Regularization fixes + switch for the pre-PR-15610 compatibility mode

Common/DCAFitter/DCAFitterN_derivation.md

@@ -479,9 +479,11 @@ I_XX -> I_XX + 1/sigma_X,prior^2 .
 In code this is implemented as
 
 ```cpp
-constexpr float XRegErrFactor = 10.f;
-const float sigmaX2 = C_YY * XRegErrFactor;
-sxx += 1.f / sigmaX2;
+static constexpr float XRegErrFactor = 10.f;
+...
+if (xRegErrFactor > 0.f) {
+  sxx += 1.f / (cyy * xRegErrFactor);
+}
 ```
 
 This is different from multiplying `I_XX` by a number below one.  A reduction of
@@ -491,7 +493,15 @@ not alter `I_YY`, `I_YZ`, or `I_ZZ`.
 
 The regularization should remain weak.  It is a numerical stabilizer for badly
 conditioned geometries, not an additional detector measurement of the local
-track `X` coordinate.
+track `X` coordinate.  For this reason it is applied **only** where an invertible
+single-track contribution is actually required, i.e. for the `I_i` entering the
+chi2 minimization (`mTrcEInv`, hence `calcInverseWeight()`, `calcPCACoefs()`,
+`calcChi2()` and the Newton Hessian).  `calcPCACovMatrix()` rebuilds the `I_i`
+with `TrackCovI::XRegNone`: there the prior is not needed (the sum over prongs is
+inverted, not the individual terms, and a genuinely ill-conditioned sum is
+detected and replaced by a loose dummy covariance), and including it would make
+the reported longitudinal vertex error follow the dummy `XRegErrFactor * C_YY`
+instead of the track slopes.
 
 ### `calcPCACovMatrix()`
 

Common/DCAFitter/test/testDCAFitterN.cxx

@@ -171,6 +171,7 @@ inline void printStat(const FitStatusArray& a)
 
 BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
 {
+  constexpr bool oldMode = false; // if true, use the old mode of DCAFitterN, which is less correct but faster
   constexpr int NTest = 10000;
   o2::utils::TreeStreamRedirector outStream("dcafitterNTest.root");
 
@@ -196,6 +197,7 @@ BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
     std::memset(fitstat.data(), 0, sizeof(fitstat));
 
     o2::vertexing::DCAFitterN<2> ft; // 2 prong fitter
+    ft.setOldMode(oldMode);          // use the old mode of DCAFitterN
     ft.setBz(bz);
     ft.setPropagateToPCA(true);  // After finding the vertex, propagate tracks to the DCA. This is default anyway
     ft.setMaxR(200);             // do not consider V0 seeds with 2D circles crossing above this R. This is default anyway
@@ -280,6 +282,7 @@ BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
     std::memset(fitstat.data(), 0, sizeof(fitstat));
 
     o2::vertexing::DCAFitterN<2> ft; // 2 prong fitter
+    ft.setOldMode(oldMode);          // use the old mode of DCAFitterN
     ft.setBz(bz);
     ft.setPropagateToPCA(true);  // After finding the vertex, propagate tracks to the DCA. This is default anyway
     ft.setMaxR(200);             // do not consider V0 seeds with 2D circles crossing above this R. This is default anyway
@@ -366,6 +369,7 @@ BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
     std::memset(fitstat.data(), 0, sizeof(fitstat));
 
     o2::vertexing::DCAFitterN<2> ft; // 2 prong fitter
+    ft.setOldMode(oldMode);          // use the old mode of DCAFitterN
     ft.setBz(bz);
     ft.setPropagateToPCA(true);  // After finding the vertex, propagate tracks to the DCA. This is default anyway
     ft.setMaxR(200);             // do not consider V0 seeds with 2D circles crossing above this R. This is default anyway
@@ -451,6 +455,7 @@ BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
     std::memset(fitstat.data(), 0, sizeof(fitstat));
 
