[RF] Plotting shifted RooHistPdfs doesn't go well

[guitargeek]

If you plot a shifted RooHistPdf, it doesn't look good. Probably because it is sampled at the wrong points, the numeric bin integrator doesn't work in this case, or both.

This is a problem that comes up relatively often in the ROOT forum, the last time here:
https://root-forum.cern.ch/t/roofit-in-root-6-28-04/55267

By looking for the keyword "shift" in the RooFit forum, one can see that this problem also came up in the past already:
https://root-forum.cern.ch/search?expanded=true&q=shift%20%23roofit-and-roostats
For example here:
https://root-forum.cern.ch/t/how-to-implement-a-horizontal-shift-for-roohistpdf/16787/6

I think I can approximately reproduce the workflow of the user that posted on the forum with this code.

void repro()
{
   using namespace RooFit;

   RooRealVar x("x", "", 1000, 1500);
   x.setBins(50);

   RooRealVar shift("shift", "", 10.0, -100, 100);

   RooFormulaVar xShifted("x_shifted", "x - shift", {x, shift});
   // Doesn't work better either...
   // RooLinearVar xShifted("x_shifted", "", x, RooConst(1.0), shift);

   std::vector<std::unique_ptr<RooDataHist>> templateHists;
   RooArgSet pdfs;
   RooArgSet yields;

   // Fill the templates
   for (std::size_t i = 0; i < 2; ++i) {
      auto suffix = std::to_string(i);

      TF1 pdf("pdf", "gaus", x.getMin(), x.getMax());
      pdf.SetParameters(1, 1200 + 100 * i, 50);
      pdf.Print();
      TH1D h("h", "", x.numBins(), x.getMin(), x.getMax());
      h.FillRandom("pdf", 10000);

      templateHists.emplace_back(std::make_unique<RooDataHist>(("template_data_hist_" + suffix).c_str(), "", x, &h));
      pdfs.addOwned(
         *new RooHistPdf(("template_hist_pdf_" + suffix).c_str(), "", xShifted, x, *templateHists.back(), 0));
      yields.addOwned(*new RooRealVar(("n_" + suffix).c_str(), "", 1000, 100, 100000));
   }

   // Construct final model
   RooAddPdf model("model", "", pdfs, yields);

   std::unique_ptr<RooDataHist> data{model.generateBinned(x)};

   // If the range is larger than the variable range, the problem is even amplified
   model.fitTo(*data, Range(0.0, 5000));

   TCanvas c1;

   auto frame = x.frame();
   data->plotOn(frame);
   model.plotOn(frame, Range(0.0, 2000.0));
   model.plotOn(frame, Components(*pdfs[0]), LineStyle(kDashed), LineColor(kRed));
   model.plotOn(frame, Components(*pdfs[1]), LineStyle(kDashed), LineColor(kBlue));
   frame->Draw();

   c1.SaveAs("plot.png");
}

The plot looks like this:

It would be nice if this plotting would work better, sampling the RooHistPdf at the correct points.