Felix: no news, besides noticing that in the Pb-Pb production we did not use the mean-vertex as a constraint (added in #15054)

Gabriele:

• Tested the vertex function on simulated PbPb data
• Reminder: vertex function gives a score for each point in the ITS volume based on
  
• Where f_i is
  
• Where i is i-th track from 3 first three inner layers, r-p is the distance of the track to the point
• Currently tested this strategy: voxelize the 3d volume around the beampipe:
  
  const int nZ = 2000;

  const int nX = 40;

  const int nY = 40;

  const float xMin = -.3f, xMax = .3f;

  const float yMin = -.3f, yMax = .3f;

  const float zMin = -11, zMax = 11;
• Compute the vertex function for each point (i.e. sum over all tracks)

Simulated PbPb data

max over x,y of V(x,y,z) vs z, vertical line is z of true vertex in ReadOut Frame (ROF) 31:
Clear peak of the function around the true vertex

So the function can carry the signal of the presence of a vertex in PbPb conditions. However, for the next ROF n. 32

In this ROF there where no vertices, but the signal of previous vertex is still present (even if with less intensity). Also the old seeding vertex was finding a vertex there. Is this a known problem?

Pitfalls

• On CPU extremely heavyweight to compute:
  
  Old CPU implementation, 20 threads, vertexing part serial:
  Vertex seeding total elapsed time: 1666.8417 ms for 133 (320 + 85) vertices found in 36/191 ROFs

Vertex function on CPU with 20 threads, computing the vertex function for a single ROF:
  Celled vertex function time: 1811.853949 ms
  
  
• Result dependent on binning

Next steps

• Since the vertex function seems informative, try on GPU and see the performance results
• In case of good performances, try to proceed in this way
• Can reduce number of computations by calculating the function only for points where pair of tracks passes by
• Select tracks with high contribution
• Perform a fit of the vertex with that tracks