Discrete profiling

gistfile1.txt

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import ROOT\n",
      "import numpy as np\n",
      "from collections import OrderedDict\n",
      "\n",
      "import matplotlib as mpl\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "def safe_factory(func):\n",
      "    def wrapper(self, *args):\n",
      "        result = func(self, *args)\n",
      "        if not result:\n",
      "            raise ValueError('invalid factory input \"%s\"' % args)\n",
      "        return result\n",
      "    return wrapper\n",
      "\n",
      "ROOT.RooWorkspace.factory = safe_factory(ROOT.RooWorkspace.factory)\n",
      "\n",
      "import urllib\n",
      "urllib.urlretrieve(\"https://gist.githubusercontent.com/mazurov/6194738/raw/67e851fdac969e670a11296642478f1801324b8d/rootnotes.py\",\n",
      "                   \"rootnotes.py\")\n",
      "from rootnotes import default_canvas as TCanvas\n",
      "#from ROOT import TCanvas\n",
      "\n",
      "try:\n",
      "    ROOT.gROOT.ProcessLine(\".x ~/atlasstyle/AtlasStyle.C\")\n",
      "    ROOT.SetAtlasStyle()\n",
      "except AttributeError:\n",
      "    print \"no ATLAS atyle for you\"\n",
      "\n",
      "#ROOT.gROOT.ProcessLine(\".x /home/turra/cms_classes/loadClasses.C\")\n",
      "%matplotlib inline\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "colors = ROOT.kBlue, ROOT.kRed, ROOT.kOrange, ROOT.kViolet, ROOT.kGreen, ROOT.kYellow, ROOT.kSpring\n",
      "from itertools import cycle\n",
      "colors = cycle(colors)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nsignal_expected = 1000\n",
      "nbackground = 100000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define observable and POI\n",
      "-------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws = ROOT.RooWorkspace(\"workspace\")\n",
      "ws_import = getattr(ws, \"import\")\n",
      "\n",
      "mass = ws.factory(\"mass[100,160]\")\n",
      "mass.setBins(480)\n",
      "mH = ws.factory(\"mH[125,110,150]\")\n",
      "mH_shiftted = ws.factory(\"sum::mH_shifted(mH, mH_shift[-125])\")\n",
      "mass_shifted = ws.factory(\"sum::mass_shifted(mass, mass_shift[-125])\")\n",
      "bkg_index = ROOT.RooCategory(\"bkg_index\", \"bkg_index\")\n",
      "ws_import(bkg_index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define signal\n",
      "--------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "signal = ws.factory(\"Gaussian:signal(mass, mH, res[1.3])\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define background\n",
      "-----------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bkgs = OrderedDict()\n",
      "\n",
      "bkgs['exp'] =  1, ws.factory(\"RooExponential::bkg_exp(mass, bkg_exp_par0[-0.05, -1, 0.01])\")\n",
      "\n",
      "bkgs['poly1'] = 1, ws.factory(\"RooBernstein::bkg_poly1(mass, {bkg_poly1_par0[1], bkg_poly1_par1[0.1, 0, 1000]})\")\n",
      "bkgs['poly2'] = 2, ws.factory(\"RooBernstein::bkg_poly2(mass, {bkg_poly2_par0[1], bkg_poly2_par1[0.1,0,1000], bkg_poly2_par2[0,0,1000]})\")\n",
      "bkgs['poly3'] = 3, ws.factory(\"RooBernstein::bkg_poly3(mass, {bkg_poly3_par0[1], bkg_poly3_par1[0.1,0,1000], bkg_poly3_par2[0,0,1000], bkg_poly3_par3[0,0,1000]})\")\n",
      "bkgs['poly4'] = 4, ws.factory(\"RooBernstein::bkg_poly4(mass, {bkg_poly4_par0[1], bkg_poly4_par1[0.1,0,1000], bkg_poly4_par2[0,0,1000], bkg_poly4_par3[0,0,1000], bkg_poly4_par4[0,0,1000]})\")\n",
