{
"cells": [
{
"cell_type": "markdown",
"id": "38ad06eb",
"metadata": {},
"source": [
"# rf308_normintegration2d\n",
"Multidimensional models: normalization and integration of pdfs, construction of\n",
"cumulative distribution functions from pdfs in two dimensions\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Clemens Lange, Wouter Verkerke (C++ version) \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 19, 2024 at 07:15 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "b704b36e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:50.869278Z",
"iopub.status.busy": "2024-03-19T19:15:50.868860Z",
"iopub.status.idle": "2024-03-19T19:15:52.954121Z",
"shell.execute_reply": "2024-03-19T19:15:52.952312Z"
}
},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "486f87fd",
"metadata": {},
"source": [
"Set up model\n",
"---------------------"
]
},
{
"cell_type": "markdown",
"id": "bc444789",
"metadata": {},
"source": [
"Create observables x,y"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "45f4f4c9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:52.959775Z",
"iopub.status.busy": "2024-03-19T19:15:52.959401Z",
"iopub.status.idle": "2024-03-19T19:15:53.307542Z",
"shell.execute_reply": "2024-03-19T19:15:53.306328Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "05f37055",
"metadata": {},
"source": [
"Create pdf gaussx(x,-2,3), gaussy(y,2,2)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a4ccd25a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:53.316009Z",
"iopub.status.busy": "2024-03-19T19:15:53.315624Z",
"iopub.status.idle": "2024-03-19T19:15:53.492559Z",
"shell.execute_reply": "2024-03-19T19:15:53.491271Z"
}
},
"outputs": [],
"source": [
"gx = ROOT.RooGaussian(\"gx\", \"gx\", x, -2.0, 3.0)\n",
"gy = ROOT.RooGaussian(\"gy\", \"gy\", y, +2.0, 2.0)"
]
},
{
"cell_type": "markdown",
"id": "4a218aa8",
"metadata": {},
"source": [
"gxy = gx(x)*gy(y)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b7c14839",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:53.497821Z",
"iopub.status.busy": "2024-03-19T19:15:53.497492Z",
"iopub.status.idle": "2024-03-19T19:15:53.832172Z",
"shell.execute_reply": "2024-03-19T19:15:53.830879Z"
}
},
"outputs": [],
"source": [
"gxy = ROOT.RooProdPdf(\"gxy\", \"gxy\", [gx, gy])"
]
},
{
"cell_type": "markdown",
"id": "77b642cf",
"metadata": {},
"source": [
"Retrieve raw & normalized values of RooFit pdfs\n",
"--------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "2a509a9a",
"metadata": {},
"source": [
"Return 'raw' unnormalized value of gx"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "196ca444",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:53.837813Z",
"iopub.status.busy": "2024-03-19T19:15:53.837436Z",
"iopub.status.idle": "2024-03-19T19:15:53.992937Z",
"shell.execute_reply": "2024-03-19T19:15:53.991543Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gxy = 0.4856717852477124\n"
]
}
],
"source": [
"print(\"gxy = \", gxy.getVal())"
]
},
{
"cell_type": "markdown",
"id": "16236f59",
"metadata": {},
"source": [
"Return value of gxy normalized over x _and_ y in range [-10,10]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "3bcff282",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.003979Z",
"iopub.status.busy": "2024-03-19T19:15:54.003528Z",
"iopub.status.idle": "2024-03-19T19:15:54.190630Z",
"shell.execute_reply": "2024-03-19T19:15:54.189535Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Norm[x,y] = 0.012933200957206766\n"
]
}
],
"source": [
"nset_xy = {x, y}\n",
"print(\"gx_Norm[x,y] = \", gxy.getVal(nset_xy))"
]
},
{
"cell_type": "markdown",
"id": "3ad877de",
"metadata": {},
"source": [
"Create object representing integral over gx\n",
"which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "70ce7d23",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.195555Z",
"iopub.status.busy": "2024-03-19T19:15:54.195221Z",
"iopub.status.idle": "2024-03-19T19:15:54.353443Z",
"shell.execute_reply": "2024-03-19T19:15:54.352165Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Int[x,y] = 37.552326516436096\n"
]
}
],
"source": [
"x_and_y = {x, y}\n",
"igxy = gxy.createIntegral(x_and_y)\n",
"print(\"gx_Int[x,y] = \", igxy.getVal())"
]
},
{
"cell_type": "markdown",
"id": "64aaed10",
"metadata": {},
"source": [
"NB: it is also possible to do the following"
]
},
{
"cell_type": "markdown",
"id": "48cf5486",
"metadata": {},
"source": [
"Return value of gxy normalized over x in range [-10,10] (i.e. treating y\n",
"as parameter)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a7cc6e81",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.358339Z",
