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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Einführung in Python und NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variablen und Datentypen in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Primitive Datentypen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 Hello World 3.14 True (4+3j)\n",
      "<class 'int'> <class 'str'> <class 'float'> <class 'bool'> <class 'complex'>\n"
     ]
    }
   ],
   "source": [
    "a = 5\n",
    "b = \"Hello World\"\n",
    "c = 3.14\n",
    "d = True\n",
    "e = 4 + 3j\n",
    "print(a, b, c, d, e)\n",
    "print(type(a), type(b), type(c), type(d), type(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variablen überschreiben"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n",
      "Hello World\n"
     ]
    }
   ],
   "source": [
    "var = 50\n",
    "print(var)\n",
    "var = \"Hello World\" # Neuer Datentyp\n",
    "print(var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mehrere Variablen initialisieren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 6 7\n",
      "ha ha ha\n"
     ]
    }
   ],
   "source": [
    "x, y, z = 5, 6, 7\n",
    "i = j = k = \"ha\"\n",
    "print(x, y, z)\n",
    "print(i, j, k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variablen tauschen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "a, b = 1, 2\n",
    "a, b = b, a\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operatoren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n",
      "-2\n",
      "8\n",
      "0.5\n",
      "0\n",
      "2\n",
      "16\n",
      "2.0\n"
     ]
    }
   ],
   "source": [
    "a, b = 2, 4\n",
    "print(a + b)\n",
    "print(a - b)\n",
    "print(a * b)\n",
    "print(a / b)\n",
    "print(a // b)\n",
    "print(a % b)\n",
    "print(a**b)\n",
    "print(b**(1/a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variablen mit Operatoren neu zuweisen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12 35 16807\n"
     ]
    }
   ],
   "source": [
    "i = j = k = 7\n",
    "i += 5\n",
    "j *= 5\n",
    "k **= 5\n",
    "print(i, j, k)\n",
    "# Kein i++"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolesche Operatoren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "False\n",
      "True\n",
      "True\n",
      "True\n",
      "False\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "print(1 + 1 == 2)\n",
    "print(1 + 2 != 2)\n",
    "print(1 + 2 > 3)\n",
    "print(1 + 2 <= 3)\n",
    "print(1 + 2 is 3)\n",
    "print(True or False) # ||\n",
    "print(True and False) # &&\n",
    "print(not True) # !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Listen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "python numpy scipy 10 True\n",
      "True 10 scipy numpy python\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "l = [\"python\", \"numpy\", \"scipy\", 10, True]\n",
    "print(l[0], l[1], l[2], l[3], l[4])\n",
    "print(l[-1], l[-2], l[-3], l[-4], l[-5])\n",
    "print(len(l))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Listen bearbeiten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['python', 'numpy', 'scipy', 10, True, False]\n",
      "['python', 'numpy', 'scipy', 'matplotlib', True, False]\n"
     ]
    }
   ],
   "source": [
    "l.append(False)\n",
    "print(l)\n",
    "l[3] = \"matplotlib\"\n",
    "print(l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operatoren auf Listen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8]\n",
      "[1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]\n",
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "l1, l2 = [1,2,3,4], [5,6,7,8]\n",
    "l = l1 + l2\n",
    "print(l)\n",
    "print(3 * l1)\n",
    "print(5 in l2)\n",
    "print(5 in l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mehrdimensionale Listen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1, 2, 3], [4, 5, 6], [7, 8, 9]]\n",
      "1 4 6\n",
      "[1, 2, 3] [4, 5, 6] [7, 8, 9]\n"
     ]
    }
   ],
   "source": [
    "A = [[1,2,3], [4,5,6], [7,8,9]]\n",
    "print(A[0][0], A[1][0], A[1][2])\n",
    "print(A[0], A[1], A[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List Slices\n",
    "Notation: liste[start: stop: step]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8]\n",
      "[3, 4, 5]\n",
      "[3, 4, 5, 6, 7, 8]\n",
      "[1, 2, 3, 4, 5]\n",
      "[1, 2, 3, 4, 5, 6, 7, 8]\n",
      "[3, 5]\n",
      "[6, 5, 4]\n",
      "[8, 7, 6, 5, 4, 3, 2, 1]\n"
     ]
    }
   ],
   "source": [
    "print(l)\n",
    "print(l[2:5]) # der Index von stop ist nicht mit dabei\n",
    "print(l[2:]) # stop weglassen => bis zum Ende\n",
    "print(l[:5]) # start weglassen => vom Anfang an\n",
    "print(l[:])\n",
    "\n",
    "print(l[2:5:2]) # Das erste Element (start) ist immer mit dabei\n",
    "print(l[5:2:-1])\n",
