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line3Dfit.C File Reference

Detailed Description

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Fitting of a TGraph2D with a 3D straight line

run this macro by doing:

root>.x line3Dfit.C+
Total Initial distance square = 8.65172e+07
Total final distance square 19988
Minimizer is Minuit2 / Migrad
MinFCN = 19988
NDf = 0
Edm = 1.04086e-06
NCalls = 248
Par_0 = 10.3555 +/- 0.392118
Par_1 = 19.9602 +/- 0.0688151
Par_2 = 0.999233 +/- 0.0444791
Par_3 = 2.00379 +/- 0.00783849
(int) 0
#include <TMath.h>
#include <TGraph2D.h>
#include <TRandom2.h>
#include <TStyle.h>
#include <TCanvas.h>
#include <TF2.h>
#include <TH1.h>
#include <Math/Functor.h>
#include <TPolyLine3D.h>
#include <Math/Vector3D.h>
#include <Fit/Fitter.h>
#include <cassert>
using namespace ROOT::Math;
// define the parametric line equation
void line(double t, const double *p, double &x, double &y, double &z) {
// a parametric line is define from 6 parameters but 4 are independent
// x0,y0,z0,z1,y1,z1 which are the coordinates of two points on the line
// can choose z0 = 0 if line not parallel to x-y plane and z1 = 1;
x = p[0] + p[1]*t;
y = p[2] + p[3]*t;
z = t;
bool first = true;
// function Object to be minimized
struct SumDistance2 {
// the TGraph is a data member of the object
TGraph2D *fGraph;
SumDistance2(TGraph2D *g) : fGraph(g) {}
// calculate distance line-point
double distance2(double x,double y,double z, const double *p) {
// distance line point is D= | (xp-x0) cross ux |
// where ux is direction of line and x0 is a point in the line (like t = 0)
XYZVector xp(x,y,z);
XYZVector x0(p[0], p[2], 0. );
XYZVector x1(p[0] + p[1], p[2] + p[3], 1. );
XYZVector u = (x1-x0).Unit();
double d2 = ((xp-x0).Cross(u)).Mag2();
return d2;
// implementation of the function to be minimized
double operator() (const double *par) {
assert(fGraph != nullptr);
double * x = fGraph->GetX();
double * y = fGraph->GetY();
double * z = fGraph->GetZ();
int npoints = fGraph->GetN();
double sum = 0;
for (int i = 0; i < npoints; ++i) {
double d = distance2(x[i],y[i],z[i],par);
sum += d;
if (first) {
std::cout << "Total Initial distance square = " << sum << std::endl;
first = false;
return sum;
int line3Dfit()
//double e = 0.1;
int nd = 10000;
// double xmin = 0; double ymin = 0;
// double xmax = 10; double ymax = 10;
TGraph2D * gr = new TGraph2D();
// Fill the 2D graph
double p0[4] = {10,20,1,2};
// generate graph with the 3d points
for (int N=0; N<nd; N++) {
double x,y,z = 0;
// Generate a random number
double t = gRandom->Uniform(0,10);
double err = 1;
// do a Gaussian smearing around the points in all coordinates
x += gRandom->Gaus(0,err);
y += gRandom->Gaus(0,err);
z += gRandom->Gaus(0,err);
// fit the graph now
// make the functor objet
SumDistance2 sdist(gr);
ROOT::Math::Functor fcn(sdist,4);
// set the function and the initial parameter values
double pStart[4] = {1,1,1,1};
// set step sizes different than default ones (0.3 times parameter values)
for (int i = 0; i < 4; ++i) fitter.Config().ParSettings(i).SetStepSize(0.01);
bool ok = fitter.FitFCN();
if (!ok) {
Error("line3Dfit","Line3D Fit failed");
return 1;
const ROOT::Fit::FitResult & result = fitter.Result();
std::cout << "Total final distance square " << result.MinFcnValue() << std::endl;
// get fit parameters
const double * parFit = result.GetParams();
// draw the fitted line
int n = 1000;
double t0 = 0;
double dt = 10;
for (int i = 0; i <n;++i) {
double t = t0+ dt*i/n;
double x,y,z;
// draw original line
for (int i = 0; i <n;++i) {
double t = t0+ dt*i/n;
double x,y,z;
return 0;
#define d(i)
Definition RSha256.hxx:102
#define g(i)
Definition RSha256.hxx:105
