[Minuit2] Only compute global correlation matrix when needed

For many parameters, the global correlation matrix can be very expensive
to compute. We therefore don't want to calculate it unconditionally, but
only when the user actually requests them by calling
`Minimizer::GlobalCC()`.

Author: guitargeek

math/minuit2/inc/Minuit2/MnUserParameterState.h

@@ -64,7 +64,7 @@ class MnUserParameterState {
    // user external representation
    const MnUserParameters &Parameters() const { return fParameters; }
    const MnUserCovariance &Covariance() const { return fCovariance; }
-   const MnGlobalCorrelationCoeff &GlobalCC() const { return fGlobalCC; }
+   MnGlobalCorrelationCoeff GlobalCC() const;
 
    // hessian (inverse of covariance matrix)
    MnUserCovariance Hessian() const;
@@ -161,7 +161,6 @@ class MnUserParameterState {
 
    MnUserParameters fParameters;
    MnUserCovariance fCovariance;
-   MnGlobalCorrelationCoeff fGlobalCC;
 
    std::vector<double> fIntParameters;
    MnUserCovariance fIntCovariance;

math/minuit2/src/Minuit2Minimizer.cxx

@@ -856,7 +856,7 @@ std::vector<double> Minuit2Minimizer::GlobalCC() const
    // is most strongly correlated with i.
 
    std::vector<double> out;
-   auto const &globalCC = fState.GlobalCC();
+   MnGlobalCorrelationCoeff globalCC = fState.GlobalCC();
    // no info available when minimization has failed or has some problems
    if (!globalCC.IsValid())
       return out;

math/minuit2/src/MnUserParameterState.cxx

@@ -148,7 +148,6 @@ MnUserParameterState::MnUserParameterState(const MinimumState &st, double up, co
       fIntCovariance =
          MnUserCovariance({st.Error().InvHessian().Data(), st.Error().InvHessian().size()}, st.Error().InvHessian().Nrow());
       fCovariance.Scale(2. * up);
-      fGlobalCC = MnGlobalCorrelationCoeff(st.Error().InvHessian());
 
       assert(fCovariance.Nrow() == VariableParameters());
 
@@ -219,7 +218,6 @@ void MnUserParameterState::Add(const std::string &name, double val, double err)
    if (fParameters.Add(name, val, err)) {
       fIntParameters.push_back(val);
       fCovarianceValid = false;
-      fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
       fValid = true;
    } else {
       // redefine an existing parameter
@@ -244,7 +242,6 @@ void MnUserParameterState::Add(const std::string &name, double val, double err,
    if (fParameters.Add(name, val, err, low, up)) {
       fCovarianceValid = false;
       fIntParameters.push_back(Ext2int(Index(name), val));
-      fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
       fValid = true;
    } else { // Parameter already exist - just set values
       int i = Index(name);
@@ -317,7 +314,6 @@ void MnUserParameterState::Fix(unsigned int e)
       fIntParameters.erase(fIntParameters.begin() + i, fIntParameters.begin() + i + 1);
    }
    fParameters.Fix(e);
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
 }
 
