7_Bibliotheken_einbinden.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "legal-discussion",
   "metadata": {},
   "source": [
    "# Einige wichtige Python-Bibliotheken für *DataScience*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sonic-protection",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "In diesem Notebook findest du einige Anmerkungen:\n",
    "\n",
    "- Was sind Bibliotheken?\n",
    "- Wie benutzt man Bibliotheken?\n",
    "- Beispiele wichtiger Bibliotheken für die weiteren Notebooks und kurze Beschreibungen\n",
    "    - Hier sind nur kurze Anmerkungen zu den Bibliotheks-Funktionen zu finden; doch zu allen hier benutzten Bibliotheken finden sich im Internet ausführlich Dokumentationen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "insured-berry",
   "metadata": {},
   "source": [
    "## Einführung"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hungry-circle",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Eine Programmierumgebung wie *Python* stellt neben den Basis-Datentypen und den Rechenoperationen (wie Addition, ganzzahlige Division etc.) eine Menge von Basis-Funktionen zur Verfügung. Man denke dabei z.B. an die `print`-Funktion, die jederzeit aufrufbar ist. Also:\n",
    "\n",
    "- **Die Python-Standardbibliothek liefert viele Funktionen für gängige Programmieraufgaben.**\n",
    "    \n",
    "Doch daneben gibt es viele weitere Bibliotheken, in denen Funktionen bereitgestellt werden, die in einem Python-Programm nutzbar sind, so dass man als Programmierer nicht immer wieder *das Rad neu erfinden* muss.\n",
    "    \n",
    "Viele solcher Bibliotheken (in Python auch ***Module*** genannt) sind frei zugänglich, zum großen Teil bereits bei der Installation von Python eingerichtet oder können nachgeladen werden. Daneben gibt es Module von Drittanbietern. \n",
    "    \n",
    "Ebenfalls besteht die Möglichkeit, eigene Module zu entwickeln, die Funktionalitäten beinhalten, die wir selber entwickelt haben und dann in verschiedenen Python-Programmen nutzen können.\n",
    "    \n",
    "    \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "handed-owner",
   "metadata": {},
   "source": [
    "## Eigene Bibliothek"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "atomic-filing",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Stell dir vor, du benötigst immer wieder gewisse mathematisch-interessante Funktionen, und möchtest dir eine Sammlung solcher Funktionen anlegen, die du bei Bedarf nutzen kannst, ohne den Code immer wieder neu \n",
    "schreiben zu müssen (oder per *copy-paste* zu nutzen).\n",
    "    \n",
    "Dann solltest du eine Python-Datei, z.B. unter dem Namen `meineBib.py` erzeugen, in der die Funktionen definiert sind.\n",
    "    \n",
    "Ein Beipiel:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "christian-apple",
   "metadata": {},
   "source": [
    "![Datei](Bilder/meineBib.png \"eigene Bibliothek\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sunset-incentive",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Speichere diese Datei in deinem Arbeitsverzeichnis ab.\n",
    "    \n",
    "Jetzt kannst du auf die beiden dort definierten Funktionen zugreifen. Dazu kannst du wählen:\n",
    "- Alle Funktionen, die in diesem Modul definiert sind, werden zugänglich gemacht.\n",
    "    - Dann werden die Funktionen mit dem sog. *qualifizierten Namen* aufgerufen:\n",
    "       \n",
    "    ```\n",
    "        import meineBib\n",
    "        print (meineBib.fak (10))\n",
    "    ```\n",
    "    - Man kann dann den Bibliotheksnamen ggf. abkürzen:\n",
    "    \n",
    "    ```\n",
    "        import meineBib as mb\n",
    "        print (mb.fak (10))\n",
    "    ```\n",
    "    \n",
    "       \n",
    "- Nur einzelne Funktionen sind nutzbar.\n",
    "    - Dann importiert man nur die benötigte(n) Funktion(en) und kann sie *unqualifiziert* nutzen\n",
    "    \n",
    "    ```\n",
    "        from meineBib import fak\n",
    "        print (fak (10))\n",
    "    ```\n",
    "    - Jedoch kann man dann eine Funktion mit gleichem Namen aus einer anderen Bibliothek nicht gleichzeitig nutzen!    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "floating-excess",
   "metadata": {},
   "outputs": [],
   "source": [
    "import meineBib as mb\n",
    "print (mb.fak(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "seeing-lincoln",
   "metadata": {},
   "outputs": [],
   "source": [
    "from meineBib import fak\n",
    "print (fak (10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "presidential-tissue",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Möchte man alle Funktionen einer Bibliothek unqualifiziert importieren:\n",
    "    \n",
    "```\n",
    "from meineBib import *\n",
    "print (kehrwert (10))\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "significant-office",
   "metadata": {},
   "outputs": [],
   "source": [
