pgp1-python-einfuehrung/IminuitExample.ipynb

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   "source": [
    "# Keywords Script:\n",
    "\n",
    "* Wiederholen Sie die aus dem PGP1 bekannten Konzepte:\n",
    "    * Messunsicherheiten (Messfehler), statistische und systematische Unsicherheit\n",
    "    * Korrelation und Antikorrelation\n",
    "    * Gaussverteilung (Normalverteilung)\n",
    "    * Arithmetisches Mittel und Standardabweichung\n",
    "    * Zentraler Grenzwertsatz\n",
    "    * Wahrscheinlichkeitsverteilung\n",
    "* Binominal-Verteilung\n",
    "* Poisson-Verteilung\n",
    "* Wahrscheinlichkeitsdichte-Funktion\n",
    "* kumulative Wahrscheinlichkeits-Funktion\n",
    "\n",
    "\n",
    "# Aufgaben zur Vorbereitung:\n",
    "\n",
    "\n",
    "* Verknüpfen des Zentralengrenzwertsatzs, der Normalverteilung und des arithmetischen Mittels (in Python):\n",
    "    1. Nimm random nicht Gaußverteilung, e.g., exponential decay\n",
    "    2. Plotte Zerfallsverteilung.\n",
    "    3. Ziehe 2, 5, 10, 100 verschieden \"Messungen\"\n",
    "    4. Berechne Mittelwert von \"gemessenen\" Werten und plotte"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "\n",
    "# import iminuit\n",
    "\n",
    "# print(iminuit.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "id": "36435872-d6c4-4e16-8814-82f90342d84d",
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   "source": [
    "# # Truth\n",
    "# R = 10*10**3  # Ohm\n",
    "# C = 10*10**-6  # F\n",
    "# I0 = 10/R\n",
    "\n",
    "# def discharge_current(t, I0, R, C):\n",
    "#     return I0 * np.exp(-t/(R*C))\n",
    "\n",
    "\n",
    "# time_truth = np.arange(0, 1, 0.1)\n",
    "\n",
    "\n",
    "# # Make psuedo measured values:\n",
    "# sigma_time = 0.02\n",
    "# dtime = np.random.normal(0, sigma_time, len(time_truth))\n",
    "# time_mess = time_truth + dtime\n",
    "\n",
    "# sigma_current = 0.05\n",
    "# current_truth = discharge_current(time_truth, I0, R, C)/10**-3\n",
    "# current_mes = current_truth + np.random.normal(0, sigma_current, len(current_truth))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "id": "e77a7824-f8fa-43b2-ad98-009e17c05c72",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import pandas as pd\n",
    "# df = pd.DataFrame()\n",
    "# df['time'] = time_mess\n",
    "# df['current'] = current_mes\n",
    "# df['delta_current'] = sigma_current\n",
    "# df['delta_time'] = np.abs(dtime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "id": "54c27237-effd-4396-91d8-b6b4d43d589c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# df.to_csv('data/discharge_data.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "id": "f03f0f86-7452-4528-b0a1-7e4411dbc410",
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   "source": [
    "# plt.plot(time_truth, discharge_current(time_truth, I0, R, C)/10**-3, marker='.')\n",
    "# plt.errorbar(time_mess, current_mes, xerr=sigma_time, yerr=np.abs(sigma_current), ls='', marker='.')\n",
    "# plt.ylabel('Current [mA]')\n",
    "# plt.xlabel('Time [s]')\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9a4045f-f389-40f5-9f19-32f8bbebc75d",
   "metadata": {},
   "source": [
    "# Methode der kleinsten Quadrate\n",
    "\n",
    "Im folgenden wollen wir die **Methode der kleinsten Quadrate (Least Squares)** näher beleuchten. Diese Methode wird oft benutzt, um eine Funktion $\\lambda(x; \\ $**$\\phi$**$)$ mit den Funktionsparametern $\\mathbf{\\phi}$ an die gemessenen Punkte **$(x,y)$** anzupassen. Um jedoch die **Methode der kleinsten Quadrate** zu verstehen, wollen wir sie erst einmal anschaulich und halb-mathematisch herleiten. Dabei stüzen wir uns im Folgenden auf eine Herleitung aus dem Buch **\"Statistical Data Analysis\"**  von **Glen Cowan**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a8f4ef9-222c-440f-8621-e612a8988fd0",
   "metadata": {},
   "source": [
    "Bevor wir dies jedoch tun, schauen wir uns das Problem des Fittens doch erst einmal anschaulich an. \n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/SketchLeastSquares.png\"  alt=\"{{ Beispiel PDF }}\" width=70%>\n",
    "</figure>\n",
    "\n",
    "Beim Fitten, zum Beispiel einer Geraden (lila) an eine Reihe von Messpunkten (schwarz), wollen wir den Abstand zwischen den einzelnen Messpunkten und der Geraden (orange) möglichst klein halten. Sprich die Summe über alle $\\Delta Y_i$ \n",
    "\n",
    "$$\\sum_i \\Delta Y_i $$\n",
    "\n",
    "sollte möglichst klein sein, wobei $\\Delta Y_i$ durch \n",
    "\n",
    "$$ \\Delta Y_i = y_i – f(x_i, \\vec{\\theta})$$\n",
    "\n",
    "gegeben ist und $f(x, \\vec{\\theta})$ unsere Fitfunktion repräsentiert. Hierbei symbolisiert $\\vec{\\theta}$ die Parameter unserer Funktion. Sprich im Fall einer Geraden die Steigung $m$ und den Offset $y_0$ ($\\vec{\\theta}=(m, y_0)$). \n",
    "\n",
    "Darüber hinaus sollte die Richtung des Abstandes, sprich ob ein Messpunkt unterhalb oder oberhalb der Fitfunktion liegt, keine Rolle spielen. Daher quadrieren wir das Ganze und erhalten somit\n",
    "\n",
    "$$ LS = \\sum_i = (y_i – f(x_i, \\theta))^2$$\n",
    "\n",
    "Dies ist die allgemeinste Form der Methode der kleinsten Quadrate. Sie besagt, dass die Funktion, welche die Messpunkte am besten beschreibt, sprich die optimalen Werte für $\\vec{\\theta}$ aufweist, den Ausdruck LS minimiert. \n",
    "\n",
    "Nun weisen unsere Messpunkte nicht nur Werte für X und Y aus, sondern sind noch zusätzlich durch einen Messunsicherheit (Messfehler) charakterisiert. Diese sollten wir natürlich bei der Bestimmung unserer Parameter $\\vec{\\theta}$ berücksichtigen. Sprich Messwerte mit einer großen Unsicherheit sollten weniger stark berücksichtigt werden wie Messwerte mit einer kleinen Unsicherheit. Dies können wir gewährleisten, sofern wir die Distanzen $\\Delta Y_i$ mit den jeweiligen Unsicherheiten $\\Delta y_i$ gewichten, sprich  \n",
    "\n",
    "$$ \\chi^2 = \\sum_i =\\frac{(y_i – f(x_i, \\theta))^2}{\\Delta y_i^2}$$\n",
    "\n",
    "berechnen. Das Quadrieren der Unsicherheiten sorgt dafür, dass der Ausdruck dimensionslos wird. Diese besondere Form der kleinsten Quadrate nennt man auch oft $\\chi^2$-Fit. Wir werden später noch einmal genauer beleuchten warum. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1153a474-8afe-44ae-8511-b403a4ad861d",
   "metadata": {},
   "source": [
    "Nun wollen wir uns erst einmal ein Beispiel anschauen, wie dies in der Praxis aussieht. In der nachfolgenden Animation wird ein Ohm’schwer Widerstand an eine Reihe von Spannungs- und Strommessungen gefittet. Dies entspricht unserem obigen Geradenbeispiel. \n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/Fitting_gif.gif\"  alt=\"{{ Least Square Beispiel }}\" width=100%>\n",
    "</figure>\n",
    "\n",
    "Wie die Animation zeigt, werden so lange verschiedene Widerstände ausprobiert, bis ein Wert gefunden wurde, bei dem das $\\chi^2$ minimal wird. Dieses Variieren der Widerstandswerte passiert nicht zufällig, sondern basiert auf einem Algorithmus für Optimierungsverfahren. \n",
    "\n",
    "Es gibt verschiedene Arten von Algorithmen, um Minimierungsprobleme zu lösen. Wie diese genau aufgebaut sind, lernen Sie in anderen Programmierveranstaltungen, wie zum Beispiel *Programmieren für Physiker* oder *Computer in der Wissenschaft*. Zum Glück haben uns in Python bereits andere Menschen diese Arbeit abgenommen. Im folgenden wollen wir uns das package `iminuit` etwas genauer anschauen, welches bereits ein sehr umfangreiches und mächtiges Fittingtool darstellt. \n",
    "\n",
    "[iminuit](https://iminuit.readthedocs.io/en/stable/tutorials.html) verfügt auch über eine exzellente Dokumentation, mit Hilfe derer Sie auch komplexere Probleme lösen können."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "702b9a12-539d-43b5-8314-7f8dcdf93cda",
   "metadata": {},
   "source": [
    "Um mit Hilfe von `imnuit` etwas zu fitten brauchen wir zunächst einmal ein paar Messdaten und ein Fitmodel. Im Folgenden wollen wir die Entladekurve eines Kondensators mit der Kapazität $C$ über einen Widerstand $R$ bestimmen. Die Entladekurve ist durch eine einfache Exponentialfunktion der Form \n",
    "\n",
    "$$ I = I_0 \\exp\\{-t/RC\\}$$\n",
    "\n",
    "gegeben. Die Messdaten befinden sich in einer CSV-Datei im Ordner `data`. Die CSV-Datei kann mit Hilfe des `pandas` package eingelesen werden. [pandas](https://pandas.pydata.org/) ist ähnlich wie `numpy` ein package welches eine Fülle an Funktionen zum Verarbeiten und Verwalten von Daten bereitstellt. Es gehört ähnlich wie auch `numpy`, `scipy` und `matplotlib` zu den Standardbibliotheken, welche sehr häufig in der Wissenschaft verwendet werden. Aufgrund der zeitlichen Limitierung des Versuchstages können wir leider nicht auf alle Funktionen von `pandas` eingehen und wollen uns im Folgenden lediglich auf die Grundlagen beschränken. Für ihre zukünftigen Praktika lohnt es sich jedoch, noch mehr über `pandas` in Ihrer Eigenstudienzeit zu lernen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5215840a-1276-49c1-9181-274cd8a2b4bf",
   "metadata": {},
   "source": [
    "CSV-Datein können wie folgt eingelesen werden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "id": "f8ef1be0-a42d-4a11-b674-c2ed099fefcb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "data_frame = pd.read_csv('data/discharge_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15800aa8-8a7f-4d59-ab06-3edc6bb1e443",
   "metadata": {},
   "source": [
    "Dabei gibt pandas die Daten als so genannten DataFrames zurück. Dies sind Objekte, welche ähnlich wie strukturierte `numpy.arrays` zu behandeln sind. DataFrames werden allgemein als Tabellen dargestellt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "id": "f14ca80f-e0d7-4447-9335-b3744f7a028f",
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       "   Unnamed: 0      time   current  delta_current  delta_time\n",
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       "1           1  0.088553  0.406316           0.05    0.011447\n",
       "2           2  0.194773  0.143093           0.05    0.005227\n",
       "3           3  0.306413  0.078141           0.05    0.006413\n",
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   "metadata": {},
   "source": [
    "Um die Daten aus einer bestimmente Spalte zu bekommen, können diese einfach mit dem Spaltennamen aufgerufen werden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "id": "93b7cbb1-1095-4a53-83d9-7b32f068daea",
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       "0    0.000637\n",
       "1    0.088553\n",
       "2    0.194773\n",
       "3    0.306413\n",
       "4    0.405285\n",
       "5    0.507390\n",
       "6    0.613279\n",
       "7    0.707501\n",
       "8    0.790479\n",
       "9    0.883672\n",
       "Name: time, dtype: float64"
      ]
     },
     "execution_count": 487,
     "metadata": {},
     "output_type": "execute_result"
    }
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    "data_frame['time']"
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  {
   "cell_type": "markdown",
   "id": "4476302c-eb65-409a-b1aa-2342ecbd9c88",
   "metadata": {},
   "source": [
    "oder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "id": "969d8afa-5d52-4e01-8b64-ddab090891b8",
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    {
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       "0    1.066538\n",
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       "2    0.143093\n",
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       "8    0.006881\n",
       "9   -0.019052\n",
       "Name: current, dtype: float64"
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     "execution_count": 488,
     "metadata": {},
     "output_type": "execute_result"
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    "data_frame['current']"
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  {
   "cell_type": "markdown",
   "id": "32249263-ec9f-44de-81b7-7a6c69e23332",
   "metadata": {},
   "source": [
    "Einzelne Messwerte lassen sich mit Hilfe von `.loc` bestimmen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "id": "e4b44637-8e25-46c1-863d-3cd7604f52dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0118852615051639"
      ]
     },
     "execution_count": 489,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_frame.loc[5, 'current']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2c0c04b-be37-482d-aabc-802bfa2965d2",
   "metadata": {},
   "source": [
    "Sollten Sie eine Spalte von Messdaten in ein `numpy.array` umwandeln wollen, so können Sie dies wie folgt erreichen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "id": "f246f55e-5fc8-427c-990d-3e97799b5aeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.06653795,  0.40631626,  0.1430927 ,  0.07814083,  0.06504185,\n",
       "        0.01188526, -0.01882397,  0.04451315,  0.00688072, -0.01905164])"
      ]
     },
     "execution_count": 490,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_frame['current'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d2bd9ed-852d-4448-a051-a6f677ea891d",
   "metadata": {},
   "source": [
    "Die Messdaten können Sie auch wie gewohnt mit Hilfe von `matplotlib` darstellen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "id": "e3898686-3926-48a0-be4c-4d460a1792f3",
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   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.errorbar(\n",
    "    data_frame['time'], \n",
    "    data_frame['current'], \n",
    "    data_frame['delta_current'], \n",
    "    ls='', \n",
    "    marker='.', \n",
    "    color='k'\n",
    ")\n",
    "plt.xlabel('Time []')\n",
    "plt.ylabel('Current []')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "100a4fe4-a5c4-4be3-a7f7-13337b97a194",
   "metadata": {},
   "source": [
    "Nun wollen wir die Messdaten mit Hilfe von `iminuit` fitten. Hierzu müssen wir zunächste zwei Module des packages importieren und eine Funktion für die Entladekurve des Kondensators definieren:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "520f4973",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Diese Zelle nur auf JupyterHub des ZDV ausführen um `iminuit` zu installieren!\n",
    "# import sys\n",
    "# import subprocess\n",
    "# subprocess.check_call([\n",
    "#     sys.executable, \n",
    "#     '-m',\n",
    "#     'pip',\n",
    "#     'install',\n",
    "#     '--proxy',\n",
    "#     'http://webproxy.zdv.uni-mainz.de:3128',\n",
    "#     'iminuit'\n",
    "# ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 492,
   "id": "2ffe340b-cd0f-45ec-b5b8-42e7a0349d4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from iminuit import Minuit, cost\n",
    "import numpy as np\n",
    "\n",
    "def discharge_current(t, I0, R, C):\n",
    "    return I0 * np.exp(-t/(R*C))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef87da8f-7af9-4e3f-af63-c28a2e1d9830",
   "metadata": {},
   "source": [
    "Nun können wir den Fit selbst durchführen. Hierzu muss zuerst mittels dem `cost` Modul eine sogenannte Kostenfunktion erstellt werden. Die Kostenfunktion ist im Grunde unsere $\\chi^2$ Funktion\n",
    "\n",
    "$$ \\chi^2 = \\sum_i =\\frac{(y_i – f(x_i, \\theta))^2}{\\Delta y_i^2}$$\n",
    "\n",
    "welche minimiert werden soll. Dies ist bereits bei `iminuit` für uns vordefiniert. Anschließend können wir die genutzt Kostenfunktion über `Minuit` minimieren lassen. Hierzu müssen wir zunächst geeignete Startwerte für den Minimierungsprozess vorgeben. Diese sollten im Idealfall nicht allzu weit von den wahren Werten entfernt liegen. Wir werden an einem späteren Beispiel noch einmal genauer zeigen, wie man hier vorgehen kann. Um den Minimierungsprozess zu starten muss noch am Ende `migrad()` aufgerufen werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "id": "bf36b7b9-fb20-47b7-8538-479026b48fb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 2.707 (χ²/ndof = 0.4) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 103 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.18e-10 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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:#FFF79A;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\"> Covariance FORCED pos. def. </td>\n",
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       "    <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",
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       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> I0 </td>\n",
       "        <td> 1.07 </td>\n",
       "        <td> 0.05 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> R </td>\n",
       "        <td> 0.03e6 </td>\n",
       "        <td> 0.05e6 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> C </td>\n",
       "        <td> 3e-6 </td>\n",
       "        <td> 5e-6 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "        <td></td>\n",
       "        <th> I0 </th>\n",
       "        <th> R </th>\n",
       "        <th> C </th>\n",
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       "        <th> I0 </th>\n",
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       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -3.448e-9 <strong>(-0.014)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> R </th>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -34.4329 <strong>(-0.014)</strong> </td>\n",
       "        <td> 2.25e+09 </td>\n",
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       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -3.448e-9 <strong>(-0.014)</strong> </td>\n",
       "        <td style=\"background-color:rgb(120,120,250);color:black\"> -224.599380820e-3 <strong>(-0.997)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.707 (χ²/ndof = 0.4)      │              Nfcn = 103              │\n",
       "│ EDM = 2.18e-10 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │     Covariance FORCED pos. def.      │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ I0   │   1.07    │   0.05    │            │            │         │         │       │\n",
       "│ 1 │ R    │  0.03e6   │  0.05e6   │            │            │         │         │       │\n",
       "│ 2 │ C    │   3e-6    │   5e-6    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬───────────────────────────────────────────────────────┐\n",
       "│    │                I0                 R                 C │\n",
       "├────┼───────────────────────────────────────────────────────┤\n",
       "│ I0 │           0.00253          -34.4329         -3.448e-9 │\n",
       "│  R │          -34.4329          2.25e+09 -224.599380820e-3 │\n",
       "│  C │         -3.448e-9 -224.599380820e-3          2.25e-11 │\n",