      "bkgs['poly5'] = 5, ws.factory(\"RooBernstein::bkg_poly5(mass, {bkg_poly5_par0[1], bkg_poly5_par1[0.1,0,1000], bkg_poly5_par2[0,0,1000], bkg_poly5_par3[0,0,1000], bkg_poly5_par4[0,0,1000], bkg_poly5_par5[0,0,1000]})\")\n",
      "\n",
      "bkgs['landau'] = 2, ws.factory(\"Landau::bkg_landau(mass, bkg_landau_par0[80, 70, 130], bkg_landau_par1[10, 0, 1000])\")\n",
      "\n",
      "bkgs['exppol2'] = 2, ws.factory(\"EXPR::bkg_exppol2('exp(@1*(@0-100)/100.0 + @2*(@0-100)*(@0-100)/10000.0)', mass, bkg_exppol2_par0[-0.0025,-100.,100.],bkg_exppol2_par1[-0.02,-100,100.])\")\n",
      "bkgs['exppol3'] = 3, ws.factory(\"EXPR::bkg_exppol3('exp(@1*(@0-100)/100.0 + @2*(@0-100)*(@0-100)/10000.0 + @3*(@0-100)*(@0-100)*(@0-100)/1000000.0)', mass, bkg_exppol3_par0[-0.0025,-100.,100.],bkg_exppol3_par1[-0.02,-100,100.],bkg_exppol3_par2[-0.02,-100,100.])\")\n",
      "bkgs['exppol4'] = 4, ws.factory(\"EXPR::bkg_exppol4('exp(@1*(@0-100)/100.0 + @2*(@0-100)*(@0-100)/10000.0 + @3*(@0-100)*(@0-100)*(@0-100)/1000000.0 + @4*(@0-100)*(@0-100)*(@0-100)*(@0-100)/100000000.0)', mass, bkg_exppol4_par0[-0.0025,-100.,100.],bkg_exppol4_par1[-0.02,-100,100.],bkg_exppol4_par2[-0.02,-100,100.], bkg_exppol4_par3[-0.02,-100,100.])\")\n",
      "\n",
      "bkgs['laurent2'] = 2, ws.factory(\"EXPR::bkg_laurent2('@1 + @2/@0 + @3/(@0 * @0)',                     mass, bkg_laurent2_par0[0.002, -100, 100], bkg_laurent2_par1[-0.3, -100, 100], bkg_laurent2_par3[60, -100, 100])\")\n",
      "bkgs['laurent3'] = 3, ws.factory(\"EXPR::bkg_laurent3('@1 + @2/@0 + @3/(@0 * @0) + @4/(@0 * @0 * @0)', mass, bkg_laurent3_par0[0.002, -100, 100], bkg_laurent3_par1[-0.3, -100, 100], bkg_laurent3_par3[60, -100, 100], bkg_laurent3_par4[1, -1000, 1000])\")\n",
      "\n",
      "bkgs['laurent_half'] = 4, ws.factory(\"EXPR::bkg_laurent_half('@1 + @2/@0 + @3/(@0 * @0) + @4/(sqrt(@0)) + @5 * @0', mass, bkg_laurent_half_par0[0.002, -100, 100], bkg_laurent_half_par1[-0.3, -100, 100], bkg_laurent_half_par3[60, -100, 100], bkg_laurent_half_par4[1, -1000, 1000], bkg_laurent_half_par5[1, -1000, 1000])\")\n",
      "\n",
      "ws.factory(\"RooBernstein::bkg_poly5_clone(mass, {bkg_poly5_par0_clone[1], bkg_poly5_par1_clone[0.5,0,1000], bkg_poly5_par2_clone[0.4,0,1000], bkg_poly5_par3_clone[0.3,0,1000], bkg_poly5_par4_clone[0.2,0,1000], bkg_poly5_par5_clone[0.2,0,1000]})\")\n",
      "ws.factory(\"EXPR::bkg_exppol3_clone('exp(@1*(@0-100)/100.0 + @2*(@0-100)*(@0-100)/10000.0 + @3*(@0-100)*(@0-100)*(@0-100)/1000000.0)', mass, bkg_exppol3_par0_clone[-0.0025,-100.,100.],bkg_exppol3_par1_clone[-0.02,-100,100.],bkg_exppol3_par2_clone[-0.02,-100,100.])\")\n",
      "ws.factory(\"Landau::bkg_landau_clone(mass, bkg_landau_clone_par0[80, 70, 130], bkg_landau_clone_par1[10, 0, 1000])\")\n",
      "ws.factory(\"SUM::bkg_complicated(nc1[0.4] * bkg_poly5_clone, nc2[0.4] * bkg_landau_clone, bkg_exppol3_clone)\")\n",
      "\n",
      "bkgs['complicated'] = 999, ws.pdf(\"bkg_complicated\")\n",
      "\n",
      "#bkg_multi = ROOT.RooMultiPdf(\"bkg_multi\", \"bkg_multi\", bkg_index, bkg_list)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu = ws.factory(\"mu[1, 0, 3]\")\n",
      "nsignal = ws.factory(\"prod::nsignal(mu, nsignal_expected[%d])\" % nsignal_expected)\n",
      "\n",
      "models = OrderedDict()\n",
      "models['exp'] = ws.factory(\"SUM::model_exp(nbkg[%d, 0, 1000000] * bkg_exp, nsignal * signal)\" % nbackground)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def create_model_from_template(template, new_name, old_bkg, new_bkg):\n",
