pgp1-python-einfuehrung/Kapitel_1._Einstieg_in_die_Welt_von_Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kapitel 1. Einstieg in die Welt von Python:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Ihrer Vorbereitung haben Sie bisher die folgenden Konzepte kennengelernt:\n",
    "\n",
    "* Aufbau eines Jupyter-Notebooks (Aufgabe 1).\n",
    "* Einfache Rechenoperationen (Aufgabe 2 a.)\n",
    "* Einfache Zeichenketten (engl. Strings) und formatierte Strings (Aufgabe 2 b.).\n",
    "* Das Definieren von Funktionen (Aufgabe 3.)\n",
    "* Das Definieren von Messtabellen.\n",
    "\n",
    "Hierauf wollen wir an unserem heutigen Versuchstag aufbauen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arbeiten mit Messreihen:\n",
    "\n",
    "Bisher hat uns das programmieren eher mehr Arbeit gemacht als uns welche abgenommen. Zeitersparnis bekommen wir, wenn wir viele Rechnungen hintereinander ausführen müssen. Hierfür gibt es die **for**-Schleife. Diese Schleife führt die gleichen Zeilen eins Codes wiederholt für die Elemente in einer Liste aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:07:49.905202Z",
     "start_time": "2019-11-04T12:07:49.889579Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wert: 1\n",
      "Wert: 2\n",
      "Wert: 3\n",
      "Wert: 4\n",
      "Ergebnis: 6\n"
     ]
    }
   ],
   "source": [
    "liste = [1, 2, 3, 4]\n",
    "\n",
    "for wert in liste:\n",
    "    print('Wert:', wert)\n",
    "    rechnung = wert + 2\n",
    "print('Ergebnis:', rechnung)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei einer Schleife ist darauf zu achten, dass der Anweisungsblock, welcher wiederholt ausgeführt werden soll, mit 4x Leerzeichen eingrückt wurde. Dies entspricht einmal die **Tab-Taste**:\n",
    "\n",
    "<img src=\"images/Tab-Key.png\" alt=\"Tab-Taste\" width=\"80\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:08:53.901374Z",
     "start_time": "2019-11-04T12:08:53.885753Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hier läuft das Hauptprogramm\n",
      "Schleife\n",
      "Wert: 1\n",
      "Schleife\n",
      "Wert: 2\n",
      "Schleife\n",
      "Wert: 3\n",
      "Schleife\n",
      "Wert: 4\n",
      "Hier läuft wieder das Hauptprogramm\n",
      "Letztes Ergebnis + 5:  11\n"
     ]
    }
   ],
   "source": [
    "liste = [1, 2, 3, 4]\n",
    "print('Hier läuft das Hauptprogramm')\n",
    "\n",
    "for wert in liste:\n",
    "    print('Schleife')\n",
    "    print('Wert:', wert)\n",
    "    rechnung = wert + 2\n",
    "    \n",
    "print('Hier läuft wieder das Hauptprogramm')\n",
    "rechnung = rechnung + 5\n",
    "print('Letztes Ergebnis + 5: ', rechnung)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statt das Ergebnis lediglich per `print`-Anweisung darstellen zu lassen, können wir auch unser Wissen um Listen benutzen und die berechneten Werte einer neuen Liste anfügen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# (Funktion haben wir bereits in der Vorbereitung definiert)\n",
    "def Spannung(Strom, Widerstand):\n",
    "    '''\n",
    "    Diese Funktion berechnet die Spannung eines Ohmschen \n",
    "    Widerstands.\n",
    "    \n",
    "    Args:\n",
    "        Strom (float): Der gemessene Strom in mA.\n",
    "        Widerstand (float): Der Wert des verwendeten Widerstands\n",
    "            in Ohm.\n",
    "         \n",
    "    Returns:\n",
    "        float: Die berechnete Spannung in V.\n",
    "    '''\n",
    "    return Widerstand * Strom/1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:10:08.503300Z",
     "start_time": "2019-11-04T12:10:08.472059Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10.1, 10.5, 9.8, 8.7, 11.2]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Stromwerte = [101, 105, 98, 87, 112]    # mA\n",
    "Spannungswerte = [] # Einheit? <-- Deshalb Docstrings und Help!\n",
    "Widerstand = 100    # Ohm\n",
    "\n",
    "for Strom in Stromwerte:\n",
    "    res = Spannung(Strom, Widerstand)\n",
    "    Spannungswerte.append(res)\n",
    "\n",
    "Spannungswerte"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python ermöglicht uns auch eine kompaktere Schreibweise, die so genannte \"list comprehension\": "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:11:40.799393Z",
     "start_time": "2019-11-04T12:11:40.783772Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10.1, 10.5, 9.8, 8.7, 11.2]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Spannungswerte = [Spannung(Strom, 100) for Strom in Stromwerte]\n",
    "Spannungswerte"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir können auch über mehrere Daten gleichzeitig \"loopen\". Hierzu kann die `zip` Anweisung genutzt werden. `zip` verbindet hierbei die einzelnen Elemente einer Liste wie bei einem Reißverschluss miteinander:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:12:42.522873Z",
     "start_time": "2019-11-04T12:12:42.507254Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A  und  0\n",
      "B  und  1\n",
      "C  und  2\n",
      "D  und  3\n"
     ]
    }
   ],
   "source": [
    "Werte1 = ['A', 'B', 'C', 'D']\n",
    "Werte2 = [0, 1, 2, 3]\n",
    "\n",
    "for w1, w2 in zip(Werte1, Werte2):\n",
    "    print(w1, ' und ', w2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dies kann zum Beispiel dann hilfreich sein, wenn sich mehr als eine Variable ändern soll, z.B. bei einer Messreihe für die Schallgeschwindigkeit in Luft:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:13:30.363510Z",
     "start_time": "2019-11-04T12:13:30.347888Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n",
      "[335.4904, 347.3442, 343.6145, 337.275, 331.6212, 342.0115, 336.2262]\n"
     ]
    }
   ],
   "source": [
    "# Gemessene Werte:\n",
    "frequenzen = [30.17, 30.63, 30.01, 29.98, 30.12, 29.87, 29.94] #kHz\n",
    "wellenlängen = [11.12, 11.34, 11.45, 11.25, 11.01, 11.45, 11.23] # mm\n",