       "└────┴───────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 493,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Kostenfunktion:\n",
    "ls = cost.LeastSquares(\n",
    "    data_frame['time'],\n",
    "    data_frame['current'], \n",
    "    data_frame['delta_current'], \n",
    "    discharge_current,\n",
    ")\n",
    "\n",
    "# Minimierung\n",
    "mi = Minuit(ls,        # Kostenfunktion \n",
    "            I0=0.9,    # Startwerte\n",
    "            R=10*10**3, \n",
    "            C=10**-6\n",
    "           )\n",
    "mi.migrad()\n",
    "mi.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5df2d60-8284-4757-96c8-7f26afc17942",
   "metadata": {},
   "source": [
    "Wie ihr seht gibt euch minuit euch vier verschiedene Objekte zurück. Für euch am wichtigsten ist die erste Tabelle, welche euch zeigt, ob euer Fit funktioniert hat. Im Allgemeinen gilt sind hier alle Felder grün hat euer Fit funktioniert, gelbe Felder können ein Problem andeuten müssen sie aber nicht und lila Felder bedeuten, dass etwas mit eurem Fit nicht in Ordnung ist. Die Bedeutungen der einzelnen Felder für unseren obigen Fit sind auch nochmal in der nachfolgenden Abbildung einzeln erklärt. Die Bedeutung der meisten Felder werden wir noch im laufe des Kurses kennen lernen. \n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/FitPerformance.png\"  alt=\"{{Fit Performance }}\" width=100%>\n",
    "</figure>\n",
    "\n",
    "Wie wir unserer Tabelle entnehmen können, gibt es also ein Problem mit unserem Fit. Um besser verstehen zu können, was das Problem sein könnte, wollen wir uns auch noch die anderen Outputs ansehen.\n",
    "\n",
    "Die zweite Tabelle zeigt uns die bestimmten Werte für die Parameter in der Spalte `Value` und deren Unsicherheiten in der Spalte `Hess error`. Hierbei fällt auf, dass für unseren obigen Fit die Unsicherheiten der Parameter $R$ und $C$ größer sind als die bestimmten Werte selbst. \n",
    "\n",
    "Die dritte Tabelle ist die sogennnante **Kovarianzmatrix**. Die Kovarianzmatrix hat als Einträge auf ihrer **Hauptdiagonalen** die **Varianzen der entsprechenden Parameter** auf der **Nebendiagonalen** stehen die **Kovarianzen**. Der Wert in Klammern gibt die **Korrelation** zwischen den entspechenden Parametern an. Sind zwei Parameter stark **korreliert**, wird das entsprechende Feld **blau** dargestellt, bei einer **Antikorrelation** ist das Feld **rot**. \n",
    "\n",
    "Die letzte Ausgabe ist ein Plot unserer Messwerte zusammen mit der Fitfunktion basierend auf den Parametern des besten Fits. (Nur für neuere Version von `iminuit`)"
   ]
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   "id": "72665daa-1d74-41da-8b9a-1e4c427eed07",
   "metadata": {},
   "source": [
    "Obwohl underser Fit unsere Messdaten gut widerspiegelt, scheint es ein Problem mit der Bestimmung einiger Parameter zu geben. Die große Unsicherheit in $R$ und $C$ deutet an, dass hier das Problem liegt. Um dies zu bestätigen, können wir uns einmal das reduzierte $\\chi^2(x, I_0, R, C)$ als Funktion des entsprechenden Parameters von `iminuit` plotten lassen, während wir die anderen Parameter, so wie die x-Werte, konstant lassen. \n",
    "\n",
    "Für $I_0$ sieht das entsprechende Profil so aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 494,
   "id": "d3230cb6-fbe3-4093-ba09-5271dc168a4d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\Matthias\\.venv\\jupyter\\lib\\site-packages\\iminuit\\minuit.py:2579: IMinuitWarning: Specified nsigma bound, but error matrix is not accurate\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mi.draw_profile('I0')\n",
    "plt.ylabel('$\\chi^2(I_0, x, R, C)/ndof$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b837e542-d3c9-4f61-a8d1-4f22db7d5137",
   "metadata": {},
   "source": [
    "Bei den anderen beiden Parametern ist dies nicht der Fall:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "id": "af339c6e-f0e7-40cd-a2cf-61aaaa4df1e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mi.draw_profile('R')\n",
    "plt.ylabel('$\\chi^2(R, x, I_0, C)/ndof$')\n",
    "plt.show()\n",
    "\n",
    "mi.draw_profile('C')\n",
    "plt.ylabel('$\\chi^2(C, x, I_0 R)/ndof$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "499ffb9a-00a7-4c06-ada4-1d3a41a7f1d4",
   "metadata": {},
   "source": [
    "Das liegt daran, dass $R$ und $C$ vollständig korreliert sind. Reduziert `iminuit` $C$ um ein Faktor zwei, so wird dies dadurch kompensiert, dass das optimale Minimum verlangt, dass $R$ um einen Faktor zwei größer sein muss. Das heißt, es ist ohne weitere Information nicht möglich, $R$ und $C$ näher zu bestimmen, sondern lediglich das Produkt der beiden Größen.\n",
    "\n",
    "Deshalb müssen wir in unserer Fitfunktion $R$ und $C$ durch die Zeitkonstante $\\tau$ ersetzen und schreiben\n",
    "\n",
    "$$ I = I_0 \\exp\\{-t/\\tau\\}$$\n",
    "\n",
    "mit $\\tau = R \\cdot C$.\n",
    "\n",
    "Führen wir nun erneut den Fit durch, so erhalten wir ein fehlerfreies Ergebnis..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "id": "847419a7-d77b-4207-8607-44af9d615ffc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 2.707 (χ²/ndof = 0.3) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 97 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.11e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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> I0 </td>\n",
       "        <td> 1.07 </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> 1 </th>\n",
       "        <td> tau </td>\n",
       "        <td> 0.097 </td>\n",
       "        <td> 0.011 </td>\n",
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       "        <th> I0 </th>\n",
       "        <th> tau </th>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.707 (χ²/ndof = 0.3)      │              Nfcn = 97               │\n",
       "│ EDM = 1.11e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ I0   │   1.07    │   0.05    │            │            │         │         │       │\n",
       "│ 1 │ tau  │   0.097   │   0.011   │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌─────┬───────────────────┐\n",
       "│     │       I0      tau │\n",
       "├─────┼───────────────────┤\n",
       "│  I0 │  0.00254 -0.22e-3 │\n",
       "│ tau │ -0.22e-3 0.000116 │\n",
       "└─────┴───────────────────┘"
      ]
     },
     "execution_count": 496,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from iminuit import Minuit, cost\n",
    "\n",
    "def discharge_current2(t, I0, tau):\n",
    "    return I0 * np.exp(-t/tau)\n",
    "\n",
    "ls = cost.LeastSquares(\n",
    "    data_frame['time'],\n",
    "    data_frame['current'], \n",
    "    data_frame['delta_current'], \n",
    "    discharge_current2\n",
    ")\n",
    "mi = Minuit(ls, I0=0.9, tau=0.3)\n",
    "mi.migrad()\n",
    "mi.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a46c76ec-5b00-48f4-9a46-2ea083ca5dba",
   "metadata": {},
   "source": [
    "... und die Werte und Fehler lassen sich über ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "id": "69f540a5-e89b-4c24-aa7e-b03eaedb28d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0670397937137222"
      ]
     },
     "execution_count": 497,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.values['I0']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66733c05-692d-46e3-ae82-6f84d66ef28c",
   "metadata": {},
   "source": [
    "... bzw. ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "id": "66e6da5b-ff32-4982-a3aa-5b9b93262073",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.050401508019580855"
      ]
     },
     "execution_count": 498,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.errors['I0']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c670cd3f-fcfb-4cfc-a8d4-eded75e9a669",
   "metadata": {},
   "source": [
    "... für jeden Parameter auslesen. Dies lässt sich nun auch nutzen, um unsere Messwerte samt Fit in einem etwas schöneren Plot mit Achsenbeschriftungen darzustellen. Hierbei können wir ausnutzen, dass `iminuit` die Parameter in der Reihenfolge der Argumente unser definierten Fitfunktion speichert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "id": "45fcf856-c58e-424d-8fd7-15037cb6698e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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Pn0ZQUJBqnlQqRVBQEI4dO1bpetHR0bCysqpySk3V3TP5NK3zt99+Uz3WwcnJCX5+fli1alWV2/3pp5/wxhtvqB65Y8h6q7vO9evX4ebmBi8vL4wePVrtXFf3M63N+GwpHSvrd3P16lWRKyEi0r2srCwoFAo4OzurzXd2dq7y373Jkyfj1VdfrXLbbm5uOqkR0LzOmzdvYsWKFQgLC8PHH3+MkydP4r333oNcLse4cePKbXf79u14+PAhxo8fX+F+o6OjER0drXpdUFCA48eP491331XNu3z5Mjw81MdCq8551XSdgIAAxMTEoFWrVkhPT8fcuXPx3HPP4eLFi7C2tq72Z1qbMdzomKl9EwBsuSEiepK9vT3s7e3FLqMcpVKJzp07qwKJn58fLl68iJUrV1YYblavXo2BAwdWGsSeDnGjR4/GiBEjMHz4cNU8XYY4TQwcOFD1e8eOHREQEICmTZvi559/xsSJEw1ai6Ew3OhYWbi5du0aBEHQabMlEZHYHBwcIJPJkJmZqTY/MzMTLi4ula73dItGRSpq0dB3na6urmjbtq3aMm3atMEvv/xSbpu3bt3C/v37sXXr1kr3+3SIs7CwgJOTE1q0aKGTemu6DgDY2dnB29sbSUlJNdpObcY+NzpiKTdByoLBSPn2DZiYmCAvLw+3b98WuywiIp2Sy+Xw9/dHXFycap5SqURcXBwCAwMrXW/y5MlISEioctJli4amdfbo0aNcS/u1a9fQtGnTcttcu3YtnJycMHjwYJ3VqW29NV0HAHJzc3Hjxg24urrWaDu1mh46O2vs8OHDwpAhQwRXV1eNe78fPHhQ8PPzE+RyudC8eXONe6GX0dfdUk/y9vYWAAj79u3T2z6IiHRF27ulNm3aJJiZmQkxMTHC5cuXhUmTJgl2dnZCRkaG3mp89OiRcPbsWeHs2bMCAGHRokXC2bNnhVu3bqmWWbp0qdC3b1+t6oyPjxdMTEyEf/3rX8L169eF9evXC5aWlsJPP/2ktn+FQiF4eHgIs2bNemad6enpVU6lpaUVrvusep8+Pk2P8YMPPhAOHTokJCcnC3/++acQFBQkODg4CHfv3tVqO4agq7ulRA03u3btEj755BNh69atGoWbmzdvCpaWlkJYWJhw+fJlYenSpYJMJhNiY2M13qchwk1ISIgAQFi2bJne9kFEpCvahhtBePxF6+HhIcjlcqFr167C8ePH9VrjwYMHBQDlpnHjxqmWiYqKEpo2bap1nb///rvQvn17wczMTGjdurXw/fffl1tmz549AgAhMTGxyjqjoqIqrPPJKTk5udL1q6q3ouPT5BhDQ0MFV1dXQS6XC40bNxZCQ0OFpKQkrbdjCLoKNxJBEAQDNhRVSiKRYNu2beVGwXzSrFmzsHPnTly8eFE177XXXsPDhw8RGxur0X5ycnJga2uL7Oxs2NjY1LTsCs2cORNffvklpk2bhm+++UYv+yAi0pXCwkIkJyejWbNmMDc3F7scqseq+lvU5vu7TvW5OXbsmNp9+AAQHBxc5X34RUVFyMnJUZv0rVWrVgB4OzgREZEY6lS4ycjIqPA+/JycHBQUFFS4zvz582Fra6ua3N3d9V5nWbjh7eBERESGV6fCTXVEREQgOztbNaWlpel9n2UPJEtNTUV+fr7e90dERET/U6fCjYuLS4X34dvY2MDCwqLCdczMzGBjY6M26ZuDg4NqnAM+QJOIiMiw6lS4CQwMVLsPHwD27dtXK+/D56UpIiIicYgabnJzc1WDNwFAcnIyEhISVA/0ioiIwNixY1XLT548GTdv3sTMmTNx9epVfPvtt/j555/x/vvvi1F+lRhuiIiIxCFquDl16hT8/Pzg5+cHAAgLC4Ofnx8iIyMBAOnp6WpPLm3WrBl27tyJffv2wcfHB19//TV++OEHBAcHi1J/Vcr63TDcEFFd17t3b8yYMUPsMjS2fPlyeHp6wtzcHAEBAYiPj6/xOo8ePcKMGTPQtGlTWFhYoHv37jh58qTaMp6enpBIJOWmqVOnin58mqx35MgRhISEwM3NDRKJBNu3b9fq/dpE1HDTu3dvCI8HElSbYmJiAAAxMTE4dOhQuXXOnj2LoqIi3Lhxo9Ins4qNt4MTERne5s2bERYWhqioKJw5cwY+Pj4IDg7G3bt3a7TOm2++iX379uHHH3/EhQsX0L9/fwQFBak9ZufkyZNIT09XTfv27QMAvPLKK8+su3fv3qrvPl0fn6br5eXlwcfHB8uXL69wG896v1bR6dCCdYAhRigWBEG4fPmyAECwsrISlEqlXvdFRFQTVY0KO27cuApH2N29e7fQo0cPwdbWVrC3txcGDx6sNupt06ZNhX//+99q2/Lx8RGioqL0eixdu3YVpk6dqnqtUCgENzc3Yf78+dVeJz8/X5DJZMKOHTvU1uvUqZPwySefVLrd6dOnC82bN9foO6BXr14aPU6oOsdXnfXwjKcGPOv96tLVCMV1qkNxXdK8eXPIZDLk5ubizp07YpdDRFQtS5YsQWBgIN566y1Vi4S7uzvy8vIQFhaGU6dOIS4uDlKpFC+99BKUSmWN9hcdHQ0rK6sqpye7KzypuLgYp0+fVhvsVSqVIigoqNLBXjVZp7S0FAqFotyIuRYWFjh69Gil2/3pp5/wxhtvQCKRaHUOKlOd46vJenWZidgFGCu5XA4vLy9cv34dV69eRePGjcUuiYhIa7a2tpDL5bC0tISLi4tq/ogRI9SWW7NmDRwdHXH58mW0b9++2vubPHkyXn311SqXqezp4VlZWVAoFBUO9lpZFwFN1rG2tkZgYCDmzZuHNm3awNnZGRs3bsSxY8fQokWLCre7fft2PHz4sNKuE9HR0YiOjla9LigowPHjx/Huu++q5l2+fBkeHh41Or6arFeXMdzoUatWrVThpl+/fmKXQ0SkM9evX0dkZCROnDiBrKwsVYtNampqjcKNvb29apyw2uTHH3/EG2+8gcaNG0Mmk6FTp04YOXIkTp8+XeHyq1evxsCBAysNYk+HuNGjR2PEiBEYPny4al5l69KzMdzoUbt27bBjxw5cunRJ7FKIiHQqJCQETZs2xapVq+Dm5galUon27dujuLgYwOPLHsJTz2UuKSl55nafbtGoyNMtGmUcHBwgk8kqHOz1yVan6qzTvHlzHD58GHl5ecjJyYGrqytCQ0Ph5eVVbpu3bt3C/v37sXXr1kqP4ekQZ2FhAScnp0pbgqp7fDVZry5jnxs9ateuHQAw3BBRnSaXy6FQKFSv79+/j8TERMyePRv9+vVDmzZt8ODBA7V1HB0dkZ6ernqdk5OD5OTkZ+5r8uTJqvHPKpsqa9GQy+Xw9/dXG+xVqVQiLi6u0sFetV2nQYMGcHV1xYMHD7Bnzx4MGzas3DJr166Fk5MTBg8e/Mzj1UZ1jq8m69VlbLnRo7Km2YsXL0IQBJ11KiMiMiRPT0+cOHECKSkpsLKygr29PRo1aoTvv/8erq6uSE1NRXh4uNo6ffv2RUxMDEJCQmBnZ4fIyEjIZLJn7quml6XCwsIwbtw4dO7cGV27dsXixYuRl5eHCRMmqJZZtmwZtm3bpvqy12SdPXv2QBAEtGrVCklJSfjoo4/QunVrtWWAx6Fh7dq1GDduHExMKv+Kzc3NRW5urur1pk2bADx+QHQZR0fHcuesOsen6Xq5ublISkpSvS4bWNfe3h4eHh7PfL9W0fl9XLWcoW4FF4THtw9KpVIBgJCenq73/RERVUdVt98KgiAkJiYK3bp1EywsLFS3gu/bt09o06aNYGZmJnTs2FE4dOiQ2u3B2dnZQmhoqGBjYyO4u7sLMTExBrkVXBAEYenSpYKHh4cgl8uFrl27CsePH1d7PyoqSmjatKlW62zevFnw8vIS5HK54OLiIkydOlV4+PBhuX3v2bNHACAkJiZWWWNUVFS5W+yfnpKTk3V2fJqsd/DgwQrrGDdunEbv64KubgWXCMJTF0WNXE5ODmxtbZGdnW2Qh2h6e3vj+vXr2Ldvn9pteEREtUVhYSGSk5PRrFmzcrc7ExlSVX+L2nx/s8+Nnj15aYqIiIj0j+FGz9ipmIiIyLAYbvSMLTdERESGxXCjZ0+23NSz7k1ERESiYLjRM29vb5iYmODRo0dIS0sTuxwiIiKjx3CjZ3K5HK1atQLAfjdERESGwHBjAGWXptjvhoiISP8YbgyAnYqJiIgMh+HGAHg7OBER6dunn34KZ2dnSCQSbN++HePHj8eLL74odlmiYLgxgLKWm8uXL0OpVIpcDRER6cL48eMhkUhUU6NGjTBgwACcP39eZ/v49NNP4evr+8zlrly5grlz5+K7775Deno6Bg4ciCVLliAmJka1TO/evTFjxgyd1VabMdwYQPPmzWFmZoaCggKNnopLRER1w4ABA5Ceno709HTExcXBxMQEQ4YMMXgdN27cAAAMGzYMLi4uMDMzg62tLezs7AxeS23AcGMAMpkMbdq0AcB+N0RExsTMzAwuLi5wcXGBr68vwsPDkZaWhnv37qmWSUtLw6uvvgo7OzvY29tj2LBhSElJUb1/6NAhdO3aFQ0aNICdnR169OiBW7duISYmBnPnzsW5c+dUrUNPtsSU+fTTTxESEgIAkEqlkEgkAKB2WWr8+PE4fPgwlixZotrWkzUYm8qfx0461b59eyQkJODSpUsYNmyY2OUQEdVagiAgPz9flH1bWlqqwoG2cnNz8dNPP6FFixZo1KgRAKCkpATBwcEIDAzEH3/8ARMTE3z++eeqy1dSqRQvvvgi3nrrLWzcuBHFxcWIj4+HRCJBaGgoLl68iNjYWOzfvx8AYGtrW26/H374ITw9PTFhwgSkp6dXWNuSJUtw7do1tG/fHp999hkAwNHRsVrHWRcw3BgIbwcnItJMfn4+rKysRNl3bm4uGjRooPHyO3bsUNWal5cHV1dX7NixA1Lp4wsjmzdvhlKpxA8//KAKTWvXroWdnR0OHTqEzp07Izs7G0OGDEHz5s0BQNXSDwBWVlYwMTGBi4tLpTVYWVmpLj9VtpytrS3kcjksLS2r3Jax4GUpA+Ht4ERExqdPnz5ISEhAQkIC4uPjERwcjIEDB+LWrVsAgHPnziEpKQnW1tawsrKClZUV7O3tUVhYiBs3bsDe3h7jx49HcHAwQkJCsGTJkkpbX0hzbLkxkLJwk5iYiJKSEpiamopcERFR7WRpaYnc3FzR9q2NBg0aoEWLFqrXP/zwA2xtbbFq1Sp8/vnnyM3Nhb+/P9avX19u3bLLQmvXrsV7772H2NhYbN68GbNnz8a+ffvQrVu3mh1MPcZwYyAeHh5o0KAB8vLykJSUpNbsSERE/yORSLS6NFSbSCQSSKVSFBQUAAA6deqEzZs3w8nJCTY2NpWu5+fnBz8/P0RERCAwMBAbNmxAt27dIJfLoVAodFKbLrdV2/GylIFIpVIO5kdEZGSKioqQkZGBjIwMXLlyBdOmTUNubq7q7qXRo0fDwcEBw4YNwx9//IHk5GQcOnQI7733Hv7++28kJycjIiICx44dw61bt7B3715cv35d9T/Anp6eSE5ORkJCArKyslBUVFTtWj09PXHixAmkpKQgKyvLqMddY7gxIHYqJiIyLrGxsXB1dYWrqysCAgJw8uRJbNmyBb179wbw+DLXkSNH4OHhgeHDh6NNmzaYOHEiCgsLYWNjA0tLS1y9ehUjRoyAt7c3Jk2ahKlTp+Ltt98GAIwYMQIDBgxAnz594OjoiI0bN1a71g8//BAymQxt27aFo6MjUlNTdXEKaiWJIAiC2EUYUk5ODmxtbZGdnV1lE6E+LFq0CB988AFefvllbNmyxaD7JiKqTGFhIZKTk9GsWTOYm5uLXQ7VY1X9LWrz/c2WGwNiyw0REZH+MdwYUNkdU9evX1d1NiMiIiLdYrgxIDc3Nzg4OEChULBTMRERkZ4w3BiQRCKBn58fAODs2bMiV0NERGScGG4MrOzR9QkJCaLWQUREZKwYbgyM4YaIiEi/GG4MrOyy1Llz5+rNSJFERESGxHBjYN7e3rCwsEBeXh5u3LghdjlERERGh+HGwGQyGTp06ACAl6aIiHQpv7gUnuE74Rm+E/nFpWKXQyJiuBFBWb8b3jFFRESkeww3Iijrd8OWGyKium38+PGQSCSQSCQwNTWFs7MzXnjhBaxZs0arB1PGxMTAzs5Of4XWMww3IuAdU0RExmPAgAFIT09HSkoKdu/ejT59+mD69OkYMmQISkt5eUwMDDci6NChAyQSCTIyMpCRkSF2OURERicju9Bg+zIzM4OLiwsaN26MTp064eOPP8avv/6K3bt3IyYmBsDjByd36NABDRo0gLu7O9555x3k5uYCAA4dOoQJEyYgOztb1Qr06aefAgB+/PFHdO7cGdbW1nBxccGoUaNw9+5dgx1bXcVwI4IGDRqgVatWANh6Q0RUHfnFpeWmDSdSVe8HLTqMH4+llFvGUPr27QsfHx9s3boVACCVSvHNN9/g0qVLWLduHQ4cOICZM2cCALp3747FixfDxsYG6enpSE9Px4cffggAKCkpwbx583Du3Dls374dKSkpGD9+vMGOo64yEbuA+srX1xdXr15FQkICBgwYIHY5RER1StvIPVW+rxSAOb9ewpxf1Z/jl7JgsD7LUtO6dWucP38eADBjxgzVfE9PT3z++eeYPHkyvv32W8jlctja2kIikcDFxUVtG2+88Ybqdy8vL3zzzTfo0qULcnNzYWVlZZDjqIvYciMS9rshIjJugiBAIpEAAPbv349+/fqhcePGsLa2xpgxY3D//n3k5+dXuY3Tp08jJCQEHh4esLa2Rq9evQAAqampVa5X37HlRiR8gCYRUfVd/ixY7XVGdiGCFh2GUvjfPKkE2B/WCy625gau7rErV66gWbNmSElJwZAhQzBlyhT861//gr29PY4ePYqJEyeiuLgYlpaWFa6fl5eH4OBgBAcHY/369XB0dERqaiqCg4NRXFxs4KOpW0RvuVm+fDk8PT1hbm6OgIAAxMfHV7n84sWL0apVK1hYWMDd3R3vv/8+CgsN13FMV3x8fAAA169fV3UqIyIizVjKTdQmL0crzB3aTvW+VALMH94BXo5WassZyoEDB3DhwgWMGDECp0+fhlKpxNdff41u3brB29sbd+7cUVteLpeXeyTP1atXcf/+fSxYsADPPfccWrduzc7EGhI13GzevBlhYWGIiorCmTNn4OPjg+Dg4Eo/vA0bNiA8PBxRUVG4cuUKVq9ejc2bN+Pjjz82cOU15+zsDFdXVwiCgAsXLohdDhFRnTfCv4nq9/1hvRDaxcMg+y0qKkJGRgZu376NM2fOIDo6GsOGDcOQIUMwduxYtGjRAiUlJVi6dClu3ryJH3/8EStXrlTbhqenJ3JzcxEXF4esrCzk5+fDw8MDcrlctd5vv/2GefPmGeSY6jpRw82iRYvw1ltvYcKECWjbti1WrlwJS0tLrFmzpsLl//rrL/To0QOjRo2Cp6cn+vfvj5EjRz6ztae24qUpIiL9MOSlqNjYWLi6usLT0xMDBgzAwYMH8c033+DXX3+FTCaDj48PFi1ahC+++ALt27fH+vXrMX/+fLVtdO/eHZMnT0ZoaCgcHR2xcOFCODo6IiYmBlu2bEHbtm2xYMECfPXVVwY7rrpMtD43xcXFOH36NCIiIlTzpFIpgoKCcOzYsQrX6d69O3766SfEx8eja9euuHnzJnbt2oUxY8ZUup+ioiIUFRWpXufk5OjuIGrI19cXu3btYqdiIqI6KiYmRjWWTVXef/99vP/++2rznv7uWrFiBVasWKE2b+TIkRg5cqTaPEEQQFUTLdxkZWVBoVDA2dlZbb6zszOuXr1a4TqjRo1CVlYWevbsCUEQUFpaismTJ1d5WWr+/PmYO3euTmvXFd4xRUREpHuidyjWxqFDhxAdHY1vv/0WZ86cwdatW7Fz584qr0FGREQgOztbNaWlpRmw4qqVXZa6cOECh+gmIqohS7kJUhYMRsqCwQbtPEy1j2ifvoODA2QyGTIzM9XmZ2ZmlhvEqMycOXMwZswYvPnmmwAeP8YgLy8PkyZNwieffAKptHxWMzMzg5mZme4PQAe8vLxgZWWF3NxcJCYmol27ds9eiYiIiKokWsuNXC6Hv78/4uLiVPOUSiXi4uIQGBhY4Tr5+fnlAoxMJgNQN69BSqVS1S3hvDRFRESkG6JelgoLC8OqVauwbt06XLlyBVOmTEFeXh4mTJgAABg7dqxah+OQkBCsWLECmzZtQnJyMvbt24c5c+YgJCREFXLqmrJLU2fOnBG5EiKq7+ri/ySScdHV36CoFyVDQ0Nx7949REZGIiMjA76+voiNjVV1Mk5NTVVrqZk9ezYkEglmz56N27dvw9HRESEhIfjXv/4l1iHUWOfOnQEAJ0+eFLkSIqqvyv7nsLi4GBYWFiJXQ/VZ2cjLNW2wkAj1LKrn5OTA1tYW2dnZsLGxEbscXLlyBW3btoWlpSWys7NhYsJOcERkWIIgIDU1FSUlJXBzc6uw/yKRvimVSty5cwempqbw8PBQPZerjDbf3/wmFVmrVq1gbW2NR48e4fLly+jYsaPYJRFRPSORSODq6ork5GTcunVL7HKoHpNKpRUGG20x3IhMKpWic+fOOHjwIE6ePMlwQ0SikMvlaNmyJR/ISKKSy+U6aTlkuKkFunbtioMHDyI+Ph4TJ04UuxwiqqekUinMzcV5gjaRLvHCai3QpUsXAOxUTEREpAsMN7VA165dAQDnz59HQUGByNUQERHVbQw3tUCTJk3g7OwMhULBJ4QTERHVEMNNLSCRSFStN7w0RUREVDMMN7VEWb+b+Ph4kSshIiKq2xhuagm23BAREekGw00tUdZyc/36dTx48EDkaoiIiOouhptawt7eHs2bNwcAnDp1SuRqiIiI6i6Gm1qk7NIU+90QERFVH8NNLcJOxURERDXHcFOLPNlyU88e1k5ERKQzDDe1iJ+fH2QyGTIyMnD79m2xyyEiIqqTGG5qEUtLS7Rv3x4AbwknIiKqLoabWoadiomIiGqG4aaWYadiIiKimmG4qWXKWm5OnToFpVIpcjVERER1D8NNLdOuXTtYWloiJycHV65cEbscIiKiOofhppYxMTFBQEAAAODPP/8UuRoiIqK6h+GmFurRowcAhhsiIqLqYLiphXr27AkAOHr0qMiVEBER1T0MN7VQt27dIJFIcPPmTaSnp4tdDhERUZ3CcFML2draomPHjgB4aYqIiEhbDDe1FPvdEBERVQ/DTS1VFm7Y74aIiEg7DDe1VFmn4rNnzyIvL0/kaoiIiOoOE00W+uabb7Te8IQJE2Btba31evSYh4cHmjRpgr///hvx8fHo06eP2CURERHVCRqFmxkzZqBJkyaQyWQabTQtLQ1DhgxhuKmhnj17YtOmTTh69CjDDRERkYY0CjfA42cdOTk5abQsQ41u9OjRA5s2bWKnYiIiIi1o1OcmKioKVlZWGm/0448/hr29fbWLosfK+t389ddfUCgUIldDRERUN0gEQRDELsKQcnJyYGtri+zsbNjY2IhdTpUUCgUaNmyIR48eISEhAT4+PmKXREREJAptvr91crdUTk4OVqxYgc6dO+tic/T/ZDIZunXrBoC3hBMREWmqRuHm4MGDGDNmDFxdXTFv3jzV06xJd8ouTbHfDRERkWY07lBc5vbt24iJicHatWvx8OFDPHjwABs2bMCrr74KiUSijxrrNY5UTEREpB2NW25++eUXDBo0CK1atUJCQgK+/vpr3LlzB1KpFB06dGCw0ZOAgADIZDKkpqYiLS1N7HKIiIhqPY3DTWhoKPz8/JCeno4tW7Zg2LBhkMvl+qyNAFhZWcHX1xcAW2+IiIg0oXG4mThxIpYvX44BAwZg5cqVePDggT7roieU9bv5448/RK6EiIio9tM43Hz33XdIT0/HpEmTsHHjRri6umLYsGEQBAFKpVKfNdZ7zz//PADg8OHDIldCRERU+2l1t5SFhQXGjRuHw4cP48KFC2jXrh2cnZ3Ro0cPjBo1Clu3btVXnfVar169IJFIcOnSJWRmZopdDhERUa1W7VvBW7ZsiejoaKSlpeGnn35Cfn4+Ro4cqcva6P81atRINYDfwYMHRa6GiIiodqvxIH5SqRQhISHYvn077+bRo759+wIADhw4IHIlREREtZvW49wAwJ07d3D06FHcvXtXrb+NRCLBtGnTdFYc/U/fvn2xaNEihhsiIqJn0PrZUjExMXj77bchl8vRqFEjtfFtJBIJbt68qfMidakuPVvqSTk5ObC3t4dCoUBKSgqaNm0qdklEREQGo9dnS82ZMweRkZHIzs5GSkoKkpOTVVNtDzZ1mY2NDbp06QKA/W6IiIiqonW4yc/Px2uvvQapVCfP3MTy5cvh6ekJc3NzBAQEID4+vsrlHz58