HistogramInterpolation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "require(['codemirror/mode/clike/clike'], function(Clike) { console.log('ROOTaaS - C++ CodeMirror module loaded'); });"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "IPython.CodeCell.config_defaults.highlight_modes['magic_text/x-c++src'] = {'reg':[/^%%cpp/]};"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to ROOTaaS 6.06/00\n"
     ]
    }
   ],
   "source": [
    "import ROOT\n",
    "import numpy as np\n",
    "from math import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r\n",
      "\u001b[1mRooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby\u001b[0m \r\n",
      "                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University\r\n",
      "                All rights reserved, please read http://roofit.sourceforge.net/license.txt\r\n",
      "\r\n",
      "[#1] INFO:DataHandling -- RooDataHist::adjustBinning(histo_central): fit range of variable x expanded to nearest bin boundaries: [0,10] --> [0,10]\r\n",
      "[#1] INFO:DataHandling -- RooDataHist::adjustBinning(histo_up): fit range of variable x expanded to nearest bin boundaries: [0,10] --> [0,10]\r\n",
      "[#1] INFO:DataHandling -- RooDataHist::adjustBinning(histo_down): fit range of variable x expanded to nearest bin boundaries: [0,10] --> [0,10]\r\n"
     ]
    }
   ],
   "source": [
    "x = ROOT.RooRealVar(\"x\", \"x\", 0, 10)\n",
    "\n",
    "histo_central = ROOT.TH1F(\"hcentral\", \"central\", 10, 0, 10)\n",
    "for i in xrange(1, 10 + 1):\n",
    "    histo_central.SetBinContent(i, 1 + 10 * exp(-i / 2.))\n",
    "histo_central = ROOT.RooDataHist(\"histo_central\", \"central\", ROOT.RooArgList(x), histo_central)\n",
    "\n",
    "histo_up = ROOT.TH1F(\"hup\", \"up\", 10, 0, 10)\n",
    "for i in xrange(1, 10 + 1):\n",
    "    histo_up.SetBinContent(i, 1 + 10 * exp(-i / 4.))\n",
    "histo_up = ROOT.RooDataHist(\"histo_up\", \"up\", ROOT.RooArgList(x), histo_up)\n",
    "\n",
    "histo_down = ROOT.TH1F(\"hdown\", \"down\", 10, 0, 10)\n",
    "for i in xrange(1, 10 + 1):\n",
    "    histo_down.SetBinContent(i, 1 + 10 * exp(-i / 1.02))\n",
    "histo_down = ROOT.RooDataHist(\"histo_down\", \"down\", ROOT.RooArgList(x), histo_down)\n",
    "\n",
    "h_central = ROOT.RooHistFunc(\"histo_func_central\", \"central\", ROOT.RooArgSet(x), histo_central)\n",
    "h_up = ROOT.RooHistFunc(\"histo_func_up\", \"up\", ROOT.RooArgSet(x), histo_up)\n",
