Week7/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",
    "***\n",
    "### Authors:\n",
    "- Troels Petersen ([email](mailto:petersen@nbi.dk))\n",
    "\n",
    "### Last update:\n",
    "- 6th of January 2021"
   ]
  },
  {
   "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",
    "The initial fitting function is the following:\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 $[-\\infty,\\infty]$\n",
    "\n",
    "It disregards both the \"outliers\" in the main peak, and perhaps also something else at higher values. Your job is to expand the fit until it really describes the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  The bin width is:  0.10\n"
     ]
    }
   ],
   "source": [
    "Npoints_gauss = 400\n",
    "mux    = 3.50\n",
    "sigmax = 0.25\n",
    "\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",
    "\n",
    "signal = np.random.normal(loc=mux,scale=sigmax,size=Npoints_gauss)\n",
    "signal_2=np.random.normal(loc=mux+4.1,scale=sigmax,size=int(Npoints_gauss/3.14))\n",
    "\n",
    "bkg = np.random.uniform(low=minx,high=maxx,size=Npoints_pol0)\n",
    "\n",
    "Y = np.concatenate([signal,bkg,signal_2])\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('x  i.e. 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": [],
   "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.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 (see below), 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/why not?\n",
    "    And does the fitting function include all features of the data? Why/why not? Try for\n",
    "    5-10 minutes and discuss it with others (if possible), 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 it acceptable?\n",
    "\n",
    "---\n",
    "_5-10 minutes later_...\n",
    "\n",
    "---\n",
    "\n",
    " 3. As it happens, there are tails on the main peak, and there also seem to be a\n",
    "    suspectable bump around 7 < x < 8. Try to write\n",
    "    an expanded 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 the 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 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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n"
     ]
    }
   ],
   "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\n",
    "print(binwidth_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": {
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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('t',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 = 212.9                   |     Ncalls=214 (214 total)     |\n",
      "| EDM = 0.000143 (Goal: 0.0002) |            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",
    "\n",
    "#the bad fit:\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.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') 1.0000000000000002\n",
      "('N1', 'r1') -0.042377232642779886\n",
      "('N1', 'N2') -0.9904393257822472\n",
      "('N1', 'r2') -0.025054100833637644\n",
      "('r1', 'N1') -0.042377232642779886\n",
      "('r1', 'r1') 1.0\n",
      "('r1', 'N2') -0.02419827526799987\n",
      "('r1', 'r2') 0.9517074615915235\n",
      "('N2', 'N1') -0.9904393257822472\n",
      "('N2', 'r1') -0.02419827526799987\n",
      "('N2', 'N2') 0.9999999999999998\n",
      "('N2', 'r2') -0.011308944614162004\n",
      "('r2', 'N1') -0.025054100833637644\n",
      "('r2', 'r1') 0.9517074615915235\n",
      "('r2', 'N2') -0.011308944614162004\n",
      "('r2', 'r2') 1.0\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": {
    "scrolled": true
   },
   "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",
       "      <th>N1</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.990439</td>\n",
       "      <td>-0.042377</td>\n",
       "      <td>-0.025054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>N2</th>\n",
       "      <td>-0.990439</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.024198</td>\n",
       "      <td>-0.011309</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r1</th>\n",
       "      <td>-0.042377</td>\n",
       "      <td>-0.024198</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.951707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r2</th>\n",
       "      <td>-0.025054</td>\n",
       "      <td>-0.011309</td>\n",
       "      <td>0.951707</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          N1        N2        r1        r2\n",
       "N1  1.000000 -0.990439 -0.042377 -0.025054\n",
       "N2 -0.990439  1.000000 -0.024198 -0.011309\n",
       "r1 -0.042377 -0.024198  1.000000  0.951707\n",
       "r2 -0.025054 -0.011309  0.951707  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 N1 and N2 correlated, as well as r1 and r2.\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 are 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 (as above). 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 = 152.8                   |     Ncalls=683 (683 total)     |\n",
      "| EDM = 0.000276 (Goal: 0.0002) |            up = 1.0            |\n",
      "------------------------------------------------------------------\n",
      "|  Valid Min.   | Valid Param.  | Above EDM | Reached call limit |\n",
      "------------------------------------------------------------------\n",
      "|     False     |     True      |   False   |        True        |\n",
      "------------------------------------------------------------------\n",
      "| Hesse failed  |   Has cov.    | Accurate  | Pos. def. | Forced |\n",
      "------------------------------------------------------------------\n",
      "|     False     |     True      |   False   |   True    | False  |\n",
      "------------------------------------------------------------------\n",
      "  WARNING: The ChiSquare fit DID NOT converge!!!\n",
      "0.8857153961970435\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:6: DeprecationWarning: get_fmin is deprecated: use `this_object.fmin` instead\n",
      "  \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",
       "      <th>N</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.999801</td>\n",
       "      <td>0.999977</td>\n",
       "      <td>0.246152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f</th>\n",
       "      <td>0.999801</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.999746</td>\n",
       "      <td>0.234786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r1</th>\n",
       "      <td>0.999977</td>\n",
       "      <td>0.999746</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.247965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r2</th>\n",
       "      <td>0.246152</td>\n",
       "      <td>0.234786</td>\n",
       "      <td>0.247965</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           N         f        r1        r2\n",
       "N   1.000000  0.999801  0.999977  0.246152\n",
       "f   0.999801  1.000000  0.999746  0.234786\n",
       "r1  0.999977  0.999746  1.000000  0.247965\n",
       "r2  0.246152  0.234786  0.247965  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": "3.7.6"
  },
  "main_language": "python"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}