iKlTp8LV1RVmZmbw9vbGrl27dFJLbdenTx8ADDdERERV0TqhTJw4EVu2bNHJzjdv3oywsDBERUXhzJkz8PHxQXBwMO7evVvh8sXFxXjhhReQkpKC//73v0hMTMSqVavQuHFjndRT2z3ZqVjLq4lERET1htZ9bhQKBYYMGYKCggJ06NABpqamau8vWrRI420FBASgS5cuWLZsGQBAqVTC3d0d06ZNQ3h4eLnlV65ciS+//BJXr14tt9/KFBUVoaioSPU6JycH7u7uda7PDfC41axhw4YoLi7GtWvX0LJlS7FLIiIiMgi99rmZP38+9uzZg8zMTFy4cAFnz55VTQkJCRpvp7i4GKdPn0ZQUND/ipFKERQUhGPHjlW4zm+//YbAwEBMnToVzs7OaN++PaKjo6FQKKqs19bWVjW5u7trXGNtY2lpicDAQAC8JZyIiKgyWt8K/vXXX2PNmjUYP358jXaclZUFhUIBZ2dntfnOzs64evVqhevcvHkTBw4cwOjRo7Fr1y4kJSXhnXfeQUlJCaKioipcJyIiAmFhYarXZS03dVXfvn1x+PBhHDhwAG+//bbY5RAREdU6WrfcmJmZoUePHvqo5ZmUSiWcnJzw/fffw9/fH6Ghofjkk0+wcuXKStcxMzODjY2N2lSXlfW7OXjwIJ/pRUREVAGtw8306dOxdOnSGu/YwcEBMpms3LOSMjMz4eLiUuE6rq6u8Pb2hkwmU81r06YNMjIyUFxcXOOa6oKuXbvC0tIS9+7dw6VLl8Quh4iIqNbROtzEx8dj3bp18PLyQkhICIYPH642aUoul8Pf3x9xcXGqeUqlEnFxcap+JU/r0aMHkpKS1Fosrl27BldXV8jlcm0PpU6Sy+Xo2bMnAN4STkREVBGtw42dnR2GDx+OXr16wcHBQa2zrq2trVbbCgsLw6pVq7Bu3TpcuXIFU6ZMQV5eHiZMmAAAGDt2LCIiIlTLT5kyBf/88w+mT5+Oa9euYefOnYiOjsbUqVO1PYw6jc+ZIiIiqpzWHYrXrl2rs52Hhobi3r17iIyMREZGBnx9fREbG6vqZJyamqo2WKC7uzv27NmD999/Hx07dkTjxo0xffp0zJo1S2c11QVl4ebQoUNQKBRql+mIiIjqO63Huanr6uqzpZ5UWloKBwcHZGdn48SJE+jatavYJREREemVzse56dSpEx48eKBxAT179sTt27c1Xp60Y2Jign79+gEAdu/eLXI1REREtYtGl6USEhJw7tw52Nvba7TRhIQEtVGBSfcGDhyIrVu3Yvfu3ZWO8UNERFQfadznpl+/fho/z0gikVS7INLMgAEDADy+ey0rKwsODg4iV0RERFQ7aBRukpOTtd5wkyZNtF6HNNekSRN06NABFy5cwN69ezFq1CixSyIiIqoVNAo3TZs21XcdVA0DBw7EhQsXsHv3boYbIiKi/6f1ODdUewwcOBAAsGfPHj6KgYiI6P8x3NRhPXr0gLW1Ne7du4fTp0+LXQ4REVGtwHBTh5mamiIoKAgAbwknIiIqw3BTx5VdmmK4ISIiekzrcOPl5YX79++Xm//w4UN4eXnppCjSXFm4OXHiRIWfCxERUX2jdbhJSUmBQqEoN7+oqIijEougSZMmaN++PQRBwN69e8Uuh4iISHQaD+L322+/qX7fs2eP2hPAFQoF4uLi4OnpqdPiSDMDBw7ExYsXsXv3bowcOVLscoiIiESl8YMzy57OLZFIyo1UbGpqCk9PT3z99dcYMmSI7qvUIWN4cObTDh48iL59+8LR0REZGRlqT1InIiIyBtp8f2vcclM2jkqzZs1w8uRJDvdfi/To0QNWVla4d+8ezpw5g86dO4tdEhERkWi0/l/85ORkBptaRi6X85ZwIiKi/6dxy82T4uLiEBcXh7t375YbGXfNmjU6KYy0M2jQIGzfvh07d+7EnDlzxC6HiIhINFq33MydOxf9+/dHXFwcsrKy8ODBA7WJxDFkyBBIJBKcOHGCd60REVG9pnXLzcqVKxETE4MxY8boox6qJldXV3Tr1g3Hjh3Dr7/+infeeUfskoiIiEShdctNcXExunfvro9aqIZeeuklAMC2bdtEroSIiEg8WoebN998Exs2bNBHLVRDZeHm0KFDvERIRET1ltaXpQoLC/H9999j//796NixI0xNTdXeX7Rokc6KI+20aNEC7du3x8WLF7Fjxw5eOiQionpJ63Bz/vx5+Pr6AgAuXryo9p5EItFJUVR9L730Ei5evIht27Yx3BARUb2k8QjFxsIYRyh+0tmzZ9GpUydYWFggKysLlpaWYpdERERUY9p8f1d7nP6kpCTs2bMHBQUFAFDukQwkDl9fXzRt2hQFBQV8kCYREdVLWoeb+/fvo1+/fvD29sagQYOQnp4OAJg4cSI++OADnRdI2pFIJLxrioiI6jWtw837778PU1NTpKamql3yCA0NRWxsrE6Lo+opCze///47SkpKRK6GiIjIsLQON3v37sUXX3yBJk2aqM1v2bIlbt26pbPCqPp69OgBR0dHPHjwAEeOHBG7HCIiIoPSOtzk5eVV2En1n3/+gZmZmU6KopqRyWQYOnQoAF6aIiKi+kfrcPPcc8/hP//5j+q1RCKBUqnEwoUL0adPH50WR9VXdmlq+/bt5R5uSkREZMy0Hudm4cKF6NevH06dOoXi4mLMnDkTly5dwj///IM///xTHzVSNfTr1w9WVla4ffs2Tp48iYCAALFLIiIiMgitW27at2+Pa9euoWfPnhg2bBjy8vIwfPhwnD17Fs2bN9dHjVQN5ubmGDJkCABg06ZNIldDRERkOFoN4ldSUoIBAwZg5cqVaNmypT7r0htjH8TvSb///juGDh0KV1dXpKWlQSaTiV0SERFRtehtED9TU1OcP3++RsWR4QQHB6Nhw4ZIT0/H4cOHxS6HiIjIILS+LPX6669j9erV+qiFdEwul+Pll18GAPznp5/gGb4TnuE7kV9cKnJlRERE+qN1h+LS0lKsWbMG+/fvh7+/Pxo0aKD2Pp8KXruMGjUKq1atwvatW2H75lBITEyfvRIREVEdpnW4uXjxIjp16gQAuHbtmtp7fCp47fPcc8+hcePGuH37NuTJp2HZspvYJREREemVVuFGoVBg7ty56NChAxo2bKivmkiHZDIZQkNDsWjRIuRdPsxwQ0RERk+rPjcymQz9+/fHw4cP9VQO6cOoUaMAAAVJJ6Asyhe5GiIiIv2q1jg3N2/e1EctpCedOnVCy5beEEqLkX/9uNjlEBER6ZXW4ebzzz/Hhx9+iB07diA9PR05OTlqE9U+EokEr4SGAgDyrvCWcCIiMm5aDeIHAFLp//LQkx2IBUGARCKBQqHQXXV6UJ8G8XtSwoVL8OvYHpBIkZL2N5o2dhW7JCIiIo1p8/2t9d1SBw8erHZhJB7vVq0gd2mB4owkbPvlv5jx3jSxSyIiItILrcNNr1699FEHGUCDNr1QnJGEzZs2MtwQEZHR0jrcHDlypMr3n3/++WoXQ/pl2eZ5PDi0FsePHUNiYiJatWoldklEREQ6p3W46d27d7l5T/a9qe19buozE+tGsAkYgbxLB7B69WosXLhQ7JKIiIh0Tuu7pR48eKA23b17F7GxsejSpQv27t1brSKWL18OT09PmJubIyAgAPHx8Rqtt2nTJkgkErz44ovV2q+xyy8uVU0bTqQCABr2GofGk9fix79uIjuvgM+ZIiIio6P13VKVOXz4MMLCwnD69Gmt1tu8eTPGjh2LlStXIiAgAIsXL8aWLVuQmJgIJyenStdLSUlBz5494eXlBXt7e2zfvl2j/dWnu6U8w3dW+p6gVKAw5SwsvDojZcFgA1ZFRESkPW2+v7VuuamMs7MzEhMTtV5v0aJFeOuttzBhwgS0bdsWK1euhKWlJdasWVPpOgqFAqNHj8bcuXPh5eVVk7LrLYlUhsK0i2KXQUREpHNa97k5f/682mtBEJCeno4FCxbA19dXq20VFxfj9OnTiIiIUM2TSqUICgrCsWPHKl3vs88+g5OTEyZOnIg//vijyn0UFRWhqKhI9bo+DTR4+bNgAEBGdiGCFh2G8ok2OkGpQMHlwzi94SuRqiMiItIPrVtufH194efnB19fX9XvgwYNQnFxMX744QettpWVlQWFQgFnZ2e1+c7OzsjIyKhwnaNHj2L16tVYtWqVRvuYP38+bG1tVZO7u7tWNdZllnITWMpN4OVohblD26nmSyVAo+S9KMm5h80bfhKxQiIiIt3TOtwkJyfj5s2bSE5ORnJyMm7duoX8/Hz89ddfaN26tT5qVHn06BHGjBmDVatWwcHBQaN1IiIikJ2drZrS0tL0WmNtNcK/ier3/WG9MCOkKwBg9erVUCqVYpVFRESkc1pflmratKnOdu7g4ACZTIbMzEy1+ZmZmXBxcSm3/I0bN5CSkoKQkBDVvLIvZhMTEyQmJqJ58+Zq65iZmcHMzExnNRsDF1tzvPzyy5g2bRqSk5Nx6NAh9O3bV+yyiIiIdELjlpsDBw6gbdu2FfZZyc7ORrt27Z7Z/+Vpcrkc/v7+iIuLU81TKpWIi4tDYGBgueVbt26NCxcuICEhQTUNHToUffr0QUJCQr265FRTlpaWGD16NABofTmRiIioNtM43CxevBhvvfVWhbdf2dra4u2338aiRYu0LiAsLAyrVq3CunXrcOXKFUyZMgV5eXmYMGECAGDs2LGqDsfm5uZo37692mRnZwdra2u0b98ecrlc6/3XZxMnTgQAbN26Ff/884/I1RAREemGxuHm3LlzGDBgQKXv9+/fX+sxbgAgNDQUX331FSIjI+Hr64uEhATExsaqOhmnpqYiPT1d6+3Ss3Xq1Am+vr4oKirCf/7zH7HLISIi0gmNB/EzNzfHxYsX0aJFiwrfT0pKQocOHVBQUKDTAnWtPg3i96T84lK0jdwD4PEt4pbyx92tvvvuO0yePBnNmzdHYmIiZDKZmGUSERFVSC+D+DVu3BgXL1Y+6Nv58+fh6uqqeZVUK7z++uto2LAhbty4gd27d4tdDhERUY1pHG4GDRqEOXPmoLCwsNx7BQUFiIqKwpAhQ3RaHOlfgwYN8OabbwIAlixZInI1RERENafxZanMzEx06tQJMpkM7777Llq1agUAuHr1KpYvXw6FQoEzZ86UG5CvtuFlKfXLUgBw69YteHl5QalU4tKlS2jbtq1YZRIREVVIL5elnJ2d8ddff6F9+/aIiIjASy+9hJdeegkff/wx2rdvj6NHj9b6YEMVa9q0qerJ6kuXLhW3GCIiohqq1lPBHzx4gKSkJAiCgJYtW6Jhw4b6qE0v2HJTvuUGePxU9969e8PS0hJ///13nfpMiYjI+Gnz/V2tcFOX1ddw8yyCIMDX1xfnz5/Hl19+iQ8//FDskoiIiFT0clmKjJtEIsH06dMBAMuWLYNCoRC5IiIiouphuCGVkSNHolGjRrh16xZ+++03scshIiKqFoYbUrGwsMDbb78NgLeFExFR3cVwQ2qmTJkCExMTHD58GCdOnBC7HCIiIq0x3JCaJk2a4PXXXwcAREdHi1wNERGR9hhuqJzw8HBIJBL89ttvuHDhgtjlEBERaYXhhspp1aoVXn75ZQDAggULRK6GiIhIOww3VKGIiAgAwKZNm5CUlCRyNURERJpjuKEK+fn5YdCgQVAqlVi4cKHY5RAREWmM4YYq9fHHHwMAYmJi8Pfff4tcDRERkWYYbqhSPXr0wPPPP4+SkhJ8/fXXYpdDRESkEYYbqtInn3wCAPjuu+9w7949kashIiJ6NoYbqtILL7wAf39/FBQUsPWGiIjqBIYbqpJEIkFkZCQA4JtvvkF6errIFREREVWN4YaeKSQkBIGBgSgoKMC8efPELoeIiKhKDDf0TBKJRDWY36pVq3Djxg2RKyIiIqocww1p5Pnnn8eAAQNQWlqqukxFRERUGzHckMbKHqS5YcMGnDt3TuRqiIiIKsZwQxrz8/PDa6+9BuB/t4gTERHVNgw3pJV58+bBxMQEO3fuxB9//CF2OUREROUw3JBWWrRogYkTJwJ4/HBNQRBEroiIiEgdww1pLTIyEhYWFvjzzz/x3//+V+xyiIiI1DDckNbc3Nwwa9YsAMAHH3yAvLw8kSsiIiL6H4YbqpaZM2eiadOmSEtLwxdffCF2OURERCoMN1QtFhYWWLRoEQBg4cKFuHnzpsgVERERPcZwQ9X20ksvISgoCEVFRfjggw/ELoeIiAgAww3VgEQiwZIlS2BiYoLt27dj7969YpdERETEcEM107ZtW0ybNg0A8N5776G4uFjkioiIqL5juKEai4qKgpOTExITE7FkyRKxyyEionqO4YZqzNbWVnXHVFRUFJKSkkSuiIiI6jOGG9KJcePGoV+/figoKMBbb70FpVIpdklERFRPMdyQTkgkEqxatQqWlpY4dOgQVq1aJXZJRERUTzHckM40a9YM0dHRAICPPvoIaWlpIldERET1EcMN6dS7776LwMBAPHr0CFOmTOGDNYmIyOAYbkinZDIZVq9eDblcjp07d2LDhg1il0RERPUMww3pXJs2bRAZGQkAmD59OtLT00WuiIiI6hOGG9KLmTNnws/PD/fv38e4ceN49xQRERkMww3phampKdavXw8LCwvs27dP9ZBNIiIifWO4Ib1p06aNasTijz/+GKdPnxa5IiIiqg8Ybkiv3nzzTQwfPhwlJSUYOXIkcnNzxS6JiIiMXK0IN8uXL4enpyfMzc0REBCA+Pj4SpddtWoVnnvuOTRs2BANGzZEUFBQlcuTuMoG92vSpAmuX7+uesgmERGRvogebjZv3oywsDBERUXhzJkz8PHxQXBwMO7evVvh8ocOHcLIkSNx8OBBHDt2DO7u7ujfvz9u375t4MpJU/b29li/fj2kUiliYmKwceNGsUsiIiIjJhFEHmUtICAAXbp0wbJlywAASqUS7u7umDZtGsLDw5+5vkKhQMOGDbFs2TKMHTv2mcvn5OTA1tYW2dnZsLGxqXH9pLnIyEjMmzcPDRo0wPHjx9G+fXuxSyIiojpCm+9vUVtuiouLcfr0aQQFBanmSaVSBAUF4dixYxptIz8/HyUlJbC3t6/w/aKiIuTk5KhNJI7IyEj069cPeXl5ePHFF/HgwQOxSyIiIiMkarjJysqCQqGAs7Oz2nxnZ2dkZGRotI1Zs2bBzc1NLSA9af78+bC1tVVN7u7uNa6bqsfExASbNm2Cp6cnbty4gZEjR0KhUIhdFhERGRnR+9zUxIIFC7Bp0yZs27YN5ubmFS4TERGB7Oxs1cSHOYrLwcEB27dvh4WFBfbs2YPZs2eLXRIRERkZUcONg4MDZDIZMjMz1eZnZmbCxcWlynW/+uorLFiwAHv37kXHjh0rXc7MzAw2NjZqE4nLx8cHa9asAfA4oG7ZskWj9fKLS+EZvhOe4TuRX1yqzxKJiKgOEzXcyOVy+Pv7Iy4uTjVPqVQiLi4OgYGBla63cOFCzJs3D7GxsejcubMhSiUde+211/Dhhx8CAMaPH4+zZ8+KXBERERkL0S9LhYWFYdWqVVi3bh2uXLmCKVOmIC8vDxMmTAAAjB07FhEREarlv/jiC8yZMwdr1qyBp6cnMjIykJGRwcHh6qD58+ejf//+yM/Px6BBg5CSkiJ2SUREZAREDzehoaH46quvEBkZCV9fXyQkJCA2NlbVyTg1NVXtqdIrVqxAcXExXn75Zbi6uqqmr776SqxDoGoyMTHBzz//jI4dOyIjIwMDBgzA/fv3xS6LiIjqONHHuTE0jnNT+9y+fRuBgYFIS0tD9+7dsX//flhYWJRbLr+4FG0j9wAALn8WDEu5iaFLJSIikdSZcW6IAKBx48aIjY2FnZ0d/vrrL4wePZq3iBMRUbUx3FCt0LZtW/z2228wMzPDtm3b8O6776KeNSoSEZGOMNxQrfHcc8/hp59+gkQiwcqVK/H+++8z4BARkdYYbqhWefnll/HDDz8AAJYsWYIPP/yQAYeIiLTCcEO1zhtvvIHvvvsOALBo0SKEh4cz4BARkcYYbqhWmjRpEr799lsAjwdtnD17NgMOERFphPfSUq01ZcoUlJaW4r333kN0dDQe5eVDMOsLiUSKjOxCeDlaiV0iERHVQmy5oVpt2rRpWLx4MQBg7cFLqvlBiw5j88lUkaoiIqLajIP4UZ3gOCwClq26QyL9Xx6XSSQ4Gt4HrrblB/wjIiLjwkH8yOg0aNNTLdgAgEIQkJKVL1JFRERUWzHcUJ1w4INekEqemqlUQpbPZ1EREZE6hhuqE7wcrTB3aDvVa0GpwP09SzGoT3ccPnxYxMqIiKi2YbihOmOEfxPV7xtfb4NWpv/g/v37CAoKwvfffy9iZUREVJsw3FCd5Nu6GY4cOYLQ0FCUlpbi7bffxnvvvYfS0lKxS3um/OJSeIbvhGf4TuQX1/56iYjqGoYbqrMsLS2xceNGzJs3DwCwdOlS9OnTB3///bfIlRERkZgYbqhOk0gkmD17NrZu3Qpra2scPXoUvr6+2LVrl9ilERGRSBhuyCi89NJLOHPmDDp16oT79+9j8ODBmDlzJkpKSsQujYiIDIzhhoxGixYt8Ndff2HatGkAgC+//BI9e/ZEYmKiyJXVfewnRER1CcMNGRUzMzN88803+OWXX2Bra4v4+Hj4+vri3//+NxQKhdjlERGRATDckFEaPnw4zp8/jxdeeAGFhYUICwtD7969kZSUJHZpRESkZww3ZLQ8PDywZ88efPfdd7CyssLRo0fRsWNHfPXVV+yLQ0RkxBhuyKhJJBJMmjQJFy5cQN++fVFQUICPPvoIfn5+OHLkiNjlERGRHjDcUL3g6emJffv2YfXq1XBwcMClS5fQq1cvjB07FpmZmWKXR0REOsRwQ3WGpdwEKQsGI2XBYFjKTbReXyqV4o033kBiYiLefvttSCQS/Pjjj/D29saCBQtQUFCgh6qJ6g/eVUe1BcMN1Tv29vZYuXIljh8/Dn9/f+Tk5CAiIgLe3t6IiYkx6F1VGdmFBtsXEVF9wXBD9VbXrl0RHx+PH3/8ER4eHvj7778xYcIE+Pn54ffff4cgCDrfZ35xKTacSFW9Dlp0GD8eS9H5foiI6jOGG6rXpFIpXn/9dSQmJuLLL7+EnZ0dLly4gKFDh8Lf3x/bt2+HUqnU2f7aRu7B5zuvqF4rBWDOr5eQns1LYkREusJwQwTA3NwcH374IW7cuIFZs2ahQYMGOHv2LF566SX4+flhy5Yter1clZKVr7dtExHVNww3RE+wt7fHggULkJKSgk8++QTW1tY4f/48Xn31VXh7e+Obb77Bo0ePqr39Ax/0glSiPk8qATwdLGtYueGwnxAR1XYMN0QVcHBwwOeff46UlBRERkbC3t4eN2/exPTp0+Hu7o6PPvoIt27d0nq7Xo5WmDu0neq1VALMH94BrrYWuixf59hPiIjqEoYboirY29tj7ty5SEtLw4oVK+Dt7Y3s7Gx89dVXaNasGQYPHoxff/0VpaWa3/Y6wr+J6vf9Yb0Q2sVDH6XrTHp2AfsJEVGdwnBDpAFLS0tMnjwZV65cwY4dOxAUFARBELBr1y68+OKL8PT0RGRkJG7cuKHVdl1szfVUse4kZ+VVOJ/9hIiotmK4IdKCVCrF4MGDsW/fPly7dg0zZ86Eo6Mjbt++jXnz5qFFixbo3r07VqxYgfv374tdrk40c2hQp/sJcWA5ovqH4Yaomlq2bIkvvvgCaWlp2LRpE4KDgyGVSnHs2DG88847cHV1RUhICNatW4cHDx6IXW61udpa1Ml+QkRlGHDrH4YbohoyMzNDaGgoYmNj8ffff2PRokXw8/NDSUkJduzYgfHjx8PJyQnBwcH4/vvvkZ6eLnbJWqtr/YRIfLyrjsTEcEOkQ66urnj//fdx5swZXLp0CXPnzkWHDh1QWlqKvXv34u2330YLTw+kr5uBh3+sx6mT8TodJNAQ6kI/ITI8jr5NtQnDDZGetG3bFpGRkTh//jwSExMRHR2NLl26AACKM5KQ/ddG9OrZA87Oznjttdfwww8/ICUlRdyiiaqJo29TbcJwQ2QA3t7eiIiIQHx8PG7cSkOjgdNh6d0d1tbWyMrKwubNm/HWW2+hWbNmaNGiBSZOnIh169bh5s2bennGFZGh8K46EoOJ2AUQ1TcuLi6w6vgCrDq+gITZfXAx4Qz279+P/fv34/jx47hx4wZu3LiBNWvWAAAaN26Mnj17IiAgAAEBAejUqRPMzXlpiGqXAx/0QtCiw1A+kcXr0l11ZFwYbohEJJfL0bNnT/Ts2ROffvopcnJy8Mcff+DIkSP4448/cOrUKdy+fRubN2/G5s2bAQCmpqbw8fFB586d0alTJ3Tq1Ant27eHmZmZyEdD9VnZ6Ntzfr0EgHfVkbgYbohqERsbGwwePBiDBw8GAOTn5+PEiRM4duwYjh8/jhMnTuDu3bs4deoUTp06pVrPxMQEbdu2RYcOHdSmJk2aQCKRVLY7Ip0a4d9EFW72h/WCl6OVyBVRfcVwQ2RglnITpCwYrNmylpbo06cP+vTpAwAQBAG3bt3CiRMncObMGZw9exZnzpzB/fv3cf78eZw/f15tfRsbG7Ru3RqtW7dGmzZt0Lp1a7Rs2RJeXl6wsOD/UdcF+cWlaBu5BwBw+bNgWMrrxj/bvKtOe3X1s66NeOaI6hCJRAJPT094enoiNDQUwOPAk5aWhnPnzuHChQs4f/48Lly4gMTEROTk5CA+Ph7x8fHlttOkSRNV0GnWrJna5OTkxBYfIqqzGG6I6jiJRAIPDw94eHggJCRENb+oqAg3btzAlStXcPXqVVy5cgWJiYm4fv06srOzkZaWhrS0NBw4cKDcNs3MzODu7q7arrOrGx6dfQiZdSOcPeuIFp5N4eDgAJlMZshDrbGM7EJeKiGqBxhuiIyUmZkZ2rZti7Zt26rNFwQB9+/fx/Xr13H9+nXcvHkTycnJqun27dsoKipCUlISkpKSym235y/zAAAymQxOTk5wcXFRTY6OjnByclJNDg4OaNSoERwcHNCgQQODtwZVNLDc3KHtMCbQ06B1UO3BgFs/MNwQ1TMSiQQODg5wcHBAYGBgufeLi4tx+/ZtpKWlITU1Fbdu3cLt27dx+/Zt3LlzB7dv30ZGRgYUCgXS09M1fpyEmZkZGjVqBHt7e9jb26Nhw4aqn3Z2dmqTjY0NbGxsYGtrCxsbG1hbW1frbrCy/gtlygaWC2rrzLt46oGy50hVFHBH+DdhnxYjVis+2eXLl+PLL79ERkYGfHx8sHTpUnTt2rXS5bds2YI5c+YgJSVF9fDCQYMGGbBiIuMll8tVfW8qU1painv37iEjIwPp6enIyMhARkYG7t27h3v37uHu3bu4e/cusrKykJWVhaKiIhQVFeHOnTu4c+dOteuytrZWTVZWVrCyskKDBg1UPxs0aABLS0vVz/ykf2DZoku5bR08eRFdPRvCwsIC5ubmMDMzg7m5OUxMasU/iaQjT4db4H8Bd86vlzTu2E91j+j/JW/evBlhYWFYuXIlAgICsHjxYgQHByMxMRFOTk7llv/rr78wcuRIzJ8/H0OGDMGGDRvw4osv4syZM2jfvr0IR0BU/5iYmMDV1RWurq7w8/OrcllBEJCfn68KOg8ePMCDBw/wzz//4J9//sHDhw/LTTk5OcjOzkZOTg7y8vIAPG5Run//Pu7fv69xnTLrRrDwWguJ9H+DsQtKBcYOHwjFo/LbkclkMDMzq3CSy+Wqn09Opqamqp+VTSYmJpX+LJtkMlm5nzKZDKWCBIVpFwGJDCfj7dDA3Ez1nkwmg1QqLff7kz/LpqdfPz1JJBJ2IiejIRFEHts9ICAAXbp0wbJlywAASqUS7u7umDZtGsLDw8stHxoairy8POzYsUM1r1u3bvD19cXKlSvLLV/2f4xlcnJy4O7ujuzsbNjY2OjhiIhIl0pLS/Ho0SM8evQIubm5ar/n5uYiLy8Pjx49Ql5eHvLz89V+FhQU4I55M9zzDHoccJRKCCc3oOBSHAoLC1FQUIDS0lKxD7HWKAs4ZWHnWT+f/l0ilSIrtxgA4GxrAenT7z8RoJ6ep8n7T84v+72ieWW/CwAUZtb4p/sMQPLE04YEJZxOLINpSW6F26rovOhymcrmKZQC/rrxOHT3aOEAmbTibWkSQnW1THW31bp1a3z55ZcabV9TOTk5sLW11ej7W9SWm+LiYpw+fRoRERGqeVKpFEFBQTh27FiF6xw7dgxhYWFq84KDg7F9+/YKl58/fz7mzp2rs5qJyLBMTEzQsGFDNGzYsFrrPzl2yIGP+sDLMUTtfYVCgaKiIhQWFqr9fHIqLi4u97OkpATFxcWqqex1SUmJ2lRaWqr2+5NTSUkJFAqF6rVCoVDNK5tKSkqRdDcHUCrR2NYMSuX/3lMqlWrLKpVKtXnaPnFeEAQIgqCTJ9Xfya3xJnTGKkcG++B3IZHKICgV+GfPMtw6v0/ssqoUlyJ2BTWjTQurPogabrKysqBQKODs7Kw239nZGVevXq1wnYyMjAqXz8jIqHD5iIgItTBU1nJDRPVPRQPLyWQyWFpawtKydj4DqaYDu5WFlSfDz5Mh6MlA8/Trsqns9ZPzy5Z78r384hIMX/4XAAFbJneDuYlM7X1NprKan/69omUqWvbJ4y57XVhcind/PgeJqTnmDvSCc/d3ALxT4baeXP/pedVZRpt5hSWlmPXLBQDAFyM6wOz/z191ti3mMgAq7FZiSKL3udG3suvlRET1kUQiUfXJMYQ7a/0Nsh9t5BeX4qOTcgDAmFdq78i/+cWlmHf1cZAdOar21lkXSJ+9iP6UDQKWmZmpNj8zMxMuLi4VruPi4qLV8kRExiIju1DsEshA+FnXjKjhRi6Xw9/fH3Fxcap5SqUScXFxFY6/AQCBgYFqywPAvn37Kl2eiKguyS8uVZueHqPlx2Mpau9T3fT056zJZ83PXHOit3mFhYVh3Lhx6Ny5M7p27YrFixcjLy8PEyZMAACMHTsWjRs3xvz58wEA06dPR69evfD1119j8ODB2LRpE06dOoXvv/9ezMMgItKJisZmKfPkGC1lOFZL3VTV5wxU/FmX4Wf+bKKHm9DQUNy7dw+RkZHIyMiAr68vYmNjVZ2GU1NTIX1ijIru3btjw4YNmD17Nj7++GO0bNkS27dv5xg3REREBKAWjHNjaNrcJ09EdV9N7zYytCcvO2RkFyJo0WEon/hXWioB9of1Ut35VduPpzaojX8DT19e0uSzLlMb6heDNt/fova5ISIidZZyE9Xk5WiFuUPbqd6TSoD5wzvAy9FKtQzVTU9+zpp+1vzMNcdwQ0RUi43wb6L6fX9YL4R28RCxGtInfta6w3BDRFRHVDQIIRknftY1w/YtIjJqlnIT3l1CVM+w5YaIiIiMCltuiIjIqLH1rv5hyw0REREZFYYbIiIiMioMN0RERGRUGG6IiIjIqDDcEBERkVFhuCEiIiKjwgdnEhERUa3HB2cSERFRvcVwQ0REREaF4YaIiIiMCsMNERERGRWGGyIiIjIqDDdERERkVBhuiIiIyKgw3BAREZFRYbghIiIio8JwQ0REREaF4YaIiIiMCsMNERERGRWGGyIiIjIqDDdERERkVBhuiIiIyKiYiF2AoQmCAADIyckRuRIiIiLSVNn3dtn3eFXqXbh59OgRAMDd3V3kSoiIiEhbjx49gq2tbZXLSARNIpARUSqVuHPnDqytrSGRSHS67ZycHLi7uyMtLQ02NjY63Tap47k2HJ5rw+G5Nhyea8PR1bkWBAGPHj2Cm5sbpNKqe9XUu5YbqVSKJk2a6HUfNjY2/I/FQHiuDYfn2nB4rg2H59pwdHGun9ViU4YdiomIiMioMNwQERGRUWG40SEzMzNERUXBzMxM7FKMHs+14fBcGw7PteHwXBuOGOe63nUoJiIiIuPGlhsiIiIyKgw3REREZFQYboiIiMioMNwQERGRUWG40dLy5cvh6ekJc3NzBAQEID4+vsrlt2zZgtatW8Pc3BwdOnTArl27DFRp3afNuV61ahWee+45NGzYEA0bNkRQUNAzPxv6H23/rsts2rQJEokEL774on4LNCLanuuHDx9i6tSpcHV1hZmZGby9vfnviIa0PdeLFy9Gq1atYGFhAXd3d7z//vsoLCw0ULV115EjRxASEgI3NzdIJBJs3779mescOnQInTp1gpmZGVq0aIGYmBjdFiWQxjZt2iTI5XJhzZo1wqVLl4S33npLsLOzEzIzMytc/s8//xRkMpmwcOFC4fLly8Ls2bMFU1NT4cKFCwauvO7R9lyPGjVKWL58uXD27FnhypUrwvjx4wVbW1vh77//NnDldY+257pMcnKy0LhxY+G5554Thg0bZphi6zhtz3VRUZHQuXNnYdCgQcLRo0eF5ORk4dChQ0JCQoKBK697tD3X69evF8zMzIT169cLycnJwp49ewRXV1fh/fffN3Dldc+uXbuETz75RNi6dasAQNi2bVuVy9+8eVOwtLQUwsLChMuXLwtLly4VZDKZEBsbq7OaGG600LVrV2Hq1Kmq1wqFQnBzcxPmz59f4fKvvvqqMHjwYLV5AQEBwttvv63XOo2Btuf6aaWlpYK1tbWwbt06fZVoNKpzrktLS4Xu3bsLP/zwgzBu3DiGGw1pe65XrFgheHl5CcXFxYYq0Whoe66nTp0q9O3bV21eWFiY0KNHD73WaWw0CTczZ84U2rVrpzYvNDRUCA4O1lkdvCyloeLiYpw+fRpBQUGqeVKpFEFBQTh27FiF6xw7dkxteQAIDg6udHl6rDrn+mn5+fkoKSmBvb29vso0CtU915999hmcnJwwceJEQ5RpFKpzrn/77TcEBgZi6tSpcHZ2Rvv27REdHQ2FQmGosuuk6pzr7t274/Tp06pLVzdv3sSuXbswaNAgg9Rcnxjiu7HePTizurKysqBQKODs7Kw239nZGVevXq1wnYyMjAqXz8jI0FudxqA65/pps2bNgpubW7n/gEhddc710aNHsXr1aiQkJBigQuNRnXN98+ZNHDhwAKNHj8auXbuQlJSEd955ByUlJYiKijJE2XVSdc71qFGjkJWVhZ49e0IQBJSWlmLy5Mn4+OOPDVFyvVLZd2NOTg4KCgpgYWFR432w5YaMzoIFC7Bp0yZs27YN5ubmYpdjVB49eoQxY8Zg1apVcHBwELsco6dUKuHk5ITvv/8e/v7+CA0NxSeffIKVK1eKXZrROXToEKKjo/Htt9/izJkz2Lp1K3bu3Il58+aJXRpVA1tuNOTg4ACZTIbMzEy1+ZmZmXBxcalwHRcXF62Wp8eqc67LfPXVV1iwYAH279+Pjh076rNMo6Dtub5x4wZSUlIQEhKimqdUKgEAJiYmSExMRPPmzfVbdB1Vnb9rV1dXmJqaQiaTqea1adMGGRkZKC4uhlwu12vNdVV1zvWcOXMwZswYvPnmmwCADh06IC8vD5MmTcInn3wCqZRtAbpS2XejjY2NTlptALbcaEwul8Pf3x9xcXGqeUqlEnFxcQgMDKxwncDAQLXlAWDfvn2VLk+PVedcA8DChQsxb948xMbGonPnzoYotc7T9ly3bt0aFy5cQEJCgmoaOnQo+vTpg4SEBLi7uxuy/DqlOn/XPXr0QFJSkipAAsC1a9fg6urKYFOF6pzr/Pz8cgGmLFQKfASjThnku1FnXZPrgU2bNglmZmZCTEyMcPnyZWHSpEmCnZ2dkJGRIQiCIIwZM0YIDw9XLf/nn38KJiYmwldffSVcuXJFiIqK4q3gGtL2XC9YsECQy+XCf//7XyE9PV01PXr0SKxDqDO0PddP491SmtP2XKempgrW1tbCu+++KyQmJgo7duwQnJychM8//1ysQ6gztD3XUVFRgrW1tbBx40bh5s2bwt69e4XmzZsLr776qliHUGc8evRIOHv2rHD27FkBgLBo0SLh7Nmzwq1btwRBEITw8HBhzJgxquXLbgX/6KOPhCtXrgjLly/nreBiW7p0qeDh4SHI5XKha9euwvHjx1Xv9erVSxg3bpza8j///LPg7e0tyOVyoV27dsLOnTsNXHHdpc25btq0qQCg3BQVFWX4wusgbf+un8Rwox1tz/Vff/0lBAQECGZmZoKXl5fwr3/9SygtLTVw1XWTNue6pKRE+PTTT4XmzZsL5ubmgru7u/DOO+8IDx48MHzhdczBgwcr/Pe37PyOGzdO6NWrV7l1fH19BblcLnh5eQlr167VaU0SQWB7GxERERkP9rkhIiIio8JwQ0REREaF4YaIiIiMCsMNERERGRWGGyIiIjIqDDdERERkVBhuiIiIyKgw3BAREZFRYbghItGNHz8eL774osH3GxMTA4lEAolEghkzZmi0zvjx41XrbN++Xa/1EVH18KngRKRXEomkyvejoqKwZMkS0R5OaGNjg8TERDRo0ECj5ZcsWYIFCxbA1dVVz5URUXUx3BCRXqWnp6t+37x5MyIjI5GYmKiaZ2VlBSsrKzFKA/A4fLm4uGi8vK2tLWxtbfVYERHVFC9LEZFeubi4qCZbW1tVmCibrKysyl2W6t27N6ZNm4YZM2agYcOGcHZ2xqpVq5CXl4cJEybA2toaLVq0wO7du9X2dfHiRQwcOBBWVlZwdnbGmDFjkJWVpXXN3377LVq2bAlzc3M4Ozvj5ZdfrulpICIDYrgholpp3bp1cHBwQHx8PKZNm4YpU6bglVdeQffu3XHmzBn0798fY8aMQX5+PgDg4cOH6Nu3L/z8/HDq1CnExsYiMzMTr776qlb7PXXqFN577z189tlnSExMRGxsLJ5//nl9HCIR6QkvSxFRreTj44PZs2cDACIiIrBgwQI4ODjgrbfeAgBERkZixYoVOH/+PLp164Zly5bBz88P0dHRqm2sWbMG7u7uuHbtGry9vTXab2pqKho0aIAhQ4bA2toaTZs2hZ+fn+4PkIj0hi03RFQrdezYUfW7TCZDo0aN0KFDB9U8Z2dnAMDdu3cBAOfOncPBgwdVfXisrKzQunVrAMCNGzc03u8LL7yApk2bwsvLC2PGjMH69etVrUNEVDcw3BBRrWRqaqr2WiKRqM0ruwtLqVQCAHJzcxESEoKEhAS16fr161pdVrK2tsaZM2ewceNGuLq6IjIyEj4+Pnj48GHND4qIDIKXpYjIKHTq1Am//PILPD09YWJSs3/aTExMEBQUhKCgIERFRcHOzg4HDhzA8OHDdVQtEekTW26IyChMnToV//zzD0aOHImTJ0/ixo0b2LNnDyZMmACFQqHxdnbs2IFvvvkGCQkJuHXrFv7zn/9AqVSiVatWeqyeiHSJ4YaIjIKbmxv+/PNPKBQK9O/fHx06dMCMGTNgZ2cHqVTzf+rs7OywdetW9O3bF23atMHKlSuxceNGtGvXTo/VE5EuSQSxhgUlIhJZTEwMZsyYUa3+NBKJBNu2bRPlsRFEVDW23BBRvZadnQ0rKyvMmjVLo+UnT54s6ojKRPRsbLkhonrr0aNHyMzMBPD4cpSDg8Mz17l79y5ycnIAAK6urho/k4qIDIfhhoiIiIwKL0sRERGRUWG4ISIiIqPCcENERERGheGGiIiIjArDDRERERkVhhsiIiIyKgw3REREZFQYboiIiMio/B98F7WANTmb4AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(data_frame['time'], \n",
    "             data_frame['current'], \n",
    "             xerr=data_frame['delta_time'], \n",
    "             yerr=data_frame['delta_current'], \n",
    "             ls='', \n",
    "             marker='.',\n",
    "             label='Data'\n",
    "            )\n",
    "x = np.arange(0, 1, 0.01)\n",
    "plt.plot(x, \n",
    "         discharge_current2(x, *mi.values), # Sternchen operator zum entpacken der Werte\n",
    "         color='k',\n",
    "         label='Best fit'\n",
    "        )\n",
    "fit_info = [\n",
    "    f\"$\\\\chi^2$/$n_\\\\mathrm{{dof}}$ = {mi.fval:.1f} / {mi.ndof:.0f} = {mi.fmin.reduced_chi2:.1f}\",\n",
    "]\n",
    "for p, v, e in zip(mi.parameters, mi.values, mi.errors):\n",
    "    fit_info.append(f\"{p} = ${v:.3f} \\pm {e:.3f}$\")\n",
    "\n",
    "plt.legend(title=\"\\n\".join(fit_info))\n",
    "plt.ylabel('Current [mA]')\n",
    "plt.xlabel('Time [s]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cd73609-8593-4725-a7c4-317d6a48a72f",
   "metadata": {},
   "source": [
    "# Mathematisch motivierte Herleitung des $\\chi^2$-Fits:\n",
