[tutorials] Re-organize math tutorials

math/mathcore/inc/Math/PdfFuncMathCore.h

@@ -386,9 +386,9 @@ namespace Math {
 
   /**
 
-  Probability density function of the normal (Gaussian) distribution.
+  Probability density function of the normal (Gaussian) distribution with mean x0 and standard deviation sigma.
 
-  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-x^2 / 2\sigma^2} \f]
+  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-(x-x_0)^2 / 2\sigma^2} \f]
 
   For detailed description see
   <A HREF="http://mathworld.wolfram.com/NormalDistribution.html">
@@ -493,9 +493,9 @@ namespace Math {
 
   /**
 
-  Probability density function of the normal (Gaussian) distribution.
+  Probability density function of the normal (Gaussian) distribution with mean x0 and standard deviation sigma.
 
-  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-x^2 / 2\sigma^2} \f]
+  \f[ p(x) = {1 \over \sqrt{2 \pi \sigma^2}} e^{-(x-x_0)^2 / 2\sigma^2} \f]
 
   For detailed description see
   <A HREF="http://mathworld.wolfram.com/NormalDistribution.html">
@@ -552,7 +552,7 @@ namespace Math {
 
   \f[ p_{r}(x) = \frac{\Gamma(\frac{r+1}{2})}{\sqrt{r \pi}\Gamma(\frac{r}{2})} \left( 1+\frac{x^2}{r}\right)^{-(r+1)/2}  \f]
 
-  for \f$k \geq 0\f$. For detailed description see
+  for \f$r \geq 0\f$. For detailed description see
   <A HREF="http://mathworld.wolfram.com/Studentst-Distribution.html">
   Mathworld</A>.
 

math/mathcore/src/TMath.cxx

@@ -2593,11 +2593,10 @@ Bool_t TMath::Permute(Int_t n, Int_t *a)
 
 ////////////////////////////////////////////////////////////////////////////////
 /// Computes density function for Student's t- distribution
-/// (the probability function (integral of density) is computed in StudentI).
-///
-/// First parameter stands for x - the actual variable of the
-/// density function p(x) and the point at which the density is calculated.
-/// Second parameter stands for number of degrees of freedom.
+/// \f[ p_{n}(x) = \frac{\Gamma(\frac{n+1}{2})}{\sqrt{n \pi}\Gamma(\frac{n}{2})} \left( 1+\frac{x^2}{n}\right)^{-(n+1)/2}  \f]
+/// for \f$n \geq 0\f$, at point x for n (ndf) degrees of freedom. 
+/// This is equivalent to ROOT::Math::tdistribution_pdf(x,ndf)
+/// The probability function (integral of density) is computed in StudentI.
 ///
 /// About Student distribution:
 /// Student's t-distribution is used for many significance tests, for example,

tutorials/CMakeLists.txt

@@ -67,11 +67,11 @@ set(need_network dataframe/df027_SQliteDependencyOverVersion.C)
 #---Tutorials disabled depending on the build components-------------
 
 if(NOT clad)
-  set(clad_veto fit/minuit2GausFit.C
+  set(clad_veto math/fit/minuit2GausFit.C
                 # TODO: the next veto should not be necessary!
                 # The tutorial should also work without clad.
                 # See https://github.com/root-project/root/issues/15091.
-                fit/exampleFit3D.C
+                math/fit/exampleFit3D.C
   )
 endif()
 
@@ -156,7 +156,7 @@ else()
 endif()
 
 if(NOT ROOT_unuran_FOUND)
-  set(unuran_veto  math/testrandom.C unuran/unuranDemo.C unuran/unuranFoamTest.C
+  set(unuran_veto  math/testrandom.C math/unuran/unuranDemo.C math/unuran/unuranFoamTest.C
                    math/multidimSampling.C)
 endif()
 
@@ -197,7 +197,7 @@ endif()
 
 # variables identifying the package must have the package name  in lower case (it corresponds to the CMake option name)
 if(NOT ROOT_r_FOUND)
-  set(r_veto  r/*.C)
+  set(r_veto  math/r/*.C)
 endif()
 
 set(histfactory_veto histfactory/makeExample.C)
@@ -210,18 +210,18 @@ if(NOT ROOT_mathmore_FOUND)
   set(mathmore_veto
       math/quasirandom.C
       math/exampleMultiRoot.C
-      math/Bessel.C
+      math/pdf/pdf009_Bessel.C
       math/LegendreAssoc.C
       math/Legendre.C
       math/mathmoreIntegration.C
-      math/multivarGaus.C
-      math/tStudent.C
-      math/normalDist.C
+      math/pdf/pdf007_multivarGaus.C
+      math/pdf/pdf012_tStudent.C
+      math/pdf/pdf001_Nornal.C
       roostats/TestNonCentral.C
       roostats/TestNonCentral.py
       math/Legendre.py
-      math/Bessel.py
-      math/tStudent.py)
+      math/pdf/pdf009_Bessel.py
+      math/pdf/pdf012_tStudent.py)
 endif()
 
