pgp1-python-einfuehrung/Erweiterete_Musterloesung_Fitten_mit_der_Schiefenebene.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Musterlösung:\n",
    "\n",
    "Die Musterlösugen der einzelnen Aufgaben befindet sich direkt in den entsprechenden Jupyter-Notebooks. In diesem Notebook wird auf einige beliebte Fehler so wie die Auswertungsaufgabe zum Thema Fitten eingegangen. \n",
    "\n",
    "## Fehlermeldungen in Python:\n",
    "Einige von Ihnen sind bestimmt über ein paar Fehlermeldungen gestolpert und wussten nicht genau wie diese zu beheben sind. Im Grunde sind Fehlermeldungen in Python sehr einfach zu verstehen und es bedarf lediglich ein wenig Übung. Schauen wir uns zunächst einmal eine typische Fehlermeldung in Python an:\n",
    "\n",
    "<img src=\"images/ExampleTraceback.png\" alt=\"Tab-Taste\" width=\"1000\"/>\n",
    "\n",
    "Diese sieht erst einmal schrecklich kompliziert aus, die wichtigsten Informationen sind jedoch farbig hervorgehoben. Gehen wir diese doch einmal Schritt für Schritt durch:\n",
    "\n",
    "1. Art der Fehlermeldung. Meistens ist dies ein erster guter Indikator, wie der Fehler zustande gekommen ist.\n",
    "2. Beschreibung des Fehlers, hier steht meistens etwas ausführlicher, was genau das Problem ist. Wir werde uns im Nachfolgenden noch ein paar Beispiele angucken.\n",
    "3. Ort in Ihrem Hauptprogramm, an dem der Fehler aufgetreten ist.\n",
    "4. Exakte Position, an welcher der Fehler aufgetreten ist. Dies kann gleich sein mit Punkt 3., sofern Ihre Funktion nicht innerhalb einer weiteren Funktion (hier `curve_fit`) verwendet wird. \n",
    "\n",
    "Der schwarz umrandete Teil kann bei sehr komplexen Funktionen sehr länglich ausfallen. In der Regel können wir dies jedoch ignorieren und uns nur auf den Anfang und das Ende der Fehlermeldung konzentrieren.\n",
    "\n",
    "### Beispiele:\n",
    "\n",
    "Im Folgenden werden ein paar beliebte Fehler vorgestellt. Führen Sie einfach die entsprechenden Zellen aus, um die Fehlermeldung zu sehen.\n",
    "\n",
    "Fangen wir einfach an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'nicht_definiert' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_5876/3008136902.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnicht_definiert\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'nicht_definiert' is not defined"
     ]
    }
   ],
   "source": [
    "nicht_definiert"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diese Fehlermeldung ist relativ selbsterklärend. Der Fehlertyp ist ein `NameError` und der dazugehörige Fehlertext sagt uns, dass die Variable `nicht_definiert` noch nicht definiert wurde. \n",
    "\n",
    "Außerdem verrät uns Python, dass `nicht_definiert` in Zeile 1 unserer Zelle ausgeführt wird. Um die Zellennummerierung angezeigt zu bekommen, müssen Sie die Zelle anwählen und mit Esc in den Editiermodus wechseln. Nun können Sie mit dem Buchstaben \"L\" die Zeilennummerierung aktivieren. Dies kann bei längeren Code-Blöcken sehr hilfreich sein. \n",
    "\n",
    "Ein ähnlicher Fehler tritt auf, wenn man versucht, eine Funktion aus einem Package zu laden, welche nicht existiert. Zum Beispiel, weil man sich vertippt hat:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'matplotlib.pyplot' has no attribute 'plott'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_5876/3467793535.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplott\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# vertippt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: module 'matplotlib.pyplot' has no attribute 'plott'"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plott([1,2,3,4])  # vertippt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da es sich hierbei jedoch um eine Funktion innerhalb eins Packages handelt, spricht man von einem `AttributeError` (Warum es sich um ein Attribut handelt lernt man ausführlicher in anderen Programmierveranstaltungen).\n",
    "\n",
    "Richtig wäre:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb229fc4e50>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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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]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ein weiterer beliebter Fehler ist der folgende:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "unexpected EOF while parsing (3139088544.py, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/tmp/ipykernel_5876/3139088544.py\"\u001b[0;36m, line \u001b[0;32m3\u001b[0m\n\u001b[0;31m    [[1,a,b,4] # Beispiel verschachtelte Liste\u001b[0m\n\u001b[0m                                              ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m unexpected EOF while parsing\n"
     ]
    }
   ],
   "source": [
    "a = 1+1\n",
    "b = 2\n",
    "[[1,a,b,4] # Beispiel verschachtelte Liste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei diesem Fehler handelt es sich um einen Syntaxfehler, der besagt, dass Python das Ende Ihres Codes erreicht hat (end of file EOF), jedoch nicht alle Code-Blöcke abgeschlossen sind. In diesem konkreten Beispiel liegt es daran, dass wir vergessen haben, die Klammer der zweiten Liste zu schließen. Korrigiert sieht die Zelle wie folgt aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 2, 4]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1+1\n",
    "b = 2\n",
    "[[1,a,b,4]] # Beispiel verschachtelte Liste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dieser Fehler kann auch vorkommen, wenn man Code-Blöcke in for-Schleifen vergisst:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "expected an indented block (2543293741.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/tmp/ipykernel_5876/2543293741.py\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    for i in range(4):\u001b[0m\n\u001b[0m                      ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m expected an indented block\n"
     ]
    }
   ],
   "source": [
    "for i in range(4):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Manche von Ihnen haben versehentlich einen Zeilenumbruch innerhalb eines string verwendet. Hier bekommt man eine ähnliche Fehlermeldung."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "EOL while scanning string literal (985735555.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/tmp/ipykernel_5876/985735555.py\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    print(\"String mit\u001b[0m\n\u001b[0m                      ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m EOL while scanning string literal\n"
     ]
    }
   ],
   "source": [
    "print(\"String mit \n",
    "      Zeilenumbruch\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So wäre es richtig:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "String mit Zeilenumbruch\n"
     ]
    }
   ],
   "source": [
    "print(\"String mit \" \n",
    "      \"Zeilenumbruch\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ein anderer Fehler, welcher mal leicht durch das überdefinieren von Variablen passieren kann, ist der folgende:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'list' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_5876/454878668.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mquadrat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mquadrat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'list' object is not callable"
     ]
    }
   ],
   "source": [
    "def quadrat(x):\n",
    "    return x**2\n",
    "\n",
    "quadrat = [1**2, 2**2, 3**2]\n",
    "\n",
    "quadrat(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "oder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'int' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_5876/2306426342.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mquadrat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mquadrat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'int' object is not callable"
     ]
    }
   ],
   "source": [
    "quadrat = 2\n",
    "quadrat(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei dieser Art von Fehlern handelt es sich um einen TypeError. Ein TypeError besagt, dass ein Objekt (hier `quadrat`) nicht mit dem von Python erwartenden Typ übereinstimmt. In unserem obigen Beispiel erwarten wir ein Objekt vom Typ `callable`, was im Allgemeinen eine Funktion represntiert z.B. unsere Funktion:\n",
    "\n",
    "```python\n",
    "def quadrat(x):\n",
    "    return x**2\n",
    "```\n",
    "\n",
    "Leider haben wir diese jedoch versehentlich einmal mit einer Liste und einmal mit einem Integer überdefiniert. Python weiß hierdurch leider nicht, was `[1**2, 2**2, 3**2](3)` bzw. `3(3)` bedeuten soll. Versuchen Sie daher, eindeutige Variablennamen zu benutzen.\n",
    "\n",
