Week5/original/FittingAndTestingDistributions/FitAndTestingDistributions_original.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting is an Art!\n",
    "\n",
    "## Description\n",
    "Python macro for testing which fitting procedure is likely to give the \"best\" results. The two cases in question are:\n",
    "   * Gaussian distribution(s?) on constant background (peak searching)\n",
    "   * Double exponential distribution (high correlations)\n",
    "\n",
    "## Your Task\n",
    "Consider each case and argue/discuss which fitting function and method should be used.\n",
    "\n",
    "### Authors:\n",
    "- Troels Petersen ([email](mailto:petersen@nbi.dk))\n",
    "- Étienne Bourbeau (notebook conversion) ([email](mailto:etienne.bourbeau@icecube.wisc.edu))\n",
    "\n",
    "### Last update:\n",
    "10th December 2019\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from iminuit import Minuit\n",
    "from scipy import stats\n",
    "import os, sys                                         # Modules to see files and folders in directories\n",
    "from os.path import dirname as parent_folder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.path.append('../../../External_Functions')\n",
    "from ExternalFunctions import Chi2Regression, BinnedLH, UnbinnedLH\n",
    "from ExternalFunctions import nice_string_output, add_text_to_ax    # Useful functions to print fit results on figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set som plotting standards:\n",
    "font = {'family' : 'serif',\n",
    "        'weight' : 'normal',\n",
    "        'size'   : 18}\n",
    "mpl.rc('font', **font)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "SavePlots = False         # Determining if plots are saved or not"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "pi = np.pi\n",
    "r = np.random                         # Random generator\n",
    "r.seed(41)                            # Set a random seed (but a fixed one - more on that later.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## CASE 1: Gaussian distribution on a constant background:\n",
    "\n",
    " * $f_{1}(x) = C+ \\frac{N}{\\sigma\\sqrt(2\\pi)}\\cdot \\exp \\left[-0.5 \\cdot\\left(\\frac{(x-\\mu)}{\\sigma}\\right)^{2} \\right]$ for $x$ in $[-\\infty,\\infty]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  The bin width is:  0.10\n"
     ]
    }
   ],
   "source": [
    "Npoints_gauss = 200\n",
    "mux    = 3.50\n",
    "sigmax = 0.25\n",
    "Npoints_pol0 = 2000\n",
    "minx   =  0.0\n",
    "maxx   = 10.0\n",
    "Nbins = 100\n",
    "binwidth_gauss = (maxx-minx) / float(Nbins)\n",
    "print(f\"  The bin width is: {binwidth_gauss:5.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fill histogram with signal and background events:\n",
    "signal = np.random.normal(loc=mux,scale=sigmax,size=Npoints_gauss)\n",
    "bkg = np.random.uniform(low=minx,high=maxx,size=Npoints_pol0)\n",
    "Y = np.concatenate([signal,bkg,np.random.normal(loc=mux+2.1,scale=sigmax,size=int(Npoints_gauss/3.14))])\n",
    "binning = np.linspace(minx,maxx,Nbins)\n",
    "\n",
    "counts,bin_edges = np.histogram(Y,bins=binning)\n",
    "unc_count = np.sqrt(counts)\n",
    "X = bin_edges[:-1]+(bin_edges[1]-bin_edges[0])/2.\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16, 8))\n",
    "ax.errorbar(X, counts, yerr=unc_count, marker = '.', drawstyle = 'steps-mid')\n",
    "ax.set_xlabel('Wave length (nm)', fontsize=18)\n",
    "ax.set_ylabel('Frequency / 0.1', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define function (including bin width to get normalisation right):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func_gpol0(x,a,mu,sigma,cst) :\n",
    "    norm = binwidth_gauss * a / np.sqrt(2.0*pi) / sigma\n",
    "    z = (x-mu)/sigma\n",
    "    return norm * np.exp(-0.5*z*z) + cst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  WARNING: The ChiSquare fit DID NOT converge!!!\n"
