[Rivet] yodamerge for Histo1D

[Frank Siegert]

Hi Leif and all (especially the YODA devs),

For the completely general solution to run merging we'll have to wait for
the Rivet improvements discussed during the dev meeting and summarised in
Andy's mail. But what I was referring to is the "hack-ish" intermediate
solution of using yodamerge for histograms that Andy suggested: since we
store sumW, sumW2 and ScaledBy we can do a reasonable merging for dsigma/dX
type distributions. But currently, yodamerge (and implicitly the
YODA::Histo1D::operator+) does not take into account the ScaledBy property
at all. Instead it simply adds the sumW(2)'s and uses the last(?) ScaledBy
encountered. Thus the final normalisation is obviously arbitrary.

To fix that, I'm suggesting the following change to the
YODA::Histo1D::operator+:

     /// Add another histogram to this
     Histo1D& operator += (const Histo1D& toAdd) {
-      _axis += toAdd._axis;
+
+      // Undo scaling of both histograms
+      double scaledBy = annotation<double>("ScaledBy", 1.0);
+      _axis.scaleW(1.0/scaledBy);
+
+      double toAddScaledBy = toAdd.annotation<double>("ScaledBy", 1.0);
+      Axis1D<HistoBin1D, Dbn1D> toAddAxis = toAdd._axis;
+      toAddAxis.scaleW(1.0/toAddScaledBy);
+
+      // Add
+      _axis += toAddAxis;
+
+      // Re-apply combined scaling
+      double newScaledBy = scaledBy*toAddScaledBy/(scaledBy+toAddScaledBy);
+      _axis.scaleW(newScaledBy);
+      setAnnotation("ScaledBy", newScaledBy);
+
       return *this;
     }

I have tested this by merging Histo1D's from different runs with very
different numbers of events in them, and it looks like it's working nicely.

If there are no objections, and since I seem to have YODA write
permissions, I would push this into the central repo.

Cheers,
Frank
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