    "\n",
    "# Variante 1:\n",
    "schallgeschindigkeiten = []  # m/s\n",
    "\n",
    "for f, l in zip(frequenzen, wellenlängen):\n",
    "    schallgeschindigkeiten.append(f*l)\n",
    "\n",
    "print(schallgeschindigkeiten)\n",
    "\n",
    "# oder Variante 2:\n",
    "schallgeschindigkeiten2 = [f*l for f,l in zip(frequenzen, wellenlängen)]\n",
    "print(schallgeschindigkeiten2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir können auch die `zip`-Anweisung mit mehr als nur zwei Listen verwenden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:13:49.912658Z",
     "start_time": "2019-11-04T12:13:49.897039Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a und 1 und x\n",
      "b und 2 und y\n",
      "c und 3 und z\n"
     ]
    }
   ],
   "source": [
    "l1 = ['a', 'b', 'c']\n",
    "l2 = [1, 2, 3]\n",
    "l3 = ['x', 'y', 'z']\n",
    "\n",
    "for i,j,k in zip(l1, l2, l3):\n",
    "    print(i, 'und', j, 'und', k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=task>\n",
    "    \n",
    "#### Aufgabe 4.b.: Werte berechnen:\n",
    "Kopieren Sie Ihre Lösung von Aufgabe 4.a. aus der Vorbereitung in das Notebook und berechnen Sie nun für die Messwerte aus Aufgabe 4 a. die Leistung $P$ und den Widerstand $R$ sowie deren Fehler. Nutzen Sie hierfür die ausführliche schrebweise der **for**-Schleife im Fall des Widerstands $R$ und den list-comprehension Syntax für die Leistung $P$. Fügen Sie die berechneten Werte als neue Spalten an die Liste *daten* an. \n",
    "<div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:46:37.221396Z",
     "start_time": "2019-11-04T12:46:37.190151Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spalte mit Index 0:  [1, 2, 3, 4, 5, 6]\n",
      "Spalte mit Index 1:  [12.0, 11.78, 12.56, 12.34, 12.01, 11.94]\n",
      "Spalte mit Index 2:  [110, 98, 102, 124, 105, 95]\n",
      "Spalte mit Index 3:  [0.32, 0.15, 0.63, 0.12, 0.2, 0.17]\n",
      "Spalte mit Index 4:  [10, 10, 10, 10, 10, 10]\n",
      "Spalte mit Index 5:  [0.10909090909090909, 0.12020408163265306, 0.12313725490196079, 0.09951612903225807, 0.11438095238095237, 0.1256842105263158]\n",
      "Spalte mit Index 6:  [0.010335218792552269, 0.012360854546774054, 0.01356055790616861, 0.008083630548247704, 0.01105869816696616, 0.013350390150906498]\n",
      "Spalte mit Index 7:  [1320.0, 1154.4399999999998, 1281.1200000000001, 1530.16, 1261.05, 1134.3]\n",
      "Spalte mit Index 8:  [125.05614738988244, 118.71364706721802, 141.0840444557782, 124.29390330985667, 121.92214729080192, 120.48727111193115]\n"
     ]
    }
   ],
   "source": [
    "messwert_nummer = list(range(1,7,1))\n",
    "spannungs_wert = [12., 11.78, 12.56, 12.34, 12.01, 11.94]\n",
    "strom_werte = [110, 98, 102, 124, 105, 95]\n",
    "dspannung_wetre = [0.32, 0.15, 0.63, 0.12, 0.20, 0.17]\n",
    "dstrom_werte = [10]*len(messwert_nummer)\n",
    "daten = [messwert_nummer, spannungs_wert, strom_werte, dspannung_wetre, dstrom_werte]\n",
    "\n",
    "def res(i, u):\n",
    "    r = u/i\n",
    "    return r\n",
    "\n",
    "# Widerstand:\n",
    "widerstand = []\n",
    "dwiderstand = []\n",
    "\n",
    "for strom, spannung in zip(daten[2], daten[1]):\n",
    "    widerstand.append(res(strom, spannung))\n",
    "daten.append(widerstand)\n",
    "\n",
    "# Fehler des Widerstands:\n",
    "for strom, spannung, dstrom, dspannung in zip(daten[2], daten[1], daten[4], daten[3]):\n",
    "    dwiderstand.append(((dstrom * spannung/(strom)**2)**2 + (dspannung/strom)**2)**0.5)\n",
    "daten.append(dwiderstand)\n",
    "\n",
    "# Leistung:\n",
    "p = [u*i for u,i in zip(daten[1], daten[2])]\n",
    "\n",
    "# Fehler der Leistung:\n",
    "dp = [((u*di)**2 + (du*i)**2 )**0.5 for u,i,du,di in zip(daten[1], daten[2], daten[3], daten[4])]\n",
    "daten.append(p)\n",
    "daten.append(dp)\n",
    "\n",
    "for ind, spalte in enumerate(daten): \n",
    "    # enumerate ist hilfreich, falls man noch zusätzlich einen Index braucht\n",
    "    print(f'Spalte mit Index {ind}: ', spalte)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Darstellung von Messdaten mittels `Matplotlib`:\n",
    "Das Plotten von Daten ist eines der wichtigsten Mittel, um eine Fülle von Informationen kompakt und verständlich seinem Gegenüber darzubieten. Gute Plots zu erstellen kann eine regelrechte Kunst sein und ist für ein gutes Paper, bzw. eine gute Bachelor- bzw. Masterarbeit unverzichtbar.  \n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/Xenon1tResults1yearx1texposure.png\"  alt=\"{{ Xenon1t results 2018 }}\" width=50%>\n",
    "<figcaption>Resultate des XENON1T Dunkle Materie Experiments. Die Graphik wurde mittels Matplotlib in Python erstellt. </figcaption>\n",
    "</figure>\n",
    "\n",
    "Jede Programmiersprache verfügt über zusätzliche Pakete (im Englischen \"packages\"), welche die Funktionalität der verwendeten Programmiersprache erweitern. **Matplotlib** ist ein umfangreiches Package, welches das Zeichnen von 2D und 3D Grafiken ermöglicht. Alle Parameter und Einstellungen einer Grafik werden entsprechend des Python-Codes eingestellt. Dadurch wird das Erstellen der Grafik reproduzierbar und man kann schnell dieselbe Grafik mit neuen Daten füttern.\n",
    "\n",
    "Es ist unmöglich, alle Möglichkeiten und Einstellungen, die **Matplotlib** bietet, auswendig zu kennen. Mit der Zeit werden Sie ein solides Grundwissen der gängisten Befehle haben. Für alles Weitere hilft die [Matplotlib-Dokumentation mit ihren Beispielen](http://matplotlib.org/). Des Weiteren ist insbesondere hier die **IPython-Hilfe** und die **automatische Vervollständigung von Befehlen** besonders hilfreich.\n",
    "\n",
    "Für das Praktikum wollen wir uns zunächst lediglich drei unterschiedliche Arten von Plots angucken:\n",
    "\n",
    "* Normale Liniengrafiken\n",
    "* Plots mit Fehlerbalken\n",