    "from meineBib import *\n",
    "print (kehrwert (10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cardiovascular-sweden",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "***Hinweis: Wo sucht das Python-System die importierten Module?***\n",
    "    \n",
    "Es gibt eine Reihenfolge vorgegeben, nach der verfahren wird, wenn ein Modul importiert werden soll:\n",
    "\n",
    "1. Zunächst wird der lokale Programmordner durchsucht. Wenn ein solches lokales Modul existiert, wird dieses eingebunden und keine weitere Suche durchgeführt.\n",
    "    - Also kann man ein eigenes Modul erstellen, das einen Namen hat, wie ein ggf. intern vorhandenes gleichnamiges Modul.\n",
    "2. Wenn kein lokales Modul mit dem angegebenen Namen gefunden wurde, wird ein global-vorhandenes Modul gesucht.\n",
    "3. Wenn auch das nicht gefunden wurde, wird ein ModuleNotFoundError erzeugt: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "single-waters",
   "metadata": {},
   "source": [
    "## Untermodule"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "honey-philippines",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Man kann auch mehrere Python-Bibliotheken aus inhaltlichen Gründen in einem Unterverzeichnis zusammenfassen. Schau dir dazu die folgenden Zeilen sowie die Bibliotheken dazu an:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "naughty-cleaner",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3628800"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import myFunctions.meineBib1 as mb1\n",
    "\n",
    "mb.fak (10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "radio-keeping",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import myFunctions as mf\n",
    "mf.meineBib1.kehrwert (3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "fallen-breathing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hallo Erna\n"
     ]
    }
   ],
   "source": [
    "mf.meineBib2.gruss(\"Erna\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "institutional-chamber",
   "metadata": {},
   "source": [
    "## Fremde Bibliotheken"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ideal-leonard",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Sehr oft benutzt man Module, die aus anderen Quellen stammen. \n",
    "\n",
    "Wenn man die Anaconda-Installation benutzt, kann man auf eine Vielzahl solcher Module zurückgreifen. \n",
    "Eine Übersicht über\n",
    "    \n",
    "- bereits installierte\n",
    "- mögliche weitere installierbare\n",
    "\n",
    "Module kann man über die Anaconda-Oberfläche bekommen. \n",
    "    \n",
    "Dort kann man dann\n",
    "    \n",
    "- neue Module installieren\n",
    "- neue Versionen von bereits installierten Modulen laden\n",
    "- Module entfernen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vertical-freight",
   "metadata": {},
   "source": [
    "![Anaconda-Environment](Bilder/anaconda.png \"Anaconda-Environment\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "endangered-projection",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Die Syntax für den Import eines solchen Moduls ist identisch zu dem Import eigener Bibliotheken."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "expanded-amber",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "***Hinweis:***\n",
    "    \n",
    "Man sollte regelmäßig die Versionen der benutzten Module überprüfen.\n",
    "    \n",
    "Alle externen, über Anaconda importierten Module haben eine Versionsnummer, die man in der Anaconda-Oberfläche erkennen kann. Es gibt auch die Möglichkeit, per Python-Anweisung diese Versionsnummer zu erfragen.\n",
    "    \n",
    "Am Beispiel der Bibliothek `numpy` (ein wichtige Bibliothek, die wir im folgenden Abschnitt genauer kennen lernen):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "rational-jesus",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "numpy.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rough-practice",
   "metadata": {},
   "source": [
    "## Die Bibliothek *numpy*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dying-agency",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Dieses Modul stellt Funktionen für die numerische Analyse von Daten zur Verfügung. \n",
    "    \n",
    "Insbesondere ermöglicht es den einfachen Umgang mit Arrays (Listen) und Matrizen. Es beinhaltet viele effizient implementierte Funktionen für numerische Berechnungen.\n",
    "    \n",
    "Der zentrale Datentyp in numpy ist `ndarray` (Abk. für *n-dimensionales Array*)\n",
    "    \n",
    "An einem einfachen Beispiel soll die Benutzung demonstriert werden."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hidden-slave",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Der Wechselkurs Euro --> Dollar ist zur Zeit 1:1.21. Wir wollen eine Tabelle anlegen, aus der man für einige Euro-Beträge den zugehörigen Wert in Dollar ablesen kann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "unable-howard",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100, 200, 300, 400, 500, 600, 700, 800, 900])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "factor = 1.21\n",