    "\n",
    "Nach diesen anfänglichen Beispielen wollen wir uns eine semi-mathematische Herleitung des $\\chi^2$-Fits angucken um etwas besser zu verstehen, warum diese Methode für uns in der Physik so wichtig ist. In unserem Grundpraktikum haben wir bereits gelernt, dass Messwerte durch Zufallszahlen $x_i$ repräsentiert werden und einer gewissen **Wahrscheinlichkeitsdichtefunktion (probability density function)** $f(x)$ unterliegen.\n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/PorbDensFun.png\"  alt=\"{{ Beispiel PDF }}\" width=70%>\n",
    "</figure>\n",
    "\n",
    "\n",
    "Eine **pdf** gibt an, mit welcher **Wahrscheinlichkeit ein Wert $x_i$** innerhalb eines **infinitesimalen Intervals $\\text{d}x_i$** zu finden ist. Des Weiteren gilt, dass die Gesamtwahrscheinlichkeit gegeben ist durch $\\int_S f(x) dx = 1$. \n",
    "\n",
    "Nun betrachten wir folgendes Beispiel: In unserem Labor messen wir genau drei mal die Raumtemperartur T. Auch hier gilt, dass unsere Messungen der einzelnen $T_i$ einer gewissen **Wahrscheinlichkeitsdichtefunktion** folgen. Betrachten Sie nun das folgende Bild; Welche **Wahrscheinlichkeitsdichtefunktion** passt besser zu den gezeigten Daten und **Warum?**\n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/ProbMaxTemp.png\"  alt=\"{{ Beispiel PDF }}\" width=100%>\n",
    "</figure>\n",
    "\n",
    "Die rechte Verteilung spiegelt unsere Messdaten besser wider. Dies können wir auch mathematisch ausdrücken. Für $N$ voreinander unabhängige Zufallszahlen bzw. Messpunkte (in unserem Beispiel $N = 3$) ist die Gesamtwahrscheinlichkeit gegeben durch das Produkt der einzelnen Wahrscheinlichkeitsdichten $f(x_i, \\theta)$ multipliziert mit dem jeweiligen infinitesimalen Element $dx_i$\n",
    "\n",
    "$$\\prod_{i = 1}^{N} f(x_i,\\theta) \\  dx_i \\text{   für alle } x_i \\text{ in } [x_i, x_i + dx_i]$$\n",
    "\n",
    "wobei $x_i$ in unserem Beispiel den Messpunkten $T_i$ und $f(x_i,\\theta)$ unserer Gaussverteilung mit $\\theta = (\\mu, \\sigma)$ entspricht. Sofern unsere Werte gut von der jeweiligen **Wahrscheinlichkeitsdichtefunktion** repräsentiert werden, d.h. wir die richtigen Parameter $\\theta$ gewählt haben (wie im rechten oberen Plot), gilt \n",
    "\n",
    "$$ \\prod_{i = 1}^{N} f(x_i,\\theta)  dx_i \\ \\ \\text{ist} \\ \\textbf{maximal.}$$\n",
    "\n",
    "Da die einzelnen $dx_i$ von unseren Parametern $\\theta$ unabhängig sind, gilt die gleiche Argumentation auch für \n",
    "\n",
    "$$ \\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N) = \\prod_{i = 1}^{N} f(x_i,\\theta)$$ \n",
    "\n",
    "wobei $\\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N)$ die sogenannte **\"likelihood\"** function darstellt.\n",
    "\n",
    "Wie kommen wir nun von der **likelihood function** auf unsere **Methode der kleinsten Quadrate** und das Fitten einer Funktion $\\lambda(x; \\ $**$\\phi$**$)$ an die gemessenen Punkte **$(x,y)$**? Dazu brauchen wir noch einen Zwischenschritt. Oftmals ist es einfacher, statt die **likelihood function** zu maximieren, die so genannte **log likelihood function**\n",
    "\n",
    "$$ \\log( \\mathcal{L}(x_1 ... x_N; \\theta_1 ... \\theta_N)) = \\sum_{i = 1}^{N} \\log(f(x_i,\\theta))$$\n",
    "\n",
    "zu maximieren. Dies ist im Grunde das Gleiche, da der Logarithmus eine monoton-steigende Funktion ist. Auch in unserem Fall der **Methode der kleinsten Quadrate** benötigen wir die **log likelihood function**. \n",
    "\n",
    "Stellen Sie sich nun vor, wir haben eine Messung mit $N$ voneinander unabhängigen Messpunkten (x,y). Des Weiteren nehmen wir an, dass alle $x_i$ ohne Fehler sind und dass unsere $y_i$ gaußförmig um einen unbekannten wahren Wert $\\lambda_i$ (sprich $\\lambda_i$ entspricht dem Erwartungswert $\\mu_i$ unserer Gaußverteilung) mit einer bekannten Varianz $\\Delta y_i^2$ verteilt sind (Diese Annahme lässt sich mit dem zentralen Grenzwertsatz begründen, so lange der Fehler sich aus der Summe kleiner Fehler zusammensetzt). Die dazugehörige  **likelihood function** ist dann gegeben durch:\n",
    "\n",
    "$$ \\mathcal{L}(y_1 ... y_N; \\lambda_1 ... \\lambda_N, \\Delta y_1 ... \\Delta y_N)) = \\prod_{i = 1}^{N}\\frac{1}{\\sqrt{2 \\pi \\Delta y_i^2}} \\cdot \\exp \\bigg( \\frac{ -(y_i - \\lambda_i)^2}{2 \\cdot \\Delta y_i^2}\\bigg)$$\n",
    "\n",
    "Beziehungsweise die **log likelihood function** mit $\\lambda_i = \\lambda(x_i; \\phi)$ ergibt sich zu\n",
    "\n",
    "$$ \\log(\\mathcal{L}(y, \\theta)) \\approx -\\frac{1}{2} \\sum_{i = 1}^{N}\\bigg( \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}\\bigg)$$\n",
    "\n",
    "wobei die konstanten Terme, welche nicht von unserer Funktion $\\lambda(x_i; \\phi)$ abhängen, vernachlässigt worden sind. Durch den Faktor $-\\frac{1}{2}$ ist das Maximieren dieser **log likelihood function** gleich dem Minimieren von\n",
    "\n",
    "$$ \\chi(\\phi_1 ... \\phi_N)^2 = \\sum_{i = 1}^{N} \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}$$\n",
    "\n",
    "Diese Funktion ist unsere gesuchte **Methode der kleinsten Quadrate**. Mit ihrer Hilfe kann eine beliebige Funktion $\\lambda(x; \\phi)$, welche linear in ihren Parametern $\\phi$ ist, an unsere Messdaten $(x,y\\pm\\Delta y)$ gefittet werden. Dabei stellt der Fitprozess selbst lediglich ein Minimierungsproblem dar. Im Folgenden sind unsere Annahmen noch einmal grafisch in einem Beispiel dargestellt.\n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/LeastSquare.png\"  alt=\"{{ Least Square Beispiel }}\" width=100%>\n",
    "</figure>"
   ]
  },
  {
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   "source": [
    "Wie ein Algorithmus bei der Minimierung vorgeht, sprengt den Rahmen dieses Vorversuchs. Hier sei auf entsprechende Vorlesungen verwiesen. Aber um einen kleinen Einblick zu erhalten, kann man sich die Werte der Parameter und von $\\chi^2$ für jeden Schritt ausgeben lassen. Dazu wird der Parameter `verbose` auf 1 gesetzt.\n",
    "\n",
    "Man erkannt, dass für jeden Parameter zunächst separat geprüft wird, welche Änderung (größer oder kleiner) die Kostenfunktion minimiert. Danach beginnt die eigentliche Minimierung der Kostenfunktion durch den Algorithmus."
   ]
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   "id": "43bfd15e-7b68-4b70-bc06-0b23f89f7bff",
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      "(0.9, 10000.0, 1e-06) -> 99.20912665811522\n",
      "(0.9000900000000001, 10000.0, 1e-06) -> 99.19412063461034\n",
      "(0.89991, 10000.0, 1e-06) -> 99.22413838602546\n",
      "(0.9002604809700815, 10000.0, 1e-06) -> 99.16571136645308\n",
      "(0.8997395190299186, 10000.0, 1e-06) -> 99.25258973321158\n",
      "(0.9, 10001.0, 1e-06) -> 99.2081333982375\n",
      "(0.9, 9999.0, 1e-06) -> 99.21012010104333\n",
      "(0.9, 10010.0, 1e-06) -> 99.19920228362008\n",
      "(0.9, 9990.0, 1e-06) -> 99.21906933767059\n",
      "(0.9, 10000.0, 1.0001e-06) -> 99.2081333982375\n",
      "(0.9, 10000.0, 9.999e-07) -> 99.21012010104333\n",
      "(0.9, 10000.0, 1.001e-06) -> 99.19920228362008\n",
      "(0.9, 10000.0, 9.989999999999999e-07) -> 99.21906933767059\n",
      "(1.1367992341436675, 15426.65629293471, 1.5426656292934658e-06) -> 71.48428998018905\n",
      "(1.1639942960414291, 16049.877285679564, 1.6049877285679507e-06) -> 69.75101904460233\n",
      "(1.308096945474447, 19352.234036123315, 1.9352234036123227e-06) -> 64.0373348681763\n",
      "(1.377047580024234, 20932.354834379075, 2.093235483437897e-06) -> 65.47264288596953\n",
      "(1.3083067929414927, 19352.234036123315, 1.9352234036123227e-06) -> 64.06897571595725\n",
      "(1.3078870980074015, 19352.234036123315, 1.9352234036123227e-06) -> 64.00572838249478\n",
      "(1.308096945474447, 19363.537683275055, 1.9352234036123227e-06) -> 63.99858990110189\n",
      "(1.308096945474447, 19340.930388971574, 1.9352234036123227e-06) -> 64.0760877366588\n",
      "(1.308096945474447, 19352.234036123315, 1.9365250134806992e-06) -> 63.99272090590841\n",
      "(1.308096945474447, 19352.234036123315, 1.933921793743946e-06) -> 64.08195930724722\n",
      "(1.308096945474447, 19352.234036123315, 1.9374628097120974e-06) -> 63.96058355345421\n",
      "(1.308096945474447, 19352.234036123315, 1.932983997512548e-06) -> 64.11411719500667\n",
      "(1.4518988196469205, 28189.753065444456, 2.8189750163700463e-06) -> 61.272614820982845\n",
      "(1.385496103118641, 24108.893380587735, 2.4108891818768406e-06) -> 49.65617486041412\n",
      "(1.385672043336562, 24108.893380587735, 2.4108891818768406e-06) -> 49.694760759553645\n",
      "(1.3853201629007201, 24108.893380587735, 2.4108891818768406e-06) -> 49.61761439538809\n",
      "(1.385496103118641, 24122.984567537602, 2.4108891818768406e-06) -> 49.6271750967005\n",
      "(1.385496103118641, 24094.80219363787, 2.4108891818768406e-06) -> 49.6852350578246\n",
      "(1.385496103118641, 24117.03763372327, 2.4108891818768406e-06) -> 49.63940655944544\n",
      "(1.385496103118641, 24100.7491274522, 2.4108891818768406e-06) -> 49.67296334907033\n",
      "(1.385496103118641, 24108.893380587735, 2.4128655527857186e-06) -> 49.61551806057589\n",
      "(1.385496103118641, 24108.893380587735, 2.4089128109679626e-06) -> 49.69695054357015\n",
      "(1.385496103118641, 24108.893380587735, 2.411780041418529e-06) -> 49.63783388084468\n",
      "(1.385496103118641, 24108.893380587735, 2.409998322335152e-06) -> 49.67453999473487\n",
      "(1.3346958218375284, 26342.987535930857, 2.6342989994964907e-06) -> 32.40412806990936\n",
      "(1.218308580069807, 31461.464245752708, 3.146147591686242e-06) -> 14.072342058026457\n",
      "(1.2041974408796614, 32082.043754269307, 3.2082056542278777e-06) -> 13.53676656364805\n",
      "(1.1905385220654157, 32682.73552056781, 3.2682749389683696e-06) -> 13.309190968111414\n",
      "(1.1906296495547257, 32682.73552056781, 3.2682749389683696e-06) -> 13.321746128711856\n",
      "(1.1904473945761056, 32682.73552056781, 3.2682749389683696e-06) -> 13.296643836281426\n",
      "(1.1905385220654157, 32687.064556715202, 3.2682749389683696e-06) -> 13.31564880356511\n",
      "(1.1905385220654157, 32678.40648442042, 3.2682749389683696e-06) -> 13.302737182521517\n",
      "(1.1905385220654157, 32682.73552056781, 3.2687484177659625e-06) -> 13.316254288012424\n",
      "(1.1905385220654157, 32682.73552056781, 3.2678014601707767e-06) -> 13.30213249281902\n",
      "(0.9801502312575129, 30448.619847559406, 3.0448628816425382e-06) -> 6.96972301330329\n",
      "(1.0625849715773497, 31323.995300450377, 3.1324006189341594e-06) -> 2.723232319724203\n",
      "(1.0626278234687758, 31323.995300450377, 3.1324006189341594e-06) -> 2.723145418857497\n",
      "(1.0625421196859235, 31323.995300450377, 3.1324006189341594e-06) -> 2.723320943276277\n",
      "(1.0625849715773497, 31326.53248355612, 3.1324006189341594e-06) -> 2.7233762521216955\n",
      "(1.0625849715773497, 31321.458117344635, 3.1324006189341594e-06) -> 2.7230896436266336\n",
      "(1.0625849715773497, 31323.995300450377, 3.132687245408039e-06) -> 2.7233950126392372\n",
      "(1.0625849715773497, 31323.995300450377, 3.13211399246028e-06) -> 2.72307123013582\n",
      "(1.0663872573694309, 31176.616934344333, 3.117662764856898e-06) -> 2.707996462603649\n",
      "(1.0676346425311973, 31128.267705196715, 3.112827836211991e-06) -> 2.7070251240566323\n",
      "(1.0676780500361664, 31128.267705196715, 3.112827836211991e-06) -> 2.70705000293859\n",
      "(1.0675912350262282, 31128.267705196715, 3.112827836211991e-06) -> 2.707002005340193\n",
      "(1.0676346425311973, 31130.901765918446, 3.112827836211991e-06) -> 2.707043830842127\n",
      "(1.0676346425311973, 31125.633644474983, 3.112827836211991e-06) -> 2.7070077881609484\n",
      "(1.0676346425311973, 31128.267705196715, 3.113128792280756e-06) -> 2.7070466092241365\n",
      "(1.0676346425311973, 31128.267705196715, 3.112526880143226e-06) -> 2.7070054284929457\n",
      "(1.067212269933915, 31118.34694378787, 3.1118357598238063e-06) -> 2.706823247817995\n",
      "(1.067168761630552, 31117.325013151873, 3.1117335667347323e-06) -> 2.706821465977302\n",
      "(1.0672122600973335, 31117.325013151873, 3.1117335667347323e-06) -> 2.7068223416968538\n",
      "(1.0671252631637707, 31117.325013151873, 3.1117335667347323e-06) -> 2.706822357390249\n",
      "(1.067168761630552, 31119.94657401041, 3.1117335667347323e-06) -> 2.706822163448656\n",
      "(1.067168761630552, 31114.703452293335, 3.1117335667347323e-06) -> 2.7068221260943885\n",
      "(1.067168761630552, 31117.325013151873, 3.112032662687679e-06) -> 2.7068223708425214\n",
      "(1.067168761630552, 31117.325013151873, 3.1114344707817854e-06) -> 2.7068223282441966\n",
      "(1.067168761630552, 31117.325013151873, 3.1117335667347323e-06) -> 2.706821465977302\n",
      "(1.0672122600973335, 31117.325013151873, 3.1117335667347323e-06) -> 2.7068223416968538\n",
      "(1.0671252631637707, 31117.325013151873, 3.1117335667347323e-06) -> 2.706822357390249\n",
      "(1.067168761630552, 31119.94657401041, 3.1117335667347323e-06) -> 2.706822163448656\n",
      "(1.067168761630552, 31114.703452293335, 3.1117335667347323e-06) -> 2.7068221260943885\n",
      "(1.067168761630552, 31117.325013151873, 3.112032662687679e-06) -> 2.7068223708425214\n",
      "(1.067168761630552, 31117.325013151873, 3.1114344707817854e-06) -> 2.7068223282441966\n",
      "(1.0671774613239084, 31117.325013151873, 3.1117335667347323e-06) -> 2.706821499750613\n",
      "(1.0671600619371957, 31117.325013151873, 3.1117335667347323e-06) -> 2.706821502889292\n",
      "(1.067168761630552, 31117.84932532358, 3.1117335667347323e-06) -> 2.7068214968699196\n",
      "(1.067168761630552, 31116.800700980166, 3.1117335667347323e-06) -> 2.7068214893882208\n",
      "(1.067168761630552, 31117.325013151873, 3.1117933859253217e-06) -> 2.7068215055878295\n",
      "(1.067168761630552, 31117.325013151873, 3.111673747544143e-06) -> 2.7068214970520583\n",
      "(1.0672122600973335, 31119.94657401041, 3.1117335667347323e-06) -> 2.70682365283658\n",
      "(1.0672122600973335, 31117.325013151873, 3.112032662687679e-06) -> 2.7068239467067996\n",
      "(1.067168761630552, 31119.94657401041, 3.112032662687679e-06) -> 2.7068246172709194\n"
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 2.707 (χ²/ndof = 0.4) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 87 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.18e-10 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
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       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#FFF79A;color:black\"> Covariance FORCED pos. def. </td>\n",
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       "        <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",
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       "        <th> 0 </th>\n",
       "        <td> I0 </td>\n",
       "        <td> 1.07 </td>\n",
       "        <td> 0.05 </td>\n",
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       "        <th> 1 </th>\n",
       "        <td> R </td>\n",
       "        <td> 0.03e6 </td>\n",
       "        <td> 0.05e6 </td>\n",
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       "   <rect x=\"25.903365\" y=\"3.00024\" width=\"331.096395\" height=\"265.321395\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 2.707 (χ²/ndof = 0.4)      │              Nfcn = 87               │\n",
       "│ EDM = 2.18e-10 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │     Covariance FORCED pos. def.      │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ I0   │   1.07    │   0.05    │            │            │         │         │       │\n",
       "│ 1 │ R    │  0.03e6   │  0.05e6   │            │            │         │         │       │\n",
       "│ 2 │ C    │   3e-6    │   5e-6    │            │            │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌────┬───────────────────────────────────────────────────────┐\n",
       "│    │                I0                 R                 C │\n",
       "├────┼───────────────────────────────────────────────────────┤\n",
       "│ I0 │           0.00253          -34.3309         -3.459e-9 │\n",
       "│  R │          -34.3309          2.25e+09 -224.592785048e-3 │\n",
       "│  C │         -3.459e-9 -224.592785048e-3          2.25e-11 │\n",
       "└────┴───────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 500,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls = cost.LeastSquares(data_frame['time'], data_frame['current'], data_frame['delta_current'], discharge_current, verbose=1)\n",
    "\n",
    "mi = Minuit(ls, I0=0.9, R=10*10**3, C=10**-6)\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c664e4f0-0226-4be0-91f4-7c28aee16a4a",
   "metadata": {},
   "source": [
    "__Zur Erinnerung__: die Methode der kleinsten Quadrate berücksichtigt nur Fehler in `y` aber nicht in `x`. Hierfür sind komplexere Methoden notwendig, die wir hier nicht betrachten wollen.\n",
    "Ebenfalls wichtig ist, die Statusmeldungen von `iminuit` zu prüfen, d.h. eine <span style=\"color:yellow\"> gelbe </span> Box zeigt an, das man sich Gedanken über das Ergebnis machen sollte (in unserem Fall, dass die Variablen $R$ und $C$ korreliert sind) und eine ,<span style=\"color:DarkOrchid\"> violette </span> Box, dass der Fit nicht konvergiert ist und das Ergebnis nicht verwendet werden kann."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb3aeee8",
   "metadata": {},
   "source": [
    "***\n",
    "--- Split Notebook here ---\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5064e2e2",
   "metadata": {},
   "source": [
    "# Fortgeschrittenes Beispiel\n",
    "In diesem Abschnitt wollen wir uns mit einem komplexeren Beispiel beschäftigen, um weitere Methoden von `iminuit` kennzulernen.\n",
    "Hierzu betrachten wir ein Zählexperiment, z.B. ein Teilchendetektor, bei dem ein Energiespektrum aufgenommen wird. Für jedes Energieintervall (Bin) wird die Anzahl der registrierten Ereignisse bestimmt. Hierbei können wir annehmen, dass die Verteilung der gemessenen Anzahl durch eine Poisson-Verteilung beschrieben wird. Dann entspricht der Fehler in jedem Bin gerade $\\sqrt n$. \n",
    "Dieses Spektrum soll aus zwei gauß-förmigen Peaks über einem exponentiellen Untergrund bestehen und wird mit Hilfe eines Zufallszahlengenerator \"erzeugt\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "id": "143a2a23-0a62-439f-9d28-9f555ae85589",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of counts per bin')"
      ]
     },
     "execution_count": 501,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnd_bkd = np.random.exponential(39.7, 5000)\n",
    "rnd_bkd += 40\n",
    "\n",
    "peak1 = np.random.normal(53.3, 2.1, 5000)\n",
