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 three cases in question are:\n",
    "   * Linear function with x-values far from zero.\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 2022"
   ]
  },
  {
   "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(42)                            # Set a random seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## CASE 1: Linear fit with x-values far from zero:\n",
    "\n",
    "The initial fitting function is the following:\n",
    "\n",
    "* $f_{1}(x) = ax + b$\n",
    "\n",
    "If the x-values are far from zero (e.g. the year we are in), then any change in $a$ gives a major change in $b$, and the two gets very correlated. However, if the mean $x$-value (or some value close to it) is subtracted from $a$ in the function, then this is avoided, as $b$ is now the $y$ value at the middle of this point, which is not subject to much change.\n",
    "\n",
    "* $f_{1}(x) = a(x - \\bar{x}) + b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020]\n",
      "[ 6.26192059  7.05189392  8.67337223  8.42843866  9.05378677  9.89441221\n",
      " 10.36416143 10.65639991 10.91366581 11.36266578 12.44894941]\n"
     ]
    }
   ],
   "source": [
    "a =     0.501\n",
    "b = -1000.0\n",
    "sigmay = 0.5\n",
    "\n",
    "Npoints_lin = 11\n",
    "minx = 2010\n",
    "maxx = 2020\n",
    "\n",
    "x = np.arange(minx,maxx+1)\n",
    "y = a*x + b + r.normal(0.0, sigmay, len(x))\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 5.688 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 45 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.85e-15 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\" title=\"Is covariance matrix accurate?\"> APPROXIMATE </td>\n",
       "        <td style=\"text-align:center;background-color:#c15ef7;color:black\" title=\"Is covariance matrix positive definite?\"> NOT pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#c15ef7;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> FORCED </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> a </td>\n",
       "        <td> 0.5515 </td>\n",
       "        <td> 0.0012 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> b </td>\n",
       "        <td> -1.1017e3 </td>\n",
       "        <td> 0.0024e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> a </th>\n",
       "        <th> b </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> a </th>\n",
       "        <td> 1.4e-06 </td>\n",
       "        <td style=\"background-color:rgb(120,120,250);color:black\"> -0.00282 <strong>(-0.998)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> b </th>\n",
       "        <td style=\"background-color:rgb(120,120,250);color:black\"> -0.00282 <strong>(-0.998)</strong> </td>\n",
       "        <td> 5.69 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 5.688                      │              Nfcn = 45               │\n",
       "│ EDM = 1.85e-15 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │APPROXIMATE│NOT pos. def.│   FORCED   │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ a    │  0.5515   │  0.0012   │            │            │         │         │       │\n",
       "│ 1 │ b    │ -1.1017e3 │ 0.0024e3  │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───┬───────────────────┐\n",
       "│   │        a        b │\n",
       "├───┼───────────────────┤\n",
       "│ a │  1.4e-06 -0.00282 │\n",
       "│ b │ -0.00282     5.69 │\n",
       "└───┴───────────────────┘"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func_bad(x, a, b) :\n",
    "    return a*x + b\n",
    "\n",
    "def func_good(x, a, b) :\n",
    "    return a*(x-2000) + b\n",
    "\n",
    "fit_chi2 = Chi2Regression(func_bad, x, y, sigmay)\n",
    "minuit_chi2 = Minuit(fit_chi2, a=0.0, b=0.0)\n",
    "minuit_chi2.errordef = 1.0\n",
    "minuit_chi2.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_fit = np.linspace(minx, maxx, 1000)\n",
    "y_fit = func_bad(x_fit, *minuit_chi2.values[:])\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15, 8))\n",
    "plot_data = ax.errorbar(x, y, sigmay, fmt='.', linewidth=2, color='blue', label=\"Data\")\n",
    "ax.plot(x_fit, y_fit, '-', color='red', linewidth=2, label='ChiSquare fit')\n",
    "ax.set(xlabel='x (year)', ylabel='y')\n",
    "ax.legend()\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## CASE 2: 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": {
      "image/png": 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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', 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, N, mu, sigma, cst) :\n",
    "    norm = binwidth_gauss * N / 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": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 351.7 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 195 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = nan (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> N </td>\n",
       "        <td> -3.3067e7 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> mu </td>\n",
       "        <td> 1.9282e1 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> sigma </td>\n",
       "        <td> 1.4017 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> cst </td>\n",
       "        <td> 2.1973e1 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> N </th>\n",
       "        <th> mu </th>\n",
       "        <th> sigma </th>\n",
       "        <th> cst </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N </th>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -2.52e+10 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 6.71e+09 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.69 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -2.52e+10 </td>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 20.8 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.74e-09 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 6.71e+09 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 20.8 </td>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -2.26e-09 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> cst </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.69 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.74e-09 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -2.26e-09 </td>\n",