    "\n",
    "# es werden 10 Werte erzeugt im Intervall [100 ... 1000]; die Schritteweite wird automatisch berechnet\n",
    "#euros = np.linspace (start=100, stop = 1000, num = 10) \n",
    "\n",
    "# alternativ:\n",
    "# es werden Werte erzeugt im Intervall [100 ... 1000] mit Schrittweite 100\n",
    "\n",
    "euros = np.arange(100, 1000, 100)\n",
    "\n",
    "euros"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "small-montgomery",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Die Rechenoperationen `+`, `-`, `*` sowie viele mathematische Funktionen wie die Betragsfunktion `abs()`, die Wurzelfunktion `sqrt()` oder trigonometrische Funktionen wie `sin()`, `cos()` und `tan()`, können auf Numpy-Arrays angewendet werden. Dabei wird die Funktion auf jedes einzelne Element des Arrays angewendet. Als Ergebnis wird dann ein Array mit den entsprechenden Funktionswerten zurückgegeben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "urban-cathedral",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 100.  121.]\n",
      " [ 200.  242.]\n",
      " [ 300.  363.]\n",
      " [ 400.  484.]\n",
      " [ 500.  605.]\n",
      " [ 600.  726.]\n",
      " [ 700.  847.]\n",
      " [ 800.  968.]\n",
      " [ 900. 1089.]]\n"
     ]
    }
   ],
   "source": [
    "dollars = factor * euros # für unser Beispiel sinnvoll:\n",
    "\n",
    "# erzeugt eine zwei-dimensionale Tabelle\n",
    "table = np.array ([euros, dollars]) \n",
    "\n",
    "# Zeilen und Spalten transponiert, um besser lesen zu können\n",
    "print (np.transpose (table))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "collaborative-scene",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Man kann mit Hilfe von numpy auch (Pseudo-)Zufallszahlen erzeugen. Das geschieht mit der Funktion `random()` aus dem Untermodul `random`. Diese Funktion erzeugt die im Parameter angegebene Anzahl von zufälligen float-Werten im halboffenen Intervall [0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "first-harbor",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.44901897 0.29350614 0.37489722 0.77569975 0.34075487 0.72833505\n",
      " 0.59000326 0.49466712 0.48726681 0.52533045]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "zufListe = np.random.random(10)\n",
    "print (zufListe)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "naughty-institute",
   "metadata": {},
   "source": [
    "## Die Bibliothek *matplotlib* mit der Teilbibliothek *pyplot*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fabulous-artwork",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "Diese Bibliothek gestattet es, Digramme zu erzeugen. Das kann z.B. auf der Grundlage von den Python-Listen erfolgen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "entertaining-portuguese",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "Y = [4, 7, 1, 9, 5, 2, 8]\n",
    "X = [1, 2, 3, 4, 5, 6, 7]\n",
    "plt.plot(X, Y,color='blue')\n",
    "#plt.scatter(X, Y, color='red')\n",
    "plt.plot (X, Y, 'ro')   # Alternativ\n",
    "# Abkürzungen der Symbole sind z.B. \n",
    "# \".\", o\", \"+\", \"x\" für die Punktsymbole sowie\n",
    "# \"r\", \"b\", \"m\", \"g\" für Farben\n",
    "plt.xlabel(\"X-Werte\")\n",
    "plt.ylabel(\"Y-Werte\")\n",
    "\n",
    "x1 = X[0]\n",
    "x2 = X[-1]\n",
    "y1 = Y[0]\n",
    "y2 = Y[-1]\n",
    "plt.plot((x1, x2), (y1, y2), 'r-.')\n",
    "# bei der Linienart kann man z.B. '-', '-.' oder '--' nutzen\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abstract-punch",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "modified-funeral",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lxIgRjBgxggcffJCoqCgAHnzwQebNmwfAjBkzSE1NZfDgwcyYMYNZs2YdV8+0adPYsmXLSe9pS/DqPcJbS0pKijlxrHJ7kZ6eXuvpaHuh8XtXU+PfvHnzcd9WvaU5czfdeOONHnVstyZfn3vqqNp+3yKyyhhzcqfMCfRMQymllMe0I1wpdUo4sYlGtQ4901BKKeUxTRpKKaU8pklDKaWUxzRpKKWU8pgmDaWUz9Cp0eHCCy+kY8eO1THXpqKigilTptCnTx9GjRrF7t27AZ0aXSl1mjndp0YH6wryf//73/WWee2114iMjGTHjh3cdddd1dOI6NToqkEL9izgge8eYF7GvFonO1OqvdCp0S0TJ05s8ALBjz/+mBtuuAGAK6+8kgULFmCM0anRVf0+2PYBf1/2d4L8gpiXMY99Rfu4Pe12b4el2rsv7oeD61u2zk4DYdIj9RbRqdE9V3MKdbvdTkREBLm5uTo1uqpbTlkOj654lDM6n8ELE1/gb9//jRfXvsg53c8hJaruSdqU8lU6Nbrn6ptCXadGV7V6a9NbVDoreWDUA/j7+XP/qPtZlLmIl9a9xJMTnvR2eKo9a+CMoDXo1OiNk5CQQGZmJgkJCTgcDgoKCqonNtSp0dVJHC4H8zLmMTZhLD0jegIQHhDONf2u4es9X5NZlOndAJVqJJ0avXEuvfRSZs+eXR3rOeecU53YdGp0dZJl+5dxuOwwP+v9s+PWX5V8FYLw6c6TOwCV8mU6NfoxY8eO5aqrrmLBggUkJCQwf/584Pip0W+66SZyc3Pp06cPTz75ZPUw4qNac2p0jDFeewCvA9nAhjq2CzAD2AGsA4Z6Um9ycrJprxYtWtRgmenfTzej3h5lKh2VJ2371Ze/Mhd9cJFxuVytEF3DPInfl52u8W/atKllA2miwsLCJu97ww03mPfee68Fo2m85sTflmr7fQMrjQefr94+05gFXFjP9klAkvtxK/BiG8Tk04wxLN23lFGdRuHv53/S9kmJk9hbtJcdR2ofNaKUUs3h1Y5wY8wSEelZT5HLgDfdWXC5iHQUkc7GmAP