 if(NOT ROOT_fftw3_FOUND)
@@ -233,9 +233,9 @@ if(NOT ROOT_fftw3_FOUND)
                  roofit/rf210_angularconv.py
                  roofit/rf211_paramconv.py
                  roofit/rf512_wsfactory_oper.py
-                 fft/FFT.C
-                 fit/fitConvolution.C
-                 fit/fitConvolution.py)
+                 math/fft/FFT.C
+                 math/fit/fitConvolution.C
+                 math/fit/fitConvolution.py)
 endif()
 
 if(NOT ROOT_opengl_FOUND)
@@ -268,7 +268,7 @@ if(NOT gdml)
 endif()
 
 #---These ones requires a display to run-----------------------------
-set(gui_veto fit/fitpanel_playback.C
+set(gui_veto math/fit/fitpanel_playback.C
              cocoa/*.C
              geom/building.C geom/cheongwadae.C geom/geom*.C geom/lego.C geom/robot.C geom/south_gate.C geom/station*.C geom/tank.C geom/webdemo.C geom/web_cms.cxx
              gl/glViewerExercise.C gl/glViewerLOD.C gl/gviz3d.C gl/nucleus.C gl/viewer3DLocal.C gl/viewer3DMaster.C
@@ -417,7 +417,7 @@ set(extra_veto
   tree/h1chain.C
   http/*.C
   eve7/*.C
-  r/rootlogon.C)
+  math/r/rootlogon.C)
 
 if(MSVC AND NOT llvm13_broken_tests)
   list(APPEND extra_veto
@@ -500,7 +500,7 @@ if(mpi)
 endif()
 
 #---Special return code------------------------------------------------
-set(returncode_1 fit/fit2a.C
+set(returncode_1 math/fit/fit2a.C
                  graphics/earth.C
                  graphics/pavetext.C
                  graphics/tmathtext.C graphics/tmathtext2.C
@@ -515,7 +515,7 @@ set(returncode_1 fit/fit2a.C
                  hist/hlabels2.C
                  tree/h1analysis.C
                  math/chi2test.C
-                 r/SimpleFitting.C)
+                 math/r/SimpleFitting.C)
 #---Dependencies------------------------------------------------------
 set(unfold-testUnfold5d-depends tutorial-unfold-testUnfold5c)
 set(unfold-testUnfold5c-depends tutorial-unfold-testUnfold5b)
@@ -527,15 +527,15 @@ set(xml-xmlmodifyfile-depends tutorial-xml-xmlnewfile)
 set(xml-xmlreadfile-depends tutorial-xml-xmlnewfile)
 set(roofit-rf503_wspaceread-depends tutorial-roofit-rf502_wspacewrite)
 set(io-readCode-depends tutorial-io-importCode)
-set(fit-fit1-depends tutorial-hist-fillrandom)
-set(fit-myfit-depends tutorial-fit-fitslicesy)
-set(foam-foam_demopers-depends tutorial-foam-foam_demo)
+set(math-fit-fit1-depends tutorial-hist-fillrandom)
+set(math-fit-myfit-depends tutorial-math-fit-fitslicesy)
+set(math-foam-foam_demopers-depends tutorial-math-foam-foam_demo)
 set(tree-tree502_staff-depends  tutorial-tree-tree500_cernbuild)
 set(tree-tree501_cernstaff-depends  tutorial-tree-tree500_cernbuild)
 set(hist-hbars-depends  tutorial-tree-tree500_cernbuild)
 set(benchmarks-depends tutorial-hsimple
-                       tutorial-fit-fit1
-                       tutorial-fit-myfit
+                       tutorial-math-fit-fit1
+                       tutorial-math-fit-myfit
                        tutorial-hist-h1ReadAndDraw
                        tutorial-hist-FirstContour
                        tutorial-geom-na49view
@@ -863,8 +863,8 @@ if(ROOT_pyroot_FOUND)
   file(GLOB requires_numpy   RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}
       dataframe/df026_AsNumpyArrays.py
       dataframe/df032_RDFFromNumpy.py
-      fit/combinedFit.py
-      fit/multifit.py
+      math/fit/combinedFit.py
+      math/fit/multifit.py
       roofit/rf409_NumPyPandasToRooFit.py)
   file(GLOB requires_numba   RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} pyroot/pyroot004_NumbaDeclare.py)
   file(GLOB requires_pandas  RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}

