programmieren_wise_24_25/Material/wise_24_25/SciPy_Lösungen.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5fbb6606-ab9a-4481-bfb5-72a958b0d72c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Lösungen SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8455dadf-ad76-4c6e-b6c4-e72764d41e86",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78aed4e3-89b5-4baa-995a-2235e17ddd8b",
   "metadata": {
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     "slide_type": "slide"
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   },
   "source": [
    "### Aufgabe\n",
    "\n",
    "*7 Punkte*\n",
    "\n",
    "Bestimme mittels Linearer Regression die *best fit* Funktion für die beiden gegebenen Datensets `x_data` & `y_data`, unter beachtung folgender Punkte:\n",
    "\n",
    "- Plotte das Ergebnis angemessen\n",
    "- Nutze SciPys `linregress` Funktion, speichere den Output vor dem entpacken in der Variablen `l`\n",
    "- Definiere die Funktion `reg_line` mit einem Eingabeparameter\n",
    "- Bestimme die Werte für `-0.3` & `3.4` speichere diese als liste in variablen `future`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a5dadce5-e415-4b39-80a5-0ad3cb5e6352",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "random = np.random.default_rng(420)\n",
    "\n",
    "# 2 scuffed up One-Liners :)\n",
    "x_data: np.array = np.sort(np.round(random.random(40)*np.pi, decimals=2))\n",
    "y_data: np.array = np.flip(np.sort(np.round(random.random(40)*np.sqrt(2), decimals=2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7b2b2652-1771-4434-ac6e-bf7d80ba15cf",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "l = stats.linregress(x_data,y_data)\n",
    "slope, intercept, _, _, stderr = l\n",
    "\n",
    "def reg_line(x: float) -> float:\n",
    "    return float(np.round(slope*x+intercept,decimals=2))\n",
    "\n",
    "ext: tuple = (-0.3, 3.4)\n",
    "rl: np.array = np.vectorize(reg_line)(ext)\n",
    "\n",
    "future: list = [reg_line(ext[0]), reg_line(ext[1])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bf16eea1-0524-46e4-84d5-b5b87308941e",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Y')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Scattered Random Values\")\n",
    "plt.grid()\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0a27e646-5b06-4f83-abf4-7925350a0ea7",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_data,y_data, color='g', label=\"Original Data\")\n",
    "plt.plot(ext, rl, color='m', label=\"Fitted Line\")\n",
    "plt.scatter(ext, future, color='r', label=\"Predicted Data\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ca0bc7d-6fcb-475f-bdfc-c0b63579cc93",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Aufgabe \n",
    "\n",
    "*6 Punkte*\n",
    "\n",
    "Gegeben sind die nach Altersgruppe aufgeschlüsselten Durschnittskörpergrößen (in cm) von Frauen in Deutschland. (Zu finden beim [Statistischen Bundesamt](https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Gesundheit/Gesundheitszustand-Relevantes-Verhalten/Tabellen/koerpermasse-frauen.html))\n",
    "\n",
    "Gehe wie folgt vor:\n",
    "\n",
    "- Berechne das arithmetische Mittel nutze dafür NumPy. und speichere das Ergebnis mit einer Genauigkeit von 1 Dezimalstelle nach dem Komma in der Variablen `avg_height`.\n",
    "- Gegeben ist auch die Standardabweichung von 15cm, stelle die Normalverteilung mittels `norm.pdf` auf. Speichere den Wert in `norm_height` und finde einen geeigneten linespace zum plotten.\n",
    "- Berechne folgend die Körpergröße unter die 80% aller Frauen (nach Datenset) fallen. Speichere den Wert in der Variablen `avg_percentile`.\n",
    "- Plotte das Ergebnis. Orientiere dich gerne an dem Bienenbeispiel. Finde eine geeignete Darstellung. *Tipp: Da die Y-Achse in diesem Beispiel keinen Sinn ergibt kannst du sie einfach austellen mit `plt.yticks([])`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2b3711d0-aed5-4be2-a6a5-18df1767a97f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Given\n",
    "avg_height_per_woman = {\n",
    "    \"18 - 20\": 167.6,\n",
    "    \"20 - 25\": 167.7,\n",
    "    \"25 - 30\": 167.3,\n",
    "    \"30 - 35\": 167.2,\n",
    "    \"35 - 40\": 167.3,\n",
    "    \"40 - 45\": 167.5,\n",
    "    \"45 - 50\": 167.1,\n",
    "    \"50 - 55\": 167.1,\n",
