{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "258b92c7",
   "metadata": {},
   "source": [
    "# line3Dfit\n",
    "Fitting of a TGraph2D with a 3D straight line\n",
    "\n",
    "run this macro by doing:\n",
    "\n",
    "```cpp\n",
    "root>.x line3Dfit.C+\n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Lorenzo Moneta  \n",
    "<i><small>This notebook tutorial was automatically generated with <a href= \"https://github.com/root-project/root/blob/master/documentation/doxygen/converttonotebook.py\">ROOTBOOK-izer</a> from the macro found in the ROOT repository  on Tuesday, May 19, 2026 at 08:25 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c37dde9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include <TMath.h>\n",
    "#include <TGraph2D.h>\n",
    "#include <TRandom2.h>\n",
    "#include <TStyle.h>\n",
    "#include <TCanvas.h>\n",
    "#include <TF2.h>\n",
    "#include <TH1.h>\n",
    "#include <Math/Functor.h>\n",
    "#include <TPolyLine3D.h>\n",
    "#include <Math/Vector3D.h>\n",
    "#include <Fit/Fitter.h>\n",
    "\n",
    "#include <cassert>\n",
    "\n",
    "using namespace ROOT::Math;\n",
    "\n",
    "\n",
    "%%cpp -d\n",
    "bool first = true;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0571e4b2",
   "metadata": {},
   "source": [
    "function Object to be minimized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d1388458",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "struct SumDistance2 {\n",
    "   // the TGraph is a data member of the object\n",
    "   TGraph2D *fGraph;\n",
    "\n",
    "   SumDistance2(TGraph2D *g) : fGraph(g) {}\n",
    "\n",
    "   // calculate distance line-point\n",
    "   double distance2(double x,double y,double z, const double *p) {\n",
    "      // distance line point is D= | (xp-x0) cross  ux |\n",
    "      // where ux is direction of line and x0 is a point in the line (like t = 0)\n",
    "      XYZVector xp(x,y,z);\n",
    "      XYZVector x0(p[0], p[2], 0. );\n",
    "      XYZVector x1(p[0] + p[1], p[2] + p[3], 1. );\n",
    "      XYZVector u = (x1-x0).Unit();\n",
    "      double d2 = ((xp-x0).Cross(u)).Mag2();\n",
    "      return d2;\n",
    "   }\n",
    "\n",
    "   // implementation of the function to be minimized\n",
    "   double operator() (const double *par) {\n",
    "      assert(fGraph != nullptr);\n",
    "      double * x = fGraph->GetX();\n",
    "      double * y = fGraph->GetY();\n",
    "      double * z = fGraph->GetZ();\n",
    "      int npoints = fGraph->GetN();\n",
    "      double sum = 0;\n",
    "      for (int i  = 0; i < npoints; ++i) {\n",
    "         double d = distance2(x[i],y[i],z[i],par);\n",
    "         sum += d;\n",
    "      }\n",
    "      if (first) {\n",
    "         std::cout << \"Total Initial distance square = \" << sum << std::endl;\n",
    "      }\n",
    "      first = false;\n",
    "      return sum;\n",
    "   }\n",
    "\n",
    "};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59f468c9",
   "metadata": {},
   "source": [
    " define the parametric line equation\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98ac044e",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "void line(double t, const double *p, double &x, double &y, double &z) {\n",
    "   // a parametric line is define from 6 parameters but 4 are independent\n",
    "   // x0,y0,z0,z1,y1,z1 which are the coordinates of two points on the line\n",
    "   // can choose z0 = 0 if line not parallel to x-y plane and z1 = 1;\n",
    "   x = p[0] + p[1]*t;\n",
    "   y = p[2] + p[3]*t;\n",
    "   z = t;\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86e71891",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gStyle->SetOptStat(0);\n",
    "gStyle->SetOptFit();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8767e40c",
   "metadata": {},
   "source": [
    "double e = 0.1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48f99a81",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "int nd = 10000;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90125fac",
   "metadata": {},
   "source": [
    "double xmin = 0; double ymin = 0;\n",
    "double xmax = 10; double ymax = 10;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7746dc8b",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TGraph2D * gr = new TGraph2D();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee3909f7",