     ]
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(func_gpol0, X[select], counts[select], unc_count[select])\n",
    "minuit_obj = Minuit(chi2reg, pedantic=False, print_level=0, a=1.0, mu=1.0, sigma=1.0)\n",
    "minuit_obj.migrad()   \n",
    "\n",
    "if (not minuit_obj.get_fmin().is_valid) :                                   # Check if the fit converged\n",
    "    print(\"  WARNING: The ChiSquare fit DID NOT converge!!!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bf_a, bf_mu, bf_sigma, bf_cst = minuit_obj.args\n",
    "ax.plot(X,func_gpol0(X, bf_a, bf_mu, bf_sigma, bf_cst), 'r', linewidth=2.0, label='Const + Gauss fit')\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "Look at the first case, but make sure that you also do the second case, as this is\n",
    "at least as important as the first one!\n",
    "\n",
    "Questions on CASE 1:\n",
    "--------------------\n",
    " 1. Look at the data plot and the corresponding fit. What type of fit is it? Does it\n",
    "    run well (or at all)? And once it runs, does it seem to be reasonable? Why? And\n",
    "    does the fitting function include all features of the data? Why/why not? Try for\n",
    "    5-10 minutes and discuss it with your neighbor, before reading on!\n",
    "\n",
    "---\n",
    "_5-10 minutes later_...\n",
    "\n",
    "---\n",
    "\n",
    " 2. What is the p-value from the minimal Chi2 that your fit obtained? Is the acceptable?\n",
    "\n",
    "---\n",
    "_5-10 minutes later_...\n",
    "\n",
    "---\n",
    "\n",
    " 3. As it happens, there seem to be a suspectable bump around 5 < x < 6. Try to write\n",
    "    an additional fitting function, which includes this bump in the model, and get the\n",
    "    fit to run. How significant is the bump, based on significance of the amplitude of\n",
    "    the second Gaussian peak? And what test would you apply to this, if you wanted to\n",
    "    make a full-fledged hypothesis test between the two models? Are they nested? Can\n",
    "    you actually get a number out?\n",
    "\n",
    "---\n",
    "_10-20 minutes later_...\n",
    "\n",
    "---\n",
    "\n",
    " 4. Imagine that you concluded, that there was a new peak, and that you were sure that\n",
    "    it had the same width as the original peak (for example because the width was due to\n",
    "    the resolution of te apperatus, and not the peak itself). Does that help you in the fit,\n",
    "    and if so, how? Does the significance of the peak increase? Would it always do that?\n",
    "    Also imagine, that the parameter of interest is the distance between the peaks. How\n",
    "    would you now write your fitting function?\n",
    "\n",
    "\n",
    "## NOTE: \n",
    "\n",
    "If one wanted to test the G+pol0 vs. the G+G+pol0 models against each other, which might be relevant, then a likelihood ratio test would be obvious, and Wilk's theorem would provide the way to produce a p-value, thus doing a proper hypothesis test:\n",
    "\n",
    "* Using iminuit and the `UnbinnedLH` function instead of the $\\chi^{2}$ regression, you can minimize the data again\n",
    "* You can minimize both cases, and save the value of the LLH using `minuit_obj.fval`.\n",
    "* After that, you can compute the test statistic $-2\\log{\\frac{LH_{1}}{LH_{2}}}$, and see that it is $\\chi^{2}$ distributed (Wilk's Theorem).\n",
    "\n",
    "The the test statistic distribution will have $N_{dof} = 3$, unless you (smartly) eliminated one parameter from the second fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "\n",
    "## CASE 2: Double exponential distribution\n",
    "\n",
    "Here we are considering the fitting of exponential data, and how the writing of the fitting function is important.\n",
    "\n",
    "* The \"bad\" fitting function:\n",
    "    $f_{2,bad}(t)  = N_{1}\\cdot\\exp(-t/r_{1}) + N_{2}\\cdot\\exp(-t/r_{2})$ for $t$ in $[0,\\infty]$\n",
