{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Von Java nach Python\n",
    "## Erstes Programm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello Hoenggerbergg!\n"
     ]
    }
   ],
   "source": [
    "# prints 'Hello World!'to the console\n",
    "print(\"Hello Hoenggerbergg!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formattierung ist relevant\n",
    "### Anweisungen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hurray, finally ...\n",
      "... no Semicolons!\n"
     ]
    }
   ],
   "source": [
    "# two print-statements\n",
    "print(\"Hurray, finally ...\")\n",
    "print(\"... no Semicolons!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bloecke"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.392726722865772\n"
     ]
    }
   ],
   "source": [
    "# Harmonische Reihe in Python\n",
    "x = 0\n",
    "i = 1000000\n",
    "\n",
    "while i > 0:\n",
    "    x = x + 1 / i\n",
    "    i = i - 1\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Literale\n",
    "### Ganzzahlen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42 -5 27 27 7729684762313578932578932\n"
     ]
    }
   ],
   "source": [
    "i1 = 42\n",
    "i2 = -5\n",
    "i3 = 0x1b\n",
    "i4 = 0o33\n",
    "i5 = 7729684762313578932578932\n",
    "\n",
    "print(i1, i2, i3, i4, i5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fliesskommazahlen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.1 0.0034567\n"
     ]
    }
   ],
   "source": [
    "f1 = -0.1\n",
    "f2 = 34.567e-4\n",
    "\n",
    "print(f1, f2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wahrheitswerte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True False\n"
     ]
    }
   ],
   "source": [
    "b1 = True\n",
    "b2 = False\n",
    "\n",
    "print(b1, b2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zeichenketten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a single quoted string\n",
      "and a second line\n",
      "\n",
      "a double quoted string\n",
      "and a second line\n",
      "\n",
      "a multipline string string\n",
      "and a second line\n"
     ]
    }
   ],
   "source": [
    "str1 = 'a single quoted string\\nand a second line'\n",
    "str2 = \"a double quoted string\\nand a second line\"\n",
    "str3 = \"\"\"a multipline string string\n",
    "and a second line\"\"\"\n",
    "\n",
    "print (str1, str2, str3, sep = '\\n\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Listen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[17, True, 'abc'] [42] []\n"
     ]
    }
   ],
   "source": [
    "l1 = [ 17, True, \"abc\"]\n",
    "l2 = [ 42 ]\n",
    "l3 = []\n",
    "\n",
    "print(l1, l2, l3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tupel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(17, True, 'abc') (42,) ()\n"
     ]
    }
   ],
   "source": [
    "t1 = ( 17, True, \"abc\")\n",
    "t2 = ( 42, ) #trailing comma required for 1 element tuples.\n",
    "t3 = ()\n",
    "\n",
    "print (t1, t2, t3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': 42, 'b': 27, False: 'Zonk!'} {}\n"
     ]
    }
   ],
   "source": [
    "d1 = { \"a\": 42, \"b\": 27, False: \"Zonk!\" }\n",
    "d2 = {}\n",
    "\n",
    "print(d1, d2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{17, 'abc', True} {42}\n"
     ]
    }
   ],
   "source": [
    "s1 = {17, True, \"abc\"}\n",
    "s2 = {42}\n",
    "\n",
    "print(s1, s2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variablen\n",
    "### Dynamisch typisiert"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wert: Ein Text \n",
      "Typ: <class 'str'>\n",
      "\n",
      "Wert: 42 \n",
      "Typ: <class 'int'>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = \"Ein Text\";\n",
    "print(\"Wert:\", a, \"\\nTyp:\", type(a), end=\"\\n\\n\")\n",
    "\n",
    "a = 42\n",
    "print(\"Wert:\", a, \"\\nTyp:\", type(a), end=\"\\n\\n\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zuweisung mehrerer Variablen gleichzeitig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "x, y = 4, 5\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fehler: Lesen vor initialisierung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'b' 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<ipython-input-1-488068fe1e94>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'b' is not defined"
     ]
    }
   ],
   "source": [
    "a=b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interessante Operatoren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32\n",