   "metadata": {},
   "source": [
    "Fill the 2D graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "586a9b22",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "double p0[4] = {10,20,1,2};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c794e107",
   "metadata": {},
   "source": [
    "generate graph with the 3d points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36d17d8a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for (int N=0; N<nd; N++) {\n",
    "   double x,y,z = 0;\n",
    "   // Generate a random number\n",
    "   double t = gRandom->Uniform(0,10);\n",
    "   line(t,p0,x,y,z);\n",
    "   double err = 1;\n",
    "   // do a Gaussian smearing around the points in all coordinates\n",
    "   x += gRandom->Gaus(0,err);\n",
    "   y += gRandom->Gaus(0,err);\n",
    "   z += gRandom->Gaus(0,err);\n",
    "   gr->SetPoint(N,x,y,z);\n",
    "   //dt->SetPointError(N,0,0,err);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52ad2c37",
   "metadata": {},
   "source": [
    "fit the graph now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7bbcb75d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ROOT::Fit::Fitter  fitter;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71ecf9dd",
   "metadata": {},
   "source": [
    "make the functor objet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b5179f51",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "SumDistance2 sdist(gr);\n",
    "ROOT::Math::Functor fcn(sdist,4);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe6d416",
   "metadata": {},
   "source": [
    "set the function and the initial parameter values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe914877",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "double pStart[4] = {1,1,1,1};\n",
    "fitter.SetFCN(fcn,pStart);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2e7686c",
   "metadata": {},
   "source": [
    "set step sizes different than default ones (0.3 times parameter values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1955793c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for (int i = 0; i < 4; ++i) fitter.Config().ParSettings(i).SetStepSize(0.01);\n",
    "\n",
    "bool ok = fitter.FitFCN();\n",
    "if (!ok) {\n",
    "   Error(\"line3Dfit\",\"Line3D Fit failed\");\n",
    "   return 1;\n",
    "}\n",
    "\n",
    "const ROOT::Fit::FitResult & result = fitter.Result();\n",
    "\n",
    "std::cout << \"Total final distance square \" << result.MinFcnValue() << std::endl;\n",
    "result.Print(std::cout);\n",
    "\n",
    "\n",
    "gr->Draw(\"p0\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f91b0159",
   "metadata": {},
   "source": [
    "get fit parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a1e43f62",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "const double * parFit = result.GetParams();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1192eb31",
   "metadata": {},
   "source": [
    "draw the fitted line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a7833a9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "int n = 1000;\n",
    "double t0 = 0;\n",
    "double dt = 10;\n",
    "TPolyLine3D *l = new TPolyLine3D(n);\n",
    "for (int i = 0; i <n;++i) {\n",
    "   double t = t0+ dt*i/n;\n",
    "   double x,y,z;\n",
    "   line(t,parFit,x,y,z);\n",
    "   l->SetPoint(i,x,y,z);\n",
    "}\n",
    "l->SetLineColor(kRed);\n",
    "l->Draw(\"same\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d81b9015",
   "metadata": {},
   "source": [
    "draw original line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51bb7d86",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TPolyLine3D *l0 = new TPolyLine3D(n);\n",
    "for (int i = 0; i <n;++i) {\n",
    "   double t = t0+ dt*i/n;\n",
    "   double x,y,z;\n",
    "   line(t,p0,x,y,z);\n",
    "   l0->SetPoint(i,x,y,z);\n",
    "}\n",
    "l0->SetLineColor(kBlue);\n",
    "l0->Draw(\"same\");\n",
    "return 0;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c94bb9ab",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62d7e147",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
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