    "\n",
    "* The \"good\" fitting function:\n",
    "    $f_{2,good}(t) = N \\cdot\\left(\\frac{f}{r_{1}}\\cdot \\exp\\left[-t/r_{1}\\right] + \\frac{(1-f)}{r_{2}}\\cdot\\exp\\left[-t/r_{2}\\right]\\right)$ for $t$ in $[0,\\infty]$\n",
    "\n",
    "## NOTE\n",
    "The parameters $r_1$ and $r_2$ need to be positive, and $f$ in [0,1], in order for this to be a PDF.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Npoints_2exp = 2000\n",
    "frac = 0.5   # Fraction that \"belongs to\" first exponential\n",
    "r1 = 10.0\n",
    "r2 =  2.0     # Note that the two lifetimes are not very different!\n",
    "nbins_2exp = 200\n",
    "xmin_2exp = 0.0\n",
    "xmax_2exp = 20.0\n",
    "binning = np.linspace(xmin_2exp, xmax_2exp, nbins_2exp)\n",
    "binwidth_2exp = (xmax_2exp - xmin_2exp) / nbins_2exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_pts = np.random.uniform(size=Npoints_2exp)\n",
    "N1 = sum(all_pts<frac)\n",
    "\n",
    "t = np.concatenate([np.random.exponential(scale=r1, size=N1),\n",
    "                    np.random.exponential(scale=r2, size=(Npoints_2exp-N1))])\n",
    "\n",
    "counts,bin_edges = np.histogram(t,bins=binning)\n",
    "unc_2exp = np.sqrt(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'count')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = bin_edges[:-1]+(bin_edges[1]-bin_edges[0])/2.\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(16, 8))\n",
    "ax.errorbar(X,counts,yerr=unc_2exp,marker = '.',drawstyle = 'steps-mid')\n",
    "ax.set_xlabel('x',fontsize=13)\n",
    "ax.set_ylabel('count',fontsize=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's try to fit the data with the bad model:\n",
    "I include the binwidth (here 0.1) in the fit to ensure that the normalisations are (or could be) right!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_2expBad(x,N1,r1,N2,r2):\n",
    "    binwidth = binwidth_2exp\n",
    "    return binwidth*(N1*np.exp(-x/r1)+N2*np.exp(-x/r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------------\n",
      "| FCN = 250.6                   |     Ncalls=212 (212 total)     |\n",
      "| EDM = 1.84E-07 (Goal: 1E-05)  |            up = 1.0            |\n",
      "------------------------------------------------------------------\n",
      "|  Valid Min.   | Valid Param.  | Above EDM | Reached call limit |\n",
      "------------------------------------------------------------------\n",
      "|     True      |     True      |   False   |       False        |\n",
      "------------------------------------------------------------------\n",
      "| Hesse failed  |   Has cov.    | Accurate  | Pos. def. | Forced |\n",
      "------------------------------------------------------------------\n",
      "|     False     |     True      |   False   |   False   |  True  |\n",
      "------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(f_2expBad, X[select], counts[select], unc_2exp[select])\n",
    "minuit_obj = Minuit(chi2reg, pedantic=False, print_level=1)\n",
    "#minuit_obj = Minuit(chi2reg, pedantic=False, print_level=1, N1=frac*Npoints_2exp, r1=r1, N2=(1-frac)*Npoints_2exp, r2=r2)\n",
    "minuit_obj.migrad()\n",
    "\n",
    "if (not minuit_obj.get_fmin().is_valid) :                                   # Check if the fit converged\n",
    "    print(\"  WARNING: The ChiSquare fit DID NOT converge!!!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bf_N1,bf_r1,bf_N2,bf_r2 = minuit_obj.args\n",
    "Chi2 = minuit_obj.fval\n",
    "Ndof = len(X[select])-len(minuit_obj.args)\n",
    "ProbChi2 = stats.chi2.sf(Chi2, Ndof)\n",
    "\n",
    "ax.plot(X, f_2expBad(X,bf_N1,bf_r1,bf_N2,bf_r2), 'r', linewidth=2.0, label='Bad fitting function')\n",
    "\n",
    "d = {'Entries'   : \"{:d}\".format(sum(counts)),\n",
    "     'Chi2/d.o.f': \"{:.3f} / {:d}\".format(Chi2, Ndof),\n",
