehoff]

I guess for different DY I would get different orders as well? For instance, for one of the DY_13TeV I get:

[orde.as_tuple() for orde in pine.orders()]

[(0, 2, 0, 0),
 (0, 3, 0, 0),
 (0, 3, 1, 0),
 (0, 3, 0, 1),
 (1, 2, 0, 0),
 (1, 2, 1, 0),
 (1, 2, 0, 1)]

So I guess in this case I need indeed [True, False, False, False, True] for QCD and [True, True, ... False...] for EW. Ok. If this kind of agreement (NLO QCD - NLO QCD) is the one expected between NNPDF fktables and pineappl (It's better than 1% sometimes even 1/1000 everywhere) then done 🎉

60728.104880 | 60522.719962
81917.298892 | 81734.695100
100762.631824 | 100868.942643
116706.650959 | 117000.740717
129694.870399 | 129659.852907
138809.684960 | 139312.762054
144109.582766 | 144696.949294
143703.496201 | 143953.700108
134733.578628 | 134808.297653
117564.704629 | 117600.032637
97699.892159 | 98277.907191
77189.144055 | 77139.725131
57170.074805 | 57260.858459
38933.969678 | 38963.564297
17959.886482 | 17931.200391

[cschwan]

60728.104880 | 60522.719962
81917.298892 | 81734.695100
100762.631824 | 100868.942643
116706.650959 | 117000.740717
129694.870399 | 129659.852907
138809.684960 | 139312.762054
144109.582766 | 144696.949294
143703.496201 | 143953.700108
134733.578628 | 134808.297653
117564.704629 | 117600.032637
97699.892159 | 98277.907191
77189.144055 | 77139.725131
57170.074805 | 57260.858459
38933.969678 | 38963.564297
17959.886482 | 17931.200391

This looks pretty good. In general, we expect differences due to

• Monte Carlo uncertainties, which for the FK table is lost, but for the PineAPPL grid you get them by running pineappl info --get results grid.pineappl.lz4 on it (the convoluted numbers use the PDF selected by the MC, which you can read off the runcard using pineappl info --get runcard); the Monte Carlo uncertainty is the third column,
• interpolation error, which for the PineAPPL you can also read off, that's the difference between the first two column, also shown in central, once as multiples of the Monte Carlo uncertainty (sigma) and once in per mille (1/1000); the remaining columns are the differences for a 9-point scale-varied result,
• evolution and x-grid compression (typically the 50 points in the APPLgrid are compressed to 20 points in the FK table) in the FK table, which should incur a difference of subpermille to subpercent, in extreme cases, for instance DY high mass there are up to per cent differences (but we don't fit these bins)
• and finally differences in the parameters. The PineAPPL grid was generated using slightly different parameters of the W and Z masses and widths, and also with a diagonal CKM matrix. However, both changes should not yield differences larger than a few per mille.

[alecandido]

Notice that pineappl info --get runcard for the time being will be available only for the madgraph generated pineapplgrids. The one produced by yadism are lacking it (I will concatenate the two runcards and put there at some point).

[alecandido]

Since #74 is not going to do it maybe we would still like to implement:

• a function to generate order masks from something similar to "NLO QCD" or "NLO EW"

[cschwan]

Since #74 is not going to do it maybe we would still like to implement:

* [ ]  a function to generate order masks from something similar to "NLO QCD" or "NLO EW"

I agree, I've changed the title to reflect this.

[cschwan]

Commit b824458 adds two new functions, which allow the selection of NLO EW and QCD. I've named them Order::mask_highest_alphas and Order::mask_highest_alpha, which IMO describe a bit better what they do. If the grid contains all orders for the specific process at LO, NLO, NNLO, ... then mask_highest_alphas will return the mask for LO, NLO, NNLO, ... QCD, and the other function for EW.

@alecandido @felixhekhorn @scarlehoff

• Can you please let me know whether it's clear what those functions do?
• To do understand them you can either read the docstrings from the commit b824458 or generate HTML documentation if you run cd pineappl && cargo doc --no-deps --open && cd .. in the repository
• Do you need more functionality, for instance specifically LO QCD, LO EW, etc.?
• The Python wrapper functions are still missing, we'll implement them once we've agreed upon what we want

[scarlehoff]

I'm afraid it is not super clear. In particular you said

mask_highest_alphas will return the mask for LO, NLO, NNLO

Do you mean it will return a mask for each of the orders or one containing LO + NLO + NNLO?

It might be silly but I'm confused about "mask_highest" returning "orders". Should I expect one mask or several? Or one mask with all orders? What do I have to give as the input?

The example didn't clarify it for me I'm afraid.

[felixhekhorn]

• I think you should also provide a short cut for Order::mask_highest_alphas(grid.orders())
• does this also work for NNLO grids (such as DIS)?

[alecandido]

Moreover: yesterday we said that might be useful to mask lower orders as well.

I would do instead a single function that accepts two ranges, first for QCD and second for QED, inside an option to make it None for unconstrained.