    "* Histogramme "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zunächst müssen wir Python mitteilen, dass wir das **Matplotlib** package nutzen wollen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:52:38.927838Z",
     "start_time": "2019-11-04T12:52:36.881444Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`import` läd für uns aus dem package matplotlib das Modul `pyplot`. Mit Hilfe des Zusatzes `as plt` wird ein \"alias\" (Abkürzung) erstellt. Dieser Alias erspart uns im Nachfolgenden Arbeit, wie wir im nachfolgenden Beispiel sehen können:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:53:06.331480Z",
     "start_time": "2019-11-04T12:53:05.987810Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1,2,3,4,5],   # <-- x-Daten\n",
    "         [1,2,3,4,5]    # <-- y-Daten\n",
    "        )\n",
    "plt.show()              # <-- Zeigen des Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hätten wir den Alias nicht definiert, hätten wir den folgenden etwas länglichen Code benötigt, den Sie niemals nutzen sollten:\n",
    "\n",
    "```python\n",
    "matplotlib.pyplot.plot([1,2,3,4,5], [1,2,3,4,5])\n",
    "matplotlib.pyplot.show()\n",
    "```\n",
    "\n",
    "Innerhalb der Python-Community haben sich ein paar Standards etabliert, an welche man sich halten sollte. So ist für `matplotlib.pyplot` der Alias `plt` zu verwenden.\n",
    "\n",
    "Im oberen Beispiel haben Sie nun auch bereits gesehen, wie wir einfache Liniengrafiken erstellen können. Dabei sieht der Plot noch etwas blass aus. Dies können wir mit ein paar zusätzlichen Befehlen und Argumenten ändern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:54:21.547247Z",
     "start_time": "2019-11-04T12:54:21.226301Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+IyQMEclFjRrBpEmw+eYqGZ1h0pII3H08MD7avrrC6yuAPumIQUQSUlYGQ4aE4nG6xpeRdGexiMTr6qtDyYjy8tGScZQIRCQ+zz4LN94YegM9eyYdjVRBiUBE4vH553DyyWFd4UGDko5GqqFEICJ1zz0kAQhrCzdqlGw8Ui2tRyAidc8M7rknrC2g0hEZT4lAROrW//1f+PDv3DnpSKSWNDQkInXn/fdDCem77ko6EtkASgQiUjcWLYLevUM1US0wn1U0NCQim84dTj01DAu9/jpsvXXSEckGUCIQkU13223w9NPhZ48eSUcjG0hDQyKy6dq0CT2Ciy5KOhLZCOoRiMjGcw9TRfv0CQ/JSuoRiMjGKSuDI46A++5LOhLZREoEIrJxrrwSXn5Zdw3nACUCEdlwY8bAzTfD738PJ52UdDSyieJcs7iRmU02s/fNbLqZXZdin1PNbL6ZTY0eZ8QVj4jUkc8+C3WEunULS09K1ovzYvFK4CB3X2JmDYA3zewFd59Yab/h7n5ujHGISF165RWoX1/F5HJInGsWu7sviZ42iB5aj1gk2/3+9/Dxx1BUlHQkUkdivUZgZvXMbCrwLTDO3Sel2O04M/vAzEaZ2Q5VvE9/Mys1s9L58+fHGbKIVGXoUHjjjbDdokWysUidijURuPtP7t4FaAV0N7MOlXZ5Fihy907AOODhKt5niLsXu3txodY8FUm/qVPhtNPgr38N9w5ITknLrCF3/wF4DTii0usL3X1l9PR+oFs64hGRDfDDD3DccaEX8Mgj4QYyySlxzhoqNLNm0fYWwKHAR5X22a7C057AzLjiEZGNUF5M7ssvYcQIFZPLUXHOGtoOeNjM6hESzgh3f87MBgKl7j4GON/MegJlwHfAqTHGIyIbatQoeOYZuP122HffpKORmJhn2XhfcXGxl5aWJh2GSH5YsyZUFe3VS0NCWc7Mprh7cao23VksIuv7z3/giy9gs83g2GOVBHKcEoGI/FxZWVhhbP/9YeXKmveXrFfjNQIz2xK4BGjt7mea2S7Abu7+XOzRiUj6XXFFuF/gscegYcOko5E0qE2P4J+EchH7RM+/Av4SW0Qikpynn4Zbb4Wzz4bf/CbpaCRNapMIdnL3W4DVAO6+DNCAoUiu+ewzOOUU2HPPMEtI8kZtEsGq6D4ABzCznQg9BBHJJdtsA/36wciRGhLKM7W5j+Aa4EVgBzN7HOiB5vuL5A53WLUKGjeGf/wj6WgkATX2CNx9HHAs4cN/KFDs7uPjDUtE0uaBB8Jw0DffJB2JJKTGRGBmPYAV7v480Ay4wszaxB2YiKTBu+/CuefCtttCQUHS0UhCanON4F5gmZl1Bi4GPgMeiTUqEYnf999D795QWAiPPw716iUdkSSkNomgzEMdimOAe9z9HqBJvGGJSKzWrAkzhObMCcXkVN49r9XmYvFiM7sc+C1wgJltRlhtTESy1fffw9y5cNttsM8+Ne8vOa02ieB44ETgdHf/j5m1Bm6NNywRiVWLFjBhAmy+edKRSAaozayh/7j7393939HzL91d1whEstHXX8OZZ8KiReFeARWTE2o3a+hYM/vUzBaZ2Y9mttjMfkxHcCJSh1avDsXknngCvvoq6Wgkg9RmaOgW4H/cXauHiWSzyy+HN98MM4TatUs6GskgtZk19M3GJAEza2Rmk83sfTObbmbXpdinoZkNN7NZZjbJzIo29DgiUgtPPhkuDA8YACeemHQ0kmGq7BGY2bHRZqmZDQeepkKNIXd/sob3Xgkc5O5LzKwB8KaZveDuEyvsczrwvbvvbGb9gJsJF6dFpK6UlcFll0H37iEZiFRS3dDQ/1TYXgYcVuG5A9UmgujegyXR0wbRo/K6mMcA10bbo4C7zcw829bPFMlk9evD+PHh3gEVk5MUqkwE7v67TX3zaOH6KcDOhJvRJlXapSUwJzpemZktAloACyq9T3+gP0Dr1q03NSyR/OAeFp7v2RNatkw6GslgtZk19LCZNavwfCsze7A2b+7uP7l7F6AV0N3MOmxMkO4+xN2L3b24UHdAitTOffeFRecffzzpSCTD1eZicSd3/6H8ibt/D3TdkINEf/414IhKTV8BOwCYWX2gKbBwQ95bRFKYMgXOOw8OP1wrjUmNapMINjOzrcqfmFlzarfWcWF5TyJa2OZQ4KNKu40BTom2ewOv6vqAyCb67rtQTG6bbcK6w5vV5tdc8llt7iO4DZhgZiMJS1T2Bv5aiz+3HfBwdJ1gM2CEuz9nZgOBUncfAzwAPGpms4DvgH4b85cQkQrOOCPcMPbvf6u0tNSK1eYLuJm1Aw6Knr7q7jNijaoaxcXFXlpamtThRTLf22/Dp5+G6qIiETOb4u7Fqdpq0yMg+uCfEa1XfKKZjXT39nUZpIhsou++g+bNYd99w0Oklmoza2h7M7vIzN4Bpkd/RkM4Ipnkq69g993hjjuSjkSyUJWJwMz6m9lrwHjC3P7TgXnufp27T0tTfCJSk9WroW9fWLo0zBIS2UDVDQ3dDUwATnT3UgAz04wekUxz6aXhusCwYaFXILKBqksE2wF9gNvMbFtgBFqZTCSzjBwZhoPOOy+UmBbZCFUODbn7Qncf7O4HAgcDPwDfmNlMM6vN9FERidvy5VBSAn/7W9KRSBar1Z0m7j7X3W+Lph4dA6yINywRqZWTT4ZXX9WSk7JJNuiWQzN7190/cfeBcQUkIjVwh7POWldDSMtNyiaqbtbQ2BQLxeh/nEjS/vGP8Pj886QjkRxRXY/gn8DLZvbnaGEZgOfTEJOIVKW0FC64AI48Ev7856SjkRxR3cXikcAewC8Jq5T9AfjOzC42s4vTFaCIRBYuDMXktt0WHn1UxeSkztRUYmIVsBRoCDQB1sQekYik9uSTMG9eWIC+RYuko5EcUt2axUcAfyeUit7D3ZelLSoRWd+ZZ8LBB8OOOyYdieSY6noEfwb6uPv0dAUjIimMHw+NG0NxsZKAxKK6NYv3T2cgIpLCnDnQpw+0bh0uFGuqqMRAV5tEMtWqVaFsxIoV8MQTSgISm9gSgZntYGavmdkMM5tuZhek2KfEzBaZ2dTocXVc8YhknUsvhQkT4MEHYbfdko5GclitFqbZSGXAJe7+rpk1AaaY2bgUq5v9292PjjEOkezzyitw553hnoE+fZKORnJcbInA3ecB86LtxWY2E2gJJLbMpUjWKCmBe+4J6w+LxCwt1wiiUhVdgUkpmvcxs/fN7AUzS7n8ZbRITqmZlc6fPz/OUEWStXQpfPMN1K8P55yjYnKSFrEnAjNrDIwGLnT3Hys1vwu0cffOwF3A06new92HuHuxuxcXFhbGGq9IYtyhf/8wTXTJkqSjkTwSayKIahSNBh539ycrt7v7j+6+JNoeCzQws4I4YxLJWPfeG2YHnXVWuG9AJE3inDVkwAPATHf/exX7bBvth5l1j+JZGFdMIhlr8mS48EI46ii4/PKko5E8E+esoR7AScA0M5savXYF0BrA3QcDvYGzzawMWA70c3etiyz5ZcGCUEyuZUt45BEVk5O0i3PW0JvUsH6Bu98N3B1XDCJZoV492HPP0BNo3jzpaCQPxdkjEJGauMNWW8Ho0UlHInlMfVCRpLz0EvToAf/5T9KRSJ5TIhBJwpdfwm9+A4sXwy9/mXQ0kueUCETSbdUq6Ns3/Bw9GrbcMumIJM/pGoFIul1yCUyaBCNHwq67Jh2NiHoEImm1eDGMGwcXXRSmjIpkAPUIRNKpSRN45x1o1CjpSETWUo9AJB2WLIErr4Rly0IyaNAg6YhE1lIiEImbe1h4/sYb4b33ko5GZD0aGhKJ2z33wLBh8Ne/hvsGRDKMegQicZo4ES6+GI4+Gi67LOloRFJSIhCJy5o1YUioVSsVk5OMpqEhkbhsthk89VS4QLzVVklHI1IlfUURicOECeEi8c47Q6dOSUcjUi0lApG69uKL4aLw4MFJRyJSK3GuULaDmb1mZjPMbLqZXZBiHzOzQWY2y8w+MLM94opHJC2++CIUk+vYEU45JeloRGolzmsEZcAl7v6umTUBppjZOHefUWGfI4FdosdewL3RT5Hss3Il9OkDZWUwapSKyUnWiHOFsnnAvGh7sZnNBFoCFRPBMcAj0fKUE82smZltF/1