17HNK21W4i/0l+7lp4E21bh/bdSwAS7KWkBSZ1JahKeVVOjV62/D2mUZDugI1e3Wz3OtOWysOrABgdOfRtW6PD42nX1Q/lmQtacuwlFKnCV8fclvbeLlaL3sWkVuxmrCIjY0lPT29FcNqPcXFxfXG/lXOV4TZwtixagcZklFrmQRHAgvyFjB/4XwCbYG1lmktDcXv607X+CMiImodLtrWnE6nT8TRVO0l/vLy8ib/nft60sgCutVYTgD211bQGPMy8DJY9whvr/d5bugez098+ATDugzj7LPPrrOM/z5/vv7ma8L6hjGmy5hWiLJup+s9tn1Fc+4R7gv3tm4v99iuS3uJPygoiCFDhjRpX19vnpoHXC+WM4CC07k/o6CigN2FuxkUO6jecmlxafiJHysPtt5MnEqp05NXk4aIzAGWASkikiUiN4nIbSJym7vI58BOrCG3rwC/8VKoPmFDzgaABpNGqH8o/aL6serQqrYIS6kWo1OjezY1+qxZs4iNjSUtLY20tDReffVV4DSYGt0YM80Y09kY42+MSTDGvGaMmWmMmenebowxvzXG9DbGDDTGnNZfndflrEMQUqNTGyw7vNNw1uesp9xR3mBZpXyFTo3u2dToAFOmTKm+uvzmm28GdGp0dYLt+dvpHt6dDgEdGiybFpdGlauKLXkt941NqdakU6NbPJkavS46Nbo6zvb87fTp2MejsgOiBwCwMXcjaXFprRiVOtU8+uOjLf5lo29UX/408k/1ltGp0Rvngw8+YMmSJSQnJ/PUU0/RrVs3nRpdHVPuKGdv0V4uTKzvAvpj4kPjiQ2OZWPOxlaOTKmWoVOje+6SSy5h2rRpBAYGMnPmTG644QYWLlwI6NToym1XwS5cxuXxmQZAanQqG3I3tGJU6lTU0BlBa9Cp0RsnOjq6+vktt9xSfbtX0KnRldvRuaSSOno+NUhqTCq7C3ZTXNn8dlalWpNOjd44Bw4cu/Jg3rx59OvXr3pZp0ZXAGw/sh1/mz/dw7t7vM+AmAEYDJvzNrdiZEo1n06NfownU6PPmDGD1NRUBg8ezIwZM06ad+uUnRq9tR6n4tTot399u/n5xz9vVF15ZXlmwKwB5vX1r7dAZJ45XacW9xU6NbpOje6J9jw1uvLQ7sLdJEYkNmqfyKBIuoR2YVOu741FV0q1T9oR3g5UuarYX7yfC3t6NnKqpuTIZLbnN/+UWSlfp1Ojtw0902gH9hXtw2mc9Ahv/AU6SZFJ7C7cTaWzshUiU6cSq4VCneqa+3vWpNEO7C3aC9CkpJEclYzTONlZsLOlw1KnkKCgIHJzczVxnOKMMeTm5tY7QKAh2jzVDuwp3APQqJFTRyVHJgOwLX8bfaP6tmhc6tSRkJBAVlYWhw8f9moc5eXlzfpA87b2EH9QUBAJCQlN3l+TRjuwp3APYf5hRAZGHr/B6YDVb8Le5dBpEIy4GfyP/4PtHtadAFuA9muoevn7+5OY2LiBFq0hPT29yfd58AXtPX5PaNJoB/YW7qVbeLfjr0p1ueD9X8LmeRAaB+v+A5s+hus/hoCQ6mJ2m53eHXuzLX+bFyJXSp1qtE+jHdhbtJceYSf0Zyx9ykoY5z0M926DK9+ArBXw6R9O2j85MlmThlKqRWjS8HEOl4ODJQdJCKvRBll0EJY8AX0nw5jfgQgM+DmM/6N1xpGx6Lg6kiKTyCnLIa88r42jV0qdajRp+LhDpYdwGiddO3Q9tvL7Z8FZAec/bCWMo866GyJ7wtcPQo1RMEc7w7VfQynVXJo0fNz+4v0AdO5gTQtNZSms/jf0uwSieh1f2D8Ixt4DB9dBxoLq1UmR1iSHmjSUUs2lScPHHSixZrOsPtPYPA/KC2DELbXvMGgqhHWG5TOrV0UHRRMRGKHXaiilmk2Tho/bV7wPgE6hnawVmz6G8AToMab2HewBkHatdaZRYO0rIvSK6KVJQynVbJo0fNyB4gPEBscS6BcIFUWwY4HVNFXfzWWGXAvGBWuP3RymV0QvdhXsaoOIlVKnMk0aPm5/8f5j/Rnb5lsd4P0vq3+nqF7Q4yxYO7e6QzwxIpG88jzyy/NbOWKl1KlMk4aP21+yn66h7v6M7V9BSAx0G9XwjgMuh9ztcHgrYJ1pANpEpZRqFk0aPsxlXBwoOWCdaRgDu5ZA4jiwefBr6zsZENj8CQC9OmrSUEo1nyYNH3a49DAOl8MaOZWzHYoOQK/xnu0c1gkSRsAWK2l0Du1MsD2YnUc0aSilmk6Thg87Oty2c2hn2LXYWpk4zvMK+l0CB9ZC/h5sYqNneE/tDFdKNYsmDR92dLht1w5draapiO4Q2YiZSPtebP3c/hVgdYZr85RSqjk0afiwo2canULiIfNH6DG6/qG2J4rubU0rkrEQsDrDD5QcoLSqtBWiVUqdDryaNETkQhHZKiI7ROT+WrZPEJECEVnjfjzojTi9Jbs0mzD/MELK8qH4IHQd3vhKep9jnaU4q6o7w3cVahOVUqppvJY0RMQPeB6YBPQHpolI/1qKfmuMSXM/HmrTIL0suzSbuJA4a8pzgIRhja+k9zlQWQxZK44Nu9XOcKVUE3nzTGMksMMYs9MYUwnMBRq4au30cixprAS/QIgf2PhKeo4F8YOMhXQP646f+GlnuFKqybx5576uQGaN5SygtqvWRovIWmA/cK8xZmNtlYnIrcCtALGxsaSnp7dstG2kuLi4OvbM/ExSglIo2LsAQnuy+rvvm1TnkLAkZPVH/GQ7i2i/aH7Y8QPphektF3QNNeNvjzR+79L4fZ83k0ZtPbrmhOWfgB7GmGIRuQj4CEiqrTJjzMvAywApKSlmwoQJLRdpG0pPT2fChAk4XU6K3ipiUOJAIrZ8CsNupOmv6XJIf4QJIwfx4fIB7Crc1Yy66nc0/vZK4/cujd/3ebN5KgvoVmM5AetsopoxptAYU+x+/jngLyIxbRei9+SW5+I0TuKNgKMMOg9qemU9xwIG9i4jMSKRzMJMqlxVLRarUur04c2ksQJIEpFEEQkApgLzahYQkU4i1hhTERmJFW9um0fqBdml2QDElRdZK+IHNL2yrsOsPpE935MYkYjDOMgqymqBKJVSpxuvJQ1jjAO4A5gPbAbeNcZsFJHbROQ2d7ErgQ3uPo0ZwFRjzIlNWKekQ6WHAIgvzAabHWJTml6Zf5A1pcju70iMsC4O1M5wpVRTeLNP42iT0+cnrJtZ4/lzwHNtHZcvqD7TyN0DMSlgD2xehT3GwLf/R2Kg1bqnSUMp1RR6RbiPyi7Nxm6zE5W9BTo1o2nqqJ5ngnERdmgjscGxmjSUUk2iScNHZZdmExsUja3oQPP6M45KGGE1c7mbqPSqcKVUU3i1eUrV7VDpIeL8QqyFTrVf1JeZV8p7q7LYk1tC54hgLkvrQr/O4bVXGBAKXYZaneEDxvP5rs8xxiCNmctKKXXa06Thow6VHCLJuE8EaznTeGPpLv752WYM0DkiiEOFB3hpSQY3junJAxf1w+5Xy0lkjzGw7DkSR02jqLKI3PJcYoJPixHMSqkWoknDR2WXZnOWXxQER0GH2OO2vZiewaNfbuG8/vE8fNkAOkUEcaS0kqe+3sYbS3ezN7eUF38xjAD7CYmj51mw9GkSKysAqzNck4ZSqjG0T8MHFVcWU+ooJa6s8KShtt9tz+HRL7dwyeAuvPSLYXSKCAKgY0gA0y8bwMOXpbJgSzYPfLiek0YndxsJCIl51n06tDNcKdVYeqbhg6qH2xZlQ89jM9sWlFVx73tr6R0bymNXDMJmO7k/4rrRPTlcVMGMhTsY1iOSqSO7H9sYFAGdBhC/fw3B9uB2lzS25G1hXsY89hbupWNgR8YmjGVi94nYbfpnrFRb0TMNH5Rd5k4apQUQk1y9/oX0HRwqKuepKWkEB/jVuf8fzk1mdK9oHv50E5l5J9xwqftobFmr6BnWo90kDYfLwaM/PspVn1zFf7b8h4MlB/l237fcu/hervnsGrbnb/d2iEqdNjRp+KDcMmumlBins7p5at+RMt5YupufD0lgUELHeve32YT/u3owNhHu/++645upuo+GqlJ6BnRsF0nD6XJy3+L7eGvzW0xNmcqiKYt4/9L3WXjVQh4d+yjZpdlc/8X1/HjgR2+HqtRpQZOGD8opywEg2umEGGtS35cWZ4CBu89Prm/Xal07BnPfhSks3ZHL/I0Hj23oMQaAXlUO9pfsp8xR1rLBt7Cnf3qab/Z+w33D7+OBMx4gPMAaUuxn8+OiXhcxd/JcOoV24o6Fd7D+8HovR6vUqU+Thg/KLcslABthtkCI6M6R0kreW5nFJYO70LVjsMf1XDOyOynxYfzjs82UVzmtlWGdIDKRxEKrCWxP4Z7WeAktYum+pczaOIupKVO5PvX6Wst0Cu3EK+e/QlRQFHcsvKO6P0gp1To0afignLIcYrAh0UlgszHnx0zKqpzcdFZio+qx+9l48JL+ZOWX8dbyGsmhxxgSD24BfHcEVWlVKdOXTScxIpH7RtxXb9mY4Bien/g8ZY4y7v/2fpwuZxtFqdTpR5OGD8otzyXa4YDYZJwuw5vLdjOmdzT9u9RxtXc9zuwTw5je0cxcnEFppcNa2f0MehTnIIjPJo3Zm2ZzoOQA08dMJ8AvoMHyvTv25oFRD7Di4Are2PhGG0So1OlJk4YPyinNJrqiDGKS+T4jhwMF5VwzqnvDO9bh7vOSySmuZPb37rON7mMINNDVP9wnk8aR8iPM3jibid0nMiRuyMkFnA6oZYb8y/pcxnk9zuPFNS+yu2B36weq1GlIk4YPyinNJsbpgJhk/vvTPsKD7JzbL77J9Q3vGcW45FheWpJBUXkVRPeG0FgSXb55pvH6xtcprSrljrQ7jq3c+wO8/yt4PAkejoZ/doLXJ8GK16Dy2LDiP4/8M4F+gTy0/KGTL25USjWbJg0f4zRO8iuLiHa6KA1P5MsNB5k8uAtB/nVfl+GJu89L5khpFW8t3wsi0H00icVH2F2426f6AIori3l367tc2PNC+kT2gYpi+Og38Pr5sGMB9JkIE/4Mw34J5QXw2d3w/EjYYt2WJTYklruG38WKgyv4dOenXn41Sp16NGn4mBJXCQZDjNPJVwdCKKtycsXQrs2uN61bR87sE83rS3dZI6l6jCGxJJcKZwUHSg60QOQt46MdH1FSVWKNlirOhjcmwdo5MPYeuHszXD4TJtwPkx6B25fCDZ9AQAeYOw2+/As4HVyRdAWp0ak8/dPTlFaVNnxQpZTHNGn4mEJnIQAx/h34dEshXTsGM7R7ZIvUffv4PhwuquDD1fusMw13x7ivNFE5XU7e2fIOabFpDAjrAW9dAbk7YNp/YOKDEBBy/A4ikDgObvsWRv4alj8P/7kWm6OSP474I9ml2czaOMsrr0WpU5UmDR9zNGlEhnRiyfYczk+Nb7F7XpzZJ5oBXcN5eclOnHGp9BJrVJKvJI2l+5eSWZTJtX2vgXdvgOxNcPW/Ifn8+nf084eLHoOLn4BtX8KcqQyN7MsFPS/gjQ1vcLDkYP37K6U8pknDxxQ5iwBw2jpR6XBxQWqnFqtbRLhtfG925ZTw1eYcIruOoKPBZ+7i9/GOj4kMjGRi1gbIWAAXPQ5J53pewYib4bLnYWc6fHATd6Xdicu4mPHTjFaLWanTjSYNH1NUlQfAvtJYokIDGNEzqkXrnzSgMz2iQ5i5OAPTfTSJFeXsyvP+hH8FFQUsylzERXHD8U9/BPr/zOrsbqwhv7CSzdbP6frtU1zX/zo+3fkpm3I3tXjMSp2ONGn4mNLKQ4S4XCw/HMm5/eLwq2X68+bwswm3jO3F2qwCNvqnkljlYFdBRoseoynm755PlauKy3b8ACExcMkzVp+Fm8tl2J1TwqKt2Xyydj9fbzrEuqwjx6ZHqWnkLXDWXbDydW4qLqNjYEeeWPmEDsFVqgXojQh8THFVDtFOJ1srY7ijf8s1TdV05bAEnv5mO09uDGCcw8V/q4opqCggIjCiVY7niY93fExSYDR9d62GK16D4I4AbNhXwNs/7GH+xkPklVSetJ+/nzAooSMXDezMJYM7Exdm3ZSKiX+Dgn2ELXqEX0/4LY/s+YRv933LuIRxbfiqmqfcUc6BkgMUVxZjt9mJCooiLiRO7+uuvEqTho8pchYS43SyxdaZMX2iW+UYQf5+/Oqsnjz25VamJCYAhewq2EVaXFqrHK8hewv3si5nHfcUliE9x8KAK8g4XMw/P9vMwi3ZhAb4MbFfPGN6R5MU34GwIH/Kq5zsyy9jbVYBi7cd5uFPN/HoF1u4LK0Lt47rRVJ8GFz6LOTu4OrvZzMnKZUnVz7JmC5jfPqmTVvytvBJxicsO7Cs1vuEBNuDGRQziFGdRzGxx0R6RfTyQpTqdFbv/x4RuRL41BhT3kbxnPYKXaX0cgpJPbsREtB6H26/OKMHLy7KILeyNwStZlfeVq8lja/3fA3ABUfycV31GC8v2cmTX28jyG7jvgtSuG50D8KD/E/ab1BCRyYN7Mz9k/qyI7uYN5ft5t2VmXzwUxZXDevG3ecnEz/1bfxfnsAfDh/irlAXH+74kKuSr2rrl9igFQdXMOOnGaw5vAZ/mz9D44fym8G/IaFDVyL8Q6kyLnLK89hZsJOVh1YyY/UMZqyewaDYQVyZdCUX97rYozm6lGquhj6VrgVeEJEvgTnAV8YY37l8+BSUTyV2RxDjB8S16nHCg/y5bnQPvvm2N/5hP7Fr3w/Qd0qrHrMu3+z6goEVVcT0/Tm3zi/lm827uCA1nod/NuBYc1MD+sR14KHLBvCHc5N5buEO/r18Nx+v3cevx/XmNz+fzcS3L2VIaA+eX/08FydeTIh/SMOVtoGcshweXvYwCzMXEh8cxx8TLuDSMicRmRth3bdQchiO/pezB0NEAnTszuFOF/GZv+Gjgk08+P2DPLf6Oa5PvZ5OrtZp0lTqqHqThjHmchEJBy4H7gReE5GPgTnGmCVtEeDppNJZSZHNgCOMccmxrX68X52VyKTv+tO9ysGu3M2tfrza7C/ez4b8rfyhtIybCyfyXV42f7+kPzeM6dmktvuo0AAevKQ/N47pyaNfbuGZBdt5b2UQLwz+G/dsnM4vunTijY1v8Nu037bCq2mcBXsW8Pdlf6esspjf22L5xda1BDlXgn8IdB4MSedBhzhr2eWEikI4shfydxH7w2JudDm4AWFZwkBeCxL+b+X/EWILIXN9JtP6TiPUP9TbL1Gdghps/zDGFAKzgdkiEg1cCTwrIlHGmG7NObiIXAg8A/gBrxpjHjlhu7i3XwSUAjcaY35qzjF9WV7JIfezKFLiw1r9eDEdApk0oh8HsuzsLPXOBXBfb3kPAClL46fySN781TDO7BPT7Hq7R4fw/LVDuX5nLn//ZBM/+z6RF6ImcUHxd8xe/xpXJV9FXEjrns3VxWVcPPfTDF7Z8Br9HfC/B/fTPaCEPb2uY0XQGNaaPhwqdpCbWUGFw4XTZXAaQ2iAnQ6BdsJC7HRKhcF+e+hf/hODc77l1ayVrA/054XoeJ756RlmrX+dGwf+ymeThzGGIxVHOFBygAPFB8gpy6HUUcqmI5tYvWo1dpsdu81OgC2AjoEdiQyKJCooitiQWOJD4n26X+pU5/E7LyKRwM+BKUAU8EFzDiwifsDzwHlAFrBCROYZY2oOqJ8EJLkfo4AX3T9PSYeyrZceFd6jzUbI3DK2Fw/PjmFfaA6VlaUEnDhVRyubv+V9UioqmVtxNW/dPIrB3Tq2aP2jekXz6e/OYu6KvfztS+F/yrexILSYp9L/h/+96OUWPZYnSitL+POXv2Jh/iauKCxmWlEsMyp+y6dFw3Dk2hGB6NBc4sICiQkLJNBuw99PEBHKKp0UlVexN6+UlXsqeLMkCBgDjCGGAq60rea3B7/lDnsGL0aWWcljzUxuTJnKtCG3ezV5HCjax8pdX7Ml+yc2Hclga+kBikxVrWXtRwyOev7+/RA62TuQEBRNt9DOJIT3oFtUMt1i+tMtvAcdAjq01stoMqfLSXFVMVWuKhwuB1XOSqqcVVQZB06XA5vNDz9xP2x+2MSGXewE+AUQbA8myB6ETXzjComGOsLDgJ8B04ChwDzgH8Ai0/xB7yOBHcaYne5jzQUuA2omjcuAN93HWi4iHUWkszHGd2bYa0Ebd60BILFr/zY7ZreoEKLC+uOUb9m89SsGD/xZmx17674trHce4YKSWG68ZTIDurbOkF8/m3DtqB5MHtiFmfMjmbT3Zj7je7p9+ha3TLoGf7/W/8/ochlWb1rF//7wa7b7VXBTrouNuddzc8Q4zhkWz6MJHUnpFEafuA4ez2hcWulgX34ZmfmlbD9UzLZDqdy54xxMWR4TS5YyPeR7vok6wjObZ/P6htmMcyWT1u0WuvceTreoEOLDgwiwN/+1l1c5ySmuILe4kpziCopy91F+aDVZBcvYU7WdbfZ89tutj4tAl4vkyiourKwkttJOsCOYkKog/BwhVLmCMa4ABMFglfezVYBfGS57GQ6/Csr8Kij0r+SQfzH77DksLMgg79Cy4+IJd0K8048oVzCRhBMu0YT7d6ZDQAKhQXEEBkbgF9QBExCKyx6Cy88fGwIi2Gwg2BDjwllVDo4yqCzD5ajAVJZS6SiisiqPckchFY4Cyp1FVLiKKTellJsyihzFzN7mokwqKRUHJeKi2OaitAX+xAJchkADgUYIqH7YCMCGv7FhNzbs2PDDz/pp/LDj5/5nxw87In4YsSGAYNw/AfH841zq++wXkRxgPjAX+NKYOr4aNIF7ZNaFxpib3cvXAaOMMXfUKPMp8Igx5jv38gLgT8aYlbXUdytwK0BsbOywd999t6VCbTM/7HyfdGc6v4y7m7g2HEq5IXstL5W9ytVFAxg74NfNqqu4uJgOHRr+plfhMMxb9xxLorfxO/s0kruOadZxG2N/zk6eLXySlAoXhw//D5P6xzEgxvr+5Gn8nqhwGjblOll7qIrEvHls7LSI7YF2JuYOwNbxBgbHBdKlg7ToWWVxcTEhoaHklhn2FbuoOHIQe/F81gavZXWIoaPTySVHDFEFSayrGshmewqVgTGEB9oItkOQXQj2o/qi0qOfDg6XodwBZY5jP6sqK4ityiTRZNLHthv/4N0cDslnXbCwMTAAlwjBLkNKuZ2ulTFEOHtj9+tDZVA8VUEx+Pn5E+AnBPhBgE3w94PysjKCg4MxWPfZMoDLQJXLUOmESqehwglUlRFUlU9QVQF+jmyqOEiZ5FAiRyj0KyXPXs5hu4scO7hOeH+DXS4inS4iXC6CjQt/A/7G4G+sVFUlgkOEKoEKEYpstupHvWdAxhDmMoQ5IcQlhLhshLhsBLnsBLrs+JsAbMYfIwEY/LFhw88INiO4xGAwuDC4AMQFxoFLHDjFiVMcONzPK8WFQ5xUiYsqMVSKi0obVInBAVSJ9ah0/zzx9ddlw40bVhljhjdUrqHmqf8CXwDpLZkw3Gp7JSdmME/KWCuNeRl4GSAlJcVMmDChWcF5w4QJExi5aBFnn312mx53ZNVIXnrnVYqqdjNg+GhiOgQ2ua709HQaeu8dThe3vfkjErSZeJc/t1zz5za+YG0ClUv388SO//A/QY/wvyv/Qmqfnlw/uifBrs0Nxl+f/UfKSN96mAWbD/Hdjhx6OPfwP0Gv8EznYnYFBPCPtL9wcdq0lnspJ6j9/f8FAGt3fs3zK57i336Z+EXtZGzpRu4pKWVQhR9HyruxW7pwyBnOAUc4hSYI4/4uGihVdJRSYu1ldLLl05Vsol2HyPYvYkV4AD8EB/FqYBAVNsFGEKkB8dwcN4Qze1/IwG5j8W/EUGBP/n4ao8pZxb78DPbmbODgkd3kl+WSW55PXvkRCqpKqHRVUGocVBkXlcaJDcGODbvYCLD508Fmp7M9hPCADoT7hxERGE5EUAThwVFEBEUTERJDRGgcEaGdCAkIY/HixS0af0twuBxUOiupcFbgcjmtbCxy3IwLBkPsjZ4NvmkoabwOXAjcLSKVwFdYZxxrmxh/TVlAzY70BGB/E8qcUrxxtW+Ifwhx+OP0z+O5Bdv5+2UDWu1YxhgenLcR2fEpa/sIl8YP98prvuaMP/LhvnRei97PPL8nuCX7AX7971w6BgqXFm3g3H7xDO0RSYfAuv+LGGM4WFjO+qwClu3M5dvtOezILgYgsaOdlxPm0zfnbW7tHMd+/xCem/g8Y9rwjOpEg3udx8u9zmN7/nY+2fExn+74mPTQIwjQ31TQr3wzfUqLGFNVRbjLRYhxUYVQbhNy/fzYb/dnWXAYW4IC2SqhVGH1f/UJ685VXc9iVJfRDI8f7lN9Cv5+/vSM6UvPmL7eDsVrjg4qaKlh5g0NuV0OLAf+7h45dT5wj4gMBFZjJZCmtgOtAJJEJBHYB0wFrjmhzDzgDnd/xyig4FTtz/C2XqGd2Vexnbwfl5M5thfdolqnQ/yF9Aze+WEvz3RZwHKbjXEDftEqx2lIgF8A0yf8H9d/cT1vBebxZdAjfHvu8zz13WHeXZnJm8v2WLfriAklITKEuLBAd9+HIb+kikNF5ezNLSXXPbVJoN3GyMQopo7oxvlhu+j23f0cOpzBr3r0JsdPeGHi84zoNMIrr/VESZFJ3D3iXu4c9gc25Gxg2f5l/HjwR74+sp33g+vvT4kIjKBvZF9+Ed2f/jH9GR4/nJjg5o92U+2HR6OnROTBGosZwE5gGNCnqQc2xjhE5A6sPhM/4HVjzEYRuc29fSbwOdZw2x1YQ26bMO2p8kSf2IF8ULSbc21beHz+VmZMG9Lix/hwdRaPz9/K71IK2Vx0gEDpyIguZ7T4cTyVFpfGNf2u4Z3N73B+ziHGLZ5Kh+S76TfpVn7Ylcu6rAI27i/gYEE52w8V4XBZLaMdg/2JDw9iYr84UrtEMKBrOKldIgiqyINF/4QFb5AZ2Z1bkgZS4KrkpXNf9NrV9vWx2+ykxaWRFpfG7dyOMYbc8lwOlRyioLKA0qpSAvwCCPALIDoomi4duvjk8F3VtjwdcltS43kQMBnYbIz5V3MOboz5HCsx1Fw3s8ZzA3j/KqzTQHKXUZTt/oxzOu/k5rX7mTqyG2N6t9w3yKU7cvjj++sY3Sua34e+z6WuEEZ2GkmwPbjFjtEUdw65k2+zvuVPgcW8l53PkNV/QUKzmTD+T0xI8fA6jopiWP4MfPskVJWyc/j13FK6gQpXFa9e8Cqp0amt+yJaiIgQExyjZw6qXh4NBDPGPFHj8U9gAtD8G1crn5EclQyAy7mZbpFB/PWjDVQ6XC1S94Z9Bfz636voFdOBly7rTOaOz8i0+zGu+zktUn9zhPiH8MSEJzhSVcyfU0awr9PZ8N2T8OxQ+PEVKC+ofUdj4NAm+PpBeLI/LJgOPc9i6y/m8suSdTiN4Y0L3mg3CUMpTzX1ssoQQKfXPIX0juiNDWG7s4Qnxgdw9UeFPL9oB3edl9ysejPzSrnxjRWEB9mZ/auRhP/4v3wUbI3O8pVpyvtG9eXPo/7M9GXT+VfcWJ4/fx6y4CH4/F6Y/wAkjIBOAyA4EqrKoCAT9q2C/N0gNuh/GYy+g++lknsW30Oofyivnv8qPSN6evulKdXiPO3TWM+xoa5+QCzwUGsFpdpekD2IHh0S2FZSwm8dq7h8yASeXbidsUkxDG/i3QMPFZZz/es/UuV0MffW0XQKdsKqWSzpmkCf8E506dClZV9EM1yZfCV7Cvcwa+Msnivoxx03fY0cWAPr34e938Oad6y5n2z+ENYZOg2EM38PKRdjOsQxd+tcHv3xUXp37M1z5zxH5w6dvf2SlGoVnp5pTK7x3AEcMsY4WiEe5UXJMf3ZWJgFO77hoam/ZeWePH4/dw0f/fZMYsMad+3GwYJypr2ynOzCct68aSR94sLgx1coqShglYnkuq5jW+lVNN1dw+5i656tvLzuZfLK8/jLyL/g33XosQJOB9j8jhvffqT8CH9Pv4sFexcwPmE8j457VDuL1SnN0z6NPTUe+zRhnJqSI5PJshmKM5cTRhkvXDOMvJJKbp69gtJKz3/lOw8XM+XlZRwuquDNm0YyrEcUuFyw/EWWdU3FYZyMTfC9pGETG9OipnHLwFt4f9v7TPlsCmuy1xwr4GevThilVaW8tektJn80mcVZi7l3+L3MOGeGJgx1ytOpIlW15Eir/2KHXUjbtYSB/SYzY9oQfv3vldz4xgpevWF4rTdDqmn9YQd3Pr8Uu5+NN28aydDukdaG7V9BXgZLel1KWGGGTw5BBWsE0Z1D72RQ7CAeXvYw131xHQNjBjK6y2jiQ+Ipc5SxOW8z6ZnplFSVMKrzKO4bfh8pUSneDl2pNqFJQ1VLibQ++LaFhJO27QvoN5nz+sfzzNQh3P3uGi599jueuDqNYT0iT9o3v6SSx7/ayjurKujbKYxXrh9+/AWCy57DFd6Vb0uyGNN1DP62+pOPt03oNoERnUbw3+3/5fOdn/PKuleqJ9GLDopmYveJ/Dzp5wyNG6r37FanFU0aqlqn0E6E+YexLSYOtnwOkx3gZ+eSwV2IDw/iD3NXc8WL3zMuOZbz+sfTJSKI/NIqftiZy6frDlDhcHJBTztP/WrM8beq3b8Gdn/LlrF3kpP1kc+MmmpIqH8o1/W/juv6X0els5K88jyC7cGEB4RrolCnLU0aqpqIkBSZxLbSXCjLgz3fQa8JAIxMjGL+XeOYtXQ3c1dksmTb4er9woLsXDyoM7eO68X+zatOvrf5989CQBhLOsYgWcJZXc9qw1fVMgL8AugUqrdSVUqThjpOcmQy8/Lm4fIPwbbp4+qkARAW5M/vJiZxxzl9yMovI7ekkohgfxIig6vvSbH/xLvGHtkLGz+EM27n24M/MjBmIFFBTRvCq5TyPt+4FZTyGakxqZQ6Stndeyxs/tS6N/UJRIRuUSGkdetIYkxo/TcxWv4iiJA7ZBrrc9b75KgppZTnNGmo4wyItqZF39ClP5RkQ8aipldWlg+rZsOAK/iuMAODaTf9GUqp2mnSUMdJjEgk2B7MBn87hETD6jebXtnymVBVAmN+x5KsJcQGx9Ivql/LBauUanOaNNRx/Gx+pEansiFvEwyaYo2iKsltfEWlebD8Beh3CVVxffl+//eMSxino46Uauc0aaiTDIgZwJa8LVQNngauKlg7p/GVfP8sVBTBhL+w+tBqiquKtT9DqVOAJg11ktSYVKpcVWzz94Puo+GHl8DZiFvEFx2y9km9HOL7syRrCf42f0Z3Ht16QSul2oQmDXWSgTEDAdiQs8GaybXAPWzWU18/aJ2hnPM/ACzZt4Th8cNb7B7FSinv0aShTtIltAuRgZFsyN0ASRdAbD9Y/JhHZxsRRzbBurkw5ncQ3ZvMwkx2FezSUVNKnSI0aaiTiAiDYgdZM7zabHDu3yF3O6x4tf4dK4pJ2foshCfA2HsAWJy1GPCdGy4ppZpHk4aq1bD4Yewu3M3h0sOQfAH0ngiL/gV5O2vfwRj4/F6Cyw7A5TMhwJoi/Ju939CnYx+6h3dvw+iVUq1Fk4aq1fD44QCsOrTKuofE5KesW5u+e701KqomY2DRP2HtHPb0mAKJ1iipnLIcfjr0E+f2OLetw1dKtRJNGqpW/aL7EWIPYeWhldaKyB7w81fg0CaYNdn6CVCcDR/9BpY8DkOuY3fPqdV1pGemYzCc212ThlKnCp2wUNXKbrMzJH4IKw6uOLYy+XyY+jZ8eBu8OBpC46A0BxAY90eY8GdYsqS6+Dd7v6FbWLfqmzsppdo/TRqqTsPjh/PMvmfILcslOjjaWpkyCX63CtbOhZytENYZBl4FMUnH7VtYWcgPB37gun7X6VXgSp1CNGmoOo3sNBKA5QeWc3Gvi49tCI2BMXfUu++CPQtwuBzan6HUKUb7NFSdUqNTiQqKYknWkoYLn+CTnZ/QI7xH9YWCSqlTgyYNVSc/mx9ndT2L7/Z9h8Pl8Hi/A8UHWHFwBRf3ulibppQ6xXglaYhIlIh8LSLb3T8j6yi3W0TWi8gaEVnZ1nEqGJ8wnsLKQtYeXuvxPp/t+gyAyb0mt1ZYSikv8daZxv3AAmNMErDAvVyXs40xacaY4W0TmqppTJcx+Nv8+WbPNx6VdxkXH27/kKFxQ+kW1q2Vo1NKtTVvJY3LgNnu57OBn3kpDtWADgEdGJ8wni92feFRE9WW8i3sLdrLlJQpbRCdUqqtiTGm7Q8qcsQY07HGcr4x5qQmKhHZBeQDBnjJGPNyPXXeCtwKEBsbO+zdd99t8bjbQnFxMR06dPB2GMdZW7qWVw+/ym1xt5EanFpv2ef3P88+5z4eSngIu7S/wXm++P43hsbvXe05/rPPPnuVRy06xphWeQDfABtqeVwGHDmhbH4ddXRx/4wD1gLjPDl2cnKyaa8WLVrk7RBOUumoNGfOOdPcteiuesttyd1iBswaYJ5f/XwbRdbyfPH9bwyN37vac/zASuPB52urfRU0xtQ5QF9EDolIZ2PMARHpDGTXUcd+989sEfkQGAk0fvynahZ/P3+uSLqCWRtnkVWURUJYQq3lXlz7IsESzLX9rm3jCJVSbcVbfRrzgBvcz28APj6xgIiEikjY0efA+VhnKsoLru13LTax8er62qdHX5O9hgV7FzAhfAIRgRFtHJ1Sqq14K2k8ApwnItuB89zLiEgXEfncXSYe+E5E1gI/Ap8ZY770SrSKuJA4pqZM5b/b/8um3E3HbStzlDF92XQ6hXZiYvhEL0WolGoLXkkaxphcY8xEY0yS+2eee/1+Y8xF7uc7jTGD3Y9UY8w/vRGrOub2tNuJCY7h3sX3kleeB0CVq4q/Lv0rGUcy+NvovxFoC/RylEqp1qRXhCuPhQeE8+SEJzlUcoirP7maGT/N4IYvbmD+7vncNewuzup6lrdDVEq1Mk0aqlHS4tJ4c9KbRAdH88r6V8grz+PRsY/yywG/9HZoSqk20P4G0iuvS41J5T+T/0OVqwp/m7+3w1FKtSE901BNpglDqdOPJg2llFIe06ShlFLKY5o0lFJKeUyThlJKKY9p0lBKKeUxTRpKKaU8pklDKaWUxzRpKKWU8pgmDaWUUh7TpKGUUspjmjSUUkp5TJOGUkopj2nSUEop5TFNGkoppTymSUMppZTHNGkopZTymCYNpZRSHtOkoZRSymOaNJRSSnlMk4ZSSimPadJQSinlMU0aSimlPKZJQymllMe8kjRE5CoR2SgiLhEZXk+5C0Vkq4jsEJH72zJGpZRSJ/PWmcYG4OfAkroKiIgf8DwwCegPTBOR/m0TnlJKqdrYvXFQY8xmABGpr9hIYIcxZqe77FzgMmBTqweolFKqVr7cp9EVyKyxnOVep5RSykta7UxDRL4BOtWy6QFjzMeeVFHLOlPP8W4FbgWIjY0lPT3dkzB9TnFxcbuNHTR+b9P4vau9x++JVksaxphzm1lFFtCtxnICsL+e470MvAyQkpJiJkyY0MzDe0d6ejrtNXbQ+L1N4/eu9h6/J3y5eWoFkCQiiSISAEwF5nk5JqWUOq15a8jt5SKSBYwGPhOR+e71XUTkcwBjjAO4A5gPbAbeNcZs9Ea8SimlLN4aPfUh8GEt6/cDF9VY/hz4vA1DU0opVQ9fbp5SSinlYzRpKKWU8pgmDaWUUh7TpKGUUspjmjSUUkp5TJOGUkopj2nSUEop5TFNGkoppTymSUMppZTHNGkopZTymCYNpZRSHtOkoZRSymOaNJRSSnlMk4ZSSimPadJQSinlMU0aSimlPKZJQymllMc0aSillPKYJg2llFIe06ShlFLKY5o0lFJKeUyThlJKKY9p0lBKKeUxTRpKKaU8pklDKaWUxzRpKKWU8pgmDaWUUh7TpKGUUspjXkkaInKViGwUEZeIDK+n3G4RWS8ia0RkZVvGqJRS6mR2Lx13A/Bz4CUPyp5tjMlp5XiUUkp5wCtJwxizGUBEvHF4pZRSTeStMw1PGeArETHAS8aYl+sqKCK3Are6FytEZENbBNgKYoD2fGal8XuXxu9d7Tn+FE8KtVrSEJFvgE61bHrAGPOxh9WcaYzZLyJxwNcissUYs6S2gu6E8rL72CuNMXX2lfiy9hw7aPzepvF7V3uO39N+41ZLGsaYc1ugjv3un9ki8iEwEqg1aSillGp9PjvkVkRCRSTs6HPgfKwOdKWUUl7irSG3l4tIFjAa+ExE5rvXdxGRz93F4oHvRGQt8CPwmTHmSw8PUWffRzvQnmMHjd/bNH7vas/xexS7GGNaOxCllFKnCJ9tnlJKKeV7NGkopZTy2CmZNDydpsTXiMiFIrJVRHaIyP3ejqcxROR1Eclur9fHiEg3EVkkIpvdfzu/93ZMnhKRIBH5UUTWumOf7u2YmkJE/ERktYh86u1YGqu9T3kkIh1F5H0R2eL+PzC6rrKnZNLg2DQl7WZ4roj4Ac8Dk4D+wDQR6e/dqBplFnCht4NoBgdwjzGmH3AG8Nt29P5XAOcYYwYDacCFInKGd0Nqkt8Dm70dRDOcbYxJa6fXaTwDfGmM6QsMpp7fwymZNIwxm40xW70dRyONBHYYY3YaYyqBucBlXo7JY+6LLvO8HUdTGWMOGGN+cj8vwvpP09W7UXnGWIrdi/7uR7sa4SIiCcDFwKvejuV0IyLhwDjgNQBjTKUx5khd5U/JpNFOdQUyayxn0U4+tE41ItITGAL84OVQPOZu2lkDZANfG2PaTexuTwN/BFxejqOpjk55tMo9pVF70gs4DLzhbh581X1tXK3abdIQkW9EZEMtj3bz7fwEtc3e2K6+LZ4KRKQD8AHwB2NMobfj8ZQxxmmMSQMSgJEiMsDLIXlMRCYD2caYVd6OpRnONMYMxWpe/q2IjPN2QI1gB4YCLxpjhgAlQJ19qr4+YWGdWmKaEh+TBXSrsZwA7PdSLKclEfHHShhvG2P+6+14msIYc0RE0rH6l9rLoIQzgUtF5CIgCAgXkbeMMb/wclwea+dTHmUBWTXOTt+nnqTRbs80TkErgCQRSRSRAGAqMM/LMZ02xJqn/zVgszHmSW/H0xgiEisiHd3Pg4FzgS1eDaoRjDF/NsYkGGN6Yv3dL2xPCaO9T3lkjDkIZIrI0VluJwKb6ip/SiaNuqYp8WXGGAdwBzAfqxP2XWPMRu9G5TkRmQMsA1JEJEtEbvJ2TI10JnAdcI572OQa9zff9qAzsEhE1mF9+fjaGNPuhq22Y82Z8shX/A542/03lAb8q66COo2IUkopj52SZxpKKaVahyYNpZRSHtOkoZRSymOaNJRSSnlMk4ZSSimPadJQqpncM4T+5oR1X4qITgOjTjmaNJRqvo5AddJwX2AXZYzZ57WIlGolmjSUar5HgN7uCwIfByYA6VB9n4V/icgyEVkpIkNFZL6IZIjIbe4ynUVkiXv/DSIy1muvRKkGtNu5p5TyIfcDA9wTBiIiM4CPamzPNMaMFpGnsO47cibWHEsbgZnANcB8Y8w/3fdVCWm70JVqHE0aSrW8M4F7aywfnUNsPdDBfb+OIhEpd88ZtQJ43T1h4kfGmDVtGaxSjaHNU0q1IBHphXVmUVljdYX7p6vG86PLdvcNrMYB+4B/i8j1bRKsUk2gSUOp5isCwtzPJwGNmqxORHpg3U/iFayZdoe2bHhKtRxtnlKqmYwxuSKyVEQ2AAeAWxpZxQTgPhGpAooBPdNQPktnuVWqhYhIILDUGDPc27Eo1Vo0aSillPKY9mkopZTymCYNpZRSHtOkoZRSymOaNJRSSnlMk4ZSSimPadJQSinlsf8HppXDPNFSZq4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from numpy import sin, exp, linspace, arange, pi \n",
    "x=linspace(0.0, 2*pi, 1000)\n",
    "for a in arange(0.5,2, 0.5):    \n",
    "    y = a * sin(5*x)*exp(-x)    \n",
    "    plt.plot(x, y, label = \"Amplitude = \" + str(a)+ \"V\" )\n",
    "plt.grid(True)\n",
    "plt.xlim(-1.0, 6.0)\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.xlabel(\"t/ms\")\n",
    "plt.ylabel(\"u/V\")\n",
    "plt.title (\"Gedämpfte Sin-Schwingung\")\n",
    "plt.legend() \n",
    "plt.show"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "driving-latex",
   "metadata": {},
   "source": [
    "### Ein ausführlicheres Beispiel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "social-bhutan",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Wertebereich für x-Achse festlegen:\n",
    "x = np.arange (-6,6,0.1)\n",
    "\n",
    "x2 = np.sin(x)\n",
    "x3 = np.cos(x)\n",
    "\n",
    "# Einzelne Diagramm-Linien plotten:\n",
    "#plt.plot(x, x, 'r--')\n",
    "plt.plot(x, x2,'b--')\n",
    "plt.plot(x, x3,'g-')\n",
    "\n",
    "# Diagramm-Gitter einblenden:\n",
    "plt.grid(True)\n",
    "\n",
    "# Diagramm ausgeben:\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "expressed-player",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Werte-Listen für eine Sinus- und Cosinus-Funktion erstellen:\n",
    "x = np.linspace(-np.pi, np.pi, 500, endpoint=True)\n",
    "cos_x = np.cos(x)\n",
    "sin_x = np.sin(x)\n",
    "\n",
    "# Diagramm-Linien plotten:\n",
    "plt.plot(x, cos_x)\n",
    "plt.plot(x, sin_x)\n",
    "\n",
    "# Diagramm anzeigen:\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "patient-connecticut",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Module importieren\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Werte-Listen für eine Sinus- und Cosinus-Funktion erstellen:\n",
    "x = np.linspace(-np.pi, np.pi, 500, endpoint=True)\n",
    "cos_x = np.cos(x)\n",
