Math Libraries

MathCore

TMath

• Add some new functions based on std::numeric_limits:
  • double TMath::QuietNaN() returning a quite NaN
  • double TMath::SignalingNaN() returning a signaling NaN
  • double TMath::Infinity() returning an infinity double value
• Added also (based on numeric_limits) templated functions on T (where T can be double, float or int) for computing the limits for a given type:
  • T TMath::Limits< T >::Max() returning the maximum number which can be represented for the type T ( T TMath::Limits< double >::Max()=1.79769e+308)
  • T TMath::Limits< T >::Min() returning the minimum number which can be represented for the type T ( T TMath::Limits< double >::Max()=2.22507e-308)
  • T TMath::Limits< T >::Epsilon() returning the epsilon (see Wikipedia for its definition) for the type T ( T TMath::Limits< double >::Epsilon()=2.22045e-16)

TRandom1 and TRandom3

• Add an implementation of UInt_t GetSeed() to return the first element of the seed table. Before always a fixed value was returned, independently of the random generator state

ROOT::Fit::Fitter and related classes

• Add new version of the Fitter class with various improvements:
  • add the possibility to just evaluate the objective function (FCN) one time (Fitter::EvalFCN) and fill the result (class ROOT::Fit::FitResult using the obtained value of FCN plus the parameter values and errors from the Fit configuration class (ROOT::Fit::FitConfig). This required adding a nw constructor of FitResult from FitConfig. This originated from the Savannah request.
  • Add also new methods Fitter::SetFCN.
  • Update the configuration (parameter values and errors) after a fit with the FitResult values So next fit will use improved parameter values and errors. This update can be switched on/off by using FitConfig::SetUpdateAfterFit(on/off). By default is on.
  • Add new method FitConfig::SetFromFitResult.
  • Add possibility to run Hesse (Fitter:::CalculateHessErrors) without having done the minimization.
• Add support for weighted likelihood fits.
  • Add a new method Fitter::ApplyWeightCorrection(fcn2) which corrects covariance matrix for the weights using the likelihood function built using the weight square
  • Add the support for weights for the binned Poisson likelihood fits (in the ROOT::Fit::PoissonLikelihoodFCN class). A new option (WL) has been added also in TH1::Fit for performing weighted fits of histograms (see ).

ROOT::Math::Minimizer

MathMore

• New class ROOT::Math::GSLMultiRootFinder for finding the root of system of functions. The class is based on the GSL multi-root algorithm (see the GSL online manual) and it is used to solve a non-linear system of equations:

       f1(x1,....xn) = 0
       f2(x1,....xn) = 0
       ..................
       fn(x1,....xn) = 0
  

  The available GSL algorithms require the derivatives of the supplied functions or not (they are computed internally by GSL). In the first case the user needs to provide a list of multidimensional functions implementing the gradient interface (ROOT::Math::IMultiGradFunction) while in the second case it is enough to supply a list of functions implementing the ROOT::Math::IMultiGenFunction interface. The available algorithms requiring derivatives (see also the GSL documentation ) are the followings:
  • ROOT::Math::GSLMultiRootFinder::kHybridSJ with name "HybridSJ": modified Powell's hybrid method as implemented in HYBRJ in MINPACK
  • ROOT::Math::GSLMultiRootFinder::kHybridJ with name "HybridJ": unscaled version of the previous algorithm
  • ROOT::Math::GSLMultiRootFinder::kNewton with name "Newton": Newton method
  • ROOT::Math::GSLMultiRootFinder::kGNewton with name "GNewton": modified Newton method
  The algorithms without derivatives (see also the GSL documentation ) are the followings:
  • ROOT::Math::GSLMultiRootFinder::kHybridS with name "HybridS": same as HybridSJ but using finate difference approximation for the derivatives
  • ROOT::Math::GSLMultiRootFinder::kHybrid with name "Hybrid": unscaled version of the previous algorithm
  • ROOT::Math::GSLMultiRootFinder::kDNewton with name "DNewton": discrete Newton algorithm
  • ROOT::Math::GSLMultiRootFinder::kBroyden with name "Broyden": Broyden algorithm

Minuit2

• Improve Printing of information and Error messages. Use the class ROOT::Minuit2::MnPrint to store a static print level, which can be set by using the static function MnPrint::SetLevel(int ).
• Add new information messages in the VariableMetricBuilder (i.e. Migrad), to print some messages during the minimization.The new printing level is now also controlled by the Minuit2Minimizer class.
• Print now in the messages the parameter names instead of the parameter indices.
• fix the update of the number of function calls in Minuit2 after calling Hess after Migrad. The number is now not reset in MnHesse
• Fix a problem, when, after calling Hesse ,the edm was correct to values below the required tolerance. Now do not flag these cases as failed minimizations but as good ones.
• Correct tolerance by 2E-3 instead 2E-4 to ve conistent with what is done in F77 Minuit or TMinuit
• Avoid when using the CombinedMinimumBuilder (i.e. the Minimize algorithm) to call two times ModularFunctionMinimize::Minimum. Since this last function correct the tolerance by the Up value, a double correction was applied in this case.
• Implement the methods Minuit2Minimizer::GetHessianMatrix(double * mat) and Minuit2Minimizer::GetCovMatrix(double * mat).
• For retrieving the Hessian, a new method has been added, MnUserParameterState::Hessian, which returns the Hessian by inverting the covariance matrix, since the Hessian is not stored inside the Minuit2 classes.
• Fix a bug in MnUserTransformation when using unnamed parameters (bug 82552).
• Add the possibility when using Minos to pass the tolerance for the Migrad calls. (use a default of 0.1 * Up, which is the same value used in F77).

Minuit

• Implement the methods TMinuitMinimizer::GetHessianMatrix(double * mat) and TMinuitMinimizer::GetCovMatrix(double * mat).