ZSZJ7KIWwbFkok7xH1Fl75x1YuvTn+261FXTuHLYnToQVK37eXlAAHTqE7bfegtWrf96+zTaw++5h+/XXw7EratkSdtklzMJ54431Y23dGnbcMbzvW2+t3962LbRpE+KaOHH99p13DjN7li4Nf7/KdtsNttsOFi1KfUNY+/ZQWBiKyb3zTqgoussu6+8nkqncPfYHUAR8Cfyy0uvPAftVeP4voDjFn+8PlAKlrVu3donZrFnuBx3kHj6S3ffee11bx47rXi9/HHLIuvaiovXbe/Va196ixfrtJ5+8rn3zzddvHzAgtK1atX4buP/pT6F94cLU7X/5S2ifPTt1+513hvZp01K3P/hgaH/77dTtI0eG9pdfdh84sO7+HUTqEFDqVXxGxz591MwaA6OBC939x415D3cfAgwBKC4u1uL2cRo1Ck4+OdTCGTQojHVXXDjlgQdS9wjKDR2aukdQ7plnUvcIyr38cuoeAYS1fV97bf2YW7cOP5s0Sd3etu2646Rq33nndfulat9tt/CzXbvU7e3bh5+HHhoeIlnGvPIvXV2+uVkDwrf+l9z97yna/wGMd/eh0fOPgRKvZmiouLjYS0tL4wo5f7mDGXz6KVxxBdx+exguEZGcYGZT3L04VVucs4YMeACYmSoJRMYAJ0ezh/YGFlWXBCQGq1bBdddBv34hGeyyS1gwRUlAJG/EOTTUAzgJmGZmU6PXrgBaA7j7YGAs8N/ALGAZ8LsY45HKJk+G00+HDz+EE08MSaFhw6SjEpE0i3PW0JuA1bCPAwPiikGqsGwZXH11GP7Zbjt49tlQFE1E8pLuLM5Hy5fDY49B//4wY4aSgEieU9G5fLFoEdx9dyiF3KIFzJypQmgiAqhHkB+efTZMfbz6anjzzfCakoCIRJQIctn8+XDCCdCzZ+gFTJoEJSVJRyUiGUZDQ7nsuONCSYWBA8OQ0OabJx2RiGQgJYJcM3cuNGsGjRvDHXeE6aDld76KiKSgoaFcsWYN/OMf4VrAVVeF1/bYQ0lARGqkRJALPv0UDjoIzjoLuneH885LOiIRySJKBNlu5MiwFOLUqaEg3LhxoSSziEgtKRFkq/JigV27wjHHhBvDTjstFI4TEdkASgTZZuXKcD9A377rFkcfNgy23z7pyEQkSykRZJOJE8MF4Ouvhy22CEXiREQ2kRJBNli6FC66CPbdFxYvhrFj4ZFHVClUROqEEkE2WLEiDP+ccw5Mnw5HHpl0RCKSQ3RDWab64Qe46y64/PJ1ReKaNUs6KhHJQeoRZKKnnw43hl13Hbz9dnhNSUBEYhLnUpUPmtm3ZvZhFe0lZrbIzKZGj6vjiiVrfPNNmA3UqxdsvXUoEnfAAUlHJSI5Ls6hoYeAu4FHqtnn3+6uVVHK9e4dlo/8y1/g0kuhQYOkIxKRPBDnUpVvmFlRXO+fM778MqwN0KQJDBoUZgK1a5d0VCKSR5K+RrCPmb1vZi+YWZXV0cysv5mVmlnp/Pnz0xlffNasgXvuCUXhro5Gxbp2VRIQkbRLMhG8C7Rx987AXcDTVe3o7kPcvdjdiwsLC9MVX3w+/hgOPBDOPRf22QcuuCDpiEQkjyWWCNz9R3dfEm2PBRqYWUFS8aTNiBHQuTN8+CH885/w0ktQVJR0VCKSxxJLBGa2rVmokGZm3aNYFiYVT+zKi8R16wbHHhvuCzj1VBWJE5HExXax2MyGAiVAgZnNBa4BGgC4+2CgN3C2mZUBy4F+7uWfljlkxYpQG+ijj2DUKNhpJ3jiiaSjEhFZK85ZQyfU0H43YXpp7nr7bTj99JAETjklFIlTfSARyTBJzxrKTUuWwPnnw377wbJl8OKL8NBDSgIikpGUCOKwalUYBhowIFwUPvzwpCMSEamSis7Vle++CzeEXXklNG8eLgY3bZp0VCIiNVKPoC6MHh1uBPvLX9YViVMSEJEsoUSwKebNg+OOCzWCtt8eSktVJE5Eso6GhjZF377wzjtw001wySVQX6dTRLKPPrk21BdfhGsATZqEhWO22AJ22y3pqERENpqGhmprzZrwwd++PVx1VXitSxclARHJeuoR1MZHH8EZZ8Bbb8ERR4SF5EVEcoR6BDUZNiwUiZs5Ex55BMaOhTZtko5KRKTOKBFUZc2a8HPPPaFPH5gxA046SUXiRCTnKBFUtnw5/OlPYVqoeygS99hjsM02SUcmIhILJYKK/v3vcAH45puhRQtYvTrpiEREYqdEALB4cagLdMAB4cN/3Di4/37YfPOkIxMRiZ0SAYQP/6efhgsvhGnT4JBDko5IRCRt8nf66MKFcOedYeH45s3DFNEmTZKOSkQk7WLrEZjZg2b2rZl9WEW7mdkgM5tlZh+Y2R5xxfIz7jByZCgSd+ONMGFCeF1JQETyVJxDQw8BR1TTfiSwS/ToD9wbYyzB11+H9YL79oUddghF4vbfP/bDiohkstgSgbu/AXxXzS7HAI94MBFoZmbbxRUPEBLAiy/CLbfAxInhRjERkTyX5DWClsCcCs/nRq/Nq7yjmfUn9Bpo3br1xh/xnntCkbhdd9349xARyTFZMWvI3Ye4e7G7FxcWFm78G3XurCQgIlJJkongK2CHCs9bRa+JiEgaJZkIxgAnR7OH9gYWuft6w0IiIhKv2K4RmNlQoAQoMLO5wDVAAwB3HwyMBf4bmAUsA34XVywiIlK12BKBu59QQ7sDA+I6voiI1E5WXCwWEZH4KBGIiOQ5JQIRkTynRCAikucsXLPNHmY2H/hiI/94AbCgDsOpK5kaF2RubIprwyiuDZOLcbVx95R35GZdItgUZlbq7sVJx1FZpsYFmRub4towimvD5FtcGhoSEclzSgQiInku3xLBkKQDqEKmxgWZG5vi2jCKa8PkVVx5dY1ARETWl289AhERqUSJQEQkz+VkIjCzB83sWzP7sIp2M7NBZjbLzD4wsz0yJK4SM1tkZlOjx9VpiGkHM3vNzGaY2XQzuyDFPmk/X7WMK4nz1cjMJpvZ+1Fc16XYp6GZDY/O1yQzK8qQuE41s/kVztcZccdV4dj1zOw9M3suRVvaz1ct40ryfM02s2nRcUtTtNft76S759wDOADYA/iwivb/Bl4ADNgbmJQhcZUAz6X5XG0H7BFtNwE+Adolfb5qGVcS58uAxtF2A2ASsHelfc4BBkfb/YDhGRLXqcDd6TxfFY59MfBEqn+vJM5XLeNK8nzNBgqqaa/T38mc7BG4+xvAd9XscgzwiAcTgWZmtl0GxJV27j7P3d+NthcDMwlrR1eU9vNVy7jSLjoHS6KnDaJH5RkXxwAPR9ujgIPNzDIgrkSYWSvgKOD+KnZJ+/mqZVyZrE5/J3MyEdRCS2BOhedzyYAPmcg+Uff+BTNrn84DR13yroRvkxUler6qiQsSOF/RcMJU4FtgnLtXeb7cvQxYBLTIgLgAjouGEkaZ2Q4p2uNwB3ApsKaK9kTOVy3igmTOF4Qk/rKZTTGz/ina6/R3Ml8TQaZ6l1APpDNwF/B0ug5sZo2B0cCF7v5juo5bkxriSuR8uftP7t6FsM52dzPrkI7j1qQWcT0LFLl7J2Ac676Fx8bMjga+dfcpcR9rQ9QyrrSfrwr2c/c9gCOBAWZ2QJwHy9dE8BVQMbu3il5LlLv/WN69d/exQAMzK4j7uGbWgPBh+7i7P5lil0TOV01xJXW+Khz/B+A14IhKTWvPl5nVB5oCC5OOy90XuvvK6On9QLc0hNMD6Glms4FhwEFm9lilfZI4XzXGldD5Kj/2V9HPb4GngO6VdqnT38l8TQRjgJOjK+97A4vcfV7SQZnZtuVjo2bWnfDvE+svRHS8B4CZ7v73KnZL+/mqTVwJna9CM2sWbW8BHAp8VGm3McAp0XZv4FWPrvAlGVelMeSehOsusXL3y929lbsXES4Ev+ruv620W9rPV23iSuJ8Rcf9hZk1Kd8GDgMqzzSs09/J2NYsTpKZDSXMKCkws7nANYSLZ7j7YGAs4ar7LGAZ8LsMias3cLaZlQHLgX5x/0IQvhmdBEyLxpcBrgBaV4grifNVm7iSOF/bAQ+bWT1C4hnh7s+Z2UCg1N3HEBLYo2Y2izA5oF/MMdU2rvPNrCdQFsV1ahriSikDzldt4krqfG0DPBV9x6kPPOHuL5rZWRDP76RKTIiI5Ll8HRoSEZGIEoGISJ5TIhARyXNKBCIieU6JQEQkzykRSF6zUOX0/8ysefR8q+h5UYp97zCzr8ys2t8bMyuyKirMimQiJQLJa+4+B7gXuCl66SZgiLvPrrhf9OHfi1Df5cB0xigSNyUCEbgd2NvMLgT2A/6WYp8SYDohaZxQ/qKZbWNmT0WF7943s32jpnpmdp+FtQFeju72xczOt7DGwgdmNix67RcW1qqYbKE2/jHx/VVF1qcbykQAMzsceBE4zN3HpWi/D3gDeIZQaqDI3Veb2XBggrvfEd3V2xjYinDHZ7G7TzWzEcAYd3/MzL4G2rr7SjNr5u4/mNlfgRlRezNgMtDV3Zem4a8uoh6BSORIYB6wXiVRM9uccDv/01EF1EnA4VHzQYReQnn1z0XR6//n7lOj7SlAUbT9AfC4mf2WULoAQi2ZP0WlNMYDjYhKaYikQ07WGhLZEGbWhVCkbW/gTTMbRShBDDCYUNWxGaHuEcCWhNpG6y1vWMHKCts/AVtE20cRVqr7H+DPZtaRsMrUce7+cR38dUQ2mHoEktei6qX3EtY7+BK4FbjJ3btEj8GEawJnuHtRVK2yLXComW0J/As4O3qvembWtJpjbQbs4O6vAZcRyi03Bl4CzqtQSbVrTH9dkZSUCCTfnQl8WeG6wP8Cu5vZgQDRh/0RwPPlfyAau3+T8K3+AuBXZjaNMATUrppj1QMei/Z9DxgUrR1wPaEK7QdmNj16LpI2ulgsIpLn1CMQEclzSgQiInlOiUBEJM8pEYiI5DklAhGRPKdEICKS55QIRETy3P8D02RWgXwopNAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdaten = [1,2,3,4,5]\n",
    "ydaten = [1,2,2,4,5]\n",
    "\n",
    "plt.plot(xdaten, ydaten,         # <-- Wie eben die x und y daten\n",
    "         color='red',            # <-- Farbe der Linie\n",
    "         linestyle='dashed',     # <-- Linientyp\n",
    "         label='Spannungskurve', # <-- Name der Linie\n",
    "        )\n",
    "plt.xlabel('X-Achse')           # <-- Beschriftung der x-Achse\n",
    "plt.ylabel('Y-Achse')           # <-- Beschiftung der y-Achse\n",
    "plt.legend()                    # <-- Hinzufügen der Legend mit den \n",
    "                                #     in plot definierten labels\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Viele der eben verwendeten Optionen bieten euch unterschiedliche Auswahlmöglichkeiten:\n",
    "\n",
    "**Linestyle:**\n",
    "* `''`:  keine Linie\n",
    "* `'-'`: durchgehende Linie\n",
