[ALICE3] Protect LUT smearing against negative eigenvalues

A LUT covariance matrix close to singular (strongly correlated track
parameters at low pT) can carry a tiny negative eigenvalue (~ -1e-7) from
numerical precision. std::sqrt of it gives NaN, the smeared track gets NaN
parameters and is dropped by the on-the-fly tracker (hNaNBookkeeping).
This shows up as holes in the tracking efficiency in single pT bins and eta
halves, e.g. for e, pi, K, p between 0.09 and 0.25 GeV/c with 0.5 T LUTs.

Clamp the eigenvalue at zero before taking the square root: such a mode has
practically zero width, so it is simply not smeared.

Author: mario-krueger

ALICE3/Core/FlatTrackSmearer.cxx

@@ -21,6 +21,7 @@
 
 #include <TRandom.h>
 
+#include <algorithm>
 #include <cmath>
 #include <cstddef>
 #include <cstdint>
@@ -323,7 +324,10 @@ bool TrackSmearer::smearTrack(O2Track& o2track, const lutEntry_t* lutEntry, cons
     for (int j = 0; j < kNumEigenModes; ++j) {
       val += lutEntry->eigvec[j][i] * o2track.getParam(j);
     }
-    params[i] = gRandom->Gaus(val, std::sqrt(lutEntry->eigval[i]));
+    // A LUT covariance close to singular (strongly correlated parameters at low pT) can carry a tiny negative
+    // eigenvalue from numerical precision. std::sqrt of it gives NaN and the track is dropped later on, which
+    // shows up as holes in the tracking efficiency. Such a mode has practically zero width: do not smear along it.
+    params[i] = gRandom->Gaus(val, std::sqrt(std::max(0.f, lutEntry->eigval[i])));
   }
 
   // Transform back params vector