[RF] Plots of nested RooSimultaneous ignore ProjWData

[elusian]

• Checked for duplicates

Describe the bug

Nested RooSimultaneous are flattened into a single RooSimultaneous with a RooSuperCategory as index.
When plotting a RooSimultaneous, if the index category is derived its servers are searched inside the ProjWData set, and if not found the plot becomes a slice in the categories.
However, the only server of a RooSuperCategory is the internal RooMultiCategory, so in case of a nested RooSimultaneous the plot is always a slice.
This is basically #12020, except during plots and not generation. The solution is probably the same.

Expected behavior

Categories are summed over and not sliced

To Reproduce

import ROOT

x = ROOT.RooRealVar('x', '', 0, 1)

c1 = ROOT.RooCategory('c1', '', {'c11': 0, 'c12': 1})
c2 = ROOT.RooCategory('c2', '', {'c21': 0})

u = ROOT.RooUniform('u', '', x)
g = ROOT.RooGaussian('g', '', x, ROOT.RooFit.RooConst(0.5), ROOT.RooFit.RooConst(0.1))
s1 = ROOT.RooSimultaneous('s1', '', {'c11': u, 'c12': g}, c1)
s2 = ROOT.RooSimultaneous('s2', '', {'c21': s1}, c2)

proto = ROOT.RooDataSet('proto', '', {c1, c2})
c1.setIndex(0)
for i in range(50):
    proto.add({c1, c2})
c1.setIndex(1)
for i in range(50):
    proto.add({c1, c2})
    
frame = x.frame()
s2.plotOn(frame, ProjWData = ({c1, c2}, proto)) # only gauss
c1.setIndex(0)
s2.plotOn(frame, ProjWData = ({c1, c2}, proto)) # only uniform
frame.Draw()

Setup

ROOT master from LCG dev3

Additional context

[guitargeek]

Thanks! Yes, the solution was exactly the same, and thanks to your reproducer I also found some other problem with nested RooSimultaneous pdfs that I fixed in the linked PR 👍

[guitargeek]

I forgot to mention, in your reproducer code there is also a small problem. You are only specifying how c1 and c2 are projected, not that they are projected. For this, you also need to add the Project keyword arg:

frame = x.frame()
s2.plotOn(frame, Project={c1, c2}, ProjWData = ({c1, c2}, proto), LineColor="r") # only gauss
c1.setIndex(0)
s2.plotOn(frame, Project={c1, c2}, ProjWData = ({c1, c2}, proto)) # only uniform
frame.Draw()

[elusian]

Thanks you for all the fixes!

You are of course correct about the reproducer bug. I am used to plotting the dataset too, since that sets the projection variables and categories for the frame. The example was too minimal in this case.