    "* `'--'`: gestrichelte Linie\n",
    "* `'-.'`: Strich-Punktlinie\n",
    "* `':'`: Punktlinie\n",
    "\n",
    "**Color**:\n",
    "* red, blue, yellow, ...\n",
    "* RGB Werte von 0 bis 1 (statt von 0 bis 255): (1, 1, 1), (1, 0.2, 0.4)\n",
    "\n",
    "Darüber hinaus gibt es auch noch andere nützliche Styleoptionen wie `alpha`, was die Transparenz der Linie ändert (Werte zwischen 0-1), oder die `linewidth`-Option, mit dessen Hilfe Sie die Linienbreite ändern können.\n",
    "\n",
    "Auch die anderen Befehle, welche wir verwendetet haben, verfügen über zusätzliche Optionen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:55:35.863633Z",
     "start_time": "2019-11-04T12:55:35.535586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdaten = [1,2,3,4,5]\n",
    "ydaten = [1,2,2,4,5]\n",
    "\n",
    "plt.plot(xdaten, ydaten,       \n",
    "         color='red',        \n",
    "         linestyle='dashed',   \n",
    "         label='Graph 1'       \n",
    "        )\n",
    "plt.xlabel('X-Achse',\n",
    "           color=(0,1,0)     # <-- Beschriftungsfrabe\n",
    "          )          \n",
    "\n",
    "plt.ylabel('Y-Achse', \n",
    "           fontsize=14)        # <-- Beschiftungsgröße\n",
    "\n",
    "plt.legend(title='Messwerte',  # <-- Legendentitel\n",
    "           loc=3)              # <-- Legendenposition: \n",
    "                               # 0: Best, \n",
    "                               # 1: Oben Rechts \n",
    "                               # 2: Oben Links\n",
    "                               # 3: Unten Links    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sofern ihr mehrere Graphen in einen Plot zeichnen möchtet geht dies auch ganz einfach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:56:56.976082Z",
     "start_time": "2019-11-04T12:56:56.644588Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdaten = [-3, -2, -1, 0, 1, 2, 3]\n",
    "ydaten1 = xdaten\n",
    "ydaten2 = [x**2 for x in xdaten]\n",
    "ydaten3 = [x**3 for x in xdaten]\n",
    "\n",
    "plt.plot(xdaten, ydaten1, label='Linear')\n",
    "plt.plot(xdaten, ydaten2, label='Quadratisch')\n",
    "plt.plot(xdaten, ydaten3, label='Cubisch')\n",
    "\n",
    "plt.legend(title='Exponent')\n",
    "plt.xlabel('X-Werte')\n",
    "plt.ylabel('Y-Werte')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ihr seht, das `plot` zwischen den angegebene Werte interpoliert. Möchtet ihr eine glatte Kurve zeichnen so müsst ihr die Anzahl an Punkten für die Interpolation erhöhen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T12:58:19.439740Z",
     "start_time": "2019-11-04T12:58:19.116107Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cubic(x):\n",
    "    '''\n",
    "    Eine Funktion, die den cubischen Wert einer Zahl zurück gibt.\n",
    "    '''\n",
    "    return x**3\n",
    "\n",
    "\n",
    "x1 = list(range(-3, 4, 1))              # <- Werte zwischen -3 und 3\n",
    "x2 = [i/10 for i in range(-30, 31, 1)]  # <- 10 mal mehr Werte\n",
    "\n",
    "y1 = [cubic(j) for j in x1]\n",
    "y2 = [cubic(value) for value in x2]\n",
    "\n",
    "\n",
    "plt.plot(x1, y1, label='Werte 1', linestyle='dashed')\n",
    "plt.plot(x2, y2, label='Werte 2')\n",
    "\n",
    "plt.xlabel('x-Werte')\n",
    "plt.ylabel('y-Werte')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Errorbarplot\n",
    "\n",
    "In der Physik gehören zu jedem gemessen Wert eine Messunsicherheit / ein Messfehler. Diese Fehler sollten natürlich auch in unseren Grafiken korrekt dargestellt werden. Hierfür können wir den `errorbar`-Plot verwenden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:11:34.208204Z",
     "start_time": "2019-11-04T13:11:33.895770Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spannung = [0.9, 2.0, 3.0, 4.1, 4.9, 6.2] # [V]\n",
    "strom = [105, 204, 298, 391, 506, 601]    # [mA]\n",
    "spannung_error = [0.3]*len(spannung)      # Konstanter Ablesefehler [V]\n",
    "strom_error = [14, 9, 12, 8, 7, 11]       # gemessener schwankender Fehler[mA]\n",
    "\n",
    "# plt.errorbar() # <--- Wie verwende ich den errorbar plot?\n",
    "\n",
    "plt.ylabel('Spannung [V]')\n",
    "plt.xlabel('Strom [mA]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=task>\n",
    "    \n",
    "#### Aufgabe 5.: Erstellen einer `errorbar`-Plot:\n",
    "\n",
    "Editieren Sie die obere Zelle so, dass Sie mithilfe des Befehls \n",
    "\n",
    "```python\n",
    "plt.errorbar()\n",
    "```\n",
    "\n",
    "einen Errorbarplot erstellen. Verwenden Sie hierfür die IPython-Hilfe-Funktion, um die exakte Syntax zu erfahren. \n",
    "\n",
    "**Erinnerung:**\n",
    "Sie können die IPython-Hilfe aufrufen, indem Sie den Cursor innerhalb des Worts errorbar von plt.errorbar bewegen und die Tastenkombination **Shift + Tab** verwenden. Lesen Sie nun nach, wie Sie die x- und y-Werte und deren Fehler an die Funktion übergeben müssen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Leider ist diese Standardvariante des Errorbar-Plots noch nicht das, was wir möchten. Die Messwerte sind linear interpoliert und die errorbars sehen noch etwas eigenartig aus. Dies können wir jedoch im Handumdrehen ändern. Kümmern wir uns zunächst um die Plotmarker:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-31T12:32:08.949153Z",
     "start_time": "2019-10-31T12:32:08.543000Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(strom, spannung,\n",
    "             xerr=strom_error, \n",
    "             yerr=spannung_error,                   \n",
    "                                       # Änderungen für plotmarker:             | Kurzform:\n",
    "             linestyle='',             # <-- Schaltet den Linienstyle aus       | ls=''\n",
    "             marker='d',               # <-- Ändert den Markertyp in Diamanten  | -----\n",
    "             markerfacecolor='orange', # <-- Ändert die Markerfarbe zu Orange   | mfc='orange'\n",
