{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9fe29f7d",
   "metadata": {},
   "source": [
    "# fitLinear2\n",
    "Fit a 5d hyperplane by n points, using the linear fitter directly\n",
    "\n",
    "This macro shows some features of the TLinearFitter class\n",
    "A 5-d hyperplane is fit, a constant term is assumed in the hyperplane\n",
    "equation `(y = a0 + a1*x0 + a2*x1 + a3*x2 + a4*x3 + a5*x4)`\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Anna Kreshuk  \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 08:24 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "662af6c8",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:54.246279Z",
     "iopub.status.busy": "2026-05-19T20:24:54.246158Z",
     "iopub.status.idle": "2026-05-19T20:24:54.559434Z",
     "shell.execute_reply": "2026-05-19T20:24:54.559009Z"
    }
   },
   "outputs": [],
   "source": [
    "int n=100;\n",
    "int i;\n",
    "TRandom randNum;\n",
    "TLinearFitter *lf=new TLinearFitter(5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "070c661b",
   "metadata": {},
   "source": [
    "The predefined \"hypN\" functions are the fastest to fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6794545c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:54.565281Z",
     "iopub.status.busy": "2026-05-19T20:24:54.565140Z",
     "iopub.status.idle": "2026-05-19T20:24:54.772026Z",
     "shell.execute_reply": "2026-05-19T20:24:54.771051Z"
    }
   },
   "outputs": [],
   "source": [
    "lf->SetFormula(\"hyp5\");\n",
    "\n",
    "double *x=new double[n*10*5];\n",
    "double *y=new double[n*10];\n",
    "double *e=new double[n*10];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7d2b4c4",
   "metadata": {},
   "source": [
    "Create the points and put them into the fitter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0ffb2426",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:54.773496Z",
     "iopub.status.busy": "2026-05-19T20:24:54.773373Z",
     "iopub.status.idle": "2026-05-19T20:24:54.976668Z",
     "shell.execute_reply": "2026-05-19T20:24:54.975890Z"
    }
   },
   "outputs": [],
   "source": [
    "for (i=0; i<n; i++){\n",
    "   x[0 + i*5] = randNum.Uniform(-10, 10);\n",
    "   x[1 + i*5] = randNum.Uniform(-10, 10);\n",
    "   x[2 + i*5] = randNum.Uniform(-10, 10);\n",
    "   x[3 + i*5] = randNum.Uniform(-10, 10);\n",
    "   x[4 + i*5] = randNum.Uniform(-10, 10);\n",
    "   e[i] = 0.01;\n",
    "   y[i] = 4*x[0+i*5] + x[1+i*5] + 2*x[2+i*5] + 3*x[3+i*5] + 0.2*x[4+i*5]  + randNum.Gaus()*e[i];\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ba56b16",
   "metadata": {},
   "source": [
    "To avoid copying the data into the fitter, the following function can be used:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3a9c15cc",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:54.978391Z",
     "iopub.status.busy": "2026-05-19T20:24:54.978267Z",
     "iopub.status.idle": "2026-05-19T20:24:55.187377Z",
     "shell.execute_reply": "2026-05-19T20:24:55.186776Z"
    }
   },
   "outputs": [],
   "source": [
    "lf->AssignData(n, 5, x, y, e);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "482fe36e",
   "metadata": {},
   "source": [
    "A different way to put the points into the fitter would be to use\n",
    "the AddPoint function for each point. This way the points are copied and stored\n",
    "inside the fitter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "646bfb98",
   "metadata": {},
   "source": [
    "Perform the fitting and look at the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e5a7a250",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:55.189314Z",
     "iopub.status.busy": "2026-05-19T20:24:55.189195Z",
     "iopub.status.idle": "2026-05-19T20:24:55.395522Z",
     "shell.execute_reply": "2026-05-19T20:24:55.394967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "par[0]=0.000069+-0.001011\n",
      "par[1]=3.999934+-0.000164\n",
      "par[2]=0.999835+-0.000172\n",
      "par[3]=1.999892+-0.000178\n",
      "par[4]=2.999967+-0.000185\n",
      "par[5]=0.199823+-0.000174\n",
      "chisquare=70.148012\n"
     ]
    }
   ],
   "source": [
    "lf->Eval();\n",
    "TVectorD params;\n",
    "TVectorD errors;\n",
    "lf->GetParameters(params);\n",
    "lf->GetErrors(errors);\n",
    "for (int i=0; i<6; i++)\n",
    "   printf(\"par[%d]=%f+-%f\\n\", i, params(i), errors(i));\n",
    "double chisquare=lf->GetChisquare();\n",
    "printf(\"chisquare=%f\\n\", chisquare);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0dacf1bb",
   "metadata": {},
   "source": [
    "Now suppose you want to add some more points and see if the parameters will change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "167a375c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:55.397336Z",
     "iopub.status.busy": "2026-05-19T20:24:55.397202Z",