      "True\n",
      "data1 == data2:  True\n",
      "data2 == data3:  True\n",
      "data1 is data2:  False\n",
      "data2 is data3:  True\n"
     ]
    }
   ],
   "source": [
    "print(2**5)\n",
    "print(42 in [7, 19, 42])\n",
    "\n",
    "data1 = { \"Games\": 5, \"Wins\" : 3 }\n",
    "data2 = { \"Games\": 5, \"Wins\" : 3 }\n",
    "data3 = data2\n",
    "\n",
    "print(\"data1 == data2: \", data1 == data2)\n",
    "print(\"data2 == data3: \", data2 == data3)\n",
    "print(\"data1 is data2: \", data1 is data2)\n",
    "print(\"data2 is data3: \", data2 is data3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eingabe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is your name: Hermann\n",
      "Hello Hermann\n"
     ]
    }
   ],
   "source": [
    "name = input(\"What is your name: \")\n",
    "print(\"Hello\", name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Konvertierung von Typen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter a number: 42\n",
      "2^42 = 4398046511104\n"
     ]
    }
   ],
   "source": [
    "i = int(input(\"Enter a number: \"))\n",
    "print(\"2^\", i, \" = \", 2**i, sep = \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bedingungen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter a number: 42\n",
      "Naturally, the answer\n"
     ]
    }
   ],
   "source": [
    "a = int(input(\"Enter a number: \"))\n",
    "if a == 42:\n",
    "    print(\"Naturally, the answer\")\n",
    "elif a == 28:\n",
    "    print(\"A perfect number, good choice\")\n",
    "else:\n",
    "    print(a, \"is just some boring number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Schleifen\n",
    "### While-Schleifen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter a number: 27\n",
      "82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 "
     ]
    }
   ],
   "source": [
    "a = int(input(\"Enter a number: \"))\n",
    "while a != 1:\n",
    "    if a % 2 == 0:\n",
    "        a = a // 2\n",
    "    else:\n",
    "        a = a * 3 + 1\n",
    "    print(a, end=' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For-Schleifen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total of the numbers is 42\n"
     ]
    }
   ],
   "source": [
    "some_list = [14, 'lala', 22, True, 6]\n",
    "total = 0\n",
    "for item in some_list:\n",
    "    if type(item) == int:\n",
    "        total += item\n",
    "print(\"Total of the numbers is\", total)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wertebereiche"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 2 3 4 \n",
      "\n",
      "10 8 6 4 2 "
     ]
    }
   ],
   "source": [
    "for i in range(1,5):\n",
    "    print(i, end=' ')\n",
    "\n",
    "print('\\n')\n",
    "    \n",
    "for i in range(10, 0, -2):\n",
    "    print(i, end=' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methoden"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kids: 3\n",
      "Cookies: 8\n",
      "Each kid gets 2 cookies.\n",
      "Papa gets 2 cookies.\n"
     ]
    }
   ],
   "source": [
    "def readInt(prompt, atleast = 1):\n",
    "    \"\"\"Prompt for a number greater 0 (or min, if specified)\"\"\"\n",
    "    number = 0;\n",
    "    while number < atleast:\n",
    "        number = int(input(prompt))\n",
    "        if (number < atleast):\n",
    "            print(\"Too small, pick a number larger than\", atleast)\n",
    "    return number\n",
    "\n",
    "kids = readInt(\"Kids: \")\n",
    "cookies = readInt(\"Cookies: \", atleast=kids)\n",
    "print(\"Each kid gets\", cookies // kids, \"cookies.\")\n",
    "print(\"Papa gets\", cookies % kids, \"cookies.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arbeiten mit Listen\n",
    "### Basis-Operationen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "4\n",
      "12 is in the list, we just added it\n",
      "Number of elements in the list: 4\n"
     ]
    }
   ],
   "source": [
    "a = [ 3, 7, 4]\n",
    "print(a[1])\n",
    "print(a[-1])\n",
    "\n",
    "a.append(12)\n",
    "\n",
    "if 12 in a:\n",
    "    print(\"12 is in the list, we just added it\")\n",
    "\n",
    "print(\"Number of elements in the list:\", len(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a[2:4] = [3, 4]\n",
      "a[3:-3] = [4, 5, 6]\n",
      "a[-3:-1] = [7, 8]\n",
      "a[5:] = [6, 7, 8, 9]\n",
      "a[:3] = [1, 2, 3]\n"
     ]
    }
   ],
   "source": [
    "a = [ 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
    "\n",