 void MnUserParameterState::Release(unsigned int e)
@@ -328,7 +324,6 @@ void MnUserParameterState::Release(unsigned int e)
       return;
    fParameters.Release(e);
    fCovarianceValid = false;
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
    unsigned int i = IntOfExt(e);
    if (Parameter(e).HasLimits())
       fIntParameters.insert(fIntParameters.begin() + i, Ext2int(e, Parameter(e).Value()));
@@ -360,7 +355,6 @@ void MnUserParameterState::SetLimits(unsigned int e, double low, double up)
    // set limits for parameter e (external index)
    fParameters.SetLimits(e, low, up);
    fCovarianceValid = false;
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
    if (!Parameter(e).IsFixed() && !Parameter(e).IsConst()) {
       unsigned int i = IntOfExt(e);
       if (low < fIntParameters[i] && fIntParameters[i] < up)
@@ -377,7 +371,6 @@ void MnUserParameterState::SetUpperLimit(unsigned int e, double up)
    // set upper limit for parameter e (external index)
    fParameters.SetUpperLimit(e, up);
    fCovarianceValid = false;
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
    if (!Parameter(e).IsFixed() && !Parameter(e).IsConst()) {
       unsigned int i = IntOfExt(e);
       if (fIntParameters[i] < up)
@@ -392,7 +385,6 @@ void MnUserParameterState::SetLowerLimit(unsigned int e, double low)
    // set lower limit for parameter e (external index)
    fParameters.SetLowerLimit(e, low);
    fCovarianceValid = false;
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
    if (!Parameter(e).IsFixed() && !Parameter(e).IsConst()) {
       unsigned int i = IntOfExt(e);
       if (low < fIntParameters[i])
@@ -407,7 +399,6 @@ void MnUserParameterState::RemoveLimits(unsigned int e)
    // remove limit for parameter e (external index)
    fParameters.RemoveLimits(e);
    fCovarianceValid = false;
-   fGlobalCC = MnGlobalCorrelationCoeff{}; // invalidate
    if (!Parameter(e).IsFixed() && !Parameter(e).IsConst())
       fIntParameters[IntOfExt(e)] = Value(e);
 }
@@ -531,6 +522,21 @@ void MnUserParameterState::SetPrecision(double eps)
    fParameters.SetPrecision(eps);
 }
 
+MnGlobalCorrelationCoeff MnUserParameterState::GlobalCC() const
+{
+   if (!fCovarianceValid) {
+      return MnGlobalCorrelationCoeff{}; // invalidate
+   }
+   int n = fIntCovariance.Nrow();
+   MnAlgebraicSymMatrix invHessian{static_cast<unsigned int>(n)};
+   for (int i = 0; i < n; ++i) {
+      for (int j = 0; j <= i; ++j) {
+         invHessian(i, j) = fIntCovariance(i, j);
+      }
+   }
+   return MnGlobalCorrelationCoeff{invHessian};
+}
+
 } // namespace Minuit2
 
 } // namespace ROOT

roofit/roofitcore/src/RooMinimizer.cxx

@@ -613,11 +613,11 @@ double correlation(std::vector<double> const &covMat, unsigned int i, unsigned i
 void RooMinimizer::fillCorrMatrix(RooFitResult &fitRes)
 {
    const std::size_t nParams = _fcn->getNDim();
-   std::vector<double> globalCC;
    TMatrixDSym corrs(nParams);
    TMatrixDSym covs(nParams);
+   std::vector<double> globalCC = _minimizer->GlobalCC();
+   globalCC.resize(nParams); // pad with zeros
    for (std::size_t ic = 0; ic < nParams; ic++) {
-      globalCC.push_back(_result->fGlobalCC[ic]);
       for (std::size_t ii = 0; ii < nParams; ii++) {
          corrs(ic, ii) = correlation(_result->fCovMatrix, ic, ii);
          covs(ic, ii) = covMatrix(_result->fCovMatrix, ic, ii);
@@ -1256,7 +1256,6 @@ void RooMinimizer::fillResult(bool isValid)
    // if minimizer provides error provides also error matrix
    // clear in case of re-filling an existing result
    _result->fCovMatrix.clear();
-   _result->fGlobalCC.clear();
 
    if (min.Errors() != nullptr) {
       updateErrors();
@@ -1312,10 +1311,6 @@ void RooMinimizer::updateErrors()
       }
    }
    // minos errors are set separately when calling Fitter::CalculateMinosErrors()
-
-   // update global CC
-   _result->fGlobalCC = min.GlobalCC();
-   _result->fGlobalCC.resize(npar); // pad with zeros
 }
 
 double RooMinimizer::FitResult::lowerError(unsigned int i) const