     o2::vertexing::DCAFitterN<2> ft; // 2 prong fitter
+    ft.setOldMode(oldMode);          // use the old mode of DCAFitterN
     ft.setBz(bz);
     ft.setPropagateToPCA(true);  // After finding the vertex, propagate tracks to the DCA. This is default anyway
     ft.setMaxR(200);             // do not consider V0 seeds with 2D circles crossing above this R. This is default anyway
@@ -535,6 +540,7 @@ BOOST_AUTO_TEST_CASE(DCAFitterNProngs)
     std::memset(fitstat.data(), 0, sizeof(fitstat));
 
     o2::vertexing::DCAFitterN<3> ft; // 3 prong fitter
+    ft.setOldMode(oldMode);          // use the old mode of DCAFitterN
     ft.setBz(bz);
     ft.setPropagateToPCA(true);  // After finding the vertex, propagate tracks to the DCA. This is default anyway
     ft.setMaxR(200);             // do not consider V0 seeds with 2D circles crossing above this R. This is default anyway

Detectors/GlobalTrackingWorkflow/study/src/SVStudy.cxx

@@ -175,6 +175,7 @@ void SVStudySpec::updateTimeDependentParams(ProcessingContext& pc)
     const auto& svparam = o2::vertexing::SVertexerParams::Instance();
     // Note: reading of the ITS AlpideParam needed for ITS timing is done by the RecoContainer
     mFitterV0.setBz(mBz);
+    mFitterV0.setOldMode(svparam.oldDCAFitterMode);
     mFitterV0.setUseAbsDCA(svparam.useAbsDCA);
     mFitterV0.setPropagateToPCA(false);
     mFitterV0.setMaxR(svparam.maxRIni);

Detectors/GlobalTrackingWorkflow/study/src/TrackMCStudy.cxx

@@ -211,6 +211,7 @@ void TrackMCStudy::updateTimeDependentParams(ProcessingContext& pc)
     if (mCheckSV) {
       const auto& svparam = o2::vertexing::SVertexerParams::Instance();
       mFitterV0.setBz(o2::base::Propagator::Instance()->getNominalBz());
+      mFitterV0.setOldMode(svparam.oldDCAFitterMode);
       mFitterV0.setUseAbsDCA(svparam.useAbsDCA);
       mFitterV0.setPropagateToPCA(false);
       mFitterV0.setMaxR(svparam.maxRIni);

Detectors/Vertexing/include/DetectorsVertexing/SVertexerParams.h

@@ -30,6 +30,7 @@ namespace vertexing
 struct SVertexerParams : public o2::conf::ConfigurableParamHelper<SVertexerParams> {
 
   // parameters
+  bool oldDCAFitterMode = true;    ///< pre(old) or post(new) PR15610+15784 behaviour of DCAFitter
   bool createFullV0s = false;      ///< fill V0s prongs/kinematics
   bool createFullCascades = false; ///< fill cascades prongs/kinematics
   bool createFull3Bodies = false;  ///< fill 3-body decays prongs/kinematics

Detectors/Vertexing/src/SVertexer.cxx

@@ -352,6 +352,7 @@ void SVertexer::setupThreads()
   mBz = o2::base::Propagator::Instance()->getNominalBz();
   int fitCounter = 0;
   for (auto& fitter : mFitterV0) {
+    fitter.setOldMode(mSVParams->oldDCAFitterMode);
     fitter.setFitterID(fitCounter++);
     fitter.setBz(mBz);
     fitter.setUseAbsDCA(mSVParams->useAbsDCA);
@@ -372,6 +373,7 @@ void SVertexer::setupThreads()
   mFitterCasc.resize(mNThreads);
   fitCounter = 1000;
   for (auto& fitter : mFitterCasc) {
+    fitter.setOldMode(mSVParams->oldDCAFitterMode);
     fitter.setFitterID(fitCounter++);
     fitter.setBz(mBz);
     fitter.setUseAbsDCA(mSVParams->useAbsDCA);
@@ -393,6 +395,7 @@ void SVertexer::setupThreads()
   mFitter3body.resize(mNThreads);
   fitCounter = 2000;
   for (auto& fitter : mFitter3body) {
+    fitter.setOldMode(mSVParams->oldDCAFitterMode);
     fitter.setFitterID(fitCounter++);
     fitter.setBz(mBz);
     fitter.setUseAbsDCA(mSVParams->useAbsDCA);