    "h_down = ROOT.RooHistFunc(\"histo_func_down\", \"down\", ROOT.RooArgSet(x), histo_down)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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/PbJ6/V3/dN/4CzsGAJCsyEFhay3nvu+HYTjROgoAwKmdZB2FsSghjDucaB2FOXPrKJyz\nDQBQhphBIRQNTPsP2rYNoWFPPcHJbKpqs8/ZGgAAxYi/jsLZrggFAJxa/HUU9gYFcQEAchT/6pG7\nFQlvXODxpEyPjMj0SIDjlTc9MvLQQyhKaJom/Ng0zXq9PlNKAABiKyv46FGISI8CwPH0KOzR931d\n16EK4fDVnHUtAEBe4gSftm3Das0HihaHYahO/R364GoJ6UQ8PQoApSqvR+Gsj6eu69Ou0mjoISJB\nAeB45QWF+Oso9H3ftm0Ya2jbdrrU0mazMU8SADISOSh0XbdYLMIoQ1VVwzAsFgulCQCQqcg9JLsX\ngG7bdhiGM/XDGHqIyNADwPEMPRwS8sHWZR32bgQAsnCSGoUDPwIAGYk/9FBNLiA5ruhs6GHK0ANA\nqcobevhB3N2t1+vFYrF1uYdwpemzqavJSW6isCMHAGdwkuDT930YcQgLMUXf/yw9ChHpUQA4Xnk9\nCjEfTxhoOO2SSocJChEJCgDHKy8oxCxmHOsSIu4TALigyDUKy+VytVpVr0PDyIKMAJCjk8x62GXW\nw5ShB4BSlTf0EH/WQ9wdAgAXFDMojDMdIu4TALigOEFhXFgpuOTEBwAgnjhDKWHQfblcVlUVihkv\nM0IzVyJRVVVKBQFqFABKpUZh1nK5DJeTbtt2sVj0fX+pToX0ixkBIBcR1lHYKk0w6AAAxYh/9cgz\nCN0VdV0LJQBwUpGnR57BWDjZNM0wDOWNBgFAOqL1KCwWi/q1rR8Plhje5o6aptlsNn3fh2UbQm0E\nABBdZj0KoR5iTAZt2+pOAIDTidCjEM7Wh939XqbUKADAeWRWzBh6FMJSDWONwsuXL6e3qauqPtJF\nHgsApC+zoYdgXLOhqqq6rv/xj39Mf2sdBQCIJbMehTDWsDXiMAzDRRoDAMXLMiiEAYhR0zQXaQwA\nFC+zoFBVVdM0q9Vquhyk6ZEAcCJZrlY0LT+c1iuEX6Rfo+CiUAClKm8ZwCyLGcNqS5XrSgDAiZUV\nfPQoRKRHAeB4ehQyUFeTk9xEYUcOAM6gwKCQfo8CAOSiwKBAZFmsXCkaApxGftMjYY8s0gxAhgQF\nZviODoChBw7JIivoSwA4JT0KAMAsQQEAmFXg0IN1FAAglgKDgnUUACAWQw8AwCxBAQCYJSgAALME\nBQBglqAAAMwSFACAWQVOj7SOAgDEUmBQsI4CAMRi6AEAmCUoAACzBAUAYJagAADMEhQAgFmCAgAw\nS1AAAGYVuI6CBZcAIJYCg4IFlwAgFkMPAMCs/IJC13X1m/q+v3SjAKBM+Q09hFjQNM2lGwIA5auz\nK/Gr67ppmv29CHVd51CjUL+utczuyU/RWLjqyQQSUNf5nVgPy2/oYWTEAQBOLcugMAxDXdeLxaKu\n667rLt0cAChWZkFh7EVYr9fr9bppmr///e9bXQt1VdVHOv8DAYAsZD+U8kbJghqFe0iNApCS8moU\nsn884aT73aMQFO4hQQFISXlBIbOhh7CIwtZGUyUB4EQyCwpt24Z/+77v+z78qJ4RAE4kvx6Svu8X\ni8X443K5/D4oGHq4hww9ACkpb+gh18cTqhdDj8L3BIV7SFAAUiIopE1QuIcEBSAl5QWF/K71cK26\nmpw8Jgo7cgBwBgUGhdCnsCuldZVCCxNqEADsldmsh8PqmYiQqrxaC8B9VFRQAADiKnLoIfWytnEQ\nJP3LTORU2JH8k1lVyb80AXboUeCQ9KNMZjyfQG4EBTLnOzrAKZU59JCLlDv2c+pLSPhp/F5GzyfA\nRJFBYf85LuWzMgCkqcigIBIAQBxqFACAWYICADBLUAAAZgkKAMAsQQEAmCUoAACzipweaR0FAIij\nyKAgEgBAHIYeAIBZggIAMEtQAABmCQoAwCxBAQCYJSgAALOKnB5pHQUAiKPIoCASAEAchh4AgFmC\nAgAwK++gUNd13/eXbgUAFCvjoLC/ZBEAiCfXoNB13aWbAADlyzIo9H2/Wq2aprl0QwCgcFkGhcVi\n0TSNTgUAOLX8gkLbtlVVjTWMn3/++c5N6mOds/0AkJHMFlzqum4YhvV6PW55+fLlzq0suAQAcdR5\nnVTbth2GYXd7eBR1XVVVnX5QGLswUm7n