      "    command = \"EDIT::%s(%s, %s=%s)\" % (new_name, template, old_bkg, new_bkg)\n",
      "    return ws.factory(command)\n",
      "\n",
      "def create_model_from_exp(new_name, new_bkg):\n",
      "    return create_model_from_template('model_exp', new_name, 'bkg_exp', new_bkg)\n",
      "\n",
      "cmfe = create_model_from_exp\n",
      "\n",
      "for bkg_name, bkg in bkgs.iteritems():\n",
      "    models[bkg_name] = cmfe('model_%s' % bkg_name, bkg[1].GetName())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i, model in enumerate(models, 1):\n",
      "    print \"{:<5d}{:<30}{:d}\".format(i, model, bkgs[model][0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1    exp                           1\n",
        "2    poly1                         1\n",
        "3    poly2                         2\n",
        "4    poly3                         3\n",
        "5    poly4                         4\n",
        "6    poly5                         5\n",
        "7    landau                        2\n",
        "8    exppol2                       2\n",
        "9    exppol3                       3\n",
        "10   exppol4                       4\n",
        "11   laurent2                      2\n",
        "12   laurent3                      3\n",
        "13   laurent_half                  4\n",
        "14   complicated                   999\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# fit the constant to landau\n",
      "obs_set = ROOT.RooArgSet(mass)\n",
      "data_landau = models['landau'].generateBinned(obs_set, ROOT.RooFit.ExpectedData())\n",
      "for k, pdf in models.iteritems():\n",
      "    pdf.fitTo(data_landau)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu.setVal(1)\n",
      "mH.setVal(125)\n",
      "true_model = models['complicated']\n",
      "ws.var('bkg_poly5_par5_clone').setVal(ws.var('bkg_poly5_par5_clone').getVal() * 1.5)\n",
      "ws.var('bkg_poly5_par4_clone').setVal(ws.var('bkg_poly5_par4_clone').getVal() * 1.5)\n",
      "ws.var('bkg_poly5_par3_clone').setVal(ws.var('bkg_poly5_par3_clone').getVal() * 1.5)\n",
      "data = true_model.generateBinned(obs_set,\n",
      "                                 ROOT.RooFit.ExpectedData()\n",
      ")\n",
      "ws_import(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "bkg only fit\n",
      "------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.var('mu').setVal(0)\n",
      "ws.var('mu').setConstant()\n",
      "\n",
      "canvas = TCanvas()\n",
      "frame = mass.frame()\n",
      "\n",
      "legend = ROOT.TLegend(0.4, 0.7, 0.9, 0.9)\n",
      "legend.SetNColumns(2)\n",
      "\n",
      "data_bkg_only = true_model.generateBinned(obs_set,\n",
      "                                 ROOT.RooFit.ExpectedData()\n",
      ")\n",
      "data_bkg_only.plotOn(frame)\n",
      "\n",
      "\n",
      "for color, pdfname in zip(colors, models):\n",
      "    pdf = ws.pdf('model_' + pdfname)\n",
      "    pdf.fitTo(data_bkg_only)\n",
      "    pdf.plotOn(frame, ROOT.RooFit.LineColor(color), ROOT.RooFit.Name(\"curve_sb_%s\" % pdfname))\n",
      "    curve = frame.findObject(\"curve_sb_%s\" % pdfname)\n",
      "    curve.SetFillColor(0)\n",
      "    curve.SetMarkerSize(0)\n",
      "    legend.AddEntry(curve, pdfname)\n",
      "    \n",
      "frame.addObject(legend)\n",
      "frame.SetTitle(\"bkg-only fit\")\n",