tutorials/index.md

@@ -32,6 +32,18 @@ or
   root > .x $ROOTSYS/tutorials/benchmarks.C
 ```
 
+## Get started
+
+If you have never used ROOT before and don’t know where to start, we recommend that you first explore the [ROOT introductory course](https://github.com/root-project/student-course). You can also watch the recording of the course, but you should follow the material along on your PC. You also may want to have a look at the documentation of these modules:
+
+- @ref tutorial_hist
+- @ref tutorial_graphs
+- @ref tutorial_fit
+- @ref tutorial_tree
+- @ref tutorial_ntuple
+- @ref tutorial_dataframe
+- @ref tutorial_roofit
+
 The `$ROOTSYS/tutorials` directory includes several sub-directories:
 
 \defgroup tutorial_hist Histograms tutorials
@@ -70,14 +82,6 @@ The `$ROOTSYS/tutorials` directory includes several sub-directories:
 \ingroup Tutorials
 \brief Various ROOT geometry package examples.
 
-\defgroup tutorial_fft Fast Fourier Transforms tutorials
-\ingroup Tutorials
-\brief Example showing the Fast Fourier Transforms interface in ROOT.
-
-\defgroup tutorial_fit Fit Tutorials
-\ingroup Tutorials
-\brief These tutorials illustrate the main fitting features. Their names are related to the aspect which is treated in the code.
-
 \defgroup tutorial_roofit RooFit Tutorials
 \ingroup Tutorials
 \brief These tutorials illustrate the main features of [RooFit](group__Roofitmain.html): the name of the examples and their short description help in figuring out their objective.
@@ -122,9 +126,9 @@ The `$ROOTSYS/tutorials` directory includes several sub-directories:
 \ingroup Tutorials
 \brief Examples showing the Math classes.
 
-\defgroup tutorial_matrix Matrix tutorials
+\defgroup tutorial_mc Monte Carlo tutorials
 \ingroup Tutorials
-\brief Examples showing how to use TMatrix.
+\brief Monte Carlo examples.
 
 \defgroup tutorial_multicore Multicore tutorials
 \ingroup Tutorials
@@ -138,13 +142,9 @@ The `$ROOTSYS/tutorials` directory includes several sub-directories:
 \ingroup Tutorials
 \brief Selected examples illustrating how to use ROOT's Python interface: PyROOT.
 
-\defgroup tutorial_quadp Quadratic programming package.
+\defgroup tutorial_pythia Pythia tutorials
 \ingroup Tutorials
-\brief Example showing the usage of the quadratic programming package quadp.
-
-\defgroup tutorial_r R tutorials
-\ingroup Tutorials
-\brief Examples showing the R interface.
+\brief Examples showing the pythia usage.
 
 \defgroup tutorial_roostats RooStats Tutorials
 \ingroup Tutorials
@@ -170,14 +170,6 @@ The `$ROOTSYS/tutorials` directory includes several sub-directories:
 \ingroup Tutorials
 \brief Test programs for the classes TUnfold and related
 
-\defgroup tutorial_unuran Unuran tutorials
-\ingroup Tutorials
-\brief Examples showing unuran capabilities.
-
-\defgroup tutorial_vecops VecOps tutorials
-\ingroup Tutorials
-\brief These examples show the functionalities of the VecOps utilities.
-
 \defgroup tutorial_FITS FITS files interface tutorials
 \ingroup Tutorials
 \brief Examples showing the FITS file interface.

tutorials/math/FeldmanCousins.C → tutorials/legacy/math/FeldmanCousins.C

@@ -1,5 +1,5 @@
 /// \file
-/// \ingroup tutorial_math
+/// \ingroup tutorial_math_legacy
 /// \notebook -nodraw
 /// Example macro of using the TFeldmanCousins class in root.
 ///

tutorials/math/Rolke.C → tutorials/legacy/math/Rolke.C

@@ -1,5 +1,5 @@
 /// \file
-/// \ingroup tutorial_math
+/// \ingroup tutorial_math_legacy
 /// \notebook -nodraw
 /// Example of the usage of the TRolke class
 /// The TRolke class computes the profile likelihood

tutorials/legacy/math/index.md

@@ -0,0 +1,3 @@
+\defgroup tutorial_math_legacy Math tutorials
+\ingroup tutorial_legacy
+\brief Examples showing the math classes usage.

tutorials/fit/fit1.C → tutorials/math/fit/fit1.C

@@ -36,13 +36,13 @@ void fit1() {