2NGS+rOZiyyOOnBndZ3ZifVa+fUojIMOfd8Pw9A0TRiM\nAACiyzj49H2/WCzW6/UYFPQoRKRHIbK8SmEcdLit8noU8itmBE4ur1gDnFJRwUePQkR6FOLL6+zr\nuMOtlNejkFmNAmQsi8+OvNIMcHpFBoX9KyMUFvEA4AyKDAoiAQDEoZgRAJglKAAAswQFAGCWoAAA\nzBIUAIBZggIAMKvI6ZHWUQCAOIoMCiIBAMRh6AEAmCUoAACzBAUAYJagAADMEhQAgFmCAgAwq8jp\nkdZRAIA4igwKIgEAxGHoAQCYJSgAALMEBQBglqAAAMwqspiRmPbPIUmM+tX40j/uDjqchR4FSpBF\nmiEyBx3OosgeBesoRLDZbJx976PNxgkYmCoyKIgEcWTxPEoz8aV/3B10OCNDDwDALEEBAJiVZVDo\nuq6u67qu27a9dFsAoGT51Si0bTsMQ9M0VVUNw1DXdRZD6QCQo8x6FPq+H4ZhuVz2fd/3/XK5DBsv\n3S4AKFNmQSEYRxwMPQDASeXabx96FFarVTWZxVfXVVXV6U/rG+d2Jd7OLIzTI1M/6kTkLUTCyhsQ\nz/XxjKeH995776uvvnq9saqq20ywPvOT4FMuIkHhPvIWImHlBYUshx6qqtpsNuv1erlc/utf/+q6\nbueXx7nIQwCA9GUWfELd4rQ0oa7rpmnCdkMP95AehfvIW4iE6VG4sL7vF4vFpVsBAPdFZkEh9CW0\nbTvtWtgZegAA4sivh6TrujDZIVgul2NQMPRwDxl6uI+8hUhYeUMPuT6e3WKFSlC4lwSF+8hbiIQJ\nCkkTFO4hQeE+8hYiYeUFhfyu9XAD9d6r1Rd25ADgDIoMCiIB3A97vxOkxucRmcts1gNAZrJIMzBP\nUABy4zs6nFGRQw9A6bLICvoSKIIeBQBglqAAAMwSFACAWUXWKFhHAQDiKDIoiAQAEIehBwBglqAA\nAMwSFACAWYICADBLUAAAZhU56yEb6S/wav4IwD1XZFCwjkI0dS0rANxrRQaF1CPBZpNBX0J29sfD\nxKT+0uREcnhx+k7AnCKDQgbSf0tm8cmWnbquZQUSpf+QGYoZyZvzLuny4qQIehTIXhZZIYuREeLL\n4cWp/5DD9CgAALMEBQBglqAAAMwqskbBOgoAEEeRQUEkAIA4DD0AALOyDApd19V1Xdd127Z931+6\nOQBQrPzWiWvbdhiGpmmqqhqGoaqq9Xrdtm313WTg2tBDFGOdhyczirFwxquT5Hi3R1XeAqz5PZ66\nrpumGTsSpj8KChH56IhLUCBdGS24lMPbp7ygkNnQQwgEXddNN4Z+BQAKl1GmKUhmsx7atp0mtZAb\nlsvlxRoEkDsXtOWgjHtIuq5brVbVpC/39dDD0fJ9Ek7H0ENchh7gTvL5SCpv6CGzHoWg7/vFYlFV\n1bRYYaKwYwQAF5NZjUI1SQnr9drcSAA4qfx6SLZmPbz5q8qsh1jy6efLg6EHuJN8PpIMPVzYON8h\nLJww/n9rHgQAEEVmQSF0JJgPCQDnUVQPiaGHiPLp58uDoQe4k3w+kgw9AHey/yLoiSnsY46iJP8O\nKu/Nk9+sB+DUskgzkK6y3kFF9ijs/5TzJYkL2mw2zr5we5aPvJwig4JIQIqyeF1KM6Qrh3dQkWnG\n0AMAMEtQAABmCQoAwCxBAQCYJSgAALMEBQBgVpHTI62jAABxFBkURAIAiKPIoEBMWSwfIhoCnIig\nQAnqWlaILP0lGvUcwnkoZmQ/H8IkLv0oA2XQo8CsLLKCk0VcLl4FbBEUgDek36UvysA5GXoAAGYV\n2aNgHQUAiKPIoCASAEAchh4AgFlF9igA90IWVY16OMmdHgWAE8oizcABggKQGd/R4ZwMPQD5ySIr\n6EugDIIChcjiMzmHsxvAG4oMCtZRIFEuXnU/ZdG14BOSOUUGBS/4e2SzyaMvARJX17WPTvYqMihw\nv2Tx4SbN3EOusEUZsg8KdV2v1+u2bS/dEIBtWXxHH9NM+rEmi+ezPHkHha7rLt0EOE7yH8VVlUkn\nDfeQ8ZGLyDUodF23Wq0u3Qook6LLeyWvIZLEm1rk+ybXoBDGGvq+H4bh0m2B62VXdJl+a0WZiNL/\nmp54PihbxkGhbdu+7xeLxaXbAjeS/EdxVeWQD0YZNZUYcnj/VFV4VW6qol6dJSzh/NVXX725oT7W\nZdoN6ckizUDi6kxizQ3l2qMw9X//939vbki/Fw3SlcXbR7yHsykhKAD3TRZphnuoyAhbwtADAHAi\nggIAMEtQAABmFbXKVV1XVVUrZgTgIsYahZJOQ3oUAIBZggIAMKvI6ZH7l1AyIAEAxyoyKIgEABCH\noQcAYJagAADMEhQAgFmCAgAwS1AAAGYJCgDArCKnR1pHAQDiKDIoiAQAEIehBwBglqAAAMwSFACA\nWYICADBLUAAAZgkKAMCsIqdHWkcBAOIoMiiIBAAQh6EHAGCWoAAAzBIUAIBZgsJl7K+3TEwWjay0\nM7Ys2plFIyvtjCqLRlZVVVW5tPOmBAUAYJagAADMKnJ6pHUUACCOIoOCSAAAcRh6AABmZRkUuq6r\n67qu67Ztj/3ba+tmb1JYG2Unp76LMzTyPM1I4cmMtZNT34WDHvcusmingx73Ls7zfOYlv6DQdd1q\ntWqapmmaYRhukRUAgBuqsxvPr+u6aZq+76vXoWF8CHVdVVV9uEahrq95yNfeIMpOyrhBIs3wSCPe\nIJFmpHCDRJrhkZ7zBnffyU1OQ9nJrEdhzAfhx/Cf8UcAIK7MgsJeIT0AANFlNj0yZIKtuoT//e9/\nb97qmlqTRApeyrhBIs3wSCPeIJFmpHCDRJrhkZ7zBrF2UpLMgkLQ9/00K/zwhz8M/9lsqqoqaFwI\nAC4ts6GHvXMcxo25jEFk0c4sGllpZ2xZtDOLRlbaGVUWjayq6ssvv7x0E+LLctbDcrkMBYx93y8W\ni/V6bZIkAJxCfkGhbdthGEI4CANF2T0EAMhFZkMP1esOqMViEVLCer0O2++yXONF1HWdbGfa9MlM\ntpGVgx7V+GSO0mxqKFFK+aDvPpPBpdu1XxZvorGRaU6G332zpP8qPUqWxYybzWZr+sO4XGNVVWG5\nxjQ/40ZpvtyD0GczPpnJDu5stfMmS6lcVrKniiC8ZcLzmaww2lhVVViYNc2Dvvv5MwzDhdpyjSze\nRNNGrlarvu+T+njf+2Ge/qv0OJsiVFXVNE34/3K5TPlxheYF6/X60s3ZY/pk7v6YiNCTtFwuw4/h\nWU3z+QzG455sI9M80Fumjdx6DSQrtDPN4z59AtNs59ZRTqqRcx/mIdOMP2bxKj0sv6GHXXkt19i2\n7XK5TPZ729aTGaT8fWjrP2nq+37s8UpfUl/XprZenG3bbjabZN/po8VisVwuE3+JJmv3oFfJvETn\nPszH/o+gaZrVanXepsV26aQSwW7GrJL/bpRULj4g/S9t6/V6zPWXbsus8IJM/KBvfTIkeNDHV2P4\nFE78PR4k3sE5PpPJvol2OwtTO/R7T0DTt89WB0OOyulRENij67oujLSl/KVtsViEtD7tBkxKUt+B\n5ozNW6/X6/U6fAdKrc2hPeFwj6O/F27TdVarVbKvzOr1W3sYhmTfRGMPcShN8Dl/EVkWM+7lNRTR\ntGQstbPFls1mEz5Bwiddapmm67owm/fSDblG6MYff+z7PlSYJ3j0x2VUqqpKfGJO+ERK7TU5tVgs\nti7GW6XX4PV6vVgswicSF1FCj8Lh5Ro51pgS1ut1sh/B08rntm3HBbgu16L9prN5w7M6zuxNX2q1\nKeFNvfXWTq2RU8MwJPgdfbT1rgk/JjiaHlJs6OsKcTb9j/cEP4vuopygMB4YIxF3FL5kbDablJ/D\nMc0kruu65Wu748HpCPPUtzamVn25dxAntUaOwnk35TfRXqk9n6GrOPw79h6l/6xO8+tWbWOWLlgf\nEVE4DGPeTP9xJVvXFs5hzZuSrWsLFYKbN18AyUr2oG/efD5DjUKaTZ02LHzrUOsAAAFnSURBVNlG\nBlmUsO2+iRJ8s4eP9PDKTPDjffd9Pa0BT3/m9k2k9YzfxTT9pH9Ukj1n7E2+SdUYj7a+lyf4Abcl\n2YMebBVSJPt8ZtHITXrF+XtlcdC3Gnnp5mzb+76efjql+aweJf8VoyZy6ZUiIgc9riyezywamZEs\nns8sGrmlmBL7ooICABBXCcWMAMCJCAoAwCxBAQCYJSgAALMEBQBglqAAAMwSFADgaOO108KPdV3n\nchmXYwkKAHC0tm3DBdmr15f2SP86sbdjwSUAuKWxF2F6AfTCCAoAcEvjlWwLPpkaegCAW9q67nmR\nBAUAuI2+71erVbhWZBnXf9rL0AMA3EYoUNhsNmEAotQyBT0KAHC00IUQZjpMZ0CUR48CADBLjwIA\nMEtQAABmCQoAwCxBAQCYJSgAALMEBQBglqAAAMwSFACAWYICADBLUAAAZgkKAMAsQQEAmCUoAACz\nBAUAYJagAADM+v9qv7+PnfRV4AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "canvas = ROOT.TCanvas()\n",
    "frame = x.frame()\n",
    "h_central.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlack))\n",
    "h_up.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kRed))\n",