    "peak2 = np.random.normal(60.5, 2.78, 12000)\n",
    "data = np.concatenate([rnd_bkd, peak1, peak2])\n",
    "\n",
    "entries, edges = np.histogram(data, bins=120, range=(40, 80))\n",
    "center = edges[:-1] + np.diff(edges)/2\n",
    "\n",
    "plt.errorbar(center, entries, np.sqrt(entries), ls='', marker='.')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Number of counts per bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b582615c-9251-409d-bcfc-d19fd579e161",
   "metadata": {},
   "source": [
    "Zunächst wollen wir das Fitmodel in der Form\n",
    "\n",
    "$$f(x) = A_1 \\cdot \\exp \\bigg\\{\\frac{-(x - \\mu_1)^2}{2 \\cdot \\sigma_1^2}\\bigg\\} + A_2 \\cdot \\exp \\bigg\\{\\frac{-(x - \\mu_2)^2}{2 \\cdot \\sigma_2^2}\\bigg\\} + A_3 \\exp\\{-x/\\tau\\}$$\n",
    "\n",
    "definieren. Hier lohnt es sich, erst Funktionen für die einzelnen Komponenten zu definieren und dann das Gesamtmodel. Hierdurch lassen sich später die einzelnen Komponenten besser darstellen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "id": "f84d7527-c0d2-475d-966d-5363a8e09369",
   "metadata": {},
   "outputs": [],
   "source": [
    "def peak(x, A, mu, sigma):\n",
    "    return A*np.exp(-(x-mu)**2/(2*sigma**2))\n",
    "\n",
    "def bkg(x, A, tau):\n",
    "    return A*np.exp(-x/tau)\n",
    "\n",
    "def fit_model(x, A_p1, A_p2, mu_p1, mu_p2, sigma_p1, sigma_p2, A_bkg, tau_bkg):\n",
    "    return peak(x, A_p1, mu_p1, sigma_p1) + peak(x, A_p2, mu_p2, sigma_p2) + bkg(x, A_bkg, tau_bkg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32014861-316c-4692-9d52-48f2fb71321c",
   "metadata": {},
   "source": [
    "Nun wollen wir wieder die Kostenfunktion und die Minimierungsfunktion definieren. Startwerte können wir anhand unseres Plots ablesen, lediglich $\\tau$ lässt sich auf diese Weise nicht gut bestimmen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "id": "a31901cf-a0ce-4db8-a072-a661fbbb7296",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = cost.LeastSquares(center, entries, np.sqrt(entries), fit_model)\n",
    "\n",
    "mi = Minuit(ls, \n",
    "            A_p1 = 400, \n",
    "            A_p2 = 700,\n",
    "            mu_p1 = 54,\n",
    "            mu_p2 = 60,\n",
    "            sigma_p1 = 2,\n",
    "            sigma_p2 = 2,\n",
    "            A_bkg = 100,\n",
    "            tau_bkg = 10, \n",
    "           )\n",
    "mi.limits['tau_bkg'] = (0, None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "id": "1e69a046-770f-4c38-9b91-0176bb0686a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x268b8627fd0>"
      ]
     },
     "execution_count": 504,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(center, entries, np.sqrt(entries), ls='', marker='.')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Number of counts per bin')\n",
    "\n",
    "x = np.arange(40, 80, 0.1)\n",
    "plt.plot(x, fit_model(x, *mi.values), color='k', label='Initial guess')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89f755f4-b780-43a6-a923-49662c4c701a",
   "metadata": {},
   "source": [
    "Unsere Startparameter sind bereits nicht schlecht, aber weichen noch stark von den Daten ab. Bei komplexeren Daten und Fitmodellen lohnt es sich, den Fit schrittweise durchzuführen. Bevor wir uns den beiden Peaks widmen, welche uns eigentlich interessieren, sollten wir versuchen, den Untergrund etwas besser zu beschreiben. Um den Untergrund besser fitten zu können, sollten wir erst den Fitbereich auf einen Energiebereich limitieren, in welchem der Untergrund dominiert. Dem Plot können wir entnehmen, dass dies für alle Werte unterhalb von 45 keV und oberhalb von 70 keV der Fall ist. Im Allgemeinen können wir Wertebereiche in Python mit Hilfe von „Masken“ selektieren. Eine Maske lässt sich wie folgt erstellen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 505,
   "id": "d53e8386-ea7f-43fa-b4fe-65229308a2ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "mask_outside_of_peaks = (center < 45) | (center >= 70)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84cef7a6-13a0-4ba8-ac40-eb86a54411dc",
   "metadata": {},
   "source": [
    "Die Maske hat hierbei die Selbe länge wie unseren Daten…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 506,
   "id": "d1d06116-d726-4163-b414-6ccde6a19027",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 120)"
      ]
     },
     "execution_count": 506,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(mask_outside_of_peaks), len(mask_outside_of_peaks)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80db0ae0-5cbd-4db9-b184-610d77bf1c58",
   "metadata": {},
   "source": [
    "… und beinhaltet Wahrheitswerte `True` und `False`, bzw. 1 und 0, mit welchen wir unsere Daten selektieren können:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 507,
   "id": "f24d19d8-3483-45b5-aee9-1d3f8755da22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "         True,  True,  True,  True,  True,  True, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "        False, False, False, False, False, False, False, False, False,\n",
       "         True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "         True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "         True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "         True,  True,  True]),\n",
       " array([40.16666667, 40.5       , 40.83333333, 41.16666667, 41.5       ,\n",
       "        41.83333333, 42.16666667, 42.5       , 42.83333333, 43.16666667,\n",
       "        43.5       , 43.83333333, 44.16666667, 44.5       , 44.83333333,\n",
       "        70.16666667, 70.5       , 70.83333333, 71.16666667, 71.5       ,\n",
       "        71.83333333, 72.16666667, 72.5       , 72.83333333, 73.16666667,\n",
       "        73.5       , 73.83333333, 74.16666667, 74.5       , 74.83333333,\n",
       "        75.16666667, 75.5       , 75.83333333, 76.16666667, 76.5       ,\n",
       "        76.83333333, 77.16666667, 77.5       , 77.83333333, 78.16666667,\n",
       "        78.5       , 78.83333333, 79.16666667, 79.5       , 79.83333333]))"
      ]
     },
     "execution_count": 507,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask_outside_of_peaks, center[mask_outside_of_peaks]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b5c07e7-1865-48f2-bd9e-0540661fd71e",
   "metadata": {},
   "source": [
    "Unsere Selektion können wir an unsere Kostenfunktion direkt übergeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 508,
   "id": "3034bb22-0b96-498d-9736-ed9bb2189460",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls.mask = (center < 45) | (center >= 70)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77a664fd-513e-4c89-ba52-945b6f68512f",
   "metadata": {},
   "source": [
    "Nun können wir nochmal unsere Funktion und Messwerte für den ausgewählten Bereich plotten…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 509,
   "id": "81232354-a7b8-4e2a-9ac0-159ce0a03da4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x268b8259630>"
      ]
     },
     "execution_count": 509,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(center[ls.mask], entries[ls.mask], np.sqrt(entries[ls.mask]), ls='', marker='.', label='Not masked')\n",
    "plt.errorbar(center[~ls.mask], entries[~ls.mask], np.sqrt(entries[~ls.mask]), ls='', marker='.', label='Masked')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Number of counts per bin')\n",
    "\n",
    "x = np.arange(40, 80, 0.1)\n",
    "plt.plot(x, fit_model(x, *mi.values), color='k', label='Initial guess')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec675b22",
   "metadata": {},
   "source": [
    "Außerdem müssen wir noch alle Fitparameter, welche nicht zum Untergrund beitragen, als konstant festhalten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 510,
   "id": "4a93a1c2-17df-46c2-b38e-9a509fe16fc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<FixedView A_p1=True A_p2=True mu_p1=True mu_p2=True sigma_p1=True sigma_p2=True A_bkg=False tau_bkg=False>\n"
     ]
    }
   ],
   "source": [
    "mi.fixed[:] = True\n",
    "mi.fixed[['tau_bkg', 'A_bkg']] = False\n",
    "print (mi.fixed)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5a8d247-5b71-42ae-9706-d16192374686",
   "metadata": {},
   "source": [
    "bevor wir die Minmierung starten und das Resultat darstellen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "id": "3e90c2ed-c282-47c2-b0fe-3063f9545639",
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 32.8 (χ²/ndof = 0.8) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 98 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.43e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 400 </td>\n",
       "        <td> 4 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
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       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> A_p2 </td>\n",
       "        <td> 700 </td>\n",
       "        <td> 7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
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       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu_p1 </td>\n",
       "        <td> 54.0 </td>\n",
       "        <td> 0.5 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> mu_p2 </td>\n",
       "        <td> 60.0 </td>\n",
       "        <td> 0.6 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
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       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 2.00 </td>\n",
       "        <td> 0.02 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.00 </td>\n",
       "        <td> 0.02 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
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       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 137 </td>\n",
       "        <td> 15 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
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       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.9 </td>\n",
       "        <td> 2.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
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       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
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       "        <th> A_p1 </th>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 32.8 (χ²/ndof = 0.8)       │              Nfcn = 98               │\n",
       "│ EDM = 4.43e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    400    │     4     │            │            │         │         │  yes  │\n",
       "│ 1 │ A_p2     │    700    │     7     │            │            │         │         │  yes  │\n",
       "│ 2 │ mu_p1    │   54.0    │    0.5    │            │            │         │         │  yes  │\n",
       "│ 3 │ mu_p2    │   60.0    │    0.6    │            │            │         │         │  yes  │\n",
       "│ 4 │ sigma_p1 │   2.00    │   0.02    │            │            │         │         │  yes  │\n",
       "│ 5 │ sigma_p2 │   2.00    │   0.02    │            │            │         │         │  yes  │\n",
       "│ 6 │ A_bkg    │    137    │    15     │            │            │         │         │       │\n",
       "│ 7 │ tau_bkg  │   34.9    │    2.3    │            │            │    0    │         │       │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2    A_bkg  tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │        0        0        0        0        0        0        0        0 │\n",
       "│     A_p2 │        0        0        0        0        0        0        0        0 │\n",
       "│    mu_p1 │        0        0        0        0        0        0        0        0 │\n",
       "│    mu_p2 │        0        0        0        0        0        0        0        0 │\n",
       "│ sigma_p1 │        0        0        0        0        0        0        0        0 │\n",
       "│ sigma_p2 │        0        0        0        0        0        0        0        0 │\n",
       "│    A_bkg │        0        0        0        0        0        0      229      -33 │\n",
       "│  tau_bkg │        0        0        0        0        0        0      -33     5.18 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 511,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.migrad()\n",
    "mi.hesse()"
   ]
  },
  {
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   "execution_count": 512,
   "id": "0b435af3-73ea-42de-9ab7-6a16ae9dbceb",
   "metadata": {},
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(center, entries, np.sqrt(entries), ls='', marker='.')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Number of counts per bin')\n",
    "\n",
    "x = np.arange(40, 80, 0.1)\n",
    "plt.plot(x, fit_model(x, *mi.values), color='k', label='Initial guess')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6def3e2b-5edf-48bb-99b8-2b7fdaae51c5",
   "metadata": {},
   "source": [
    "Das Resultat sieht bereits sehr gut aus. Nun können wir uns den eigentlichen Peaks widmen und starten im Folgenden mit dem kleineren der beiden. Zunächst sollten wir den maskierten Bereich entweder neu definieren oder komplett entfernen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 513,
   "id": "ebd77c40-6fcd-4881-bc1d-e3ca8ae0bf3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls.mask = None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7850ae53-ae2d-49aa-ac7b-dcef60a2dab7",
   "metadata": {},
   "source": [
    "Außerdem können wir dem Plot entnehmen, dass durch den höheren Untergrund unsere Anfangsstartwerte nicht mehr ganz so gut passen. Diese können wir wie folgt aktualisieren:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "id": "823e05a0-516c-4d30-8dc7-5381e0e2e617",
   "metadata": {},
   "outputs": [],
   "source": [
    "mi.values['A_p1'] = 700\n",
    "mi.values['sigma_p1'] = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8648bf00-901e-40dc-ada2-9a6b684e8f31",
   "metadata": {},
   "source": [
    "Nun sollten wir alle Parameter wieder festhalten und nur die Parameter des ersten Peaks freigeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "id": "3c83690c-103e-47ff-b18f-13ac763ee87d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 1296 (χ²/ndof = 11.1) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 177 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.92e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 348 </td>\n",
       "        <td> 7 </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> A_p2 </td>\n",
       "        <td> 700 </td>\n",
       "        <td> 7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 2 </th>\n",
       "        <td> mu_p1 </td>\n",
       "        <td> 53.51 </td>\n",
       "        <td> 0.04 </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> mu_p2 </td>\n",
       "        <td> 60.0 </td>\n",
       "        <td> 0.6 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 2.085 </td>\n",
       "        <td> 0.034 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.00 </td>\n",
       "        <td> 0.02 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 137 </td>\n",
       "        <td> 15 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.9 </td>\n",
       "        <td> 2.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
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       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 42.2 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0042 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -0.1247 <strong>(-0.558)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> A_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0042 <strong>(-0.016)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td> 0.00167 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 0.0004 <strong>(0.252)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
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       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -0.1247 <strong>(-0.558)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,212,212);color:black\"> 0.0004 <strong>(0.252)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td> 0.00118 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
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       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td> 0 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> A_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.0000 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> tau_bkg </th>\n",
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       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 1296 (χ²/ndof = 11.1)      │              Nfcn = 177              │\n",
       "│ EDM = 2.92e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    348    │     7     │            │            │         │         │       │\n",
       "│ 1 │ A_p2     │    700    │     7     │            │            │         │         │  yes  │\n",
       "│ 2 │ mu_p1    │   53.51   │   0.04    │            │            │         │         │       │\n",
       "│ 3 │ mu_p2    │   60.0    │    0.6    │            │            │         │         │  yes  │\n",
       "│ 4 │ sigma_p1 │   2.085   │   0.034   │            │            │         │         │       │\n",
       "│ 5 │ sigma_p2 │   2.00    │   0.02    │            │            │         │         │  yes  │\n",
       "│ 6 │ A_bkg    │    137    │    15     │            │            │         │         │  yes  │\n",
       "│ 7 │ tau_bkg  │   34.9    │    2.3    │            │            │    0    │         │  yes  │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2    A_bkg  tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │     42.2        0  -0.0042        0  -0.1247        0        0        0 │\n",
       "│     A_p2 │        0        0   0.0000        0   0.0000        0        0        0 │\n",
       "│    mu_p1 │  -0.0042   0.0000  0.00167   0.0000   0.0004   0.0000   0.0000   0.0000 │\n",
       "│    mu_p2 │        0        0   0.0000        0   0.0000        0        0        0 │\n",
       "│ sigma_p1 │  -0.1247   0.0000   0.0004   0.0000  0.00118   0.0000   0.0000   0.0000 │\n",
       "│ sigma_p2 │        0        0   0.0000        0   0.0000        0        0        0 │\n",
       "│    A_bkg │        0        0   0.0000        0   0.0000        0        0        0 │\n",
       "│  tau_bkg │        0        0   0.0000        0   0.0000        0        0        0 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 515,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p1', 'mu_p1', 'sigma_p1']] = False\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34df75bf-3750-4186-ae12-4f6bb9e49931",