    "     'Prob'      : \"{:.3f}\".format(ProbChi2),\n",
    "     'N1'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['N1'], minuit_obj.errors['N1']),\n",
    "     'N2'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['N2'], minuit_obj.errors['N2']),\n",
    "     'r1'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['r1'], minuit_obj.errors['r1']),\n",
    "     'r2'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['r2'], minuit_obj.errors['r2'])}\n",
    "\n",
    "ax.text(0.65, 0.95, nice_string_output(d, 0), family='monospace', \n",
    "        transform=ax.transAxes, fontsize=13, color='red', verticalalignment='top')\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('N1', 'N1') 1.0\n",
      "('N1', 'r1') -0.0513316559290841\n",
      "('N1', 'N2') -0.9895984850347246\n",
      "('N1', 'r2') -0.03459208145027249\n",
      "('r1', 'N1') -0.0513316559290841\n",
      "('r1', 'r1') 1.0\n",
      "('r1', 'N2') -0.027084194960149667\n",
      "('r1', 'r2') 0.9465365975434357\n",
      "('N2', 'N1') -0.9895984850347246\n",
      "('N2', 'r1') -0.027084194960149667\n",
      "('N2', 'N2') 0.9999999999999998\n",
      "('N2', 'r2') -0.01135209864723872\n",
      "('r2', 'N1') -0.03459208145027249\n",
      "('r2', 'r1') 0.9465365975434357\n",
      "('r2', 'N2') -0.01135209864723872\n",
      "('r2', 'r2') 0.9999999999999998\n"
     ]
    }
   ],
   "source": [
    "# Given the covariance matrix, we calculate and print the correlation matrix:\n",
    "corrBad={}                                       # Define an empty dictionary (the correlation matrix)\n",
    "for k,v in minuit_obj.covariance.items() :       # k=key (i.e. index by which you look up), v=value (well, value!)\n",
    "    error1 = minuit_obj.errors[k[0]]       # The error object of minuit is the square root of the variance (ie. sigma)\n",
    "    error2 = minuit_obj.errors[k[1]]\n",
    "    correlation = v / float((error1*error2)) \n",
    "    print(k,correlation)\n",
    "    corrBad[k] = correlation\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N1</th>\n",
       "      <th>N2</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>N1</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.989598</td>\n",
       "      <td>-0.051332</td>\n",
       "      <td>-0.034592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>N2</td>\n",
       "      <td>-0.989598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.027084</td>\n",
       "      <td>-0.011352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r1</td>\n",
       "      <td>-0.051332</td>\n",
       "      <td>-0.027084</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.946537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r2</td>\n",
       "      <td>-0.034592</td>\n",
       "      <td>-0.011352</td>\n",
       "      <td>0.946537</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          N1        N2        r1        r2\n",
       "N1  1.000000 -0.989598 -0.051332 -0.034592\n",
       "N2 -0.989598  1.000000 -0.027084 -0.011352\n",
       "r1 -0.051332 -0.027084  1.000000  0.946537\n",
       "r2 -0.034592 -0.011352  0.946537  1.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert dictionary to numpy array:\n",
    "def print_correlation_matrix(d, params):\n",
    "    \n",
    "    ncols = int(np.sqrt(len(d.keys())))\n",
    "    nrows = int(ncols)\n",
    "    matrix = np.zeros(shape=[nrows,ncols])\n",
    "    \n",
    "    index = {}\n",
    "    i=0\n",
    "    for p in params:\n",
    "        index[p]=i\n",
    "        i+=1\n",
    "    \n",
    "    for k,v in d.items():\n",
    "        l = index[k[0]]\n",
    "        c = index[k[1]]\n",
    "        matrix[l,c] = v\n",
    "    return matrix\n",
    "\n",
    "M = print_correlation_matrix(corrBad, ['N1','N2','r1','r2'])\n",
    "\n",
    "from IPython.display import HTML, display\n",
    "import pandas as pd\n",
