Core Math Functionality (MathCore)

The Core Mathematical Library of ROOT.

MathCore provides a collection of functions and C++ classes for HEP numerical computing. This library provides only the basic mathematical functions and algorithms and not all the functionality required by the HEP community. More advanced mathematical functionalities is provided by the MathMore. The current set includes classes and functions for:

• Basic special functions used in HEP like the gamma, beta and error function;
• Statistical functions : mathematical functions used in statistics, such as the probability density functions and the cumulative distributions functions (lower and upper integral of the pdf's) for continuous and discrete distributions.;
• Function Classes and Interfaces :
  • Generic Function Evaluation Interfaces, including helper class to wrap free (static) and non-static member functions
  • Parametric Function Evaluation Interfaces.
• Numerical algorithms: user classes with (in some cases) basic implementations for:
  • Numerical Integration
  • Numerical Differentiation
  • One-dimensional Root-Finding
  • One-dimensional Minimization and Multi-dimensional Minimization
• Fitting and Parameter Estimation :classes for fitting and parameter estimation from a given data set.

Note that in this latest release the GenVector (physics and geometry vectors for 2,3 and 4 dimensions with their transformations) is not anymore part of MathCore, but is built as a separate library. MathCore contains instead now classes which were originally part of libCore. These include:

• TMath : namespace with mathematical functions and basic function algorithms.
• TComplex: class for complex numbers.
• Random classes: base class TRandom and the derived classes TRandom1, TRandom2 and TRandom3, implementing the pseudo-random number generators.
• Other classes, such as
  • TKDTree for partitioning the data using a kd-Tree and TKDTreeBinning for binning data using a kdTree
  • ROOT::Math::GoFTest for goodness of fit tests

Topics
	Fitting and Parameter Estimation
	Classes used for fitting (regression analysis) and estimation of parameter values given a data sample.
	Function Classes and Interfaces
	Interfaces (abstract classes) and Base classes used in MathCore and MathMore numerical methods for describing function classes.
	Goodness of Fit Tests
	Classical one-dimensional goodness of git tests for unbinned data.
	Interface classes for Random number generation
	Pseudo-random numbers generator classes and for generation of random number distributions.
	MathMore
	The Mathematical library providing GSL extensions to MathCore.
	Numerical Algorithms
	Numerical Algorithm classes from the Core Math Functionality (MathCore) and MathMore libraries.
	Special functions
	Special mathematical functions.
	Statistical functions
	Probability density functions, cumulative distribution functions and their inverses (quantiles) for various statistical distributions (continuous and discrete).

Classes
class	ROOT::Math::Delaunay2D
	Class to generate a Delaunay triangulation of a 2D set of points. More...
class	TKDTreeBinning
	A class providing multidimensional binning. More...
class	TStatistic
	Statistical variable, defined by its mean and variance (RMS). More...