    "sin_x = np.sin(x)\n",
    "\n",
    "# Eine neues Matplot-Figure-Objekt mit 8x6 Zoll und\n",
    "# einer Auflösung von 100 dpi erstellen:\n",
    "plt.figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "# In diese Abbildung ein 1x1 großes Diagramm-Gitter erstellen;\n",
    "# Als aktuelles Diagramm wird das erste dieses Gitters ausgewählt:\n",
    "plt.subplot(111)\n",
    "\n",
    "# Cosinus-Funktion mit blauer Farbe, durchgehender Linie und 1 Pixel\n",
    "# Linienbreite plotten:\n",
    "plt.plot(x, cos_x, color=\"blue\", linewidth=1.0, linestyle=\"-\")\n",
    "\n",
    "# Sinus-Funktion mit grüner Farbe, durchgehender Linie und 1 Pixel\n",
    "# Linienbreite plotten:\n",
    "plt.plot(x, sin_x, color=\"green\", linewidth=1.0, linestyle=\"-\")\n",
    "\n",
    "# Grenzen für die x-Achse festlegen:\n",
    "plt.xlim(-4.0, 4.0)\n",
    "\n",
    "# Grenzen für die y-Achse festlegen:\n",
    "plt.ylim(-1.0, 1.0)\n",
    "\n",
    "# \"Ticks\" (Bezugspunkte) für x-Achse festlegen:\n",
    "plt.xticks(np.linspace(-4, 4, 9,endpoint=True))\n",
    "\n",
    "# \"Ticks\" (Bezugspunkte) für y-Achse festlegen:\n",
    "plt.yticks(np.linspace(-1, 1, 5,endpoint=True))\n",
    "\n",
    "# Diagramm anzeigen:\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "standard-lighter",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Größe des Plots anpassen:\n",
    "plt.figure(figsize=(10,6), dpi=80)\n",
    "# Farbe und Dicke der Diagrammlinien anpassen:\n",
    "# Plots mit einem Label versehen:\n",
    "plt.plot(x, cos_x, color=\"blue\", linewidth=2.5, linestyle=\"-\", label=r'$\\cos(x)$')\n",
    "plt.plot(x, sin_x, color=\"red\",  linewidth=2.5, linestyle=\"-\", label=r'$\\sin(x)$')\n",
    "# Wertebereiche der Achsen anpassen:\n",
    "plt.xlim(x.min()*1.1, x.max()*1.1)\n",
    "plt.ylim(cos_x.min()*1.1, cos_x.max()*1.1)\n",
    "# Auf der x-Achse fünf Bezugspunkte (als Vielfache von pi) festlegen\n",
    "# und mittels LaTeX-Symbolen beschriften:\n",
    "plt.xticks( [-np.pi, -np.pi/2, 0, np.pi/2, np.pi],\n",
    "            [ r'$-\\pi$', r'$-\\pi/2$', r'$0$', r'$+\\pi/2$', r'$+\\pi$']\n",
    "    )\n",
    "\n",
    "# Auch Ticks für die y-Achse anpassen:\n",
    "plt.yticks( [-1.0, -0.5, 0, 0.5, 1],\n",
    "            [ r'$-1$', r'$-1/2$', r'', r'$+1/2$', r'$+1$']\n",
    "    )\n",
    "\n",
    "# Das Achsen-Objekt des Diagramms in einer Variablen ablegen:\n",
    "ax = plt.gca()\n",
    "\n",
    "# Die obere und rechte Achse unsichtbar machen:\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "# Die linke Diagrammachse auf den Bezugspunkt '0' der x-Achse legen:\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "# Die untere Diagrammachse auf den Bezugspunkt '0' der y-Achse legen:\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "\n",
    "# Ausrichtung der Achsen-Beschriftung festlegen:\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Achse-Beschriftungen durch weiß-transparenten Hintergrund hervorheben:\n",
    "for label in ax.get_xticklabels() + ax.get_yticklabels():\n",
    "    label.set_fontsize(16)\n",
    "    label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65 ))\n",
    "    \n",
    "# Titel hinzufügen:\n",
    "plt.title('Sinus und Cosinus', fontsize=20, color='gray')\n",
    "\n",
    "# Legende einblenden:\n",
    "plt.legend(loc='upper left', frameon=True)\n",
    "\n",
    "\n",
    "plt.show ()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "approved-allowance",
   "metadata": {},
   "source": [
    "## Die Bibliothek *pandas*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "rubber-offer",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "vanilla-browser",
   "metadata": {},
   "source": [
    "<div style=\"background-color: Cornsilk; padding: 5px 20px 20px\">\n",
    "\n",
    "In einer Datenerhebung werden viele Datenpaare gesammelt, die in einer ***csv***Datei z.B. unter dem Namen `abc.csv` in einem Unterordner `daten` des Arbeitsverzeichnisses abgelegt sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "level-frontier",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "intense-parts",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"daten/Auto.csv\",sep=\";\",decimal=\",\", index_col=[\"Hersteller\",\"Modell\"])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "comparable-leadership",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "successful-campus",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"daten/Auto.csv\",sep=\";\",decimal=\",\")\n",
    "df[[\"Hersteller\",\"Verbrauch\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "focused-closure",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "df[[\"Hersteller\",\"Verbrauch\"]].plot(x=\"Hersteller\")\n",
    "\n",
    "plt.show ()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "labeled-bradley",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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