    "Als Letztes hier noch ein Fehler, welcher Ihnen beim Plotten und Fitten unterlaufen kann:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (4,) and (3,)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_5876/3379473311.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0myWerte\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxWerte\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myWerte\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/.cache/pypoetry/virtualenvs/pgp1-python-einfuehrung-uZxcWp5O-py3.9/lib64/python3.9/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   3017\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0m_copy_docstring_and_deprecators\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mAxes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3018\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3019\u001b[0;31m     return gca().plot(\n\u001b[0m\u001b[1;32m   3020\u001b[0m         \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscalex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscaley\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   3021\u001b[0m         **({\"data\": data} if data is not None else {}), **kwargs)\n",
      "\u001b[0;32m~/.cache/pypoetry/virtualenvs/pgp1-python-einfuehrung-uZxcWp5O-py3.9/lib64/python3.9/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1603\u001b[0m         \"\"\"\n\u001b[1;32m   1604\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1605\u001b[0;31m         \u001b[0mlines\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1606\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlines\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1607\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.cache/pypoetry/virtualenvs/pgp1-python-einfuehrung-uZxcWp5O-py3.9/lib64/python3.9/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m    313\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    314\u001b[0m                 \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 315\u001b[0;31m             \u001b[0;32myield\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    316\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    317\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mget_next_color\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.cache/pypoetry/virtualenvs/pgp1-python-einfuehrung-uZxcWp5O-py3.9/lib64/python3.9/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs, return_kwargs)\u001b[0m\n\u001b[1;32m    499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    500\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 501\u001b[0;31m             raise ValueError(f\"x and y must have same first dimension, but \"\n\u001b[0m\u001b[1;32m    502\u001b[0m                              f\"have shapes {x.shape} and {y.shape}\")\n\u001b[1;32m    503\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (4,) and (3,)"
     ]
    },
    {
     "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": [
    "xWerte = [1, 2, 3, 4]\n",
    "yWerte = [1, 2, 4]\n",
    "\n",
    "plt.plot(xWerte, yWerte)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dieser Fehler besagt, dass die Liste für die x-Werte und die Liste für die y-Werte nicht die gleiche Länge haben. Dies kann leicht beim Abtippen von Messdaten passieren.\n",
    "\n",
    "Ich hoffe, dass diese Beispiele Ihnen helfen werden, in Zukunft besser mit Fehlermeldungen umzugehen. Hier noch drei allgemeine Tipps zum Programmieren und Fehlerbeheben in Jupyter-Notebooks:\n",
    "\n",
    "1. Wenn Sie Ihren Code schreiben, führen Sie nach jeder neuen Zeile/Funktion Ihren Code aus und überprüfen Sie, ob das Resultat mit Ihren Erwartungen übereinstimmt.\n",
    "2. Sollten Sie eine Fehlermeldung bekommen und Sie sehen nicht genau, wie dieser Fehler zu beheben ist. Dann kopieren Sie Zeile für Zeile (bzw. Funktion) den Code in eine neue Zelle und führen Sie diesen aus. Meistens findet man hierdurch sehr schnell, wo das Problem liegt. \n",
    "3. Da Sie in einem Notebook Zellen in willkürlicher Reihenfolge ausführen können, kann es leicht passieren, dass Sie Variablen überdefinieren. Sollten Sie also mal komplett verloren sein, dann kann es hilfreich sein, den Kernel neuzustarten, um alle Variablen zu löschen.\n",
    "    * Gehen Sie hierfür in der Menüleiste auf Kernel.\n",
    "    * Klicken Sie anschließend auf Restart.\n",
    "    * Anschließend müssen Sie erneut alle Zellen (in der richtigen Reihenfolge) ausführen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lösungen zum Thema Fitten:\n",
    "\n",
    "In diesem Abschnitt wollen wir uns den Lösungen zum Thema Fitten widmen. Neben den Musterlösungen zu den Aufgaben befindet sich am Ende nochmal ein weiteres Beispiel zur Illustration.\n",
    "\n",
    "## Bestimmen der Fallbeschleunigung des Planeten X:\n",
    "\n",
    "\n",
    "**Versuchsbeschreibung:**\n",
    "Stellen Sie sich den folgenden Versuch vor: Jahr 2132, die Firma SpaceY hat Sie auf eine Außenmission auf den Planeten X geschickt. Hier sollen Sie zusammen mit Ihrem Versuchspartner die Fallbeschleunigung $g_X$ des Planeten bestimmen. Als Versuch lassen Sie eine Kugel aus unterschiedlichen Fallhöhen innerhalb einer evakuierten Glasröhre fallen. Sie lassen die Kugel insgesamt aus 10 unterschiedlichen Höhen Fallen.\n",
    "\n",
    "Basierend auf der Versuchsbeschreibung wissen wir, dass es sich bei dem Versuch um einen freien Fall handelt, welcher als eine gleichförmig beschleunigte Bewegung beschrieben werden kann. D.h. es liegt der folgende Zusammenhang zwischen den gemessenen Höhen und Fallzeiten vor:\n",
    "\n",
    "$$h(t, g) = 1/2 \\cdot g \\cdot t^2$$ \n",
    "\n",
    "### Aufgabenstellung:\n",
    "\n",
    "Bestimmen Sie mithilfe Ihrer Vorbereitungsaufgabe 1 und der entsprechenden Funktion die Fallbeschleunigung $g_X$ mittels eines $\\chi^2$-Fits. Diskutieren Sie anschließend mittels der Güte Ihres Fits, ob Ihre Fitfunktion die gemessenen Daten gut widerspiegelt. Auf welchem Planeten in unserem Sonnensystem befinden Sie sich?\n",
    "Testen Sie anschließend, ob nicht ein linearerer Fit besser geeignet wäre. Begründen Sie Ihre Antwort."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:22.218156Z",
     "start_time": "2020-08-26T06:33:19.532136Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit\n",
    "height = [1, 1.2, 1.4, 1.6, 2, 2.2, 2.4, 2.6, 2.8] # in m\n",
    "dheight = [0.01]*len(height) # in m\n",
    "time = [0.74, 0.8, 0.87, 0.94, 1.03, 1.1, 1.15, 1.17, 1.24] # in s\n",
    "dtime = [12, 11, 9, 8, 11, 12, 13, 80, 10] # in ms\n",
    "\n",
    "# Achtung: Zeitfehler in s umrechnen, da in ms angegeben.\n",
    "dtime = [i/1000 for i in dtime]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Beim Fitten von Messdaten versuchen wir immer eine Funktion $y$ \n",
    "\n",
    "$$y(x, p1, p2, p3) = ... $$\n",
    "\n",
    "mit den Parameter $p_i$ an unsere Messdaten anzupassen. Genau nach diesem Schema muss man auch die Funktion in Python definieren:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fallhoehe(t, g):\n",
    "    return 0.5 * g * t**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ein paar von Ihnen haben leider die Funktion als $h(g, t)$ oder $g(t, h)$ definiert statt $h(t, g)$. Dies funktioniert leider nicht."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Anschließend können wir uns die Daten erstmal angucken:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:22.513340Z",
     "start_time": "2020-08-26T06:33:22.220084Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XAM/gjamSJKkJzRQh7wCOzcz72x2MJEnqHM3cE/ITYFq7A5EkSZ2lmSLks8CfRMSCiNgvInqql3YHKEmSJqZmLsfcVvn6LzXtQfn+kMktRSRJkjpCM0XIO9sehSRJ6jgNFyGZeedoBCJJkjpLXfeERMSvRUTd949ExBER0cwoiyRJ6hD1FhY/AvZr4Lh3A3MbD0eSJHWKekcrAvhcZYbUekxpMh5JktQh6h0J+TbwRuA36lzuBraMdNCIOD8ivh8RL0bEsxFxQ0S8sY79fisifhIRWyPi/0XEe2q2R0RcGhEbImJLRKyJiEPrPFdJkrQH1DUSkpkLRunzjweuBr5fieUyYFVEHJ6Zvxxsh4h4B+Wp488H/jewBLghIt6cmQ9Uun0G+CTwQeBx4HPAyspxt47SuUiSpAYUevNoZp5cvR4RZwPPAvMoj74M5lPAbZn5hcr60ohYCHwC+GhEBHAu8PnMXFE57gcov+fmNOAf23sWkjrRhs1beHzTLzl45j7M6XUSaakZY+0Jlt7K1+eH6XMscGVN20rKBQbAwcBsYM3AxszcHBH3VPa1CJE0ov7tLw25bfk9T/L5mx8CYFLAJacewRnzDhy0b/eUsfbPrDR2jJm/HZVHgL8EfLfqsspgZlMe1aj2TKWdqq/D9an97KnA1KqmGQClUolSqTRi7HrFQL7MW/PMYevakcPDL1xVV7+dCUtXrGXpirWDbn/kc4uajqFI/hy2rlNz2Mj5jpkihPK9IUcCxxXw2ecDF9U2rlq1iu7u7gLCGf9Wr15ddAjjnjlsXWs5bM8/j7fccktbjlMUfw5b12k57O+v90HaMVKERMRVwG8C8zNz/QjdNwL717TtX2mn6uv+wIaaPvcNccxl7HqJZwawftGiRfT0+E6+RpRKJVavXs3ChQvp6uoqOpxxyRy2rh05XHDi4Jdjnunbysl/dhc785W2SQG3ffId7N+z9279x+vlGH8OW9epOezr66u7b1N/OyLid4GPUr7/4tjMfCIizgUeH7gZtM7jBPDnwOnAgsx8vI7d7gZOoHzpZsDCSjuUn4bZWOlzX+VzeoC3AV8e7ICZuQ3YVhUXAF1dXR31g9NO5q515rB1reSwd4j9eveZxrLFR3HBtx5gRyaTI7hs8ZEcNudVrYQ6Zvlz2LpOy2Ej59pwERIRHwMupVwE/E9eeWvuC5SfSqm7CKF8CWYJ8F7gxYgYuGdjc2ZuqXze9cDPM/P8yrY/Be6MiN8HbgbOAt4C/BeAzMyI+BLwhxHxCK88ovs0cENDJytJgzjzmLnMP2wW6zb1c9DMbp+OkZrUzEjI7wH/OTNviIjPVrX/APjjBo/1scrXO2razwGurXw/F9g5sCEz74qIJcDnKc8r8ghwWs3NrFcA+wB/BewLfAc42TlCJLXLnN5pFh9Si5opQg6m/C6ZWtso/+KvW2ZGHX0WDNL2DeAbw+yTwIWVRZIkjUF1vxm3yuPA0YO0nww81FI0kiSpYzQzEnIlcHVE7E35xXZvjYj3U37M9SPtDE6SJE1cDRchmfnViNhC+Z6MbmA55Zs+P5WZzkYqSZLq0tQjupn5D8A/REQ3MD0zn21vWJIkaaJraRadzOwH6p8aTZIkqaLhG1MjYv+I+LuIeDoiXoqIHdXLaAQpSZImnmZGQq6lPHfH5yhPi57D9pYkSRpEM0XIccB/zMz72hyLJEnqIM3ME/IU5UdzJUmSmtZMEXIucHlEHNTeUCRJUiep63JMRPyCXe/92Ad4LCL6gVJ138x8dfvCkyRJE1W994ScO5pBSJKkzlNXEZKZ1412IJIkqbM0NVlZREwGTgN+tdK0FrgxM50nRJIk1aXee0J6MrOv8v0bgFuAA4CHK13OB56KiFMy87FRiVSSJE0o9T4d84uIeE3l+z8DHgN+JTPfnJlvpjx52eOVbZIkSSOq93LMu4DnK98fD7w9MwfWycx/i4jPAt9tc3ySJGmCqnck5Nd5pWDZBswYpM90YHs7gpIkSRNfvUXIpynPDQLwv4G/ioi3xSveDnwFuHE0gpQkSRNPXUVIZh6cmf9WWf0k5XtC7ga2VpbvAo8CnxqNICVJ0sTT8CO6mfkC