    "print(l[::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tupel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Audi 250 4.7 True\n",
      "True 4.7 250 Audi\n",
      "4\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "t = (\"Audi\", 250, 4.7, True)\n",
    "print(t[0], t[1], t[2], t[3])\n",
    "print(t[-1], t[-2], t[-3], t[-4])\n",
    "print(len(t))\n",
    "print(\"Audi\" in t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tupel können nicht verändert werden, nur zusammengefügt!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Audi', 250, 4.7, True, 'white')\n",
      "4.7 white\n"
     ]
    }
   ],
    "t += (\"white\",) # es wird ein neues Tupel erstellt\n",
    "print(t)\n",
    "a, b, c, d, e = t\n",
    "print(c, e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Audi\n",
      "dict_keys(['brand', 'ps', 'acc', 'color'])\n",
      "dict_values(['Audi', 250, 4.7, 'white'])\n",
      "dict_items([('brand', 'Audi'), ('ps', 250), ('acc', 4.7), ('color', 'white')])\n"
     ]
    }
   ],
   "source": [
    "c = {\n",
    "    \"brand\": \"Audi\",\n",
    "    \"ps\": 250,\n",
    "    \"acc\": 4.7\n",
    "}\n",
    "\n",
    "c[\"color\"] = \"white\"\n",
    "\n",
    "print(c[\"brand\"])\n",
    "print(c.keys())\n",
    "print(c.values())\n",
    "print(c.items()) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funktionen und Verzweigungen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello world\n"
     ]
    }
   ],
    "    print(\"Hello world\")\n",
    "\n",
    "greet()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n"
     ]
    }
   ],
    "def square(x: int) -> int:\n",
    "    return x**2\n",
    "\n",
    "print(square(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optionale Parameter und Parameter mit Namen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "100\n",
      "25\n"
     ]
    }
   ],
   "source": [
    "def pow(x, y = 0):\n",
    "    return x**y\n",
    "\n",
    "print(pow(10))\n",
    "print(pow(10, 2))\n",
    "print(pow(y=2, x=5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mehrere Rückgabewerte (Tupel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 16\n",
      "(9, 16)\n"
     ]
    }
   ],
   "source": [
    "def f(x, y):\n",
    "    return x**2, y**2\n",
    "\n",
    "a, b  = f(3, 4)\n",
    "print(a, b)\n",
    "ab = f(3, 4)\n",
    "print(ab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bedingte Anweisungen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 -1 0\n"
     ]
    }
   ],
   "source": [
    "def sign(x):\n",
    "    if x < 0:\n",
    "        return -1\n",
    "    elif x > 0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "    \n",
    "print(sign(17), sign(-3), sign(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True False\n"
     ]
    }
   ],
   "source": [
    "def positive(x):\n",
    "    return True if x > 0 else False\n",
    "\n",
    "print(positive(14), positive(0))\n",
    "\n",
    "# C/Java return x > 0 ? True : False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Schleifen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "[1, 2, 3, 4, 5]\n",
      "[1, 3, 5, 7, 9]\n"
     ]
    }
   ],
    "for i in range(5): # Python For-Schleifen iterieren immer über ein iterable z.B. Liste\n",
    "    print(i)\n",
    "    \n",
    "print(list(range(1, 6)))\n",
    "print(list(range(1, 10, 2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Funktionsweise: range(start, stop, step)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List Comprehensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16]\n",
      "[0, 4, 16, 36, 64]\n"
     ]
    }
   ],
   "source": [
    "a = [i**2 for i in range(5)]\n",
    "print(a)\n",
    "\n",
    "b = [i**2 for i in range(10) if i % 2 == 0]\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Über Datenstrukturen iterieren"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5, 6, 7, 8]\n"
     ]
    }
   ],
   "source": [
    "print(l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "for el in l2:\n",
    "    print(el)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5\n",
      "1 6\n",
      "2 7\n",
      "3 8\n"
     ]
    }
   ],
   "source": [
    "for i in range(len(l2)):\n",
    "    print(i, l2[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5\n",
      "1 6\n",
      "2 7\n",
      "3 8\n"
     ]
    }
   ],
   "source": [
    "for i, el in enumerate(l2):\n",
    "    print(i, el)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'brand': 'Audi', 'ps': 250, 'acc': 4.7, 'color': 'white'}\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "brand Audi\n",
      "ps 250\n",
      "acc 4.7\n",
      "color white\n"
     ]
    }
   ],
   "source": [
    "for key, val in c.items():\n",
    "    print(key, val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objektorientierte Programmierung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Person:\n",
    "    def __init__(self, name):\n",