   "metadata": {},
   "source": [
    "Jetzt wiederholen wir das ganze für den zweiten Peak…"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "id": "264a9891-423c-479a-8906-c048aac2fd2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 137 (χ²/ndof = 1.2) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 226 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.24e-06 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 348 </td>\n",
       "        <td> 7 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> A_p2 </td>\n",
       "        <td> 584 </td>\n",
       "        <td> 7 </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> mu_p1 </td>\n",
       "        <td> 53.51 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 3 </th>\n",
       "        <td> mu_p2 </td>\n",
       "        <td> 60.605 </td>\n",
       "        <td> 0.031 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 2.085 </td>\n",
       "        <td> 0.034 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.666 </td>\n",
       "        <td> 0.026 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 137 </td>\n",
       "        <td> 15 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.9 </td>\n",
       "        <td> 2.3 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td> yes </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> A_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 55.2 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.7e-3 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -110.5e-3 <strong>(-0.563)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0.7e-3 <strong>(0.003)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td> 0.000983 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.2e-3 <strong>(-0.210)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -110.5e-3 <strong>(-0.563)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.2e-3 <strong>(-0.210)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0.000697 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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       "    <tr>\n",
       "        <th> tau_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0e-3 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
       "        <td style=\"background-color:rgb(250,250,250);color:black\"> 0 </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 137 (χ²/ndof = 1.2)        │              Nfcn = 226              │\n",
       "│ EDM = 1.24e-06 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    348    │     7     │            │            │         │         │  yes  │\n",
       "│ 1 │ A_p2     │    584    │     7     │            │            │         │         │       │\n",
       "│ 2 │ mu_p1    │   53.51   │   0.04    │            │            │         │         │  yes  │\n",
       "│ 3 │ mu_p2    │  60.605   │   0.031   │            │            │         │         │       │\n",
       "│ 4 │ sigma_p1 │   2.085   │   0.034   │            │            │         │         │  yes  │\n",
       "│ 5 │ sigma_p2 │   2.666   │   0.026   │            │            │         │         │       │\n",
       "│ 6 │ A_bkg    │    137    │    15     │            │            │         │         │  yes  │\n",
       "│ 7 │ tau_bkg  │   34.9    │    2.3    │            │            │    0    │         │  yes  │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────────────┐\n",
       "│          │      A_p1      A_p2     mu_p1     mu_p2  sigma_p1  sigma_p2     A_bkg   tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │         0         0         0      0e-3         0         0         0         0 │\n",
       "│     A_p2 │         0      55.2         0    0.7e-3         0 -110.5e-3         0         0 │\n",
       "│    mu_p1 │         0         0         0      0e-3         0         0         0         0 │\n",
       "│    mu_p2 │      0e-3    0.7e-3      0e-3  0.000983      0e-3   -0.2e-3      0e-3      0e-3 │\n",
       "│ sigma_p1 │         0         0         0      0e-3         0         0         0         0 │\n",
       "│ sigma_p2 │         0 -110.5e-3         0   -0.2e-3         0  0.000697         0         0 │\n",
       "│    A_bkg │         0         0         0      0e-3         0         0         0         0 │\n",
       "│  tau_bkg │         0         0         0      0e-3         0         0         0         0 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 516,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p2', 'mu_p2', 'sigma_p2']] = False\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32d67543-870f-4bd9-bba4-2d01086c671a",
   "metadata": {},
   "source": [
    "Zum Schluss geben wir wieder alle Parameter frei und führen einen letzten Fit durch. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 517,
   "id": "72d43004-cd80-418a-996a-f1e7a7133ce9",
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 106.4 (χ²/ndof = 0.9) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 500 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 4.26e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 317 </td>\n",
       "        <td> 7 </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> A_p2 </td>\n",
       "        <td> 580 </td>\n",
       "        <td> 7 </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> mu_p1 </td>\n",
       "        <td> 53.24 </td>\n",
       "        <td> 0.07 </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> mu_p2 </td>\n",
       "        <td> 60.43 </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> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 1.99 </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> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.80 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 147 </td>\n",
       "        <td> 14 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.1 </td>\n",
       "        <td> 2.0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 51.5 </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td> 50.6 </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td> 0.00503 </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td> 0.00276 </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.624)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0515 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.624)</strong> </td>\n",
       "        <td> 0.00297 </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1413 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0156 <strong>(0.142)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td> 0.00171 </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0818 <strong>(0.137)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0143 <strong>(-0.172)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_bkg </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0515 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1413 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0818 <strong>(0.137)</strong> </td>\n",
       "        <td> 209 </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0156 <strong>(0.142)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0143 <strong>(-0.172)</strong> </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
       "        <td> 4.03 </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 106.4 (χ²/ndof = 0.9)      │              Nfcn = 500              │\n",
       "│ EDM = 4.26e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    317    │     7     │            │            │         │         │       │\n",
       "│ 1 │ A_p2     │    580    │     7     │            │            │         │         │       │\n",
       "│ 2 │ mu_p1    │   53.24   │   0.07    │            │            │         │         │       │\n",
       "│ 3 │ mu_p2    │   60.43   │   0.05    │            │            │         │         │       │\n",
       "│ 4 │ sigma_p1 │   1.99    │   0.05    │            │            │         │         │       │\n",
       "│ 5 │ sigma_p2 │   2.80    │   0.04    │            │            │         │         │       │\n",
       "│ 6 │ A_bkg    │    147    │    14     │            │            │         │         │       │\n",
       "│ 7 │ tau_bkg  │   34.1    │    2.0    │            │            │    0    │         │       │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2    A_bkg  tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │     51.5       10    0.103   0.1006  -0.0808  -0.0969       -0        0 │\n",
       "│     A_p2 │       10     50.6    0.026   0.0402  -0.0047  -0.1329       -0        0 │\n",
       "│    mu_p1 │    0.103    0.026  0.00503   0.0027   0.0025  -0.0020   -0.057    0.010 │\n",
       "│    mu_p2 │   0.1006   0.0402   0.0027  0.00276   0.0018  -0.0015  -0.0515   0.0062 │\n",
       "│ sigma_p1 │  -0.0808  -0.0047   0.0025   0.0018  0.00297  -0.0012  -0.1413   0.0156 │\n",
       "│ sigma_p2 │  -0.0969  -0.1329  -0.0020  -0.0015  -0.0012  0.00171   0.0818  -0.0143 │\n",
       "│    A_bkg │       -0       -0   -0.057  -0.0515  -0.1413   0.0818      209      -28 │\n",
       "│  tau_bkg │        0        0    0.010   0.0062   0.0156  -0.0143      -28     4.03 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 517,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi.fixed[:] = False\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 518,
   "id": "067fbf6f-14c4-4a46-afb3-71753d06af23",
   "metadata": {},
   "outputs": [
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(center, entries, np.sqrt(entries), ls='', marker='.')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Number of counts per bin')\n",
    "\n",
    "x = np.arange(40, 80, 0.1)\n",
    "plt.plot(x, fit_model(x, *mi.values), color='k', label='Best fit')\n",
    "plt.plot(x, peak(x, *mi.values['A_p1', 'mu_p1', 'sigma_p1']), color='gray', ls='--', label='Peak 1')\n",
    "plt.plot(x, peak(x, *mi.values['A_p2', 'mu_p2', 'sigma_p2']), color='gray', ls='-.', label='Peak 2')\n",
    "plt.plot(x, bkg(x, *mi.values['A_bkg', 'tau_bkg']), color='gray', label='Background')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ef19633-0947-4568-b537-a1c69e42b7c2",
   "metadata": {},
   "source": [
    "Das Ergebnis sieht sehr gut aus. Alle Kacheln sind grün und die Daten scheinen durch die Funktion gut beschrieben zu werden. Natürlich können wir das gesamte Fitverfahren auch etwas kompakter in einer Zelle darstellen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 519,
   "id": "2311f135-8410-4f35-8d58-b9bcef0fed53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 106.4 (χ²/ndof = 0.9) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 530 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.61e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 317 </td>\n",
       "        <td> 7 </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> A_p2 </td>\n",
       "        <td> 580 </td>\n",
       "        <td> 7 </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> mu_p1 </td>\n",
       "        <td> 53.24 </td>\n",
       "        <td> 0.07 </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> mu_p2 </td>\n",
       "        <td> 60.43 </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> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 1.99 </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> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.80 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 147 </td>\n",
       "        <td> 14 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.1 </td>\n",
       "        <td> 2.0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 51.5 </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td> 50.6 </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td> 0.00503 </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td> 0.00276 </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.623)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0513 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.623)</strong> </td>\n",
       "        <td> 0.00297 </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1409 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0155 <strong>(0.142)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td> 0.00171 </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0816 <strong>(0.137)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0142 <strong>(-0.172)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_bkg </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0513 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1409 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0816 <strong>(0.137)</strong> </td>\n",
       "        <td> 209 </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0155 <strong>(0.142)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0142 <strong>(-0.172)</strong> </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 106.4 (χ²/ndof = 0.9)      │              Nfcn = 530              │\n",
       "│ EDM = 1.61e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    317    │     7     │            │            │         │         │       │\n",
       "│ 1 │ A_p2     │    580    │     7     │            │            │         │         │       │\n",
       "│ 2 │ mu_p1    │   53.24   │   0.07    │            │            │         │         │       │\n",
       "│ 3 │ mu_p2    │   60.43   │   0.05    │            │            │         │         │       │\n",
       "│ 4 │ sigma_p1 │   1.99    │   0.05    │            │            │         │         │       │\n",
       "│ 5 │ sigma_p2 │   2.80    │   0.04    │            │            │         │         │       │\n",
       "│ 6 │ A_bkg    │    147    │    14     │            │            │         │         │       │\n",
       "│ 7 │ tau_bkg  │   34.1    │    2.0    │            │            │    0    │         │       │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2    A_bkg  tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │     51.5       10    0.103   0.1006  -0.0808  -0.0969       -0        0 │\n",
       "│     A_p2 │       10     50.6    0.026   0.0402  -0.0047  -0.1329       -0        0 │\n",
       "│    mu_p1 │    0.103    0.026  0.00503   0.0027   0.0025  -0.0020   -0.057    0.010 │\n",
       "│    mu_p2 │   0.1006   0.0402   0.0027  0.00276   0.0018  -0.0015  -0.0513   0.0062 │\n",
       "│ sigma_p1 │  -0.0808  -0.0047   0.0025   0.0018  0.00297  -0.0012  -0.1409   0.0155 │\n",
       "│ sigma_p2 │  -0.0969  -0.1329  -0.0020  -0.0015  -0.0012  0.00171   0.0816  -0.0142 │\n",
       "│    A_bkg │       -0       -0   -0.057  -0.0513  -0.1409   0.0816      209      -28 │\n",
       "│  tau_bkg │        0        0    0.010   0.0062   0.0155  -0.0142      -28     4.01 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 519,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls = cost.LeastSquares(center, entries, np.sqrt(entries), fit_model)\n",
    "\n",
    "mi = Minuit(ls, \n",
    "            A_p1 = 800, \n",
    "            A_p2 = 1400,\n",
    "            mu_p1 = 54,\n",
    "            mu_p2 = 60,\n",
    "            sigma_p1 = 2,\n",
    "            sigma_p2 = 2,\n",
    "            A_bkg = 100,\n",
    "            tau_bkg = 10, \n",
    "           )\n",
    "mi.limits['tau_bkg'] = (0, None)\n",
    "mi.fixed[:] = True\n",
    "ls.mask = (center < 45) | (center >= 70)\n",
    "mi.fixed[['tau_bkg', 'A_bkg']] = False\n",
    "mi.migrad()\n",
    "ls.mask = None\n",
    "mi.values['A_p1'] = 700\n",
    "mi.values['sigma_p1'] = 3\n",
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p1', 'mu_p1', 'sigma_p1']] = False\n",
    "mi.migrad()\n",
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p2', 'mu_p2', 'sigma_p2']] = False\n",
    "mi.migrad()\n",
    "mi.fixed[:] = False\n",
    "mi.migrad()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2d4c8e9-da2c-489e-9b2f-de24f042c341",
   "metadata": {},
   "source": [
    " # Wann fittet ein Fit?\n",
    "Nach dem wir nun unser Model an unsere Daten angepasst haben, stellt sich die Frage: „Spiegelt unser Model unsere Daten gut wider?“.  Um diese Frage beantworten zu können, gibt es verschiedene Möglichkeiten, welche wir im Folgenden etwas näher betrachten wollen. \n",
    "## Fit Residual: \n",
    "Schauen wir uns zunächst noch einmal an, wie das Chi-Quadrat definiert ist:\n",
    "$$ \\chi^2 = \\sum_i \\frac{(y_i - \\lambda_i)^2}{\\Delta y_i^2} $$\n",
    "Wir minimieren den Abstand zwischen einem Messwert und unserem Model und gewichten diesen mit den Unsicherheiten unserer Messwerte. Fitresiduen spiegeln genau dies wider. Sie sind definiert als \n",
    "$$ \\frac{(y_i - \\lambda_i)}{\\Delta y_i} $$\n",
    "Für unseren Fit sehen sie wie folgt aus.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "id": "30cafddc-ea17-4158-82cc-f132dee2c8de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Residuals [$\\\\sigma$]')"
      ]
     },
     "execution_count": 520,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals = (entries - fit_model(center, *mi.values))/np.sqrt(entries)\n",
    "\n",
    "plt.plot(center, residuals, ls='', marker='.')\n",
    "plt.xlabel('Energy [keV]')\n",
    "plt.ylabel('Residuals [$\\sigma$]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0ef61ca-afc5-472d-8e8e-b4726ef2a3dd",
   "metadata": {},
   "source": [
    "Als einzelner Plot sind sie noch nicht sehr informativ. Hilfreicher ist es bereits, wenn wir die Residuen zusammen mit unseren Daten und Fitmodel darstellen. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "id": "d9fbe83b-3146-4d72-89a4-084c29752e24",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Matthias\\AppData\\Local\\Temp\\ipykernel_67644\\53208542.py:7: UserWarning: The figure layout has changed to tight\n",
      "  fig_fit.tight_layout()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_fit = plt.figure(constrained_layout=True)\n",
    "gs = fig_fit.add_gridspec(5, 5, hspace=0)\n",
    "\n",
    "\n",
    "main_axis = fig_fit.add_subplot(gs[:4, :])\n",
    "res_axis = fig_fit.add_subplot(gs[4:, :], sharex=main_axis)\n",
    "fig_fit.tight_layout()\n",
    "\n",
    "\n",
    "main_axis.errorbar(center, entries, np.sqrt(entries), ls='', marker='.', color='k')\n",
    "\n",
    "main_axis.plot(x, peak(x, *mi.values['A_p1', 'mu_p1', 'sigma_p1']), color='gray', ls='--')\n",
    "main_axis.plot(x, peak(x, *mi.values['A_p2', 'mu_p2', 'sigma_p2']), color='gray', ls='-.')\n",
    "main_axis.plot(x, bkg(x, *mi.values['A_bkg', 'tau_bkg']), color='gray')\n",
    "\n",
    "x = np.arange(40, 80, 0.1)\n",
    "main_axis.plot(x, fit_model(x, *mi.values), color='purple', label='Best fit')\n",
    "main_axis.legend()\n",
    "main_axis.set_ylabel('Number of entries per bin')\n",