8N6IOBR4U6X5ocx8tJ2BSZKkia2peUIAMvMR4JE2xiJJkjpIw0VIZaKys4ETgNdQc0knM9/VlsgkSdKE1sxIyJ9SLkJuBh5g1xfbSZIk1aWZIuQs4H2ZeUu7g5EkSZ2j3kd0q22n/CSMJElS05opQv4E+FRERLuDkSRJnaPeF9h9q6bpXcC7I2ItUKrekJmL6/3wiJgP/HdgHjAHOD0zbxim/7XABwfZ9GBmHlHpczFwUc32hzPzTbvtJUmSClPvPSGba9b/uU2fvw9wP/C3QG2hM5hPAZ+tWt+rsv83avqtBU6sWn+phRglSdIoqKsIycxzRuPDM/NW4FaAeq7uZOZmqgqiiDgNeBVwTU3XlzJzY9sClSRJbdf0ZGVjxIeBNZn5RE37oRHxNOUp5e8Gzs/MJ4c6SERMBaZWNc0AKJVKlEqlwXfSoAbyZd6aZw5bZw5bZw5b16k5bOR8I3PkaT4i4kfUOR9IZr657k/f9TOSEe4Jqen/WuBJYElmfr2q/d2U3+j7MOX7TC4CDgCOzMwXhzjWxex+HwnLly+nu7u7sRORJKmD9ff3s2TJEoDezOwbrm+9IyE3tBrUKPgg8AI1sVUu8Qz4cUTcAzwBvA/4myGOtQy4smp9BrB+0aJF9PT0tCvejlAqlVi9ejULFy6kq6ur6HDGJXPYOnPYOnPYuk7NYV/fsHXHLuq9J+SSpqMZBZXHgz8E/F1mbh+ub2a+EBE/Bd4wTJ9twLaq4wPQ1dXVUT847WTuWmcOW2cOW2cOW9dpOWzkXJuZJ2QsOJ5yUTHUyMbLImI68Hpgw2gHJUmS6lfvPCG/oP57Ql5d74dXCoTqEYqDI+Jo4PnMfDIilgEHZOYHanb9MHBPZj4wyDH/GLiJ8iWY1wKXADuAr9UblyRJGn313hNy7ih9/luA26vWB+7LuI7yS/LmAHOrd4iIXuAMynOGDOZAygXHfsBzwHeAt2fmc22LWpIktazee0KuG40Pz8w7gCEnCMnMswdp2wwM+chKZp7VjtgkSdLoammekIjYG5hS3TbS4ziSJEnQxI2pEbFPRFwVEc8CvwR+UbNIkiSNqJmnY66g/AK7j1F+rPUjlCf6ehqovYFUkiRpUM1cjvlPwAcy846IuAb4P5n5aEQ8Afw28A9tjVCSJE1IzYyEvBr4WeX7vso6lJ9Cmd+OoCRJ0sTXTBHyM+Dgyvc/oTwdOpRHSF5oQ0ySJKkDNFOEXAP8euX7y4GPR8RW4IvAF9oVmCRJmtjqvickIg4BHs/MLw60ZeaaiHgTMA94NDN/PAoxSpKkCaiRkZBHgFkDKxHxTxGxf2Y+kZnfsgCRJEmNaKQIqZ3Z9D3APm2MRZIkdZDx+hZdSZI0zjVShCS7v0m3rjfrSpIk1WpksrIAro2IbZX1vYGvRMQvqztl5uJ2BSdJkiauRoqQ2jfp/n07A5E0dmzYvIXHN/2Sg2fuw5zeaUWHI2mCqrsIycxzRjMQSXte//aXdmtbfs+TfP7mhwCYFHDJqUdwxrwDX97ePaWll29L0sv810TqYIdfuHLY7TsTlq5Yy9IVa19uW3f5KaMdlqQO4dMxkiSpEI6ESB3swUtP2mV94+atnHjlneyseu5tUsCa845ndu/eezg6SROdIyFSB+uestcuyyGzprNs8VFMjvLchJMjWLb4KA6ZNf3lPpLULv6LImkXZx4zl/mHzWLdpn4Omtnt0zGSRo1FiKTdzOmdZvEhadR5OUaSJBXCIkSSJBXCIkSSJBXCIkSSJBXCIkSSJBXCIkSSJBWi0CIkIuZHxE0R8XREZEScNkL/BZV+tcvsmn4fj4h1EbE1Iu6JiLeO6olIkqSGFT0Ssg9wP/DxBvd7IzCnanl2YENEnAlcCVwCvLly/JUR8Zp2BCxJktqj0MnKMvNW4FaAqEwTXadnM/OFIbadB/x1Zl5TOe5HgVOADwGXNx2sJElqq/E6Y+p9ETEVeAC4ODO/CxARU4B5wLKBjpm5MyLWAMcOdbDKsaZWNc0AKJVKlEqlUQh/4hrIl3lrnjlsnTlsnTlsXafmsJHzjcwcudceEBEJnJ6ZNwzT543AAuAHlIuGjwC/C7wtM38YEa8Ffg68IzPvrtrvCuD4zHzbEMe9GLiotn358uV0d3c3e0qSJHWc/v5+lixZAtCbmX3D9R1XIyGZ+TDwcFXTXRHxeuDTlIuRZi2jfB/JgBnA+kWLFtHT09PCYTtPqVRi9erVLFy4kK6urqLDGZfMYevMYevMYes6NYd9fcPWHbsYV0XIEL4HHFf5fhOwA9i/ps/+wMahDpCZ24BtA+sD96d0dXV11A9OO5m71pnD1pnD1pnD1nVaDhs516KfjmmHo4ENAJm5HbgXOGFgY0RMqqzfPdjOkiSpGIWOhETEdOANVU0HR8TRwPOZ+WRELAMOyMwPVPqfCzwOrAX2pnxPyLuARVXHuBK4LiJ+QHmU5FzKjwJfM6onI0mSGlL05Zi3ALdXrQ/cl3EdcDblOUDmVm2fAvwJcADQD/wYODEzXz5GZv5TRMwCLgVmA/cBJ2fmM6NzCpIkqRlFzxNyBzDkBCGZeXbN+hXAFXUc9yrgqhbDkyRJo2gi3BMiSZLGIYsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQqUEbNm/hrsc2sWHzlqJDkaRxreh5QqQxq3/7S7u1ffPe9Vx041p2JkwKuOTUIzhj3oG79Ome4l8rSaqH/1pKQzj8wpXDbt+ZsHTFWpauWLtL+7rLTxnNsCRpwvByjCRJKoQjIdIQHrz0pF3WN27eyolX3snOfKVtUsCa845ndu/eezg6SRr/HAmRhtA9Za9dlkNmTWfZ4qOYHOU3DUyOYNniozhk1vRd+kmS6uO/mFIDzjxmLvMPm8W6Tf0cNLObOb3Tig5JksYtixCpQXN6p1l8SFIbeDlGkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEkiQVotAiJCLmR8RNEfF0RGREnDZC/8URsToinouIvoi4OyJOqulzceVY1ctPRvVEJElSw4oeCdkHuB/4eJ395wOrgfcA84DbgZsi4jdq+q0F5lQtx7UlWkmS1DZ7FfnhmXkrcCtARNTT/9yapgsi4r3AfwJ+VNX+UmZubFOYkiRpFBRahLQqIiYBM4DnazYdGhFPA1uBu4HzM/PJYY4zFZha1TQDoFQqUSqV2hv0BDeQL/PWPHPYOnPYOnPYuk7NYSPnG5k5iqHULyISOD0zb2hgn88AnwXelJnPVtreDUwHHqZ8KeYi4ADgyMx8cYjjXFzpt4vly5fT3d3d2IlIktTB+vv7WbJkCUBvZvYN13fcFiERsQT4a+C9mblmmH77Ak8A52Xm3wzRZ7CRkPWbNm2ip6envhMQUK6AV69ezcKFC+nq6io6nHHJHLbOHLbOHLauU3PY19fHzJkzoY4iZFxejomIs4CvAr81XAECkJkvRMRPgTcM02cbsK3q+AB0dXV11A9OO5m71pnD1pnD1pnD1nVaDhs516KfjmlYRLwfuAZ4f2beXEf/6cDrgQ2jHZskSapf0fOETI+IoyPi6ErTwZX1uZXtyyLi+qr+S4Drgd8H7omI2ZWlt6rPH0fE8RFxUES8A/hnYAfwtT11Xp1sw+atPLI52LB5a9GhSJLGuKIvx7yF8lwfA66sfL0OOJvyjaVzq7b/F8oxX11ZqOkPcCDlgmM/4DngO8DbM/O59obeufq3vzRo+zfvXc9FN65lZ07mLx76NpecegRnzDtw0L7dU4r+0ZMkFa3oeULuAIacICQzz65ZX1DHMc9qNS4N7/ALV47YZ2fC0hVrWbpi7aDb111+SrvDkiSNM+PunhBJkjQxOCauhj146Um7tW3cvJUTr7yTnVVPfE8KWHPe8czu3XsPRidJGi8cCVHDuqfstdtyyKzpLFt8FJMqF9cmBSxbfBSHzJo+aH9JkvxtoLY585i5HHvwq/j6Lbfzvve8k7kzZxQdkiRpDHMkRG01p3dvDu1N5ngJRpI0AosQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUCIsQSZJUiEKLkIiYHxE3RcTTEZERcVod+yyIiB9GxLaIeDQizh6kz8cjYl1EbI2IeyLiraMRvyRJal7RIyH7APcDH6+nc0QcDNwM3A4cDXwJ+GpEnFTV50zgSuAS4M2V46+MiNe0M/DRsmHzFu56bBMbNm8pOhRJkkbVXkV+eGbeCtwKEBH17PJR4PHM/P3K+kMRcRzwaWBlpe084K8z85rKcT8KnAJ8CLi8fdE3rn/7S8Nu/+a967noxrXsTJgUcMmpR3DGvAOH7N89pdA/PkmSWjLefosdC6ypaVtJeUSEiJgCzAOWDWzMzJ0Rsaay76AiYiowtappBkCpVKJUKrUlcIDDL1xVd9+dCUtXrGXpirVD9nnkc4vaEVZbDeSrnXnrNOawdeawdeawdZ2aw0bOd7wVIbOBZ2rangF6ImIa8Cpg8hB93jTMcc8HLqptXLVqFd3d3c1Hu5v2pvuWW25p6/HaafXq1UWHMO6Zw9aZw9aZw9Z1Wg77+/vr7jveipDRsozyfSQDZgDrFy1aRE9PT9s+ZMGJQ1+OeaZvKyf/2V3szFfaJgXc9sl3sH/P3oPuMxYvx5RKJVavXs3ChQvp6uoqOpxxyRy2zhy2zhy2rlNz2NfXV3ffsfdbbHgbgf1r2vYH+jJzS0TsAHYM0WfjUAfNzG3AtoH1gftTurq62vqD0zvMsXr3mcayxUdxwbceYEcmkyO4bPGRHDbnVW37/D2p3bnrROawdeawdeawdZ2Ww0bOdbwVIXcD76lpW1hpJzO3R8S9wAnADQARMamyftWeC7M5Zx4zl/mHzWLdpn4OmtnNnN5pRYckSdKoKbQIiYjpwBuqmg6OiKOB5zPzyYhYBhyQmR+obP8K8ImIuAL4W+BdwPsoP/0y4Erguoj4AfA94FzKjwJfM5rn0i5zeqdZfEiSOkLRIyFvoTznx4CB+zKuA84G5gBzBzZm5uMRcQrwReBTwHrgI5m5sqrPP0XELOBSyjey3gecnJm1N6tKkqQCFT1PyB3AkBOEZObZQ+zzGyMc9yrGweUXSZI6WdEzpkqSpA5lESJJkgphESJJkgphESJJkgphESJJkgphESJJkgphESJJkgphESJJkgpR9IypY1ojbwJUWalUor+/n76+vo56YVM7mcPWmcPWmcPWdWoOG/ndGZk5cq8OExEHUJ4SXpIkNefAzPz5cB0sQgYREQG8Fnix6FjGoRmUC7gDMX/NMoetM4etM4et6+QczgCezhGKDC/HDKKStGGrNw2uXL8B8GJmej2rCeawdeawdeawdR2ew7rO1xtTJUlSISxCJElSISxC1G7bgEsqX9Ucc9g6c9g6c9g6czgCb0yVJEmFcCREkiQVwiJEkiQVwiJEkiQVwiJEkiQVwiJEDYuIj0fEuojYGhH3RMRbR+h/bkQ8HBFbIuKpiPhiROy9p+IdixrJYUR0RcSFEfFYpf/9EXHynox3rImI+RFxU0Q8HREZEafVsc+CiPhhRGyLiEcj4uzRj3TsajSHETEnIpZHxE8jYmdEfGnPRDp2NZHDxRGxOiKei4i+iLg7Ik7aQ+GOSRYhakhEnAlcSfmxszcD9wMrI+I1Q/RfAlxe6f+rwIeBM4HL9kjAY1CjOQQ+D/xX4PeAw4GvAP8cEb+xB8Idq/ahnLeP19M5Ig4GbgZuB44GvgR8tcN/ATSUQ2Aq8Bzln8f7RyuocabRHM4HVgPvAeZR/nm8qZP/LvuIrhoSEfcA38/MT1TWJwFPAX+emZcP0v8q4Fcz84Sqtj8B3paZx+2hsMeUJnL4NPC/MvPqqrZvAlsy83f2UNhjVkQkcHpm3jBMnz8CTsnMI6va/hHYNzM7elQJ6sthTf87gPsy89xRDGtcaTSHVfutBf4pMy8dlcDGOEdCVLeImEK5el8z0JaZOyvrxw6x213AvIHLDRFxCOX/BdwyutGOTU3mcCqwtaZtC9CRRVyTjqUq5xUrGTrn0qir/AdkBvB80bEUxRfYqREzgcnAMzXtzwBvGmyHzFweETOB71TeTrwX8JXM7NTLMQ3nkPIvy/Mi4tvAY8AJwOLKcVSf2Qye856ImJaZWwqISfoDYDrw9aIDKYojIRpVEbEAuAD4b5Tvf1gMnBIRSwsMa7z5FPAI8BNgO3AVcA2ws8igJDWvcr/cRcD7MvPZouMpiiMhasQmYAewf037/sDGIfb5HPB3mfnVyvr/i4h9gL+KiP9VuRTRSRrOYWY+B5xWeaJoP+Bpyjf7/mwU45xoNjJ4zvscBdGeFhFnAV8Ffiszay8TdhRHQlS3zNwO3Ev5cgDw8jXNE4C7h9itm93/x75jYPd2xzjWNZnDgX23ZubPKf/n4QxgxSiGOtHcTVXOKxYyQs6ldouI91MeyXx/Zt5cdDxFcyREjboSuC4ifgB8DziX8mNq1wBExPXAzzPz/Er/myjfz/Aj4B7gDZRHR27KzB10poZyGBFvAw4A7qt8vZjyfyCu2MNxjxkRMZ3yz9KAgyPiaOD5zHwyIpYBB2TmByrbvwJ8IiKuAP4WeBfwPuCUPRj2mNJEDqlsh/J9DLMq69sz88E9E/XY0mgOK5dgrqN8ifWeiJhd2W9LZm7eg6GPHZnp4tLQAnwCeILy66nvofy47cC2O4Brq9b3onzd81HKT3Q8CVxN+dHIws9lnOTweOBByk/IbAKuB15b9DkUnL8FQA6yXFvZfi1wxyD7/KiS88eAs4s+j3GYw8H6ryv6XMZLDit/t4fs34mL84RIkqRCeE+IJEkqhEWIJEkqhEWIJEkqhEWIJEkqhEWIJEkqhEWIJEkqhEWIJEkqhEWIpDEtIu6IiC81sV9Wlhfq7L+gap8bGv08SY2zCJHUdjW/0Adbbm/gcIuBl9+6HBHrIuLcOvc9Bziszr53AXPo4NeqS3ua746RNBoGfqHXOpXye1z+ot4DZebzLcTxQtb5mvQsv1xwY0RsAaa28JmS6uRIiKS2y8ztmbmxegFeBfwxcFlmfmOgb0QcGRG3RsS/R8QzEfF3ETGzavvLl2Mi4g7gdcAXB0ZVGokrIn49Im6PiBcjoi8i7o2It7ThlCU1wSJE0qiLiH2BFZRf4LW0pv1fKb9Y7i3AycD+DH1JZDGwHriQ8kjLYKMtw/mHyv7HAPOAy4FSg8eQ1CZejpE0qiJiErAceAn47dz1rZmfAH6UmRdU9f8Q8FREHJaZP60+VmY+HxE7gBcroyuNmgt8ITN/Ull/pIljSGoTixBJo+0y4FjgrZn5Ys22XwfeGRH/Psh+rwd+Okh7K64EvhoRvwusAb6RmY+1+TMk1cnLMZJGTUScBfwBcFZmDjbqMB24CTi6ZjkU+Ha748nMi4EjgJuBdwEPRsTp7f4cSfVxJETSqIiIo4G/AT6bmSuH6PZD4AxgXWa+VOehtwOTm42rconnp5Rvbv0a5cd4/7nZ40lqniMhktqu8nTLDZRvRP37iJhds8yqdL0aeDXwtYg4JiJeHxEnRcQ1ETFUobEOmB8RB1Q/RVNHTNMi4qrKHCavi4j/QPkG1YeaPE1JLXIkRNJoOIXyo7SvAzYMsv0J4KDMfLpSDPwRsIry/BxPALcBO4c49oXAXwKPVfpHnTHtAPYDrqf8BM4m4FvARXXuL6nNYtcb1SVpYqjMIXJ6Zt7Q4H7XAvtm5mmjEJakKl6OkTSRfS0i1tfTMSL+Y+Upnd8e5ZgkVXg5RtJEdWjl6446+/+A8pM5AIM9MiypzbwcI0mSCuHlGEmSVAiLEEmSVAiLEEmSVAiLEEmSVAiLEEmSVAiLEEmSVAiLEEmSVAiLEEmSVAiLEEmSVIj/H2lPIqGSanqaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotten der Messdaten:\n",
    "plt.figure(dpi=100)\n",
    "plt.errorbar(time, \n",
    "             height, \n",
    "             xerr=dtime, \n",
    "             yerr=dheight, \n",
    "             ls='', \n",
    "             marker='.')\n",
    "\n",
    "plt.xlabel('Zeit [s]')\n",
    "plt.ylabel('Fallhöhe [m]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Messdaten sehen bereits leicht parabelförmig aus. Als Nächstes wollen wir unser Model `fallhoehe` an unsere Daten fitten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:24.562437Z",
     "start_time": "2020-08-26T06:33:24.550504Z"
    }
   },
   "outputs": [],
   "source": [
    "para, pcov = curve_fit(fallhoehe, \n",
    "                       time,\n",
    "                       height,\n",
    "                       sigma=dheight,\n",
    "                       absolute_sigma=True\n",
    "                      )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Fit hat funktioniert. Gucken wir uns also doch mal die Fitgüte und den Wert für $g$ an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:25.833057Z",
     "start_time": "2020-08-26T06:33:25.823083Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Das die Fitgüte Chi²/ndof lautet 127.31/8\n",