       "        <td> nan </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 351.7                      │              Nfcn = 195              │\n",
       "│ EDM = nan (Goal: 0.0002)         │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬───────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name  │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼───────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ N     │ -3.3067e7 │    nan    │            │            │         │         │       │\n",
       "│ 1 │ mu    │ 1.9282e1  │    nan    │            │            │         │         │       │\n",
       "│ 2 │ sigma │  1.4017   │    nan    │            │            │         │         │       │\n",
       "│ 3 │ cst   │ 2.1973e1  │    nan    │            │            │         │         │       │\n",
       "└───┴───────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌───────┬─────────────────────────────────────────┐\n",
       "│       │         N        mu     sigma       cst │\n",
       "├───────┼─────────────────────────────────────────┤\n",
       "│     N │       nan -2.52e+10  6.71e+09      2.69 │\n",
       "│    mu │ -2.52e+10       nan      20.8  2.74e-09 │\n",
       "│ sigma │  6.71e+09      20.8       nan -2.26e-09 │\n",
       "│   cst │      2.69  2.74e-09 -2.26e-09       nan │\n",
       "└───────┴─────────────────────────────────────────┘"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(func_gpol0, X[select], counts[select], unc_count[select])\n",
    "minuit_obj = Minuit(chi2reg, N=1.0, mu=1.0, sigma=1.0, cst=1.0)\n",
    "minuit_obj.errordef = 1.0\n",
    "minuit_obj.migrad()   "
   ]
  },
  {
   "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": [
    "if (not minuit_obj.fmin.is_valid) :                                   # Check if the fit converged\n",
    "    print(\"  WARNING: The ChiSquare fit DID NOT converge!!!\")\n",
    "\n",
    "bf_N, bf_mu, bf_sigma, bf_cst = minuit_obj.values[:]\n",
    "ax.plot(X, func_gpol0(X, bf_N, 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 considering the difference in ChiSquare values or -2ln of the likelihood ratio would be obvious (these two gives the same result, when errors are Gaussian and the binning does not have any effect). Wilk's theorem would provide the way to produce a p-value, thus doing a proper hypothesis test using the likelihood ratio 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 3: 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 to what the two lifetimes are different, as this decides their correlation!\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": {
      "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('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": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "../../../External_Functions/ExternalFunctions.py:121: RuntimeWarning: overflow encountered in square\n",
      "  chi2 = np.sum(self.weights*(self.y - f)**2/self.sy**2)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 279.4 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 230 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = nan (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> N1 </td>\n",
       "        <td> -2.7621e8 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> r1 </td>\n",
       "        <td> 3.4022e-3 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> N2 </td>\n",
       "        <td> 6.3017e2 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> r2 </td>\n",
       "        <td> 2.7742 </td>\n",
       "        <td> nan </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> N1 </th>\n",
       "        <th> r1 </th>\n",
       "        <th> N2 </th>\n",
       "        <th> r2 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N1 </th>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.04e+05 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -4.27e+04 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 21.1 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> r1 </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 2.04e+05 </td>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 1.51e-07 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -7.47e-11 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N2 </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -4.27e+04 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 1.51e-07 </td>\n",
       "        <td> nan </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 8.8e-12 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> r2 </th>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 21.1 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> -7.47e-11 </td>\n",
       "        <td style=\"background-color:rgb(nan,nan,nan);color:black\"> 8.8e-12 </td>\n",
       "        <td> nan </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 279.4                      │              Nfcn = 230              │\n",
       "│ EDM = nan (Goal: 0.0002)         │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ N1   │ -2.7621e8 │    nan    │            │            │         │         │       │\n",
       "│ 1 │ r1   │ 3.4022e-3 │    nan    │            │            │         │         │       │\n",
       "│ 2 │ N2   │ 6.3017e2  │    nan    │            │            │         │         │       │\n",
       "│ 3 │ r2   │  2.7742   │    nan    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────────────────────────┐\n",
       "│    │        N1        r1        N2        r2 │\n",
       "├────┼─────────────────────────────────────────┤\n",
       "│ N1 │       nan  2.04e+05 -4.27e+04      21.1 │\n",
       "│ r1 │  2.04e+05       nan  1.51e-07 -7.47e-11 │\n",
       "│ N2 │ -4.27e+04  1.51e-07       nan   8.8e-12 │\n",
       "│ r2 │      21.1 -7.47e-11   8.8e-12       nan │\n",
       "└────┴─────────────────────────────────────────┘"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(f_2expBad, X[select], counts[select], unc_2exp[select])\n",
    "\n",
    "# Random starting values:\n",
    "xf = r.uniform(0.0, 2.0, 4)\n",
    "\n",
    "# The bad fit (notice that we start it at \"perfect\" parameters!!!):\n",
    "minuit_obj = Minuit(chi2reg, N1=xf[0]*frac*Npoints_2exp, r1=xf[1]*r1, N2=xf[2]*(1-frac)*Npoints_2exp, r2=xf[3]*r2)\n",
    "minuit_obj.errordef = 1.0\n",