     "iopub.status.idle": "2026-05-19T20:24:55.616939Z",
     "shell.execute_reply": "2026-05-19T20:24:55.601779Z"
    }
   },
   "outputs": [],
   "source": [
    "for (i=n; i<n*2; i++) {\n",
    "   x[0+i*5] = randNum.Uniform(-10, 10);\n",
    "   x[1+i*5] = randNum.Uniform(-10, 10);\n",
    "   x[2+i*5] = randNum.Uniform(-10, 10);\n",
    "   x[3+i*5] = randNum.Uniform(-10, 10);\n",
    "   x[4+i*5] = randNum.Uniform(-10, 10);\n",
    "   e[i] = 0.01;\n",
    "   y[i] = 4*x[0+i*5] + x[1+i*5] + 2*x[2+i*5] + 3*x[3+i*5] + 0.2*x[4+i*5]  + randNum.Gaus()*e[i];\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c29f161e",
   "metadata": {},
   "source": [
    "Assign the data the same way as before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2be066d5",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:55.623181Z",
     "iopub.status.busy": "2026-05-19T20:24:55.623035Z",
     "iopub.status.idle": "2026-05-19T20:24:55.849092Z",
     "shell.execute_reply": "2026-05-19T20:24:55.848478Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "More Points:\n",
      "par[0]=0.000551+-0.000712\n",
      "par[1]=3.999910+-0.000121\n",
      "par[2]=0.999886+-0.000125\n",
      "par[3]=2.000067+-0.000123\n",
      "par[4]=2.999915+-0.000127\n",
      "par[5]=0.199918+-0.000130\n",
      "chisquare=145.050322490887680\n"
     ]
    }
   ],
   "source": [
    "lf->AssignData(n*2, 5, x, y, e);\n",
    "lf->Eval();\n",
    "lf->GetParameters(params);\n",
    "lf->GetErrors(errors);\n",
    "printf(\"\\nMore Points:\\n\");\n",
    "for (int i=0; i<6; i++)\n",
    "   printf(\"par[%d]=%f+-%f\\n\", i, params(i), errors(i));\n",
    "chisquare=lf->GetChisquare();\n",
    "printf(\"chisquare=%.15f\\n\", chisquare);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bd82ef7",
   "metadata": {},
   "source": [
    "Suppose, you are not satisfied with the result and want to try a different formula\n",
    "Without a constant:\n",
    "Since the AssignData() function was used, you don't have to add all points to the fitter again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2de62377",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:55.850923Z",
     "iopub.status.busy": "2026-05-19T20:24:55.850801Z",
     "iopub.status.idle": "2026-05-19T20:24:56.077910Z",
     "shell.execute_reply": "2026-05-19T20:24:56.077227Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Without Constant\n",
      "par[0]=3.999913+-0.000121\n",
      "par[1]=0.999890+-0.000125\n",
      "par[2]=2.000057+-0.000123\n",
      "par[3]=2.999919+-0.000127\n",
      "par[4]=0.199918+-0.000130\n",
      "chisquare=145.649621\n"
     ]
    }
   ],
   "source": [
    "lf->SetFormula(\"x0++x1++x2++x3++x4\");\n",
    "\n",
    "lf->Eval();\n",
    "lf->GetParameters(params);\n",
    "lf->GetErrors(errors);\n",
    "printf(\"\\nWithout Constant\\n\");\n",
    "for (int i=0; i<5; i++)\n",
    "  printf(\"par[%d]=%f+-%f\\n\", i, params(i), errors(i));\n",
    "chisquare=lf->GetChisquare();\n",
    "printf(\"chisquare=%f\\n\", chisquare);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ddfe2c7",
   "metadata": {},
   "source": [
    "Now suppose that you want to fix the value of one of the parameters\n",
    "Let's fix the first parameter at 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ffd3317c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:56.079731Z",
     "iopub.status.busy": "2026-05-19T20:24:56.079580Z",
     "iopub.status.idle": "2026-05-19T20:24:56.286083Z",
     "shell.execute_reply": "2026-05-19T20:24:56.285530Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Fixed Constant:\n",
      "par[0]=0.000536+-0.000712\n",
      "par[1]=4.000000+-1.000000\n",
      "par[2]=0.999884+-0.000125\n",
      "par[3]=2.000070+-0.000123\n",
      "par[4]=2.999910+-0.000127\n",
      "par[5]=0.199920+-0.000130\n",
      "chisquare=145.602523231222932\n"
     ]
    }
   ],
   "source": [
    "lf->SetFormula(\"hyp5\");\n",
    "lf->FixParameter(1, 4);\n",
    "lf->Eval();\n",
    "lf->GetParameters(params);\n",
    "lf->GetErrors(errors);\n",
    "printf(\"\\nFixed Constant:\\n\");\n",
    "for (i=0; i<6; i++)\n",
    "   printf(\"par[%d]=%f+-%f\\n\", i, params(i), errors(i));\n",
    "chisquare=lf->GetChisquare();\n",
    "printf(\"chisquare=%.15f\\n\", chisquare);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b2b04ed",
   "metadata": {},
   "source": [
    "The fixed parameters can then be released by the ReleaseParameter method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4720faa8",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:24:56.287805Z",
     "iopub.status.busy": "2026-05-19T20:24:56.287686Z",
     "iopub.status.idle": "2026-05-19T20:24:56.494011Z",
     "shell.execute_reply": "2026-05-19T20:24:56.493376Z"
    }
   },
   "outputs": [],
   "source": [
    "delete lf;"
   ]
  }
 ],
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