    "main_axis.xaxis.set_tick_params(direction='inout')\n",
    "main_axis.tick_params(axis='x', labelcolor=(0, 0, 0, 0))\n",
    "main_axis.set_xlim(40, 80)\n",
    "\n",
    "res_axis.set_xlabel('Energy [keV]')\n",
    "res_axis.set_ylabel('Res [$\\sigma$]')\n",
    "res_axis.set_ylim(-3, 3)\n",
    "res_axis.set_yticks([-2, 0,  2])\n",
    "res_axis.fill_between((40, 80), -1, 1, alpha=0.3, color='purple')\n",
    "res_axis.fill_between((40, 80), -2, 2, alpha=0.3, color='purple')\n",
    "res_axis.axhline(0, color='purple')\n",
    "res_axis.set_xlim(40, 80)\n",
    "res_axis.plot(center, \n",
    "              residuals,\n",
    "              color='k', marker='.', ls=''\n",
    "             )\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbe65a21-572e-4618-bcd8-78f13e945e8a",
   "metadata": {},
   "source": [
    "Sofern unser Fitmodel unsere Daten gut beschreibt, erwarten wir, dass die Residuen sich Gaußförmig zufällig um den Wert 0 herum verteilen. Dies folgt direkt aus der Annahme, dass sich die Unsicherheiten unserer Messwerte durch eine Gaußverteilung darstellen lassen. Dies können wir direkt überprüfen, sofern wir unsere Residuen in ein Histogramm eintragen. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 522,
   "id": "05e24224-66f7-45ed-99c6-f6d257e2c779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(residuals, bins=10, range=(-3, 3), histtype='step')\n",
    "plt.xlabel('Residual [$\\sigma$]')\n",
    "plt.ylabel('#Entries per bin')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24ce04cc-5234-4326-9a28-7624b9c7d23e",
   "metadata": {},
   "source": [
    "Bzw. den Anteil an Residuen berechnen, welcher innerhalb der 1 $\\sigma$ Umgebung liegt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "id": "39009321-41f4-49f4-820a-717be277b1b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6833333333333333"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.abs(residuals) < 1)/len(residuals)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08579cdf-3b28-4ea2-9c61-6ae62974af51",
   "metadata": {},
   "source": [
    "Zeigen unsere Residuen eine Struktur oder ein systematisches Verhalten, deutet dies auf einen ungenauen Fit oder ein falsches Fitmodel hin. Dies ist im Folgenden gezeigt. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "id": "850870af-e546-4d95-b9de-8a4e7b61c241",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Matthias\\AppData\\Local\\Temp\\ipykernel_67644\\2321973434.py:8: UserWarning: The figure layout has changed to tight\n",
      "  fig_fit.tight_layout()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pseudo_data = np.random.normal(0, 2, 5000)\n",
    "\n",
    "fig_fit = plt.figure(constrained_layout=True)\n",
    "gs = fig_fit.add_gridspec(5, 5, hspace=0)\n",
    "\n",
    "main_axis = fig_fit.add_subplot(gs[:4, :])\n",
    "res_axis = fig_fit.add_subplot(gs[4:, :], sharex=main_axis)\n",
    "fig_fit.tight_layout()\n",
    "\n",
    "entries1, edges1, _ = main_axis.hist(pseudo_data, bins=25, range=(-5,5), histtype='step', color='k')\n",
    "center1 = edges1[:-1] + np.diff(edges1)/2\n",
    "\n",
    "residuals1 = (entries1 - peak(center1, 400, 0.2, 2))/np.sqrt(entries1)\n",
    "\n",
    "x = np.arange(-5, 5, 0.1)\n",
    "\n",
    "main_axis.plot(x, peak(x, 400, 0.2, 2), color='purple')\n",
    "main_axis.set_ylabel('Number of entries per bin')\n",
    "main_axis.xaxis.set_tick_params(direction='inout')\n",
    "main_axis.tick_params(axis='x', labelcolor=(0, 0, 0, 0))\n",
    "main_axis.set_xlim(-5, 5)\n",
    "\n",
    "res_axis.set_xlabel('Energy [keV]')\n",
    "res_axis.set_ylabel('Res [$\\sigma$]')\n",
    "res_axis.set_ylim(-3, 3)\n",
    "res_axis.set_yticks([-2, 0,  2])\n",
    "res_axis.fill_between((-5, 5), -1, 1, alpha=0.3, color='purple')\n",
    "res_axis.fill_between((-5, 5), -2, 2, alpha=0.3, color='purple')\n",
    "res_axis.axhline(0, color='purple')\n",
    "res_axis.set_xlim(-5, 5)\n",
    "res_axis.plot(center1, \n",
    "              residuals1,\n",
    "              color='k', marker='.', ls=''\n",
    "             )\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e95a88-0742-4221-a716-17dacfc02823",
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   "source": [
    "Zusätzlich zu den Fit-Residuen bietet das $\\chi^2$ selbst einen Weg, um die „goodness-of-fit“ unseres Model bestimmen zu können ...\n",
    "\n",
    "### $\\chi^2$:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe1789cf-7ed3-4db3-a0ae-9e563a9dc85e",
   "metadata": {},
   "source": [
    "Wie gut fittet unsere obige Funktion unsere Messdaten? Sehr gut? Gut? Befriedigend? Oder doch eher schlecht?   Wäre es nicht gut, ein Maß für die Güte des Fits zu haben? Wie könnte ein solches Maß aussehen?\n",
    "\n",
    "Sie haben das entscheidende Kriterium bereits kennengelernt: bei der Methode der kleinsten Quadrate geht es darum, das  $\\chi^2$ zu minimieren. Gucken wir uns hierzu erst noch einmal an, wie sich das $\\chi^2$ berechnet:\n",
    "\n",
    "$$ \\chi(\\phi_1 ... \\phi_N)^2 = \\sum_{i = 1}^{N} \\frac{ (y_i - \\lambda(x_i; \\phi))^2}{\\Delta y_i^2}$$\n",
    "\n",
    "Bei der Minimierung werden dabei Werte mit geringerer Unsicherheit bevorzugt, d.h. stärker gewichtet (s. Bild unten).\n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/LeastSquare.png\"  alt=\"{{ Least Square Beispiel }}\" width=80%>\n",
    "</figure>\n",
    "\n",
    "Damit man für einen gegebenen Datensatz nicht hunderte von verschiedenen Funktionen durchprobieren muss, gibt es für das $\\chi^2$ eine allgemeine Faustregel, welche den berechneten $\\chi^2$-Wert mit der Anzahl unserer Freiheitsgrade vergleicht. Die Anzahl an Freiheitsgrade ist gemeinhin gegeben als *Anzahl der Messwerte - Anzahl der Funktionsparameter* ($m - n$).\n",
    "\n",
    "1. Sofern  $\\chi^2/\\text{ndof} >> 1$: sollte die Hypothese bzw. die Fitfunktion angezweifelt werden. Sie beschreibt in diesem Fall die Messdaten nur unzureichend. (Bzw. sollte $\\chi^2/\\text{ndof} > 1$ kann dies auch bedeuten, dass die Unsicherheiten unterschätzt sind)\n",
    "2. Sofern $\\chi^2/\\text{ndof} \\approx 1$: beschreibt die Hypothese bzw. die Fitfunktion die Daten wie erwartet und wird nicht abgelehnt. \n",
    "3. Falls $\\chi^2/\\text{ndof} << 1$ beschreibt die Hypothese bzw. die Fitfunktion die Daten wesentlich besser als erwartet. In diesem Fall heißt das nicht automatisch, dass unsere Hypothese falsch ist, aber man sollte überprüfen, ob die gemessenen Fehler nicht überschätzt worden sind (oder eine Korrelation zwischen den Messfehlern vorliegt).  \n",
    "\n",
    "Sofern Sie eine Arbeit schreiben und Ihre **Goodness-of-the-Fit** ($\\chi^2/\\text{ndof}$) angeben wollen, so geben Sie immer beides an, das $\\chi^2$ und die Anzahl an Freiheitsgraden *ndof*. Beide Werte getrennt haben einen größeren Informationsgehalt als der resultierende Quotient (Genaueres lernen Sie z.B. in der Vorlesung *Statistik, Datenanalyse und Simulationen* im Master).\n",
    "\n",
    "Sehen wir uns hierzu nochmal unseren Doppelpeakfit etwas genauer an. `iminuit` berechnet hier für uns bereits das reduzierete $\\chi^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 525,
   "id": "fa85a19a-f066-4567-abb0-6283ae1bc90b",
   "metadata": {},
   "outputs": [
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 106.4 (χ²/ndof = 0.9) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 530 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 1.61e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 317 </td>\n",
       "        <td> 7 </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> A_p2 </td>\n",
       "        <td> 580 </td>\n",
       "        <td> 7 </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> mu_p1 </td>\n",
       "        <td> 53.24 </td>\n",
       "        <td> 0.07 </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> mu_p2 </td>\n",
       "        <td> 60.43 </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> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 1.99 </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> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.80 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> A_bkg </td>\n",
       "        <td> 147 </td>\n",
       "        <td> 14 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 7 </th>\n",
       "        <td> tau_bkg </td>\n",
       "        <td> 34.1 </td>\n",
       "        <td> 2.0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table><table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> A_bkg </th>\n",
       "        <th> tau_bkg </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 51.5 </td>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,227,227);color:black\"> 10 <strong>(0.153)</strong> </td>\n",
       "        <td> 50.6 </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,220,220);color:black\"> 0.103 <strong>(0.202)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,242,242);color:black\"> 0.026 <strong>(0.052)</strong> </td>\n",
       "        <td> 0.00503 </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,210,210);color:black\"> 0.1006 <strong>(0.267)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,234,234);color:black\"> 0.0402 <strong>(0.108)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,142,142);color:black\"> 0.0027 <strong>(0.720)</strong> </td>\n",
       "        <td> 0.00276 </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.623)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0513 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(223,223,250);color:black\"> -0.0808 <strong>(-0.207)</strong> </td>\n",
       "        <td style=\"background-color:rgb(248,248,250);color:black\"> -0.0047 <strong>(-0.012)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,151,151);color:black\"> 0.0025 <strong>(0.659)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,156,156);color:black\"> 0.0018 <strong>(0.623)</strong> </td>\n",
       "        <td> 0.00297 </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1409 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0155 <strong>(0.142)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(208,208,250);color:black\"> -0.0969 <strong>(-0.327)</strong> </td>\n",
       "        <td style=\"background-color:rgb(191,191,250);color:black\"> -0.1329 <strong>(-0.452)</strong> </td>\n",
       "        <td style=\"background-color:rgb(163,163,250);color:black\"> -0.0020 <strong>(-0.666)</strong> </td>\n",
       "        <td style=\"background-color:rgb(162,162,250);color:black\"> -0.0015 <strong>(-0.680)</strong> </td>\n",
       "        <td style=\"background-color:rgb(183,183,250);color:black\"> -0.0012 <strong>(-0.518)</strong> </td>\n",
       "        <td> 0.00171 </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0816 <strong>(0.137)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0142 <strong>(-0.172)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_bkg </th>\n",
       "        <td style=\"background-color:rgb(246,246,250);color:black\"> -0 <strong>(-0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(247,247,250);color:black\"> -0 <strong>(-0.025)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.057 <strong>(-0.055)</strong> </td>\n",
       "        <td style=\"background-color:rgb(241,241,250);color:black\"> -0.0513 <strong>(-0.068)</strong> </td>\n",
       "        <td style=\"background-color:rgb(227,227,250);color:black\"> -0.1409 <strong>(-0.179)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0816 <strong>(0.137)</strong> </td>\n",
       "        <td> 209 </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> tau_bkg </th>\n",
       "        <td style=\"background-color:rgb(250,245,245);color:black\"> 0 <strong>(0.031)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0 <strong>(0.021)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,239,239);color:black\"> 0.010 <strong>(0.072)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,241,241);color:black\"> 0.0062 <strong>(0.059)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,229,229);color:black\"> 0.0155 <strong>(0.142)</strong> </td>\n",
       "        <td style=\"background-color:rgb(228,228,250);color:black\"> -0.0142 <strong>(-0.172)</strong> </td>\n",
       "        <td style=\"background-color:rgb(125,125,250);color:black\"> -28 <strong>(-0.965)</strong> </td>\n",
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       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 106.4 (χ²/ndof = 0.9)      │              Nfcn = 530              │\n",
       "│ EDM = 1.61e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    317    │     7     │            │            │         │         │       │\n",
       "│ 1 │ A_p2     │    580    │     7     │            │            │         │         │       │\n",
       "│ 2 │ mu_p1    │   53.24   │   0.07    │            │            │         │         │       │\n",
       "│ 3 │ mu_p2    │   60.43   │   0.05    │            │            │         │         │       │\n",
       "│ 4 │ sigma_p1 │   1.99    │   0.05    │            │            │         │         │       │\n",
       "│ 5 │ sigma_p2 │   2.80    │   0.04    │            │            │         │         │       │\n",
       "│ 6 │ A_bkg    │    147    │    14     │            │            │         │         │       │\n",
       "│ 7 │ tau_bkg  │   34.1    │    2.0    │            │            │    0    │         │       │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬─────────────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2    A_bkg  tau_bkg │\n",
       "├──────────┼─────────────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │     51.5       10    0.103   0.1006  -0.0808  -0.0969       -0        0 │\n",
       "│     A_p2 │       10     50.6    0.026   0.0402  -0.0047  -0.1329       -0        0 │\n",
       "│    mu_p1 │    0.103    0.026  0.00503   0.0027   0.0025  -0.0020   -0.057    0.010 │\n",
       "│    mu_p2 │   0.1006   0.0402   0.0027  0.00276   0.0018  -0.0015  -0.0513   0.0062 │\n",
       "│ sigma_p1 │  -0.0808  -0.0047   0.0025   0.0018  0.00297  -0.0012  -0.1409   0.0155 │\n",
       "│ sigma_p2 │  -0.0969  -0.1329  -0.0020  -0.0015  -0.0012  0.00171   0.0816  -0.0142 │\n",
       "│    A_bkg │       -0       -0   -0.057  -0.0513  -0.1409   0.0816      209      -28 │\n",
       "│  tau_bkg │        0        0    0.010   0.0062   0.0155  -0.0142      -28     4.01 │\n",
       "└──────────┴─────────────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 525,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f464246-d333-4143-baf0-aa2a632c5be4",
   "metadata": {},
   "source": [
    "Eine eigene Abschätzung für das $\\chi^2$ ergibt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "id": "b0ad46ce-f541-40bb-898c-154ad5f94787",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "106.36771764289108 112 0.9497117646686704\n"
     ]
    }
   ],
   "source": [
    "def chi_square_ndof(x_values, y_values, dy_values, fit_model, minuit):\n",
    "    ndof = len(x_values) - len(minuit.values)\n",
    "    chi2 = np.sum((y_values - fit_model(x_values, *minuit.values))**2/dy_values**2)\n",
    "    return chi2, ndof\n",
    "\n",
    "\n",
    "chi_square, ndof = chi_square_ndof(center, entries, np.sqrt(entries), fit_model, mi)\n",
    "print(chi_square, ndof, chi_square/ndof)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "295031f4-6d18-411c-b5dd-a62ed97da7f1",
   "metadata": {},
   "source": [
    "### Hypothesen-Test mittels $\\chi^2$\n",
    "Wie schon im vorherigen Abschnitt erwähnt, kann man das $\\chi^2$ auch dazu verwenden, die Gültigkeit des gewählten Models zu prüfen.\n",
    "Hierzu schauen wir uns die $\\chi^2$-Verteilung an. Der einzige freie Parameter ist die Anzahl der Freiheitsgrade. Die Anzahl der Freiheitsgrade ist auch gleichzeitig der Erwartungswert der $\\chi^2$-Verteilung. In unserem Beispiel oben ist die Anzahl der Freiheitsgrade 112 und die entsprechende Verteilung sieht wie folgt aus..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 527,
   "id": "8c11bc85-4e25-4d40-8397-257414d48a1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import chi2\n",
    "# chi_distribution = lambda x, ndof: chi2.pdf(x, ndof)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "id": "76836863-109c-4e7c-989e-04b62ec4ca9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(40., 180.)\n",
    "# plt.plot(x, chi_distribution(x, 112))\n",
    "plt.plot(x,chi2.pdf(x, 112))\n",
    "x = np.arange(chi_square, 180, 0.1)\n",
    "plt.fill_between(x, chi2.pdf(x, 112), alpha=0.3)\n",
    "plt.ylim(0, None)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('$\\chi^2(x)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b30829b3-a9e8-4d93-8895-9fd9f67ab9dc",
   "metadata": {},
   "source": [
    "Der erste Schritt für den Hypothesen-Test ist die Berechnung des $P$-Werts\n",
    "$$ P = \\int_{\\chi^2}^{\\infty} f(z,n_d)dz $$\n",
    "wobei $f(z,n_d)$ die $\\chi^2$-Verteilung und $n_d$ die Anzahl der Freiheitsgrade ist.\n",
    "Im Bild oben entspricht dies der ausgefüllten Fläche.\n",
    "\n",
    "Die praktische Berechnung erfolgt mittels der kumulativen Verteilungsfunktion via\n",
    "$$ P = 1 - \\chi^2_{CDF}(x, n_d) $$\n",
    "wobei für $x$ das im Fit bestimmte $\\chi^2$ eingesetzt wird. Die praktische Bedeutung des $P$-Werts ist die Wahrscheinlichkeit bei einer Wiederholung des Experiments in größeres $\\chi^2$ zu erhalten, wenn unser Model die Daten richtig beschreibt und die ermittelten Fitparameter den wahren Werten entsprechen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 529,
   "id": "cfa9d88a-eada-49dd-8cb3-73c7dd345c08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6323451110506132, 0.884238547608047, 0.48222800598351057)"
      ]
     },
     "execution_count": 529,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value = lambda x, ndof: 1 - chi2.cdf(x, ndof)\n",
    "p_value(chi_square, ndof), p_value(chi_square*10, ndof*10), p_value(ndof, ndof)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cba146a-6309-42d1-92cb-8bdde2da42a2",
   "metadata": {},
   "source": [
    "Kehren wir zu unserem Doppelpeak-Spektrum zurück und änderen das Fitmodell, indem wir statt eines exponentiellen einen konstanten Untergrund annehmen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "id": "9b91ee55-ac17-4dd6-9827-48677f772096",
   "metadata": {},
   "outputs": [
    {
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       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 369.6 (χ²/ndof = 3.3) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 415 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 5.63e-05 (Goal: 0.0002) </td>\n",