      "frame.Draw()\n",
      "canvas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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BV2miWuxeQncLOaJs/BrlTV6vrYWqmD2q42oYo+XeT6PZmLtE7p8GsXHbV2ln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\n",
       "prompt_number": 12,
       "text": [
        "<ROOT.TCanvas object (\"icanvas\") at 0x4fe9d10>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "signal + background fit\n",
      "------------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu.setConstant(False)\n",
      "mH.setConstant(False)\n",
      "mu.setVal(1)\n",
      "mH.setVal(125)\n",
      "\n",
      "canvas = TCanvas()\n",
      "frame = mass.frame()\n",
      "data.plotOn(frame, ROOT.RooFit.Name(\"curve_data\"))\n",
      "\n",
      "legend = ROOT.TLegend(0.4, 0.5, 0.9, 0.9)\n",
      "\n",
      "print \"{:<20s}{:^4s}{:^12s}{:^12s}{:^17s}{:^17s}\".format(\"\", \"ndof bkg\", \"min nll\", \"chi/ndof\", \"mH\", \"mu\")\n",
      "print \"=\" * 80\n",
      "\n",
      "mu_values, mu_values_err, mH_values, mH_values_err = [], [], [], []\n",
      "models_for_fit = [m for m in models.keys() if (m != 'complicated' and m != 'landau')]\n",
      "\n",
      "for i, (color, pdfname) in enumerate(zip(colors, models_for_fit)):\n",
      "    mH.setVal(1)\n",
      "    mH.setVal(125)\n",
      "    pdf = ws.pdf('model_' + pdfname)\n",
      "    fit_result = pdf.fitTo(data, ROOT.RooFit.Save())#, ROOT.RooFit.Minos(True))\n",
      "    \n",
      "    curve_sb_name = \"curve_sb_%s\" % pdfname\n",
      "    pdf.plotOn(frame, ROOT.RooFit.LineColor(color), ROOT.RooFit.Name(curve_sb_name))\n",
      "    pdf.plotOn(frame, ROOT.RooFit.Components(\"bkg*\"), ROOT.RooFit.LineColor(color), ROOT.RooFit.LineStyle(ROOT.kDashed))\n",
      "    chi2 = frame.chiSquare(curve_sb_name, \"curve_data\", bkgs[pdfname][0])\n",
      "    print u\"{:<20s}{:>4d}{:>12.0f}{:>12f}{:>8.2f} \u00b1 {:<8.2f}{:>5.3f} \u00b1 {:<7.2f}\".format(pdfname, bkgs[pdfname][0], fit_result.minNll(), chi2, mH.getVal(), mH.getError(), mu.getVal(), mu.getError())\n",
      "    curve = frame.findObject(curve_sb_name)\n",
      "    curve.SetFillColor(0)\n",
      "    curve.SetMarkerSize(0)\n",
      "    legend.AddEntry(curve, pdfname)\n",
      "    \n",
      "    mu_values.append(mu.getVal())\n",
      "    mH_values.append(mH.getVal())\n",
      "    mu_values_err.append(mu.getError())\n",
      "    mH_values_err.append(mH.getError())    \n",
      "\n",
      "legend.SetNColumns(2)\n",
      "frame.addObject(legend)\n",
      "frame.SetTitle(\"s+b fit\")\n",
      "frame.Draw()\n",
      "\n",
      "fig, ax = plt.subplots(figsize=(5, 8))\n",
      "ax.errorbar(np.arange(len(models_for_fit)) + 0.5, mu_values, mu_values_err, fmt='.')\n",
      "ax.set_ylim(1 - 3 * np.mean(mu_values_err), 1 + 3 * np.mean(mu_values_err))\n",
      "ax.set_xticks(np.arange(len(models_for_fit)) + 0.5)\n",
      "ax.set_xticklabels(models_for_fit, rotation='vertical')\n",
      "ax.hlines(1., 0.5, len(models_for_fit), linestyles='dotted')\n",
      "ax.set_ylabel(\"$\\hat{\\mu}$\")\n",
      "plt.show()\n",
      "\n",
      "canvas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                    ndof bkg  min nll     chi/ndof         mH               mu        \n",
        "================================================================================\n",
        "exp                    1     -659715    0.295886  125.02 \u00b1 0.22    0.577 \u00b1 0.10   \n",