"iopub.status.busy": "2024-03-19T19:15:54.358000Z",
"iopub.status.idle": "2024-03-19T19:15:54.485415Z",
"shell.execute_reply": "2024-03-19T19:15:54.481555Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Norm[x] = 0.1068955044839622\n"
]
}
],
"source": [
"nset_x = {x}\n",
"print(\"gx_Norm[x] = \", gxy.getVal(nset_x))"
]
},
{
"cell_type": "markdown",
"id": "b9211d0b",
"metadata": {},
"source": [
"Return value of gxy normalized over y in range [-10,10] (i.e. treating x\n",
"as parameter)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "6812649d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.500621Z",
"iopub.status.busy": "2024-03-19T19:15:54.500210Z",
"iopub.status.idle": "2024-03-19T19:15:54.648474Z",
"shell.execute_reply": "2024-03-19T19:15:54.619322Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Norm[y] = 0.12098919425696865\n"
]
}
],
"source": [
"nset_y = {y}\n",
"print(\"gx_Norm[y] = \", gxy.getVal(nset_y))"
]
},
{
"cell_type": "markdown",
"id": "ef639667",
"metadata": {},
"source": [
"Integrate normalized pdf over subrange\n",
"----------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "99b693a3",
"metadata": {},
"source": [
"Define a range named \"signal\" in x from -5,5"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "2baa030c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.663033Z",
"iopub.status.busy": "2024-03-19T19:15:54.662634Z",
"iopub.status.idle": "2024-03-19T19:15:54.783111Z",
"shell.execute_reply": "2024-03-19T19:15:54.781957Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signal' created with bounds [-5,5]\n",
"[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'signal' created with bounds [-3,3]\n"
]
}
],
"source": [
"x.setRange(\"signal\", -5, 5)\n",
"y.setRange(\"signal\", -3, 3)"
]
},
{
"cell_type": "markdown",
"id": "884fed29",
"metadata": {},
"source": [
"Create an integral of gxy_Norm[x,y] over x and y in range \"signal\"\n",
"ROOT.This is the fraction of of pdf gxy_Norm[x,y] which is in the\n",
"range named \"signal\""
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "652c1f10",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:54.787377Z",
"iopub.status.busy": "2024-03-19T19:15:54.786988Z",
"iopub.status.idle": "2024-03-19T19:15:55.021720Z",
"shell.execute_reply": "2024-03-19T19:15:55.018764Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Int[x,y|signal]_Norm[x,y] = 0.5720351351990984\n"
]
}
],
"source": [
"igxy_sig = gxy.createIntegral(x_and_y, NormSet=x_and_y, Range=\"signal\")\n",
"print(\"gx_Int[x,y|signal]_Norm[x,y] = \", igxy_sig.getVal())"
]
},
{
"cell_type": "markdown",
"id": "e32bdb58",
"metadata": {},
"source": [
"Construct cumulative distribution function from pdf\n",
"-----------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "e00ec599",
"metadata": {},
"source": [
"Create the cumulative distribution function of gx\n",
"i.e. calculate Int[-10,x] gx(x') dx'"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4dc3c720",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:55.027141Z",
"iopub.status.busy": "2024-03-19T19:15:55.026828Z",
"iopub.status.idle": "2024-03-19T19:15:55.176611Z",
"shell.execute_reply": "2024-03-19T19:15:55.175483Z"
}
},
"outputs": [],
"source": [
"gxy_cdf = gxy.createCdf({x, y})"
]
},
{
"cell_type": "markdown",
"id": "8a1c9f69",
"metadata": {},
"source": [
"Plot cdf of gx versus x"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e59b6ecd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:55.182779Z",
"iopub.status.busy": "2024-03-19T19:15:55.182415Z",
"iopub.status.idle": "2024-03-19T19:15:55.904976Z",
"shell.execute_reply": "2024-03-19T19:15:55.903626Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf308_normintegration2d.png has been created\n"
]
}
],
"source": [
"hh_cdf = gxy_cdf.createHistogram(\"hh_cdf\", x, Binning=40, YVar=dict(var=y, Binning=40))\n",
"hh_cdf.SetLineColor(ROOT.kBlue)\n",
"\n",
"c = ROOT.TCanvas(\"rf308_normintegration2d\", \"rf308_normintegration2d\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_cdf.GetZaxis().SetTitleOffset(1.8)\n",
"hh_cdf.Draw(\"surf\")\n",
"\n",
"c.SaveAs(\"rf308_normintegration2d.png\")"
]
},
{
"cell_type": "markdown",
"id": "58e07bb1",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "b2ef4746",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2024-03-19T19:15:55.910874Z",
"iopub.status.busy": "2024-03-19T19:15:55.910374Z",
"iopub.status.idle": "2024-03-19T19:15:56.182409Z",
"shell.execute_reply": "2024-03-19T19:15:56.169363Z"
}
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}