       "        <td style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> No parameters at limit </td>\n",
       "        <td 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\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance accurate </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_p1 </td>\n",
       "        <td> 319 </td>\n",
       "        <td> 7 </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> A_p2 </td>\n",
       "        <td> 583 </td>\n",
       "        <td> 7 </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> mu_p1 </td>\n",
       "        <td> 53.31 </td>\n",
       "        <td> 0.08 </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> mu_p2 </td>\n",
       "        <td> 60.52 </td>\n",
       "        <td> 0.06 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 4 </th>\n",
       "        <td> sigma_p1 </td>\n",
       "        <td> 2.23 </td>\n",
       "        <td> 0.07 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 5 </th>\n",
       "        <td> sigma_p2 </td>\n",
       "        <td> 2.72 </td>\n",
       "        <td> 0.04 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 6 </th>\n",
       "        <td> c </td>\n",
       "        <td> 21.4 </td>\n",
       "        <td> 0.6 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td> 0 </td>\n",
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       "        <td></td>\n",
       "        <th> A_p1 </th>\n",
       "        <th> A_p2 </th>\n",
       "        <th> mu_p1 </th>\n",
       "        <th> mu_p2 </th>\n",
       "        <th> sigma_p1 </th>\n",
       "        <th> sigma_p2 </th>\n",
       "        <th> c </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> A_p1 </th>\n",
       "        <td> 47.8 </td>\n",
       "        <td style=\"background-color:rgb(250,228,228);color:black\"> 10 <strong>(0.148)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.096 <strong>(0.167)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 0.0895 <strong>(0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -0.108 <strong>(-0.235)</strong> </td>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -0.0881 <strong>(-0.301)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,247,247);color:black\"> 0.1 <strong>(0.023)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> A_p2 </th>\n",
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       "        <td> 52.4 </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -0.036 <strong>(-0.060)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0034 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.064 <strong>(-0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -0.1062 <strong>(-0.347)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,249,249);color:black\"> 0.0 <strong>(0.005)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> mu_p1 </th>\n",
       "        <td style=\"background-color:rgb(250,225,225);color:black\"> 0.096 <strong>(0.167)</strong> </td>\n",
       "        <td style=\"background-color:rgb(242,242,250);color:black\"> -0.036 <strong>(-0.060)</strong> </td>\n",
       "        <td> 0.00694 </td>\n",
       "        <td style=\"background-color:rgb(250,132,132);color:black\"> 0.0038 <strong>(0.785)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,139,139);color:black\"> 0.004 <strong>(0.743)</strong> </td>\n",
       "        <td style=\"background-color:rgb(158,158,250);color:black\"> -0.0025 <strong>(-0.711)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.002 <strong>(0.030)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> mu_p2 </th>\n",
       "        <td style=\"background-color:rgb(250,216,216);color:black\"> 0.0895 <strong>(0.224)</strong> </td>\n",
       "        <td style=\"background-color:rgb(249,249,250);color:black\"> -0.0034 <strong>(-0.008)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,132,132);color:black\"> 0.0038 <strong>(0.785)</strong> </td>\n",
       "        <td> 0.00333 </td>\n",
       "        <td style=\"background-color:rgb(250,146,146);color:black\"> 0.0027 <strong>(0.695)</strong> </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -0.0017 <strong>(-0.714)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.0018 <strong>(-0.051)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> sigma_p1 </th>\n",
       "        <td style=\"background-color:rgb(219,219,250);color:black\"> -0.108 <strong>(-0.235)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.064 <strong>(-0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,139,139);color:black\"> 0.004 <strong>(0.743)</strong> </td>\n",
       "        <td style=\"background-color:rgb(250,146,146);color:black\"> 0.0027 <strong>(0.695)</strong> </td>\n",
       "        <td> 0.00444 </td>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -0.0016 <strong>(-0.559)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.005 <strong>(-0.132)</strong> </td>\n",
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       "    <tr>\n",
       "        <th> sigma_p2 </th>\n",
       "        <td style=\"background-color:rgb(211,211,250);color:black\"> -0.0881 <strong>(-0.301)</strong> </td>\n",
       "        <td style=\"background-color:rgb(205,205,250);color:black\"> -0.1062 <strong>(-0.347)</strong> </td>\n",
       "        <td style=\"background-color:rgb(158,158,250);color:black\"> -0.0025 <strong>(-0.711)</strong> </td>\n",
       "        <td style=\"background-color:rgb(157,157,250);color:black\"> -0.0017 <strong>(-0.714)</strong> </td>\n",
       "        <td style=\"background-color:rgb(177,177,250);color:black\"> -0.0016 <strong>(-0.559)</strong> </td>\n",
       "        <td> 0.00179 </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -0.0033 <strong>(-0.124)</strong> </td>\n",
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       "        <td style=\"background-color:rgb(250,246,246);color:black\"> 0.002 <strong>(0.030)</strong> </td>\n",
       "        <td style=\"background-color:rgb(243,243,250);color:black\"> -0.0018 <strong>(-0.051)</strong> </td>\n",
       "        <td style=\"background-color:rgb(233,233,250);color:black\"> -0.005 <strong>(-0.132)</strong> </td>\n",
       "        <td style=\"background-color:rgb(234,234,250);color:black\"> -0.0033 <strong>(-0.124)</strong> </td>\n",
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      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 369.6 (χ²/ndof = 3.3)      │              Nfcn = 415              │\n",
       "│ EDM = 5.63e-05 (Goal: 0.0002)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │   Below EDM threshold (goal x 10)    │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│      No parameters at limit      │           Below call limit           │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│             Hesse ok             │         Covariance accurate          │\n",
       "└──────────────────────────────────┴──────────────────────────────────────┘\n",
       "┌───┬──────────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name     │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ A_p1     │    319    │     7     │            │            │         │         │       │\n",
       "│ 1 │ A_p2     │    583    │     7     │            │            │         │         │       │\n",
       "│ 2 │ mu_p1    │   53.31   │   0.08    │            │            │         │         │       │\n",
       "│ 3 │ mu_p2    │   60.52   │   0.06    │            │            │         │         │       │\n",
       "│ 4 │ sigma_p1 │   2.23    │   0.07    │            │            │         │         │       │\n",
       "│ 5 │ sigma_p2 │   2.72    │   0.04    │            │            │         │         │       │\n",
       "│ 6 │ c        │   21.4    │    0.6    │            │            │    0    │         │       │\n",
       "└───┴──────────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘\n",
       "┌──────────┬────────────────────────────────────────────────────────────────┐\n",
       "│          │     A_p1     A_p2    mu_p1    mu_p2 sigma_p1 sigma_p2        c │\n",
       "├──────────┼────────────────────────────────────────────────────────────────┤\n",
       "│     A_p1 │     47.8       10    0.096   0.0895   -0.108  -0.0881      0.1 │\n",
       "│     A_p2 │       10     52.4   -0.036  -0.0034   -0.064  -0.1062      0.0 │\n",
       "│    mu_p1 │    0.096   -0.036  0.00694   0.0038    0.004  -0.0025    0.002 │\n",
       "│    mu_p2 │   0.0895  -0.0034   0.0038  0.00333   0.0027  -0.0017  -0.0018 │\n",
       "│ sigma_p1 │   -0.108   -0.064    0.004   0.0027  0.00444  -0.0016   -0.005 │\n",
       "│ sigma_p2 │  -0.0881  -0.1062  -0.0025  -0.0017  -0.0016  0.00179  -0.0033 │\n",
       "│        c │      0.1      0.0    0.002  -0.0018   -0.005  -0.0033     0.39 │\n",
       "└──────────┴────────────────────────────────────────────────────────────────┘"
      ]
     },
     "execution_count": 530,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def alternative_fit_model(x, A_p1, A_p2, mu_p1, mu_p2, sigma_p1, sigma_p2, c):\n",
    "    return peak(x, A_p1, mu_p1, sigma_p1) + peak(x, A_p2, mu_p2, sigma_p2) + c\n",
    "\n",
    "ls = cost.LeastSquares(center, entries, np.sqrt(entries), alternative_fit_model)\n",
    "\n",
    "mi = Minuit(ls, \n",
    "            A_p1 = 800, \n",
    "            A_p2 = 1400,\n",
    "            mu_p1 = 54,\n",
    "            mu_p2 = 60,\n",
    "            sigma_p1 = 2,\n",
    "            sigma_p2 = 2,\n",
    "            c = 100, \n",
    "           )\n",
    "mi.limits['c'] = (0, None)\n",
    "mi.fixed[:] = True\n",
    "ls.mask = (center < 45) | (center >= 70)\n",
    "mi.fixed[['c']] = False\n",
    "mi.migrad()\n",
    "ls.mask = None\n",
    "mi.values['A_p1'] = 700\n",
    "mi.values['sigma_p1'] = 3\n",
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p1', 'mu_p1', 'sigma_p1']] = False\n",
    "mi.migrad()\n",
    "mi.fixed[:] = True\n",
    "mi.fixed[['A_p2', 'mu_p2', 'sigma_p2']] = False\n",
    "mi.migrad()\n",
    "mi.fixed[:] = False\n",
    "mi.migrad()\n",
    "mi.hesse()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9fbbebc",
   "metadata": {},
   "source": [
    "Diese Änderung ist gering und der Fit scheint die Daten weiterhin zu beschreiben. Allerdings gibt bei kleinen Energien eine deutlich sichtbare Diskrepanz. Dies zeigt sich auch in einem größeren $\\chi^2$-Wert. Wie wirkt sich dies auf den $P$-Wert aus?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "id": "4aa0f3d9-1d0b-4b4c-b816-2a0cb9ae9793",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "329.01941626278426 113 2.911676250113135\n"
     ]
    }
   ],
   "source": [
    "chi_square, ndof = chi_square_ndof(center, entries, np.sqrt(entries), alternative_fit_model, mi)\n",
    "print(chi_square, ndof, chi_square/ndof)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "id": "607ddd33",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "329.01941626278426 113\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 479,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value = lambda x, ndof: 1 - chi2.cdf(x, ndof)\n",
    "print(chi_square, ndof)\n",
    "p_value(chi_square, ndof)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb62098-1e8b-4c9f-8aa3-048037f0d21e",
   "metadata": {},
   "source": [
    "Der Fit ist offensichtlich viel schlechter und der $P$-Wert liegt nahe bei null, so dass man dieses Model ausschließen sollte.\n",
    "\n",
    "Was aber, wenn die Änderung nicht so dramatisch ist? Ist ein $P$-Wert von 0,4 besser als 0,2? Nein, das kann man so nicht beantworten. Aber für einen Hypothesen-Test sollten man vorher eine Schwelle festlegen für die Akzeptanz oder Ablehnung des Models.\n",
    "\n",
    "Wie ein solcher Hypothesen-Test aussehen kann, wollen wir im Folgenden betrachten. Hierbei benutzen wir\n",
    "1. ein korrektes Model (Normalverteilung),\n",
    "2. ein korrektes Model mit überschätztem Fehler (10% größer),\n",
    "3. und ein falsches Model (Lorentzverteilung)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "c3f1f1d4-4b84-45a1-9d23-4cbb8ba32c8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def lorentzian( x, x0, a, gam ):\n",
    "    return a * gam**2 / ( gam**2 + ( x - x0 )**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e3fcfd5",
   "metadata": {},
   "source": [
    "Den Fit der drei Modelle und die Bestimmung des entsprechenden $P$-Werts wiederholen wir 5000-mal um eine ausreichende Statistik zu erhalten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9667c766",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Diese Zelle nur auf JupyterHub des ZDV ausführen um `tqdm` zu installieren!\n",
    "# import sys\n",
    "# import subprocess\n",
    "# subprocess.check_call([\n",
    "#     sys.executable, \n",
    "#     '-m',\n",
    "#     'pip',\n",
    "#     'install',\n",
    "#     '--proxy',\n",
    "#     'http://webproxy.zdv.uni-mainz.de:3128',\n",
    "#     'tqdm'\n",
    "# ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "id": "c3b58808-f155-4194-b02e-e5f649cb86aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9401e27e0abe463ab485a539ee58e61e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/5000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tqdm.notebook import tqdm\n",
    "\n",
    "res_good_model = []\n",
    "res_overfitting = []\n",
    "res_wrong_model = []\n",
    "\n",
    "def peak(x, A, mu, sigma):\n",
    "    return A*np.exp(-(x-mu)**2/(2*sigma**2))\n",
    "\n",
    "def lorentzian( x, x0, a, gam ):\n",
    "    return a * gam**2 / ( gam**2 + ( x - x0 )**2)\n",
    "\n",
    "\n",
    "for i in tqdm(range(5000)):\n",
    "    \n",
    "    test_data = np.random.normal(0, 2, 5000)\n",
    "    \n",
    "    entries, edges = np.histogram(test_data, bins=25, range=(-4,4))\n",
    "    center = edges[:-1] + np.diff(edges)/2\n",
    "    \n",
    "    ls = cost.LeastSquares(center, entries, np.sqrt(entries), peak)\n",
    "    mi = Minuit(ls, \n",
    "                mu=0.1,\n",
    "                sigma=1.5,\n",
    "                A = 300\n",
    "               )\n",
    "    mi.migrad()\n",
    "    \n",
    "    chi, ndof = chi_square_ndof(center, entries, np.sqrt(entries), peak, mi)\n",
    "    res_good_model.append(p_value(chi, ndof))\n",
    "\n",
    "\n",
    "    ls = cost.LeastSquares(center, entries, np.sqrt(entries)*1.1, peak)\n",
    "    mi = Minuit(ls, \n",
    "                mu=0.1,\n",
    "                sigma=1.5,\n",
    "                A = 300\n",
    "               )\n",
    "    mi.migrad()\n",
    "    \n",
    "    chi, ndof = chi_square_ndof(center, entries, np.sqrt(entries)*1.1, peak, mi)\n",
    "    res_overfitting.append(p_value(chi, ndof))\n",
    "\n",
    "\n",
    "    ls = cost.LeastSquares(center, entries, np.sqrt(entries), lorentzian)\n",
    "    mi = Minuit(ls, \n",
    "                x0=0,\n",
    "                gam=3,\n",
    "                a = 300,\n",
    "               )\n",
    "    mi.migrad()\n",
    "    \n",
    "    chi, ndof = chi_square_ndof(center, entries, np.sqrt(entries), lorentzian, mi)\n",
    "    res_wrong_model.append(p_value(chi, ndof))\n",
    "\n",
    "res_wrong_model = np.array(res_wrong_model)\n",
    "res_good_model = np.array(res_good_model)\n",
    "res_overfit_model = np.array(res_overfitting)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec4cf79",
   "metadata": {},
   "source": [
    "Die Schwelle des $P$-Werts für den Hypothesen-Test setzen wir auf 0,1, d.h. Ergebnisse mit eine, $P$-Wert $<$ 0,1 werden verworfen, alle anderen akzeptiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "id": "f41e0b38-56b6-4f2a-bc75-075f622a2068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, axes = plt.subplots()\n",
    "axes.hist(res_good_model, bins=25, range=(0, 1), histtype='step', color='purple', label='Good model')\n",
    "axes.hist(res_wrong_model, bins=25, range=(0, 1), histtype='step', color='orange', label='Wrong model')\n",
    "axes.hist(res_overfitting, bins=25, range=(0, 1), histtype='step', color='firebrick', label='Too large uncertainties (10 %)')\n",
    "axes.set_xlabel('p-value')\n",
    "axes.set_ylabel('Number of fits')\n",
    "axes.legend()\n",
    "axes.axvline(0.1, color='k')\n",
    "axes2 = plt.twiny()\n",
    "axes2.set_xlabel('Red. $\\chi^2$')\n",
    "axes2.set_xticks([0.2, 0.5, 0.8], ['> 1', '1', '< 1'])\n",
    "plt.show()\n",
    "\n",
    "axes.set_yscale('log')\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86237b4b",
   "metadata": {},
   "source": [
    "Wie man sieht, wird das falsche Modell nahezu immer verworfen während das richtige Modell meistens nicht verworfen wird. Das Modell mit dem überschätzten Fehler wird sogar häufiger akzeptiert, so dass man hier keine Unterscheidung vornehmen kann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "id": "fc58ee5c-308c-4479-9236-751d7f158fe5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of wrong model fits rejected: 0.9998\n",
      "Fraction of good model fits rejected: 0.1002\n",
      "Fraction of overfitting model fits rejected: 0.0250\n"
     ]
    }
   ],
   "source": [
    "print(f'Fraction of wrong model fits rejected: {np.sum(res_wrong_model<0.1)/len(res_wrong_model):.4f}')\n",
    "print(f'Fraction of good model fits rejected: {np.sum(res_good_model<0.1)/len(res_good_model):.4f}')\n",
    "print(f'Fraction of overfitting model fits rejected: {np.sum(res_overfit_model<0.1)/len(res_overfit_model):.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "392f4ef2",
   "metadata": {},
   "source": [
    "Wenn man das Limit für den Hypothesen-Test auf 0,05 festlegt, ändern die Ergebnisse wie folgt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "id": "d5f5efbe-ef8f-48b0-b27b-166f21cb5a06",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of wrong model fits rejected: 0.9986\n",
      "Fraction of good model fits rejected: 0.0534\n",
      "Fraction of overfitting model fits rejected: 0.0114\n"
     ]
    }
   ],
   "source": [
    "print(f'Fraction of wrong model fits rejected: {np.sum(res_wrong_model<0.05)/len(res_wrong_model):.4f}')\n",
    "print(f'Fraction of good model fits rejected: {np.sum(res_good_model<0.05)/len(res_good_model):.4f}')\n",
    "print(f'Fraction of overfitting model fits rejected: {np.sum(res_overfit_model<0.05)/len(res_overfit_model):.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de9861f6-7870-4dd8-8366-15e0c7dd5125",
   "metadata": {},
   "source": [
    "Der Hypothesen-Test kann das Modell nicht ablehnen, statt es zu bestätigen!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "jupyter",
   "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": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}