        "poly1                  1     -659005    3.156457  124.66 \u00b1 26.66   0.000 \u00b1 1.88   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly2                  2     -659736    0.209648  125.08 \u00b1 0.20    0.731 \u00b1 0.10   \n",
        "poly3                  3     -659785    0.004059  125.02 \u00b1 0.17    1.011 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly4                  4     -659786    0.000141  125.00 \u00b1 0.17    0.992 \u00b1 0.10   \n",
        "poly5                  5     -659786    0.000012  125.00 \u00b1 0.17    1.000 \u00b1 0.11   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "exppol2                2     -659784    0.006975  125.02 \u00b1 0.17    0.951 \u00b1 0.10   \n",
        "exppol3                3     -659786    0.002118  125.00 \u00b1 0.17    0.961 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "exppol4                4     -659786    0.000216  125.00 \u00b1 0.17    0.991 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "laurent2               2     -659782    0.016514  125.03 \u00b1 0.17    0.927 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "laurent3               3     -659783    0.013812  125.02 \u00b1 0.17    0.928 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "laurent_half           4     -659766    0.082723  125.06 \u00b1 0.18    0.844 \u00b1 0.10   "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rQhvrgJf1bs8j9Zx34QLDkrTALaUKOyld0iw5hjRp/zukwZ4jgB8BvjFuYQd4\nJM2SDqO7+zlXe5ckLcY9S0mzpNhq746GS5olNVZ7l6SZk20ldk93lDTLngQcmaOQ3XBJs6TYSuwO\n8EiaJZsHHmddid2wlDSLfph0naK+r05qQyRpGrkSuyQF1FjtXZIa77be/U7m1764I0dhR8MlzZLh\nldi/SaaV2B3gkTRLaqz2LklajHuWkmZBjZXYJUmSJEmSJEmSJEmaMf8fP1760RE/v0oAAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5059d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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fnvMOV0uk3pZuqQoetfcER1uCF0zkYvabN9rfo6y31XnxsVSNZKkKHp2r9dM0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\nAAAABgBRBQAAADAAiCoAAACAAfj/Ae7bWe0Fo208AAAAAElFTkSuQmCC\n",
       "prompt_number": 13,
       "text": [
        "<ROOT.TCanvas object (\"icanvas\") at 0x4fe9d10>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "obs = mu\n",
      "nbins = 40"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mH.setVal(125)\n",
      "mu.setVal(1)\n",
      "\n",
      "mH.setConstant(False)\n",
      "mu.setConstant(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "true_model.fitTo(data)\n",
      "mu_error = mu.getError()\n",
      "print mu.getVal(), mu.getError(), mH.getVal(), mH.getError()\n",
      "obs_min, obs_max = 1 - 8 * mu_error, 1 + 8 * mu_error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.999599047823 0.108023172576 125.000141218 0.167403437545\n"
       ]
      }
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nbins = 40\n",
      "\n",
      "canvas_noc = TCanvas()\n",
      "\n",
      "canvas = TCanvas()\n",
      "canvas.Divide(1, 2)\n",
      "canvas.cd(1)\n",
      "\n",
      "frame = obs.frame(ROOT.RooFit.Bins(nbins), ROOT.RooFit.Range(obs_min, obs_max))\n",
      "frame_noc = obs.frame(ROOT.RooFit.Bins(nbins), ROOT.RooFit.Range(obs_min, obs_max))\n",
      "frame_control = obs.frame(ROOT.RooFit.Bins(nbins), ROOT.RooFit.Range(obs_min, obs_max))\n",
      "\n",
      "legend = ROOT.TLegend(0.7, 0.7, 0.9, 0.9)\n",
      "\n",
      "\n",
      "for color, pdfname in zip(colors, models_for_fit):\n",