      "und der Wert für g ist 3.69 +/- 0.00 m/s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "chi = sum([(fallhoehe(t, para[0]) - h)**2/dh**2 for t, h, dh in zip(time, height, dheight)])\n",
    "\n",
    "print(f'''\n",
    "Das die Fitgüte Chi²/ndof lautet {chi:.2f}/{len(height) - 1}\n",
    "und der Wert für g ist {para[0]:.2f} +/- {pcov[0,0]:.2f} m/s\n",
    "''')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unser $\\chi^2$/ndof (wobei ndof die Anzahl der Freiheitsgrade ist) ist nicht schlecht. Darüber hinaus scheint der Fehler des Wertes kleiner zu sein als die Anazahl an signifikanten Stellen, die uns zur Verfügung stehen.  \n",
    "\n",
    "Als Zweites sollen wir das Ganze nochmal wiederholen, um zu testen, ob ein linearer Fit nicht besser an die Daten passt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:27.412181Z",
     "start_time": "2020-08-26T06:33:27.398218Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Das die Fitgüte Chi²/ndof lautet 236.44/7\n",
      "und der Wert für g ist 3.63 +/- 0.00 m/s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def fallhoehe2(t, v, h0):\n",
    "    return t * v + h0\n",
    "\n",
    "para2, pcov2 = curve_fit(fallhoehe2, \n",
    "                       time,\n",
    "                       height,\n",
    "                       sigma=dheight,\n",
    "                       absolute_sigma=True\n",
    "                      )\n",
    "\n",
    "chi = sum([(fallhoehe2(t, para2[0], para2[1]) - h)**2/dh**2 for t, h, dh in zip(time, height, dheight)])\n",
    "\n",
    "print(f'''\n",
    "Das die Fitgüte Chi²/ndof lautet {chi:.2f}/{len(height) - 2}\n",
    "und der Wert für g ist {para2[0]:.2f} +/- {pcov2[0,0]:.2f} m/s\n",
    "''')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier ist das $\\chi^2$ wesentlich schlechter und somit ist die Hypothese, dass es sich um ein lineares Model handeln könnte, abgelehnt. Zuletzt können wir noch unsere beiden Ergebnisse gemeinsam mit den Daten plotten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:29.443916Z",
     "start_time": "2020-08-26T06:33:29.222481Z"
    }
   },
   "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": [
    "# Plotten der Messdaten:\n",
    "plt.figure(dpi=100)\n",
    "plt.errorbar(time, \n",
    "             height, \n",
    "             xerr=dtime, \n",
    "             yerr=dheight, \n",
    "             ls='', \n",
    "             marker='.')\n",
    "\n",
    "times2 = [i/100 for i in range(70, 130)]\n",
    "\n",
    "plt.plot(times2, \n",
    "         [fallhoehe(t, para[0]) for t in times2],\n",
    "         label='Gleichförmig Beschleunigte Bewegung')\n",
    "\n",
    "plt.plot(times2, \n",
    "         [fallhoehe2(t, para2[0], para2[1]) for t in times2],\n",
    "         label='Bewegung konstanter Geschwindigkeit')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Zeit [s]')\n",
    "plt.ylabel('Fallhöhe [m]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zusatz:\n",
    "\n",
    "Wie wir bereits am Versuchstag selbst festgestellt haben, können bei einem einfachen $\\chi^2$-Fit lediglich die Fehler des Funktionswertes berücksichtigt werden. Da in unseren obigen Messdaten der Zeitfehler dominiert, wollen wir uns angucken, was passiert, wenn wir die beiden Achsen vertauschen. D.h. dieses mal wollen wir eine Funktion $t(h, g)$ an unsere Messdaten anpassen:\n",
    "\n",
    "$$t(h, g) = \\sqrt{2 \\cdot h/g}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gucken wir uns zunächst wieder die Messdaten an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:37.852532Z",
     "start_time": "2020-08-26T06:33:37.655061Z"
    }
   },
   "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": [
    "# Plotten der Messdaten:\n",
    "plt.figure(dpi=100)\n",
    "plt.errorbar(height, \n",
    "             time, \n",
    "             xerr=dheight, \n",
    "             yerr=dtime, \n",
    "             ls='', \n",
    "             marker='.')\n",
    "\n",
    "plt.xlabel('Fallhöhe [m]')\n",
    "plt.ylabel('Fallzeit [s]')\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "def fallzeit(h, g):\n",
    "    return (2 * h/g)**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:39.764472Z",
     "start_time": "2020-08-26T06:33:39.757481Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Das die Fitgüte Chi²/ndof lautet 4.17/8\n",
      "und der Wert für g ist 3.67 +/- 0.00 m/s\n",
      "\n"
     ]
    }
   ],
   "source": [
    "parat, pcovt = curve_fit(fallzeit, \n",
    "                       height,\n",
    "                       time,\n",
    "                       sigma=dtime,\n",
    "                       absolute_sigma=True\n",
    "                      )\n",
    "\n",
    "chit = sum([(fallzeit(h, para[0]) - t)**2/dt**2 for t, h, dt in zip(time, height, dtime)])\n",
    "\n",
    "print(f'''\n",
    "Das die Fitgüte Chi²/ndof lautet {chit:.2f}/{len(height) - 1}\n",
    "und der Wert für g ist {parat[0]:.2f} +/- {pcovt[0,0]:.2f} m/s\n",
    "''')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jetzt sind die Werte für $g$ fast identisch mit den Werten des vorherigen Fits, jedoch sieht das $\\chi^2$ dieses mal aufgrund der größeren Fehler besser aus. Dies spricht dafür, dass die Fehler von der Fallhöhe unterschätzt worden sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:33:48.115891Z",
     "start_time": "2020-08-26T06:33:47.902422Z"
    }
   },
   "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": [
    "plt.figure(dpi=100)\n",
    "plt.errorbar(height, \n",
    "             time, \n",
    "             xerr=dheight, \n",
    "             yerr=dtime, \n",
    "             ls='', \n",
    "             marker='.',\n",
    "            label='Messdaten')\n",
    "\n",
    "x = [i/10 for i in range(10, 30)]\n",
    "\n",
    "plt.plot(x, \n",
    "         [fallzeit(i, parat[0]) for i in x],\n",
    "         label='t(h, g)')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('Fallhöhe [m]')\n",
    "plt.ylabel('Fallzeit [s]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bestimmen der Erdbeschleunigung mittels curve_fit und einer schiefen Ebene:\n",
    "\n",
    "Der Zusammenhang der zurückgelegten Strecke $s$ einer Vollkugel auf einer schiefen Ebene ist gegeben durch:\n",
    "\n",
    "$$s(t) = \\frac{5}{14} \\cdot g \\cdot \\sin(\\alpha) \\cdot t^2$$\n",
    "\n",
    "Während des Versuchs wurden jedoch die Startfallhöhe $h$ und die benötigte Zeit $t_\\text{i}$ gemessen (wobei $i$ der Index für die drei Messversuche ist.). Dies bedeutet, dass wir unsere obige Formel in Abhängigkeit dieser beiden Parameter ausdrücken müssen, um $g$ mittels eines Fits bestimmen zu können. Das können wir erreichen, indem wir den folgenden Zusammenhang verwenden:\n",
    "\n",
    "$$\\sin(\\alpha) = \\frac{h}{l}$$\n",
    "\n",
    "wobei $l$ die Länge unserer schiefen Ebene ist. Setzen wir dies in unsere obige Formel ein und lösen die Gleichung nach $h$ auf, dann erhalten wir:\n",
    "\n",
    "$$h = \\frac{14 \\cdot l^2}{5} \\cdot \\frac{1}{g} \\cdot \\frac{1}{t_\\text{i}^2}$$\n",
    "\n",
    "wobei wir hier noch verwendet haben, dass die maximal zurückgelegte Strecke der Kugel nach einer Zeit $t_\\text{i}$ der Gesammtlänge der schiefen Ebene entspricht. Diese Formel für $h$ können wir nun auf unterschiedliche Arten und Weisen in Abhängigkeit der Zeit setzen, wobei die bereits gezeigte Variante die erste ist:\n",
    "\n",
    "**Variante 2. Parabel:**\n",
    "$$h(x=\\frac{1}{t_\\text{i}}) =  \\frac{14 \\cdot l^2}{5} \\cdot \\frac{1}{g} \\cdot x^2$$\n",
    "\n",
    "**Variante 3. Ursprungsgerade:**\n",
    "$$h(x=\\frac{1}{t_\\text{i}^2}) =  \\frac{14 \\cdot l^2}{5} \\cdot \\frac{1}{g} \\cdot x$$\n",
    "\n",
    "\n",
    "Da die erste Variante von uns am wenigsten Arbeit verlangt, werden wir im folgenden diese Verwenden.\n",
    "\n",
    "Die Messwerte sollten so oder so ähnlich aussehen. Es wurden für verschiedene Fallhöhen jeweils dreimal die Zeit gemessen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:01.100071Z",
     "start_time": "2020-08-26T06:35:01.090098Z"
    }
   },
   "outputs": [],
   "source": [
    "# Eingelesene Messwerte:\n",
    "h = [0.095, 0.112, 0.134, 0.148, 0.17, 0.188, 0.21, 0.235, 0.25, 0.276] # [m]\n",
    "t1 = [2.65, 2.4, 2.17, 2.06, 1.91, 1.8, 1.68, 1.6, 1.52, 1.46]          # [s]\n",
    "t2 = [2.71, 2.36, 2.19, 2.06, 1.9, 1.78, 1.69, 1.69, 1.53, 1.44]        # [s]\n",
    "t3 = [2.66, 2.36, 2.19, 2.06, 1.9, 1.8, 1.68, 1.59, 1.52, 1.44]         # [s]\n",
    "delta_t = [0.1]*len(h)   # [s]\n",
    "delta_h = [0.005]*len(h) # [m]\n",
    "\n",
    "l = 1.507 # [m]\n",
    "delta_l = 0.005 # [m]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun müssen wir uns unsere Formel definieren, um unsere Messdaten fitten zu können. Hierbei ist es wichtig, dass eine Fitfunktion $\\lambda$ von dieser Form ist $\\lambda(x, \\Theta)$, woebei $\\Theta$ unsere Parameter sind. In unserem Fall entspricht dies einer Funktion $h(t, g)$ bzw. in den anderen beiden Varianten $h(x, g)$ wobei $x=1/t$ und $x=1/t^2$ in den Varianten 2 und 3 ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:12.883418Z",
     "start_time": "2020-08-26T06:35:12.878431Z"