    "M = pd.DataFrame(M, columns=['N1','N2','r1','r2'], index=['N1','N2','r1','r2'])\n",
    "display(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Questions on CASE 2:\n",
    "--------------------\n",
    " 1. Does the \"bad\" fit work well? Does it extract the parameters used to produce it?\n",
    "    Can you see what is missing? There are in fact several things, but one is simple to remedy.\n",
    "    Think and discuss...\n",
    "   \n",
    "---\n",
    "_5-10 minutes later_...\n",
    "\n",
    "---\n",
    "Of course you need to give the fit good initial values! Do this (for example those the data was produced with!), and run it again. It might work now, but actually that is not always the case. The reason is that the \"bad\" fitting function has two flaws:\n",
    "\n",
    "* It does not have a correct normalisation, thus making N(1/2) and r(1/2) correlated.\n",
    "* It does not have one overall normalisation, thus making N1 and N2 correlated.\n",
    "\n",
    "This gives very high correlations between the parameters, as can be seen from the correlation matrix printed.\n",
    "\n",
    " 2. Both of these problems can be avoided by rewriting the fitting function to include\n",
    "    the correct normalisation (i.e. dividing by the lifetime) and by putting only one\n",
    "    overall normalisation and then dividing the two lifetimes with a fraction (i.e. use\n",
    "    \"frac\" and \"(1.0*frac)\" as a parameter in front of each exponential term).\n",
    "    Try this (define a \"good\" function), and see if your fit improves. The way to see\n",
    "    this would in general be to try a lot of different data, but here we will simply see\n",
    "    that the correlations a smaller (especially for the overall normalisation).\n",
    "---\n",
    "_10-20 minutes later_...\n",
    "\n",
    "---  \n",
    "\n",
    "__If you didn't manage to get this fit going, I've included a \"good\" fitting function below! (but try yourself first!)__\n",
    "\n",
    " 3. The two lifetimes are naturally very correlated with each other (and the fraction),\n",
    "    when they are very alike. The only thing one can do about this is to fix one parameter.\n",
    "    This is of course not desirable, but one can be forced to do it, if the fit does not\n",
    "    converge otherwise. Note that since the correlation is very high, it is not a great\n",
    "    loss of freedom in the fitting function.\n",
    "    \n",
    "    A very common similar example is fitting a \"Gaussian-like\" peak, which happens to have\n",
    "    more than one width, for example if the data is obtained from two or more sources with\n",
    "    different resolutions. Here, one may choose to let the two (or more) Gaussians have\n",
    "    the same mean, but two different widths (the \"good\" and the \"bad\" measurements).\n",
    "    Typically, the parameter to fix (if any) is the fraction, but never fix a parameter\n",
    "    without first having tried to let it \"float\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The GOOD fitting function and fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def good_exp(x,N,f,r1,r2):\n",
    "    binwidth = binwidth_2exp\n",
    "    # f = fraction\n",
    "    return binwidth*N*(f/r1*np.exp(-x/r1)+(1-f)/r2*np.exp(-x/r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------------\n",
      "| FCN = 172.6                   |     Ncalls=173 (173 total)     |\n",
      "| EDM = 2.7E-05 (Goal: 1E-05)   |            up = 1.0            |\n",
      "------------------------------------------------------------------\n",
      "|  Valid Min.   | Valid Param.  | Above EDM | Reached call limit |\n",
      "------------------------------------------------------------------\n",
      "|     True      |     True      |   False   |       False        |\n",
      "------------------------------------------------------------------\n",