      "    ndof = bkgs[pdfname][0]\n",
      "    print pdfname\n",
      "    mH.setVal(125)\n",
      "    mu.setVal(1)\n",
      "\n",
      "    mH_set = ROOT.RooArgSet(obs)\n",
      "    ws.pdf(\"model_\" + pdfname).fitTo(data)\n",
      "    nll = ws.pdf(\"model_\" + pdfname).createNLL(data)\n",
      "\n",
      "    nll_min_value = nll.getVal()\n",
      "\n",
      "    nllp = nll.createProfile(mH_set)\n",
      "    \n",
      "    nllp_list = ROOT.RooArgList(nllp, ROOT.RooFit.RooConst(nll_min_value))\n",
      "    nllp_list2 = ROOT.RooArgList(nllp, ROOT.RooFit.RooConst(nll_min_value), ROOT.RooFit.RooConst(ndof))\n",
      "    \n",
      "\n",
      "    nllp2 = ROOT.RooFormulaVar('nllp2', \"-2 log #\\lambda\", '2 * (@0 + @1)', nllp_list)\n",
      "    nllp2P = ROOT.RooFormulaVar('nllp2P', \"-2 log#\\lambda_P\", '2 * (@0 +@1) + @2', nllp_list2)\n",
      "    nllp2.plotOn(frame_noc, ROOT.RooFit.LineColor(color), ROOT.RooFit.LineWidth(1), ROOT.RooFit.FillColor(0), ROOT.RooFit.Precision(1), ROOT.RooFit.LineStyle(ROOT.kDotted))\n",
      "    nllp2P.plotOn(frame, ROOT.RooFit.LineColor(color), ROOT.RooFit.LineWidth(1), ROOT.RooFit.FillColor(0), ROOT.RooFit.Precision(1), ROOT.RooFit.Name(\"nll2P_%s\" % pdfname))\n",
      "    \n",
      "\n",
      "curves = []\n",
      "for pdfname in models_for_fit:\n",
      "    curve = frame.findObject(\"nll2P_%s\" % pdfname)\n",
      "    curves.append(curve)\n",
      "    curve.SetMarkerSize(0)\n",
      "    legend.AddEntry(curve, pdfname)\n",
      "\n",
      "print curves    \n",
      "    \n",
      "envelope = ROOT.TGraph()\n",
      "envelope_index = ROOT.TGraph()\n",
      "for i, x in enumerate(np.linspace(obs_min, obs_max, 50)):  \n",
      "    values = [curve.Eval(x) for curve in curves]\n",
      "    min_index = np.argmin(values)\n",
      "    envelope_index.SetPoint(i, x, min_index)\n",
      "    envelope.SetPoint(i, x, values[min_index])\n",
      "envelope.SetLineStyle(ROOT.kDashed)\n",
      "legend.AddEntry(envelope, \"envelope\")\n",
      "envelope.SetLineWidth(3)\n",
      "envelope.SetMarkerSize(0)\n",
      "envelope.SetFillStyle(0)\n",
      "\n",
      "frame.addObject(envelope)\n",
      "frame.addObject(legend)\n",
      "    \n",
      "frame.Draw()\n",
      "\n",
      "canvas.cd(2)\n",
      "envelope_index.SetMarkerSize(0)\n",
      "envelope_index.Draw(\"APL\")\n",
      "\n",
      "canvas_noc.cd()\n",
      "frame_noc.addObject(legend)\n",
      "frame_noc.Draw()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "exp\n",
        "poly1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly2"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly3"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly4"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "poly5"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "exppol2"
       ]
      }
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.writeToFile(\"f.root\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.Print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "canvas_noc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "canvas"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.var(\"bkg_laurent2_par3\").getVal()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.Print()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ws.pdf('model_poly5').fitTo(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}