    }
   },
   "outputs": [],
   "source": [
    "def fallhoehe(t, g):\n",
    "    l = 1.507\n",
    "    return 14/5 *l**2 * 1/g * 1/t**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Als nächstes sollten wir zu jeder Fallhöhe den Mittelwert unserer drei Zeitmessungen bilden und den entsprechenden Fehler berechnen. Hierdurch erhalten wir ein genaueres Ergebnis für die gesuchte Zahl von $g$.\n",
    "\n",
    "D.h. wir müssen uns zunächst eine Funktion definieren, welche den Mittelwert für die Messwerte berechnet\n",
    "\n",
    "$$\\bar{x} = \\frac{1}{n} \\sum_i^n x_i$$\n",
    "\n",
    "sowie dessen Standardabweichung\n",
    "\n",
    "$$\\sigma_\\text{n-1} = \\sqrt{\\frac{1}{n-1} \\sum_\\text{i}^\\text{n} (\\bar{x} - x_\\text{i})^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:17.670513Z",
     "start_time": "2020-08-26T06:35:17.662534Z"
    }
   },
   "outputs": [],
   "source": [
    "# Mittelwert:\n",
    "def mittelwert(l1, l2, l3):\n",
    "    '''\n",
    "    Funktion, welche den Mittelwert für drei Messspalten \n",
    "    berechnet.\n",
    "    '''\n",
    "    result = []\n",
    "    for i,j,k in zip(l1, l2, l3):\n",
    "        result.append((i + j + k)/3)\n",
    "    \n",
    "    return result\n",
    "\n",
    "# Standardabweichung\n",
    "def standardabweichung(l1, l2, l3):\n",
    "    '''\n",
    "    Funktion, welche die Standardabweichung für drei Messspalten \n",
    "    berechnet. \n",
    "    '''\n",
    "    mean = mittelwert(l1, l2, l3)  # <-- hier rufen wir unsere Funktion des \n",
    "                                     # Mittelwertes in einer weiteren Funktion\n",
    "                                     # auf.\n",
    "    result = []\n",
    "    for m, i,j,k in zip(mean, l1, l2, l3):\n",
    "        result.append( (1/2 *(m-i)**2 + (m-j)**2 + (m-k)**2 )**(1/2))\n",
    "    \n",
    "    return result\n",
    "    \n",
    "t_mean = mittelwert(t1, t2, t3)\n",
    "t_std = standardabweichung(t1, t2, t3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun können wir unsere Messwerte plotten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:20.098903Z",
     "start_time": "2020-08-26T06:35:20.094915Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:20.926337Z",
     "start_time": "2020-08-26T06:35:20.456594Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(t_mean, \n",
    "             h, \n",
    "             xerr=t_std,\n",
    "             yerr=delta_h,\n",
    "             ls='',\n",
    "             marker='.',\n",
    "             label='Rollzeit Vollkugel')\n",
    "\n",
    "plt.grid()\n",
    "plt.xlabel('Gemessene Rollzeit $t$ [s]')\n",
    "plt.ylabel('Starthöhe $h$ [m]')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Man kann anhand des Plots bereits schön den nicht linearen Zusammenhang zwischen der Starthöhe $h$ und der Rollzeit $t$ erkennen. Als Nächstes wollen wir nun aus diesen Daten unsere Erdbeschleunigung $g$ bestimmen. Hierzu verwenden wir wieder unsere Funktion `curve_fit`. Im folgenden wird jedoch nochmal anhand dieses Datensatzes illustriert, was `curve_fit` genau macht. Hierzu gucken wir uns die nachfolgenden Plots an (ignoriert zunächst einmal den Code)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:35:34.756775Z",
     "start_time": "2020-08-26T06:35:33.818248Z"
    }
   },
   "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"
    },
    {
     "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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MY0y5YmJiyMrKsqQRZlSVrKwsYmJi/KpnfRjGmHIlJiaydetWfvnll2CHUiW5ubl+fymGqupuS0xMDImJiX7VsYRhjClXdHR08UB9tVFGRoZfQ1+EslBoi92SMsYY44klDGOMMZ5YwjDGGOOJJQxjjDGeWMIwxhjjiSUMY4wxnljCMMYY40nYJgzRwsoLGWOM8SxsE0a9A9thv03KZ4wx1SVsE0ZkwUF4/kz4NTPYoRhjTFgI24Sxv35LyN0Nz58OGzOCHY4xxtR6AU0YIpIuIutEJFNE7ixj/7UiskJElovIfBHp4rPvLrfeOhE5u7JzFUTGwNWfQmwL+O+FsKTyOXWNMcaUL2AJQ0QigQnAUKALMMY3IbheU9WTVDUF+BfwuFu3CzAa6AqkA8+6x6tYfFu48kNolwbv3gof3AWFBdXTIGOMOcYE8gqjN5CpqhtV9RAwDRjuW0BV9/qsNgCKBuEfDkxT1YOqugnIdI9XuZg4GPM69LkWFj4LU0dD7t7K6xljjDlMIIc3bwls8VnfCvQpXUhEbgD+CNQBTvepu7BU3ZZl1B0HjANISEggIyOjZGe9oZzQATp8P5l9zwxgZbe7ya3X/GjaE1A5OTmHt6cWC6e2QHi1J5zaAuHVnlBoS8jNh6GqE4AJInIxcA9wuR91JwOTAZKTkzUtLa1UiTTYkE7D6ZfTd8VfYPRr0PqInBWSMjIyOLI9tVM4tQXCqz3h1BYIr/aEQlsCeUtqG9DKZz3R3VaeacD5VaxbvhMHw1UfQ91YeOk38N30Kh3GGGOONYFMGIuBDiKSJCJ1cDqxZ/sWEJEOPqvnAt+7n2cDo0WkrogkAR2Ar6scSUJH5wmqxN7wxtXwyQNQaG+GG2NMRQJ2S0pV80XkRmAuEAlMUdVVIjIeWKKqs4EbReRMIA/YhXs7yi03HVgN5AM3qOrRPe5UvzFc+ia890f44lHI+h7Onwh16h/VYY0xJlwFtA9DVecAc0ptu9fn8y0V1P078PdqDSiqDgx7BhKS4cO/wu4fYfRUOK5FtZ7GGGPCQdi+6e2ZCJx6E4yZCr+sh+dOh+3Lgx2VMcaEHEsYRZKHwpVzQSLgxaGwenbldYwx5hhiCcPX8Sc5neHNusD0S+GLx0G18nrGGHMMsIRRWmxzuOJd6DYCPrkf3roO8g8GOypjjAm6kHtxLxhGTfoKgNev6edsiK4HFz4PTTtCxj9g1w8w6r/QoGnwgjTGmCCzKwwgOzePbbsPsHTzrpKNIpB2B4yYAtu/cTrDf14TvCCNMSbIjukrjFGTviI7N4/VO7IBGDlxAZ2OjyU2JrrkaqPbhdCorTNo4QtDYMSL0OHM4AVtjDFBcsxfYezNzS/+XKiHrxdLTIVx86BRG3htJCyaZJ3hxphjzjGdMF6/ph9Pje5BhDjrMdERPDW6R8nVha+4RPj9B9AxHd6/Hd67DQryAhuwMcYE0TGdMABS28TT6fhYEuPr8epVfUltE19+4boNnc7vU2+GJS/AqyPgwO6AxWqMMcFUaR+GiDT2cJxCVd199OEEx5xbBnkvHBEJQx5whhN551aYfBpcMAla962x+IwxJhR46fTe7i5SQZlIoHW1RFRb9LgEmrSHN8bBlHTofwsM/gtE1Q12ZMYYUyO8JIw1qtqjogIi8k01xVO7tO4L130Jc++GL5+E7z+C305y3hg3xpgw46UPo4we4CqVCU91Y2HY08684ft+gcmDnSFFCo9u9HVjjAk1lSYMVc2tjjJhLzkdrl8Inc5xhhR5cSjs3BjsqIwxptp4fkpKRHqJyJsiskxEvhORFSLyXU0GV+s0aAIjX4LfPg+/rIV/D4AlU+ydDWNMWPDnTe9XgT8DKwCbz7Q8ItB9JLQ5Fd6+Ht79A6x9D4b9n03MZIyp1fx5D+MXVZ2tqptUdXPRUmOR1XZxLeGSN+GcR+GHL+HZvrByVrCjMsaYKvMnYfxNRJ4XkTEi8tuixZ+TiUi6iKwTkUwRubOM/X8UkdXuLa9PRKSNz74CEVnuLiE9u9GoSV85I+BGREDvq+Ha+c4juDN/DzOvhP07gx2iMcb4zZ9bUmOBTkA0JbekFHjDS2URiQQmAGcBW4HFIjJbVVf7FPsG6KWq+0XkOuBfwCh33wFVTfEj3qDJzs1jb24+Szfvct4cb9oefj8XvnwCMh6CzV/C8P+D9jaIoTGm9vDnCuMUVe2lqper6lh3+b0f9XsDmaq6UVUPAdOA4b4FVHWequ53VxcCiX4cPySc89TnrN6RzdZdBxg5cUHJkOmRUTDoz3DVJxDTCP57odO/cWhfUOM1xhivRD0+wSMiLwKPlLoi8H4ikRFAuqpe5a5fCvRR1RvLKf9/wP9U9UF3PR9YDuQDD6nqW2XUGQeMA0hISEidPn16VUI9Kn/K2M+vuSX/piM6RPObE+scViai4BBtf3iVVlveJjemOWs638reuM4VHjcnJ4eGDRvWSMyBFk5tgfBqTzi1BcKrPYFqy+DBg5eqaq+y9vlzS6ovsFxENgEHcYYKUVXtXg0xHkZELgF6Aaf5bG6jqttEpB3wqYisUNUNvvVUdTIwGSA5OVnT0tKqO7RKTUraxciJCyhUZ/TbMWeeUs6AhkPghy+p99a19Fz+F+h/K6TdBVF1yigLGRkZBKM9NSGc2gLh1Z5waguEV3tCoS3+JIz0ozzXNqCVz3qiu+0wInImcDdwmqoWT6atqtvcnxtFJAPoAWwoXT/Yika/3Zubz1Oje1Q8+m3b/nDtlzD3LzD/8ZKhRZp3DVzAxhjjkZfRapepas+KHqEtKlPJoRYDHUQkCSdRjAYuLnWcHsAknFtXP/tsjwf2q+pBEWkK9MfpEA9Jfo1+G3Oc0wHe6VyYfRNMToPBd8OpNzkj4xpjTIjwcoXRuZI3ugWIq+wgqpovIjcCc3FGt52iqqtEZDywRFVnA48ADYEZIgLwo6oOAzoDk0SkEKej/qGq9qWErOShztAi794KH/8N1n8A5/8bGicFOzJjjAG8JYxOHsp4GmlPVecAc0ptu9fnc5nPmarqAiD8h4Bt0BQuegW+mw5z/gz/7g/p/4Celwc7MmOMqTxh2NvcASYCJ49y+jfeuh7euQXWvkedpqPLLH7OU5976y8xxpij5E+nt6kmoyZ95amc6B0MOa4rv/v+BXp+/xmvr5jHuw0v5JDEAM4Lgqt3ZAMwcuICOh0fS2xM9FHFVuZ85sYYg83pHdJUIpjbYBi3JUzi64gURuW8whM/X82pB+aBKntz84vLFiqHrRtjTHWzK4wgqMpf8RkZ8dA2mqZz7+KWHQ9zS+I8lp5+PyPfOFD8zofdljLG1CR/5sM4XUReEJHHRGSsiKSKiE1gHUht+8PVGTD8Wdi9mdT3hnJ3w9l0jCvk1av6WrIwxtQof25JTQHewRnjqR1wL7CqJoIyFYiIgB6/g5uWwsA/cWXhm3xYcDWpmybBof2V1zfGmCry55bUZp/xm2bUQCzGH3Vj4Yy/Qs/L4OP7IOOfsOxlOPM+6DbCSSzGGFONKv1WEZGXReRWYKGI/LHmQzJ+iW8DI1+EsR9Aw2bwxtXwwlmwZXGwIzPGhBkvf4b+B+dt7ubApSKyWURmi8gDIjKyRqMz3rXpB1d9CudPhD1b4YUzYdZVzmdjjKkGXl7c+xT4tGhdRKJwhuo4GTgFuz0VOiIiIGUMdD4PvnwSFjwDa96F/jdD/1ugToNgR2iMqcX8vtGtqvmqukJV/6uqt9dEUOYo1W0Ip98DNy6GTufAZw/DM6nw7TQoLKy8vjHGlMF6RsNZo9YwYgr8/kOIbQFvXgPPnwE/Lgp2ZMaYWsgSxrGgdR9natgLJkP2/2DKEJj5e9j9Y7AjM8bUIv68uCcicomI3OuutxaR3jUXmqlWERHOoIY3LYHT7uTgync59GQqfPogHMwJdnTGmFrAnyuMZ4F+wBh3PRuYUO0RmZpVpwEMvosr4p7nbq5nacZbTv/G8tesf8MYUyF/EkYfVb0ByAVQ1V1A2RNQm5B2zlOf89VPkczI7c1FefextO4p8NZ18NxgWD8XVIMdojEmBPmTMPJEJBJQABFJAOxP0lrId1TbAhUWdv0b/PZ52L8TXrsIJg6ElW9Aoad5sYwxxwh/EsbTwJtAMxH5OzAf+EeNRGVq1FOjexAhzueY6Aj6ntgUuo+Em5c508Lm58LMsTChN3zzX8g/FNyAjTEhwXPCUNVXgduBfwI7gPNV1a+X9kQkXUTWiUimiNxZxv4/ishqEflORD4RkTY++y4Xke/dxeYsPQqpbeLpdHwsifH1Dh/lNjIaUi6GGxbByJcguj68fQM83QMWTYK8A8EN3BgTVH7Nh6Gqa4G1VTmReztrAnAWsBVYLCKzVXW1T7FvgF6qul9ErgP+BYwSkcbA34BeOLfElrp1d1UlFgNzbhlU/s6ISOh6PnQZDpmfwBePwvu3w+ePQN/r4ZQrISYuYLEaY0KD54Thzn1xIdDWt56qjvd4iN5ApqpudI83DRgOFCcMVZ3nU34hcIn7+WzgI1Xd6db9CEgHpnqN31SBCHQ401k2L4AvHoNP7of5T0KfcdDnOmjQJNhRGmMCxJ8rjLeBPcBS4GAVztUS2OKzvhXoU0H5K4H3K6jbsnQFERkHjANISEggIyOjCmGGppycnOC3J/EmGsadQ5vNM2j6+aMUzn+a7ScMYWvi+RyMaer5MCHRlmoUTu0Jp7ZAeLUnFNriT8JIVNX0GovEh4hcgnP76TR/6qnqZGAyQHJysqalpVV/cEGSkZFBaLQnDbgSfllH5PwnaPXddFpt/8Dp++h/CzQ5sdIjhE5bqkc4tSec2gLh1Z5QaIs/T0ktEJGTjuJc24BWPuuJ7rbDiMiZwN3AMFU96E9dE0AJyXDBRLj5G0i93BnY8P96wcwr4SebiNGYcORlAqUVIvIdMABY5j7l9J3Pdq8WAx1EJElE6gCjgdmlztUDmISTLH722TUXGCIi8SISDwxxt5lgi28D5z4Gt66AfjfC+g/g36fC1DGwdUmwozPGVCMvt6R+Ux0nUtV8EbkR54s+EpiiqqtEZDywRFVnA48ADYEZIgLwo6oOU9WdIvIATtIBGF/UAW5CRGxzGPIADPgDfP0cLPq3MzJu0iAYeBskncaoyQsBuC45yLEaY6rEywRKm4s+i8jJwEB39QtV/dafk6nqHGBOqW33+nw+s4K6U4Ap/pzPBEH9xpB2B/S7AZa+6Ezi9PJwaNmLlnsvZHFBMpm7nJ4QY0zt4uWW1CXuz1uAV4Fm7vJfEbmpZsMztVbdhnDqTVzS8DmeO+4mPt4WwZys49m2ex//XLSP8578lFGTvgp2lMYYP3i5JVXf/XklzgCE+wBE5GHgK+CZGorNhIE8qcPHDc5lx6E0cnNzASGSAgZnTeXE4xR2NofG7YIdpjHGA38eqxXAdzS6AnebMeV6/Zp+ACzdvIuRExdQqBAZIZzWtj6pW1+Bp2dAu8HQ6/eQPNQZnsQYE5K8JIyiAYReBBaJyJs4iWI41qdgPCoav2pvbj5XdFRSL3gK9t4By16BZS/B9EuhYXPoeZmzNGod7JCNMaV46fR+xf35uIhk4Dxeq8BYVf2mZsMz4aRo/Krit1WPO8HpIB94G2R+BEtehM8fdZYOQ6DXWOdnRGTwgjbGFPN3LKlOOI+9RgHnich5fowlZUzZIqOc21HJQ515xpe