    "             markeredgecolor='k',      # <-- Setzt die Kantenfarbe auf schwarz  | mec='k'\n",
    "             markersize=7              # <-- Ändert die Markergröße             | ms='7'\n",
    "            )\n",
    "\n",
    "plt.ylabel('Spannung [V]')\n",
    "plt.xlabel('Strom [mA]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All die Optionen, welche wir hier für die Plotmarker verwendet haben, können wir auch in der normalen `plt.plot`-Anweisung verwenden. Dabei gibt es eine ganze Fülle an unterschiedlichen [Marker-Symbole](http://matplotlib.org/api/markers_api.html):\n",
    " \n",
    "* `+`: Plus\n",
    "* `o`: Kreis\n",
    "* `*`: Stern\n",
    "* `,`,`.`: kleiner und sehr kleiner Punkt\n",
    "* `s`: Quadrat\n",
    "* `p`: Pentagon\n",
    "* `h`: Hexagon\n",
    "* `1`, `2`, `3`, `4`: nach unten, oben, links, rechts zeigendes Dreieck\n",
    " \n",
    "Nach dem wir uns um unsere Marker gekümmert haben, müssen wir nun auch noch unsere Fehlerbalken enstprechend anpassen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:11:52.919783Z",
     "start_time": "2019-11-04T13:11:52.638600Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(strom, \n",
    "             spannung,\n",
    "             xerr=strom_error,\n",
    "             yerr=spannung_error,     \n",
    "             ls='',            \n",
    "             marker='d',              \n",
    "             mfc='orange', \n",
    "             mec='k',      \n",
    "             ms=7,\n",
    "                            # Fehlerbalken optionen:\n",
    "             ecolor='k',    # <-- Ändert die Linienfarbe der errorbars\n",
    "             elinewidth=2,  # <-- Ändert die Fehlerbalkenbreite\n",
    "             capsize=5,     # <-- Ändert die Breite der Endkappen der Fehlerbalken\n",
    "             capthick=2,    # <-- Ändert die Dicke der Endkappen\n",
    "            ) \n",
    "\n",
    "plt.ylabel('Spannung [V]')\n",
    "plt.xlabel('Strom [mA]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histogramme:\n",
    "\n",
    "Ein weiterer Plottyp, welcher häufig Verwendung findet, ist das Histogramm. Um unser Histogramm mit Pseudozufallszahlen zu bestücken, müssen wir diese erst erzeugen. Hierfür können wir das `numpy`-Modul verwenden. `numpy` ist ein weiteres Standardmodul, welches viele nützliche Funktionen mit sich bringt. Hier wollen wir uns jedoch nur auf die Erstellung von Zufallszahlen beschränken. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:13:40.357937Z",
     "start_time": "2019-11-04T13:13:40.342316Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`np` ist eine konvetionelle Abkürkung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:13:40.844488Z",
     "start_time": "2019-11-04T13:13:40.828850Z"
    }
   },
   "outputs": [],
   "source": [
    "rnd_numbers = np.random.normal(0, 1, 1000) # <-- Hier werden 1000 gausförmig verteile Zufallszahlen\n",
    "                                           # mit einem Mittelwert von 0 und einer Standardabweichung \n",
    "                                           # von 1 erzeugt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Histgromm lässt sich ganz einfach mit der `plt.hist`-Anweisung erstellt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:13:52.473958Z",
     "start_time": "2019-11-04T13:13:52.177152Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rnd_numbers)\n",
    "\n",
    "plt.xlabel('Zufallswert')\n",
    "plt.ylabel('Anzahl der Einträge')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Auch für Histogramme gibt es viele unterschiedliche Optionen, welche Sie entweder mithilfe der Help-Funktion oder anhand der Beispiele in der [Matplolib-Dokumentation](http://matplotlib.org/) herrausfinden können."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:15:09.390753Z",
     "start_time": "2019-11-04T13:15:09.031464Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rnd_numbers2 = np.random.normal(1, 2, 1000)\n",
    "\n",
    "\n",
    "plt.hist(rnd_numbers, \n",
    "         bins=13, \n",
    "         range=(-3,5),         # <-- Achtung: Im Gegensatz zur range-Anweisung ist \n",
    "                               # das Intervall hier geschlossen [-3, 5]\n",
    "         histtype='step',      # Ändert den Balkentyp in Stufen\n",
    "         linestyle='dashed',\n",
    "         label='Verteilung 1'\n",
    "        )\n",
    "\n",
    "plt.hist(rnd_numbers2, \n",
    "         bins=13,\n",
    "         range=(-3,5),\n",
    "         alpha=0.5,            # Ändert die Transparenz der Balken \n",
    "         label='Verteilung 2'\n",
    "        )\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Zufallswert')\n",
    "plt.ylabel('Anzahl der Einträge')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei Histogrammen sollten Sie immer darauf achten, dass das \"binning\" sinnvoll gewählt ist. Weder zu viele noch zu wenige Bins führen zu einer sinnvollen Darstellung Ihrer Daten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T13:15:48.283946Z",
     "start_time": "2019-11-04T13:15:47.327389Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rnd_numbers, \n",
    "         bins=100, \n",
    "         range=(-3,3),\n",
    "         label='Zu viele bins'\n",
    "        )\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Zufallswert')\n",
    "plt.ylabel('Anzahl der Einträge')\n",
    "plt.show()\n",
    "\n",
    "plt.hist(rnd_numbers, \n",
    "         bins=3, \n",
    "         range=(-3,3),\n",
    "         label='Zu wenige bins'\n",
    "        )\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Zufallswert')\n",
    "plt.ylabel('Anzahl der Einträge')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nach dem wir jetzt die verschiedenen Plottypen mit ihren unterschiedlichen Optionen kennengelernt haben, möchten wir diese natürlich auch speichern können. Dies können wir auf zwei unterschiedliche Arten machen.\n",