    "        self.name = name\n",
    "        \n",
    "    def greet(self):\n",
    "        print(\"Hallo, ich bin {}\".format(self.name))\n",
    "        \n",
    "    def __repr__(self):\n",
    "        return \"Person: {}\".format(self.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hallo, ich bin Anna\n",
      "Person: Anna\n"
     ]
    }
   ],
   "source": [
    "p = Person(\"Anna\")\n",
    "p.greet()\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Student(Person):\n",
    "    def __init__(self, name, age, height):\n",
    "        Person.__init__(self, name)\n",
    "        self.__age = age # private\n",
    "        self._height = height # protected\n",
    "        \n",
    "    def __repr__(self):\n",
    "        return \"Person[name={},age={},height={}]\"\\\n",
    "            .format(self.name, self.__age, self._height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hallo, ich bin Anna\n",
      "Person[name=Anna,age=18,height=175]\n"
     ]
    }
   ],
   "source": [
    "s = Student(\"Anna\", 18, 175)\n",
    "s.greet()\n",
    "print(s)\n",
    "# print(s.__age)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Funktionale Programmierung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81\n",
      "16\n"
     ]
    }
   ],
   "source": [
    "g = lambda x: x**4\n",
    "h = lambda x, y: x**(2*y)\n",
    "print(g(3))\n",
    "print(h(2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8]\n"
     ]
    }
   ],
   "source": [
    "print(l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<map object at 0x0000029981C05508>\n",
      "[1, 4, 9, 16, 25, 36, 49, 64]\n"
     ]
    }
   ],
   "source": [
    "lsq = map(lambda x: x**2, l)\n",
    "print(lsq)\n",
    "print(list(lsq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 5, 7]\n"
     ]
    }
   ],
   "source": [
    "print(list(filter(lambda x: x % 2 == 1, l)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "36\n"
     ]
    }
   ],
   "source": [
    "from functools import reduce\n",
    "print(reduce(lambda a, b: a + b, l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "print(reduce(lambda a, b: a if a > b else b, l))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## == vs. is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "print(5 == 5)\n",
    "print(5 is 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n",
      "True\n"
     ]
    }
   ],
    "a = b = [1,2,3]\n",
    "print([1,2,3] == [1,2,3])\n",
    "print([1,2,3] is [1,2,3])\n",
    "print(a is b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy Grundlagen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5 6]\n",
      "1\n",
      "6\n",
      "[2 3 4]\n",
      "[1 2]\n",
      "[6 5 4 3 2 1]\n",
      "[2 4 6]\n",
      "[1 3 4 5]\n",
      "[1 3 6]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([1, 2, 3, 4, 5, 6])\n",
    "print(a)\n",
    "print(a[0])\n",
    "print(a[-1])\n",
    "print(a[1:4])\n",
    "print(a[:2])\n",
    "print(a[::-1])\n",
    "print(a[1::2])\n",
    "print(a[[0, 2, 3, 4]]) # Liste von Indizes\n",
    "print(a[[True, False, True, False, False, True]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operatoren auf NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5 6 7 8]\n",
      "[ 3  6  9 12 15 18]\n",
      "[ 1  4  9 16 25 36]\n",
      "[ 2  4  8 16 32 64]\n"
     ]
    }
   ],
    "print(a + 2)\n",
    "print(3 * a)\n",
    "print(a**2)\n",
    "print(2**a)"
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([6, 5, 4, 3, 2, 1]) # b = a[::-1]"
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 7 7 7 7 7]\n",
      "[ 6 10 12 12 10  6]\n",
      "[ 1 32 81 64 25  6]\n"
     ]
    }
   ],
   "source": [
    "print(a + b)\n",
    "print(a * b)\n",
    "print(a**b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zweidimensionale Arrays (Matrizen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "1 6\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "print(A)\n",
    "print(A[0,0], A[1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[1 4 7]\n"
     ]
    }
   ],
   "source": [
    "print(A[0])\n",
    "print(A[:, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [4 5]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:2, :2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 1]\n",
      " [5 4]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:2, 1::-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 5]\n",
      " [1 2]]\n"
     ]
    }
   ],
   "source": [
    "print(A[1::-1, :2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Werte überschreiben"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "B = A.copy()\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 12 12]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]]\n"
     ]
    }
   ],
   "source": [
    "B[0] = 12\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 -5 12]\n",
      " [ 4 -5  6]\n",