97CxTR8Nxie5Vx6VOgjHGBI0/b3q/jXMbKh/Y57MYU30atYbT74E/rIKLXoGmHSDjH/BEN5j2O8j82KaSNSZIQnIsKWOIjIYuw5wla4PTz/HNq7D2XWjUBlKvgB6XQMNmwY7UmGNGIMeSMqZqmpwIZ42HP66GC19wrkI+uR8e7wIzroBNn5c5D/moSV/Zux7GVKNKrzBEZAVOJ3cUMFZENuIMby6Aqmr3mg3RGFdUXThphLP8sh6W/geWvwqr3oQm7SF1rDNqbv3GAGTn5rE3N5+lm3eVzCpojKmygI0lZUy1SugI6f+AM/4Kq95yhiH58G74ZDx0PZ/rNp7K6l8TABg5cQEzrj3VkoYxR6nSW1KqutkdT+r6os++22o+RGMqEF0PUsbAlR/CdQucJ6rWvU+33Z8Q4b5nWqjKwo1ZQQ7UmNrPnz6Ms8rYNrS6AjHmqDXvCuc+Cretpe+goURRSCQFxHCIvt/e7Uwtu/vHYEdpTK3lpQ/jOpwriRNLzX8RC3xZU4EZU2V1GpA65GKmJu9i4ZpN9C1YRur2X+HjvzlLqz7Q7ULocr4zLLsxxhMvfRiv4cxh8Tww1md7ts1JYUJZapt4t9+iJ3AV7NwEq96AFbPg/dvhgzuh7UA3eQyDetbHYUxFvAwNsgfYIyLNfOfGMKbWaZzkDEMy8Db4eQ2sfANWzoR3bob3boP2Z0C3Ec4b53UbBjtaY0KOPy/uLRWRU1R1ceVFjQlxzTrD6XfD4L/AjuWwYqbzeO76DyCqHnQ823l8t/1ZEB0T7GiNCQn+JIw+wO9EZDPOkCD2Hoap/UTghB7OctYDsGWRc9Wx6i1Y/RbUiYXOv3GuPNqdZsOvm2OaPwnj7KM9mYikA0/hzOn9vKo+VGr/IOBJoDswWlVn+uwrAFa4qz+q6rCjjceYw0REQJt+zpL+MGz6zLltteYd+HYq1G8CXYY7fR6tT3XKG3MM8ZwwVHWziMQDHQDfa3RP/RoiEglMwHk8dyuwWERmq+pqn2I/AlcAfyrjEAdUNcVrvMYclcgop0+j/Rnwm8edQQ9XzoJvp8GSKRDbArr+1kkeZQxLYkw48md486uAW4BEYDnQF2eK1tM9HqI3kKmqG93jTcMZ/bY4YajqD+4+G47UhI6outDpXGc5tA/Wve9ceSx+DhZOoG/dJrBvOHRMh6RBzsuEHhSNc1U0K6ExoU7U419H7phSpwALVTVFRDoB/1DV33qsPwJIV9Wr3PVLceYIv7GMsv8B3i11SyofJ1HlAw+p6ltl1BsHjANISEhInT59uqe21QY5OTk0bBgeT+6ES1ui8nJo+usi4n5aQLO9K4kszKUgog674k8mq0kvdjbuxcGYpuXWv/fL/ezPg2tPrkv7+NCYJCpcfjdFwqk9gWrL4MGDl6pqr7L2+dOHkauquSKCiNRV1bUiklxNMXrRRlW3iUg74FMRWaGqG3wLqOpkYDJAcnKypqWlBTC8mpWRkUG4tCec2gK/ISMjgxYD+sEP84lcP5em6z+g6fp/O7uPP8m58uiYDif0LO73WLp5F1vnOnOcP7rsEK9e1TckxroKr99NeLUnFNriT8LYKiKNgLeAj0RkFx77L1zbgFY+64nuNk9UdZv7c6M7VWwPYEOFlYwJlKi6JX0eQx+GX9Y5j+iunwtfPAafPwINEpwpZzuezcJt7Sl0L+7z8gtZuDErJBKGMRXxp9P7AvfjfSIyD4gD3vfjXIuBDiKShJMoRgMXe6nodrbvV9WDItIU6A/8y49zGxM4ItCsk7MMuBX274TMT5wEsvZdWP4qfbUTdbiLPCKJjoykb7smwY7amEr50+n9sKreAaCqnxVtA+7wUl9V80XkRpxhRiKBKaq6SkTGA0tUdbaInAK8CcTjzBl+v6p2BToDk9zO8AicPozV5ZzKmNBSvzF0H+ksBfmwZRGp6z9g6oqXWbirAX0j1pD6ToTzsmDHdGesq0h/Lv6NCQx//qs8iyOTw9AytpVLVecAc0ptu9fn82KcW1Wl6y0AbLY/U/tFRkHb/tC2P6lDIHXnRlj/oXP1sfDfsOBpiIlz3jDvmO7c4nInhDIm2PwZrbadz2i1AjTERqs15ug0bgd9r3WWg9mw4VOn32P9XOeNc4mAVn2dq48TB0Pzk6rthUF7rNf4y+tote8D/wTu9Nluo9UaU53qxjpvkncZDoWFsH2Z23H+QcnQ7PXioe0ASDrNeeejaUenz6QKbApb4y8vCaMjsEVVxwCIyGXAhcBmEbnPkoYxNSAiAhJ7Ocvp98DeHfDDF85wJRs/d4YrAWjY3BmiPWmQs8S3rTSBjJr0Fdm5eazekQ04U9h2Oj6WObcMquFGmdrOS8KYBJwJxWM9PQTcBKTgvPMwoqaCM8a4jmsB3S9yFoBdP8Cmz0uWle47rnGtS5JH0kA47oQyD7c3N7/4c6Eevm5MebwkjEifq4hRwGRVnQXMEpHlNRaZMaZ88W2dpedlzlhWv653k8dn7qO7/3XKNelQkkDaDoQGTXj9mn4s3byLkROdFwdjoiN4anSPYLbG1BKeEoaIRKlqPnAG7tAbftQ3xtQkEUhIdpbeVzv9Hz+tKLn6+O51WPKCU7Z5N0gaRGrSIE5uHs0vB6N4anQP68Mwnnj5wp8KfCYivwIHgC8ARKQ9sKcGYzPGVEVEBLQ42VlOvQkK8mD7cufqY9Pnzmi7C5/lTYlw5gH5fhDkD3KexjKmAl6maP27iHwCtAA+1JLRCiNw+jKMMaEsMhpaneIsg/4EebmwdXHJFciCZ2D+ExARTUpsB8gbAq16Q2JvaJgQ7OhNCPF0S0lVF5axbX31h2OMqXHRMU6HeNJA4G44mAM/LoRNnxGx4n34agJ8+aRTNj7JefO81SnOz2ZdICI0RtY1gWd9EMYc6+o2hA5nQoczWVbnDNL693FuYW39GrZ87bxM+N00p2ydhtAy1bkCadXHeey3nvV/HCssYRhjDhddr2SqWnCewtr1g3Mba8siJ4l88RioO89Z0+SSK5DE3s7LhDZ9bViyhGGMqZgINE5ylqL3QA7mOG+ib1kEWxbD2vfgG/dR3pg4SCxKIKc4VyF1Y4MXv6k2ljCMMf6r27Dk/Q5wrkKyMkuuQLZ8DZn/ANQZD6tZl5KO9Fa9nTG0qjikiS8bDyuwLGEYY46eCDTt4Cw9LnG2HdgN25Y4VyBbFsGKmc4jvQD1Gpc8+ntCivMzPsnvJGLjYQWWJQxjTM2o1wjan+ksAIUF8MtaJ3lsWwY7vnWeyCrMc/bXjYMW3d0E4i6N20FERPGVhK+yxsOKjYk+rMx1gZxE+hhgCcMYExgRkdC8q7P0+r2zLf8g/LzaeSprx7fOsmgyFBx09teJhRbduWxvMzZGtWdTdHu2RyWiElnmeFilE4apXpYwjDHBE1XXedv8BJ+xrArynCuR4iSynHMPfgD7Djj7o+vD8SextM0gRu3qTj4RxERHljnESUZGRsCaciywhGGMCS2R0XD8Sc7Cpc62gnxngEU3gbDjW1I3PMvrdU5gYWFn+kZtIPXDGPdWltsvktA5eG0IUwFNGCKSDjyFM6f386r6UKn9g4Ange7AaFWd6bPvcuAed/VBVX0pIEEbY4IvMgqad3GWlDHOtsICUrM2kOomELYvhxUzSgZajKxDr5iWsLM3NOsMzbo69Y9rWS1PaB2LApYwRCQSmIAzN/hWYLGIzFbV1T7FfgSuAP5Uqm5j4G9AL0CBpW7dXYGI3RgTgiIiIaGjsxS9H1JYCLs2OVch25dzcO18Gm76whmxt0jdODeBdHb6U5p1dh77tbnTKxXIK4zeQKaqbgQQkWnAcKA4YajqD+6+wlJ1zwY+KpqXQ0Q+AtJxRtI1xhhHRAQ0OdFZul3IijoZpKWlwYFd8PMap4P9p9XO51VvwNIXS+rGtihJHs3cq5mmyVCnftCaE2oCmTBaAlt81rcCfY6ibstqissYE+7qxUObU52liCpk73ATyConify0Cr5+ruQpLcR5tLd5l5JE0qyLsy3y2OsCDqsWi8g43AmeEhISwuoJiZycnLBpTzi1BcKrPeHUFvDanijgZIg/GeKB5ALqHdhBg30/0jBnMw32babBD0upt+Y9BOfmR6FEs69BIvsatGFfgzbsr5/I/votyY05Hq2h0Xyr63dz75f72Z8H155cl/bx/sUayISxDWjls57obvNaN61U3YzShVR1Ms484yQnJ2taWlrpIrVWRoZ7aR0GwqktEF7tCae2QDW3J+8A/LIOfl5NxM+rif1pNbE/r4GfMkrKREQ7Y2417QhN2js/i96AP8pRfStrS1kvN5aWnZvHj9nOlEb/+Dq3zJcdKxLIhLEY6CAiSTgJYDRwsce6c4F/iEjRv/gQ4K7qD9EYY8oRXc95XPeElMO3H9gFv2ZC1vfOo7+/fu8s6+eWvMUOUL+pm0CKEombVBq1CdjtraN92TFgCUNV80XkRpwv/0hgiqquEpHxwBJVnS0ipwBv4lwYnici96tqV1XdKSIP4CQdgPFFHeDGGBNU9eJLZjT0VZAPuze7CWS9s2RlOiP77n+5pFxkHadPpGkHaNKh5KqkSXtneBWPvAzAuHTzLkZOXEChQkx0RJkvO06/tvz6Ae3DUNU5wJxS2+71+bwY53ZTWXWnAFNqNEBjjKkukVElT2wlpx++b/9OJ5EUX5Vkws9rYd37UFhyFUCDZsVXJYm7I2DtPmeQxvi2VXp6K7VNPJ2Oj2Vvbn6ZyaIyYdXpbYwxtUL9xtC6j7P4KshzJqsquirJcm9vrX6b9gd2wQafv5ljWzjJo3FSyc+izxW8UzLnlkFVDtsShjHGhIrI6JJOcs45bNf8j2YzoHNL58XEnZtKfmZ+Ajn/O/w4MXE+SaTd4YkltkWVZ0S0hGGMMbVAfvRxkJjqLKUd2u9cmRyWTDY6w6Wseefw21xRMc4trdJXJ/FJ0Kh1hTFYwjDGmNquTv2SsbZKK8iHPVuOvDLZuQk2fQZ5+0vKSsVXHpYwjDEmnEVGlfRvnFhqnyrk/OyTRDZSMsbrkSxhGGPMsUoEYps7S+u+7sbyE0bVej6MMcYccyxhGGOM8cQShjHGGE8sYRhjjPHEEoYxxhhPLGEYY4zxxBKGMcYYTyxhGGOM8cQShjHGGE8sYRhjjPHEEoYxxhhPLGEYY4zxJKAJQ0TSRWSdiGSKyJ1l7K8rIq+7+xeJSFt3e1sROSAiy91lYiDjNsYYE8DRakUkEpgAnAVsBRaLyGxVXe1T7Epgl6q2F5HRwMPAKHffBlVNCVS8xhhjDhfIK4zeQKaqblTVQ8A0YHipMsOBl9zPM4EzREQCGKMxxphyBDJhtAS2+KxvdbeVWUZV84E9QBN3X5KIfCMin4nIwJoO1hhjzOFqywRKO4DWqpolIqnAWyLSVVX3+hYSkXHAOICEhAQyMjICH2kNycnJCZv2hFNbILzaE05tgfBqTyi0JZAJYxvQymc90d1WVpmtIhIFxAFZqqrAQQBVXSoiG4COwBLfyqo6GZgMkJycrGlpaTXQjODIyMggXNoTTm2B8GpPOLUFwqs9odCWQN6SWgx0EJEkEakDjAZmlyozG7jc/TwC+FRVVUQS3E5zRKQd0AHYGKC4jTHGEMArDFXNF5EbgblAJDBFVVeJyHhgiarOBl4AXhGRTGAnTlIBGASMF5E8oBC4VlV3Bip2Y4wxAe7DUNU5wJxS2+71+ZwLjCyj3ixgVo0HaIwxplz2prcxxhhPLGEYY4zxxBKGMcYYTyxhGGOM8cQShjHGGE8sYRhjjPHEEoYxxhhPLGEYY4zxxBKGMcYYTyxhGGOM8cQShjHGGE8sYRhjjPHEEoYxxhhPLGEYY4zxxBKGMcYYTyxhGGOM8cQShjHGGE8sYRhjjPHEEoYxxhhPApowRCRdRNaJSKaI3FnG/roi8rq7f5GItPXZd5e7fZ2InB3IuI0xxgQwYYhIJDABGAp0AcaISJdSxa4Edqlqe+AJ4GG3bhdgNNAVSAeedY9njDEmQAJ5hdEbyFTVjap6CJgGDC9VZjjwkvt5JnCGiIi7fZqqHlTVTUCmezxjjDEBEhXAc7UEtvisbwX6lFdGVfNFZA/QxN2+sFTdlqVPICLjgHHu6kERWVk9oYeEpsCvwQ6imoRTWyC82hNObYHwak+g2tKmvB2BTBg1TlUnA5MBRGSJqvYKckjVJpzaE05tgfBqTzi1BcKrPaHQlkDektoGtPJZT3S3lVlGRKKAOCDLY11jjDE1KJAJYzHQQUSSRKQOTif27FJlZgOXu59HAJ+qqrrbR7tPUSUBHYCvAxS3McYYAnhLyu2TuBGYC0QCU1R1lYiMB5ao6mzgBeAVEckEduIkFdxy04HVQD5wg6oWVHLKyTXVliAJp/aEU1sgvNoTTm2B8GpP0Nsizh/wxhhjTMXsTW9jjDGeWMIwxhjjSa1OGCIyRUR+rux9CxE5RUTyRWREoGKrCi/tEZE0EVkuIqtE5LNAxuePytoiInEi8o6IfOu2ZWygY/SHiLQSkXkistqN95YyyoiIPO0OYfOdiPQMRqyV8diW37ltWCEiC0Tk5GDE6oWX9viUDenvAq9tCdr3gKrW2gUYBPQEVlZQJhL4FJgDjAh2zEfTHqARTsd/a3e9WbBjPoq2/AV42P2cgPOQQ51gx11Be1oAPd3PscB6oEupMucA7wMC9AUWBTvuo2jLqUC8+3loqLbFa3vcfSH/XeDxdxO074FafYWhqp/jfNFU5CZgFvBzzUd0dDy052LgDVX90S0fsm3y0BYFYt2hXxq6ZfMDEVtVqOoOVV3mfs4G1nDkaAPDgZfVsRBoJCItAhxqpby0RVUXqOoud3UhzrtPIcnj7wZqwXeBx7YE7XugVieMyohIS+AC4N/BjqWadATiRSRDRJaKyGXBDugo/B/QGdgOrABuUdXC4IbkjTuKcg9gUaldZQ1/U9YXV8iooC2+rsS5cgp55bWnNn4XVPC7Cdr3QFgNDVKGJ4E7VLXQ+UO21osCUoEzgHrAVyKyUFXXBzesKjkbWA6cDpwIfCQiX6jq3qBGVQkRaYjzV+qtoR5rZby0RUQG4ySMAYGMrSoqac+T1KLvgkraErTvgXBPGL2Aae5/IE2Bc0QkX1XfCmpUVbcVyFLVfcA+EfkcOBnnPmdtMxZ4SJ2bsJkisgnoRAi/wS8i0Tj/E7+qqm+UUaTWDGHjoS2ISHfgeWCoqmYFMj5/eWhPrfku8NCWoH0PhPUtKVVNUtW2qtoWZ7j060PxPxA/vA0MEJEoEamPM9rvmiDHVFU/4vyFhIg0B5KBjUGNqAJuX8sLwBpVfbycYrOBy9ynpfoCe1R1R8CC9MhLW0SkNfAGcGmoX8F6aU9t+S7w+N9Z0L4HavUVhohMBdKApiKyFfgbEA2gqhODGFqVVNYeVV0jIh8A3wGFwPOqGpJDuHv43TwA/EdEVuA8VXSHqobyMNT9gUuBFSKy3N32F6A1FLdpDs6TUpnAfpyrqFDkpS334kwt8Kz7V3m+hu6or17aU1tU2pZgfg/Y0CDGGGM8CetbUsYYY6qPJQxjjDGeWMIwxhjjiSUMY4wxnljCMMYY44klDGOMMZ5YwjAhQUSai8hrIrLRHR/nKxG5INhx1TQRKXCHqV7pDvfeyEOdHN+fVTzvAhFpJCLXV1AmUURGlbOvrYgc8HlXoKwy9dy2HRKRplWN1YQOSxgm6Ny3W98CPlfVdqqaijOfe8iOkFqNDqhqiqp2wxmx94ZAnFRVT8UZJrvchIHzJn5Fc3psUNWUCs5xwN2/vQohmhBkCcOEgtOBQ75v5KrqZlV9BkBELhGRr92/VieJSKT7F+5aEfmPiKwXkVdF5EwR+VJEvheR3kXHKqd+AxF5T5wJnFYW/SVdwfbyYlgjIs+JM5HNhyJSr7zyHv4dvsId3VZE/uief6WI3FpRJRG51j3PchHZJCLzKovBvTp5CDjR3f9IqWMOAB4HRrj721Vw/jL/zUwYCtTEG7bYUt4C3Aw8Uc6+zsA7QLS7/ixwGdAWZ/6Mk3D+8FkKTMEZZmQ48FYl9S8EnvM5T5z784jtHmJIcbdPBy4pr3w57ctxf0YCM4B0nJFIVwANcOYKWQX0KKNOTqljRQNfAOdVFgOQ48Zf0eRjHwDdytlXXLe8f0uf9R+ApsH+78yWo1/sCsOEHBGZ4P61uhjntkgqsNi9X34GUPTX7iZVXaHOPBqrgE/U+YZagfOFRgX1VwBnicjDIjJQVfe45cvaXlkMy93PS93zVlS+tHpumf8BzYGPcIYSf1NV96lqDs4ggAM9/NM9BXyqqu/4GUN5koG1HsqV929pwkytHnzQhI1VOH+lAqCqN7idpEtwrhheUtW7fCuIM7nMQZ9NhT7rhZT8t11mffcYPXEGC3xQRD5R1fGqur70dmCXxxgKcOYnKPecZTigqinijDo6lyr2YYjIFUAb4MaiTX7EUNbxmuKMtlvpLIhl/Zup6viqnNeENrvCMKHgUyBGRK7z2Vbf/fkJzn30ZgAi0lhE2vhx7DLri8gJwH5V/S/wCG7nbjnb/Y3B75hVdT/OrbnbcPoyzheR+iLSAGemuC/KqysiqcCfgEu0ZNZCLzFk48wbXZa2eOysLu/f0oQfu8IwQaeqKiLnA0+IyO3AL8A+nCHPV4vIPcCHIhIB5OH8Ff4/j8cur34c8IiIFLrbipLVSaW3+xtDBeU3VxLrNyLyHc6toP9QMpnU86r6TQVVbwQaA/PEGYp8iapeVVkMqprlPiSwEnhfVf/sc8y1OEPTrwTGqeqCCs5/xL9ZRe00tZcNb26M8Zt7O+5ddR4HrqzsD0AvDe35TowHdkvKGFMVBUCceHhxD+fprcLyypnaw64wjDHGeGJXGMYYYzyxhGGMMcYTSxjGGGM8sYRhjDHGE0sYxhhjPLGEYYwxxhNLGMYYYzyxhGGMMcaT/westCz3YPrPQwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for g in [7.1, 14.3, 9.81, 10.5,]:\n",
    "    plt.errorbar(t_mean, \n",
    "                 h, \n",
    "                 xerr=t_std,\n",
    "                 yerr=delta_h,\n",
    "                 ls='',\n",
    "                 marker='.',\n",
