Math tutorials

Examples showing the Math classes.

Table of contents

• Basic features of MathCore
• Basic features of MathMore (GSL binding)
• Fast Fourier Transform
• Fitting
• Histogramming related features
• Linear algebra
• Minimizer features
• Physics vectors
• R binding
• Random number generation with Unuran
• RVec basic features

Basic features of MathCore

To get started these examples show some of the basic features of the MathCore library.

Tutorial		Description
ChebyshevPol.C		Example of Chebyshev polynomials using TFormula pre-defined definitions of chebyshev polynomials.
	exampleFunction.py	Example of using Python functions as inputs to numerical algorithms using the ROOT Functor class.
exampleFunctor.C		Tutorial illustrating how to create a TF1 class using c++ functors or class member functions.
GammaFun.C		Example showing the usage of the major special math functions (gamma, beta, erf) in ROOT.
goftest.C		Example showing usage of goodness of fit tests.
kdTreeBinning.C		Example binning the data in cells of equal content using a kd-tree.
limit.C		This example shows random number generation for filling histograms.
mathcoreSpecFunc.C		Example macro showcasing some special mathematical functions.
multidimSampling.C		Example of random number generation by sampling a multi-dim distribution using the DistSampler class.
permute.C		Tutorial illustrating the use of TMath::Permute for computing all permutations of n natural numbers.
testrandom.C		Performance test of all the ROOT random generator (TRandom, TRandom1, TRandom2 and TRandom3).

Basic features of MathMore

To get started these examples show some of the basic features of the MathMore library, a package incorporating advanced numerical functionality and dependent on external libraries like the GNU Scientific Library (GSL).

Tutorial		Description
exampleMultiRoot.C		Example of using multiroot finder based on GSL algorithm.
Legendre Polynomials.
Legendre Polynomials.
mathmoreIntegration.C		Example on the usage of the adaptive 1D integration algorithm of MathMore.
mathmoreIntegrationMultidim.C		Example on the usage of the multidimensional integration algorithm of MathMore.
quasirandom.C		Example of quasi-random numbers generation.

Physics vectors

Examples showing usage of the GenVector library, generic class templates for modeling vectors in 2, 3 and 4 dimensions (relativistic vectors) and their rotation and transformation algorithms.

Tutorial	Description
mathcoreGenVector.C	Example macro testing available methods and operation of the GenVector classes.
mathcoreVectorCollection.C	Example showing how to write and read a std vector of ROOT::Math LorentzVector in a ROOT tree.
mathcoreVectorFloatIO.C	Macro illustrating I/O with Lorentz Vectors of floats.
mathcoreVectorIO.C	Example of I/O of a GenVector Lorentz Vectors in a Tree and comparison with legacy TLorentzVector.

Histogramming related features

Examples showing usage of mathematical features for histigrams.

Tutorial		Description
chi2test.C		Example to use chi2 test for comparing two histograms.
exampleTKDE.C		Example of using the TKDE class (kernel density estimator).
hlquantiles.C		Demo for quantiles (with highlight mode).
principal.C	principal.py	Principal Components Analysis (PCA) example.
qa2.C		Test generation of random numbers distributed according to a function defined by the user.
quantiles.C		Demo for quantiles.

Minimizer features

Examples showing usage of ROOT minimizers.

Tutorial	Description
NumericalMinimization.C	Example on how to use the Minimizer class in ROOT.

Topics
	Fast Fourier Transforms tutorials
	Example showing the Fast Fourier Transforms interface in ROOT.
	Fit Tutorials
	These tutorials illustrate the main fitting features. Their names are related to the aspect which is treated in the code.
	FOAM tutorials
	Examples showing how to use FOAM.
	Matrix tutorials
	Examples showing how to use TMatrix.
	Probability distributions tutorials
	Examples showing the available probability distributions in ROOT.
	Quadratic programming package
	Example showing the usage of the quadratic programming package quadp.
	R tutorials
	Examples showing the R interface.
	Unuran tutorials
	Examples showing unuran capabilities.
	VecOps tutorials
	These examples show the functionalities of the VecOps utilities.

Files
file	ChebyshevPol.C
	Example of Chebyshev polynomials using TFormula pre-defined definitions of chebyshev polynomials.
file	chi2test.C
	Example to use chi2 test for comparing two histograms.
file	exampleFunction.py
	Example of using Python functions as inputs to numerical algorithms using the ROOT Functor class.
file	exampleFunctor.C
	Tutorial illustrating how to create a TF1 class using C++ functors or class member functions.
file	exampleMultiRoot.C
	Example of using multiroot finder based on GSL algorithm.
file	exampleTKDE.C
	Example of using the TKDE class (kernel density estimator).
file	GammaFun.C
	Example showing the usage of the major special math functions (gamma, beta, erf) in ROOT.
file	goftest.C
	Example showing usage of goodness of fit tests.
file	hlquantiles.C
	Demo for quantiles (with highlight mode).
file	kdTreeBinning.C
	Example binning the data in cells of equal content using a kd-tree.
file	Legendre.C
	Example of first few Legendre Polynomials.
file	Legendre.py
	Example of first few Legendre Polynomials.
file	LegendreAssoc.C
	Example describing the usage of different kinds of Associate Legendre Polynomials.
file	limit.C
	This example shows random number generation for filling histograms.
file	mathcoreGenVector.C
	Example macro testing available methods and operation of the GenVector classes.
file	mathcoreSpecFunc.C
	Example macro showcasing some special mathematical functions.
file	mathcoreVectorCollection.C
	Example showing how to write and read a std vector of ROOT::Math LorentzVector in a ROOT tree.
file	mathcoreVectorFloatIO.C
	Macro illustrating I/O with Lorentz Vectors of floats.
file	mathcoreVectorIO.C
	Example of I/O of a GenVector Lorentz Vectors in a Tree and comparison with legacy TLorentzVector.
file	mathmoreIntegration.C
	Example on the usage of the adaptive 1D integration algorithm of MathMore.
file	mathmoreIntegrationMultidim.C
	Example on the usage of the multidimensional integration algorithm of MathMore.
file	multidimSampling.C
	Example of random number generation by sampling a multi-dim distribution using the DistSampler class.
file	NumericalMinimization.C
	Example on how to use the Minimizer class in ROOT.
file	permute.C
	Tutorial illustrating the use of TMath::Permute for computing all permutations of n natural numbers.
file	principal.C
	Principal Components Analysis (PCA) example.
file	principal.py
	Principal Components Analysis (PCA) example.
file	qa2.C
	Test generation of random numbers distributed according to a function defined by the user.
file	quantiles.C
	Demo for quantiles.
file	quasirandom.C
	Example of quasi-random numbers generation.
file	testrandom.C
	Performance test of all the ROOT random generator (TRandom, TRandom1, TRandom2 and TRandom3).