    "print(\"a[2:4] =\", a[2:4])\n",
    "print(\"a[3:-3] =\", a[3:-3])\n",
    "print(\"a[-3:-1] =\", a[-3:-1])\n",
    "print(\"a[5:] =\", a[5:])\n",
    "print(\"a[:3] =\", a[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Arbeiten mit Dictionaries\n",
    "### Basis-Operationen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "... one more thing!\n",
      "\n",
      "{'Firstname': 'Hermann', 'Lastname': 'Lehner', 'Salary': 450000, 'Mac User': True}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "record = { \n",
    "    \"Firstname\": \"Hermann\", \n",
    "    \"Lastname\":\"Lehner\",\n",
    "    \"Salary\": 420000, \n",
    "    \"Mac User\": True \n",
    "}\n",
    "\n",
    "record[\"Salary\"] = 450000\n",
    "if record[\"Mac User\"]:\n",
    "    print(\"... one more thing!\\n\")\n",
    "\n",
    "print(record, end=\"\\n\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dynamische Datenstrukturen mit Dicts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'key': 8, 'left': {'key': 4, 'left': None, 'right': None}, 'right': {'key': 13, 'left': {'key': 10, 'left': None, 'right': None}, 'right': {'key': 19, 'left': None, 'right': None}}}\n"
     ]
    }
   ],
   "source": [
    "tree = { \n",
    "    'key': 8,\n",
    "    'left' : {\n",
    "        'key': 4, 'left' : None, 'right': None\n",
    "    },\n",
    "    'right': {\n",
    "        'key': 13,\n",
    "        'left' : {\n",
    "            'key': 10, 'left' : None, 'right': None\n",
    "        },\n",
    "        'right': {\n",
    "            'key': 19,  'left' : None, 'right': None\n",
    "        }\n",
    "    }\n",
    "}\n",
    "\n",
    "print(tree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das wollen wir etwas schoener machen. Wir nutzen dazu das Modul 'pprint', welches in der Standardbibliotheke von Python dabei ist:\n",
    "\n",
    "[Dokumentation von 'pprint'](https://docs.python.org/3.7/library/pprint.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{ 'key': 8,\n",
      "  'left': { 'key': 4,\n",
      "            'left': None,\n",
      "            'right': None},\n",
      "  'right': { 'key': 13,\n",
      "             'left': { 'key': 10,\n",
      "                       'left': None,\n",
      "                       'right': None},\n",
      "             'right': { 'key': 19,\n",
      "                        'left': None,\n",
      "                        'right': None}}}\n",
      "\n",
      "Changing left key to 6 (Aliasing!):\n",
      "\n",
      "{ 'key': 8,\n",
      "  'left': { 'key': 6,\n",
      "            'left': None,\n",
      "            'right': None},\n",
      "  'right': { 'key': 13,\n",
      "             'left': { 'key': 10,\n",
      "                       'left': None,\n",
      "                       'right': None},\n",
      "             'right': { 'key': 19,\n",
      "                        'left': None,\n",
      "                        'right': None}}}\n",
      "There is no left child here...\n"
     ]
    }
   ],
   "source": [
    "import pprint\n",
    "pp = pprint.PrettyPrinter(indent=2, width=40, depth=3)\n",
    "\n",
    "pp.pprint(tree)\n",
    "\n",
    "print(\"\\nChanging left key to 6 (Aliasing!):\\n\")\n",
    "\n",
    "leftSubtree = tree['left'] # assign left subtree to variable l\n",
    "leftSubtree['key'] = 6     # changes key from 4 to 6\n",
    "\n",
    "pp.pprint(tree)\n",
    "\n",
    "if leftSubtree['left'] is None:   # proper way to test against None\n",
    "    print(\"There is no left child here...\")\n",
    "else:\n",
    "    print(\"Value of left subtree is\", l['left']['key'])\n",
    "          "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Klassen\n",
    "### Dynamische Datenstrukturen mit Klassen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n"
     ]
    }
   ],
   "source": [
    "class Node:\n",
    "    def __init__(self, k, l = None, r = None):\n",
    "        self.key, self.left, self.right = k, l, r\n",
    "\n",
    "# create a tree\n",
    "rightSubtree = Node(13, l = Node(10), r = Node(19))\n",
    "tree = Node(8, l = Node(4), r = rightSubtree)\n",
    "\n",
    "# an example query\n",
    "print(tree.right.right.key)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Module / Libraries\n",
    "### Verwenden von Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0\n",
      "3.0\n",
      "2020-02-17\n",
      "<class 'datetime.date'>\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "x = math.sqrt(4)\n",
    "print(x)\n",