    // (see <a href="fillrandom.C.nbconvert.ipynb">Filling histograms with random numbers from a function</a>)
    //
    TString dir = gROOT->GetTutorialDir();
-   dir.Append("/fit/");
+   dir.Append("/math/fit/");
    TFile *file = nullptr;
    if (!gSystem->AccessPathName("fillrandom.root")) {
       // file exists
       file = TFile::Open("fillrandom.root");
    } else {
-      gROOT->ProcessLine(Form(".x %s../hist/fillrandom.C(0)",dir.Data()));
+      gROOT->ProcessLine(Form(".x %s../../hist/fillrandom.C(0)",dir.Data()));
       file = TFile::Open("fillrandom.root");
       if (!file) return;
    }

tutorials/foam/foam_demopers.C → tutorials/math/foam/foam_demopers.C

@@ -23,7 +23,7 @@ Int_t foam_demopers()
 
    // need to load the foam_demo tutorial for the definition of the function
    TString macroName = gROOT->GetTutorialDir();
-   macroName.Append("/foam/foam_demo.C");
+   macroName.Append("/math/foam/foam_demo.C");
    gROOT->ProcessLine(TString::Format(".L %s+",macroName.Data()));
 
    //******************************************

tutorials/math/index.md

@@ -0,0 +1,35 @@
+\defgroup tutorial_fft Fast Fourier Transforms tutorials
+\ingroup tutorial_math
+\brief Example showing the Fast Fourier Transforms interface in ROOT.
+
+\defgroup tutorial_fit Fit Tutorials
+\ingroup tutorial_math
+\brief These tutorials illustrate the main fitting features. Their names are related to the aspect which is treated in the code.
+
+\defgroup tutorial_FOAM FOAM tutorials
+\ingroup tutorial_math
+\brief Examples showing how to use FOAM.
+
+\defgroup tutorial_matrix Matrix tutorials
+\ingroup tutorial_math
+\brief Examples showing how to use TMatrix.
+
+\defgroup tutorial_pdf Probability distributions tutorials
+\ingroup tutorial_math
+\brief Examples showing the available probability distributions in ROOT.
+
+\defgroup tutorial_quadp Quadratic programming package
+\ingroup tutorial_math
+\brief Example showing the usage of the quadratic programming package quadp.
+
+\defgroup tutorial_r R tutorials
+\ingroup tutorial_math
+\brief Examples showing the R interface.
+
+\defgroup tutorial_unuran Unuran tutorials
+\ingroup tutorial_math
+\brief Examples showing unuran capabilities.
+
+\defgroup tutorial_vecops VecOps tutorials
+\ingroup tutorial_math
+\brief These examples show the functionalities of the VecOps utilities.

tutorials/math/limit.C

@@ -1,7 +1,7 @@
 /// \file
 /// \ingroup tutorial_math
 /// \notebooks
-/// This program demonstrates the computation of 95 % C.L. limits.
+/// This program demonstrates the computation of 95 % confidence level (CL) limits.
 /// It uses a set of randomly created histograms.
 ///
 /// \macro_image

tutorials/math/mathLaplace.C → tutorials/math/pdf/pdf000_Laplace.C

@@ -1,5 +1,5 @@
 /// \file
-/// \ingroup tutorial_math
+/// \ingroup tutorial_pdf
 /// \notebook
 /// Test the TMath::LaplaceDist and TMath::LaplaceDistI functions
 ///
@@ -13,7 +13,7 @@
 #include "TF1.h"
 #include "TLegend.h"
 
-void mathLaplace(){
+void pdf000_Laplace(){
    TCanvas *c1=new TCanvas("c1", "TMath::LaplaceDist",600,800);
    c1->Divide(1, 2);
    TVirtualPad *pad1 = c1->cd(1);

tutorials/math/normalDist.C → tutorials/math/pdf/pdf001_Normal.C

@@ -1,5 +1,5 @@
 /// \file
-/// \ingroup tutorial_math
+/// \ingroup tutorial_pdf
 /// \notebook
 /// Tutorial illustrating the new statistical distributions functions (pdf, cdf and quantile)
 ///
@@ -15,7 +15,7 @@
 #include "TLegend.h"
 #include "TAxis.h"
 
-void normalDist() {
+void pdf001_Normal() {
 
    TF1 *pdfunc  = new TF1("pdf","ROOT::Math::normal_pdf(x, [0],[1])",-5,5);
    TF1 *cdfunc  = new TF1("cdf","ROOT::Math::normal_cdf(x, [0],[1])",-5,5);

tutorials/math/normalDist.py → tutorials/math/pdf/pdf001_Normal.py

@@ -1,5 +1,5 @@
 ## \file
-## \ingroup tutorial_math
+## \ingroup tutorial_dist
 ## \notebook
 ## Tutorial illustrating the new statistical distributions functions (pdf, cdf and quantile)
 ##