    "\n",
    "Entweder Sie machen mit Ihrer Maus einen Rechtsklick auf die Grafik und wählen \"Grafik speichern als\" aus, oder Sie verwenden statt der `plt.show`- die `plt.savefig`-Anweisung dafür, wobei Letzteres empfohlen ist."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=task>\n",
    "    \n",
    "#### Aufgabe 6.: Erstellen einer gauss'schen Wahrscheinlichkeitsdichte:\n",
    "\n",
    "Im folgenden wollen wir ein Plot mit einer gauss'schen Wahrscheinlichkeitsdichte erstellen. Gehen Sie hierfür wie folgt vor:\n",
    "\n",
    "1. Erstellen Sie 500000 pseudo-Zufallszahlen, welche einer Gaußverteilung mit $µ=5$ und $sigma=2$ folgen.\n",
    "2. Tragen Sie die Zufallszahlen in ein Histogramm ein und normieren Sie dieses, sodass die Gesamtfläche 1 beträgt. **Tipp: `plt.hist` hat hierfür einen optionalen Parameter. Benutzen Sie die Help oder das Internet, um herrauszufinden, welcher es ist.**\n",
    "3. Wählen Sie eine geeignete `range` und ein `binning` von 100 für das Histogram.\n",
    "4. Plotten Sie anschließend die dazugehörige Gaußverteilung als Funktion. Gehen Sie dabei wie folgt vor:\n",
    "    1. Erstellen Sie eine Gaußfunktion. *Erinnerung:* eine Gaußverteilung ist gegeben durch:\n",
    "    $$g(x, \\mu, \\sigma) = \\frac{1}{\\sqrt{2 \\pi} \\, \\sigma} \\exp\\bigg( \\frac{ -(x - \\mu)^2}{2 \\sigma^2}\\bigg) $$\n",
    "    **Tipp:** Das Numpy-Paket beinhaltet die Zahlen $\\pi$ und die Exponentialfunktion. Sie können diese über `np.pi` und `np.exp()` verwenden. \n",
    "    2. Erstellen Sie eine Liste von x-Werten in der von Ihnen gewählten range in 0.1er Schritten. Verwenden Sie hierfür die `range`-Funktion zusammen mit der list-comprehension.\n",
    "    3. Erstellen Sie den plot.\n",
    "Das Ergebnis sollte wie folgt aussehen:\n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/Gaußverteilung.png\"  alt=\"{{ Gaussverteilung }}\" width=70%>\n",
    "</figure>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "rnd = np.random.normal(5, 2, 500000)\n",
    "\n",
    "# Histogram:\n",
    "plt.figure(dpi=100)\n",
    "plt.hist(rnd, bins=100, range=(0, 10), density=True, label='Zufallszahlen')\n",
    "\n",
    "# Gaussfunktion:\n",
    "def gauss(x, mu, sig):\n",
    "    return 1/((2 * np.pi)**0.5 * sig) * np.exp(-(x - mu)**2/(2*sig**2))\n",
    "\n",
    "# x-Werte mittels listcomprehension:\n",
    "xdata = [i/10 for i in range(0, 100, 1)]\n",
    "\n",
    "# Plot:\n",
    "plt.plot(xdata, [gauss(x, 5, 2) for x in xdata], ls='dashed', color='k', label='gauss(x, 5, 2)')\n",
    "plt.legend()\n",
    "plt.ylabel('Wahrscheinlichkeitsdichte P')\n",
    "plt.xlabel('x-Werte')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Fitten von Messdaten:\n",
    "\n",
    "### Methode der kleinsten Quadrate\n",
    "\n",
    "Die Herleitung dieser Methode befindet sich im separaten Notebook `Herleitung_Methode_der_kleinsten_Quadarate.ipynb`.\n",
    "\n",
    "Diese Methode ist in der Funktion `curve_fit` implementiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:03:03.767521Z",
     "start_time": "2019-11-04T14:03:02.583918Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gucken wir uns einen Fit ohne Messfehler an um die Funktion etwas näher kennenzulernen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:04:02.759738Z",
     "start_time": "2019-11-04T14:04:02.714523Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.098259801145538\n",
      "0.15780378609977405\n",
      "Widerstand R 10.10 +/- 0.16 Ohm\n"
     ]
    }
   ],
   "source": [
    "# Und jetzt fitten wir:\n",
    "para, pcov = curve_fit(Spannung,   # <-- Funktion, die an die Messdaten gefittet werden soll\n",
    "                       strom,      # <-- gemessenen \"X\"-Werte\n",
    "                       spannung    # <-- gemessenen \"Y\"-Werte \n",
    "                      )\n",
    "\n",
    "print(para[0])\n",
    "print(pcov[0,0]**0.5)\n",
    "\n",
    "print(f'Widerstand R {para[0]:.2f} +/- {pcov[0,0]**0.5:.2f} Ohm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sie sehen `curve_fit` gibt uns zwei unterschiedliche Listen zurück. Die erste Liste `para` beinhaltet die berechneten Fitparameter. `pcov` hingegen ist eine [Kovarianzmatrix](https://de.wikipedia.org/wiki/Kovarianzmatrix) auf deren Diagonalen Sie die Varianzen ($\\sigma^2$) der einzelnen Parameter finden (auf der Nebendiagonalen befinden sich die Kovarianzen). D.h. bei einer Funktion mit drei Parametern `def f(x, p1, p2, p3):` würde `para` und `pcov` allgemein so aussehen:\n",
    "\n",
    "```\n",
    "para = [p1, p2, p3]\n",
    "pcov = [[cov_1,1, cov_1,2, cov_1,3], \n",
    "        [cov_2,1, cov_2,2, cov_2,3],\n",
    "        [cov_3,1, cov_3,2, cov_3,3]]\n",
    "```\n",
    "wobei `cov_i,i` wie bereits erwähnt die einzelnen Kovarianzen bzw. Varianzen sind. Aber was genau macht jetzt curve_fit eigentlich, um auf diese Werte zu kommen? Wie bereits erklärt, basiert `curve_fit` auf der Methode der kleinsten Quadrate. D.h. die Funktion probiert etliche verschiedene Varianten Ihrer Parameter durch, bis es die Kombination gefunden hat, bei der das $\\chi^2$ klein wird. Gucken wir uns mal ein paar Zwischenschritte für unser Beispiel des ohm'schen Widerstandes an: \n",
    "\n",
    "<figure class=\"image\">\n",
    "<img src=\"images/MaterialPythonkurs092018/Fitting_gif.gif\"  alt=\"{{ Least Square Beispiel }}\" width=100%>\n",
    "</figure>\n",
    "\n",
    "Nach dem wir nun wissen, was genau `curve_fit` macht, wollen wir unser Resultat etwas schöner darstellen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:06:00.969312Z",
     "start_time": "2019-11-04T14:06:00.676047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(strom, \n",
    "         spannung,    \n",
    "         ls='',            \n",
    "         marker='d',              \n",
    "         mfc='orange', \n",