    "    \"55 - 60\": 166.9,\n",
    "    \"60 - 65\": 165.4,\n",
    "    \"65 - 70\": 164.5,\n",
    "    \"70 - 75\": 163.9,\n",
    "    \"75+\": 162.8\n",
    "}\n",
    "\n",
    "avg_height = None\n",
    "norm_height = None\n",
    "avg_percentile = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9e931834-455b-4596-b1d6-4166a1e06852",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "avg_height = np.round(\n",
    "        np.mean(list(avg_height_per_woman.values()))\n",
    "        , decimals=1)\n",
    "std_sigma = 15\n",
    "\n",
    "norm_x = np.linspace(120, 220, 1000)\n",
    "norm_height = stats.norm(avg_height, std_sigma).pdf(norm_x)\n",
    "\n",
    "# Height of 80th percentile of woman heights\n",
    "avg_percentile = stats.norm(avg_height, std_sigma).ppf(0.8)\n",
    "\n",
    "x_percentile = np.arange(norm_x[0], avg_percentile, 0.01)\n",
    "y_percentile = stats.norm(avg_height, std_sigma).pdf(x_percentile)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e36af98b-3fa7-4c3b-9418-cb2792da5235",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(norm_x, norm_height, color='r')\n",
    "ax.fill_between(x_percentile, y_percentile, 0, alpha=.5, color='#fa0000')\n",
    "ax.text(0.4,0.18,\n",
    "f\"80th percentile of Womens heigth\\n fall under {avg_percentile:.1f}cm\",\n",
    "ha='center', va='center', transform=ax.transAxes,\n",
    "bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
    "color='#de2e0b'\n",
    ")\n",
    "plt.title(\"Woman Height Normal Distribution\")\n",
    "plt.xlabel(\"Height\")\n",
    "plt.yticks([]) # hide y\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7335367c-46e3-4396-bc41-d9d2e6621194",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Aufgabe\n",
    "\n",
    "*7 Punkte*\n",
    "\n",
    "Gegeben sind zwei Würfel aus dem Spiel **Super Mario Party**. Es wird im folgenden angenommen das die Charaktere ihre Würfel würfeln und deren Augenzahl addiert wird.\n",
    "\n",
    "- Stelle alle Kombinationen der Gegebenen Daten auf, speichere diese als Dictionary in der Variablen `dist_mp`.\n",
    "- Exthrahiere den am dritt häufigsten Aufkommenden Wert und speicher diesen in der Variablen `best3` als tuple in der Form `(<Augenzahl>, <Auftritte>)`.\n",
    "- Plotte eine geeignete binomiale Verteilung. *Tipp: schaue dir an wie du den Plot mittels matplotlib vergrößerst*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27720a28-4a96-4567-b2f0-52961bdd387f",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Einige der Würfel gebem dem Charakter Münzen. Finde eine logische Schlussfolgerung diese mit anderen Werten zu ersetzen. Überlege dabei welche Auswirkungen es auf die Augenzahl hat das der Charakter Münzen bekomment.\n",
    "\n",
    "|Charakter|Dice|\n",
    "|-|-|\n",
    "|Mario|1, 3, 3, 3, 5, 6|\n",
    "|Peach|0, 2, 4, 4, 4, 6|\n",
    "|Boo|-2 Coins, -2 Coins, 5, 5, 7, 7|\n",
    "|Donkey Kong|+5 Coins, 0, 0, 0, 10, 10|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e6b079fa-95b0-4a6c-90d2-fc39b8a045b7",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# define dices\n",
    "mario = [1, 3, 3, 3, 5, 6]\n",
    "peach = [0, 2, 4, 4, 4, 6]\n",
    "boo = [0, 0, 5, 5, 7, 7]\n",
    "dk = [0, 0, 0, 0, 10, 10]\n",
    "\n",
    "# Create Keys\n",
    "keys: set = {\n",
    "    m+p+b+d\n",
    "    for m in mario for p in peach\n",
    "    for b in boo for d in dk\n",
    "}\n",
    "\n",
    "# Creating a dict with all keys\n",
    "dist_mp: dict = {k: 0 for k in keys}\n",
    "\n",
    "# Summing all possible combinations and store them inside the dict\n",
    "for m in mario:\n",
    "    for p in peach:\n",
    "        for b in boo:\n",
    "            for d in dk:\n",
    "                dice_roll: int = m+p+b+d\n",
    "                dist_mp[dice_roll] += 1\n",
    "\n",
    "best3: tuple = (10, dist_mp[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ecbad816-1cf1-4cb8-ad95-e4da62fd6164",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot\n",
    "plt.bar(dist_mp.keys(), dist_mp.values(), color='#F00a00')\n",
    "plt.xticks(list(dist_mp.keys()))\n",
    "plt.title(\"Mario Party Dice role Distribution\")\n",
    "plt.xlabel(\"Points rolled\")\n",
    "plt.ylabel(\"Number of occurrences\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}