    "h_down.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlue))\n",
    "\n",
    "frame.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set setAllInterpCodes to 4 by this hint: https://root.cern.ch/root/html/src/PiecewiseInterpolation.cxx.html#151 (no documentation at all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "theta = ROOT.RooRealVar(\"theta\", \"theta\", 0, -5, 5)\n",
    "background = ROOT.PiecewiseInterpolation(\"background\", \"background\", h_central,\n",
    "                                         ROOT.RooArgList(h_down),\n",
    "                                         ROOT.RooArgList(h_up),\n",
    "                                         ROOT.RooArgList(theta))\n",
    "background.setAllInterpCodes(4)  # 0 linear, 1 log, ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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utws5BgKFRVoIFADgzvILFBKvzOiuV3G+Ggs4XNE5LYkPZisl56sU1LQc1Cj0k7/raBmE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\nAABEESgAAIAoAgUAABD1/7Ih19veZdZeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "canvas = ROOT.TCanvas()\n",
    "frame = x.frame()\n",
    "\n",
    "h_central.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlack))\n",
    "h_up.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kRed))\n",
    "h_down.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlue))\n",
    "\n",
    "for theta_val in np.linspace(-1, 1, 11):\n",
    "    theta.setVal(theta_val)\n",
    "    background.plotOn(frame, ROOT.RooFit.LineStyle(ROOT.kDashed), ROOT.RooFit.LineColor(ROOT.kGreen))\n",
    "\n",
    "frame.Draw()\n",
    "canvas.Draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FgLzyn2Z6Npvt5g+6rttut9ojd1VxeNtd3bKQIODEllD2zgRuR3vFjBc5zfTeyR2udppp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\nNXkOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "canvas = ROOT.TCanvas()\n",
    "frame = x.frame()\n",
    "\n",
    "h_central.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlack))\n",
    "h_up.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kRed))\n",
    "h_down.plotOn(frame, ROOT.RooFit.LineColor(ROOT.kBlue))\n",
    "\n",
    "for theta_val in [-2, -1, 0, 1, 2]:\n",
    "    theta.setVal(theta_val)\n",
    "    background.plotOn(frame, ROOT.RooFit.LineStyle(ROOT.kDashed), ROOT.RooFit.LineColor(ROOT.kGreen))\n",
    "\n",
    "frame.Draw()\n",
    "canvas.Draw()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}