    "\n",
    "from math import *\n",
    "x = sqrt(9)\n",
    "print(x)\n",
    "\n",
    "from datetime import date\n",
    "t = date.today()\n",
    "\n",
    "print(t)\n",
    "print(type(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beispiel: Plotten von Funktionen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.arange(0.0, 2*np.pi, 0.01)\n",
    "y = np.sin(x)\n",
    "\n",
    "line = plt.plot(x, y)\n",
    "\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "t = np.arange(0.0, 2.0, 0.01)\n",
    "s = np.cos(2*np.pi*t)\n",
    "line, = plt.plot(t, s, lw=2)\n",
    "\n",
    "plt.annotate('local max', xy=(1, 1), xytext=(1.2, 1.5),\n",
    "             arrowprops=dict( color=\"gray\", width=2),\n",
    "             )\n",
    "\n",
    "plt.ylim(-2, 2)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beispiel: Numerische Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# Build a vector of 10000 normal deviates with variance 0.5^2 and mean 2\n",
    "mu, sigma = 2, 0.5\n",
    "v = np.random.normal(mu,sigma,10000)\n",
    "# Plot a normalized histogram with 50 bins\n",
    "plt.hist(v, bins=50, density=1)       # matplotlib version (plot)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beispiel: Mandelbrot-Menge drucken"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def mandelbrot( h,w, maxit=20 ):\n",
    "    \"\"\"Returns an image of the Mandelbrot fractal of size (h,w).\"\"\"\n",
    "    y,x = np.ogrid[ -1.4:1.4:h*1j, -2:0.8:w*1j ]\n",
    "    c = x+y*1j\n",
    "    z = c\n",
    "    divtime = maxit + np.zeros(z.shape, dtype=int)\n",
    "\n",
    "    for i in range(maxit):\n",
    "        z = z**2 + c\n",
    "        diverge = z*np.conj(z) > 2**2         # who is diverging\n",
    "        div_now = diverge & (divtime==maxit)  # who is diverging now\n",
    "        divtime[div_now] = i                  # note when\n",
    "        z[diverge] = 2                        # avoid diverging too much\n",
    "\n",
    "    return divtime\n",
    "plt.imshow(mandelbrot(400,400))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Beispiel: Komplexe Grafiken\n",
    "(Keine Ahnung was das genau ist :-)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.tri as tri\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(19680801)\n",
    "npts = 200\n",
    "ngridx = 100\n",
    "ngridy = 200\n",
    "x = np.random.uniform(-2, 2, npts)\n",
    "y = np.random.uniform(-2, 2, npts)\n",
    "z = x * np.exp(-x**2 - y**2)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(nrows=2)\n",
    "\n",
    "# -----------------------\n",
    "# Interpolation on a grid\n",
    "# -----------------------\n",
    "# A contour plot of irregularly spaced data coordinates\n",
    "# via interpolation on a grid.\n",
    "\n",
    "# Create grid values first.\n",
    "xi = np.linspace(-2.1, 2.1, ngridx)\n",
    "yi = np.linspace(-2.1, 2.1, ngridy)\n",
    "\n",
    "# Perform linear interpolation of the data (x,y)\n",
    "# on a grid defined by (xi,yi)\n",
    "triang = tri.Triangulation(x, y)\n",
    "interpolator = tri.LinearTriInterpolator(triang, z)\n",
    "Xi, Yi = np.meshgrid(xi, yi)\n",
    "zi = interpolator(Xi, Yi)\n",
    "\n",
    "# Note that scipy.interpolate provides means to interpolate data on a grid\n",
    "# as well. The following would be an alternative to the four lines above:\n",
    "#from scipy.interpolate import griddata\n",
    "#zi = griddata((x, y), z, (xi[None,:], yi[:,None]), method='linear')\n",
    "\n",
    "\n",
    "ax1.contour(xi, yi, zi, levels=14, linewidths=0.5, colors='k')\n",
    "cntr1 = ax1.contourf(xi, yi, zi, levels=14, cmap=\"RdBu_r\")\n",
    "\n",
    "fig.colorbar(cntr1, ax=ax1)\n",
    "ax1.plot(x, y, 'ko', ms=3)\n",
    "ax1.set(xlim=(-2, 2), ylim=(-2, 2))\n",
    "ax1.set_title('grid and contour (%d points, %d grid points)' %\n",
    "              (npts, ngridx * ngridy))\n",
    "\n",
    "\n",
    "# ----------\n",
    "# Tricontour\n",
    "# ----------\n",
    "# Directly supply the unordered, irregularly spaced coordinates\n",
    "# to tricontour.\n",
    "\n",
    "ax2.tricontour(x, y, z, levels=14, linewidths=0.5, colors='k')\n",
    "cntr2 = ax2.tricontourf(x, y, z, levels=14, cmap=\"RdBu_r\")\n",
    "\n",
    "fig.colorbar(cntr2, ax=ax2)\n",
    "ax2.plot(x, y, 'ko', ms=3)\n",
    "ax2.set(xlim=(-2, 2), ylim=(-2, 2))\n",
    "ax2.set_title('tricontour (%d points)' % npts)\n",
    "\n",
    "plt.subplots_adjust(hspace=0.5)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}