      "| Hesse failed  |   Has cov.    | Accurate  | Pos. def. | Forced |\n",
      "------------------------------------------------------------------\n",
      "|     False     |     True      |   True    |   True    | False  |\n",
      "------------------------------------------------------------------\n",
      "0.6802753000981541\n"
     ]
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(good_exp, X[select], counts[select], unc_2exp[select])\n",
    "minuit_obj = Minuit(chi2reg, pedantic=False, print_level=1, N=Npoints_2exp, r1=r1, r2=r2, f=frac)\n",
    "minuit_obj.migrad()\n",
    "\n",
    "if (not minuit_obj.get_fmin().is_valid) :                                   # Check if the fit converged\n",
    "    print(\"  WARNING: The ChiSquare fit DID NOT converge!!!\")\n",
    "\n",
    "bf_N,bf_f,bf_r1,bf_r2 = minuit_obj.args\n",
    "Chi2 = minuit_obj.fval\n",
    "Ndof = len(X[select])-len(minuit_obj.args)\n",
    "ProbChi2 = stats.chi2.sf(Chi2, Ndof)\n",
    "print(ProbChi2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(X,good_exp(X,bf_N,bf_f,bf_r1,bf_r2),'g',linewidth=2.0,label='Good-fit')\n",
    "\n",
    "d = {'Entries'   : \"{:d}\".format(sum(counts)),\n",
    "     'Chi2/d.o.f': \"{:.3f} / {:d}\".format(Chi2, Ndof),\n",
    "     'Prob'      : \"{:.3f}\".format(ProbChi2),\n",
    "     'N'         : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['N'], minuit_obj.errors['N']),\n",
    "     'f'         : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['f'], minuit_obj.errors['f']),\n",
    "     'r1'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['r1'], minuit_obj.errors['r1']),\n",
    "     'r2'        : \"{:.3f} +/- {:.3f}\".format(minuit_obj.values['r2'], minuit_obj.errors['r2'])}\n",
    "\n",
    "ax.text(0.3, 0.95, nice_string_output(d, 0), family='monospace', \n",
    "        transform=ax.transAxes, fontsize=13, color='green', verticalalignment='top')\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N</th>\n",
       "      <th>f</th>\n",
       "      <th>r1</th>\n",
       "      <th>r2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>N</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.383230</td>\n",
       "      <td>0.963593</td>\n",
       "      <td>0.818889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>f</td>\n",
       "      <td>-0.383230</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.488750</td>\n",
       "      <td>-0.698331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r1</td>\n",
       "      <td>0.963593</td>\n",
       "      <td>-0.488750</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.881353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>r2</td>\n",
       "      <td>0.818889</td>\n",
       "      <td>-0.698331</td>\n",
       "      <td>0.881353</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           N         f        r1        r2\n",
       "N   1.000000 -0.383230  0.963593  0.818889\n",
       "f  -0.383230  1.000000 -0.488750 -0.698331\n",
       "r1  0.963593 -0.488750  1.000000  0.881353\n",
       "r2  0.818889 -0.698331  0.881353  1.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We calculate the correlation matrix as in the Bad fit case:\n",
    "corrGood={}\n",
    "for k,v in minuit_obj.covariance.items() :       \n",
    "    error1 = minuit_obj.errors[k[0]]       \n",
    "    error2 = minuit_obj.errors[k[1]]\n",
    "    correlation = v / float((error1*error2)) \n",
    "    corrGood[k] = correlation\n",
    "\n",
    "\n",
    "M = print_correlation_matrix(corrGood,['N','f','r1','r2'])\n",
    "M = pd.DataFrame(M, columns=['N','f','r1','r2'],index=['N','f','r1','r2'])\n",
    "display(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "executable": "/usr/bin/env python",
  "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": "3.7.4"
  },
  "main_language": "python"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}