    "         mec='k',      \n",
    "         ms=7,\n",
    "         label='Messwerte aus A. 5 (ohne Fehler)'\n",
    "        ) \n",
    "plt.plot(strom, \n",
    "         [Spannung(value, para[0]) for value in strom], \n",
    "         ls ='dashed',\n",
    "         color='orange',\n",
    "         label = f'Fitgerade mit R = {para[0]:0.2f} +/- {pcov[0,0]**(1/2):0.2f} Ohm'\n",
    "        )\n",
    "\n",
    "plt.legend()\n",
    "plt.ylabel('Spannung [V]')\n",
    "plt.xlabel('Strom [mA]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das Ergebnis sieht bereits ganz gut aus, allerdings kennt hier unsere Funktion `curve_fit` die Fehler unserer Messwerte noch gar nicht. Da dies sehr unphysikalisch ist, wiederholen wir das Ganze nochmal mit Unsicherheiten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:08:11.387120Z",
     "start_time": "2019-11-04T14:08:11.137181Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "para2, pcov2 = curve_fit(Spannung,   \n",
    "                         strom,      \n",
    "                         spannung,\n",
    "                         sigma=spannung_error, # <-- Diesesmal mit Fehler\n",
    "                         absolute_sigma=True   # <-- Diese Option müssen wir auf True (wahr) setzen, da \n",
    "                                               # wir in der Regel absolute und keine relativen \n",
    "                                               # Unsicherheiten messen.\n",
    "                        )\n",
    "\n",
    "plt.plot(strom,\n",
    "         [Spannung(value, para2[0]) for value in strom], \n",
    "         ls ='dashed',\n",
    "         color='orange',\n",
    "         label = f'Fitgerade mit R = {para2[0]:0.2f} +/- {pcov2[0,0]**(1/2):0.2f} ohm'\n",
    "        )\n",
    "\n",
    "plt.errorbar(strom, \n",
    "             spannung,\n",
    "             xerr=strom_error,\n",
    "             yerr=spannung_error,     \n",
    "             ls='',            \n",
    "             marker='d',              \n",
    "             mfc='orange', \n",
    "             mec='k',      \n",
    "             ms=7,\n",
    "             ecolor='k',    \n",
    "             elinewidth=2,  \n",
    "             capsize=5,     \n",
    "             capthick=2,     \n",
    "             label='Messwerte aus A. 5'\n",
    "            ) \n",
    "\n",
    "\n",
    "plt.legend()\n",
    "plt.ylabel('Spannung [V]')\n",
    "plt.xlabel('Strom [mA]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wie Sie sehen können, ist der Wert für den Widerstand zwar gleich geblieben, jedoch die Unsicherheit des Wertes hat sich erhöht.\n",
    "\n",
    "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",
    "Dies bedeute in unserem Fall:\n",
    "\n",
    "$$ \\chi(R)^2 = \\sum_{i = 1}^{N} \\frac{ (U_i - u(I_i; R))^2}{\\Delta U_i^2}$$\n",
    "\n",
    "wobei hier groß $U$ unsere gemessene Spannung und klein $u$ unsere Funktion entspricht."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:09:37.708408Z",
     "start_time": "2019-11-04T14:09:37.683983Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Das chi-qudrat ist 1.26\n"
     ]
    }
   ],
   "source": [
    "chi_2 = [ (u - Spannung(i, para2[0]))**2/du**2 for i,u,du in zip(strom, spannung, spannung_error)]\n",
    "chi_2 = sum(chi_2)\n",
    "print(f'Das chi-qudrat ist {chi_2:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wie vergleicht sich dieses $\\chi^2$ nun mit einer Funktion, welche unsere Daten schlechter beschreibt? Zum Beispiel sofern wir die Spannung über die Funktion\n",
    "\n",
    "$$ U(R,I) = R \\cdot I $$\n",
    "\n",
    "$$ U(R,I) = R \\cdot I^2 $$\n",
    "\n",
    "beschreiben würden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-04T14:10:02.649772Z",
     "start_time": "2019-11-04T14:10:02.619695Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chi-qudrat nach URI: 1.26\n",
      "Chi-qudrat nach URI-Parabel: 60.68\n"
     ]
    }
   ],
   "source": [
    "def Spannung2(I, R):\n",
    "    return R * I**2\n",
    "\n",
    "para3, pcov3 = curve_fit(Spannung2,   \n",
    "                         strom,      \n",
    "                         spannung,\n",
    "                         sigma=spannung_error,\n",
    "                         absolute_sigma=True     \n",
    "                        )\n",
    "\n",
    "chi_2_new = [(u - Spannung2(I, *para3))**2/du**2 for I,u,du in zip(strom, spannung, spannung_error)]\n",
    "chi_2_new = sum(chi_2_new)\n",
    "print(f'Chi-qudrat nach URI: {chi_2:.2f}\\nChi-qudrat nach URI-Parabel: {chi_2_new:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wie Sie sehen können, ist das $\\chi^2$ für unsere zweite Funktion etwas größer als für das klassische ohm'sche Gesetzt. Somit würden wir unseren zweiten Ansatz verwerfen.\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 allgemeinhin 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 es nicht, 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)."
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    "<div class=task>\n",
    "    \n",
    "#### Aufgabe 7.: PGP Auswertung:\n",
    "\n",
    "Jetzt sind Sie ein letztes mal gefordert. In dieser Aufgabe wollen wir alles, was wir heute gelernt haben, nochmal reflektieren und anwenden. Erstellen Sie hierfür ein neues Jupyter-Notebook und bearbeiten Sie die Aufgaben im Skript. Sofern Sie Fragen bzw. Probleme haben, vergessen Sie nicht auf die folgenden Hilfsmöglichkeiten zurückzugreifen:\n",
    "\n",
    "1. Verwendung der IPython-Hilfe unter Verwendung der **Shift + Tab** Tasten.\n",
    "2. Die ausführliche Dokumentation von Python und das Angebot etlicher nützlicher Hilfsbeiträge in verschiedenen Foren (z.B. stackoverflow) im Internet.\n",
    "3. Fragen Sie beim Assistenten nach: **`mobitar@students.uni-mainz.de`**"
   ]
  }
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