    "minuit_obj.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note on the covariance/correlation matrix:\n",
    "\n",
    "As stated, you want your fit to have the **least** correlations between the fitting parameters.<br>\n",
    "Try to check all the entries above, and see if you understand why the correlations are as they are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "279.40626412009385 182 4.560520020176626e-06\n"
     ]
    },
    {
     "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": [
    "if (not minuit_obj.fmin.is_valid) :                                   # Check if the fit converged\n",
    "    print(\"  WARNING: The ChiSquare fit DID NOT converge!!!\")\n",
    "    \n",
    "bf_N1, bf_r1, bf_N2, bf_r2 = minuit_obj.values[:]\n",
    "Chi2 = minuit_obj.fval\n",
    "Ndof = len(X[select]) - len(minuit_obj.values[:])\n",
    "ProbChi2 = stats.chi2.sf(Chi2, Ndof)\n",
    "print(Chi2, Ndof, ProbChi2)\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": "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\".\n",
    "    \n",
    "    However, **no fit function is perfect** and the below fitting function is not an \"absolute\"\n",
    "    improvement. The improvement lies only in some parts of the parameter space, and it is hard\n",
    "    to know, when it has been improved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The GOOD fitting function and fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def good_exp(x, N, f, r1, r2):\n",
    "    binwidth = binwidth_2exp\n",
    "\n",
    "    # Either \"just\" normalise correctly:\n",
    "    # return binwidth*(N1/r1*np.exp(-x/r1)+N2/r2*np.exp(-x/r2))\n",
    "    # Or also re-write to include f = fraction:\n",
    "    return binwidth*N*(f/r1*np.exp(-x/r1) + (1.0-f)/r2*np.exp(-x/r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 155.9 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of function evaluations in last call and total number\"> Nfcn = 115 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 8.5e-06 (Goal: 0.0002) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"No. of gradient evaluations in last call and total number\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> N </td>\n",
       "        <td> 2.07e3 </td>\n",
       "        <td> 0.30e3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> f </td>\n",
       "        <td> 0.37 </td>\n",
       "        <td> 0.05 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> r1 </td>\n",
       "        <td> 24 </td>\n",
       "        <td> 18 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> r2 </td>\n",
       "        <td> 2.34 </td>\n",
       "        <td> 0.19 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> N </th>\n",
       "        <th> f </th>\n",
       "        <th> r1 </th>\n",
       "        <th> r2 </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> N </th>\n",
       "        <td> 9.3e+04 </td>\n",
       "        <td style=\"background-color:rgb(250,117,117);color:black\"> 14.2 <strong>(0.888)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,103,103);color:black\"> 5.4e+03 <strong>(0.981)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,138,138);color:black\"> 43.2 <strong>(0.745)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> f </th>\n",
       "        <td style=\"background-color:rgb(250,117,117);color:black\"> 14.2 <strong>(0.888)</strong> </td>\n",
       "        <td> 0.00276 </td>\n",
       "        <td style=\"background-color:rgb(250,122,122);color:black\"> 0.805 <strong>(0.850)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 0.0048 <strong>(0.481)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> r1 </th>\n",
       "        <td style=\"background-color:rgb(250,103,103);color:black\"> 5.4e+03 <strong>(0.981)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,122,122);color:black\"> 0.805 <strong>(0.850)</strong> </td>\n",
       "        <td> 326 </td>\n",
       "        <td style=\"background-color:rgb(250,130,130);color:black\"> 2.74 <strong>(0.799)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> r2 </th>\n",
       "        <td style=\"background-color:rgb(250,138,138);color:black\"> 43.2 <strong>(0.745)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,178,178);color:black\"> 0.0048 <strong>(0.481)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,130,130);color:black\"> 2.74 <strong>(0.799)</strong> </td>\n",
       "        <td> 0.0362 </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 155.9                      │              Nfcn = 115              │\n",
       "│ EDM = 8.5e-06 (Goal: 0.0002)     │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ N    │  2.07e3   │  0.30e3   │            │            │         │         │       │\n",
       "│ 1 │ f    │   0.37    │   0.05    │            │            │         │         │       │\n",
       "│ 2 │ r1   │    24     │    18     │            │            │         │         │       │\n",
       "│ 3 │ r2   │   2.34    │   0.19    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬─────────────────────────────────┐\n",
       "│    │       N       f      r1      r2 │\n",
       "├────┼─────────────────────────────────┤\n",
       "│  N │ 9.3e+04    14.2 5.4e+03    43.2 │\n",
       "│  f │    14.2 0.00276   0.805  0.0048 │\n",
       "│ r1 │ 5.4e+03   0.805     326    2.74 │\n",
       "│ r2 │    43.2  0.0048    2.74  0.0362 │\n",
       "└────┴─────────────────────────────────┘"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "select = counts>0\n",
    "chi2reg = Chi2Regression(good_exp, X[select], counts[select], unc_2exp[select])\n",
    "\n",
    "minuit_obj = Minuit(chi2reg, N=xf[0]*Npoints_2exp, f=xf[3]*frac, r1=xf[1]*r1, r2=xf[2]*r2)\n",
    "minuit_obj.errordef = 1.0\n",
    "minuit_obj.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "155.89145409155037 182 0.9199293607386552\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if (not minuit_obj.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.values[:]\n",
    "Chi2 = minuit_obj.fval\n",
    "Ndof = len(X[select]) - len(minuit_obj.values[:])\n",
    "ProbChi2 = stats.chi2.sf(Chi2, Ndof)\n",
    "print(Chi2, Ndof, ProbChi2)\n",
    "\n",
    "\n",
    "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": 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
}