    "                 label='Rollzeit Vollkugel')\n",
    "\n",
    "    time = [i/10 for i in range(1,30)]\n",
    "\n",
    "    plt.plot(time, \n",
    "             [fallhoehe(t, g) for t in time],\n",
    "             label=f'h(t, g={g})')\n",
    "\n",
    "    plt.xlim(1.4, 2.7)\n",
    "    plt.ylim(0, 0.4)\n",
    "    plt.grid()\n",
    "    plt.xlabel('Gemessene Rollzeit $t$ [s]')\n",
    "    plt.ylabel('Starthöhe $h$ [m]')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir können durch einfaches Ausprobieren feststellen, welcher Wert von $g$ am besten zu unseren Messwerten passt. Genau das macht `curve_fit`. `curve_fit` probiert solange (nach der Methode der kleinsten Quadrate) verschiedene Werte von $g$ aus, bis es den am besten passenden Wert gefunden hat. Probieren wir dies nochmal aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:36:34.611760Z",
     "start_time": "2020-08-26T06:36:34.606773Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:36:34.901660Z",
     "start_time": "2020-08-26T06:36:34.894687Z"
    }
   },
   "outputs": [],
   "source": [
    "parameter, covariance_matrix = curve_fit(fallhoehe,\n",
    "                                         t_mean,\n",
    "                                         h,\n",
    "                                         sigma=delta_h,\n",
    "                                         absolute_sigma=True\n",
    "                                        )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierbei schreibt `curve_fit` das Ergebnis der besten Werte in die Variable `parameter` und deren Fehler in eine so genannte Kovarianzmatrix.\n",
    "\n",
    "Beispiel: Das Ergebnis sieht für eine Funktion mit drei Parametern `def f(x, p1, p2, p3):` allgemein so aus:\n",
    "\n",
    "```\n",
    "paramter = [p1, p2, p3]\n",
    "covariance = [[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` der Varianz, also dem $\\sigma^2$ des Parameters i entspricht. Da wir in unserem Beispiel lediglich einen Parameter haben, sieht das Ergebnis wie folgt aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:36:47.493940Z",
     "start_time": "2020-08-26T06:36:47.487956Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g ist 10.58 m/s^2\n",
      "Delta g ist 0.09 m/s^2\n"
     ]
    }
   ],
   "source": [
    "print(f'g ist {parameter[0]:.2f} m/s^2')  # <-- einfache liste\n",
    "print(f'Delta g ist {(covariance_matrix[0][0])**(1/2):.2f} m/s^2')  # <-- doppel liste"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun sollten wir noch das $\\chi^2$ und die Anzahl an Freiheitsgraden berechnen, um zu bestimmen, wie gut unser Fit funktioniert hat:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:27.965486Z",
     "start_time": "2020-08-26T06:38:27.958504Z"
    }
   },
   "outputs": [],
   "source": [
    "def chiquadrat(xwerte, ywerte, dywerte, fun, g):\n",
    "    chi = 0\n",
    "    for x,y,dy in zip(xwerte, ywerte, dywerte):\n",
    "        chi += (fun(x, g) - y)**2/dy**2   # Der Operator += addiert zu dem vorherigen Wert von chi unseren\n",
    "                                          # neuen Wert drauf und aktualisiert gleich danach chi.\n",
    "                                          # Sprich es ist die kurzschreibweise für chi = chi + ...\n",
    "    return chi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:33.333572Z",
     "start_time": "2020-08-26T06:38:33.327134Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Das chi-quadrat und die Anzhal der Freiheitsgrade sind: 22/9\n"
     ]
    }
   ],
   "source": [
    "chi = chiquadrat(t_mean, h, delta_h, fallhoehe, parameter[0])\n",
    "ndof = len(h) - 1 # Anzahl Messwerte - Anzahl der Fitparamter\n",
    "\n",
    "print(f' Das chi-quadrat und die Anzhal der Freiheitsgrade sind: {chi:.0f}/{ndof}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\chi^2/$ndof > 1 bedeutet, dass unsere Fitfunktion die Daten nicht ganz wiederspiegelt. Um dies nachvollziehen zu können, gucken wir uns den finalen Plot an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:38.267629Z",
     "start_time": "2020-08-26T06:38:37.982393Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 840x570 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5.6, 3.8), dpi=150) # <-- Größe eines A4-Blatts ausnutzen\n",
    "# Plot der Messdaten\n",
    "plt.errorbar(t_mean, \n",
    "             h, \n",
    "             xerr=t_std,\n",
    "             yerr=delta_h,\n",
    "             ls='',\n",
    "             marker='.',\n",
    "             label='Rollzeit Vollkugel')\n",
    "\n",
    "# Fitergebnis:\n",
    "time = [i/10 for i in range(1,30)]\n",
    "plt.plot(time, \n",
    "         [fallhoehe(t, parameter[0]) for t in time],\n",
    "         label=f'Fitparamter:\\ng: ({parameter[0]:.2f}+/-{(covariance_matrix[0][0])**(1/2):.2f}) m/s$^2$\\n'\n",
    "               f'$\\chi^2/$ndof: {chi:.0f}/{ndof}')\n",
    "\n",
    "plt.xlim(1.4, 2.7)\n",
    "plt.ylim(0, 0.4)\n",
    "\n",
    "plt.grid()\n",
    "plt.xlabel('Gemessene Rollzeit $t$ [s]', fontsize=10)\n",
    "plt.ylabel('Starthöhe $h$ [m]', fontsize=10)\n",
    "plt.legend(fontsize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unsere Funktion weicht lediglich leicht von dem Großteil unserer Messdaten ab. Lediglich für kleine und große Fallhöhen ist die Abweichung stärker und unsere Funktion beschreibt die Messdaten nicht genau genug. Dies erklärt den leicht erhöhten Wert für unser $\\chi^2$/ndof. Woran könnte dies liegen?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bestimmen von mehren Parameter mittels curve_fit:\n",
    "\n",
    "Und weil es so schön ist, hier noch ein letztes Beispiel zum Thema Fitten. Einige von Ihnen haben sich gefragt, warum man überhaupt Fitten muss, wenn man bei einfachen Funktionen wie zum Beispiel\n",
    "\n",
    "$$s(t) = 1/2 \\cdot g \\cdot t^2$$\n",
    "\n",
    "die Funktion einfach nach $g$ auflösen und den Mittelwert und die Standardabweichung von $g$ berechnen kann. Bei Funktionen, die lediglich von einem Parameter abhängen, geht das relativ einfach, aber wie sieht es im folgenden Beispiel aus:\n",
    "\n",
    "$$T(t, T_0, \\tau, t_0) = \\tau \\cdot \\cos\\bigg(2 \\cdot \\pi \\cdot \\bigg(\\frac{t-t_0}{365 d}\\bigg)\\bigg) + T_0$$\n",
    "\n",
    "Die Funktion $T(t, T_0, \\tau, t_0)$ soll die jährlichen Temperaturschwankungen an einem bestimmten Ort auf der Erde wiederspiegeln. Hierbei ist $T_0$ die Durchschnittstemperatur, $\\tau$ der Temperaturunterschied und $t_0$ eine Verschiebung des Cosinus entsprechend des Tages, an dem die maximale Temperatur innerhalb eines Jahres gemessen wurde. Gucken wir uns zunächst die Messdaten an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:46.482971Z",
     "start_time": "2020-08-26T06:38:46.478982Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np # trigonometrische Funktionen findet man ebenfalls in Numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:46.870189Z",
     "start_time": "2020-08-26T06:38:46.855230Z"
    }
   },
   "outputs": [],
   "source": [
    "# Gemessene Werte:\n",
    "tage = [0.28, 10.36, 20.4, 30.23, 40.22, 50.11,\n",
    "        60.25, 70.22, 80.25, 90.03, 100.24, 110.21,\n",
    "        120.22, 130.25, 140.14, 150.09, 160.33, 170.31,\n",
    "        180.27, 190.28, 200.25, 210.33, 220.18, 230.15,\n",
    "        240.19, 250.37, 260.39, 270.35, 280.56, 290.23, \n",
    "        300.31, 310.17, 320.2, 330.11, 340.28, 350.48, 360.26] # d\n",
    "\n",
    "gemessene_temperatur = [15.17, 15.31, 14.46, 16.2, 15.49,\n",
    "                        16.18, 17.18, 16.17, 17.43, 18.24,\n",
    "                        18.96, 19.69, 20.19, 21.33, 22.27, \n",
    "                        23.14, 23.6, 23.37, 23.39, 25.27, \n",
    "                        25.2, 24.63, 23.22, 23.95, 23.53, \n",
    "                        22.9, 22.59, 21.84, 20.77, 20.12, \n",
    "                        18.79, 18.29, 17.87, 16.86, 16.48, \n",
    "                        15.41, 14.2] # °C\n",
    "\n",
    "fehler_temperatur = [0.52, 0.54, 0.54, 0.54, 0.51, 0.48, \n",
    "                     0.44, 0.39, 0.33, 0.28, 0.24, 0.22, \n",
    "                     0.24, 0.28, 0.33, 0.39, 0.44, 0.48, \n",
    "                     0.52, 0.54, 0.55, 0.55, 0.53, 0.5, \n",
    "                     0.46, 0.41, 0.35, 0.29, 0.25, 0.22, \n",
    "                     0.23, 0.26, 0.31, 0.37, 0.42, 0.47, \n",
    "                     0.5]\n",
    "\n",
    "def temp(t, T0, tau, t0):\n",
    "    \"\"\"\n",
    "    Jahrestemperaturverlauf für Ort x.\n",
    "    \n",
    "    Args:\n",
    "        t: Zeit in Tagen\n",
    "        T0: Mittlere Temperatur in °C\n",
    "        tau: Temperaturschwankungsamplitude in °C\n",
    "        t0: Zeitpunkt des heißesten Tages in Tagen\n",
    "    \"\"\"\n",
    "    return tau * np.cos(2 * np.pi * (t - t0) / 365) + T0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zunächst können wir uns die Messdaten angucken:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:48.953130Z",
     "start_time": "2020-08-26T06:38:48.766630Z"
    }
   },
   "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": [
    "# Plot der Messdaten:\n",