      " [ 7 -5  9]]\n"
     ]
    }
   ],
   "source": [
    "B[:, 1] = -5\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 -5 12]\n",
      " [ 4 -5  6]\n",
      " [ 5  6  7]]\n"
     ]
    }
   ],
   "source": [
    "B[2] = [5, 6, 7]\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12 12 12]\n",
      " [ 4 -5  6]\n",
      " [ 5 12  7]]\n"
     ]
    }
   ],
   "source": [
    "B[:, 1] = B[0]\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensionen hinzufügen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 2 3]\n",
      "  [4 5 6]\n",
      "  [7 8 9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 2 3]]\n",
      "\n",
      " [[4 5 6]]\n",
      "\n",
      " [[7 8 9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1]\n",
      "  [2]\n",
      "  [3]]\n",
      "\n",
      " [[4]\n",
      "  [5]\n",
      "  [6]]\n",
      "\n",
      " [[7]\n",
      "  [8]\n",
      "  [9]]]\n"
     ]
    }
   ],
   "source": [
    "print(A[:, :, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0 -1]\n",
      "  [-1 -1]\n",
      "  [-2 -4]]\n",
      "\n",
      " [[-1  0]\n",
      "  [-2  0]\n",
      "  [-3 -3]]]\n",
      "[[[ 0 -1]\n",
      "  [-1  0]]\n",
      "\n",
      " [[-1 -1]\n",
      "  [-2  0]]\n",
      "\n",
      " [[-2 -4]\n",
      "  [-3 -3]]]\n"
     ]
    }
   ],
   "source": [
    "X = np.array([[1,0],[0,1]])\n",
    "Y = np.array([[1,1],[2,1],[3,4]])\n",
    "print(X[:, None] - Y[None, :])\n",
    "print(X[None, :] - Y[:, None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolesche Funktionen auf NumPy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = np.array([1, 0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True False  True]\n"
     ]
    }
   ],
   "source": [
    "print(b == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False  True False]\n"
     ]
    }
   ],
   "source": [
    "print(b < 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(A[b == 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(A[[True, False, True]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False False False]\n",
      " [False False  True]\n",
      " [ True  True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(A > 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(A[A > 5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nützliche NumPy Funktionen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.ndarray((4,4))\n",
    "A = np.zeros((3, 4))\n",
    "B = np.ones((3,4))\n",
    "c = np.arange(0, 1, .1)\n",
    "d = np.linspace(0, 1, 10)\n",
    "I = np.identity(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.67296746e-307 1.69121096e-306 8.01092457e-307 1.24610994e-306]\n",
      " [1.42418987e-306 1.37961641e-306 1.60220528e-306 1.24611266e-306]\n",
      " [9.34598925e-307 1.24612081e-306 1.11260755e-306 1.60220393e-306]\n",
      " [1.51320640e-306 9.34609790e-307 1.24610723e-306 1.24610723e-306]]\n"
     ]
    }
   ],
   "source": [
    "print(X) # zufällige Werte"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]\n",
      " [1. 1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
     ]
    }
   ],
   "source": [
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.         0.11111111 0.22222222 0.33333333 0.44444444 0.55555556\n",
      " 0.66666667 0.77777778 0.88888889 1.        ]\n"
     ]
    }
   ],
   "source": [
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 1. 0. 0.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.  4.]\n",
      " [ 5.  6.  7.  8.]\n",
      " [ 9. 10. 11. 12.]\n",
      " [13. 14. 15. 16.]]\n"
     ]
    }
   ],
   "source": [
    "M = np.linspace(1, 16, 16).reshape((4,4))\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  5.  9. 13.]\n",
      " [ 2.  6. 10. 14.]\n",
      " [ 3.  7. 11. 15.]\n",
      " [ 4.  8. 12. 16.]]\n"
     ]
    }
   ],
   "source": [
    "print(M.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "136.0 8.5 20922789888000.0\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(), M.mean(), M.prod())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[28. 32. 36. 40.] [ 7.  8.  9. 10.] [ 585. 1680. 3465. 6144.]\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(0), M.mean(0), M.prod(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10. 26. 42. 58.] [ 2.5  6.5 10.5 14.5] [2.400e+01 1.680e+03 1.188e+04 4.368e+04]\n"
     ]
    }
   ],
   "source": [
    "print(M.sum(1), M.mean(1), M.prod(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 2. 3. 4.]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(1,4, 4)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 30.  70. 110. 150.]\n"
     ]
    }
   ],
   "source": [
    "print(M.dot(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 30.  70. 110. 150.]\n"
     ]
    }
   ],
   "source": [
    "print(M @ x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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