@ kRed
Definition Rtypes.h:66
@ kBlue
Definition Rtypes.h:66
void Error(const char *location, const char *msgfmt,...)
Use this function in case an error occurred.
Definition TError.cxx:185
#define N
TGLVector3 Cross(const TGLVector3 &v1, const TGLVector3 &v2)
Definition TGLUtil.h:323
winID h TVirtualViewer3D TVirtualGLPainter p
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void char Point_t Rectangle_t WindowAttributes_t Float_t Float_t Float_t Int_t Int_t UInt_t UInt_t Rectangle_t result
Option_t Option_t TPoint TPoint const char x1
TRObject operator()(const T1 &t1) const
R__EXTERN TRandom * gRandom
Definition TRandom.h:62
R__EXTERN TStyle * gStyle
Definition TStyle.h:433
const ParameterSettings & ParSettings(unsigned int i) const
get the parameter settings for the i-th parameter (const method)
Definition FitConfig.h:76
class containing the result of the fit and all the related information (fitted parameter values,...
Definition FitResult.h:47
Fitter class, entry point for performing all type of fits.
Definition Fitter.h:77
const FitResult & Result() const
get fit result
Definition Fitter.h:393
bool SetFCN(unsigned int npar, Function &fcn, const double *params=nullptr, unsigned int dataSize=0, bool chi2fit=false)
Set a generic FCN function as a C++ callable object implementing double () (const double *) Note that...
Definition Fitter.h:656
const FitConfig & Config() const
access to the fit configuration (const method)
Definition Fitter.h:421
bool FitFCN(unsigned int npar, Function &fcn, const double *params=nullptr, unsigned int dataSize=0, bool chi2fit=false)
Fit using the a generic FCN function as a C++ callable object implementing double () (const double *)...
Definition Fitter.h:649
void SetStepSize(double err)
set the step size
Documentation for class Functor class.
Definition Functor.h:47
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
Graphics object made of three arrays X, Y and Z with the same number of points each.
Definition TGraph2D.h:41
Double_t * GetY() const
Definition TGraph2D.h:122
Double_t * GetX() const
Definition TGraph2D.h:121
Int_t GetN() const
Definition TGraph2D.h:120
Double_t * GetZ() const
Definition TGraph2D.h:123
virtual void SetPoint(Int_t i, Double_t x, Double_t y)
Set x and y values for point number i.
Definition TGraph.cxx:2315
void Draw(Option_t *chopt="") override
Draw this graph with its current attributes.
Definition TGraph.cxx:809
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition TObject.cxx:274
A 3-dimensional polyline.
Definition TPolyLine3D.h:33
virtual void SetPoint(Int_t point, Double_t x, Double_t y, Double_t z)
Set point n to x, y, z.
void Draw(Option_t *option="") override
Draw this 3-D polyline with its current attributes.
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition TRandom.cxx:274
virtual Double_t Uniform(Double_t x1=1)
Returns a uniform deviate on the interval (0, x1).
Definition TRandom.cxx:672
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition TStyle.cxx:1636
void SetOptFit(Int_t fit=1)
The type of information about fit parameters printed in the histogram statistics box can be selected ...
Definition TStyle.cxx:1589
TLine * line
SVector< T, D > Unit(const SVector< T, D > &rhs)
Definition Functions.h:382
T Mag2(const SVector< T, D > &rhs)
Vector magnitude square Template to compute .
Definition Functions.h:230
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17
const Int_t n
Definition legend1.C:16
TGraphErrors * gr
Definition legend1.C:25
Definition first.py:1
TLine l
Definition textangle.C:4
static uint64_t sum(uint64_t i)
Definition Factory.cxx:2345
Lorenzo Moneta

Definition in file line3Dfit.C.