    "plt.figure(dpi=100)\n",
    "plt.errorbar(tage, \n",
    "            gemessene_temperatur,\n",
    "            fehler_temperatur, \n",
    "            ls='',\n",
    "            marker='.')\n",
    "\n",
    "plt.xlabel('Tage des Jahres')\n",
    "plt.ylabel('Temperatur [°C]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Als Nächstes führen wir, wie in den anderen Beispielen auch, den Fit mittelts `curve_fit` durch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:50.796960Z",
     "start_time": "2020-08-26T06:38:50.789977Z"
    }
   },
   "outputs": [],
   "source": [
    "# Fitten der Messdaten\n",
    "para, pcov = curve_fit(temp,\n",
    "                       tage,\n",
    "                       gemessene_temperatur,\n",
    "                       sigma=fehler_temperatur,\n",
    "                       absolute_sigma=True\n",
    "                       )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Im vergleich zu vorher haben wir diesesmal mehrere Parameter, sprich `para` ist jetzt eine Liste von Werten und die Kovarianzmatrix `pcov` eine verschachtelte Liste:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:55.005310Z",
     "start_time": "2020-08-26T06:38:54.998325Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19.76428742, -4.757914  , 19.11533869])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "para"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:55.422567Z",
     "start_time": "2020-08-26T06:38:55.414589Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.29660572e-03, -1.46005392e-04, -4.33280486e-04],\n",
       "       [-1.46005392e-04,  1.13167028e-02, -9.24299792e-04],\n",
       "       [-4.33280486e-04, -9.24299792e-04,  6.93117520e-01]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pcov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Denkt daran, dass die Fehler der Parameter der Wurzel der Hauptdiagonalen der Kovarianzmatrix entsprechen. Gucken wir uns die durch den Fit berechneten Werte etwas genauer an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:38:58.444536Z",
     "start_time": "2020-08-26T06:38:58.438539Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Der Wert für ist T0 (19.76 +/- 0.06) °C\n",
      "Der Wert für ist tau (-4.76 +/- 0.11) °C\n",
      "Der Wert für ist t0 (19.12 +/- 0.83) d\n"
     ]
    }
   ],
   "source": [
    "# Printausgabe der Parameter:\n",
    "for ind, (pname, einheit) in enumerate(zip(('T0', 'tau', 't0'), ('°C', '°C', 'd'))):\n",
    "    wert = para[ind]\n",
    "    fehler = pcov[ind, ind]**0.5 # dies entspricht der Hauptdiagnolen mit den Indizes 1,1 2,2 etc.\n",
    "    print(f'Der Wert für ist {pname} ({wert:.2f} +/- {fehler:.2f}) {einheit}')\n",
    "    \n",
    "# Zusatzinfo:\n",
    "# In unserer for-Schleife haben wir einen weiteren nützlichen Befehl eingebaut:\n",
    "# enumerate gibt den Index enstsprechend dem aktuellen Schritt in der Schleife\n",
    "# Probiert doch mal das folgende aus:\n",
    "# for ind, buchstabe in enumerate(['A', 'B', 'C'], start=0):\n",
    "#     print(ind, buchstabe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun sollten wir auch das $\\chi^2$ berechnen, um ein Gefühl für die Fitgüte zu bekommen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:39:02.007699Z",
     "start_time": "2020-08-26T06:39:01.998689Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Das Chi-Quadrat beträgt 41.96 mit 34 Freiheitsgraden.\n"
     ]
    }
   ],
   "source": [
    "# Berechnen des Chi**2:\n",
    "chi_liste = []\n",
    "for t, T, dT in zip(tage, gemessene_temperatur, fehler_temperatur):\n",
    "    chi_liste.append((temp(t, para[0], para[1], para[2]) - T)**2/dT**2)\n",
    "\n",
    "chi = sum(chi_liste)    \n",
    "print(f'Das Chi-Quadrat beträgt {chi:.2f} mit {len(gemessene_temperatur) - 3} Freiheitsgraden.')\n",
    "\n",
    "\n",
    "# Zusatzinfo: \n",
    "# Sie können das Ganze auch wieder etwas kompakter als list comprehension schreiben.\n",
    "# Außerdem können Sie die Fitparameter anstatt als para[0], para[1], para[2] mithilfe von\n",
    "# *para an die Funktion geben. Der Stern ordnet die Werte in der Liste der Reihe nach den \n",
    "# Argumenten der Funktion zu:\n",
    "# chi = sum([(temp(t, *para) - T)**2/dT**2  for t, T, dT in zip(tage, gemessene_temperatur, fehler_temperatur)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Fitparameter scheinen den Funktionsverlauf ganz gut zu beschreiben. Gucken wir uns das Resultat zusammen mit den Messwerten an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:39:04.861580Z",
     "start_time": "2020-08-26T06:39:04.639174Z"
    }
   },
   "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": [
    "plt.figure(dpi=100)\n",
    "plt.errorbar(tage, \n",
    "            gemessene_temperatur,\n",
    "            fehler_temperatur, \n",
    "            ls='',\n",
    "            marker='.',\n",
    "            label='T an Ort x')\n",
    "\n",
    "tage2 = [t/10 for t in range(3650)]\n",
    "plt.plot(tage2, temp(tage2, *para), label='Fitfunktion')\n",
    "\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel('Tage des Jahres')\n",
    "plt.ylabel('Temperatur [°C]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier noch ein kleiner Zusatz: Ist Ihnen etwas aufgefallen? Der Fitparameter $T_0$ hat einen Wert von ca. 20 Tagen, obwohl das Maximum eher bei 200 Tagen liegt. Dennoch beschreibt der Fit den Verlauf der Messdaten sehr gut. Dies liegt daran, dass der Cosinus eine periodische Funktion ist. Bei der Methode der kleinsten Quadrate werden die Fitparameter so lange nach einem gewissen Schema variiert, bis $\\chi^2$ minimal ist. Bei einer periodischen Funktion gibt es mehre dieser Minima.\n",
    "\n",
    "Dies kann auch bei anderen komplexeren Funktionen der Fall sein. Da die meisten Funktionen jedoch nicht periodisch sind, handelt es sich in der Regel bei diesen zusätzlichen Minima nur um lokale Minima. Um die besten Fitparameter zu finden, wollen wir jedoch das globale Minimum finden. Um dies zu erreichen, können wir `curve_fit` ein wenig helfen und zum Beispiel noch zusätzlich Startwerte für unsere Fitparameter mitgeben:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:39:40.646282Z",
     "start_time": "2020-08-26T06:39:40.638303Z"
    }
   },
   "outputs": [],
   "source": [
    "# Die Startwerte sind entsprechend der Reihenfolge der Parameter der Fitfunktion anzugeben.\n",
    "# In unserem Fall ist dies T0, tau, t0. Sollten wir keine Idee für einen Startwert haben,\n",
    "# können wir einfach den entsprechenden Wert auf einen passenden Wert setzen, hier z.B, 1.\n",
    "startwerte = [1, 1, 200]\n",
    "\n",
    "# Fitten der Messdaten\n",
    "para, pcov = curve_fit(temp,\n",
    "                       tage,\n",
    "                       gemessene_temperatur,\n",
    "                       sigma=fehler_temperatur,\n",
    "                       absolute_sigma=True,\n",
    "                       p0=startwerte  # <-- Übergeben der Startwerte an die Funktion\n",
    "                       )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:39:41.286672Z",
     "start_time": "2020-08-26T06:39:41.278694Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Der Wert für ist T0 (19.76 +/- 0.06) °C\n",
      "Der Wert für ist tau (4.76 +/- 0.11) °C\n",
      "Der Wert für ist t0 (201.62 +/- 0.83) d\n",
      "Das Chi-Quadrat beträgt 41.96 mit 34 Freiheitsgraden.\n"
     ]
    }
   ],
   "source": [
    "# Erneute Ausgabe der Fitwerte und des Chi**2\n",
    "for ind, (pname, einheit) in enumerate(zip(('T0', 'tau', 't0'), ('°C', '°C', 'd'))):\n",
    "    wert = para[ind]\n",
    "    fehler = pcov[ind, ind]**0.5 # dies entspricht der Hauptdiagnolen mit den Indizes 1,1 2,2 etc.\n",
    "    print(f'Der Wert für ist {pname} ({wert:.2f} +/- {fehler:.2f}) {einheit}')\n",
    "\n",
    "chi = sum([(temp(t, *para) - T)**2/dT**2  for t, T, dT in zip(tage, gemessene_temperatur, fehler_temperatur)])\n",
    "chi = sum(chi_liste)    \n",
    "print(f'Das Chi-Quadrat beträgt {chi:.2f} mit {len(gemessene_temperatur) - 3} Freiheitsgraden.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-08-26T06:39:42.279956Z",
     "start_time": "2020-08-26T06:39:42.070512Z"
    }
   },
   "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": [
    "# Erneutes Plotten der Funktion:\n",
    "plt.figure(dpi=100)\n",
    "plt.errorbar(tage, \n",
    "            gemessene_temperatur,\n",
    "            fehler_temperatur, \n",
    "            ls='',\n",
    "            marker='.',\n",
    "            label='T an Ort x')\n",
    "\n",
    "tage2 = [t/10 for t in range(3650)]\n",
    "plt.plot(tage2, temp(tage2, *para), label='Fitfunktion')\n",
    "\n",
    "plt.legend(loc=2)\n",
    "plt.xlabel('Tage des Jahres')\n",
    "plt.ylabel('Temperatur [°C]')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wir konnten mithilfe der Startwerte den Fit so beeinflussen, dass `curve_fit` dieses Mal das \"richtige\" Minimum finden konnte. Daher wird bei einem komplexeren Problem empfohlen, sich immer erst die Messdaten anzugucken und ein paar Startwerte für den Fit zu raten/schätzen."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}