pr3/python/numpy/numpy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "[[1. 2. 3.]\n",
      " [4. 5. 6.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Array mit Ganzzahlen anlegen\n",
    "a = np.array([[1,2,3], [4,5,6]])\n",
    "print(a)\n",
    "\n",
    "# Array mit Fließkommazahlen anlegen\n",
    "b = np.array([[1,2,3], [4,5,6]], float)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "(2, 3)\n",
      "[[1 0 0]\n",
      " [0 2 0]\n",
      " [0 0 3]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix nur mit Nullen\n",
    "\n",
    "a = np.zeros((2,3))\n",
    "\n",
    "print(a)\n",
    "print(a.shape)\n",
    "\n",
    "# Diagonal-Matrix\n",
    "\n",
    "b = np.diag([1,2,3])\n",
    "\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.31437735 0.70638017 0.893382  ]\n",
      " [0.88031899 0.61047408 0.93577239]]\n"
     ]
    }
   ],
   "source": [
    "a = np.random.random((2,3))\n",
    "\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [0. 0.]]\n",
      "[[8. 0.]\n",
      " [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((2,2))\n",
    "\n",
    "print(a)\n",
    "\n",
    "a[0][0] = 7\n",
    "#oder a[0,0] = 7\n",
    "\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "(2, 3)\n",
      "6\n",
      "int64\n",
      "[[1 4]\n",
      " [2 5]\n",
      " [3 6]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2,3], [4,5,6]])\n",
    "\n",
    "print(a.ndim)\n",
    "print(a.shape)\n",
    "print(a.size)\n",
    "print(a.dtype)\n",
    "print(a.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  3  4 12]\n",
      "[2 2 0 1]\n",
      "[ 0  3  8 15]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(4)\n",
    "\n",
    "b = np.array([2,3,2,4])\n",
    "\n",
    "print(b * a)\n",
    "print(b - a)\n",
    "\n",
    "c = [2,3,4,5]\n",
    "\n",
    "print(a * c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,) (4,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[13], line 4\u001b[0m\n\u001b[1;32m      1\u001b[0m a \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marange(\u001b[39m3\u001b[39m)\n\u001b[1;32m      2\u001b[0m b \u001b[39m=\u001b[39m np\u001b[39m.\u001b[39marange(\u001b[39m4\u001b[39m)\n\u001b[0;32m----> 4\u001b[0m \u001b[39mprint\u001b[39m(a\u001b[39m+\u001b[39;49mb)\n",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,) (4,) "
     ]
    }
   ],
   "source": [
    "a = np.arange(3)\n",
    "b = np.arange(4)\n",
    "\n",
    "print(a+b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5]\n"
     ]
    }
   ],
   "source": [
    "# Aufgabe\n",
    "\n",
    "x = np.array([0,1,2])\n",
    "y = np.array([3])\n",
    "\n",
    "print(x+y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n",
      "6\n",
      "[-1  2 -1]\n",
      "[[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n"
     ]
    }
   ],
   "source": [
    "# Listen werden automatisch in Vektoren konvertiert\n",
    "\n",
    "u = [1,2,3]\n",
    "v = [1,1,1]\n",
    "\n",
    "print(np.inner(u, v))\n",
    "print(np.dot(u, v))\n",
    "print(np.cross(u, v))\n",
    "\n",
    "print(np.outer(u,v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4 5 6]\n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "[[3]\n",
      " [6]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2,3], [4,5,6]])\n",
    "\n",
    "# 2. Zeile, alle Spalten\n",
    "print(a[1, :])\n",
    "\n",
    "# 1. und 2. Zeile, alle Spalten\n",
    "print(a[0:2])\n",
    "\n",
    "# Alle Zeilen, Spalten 3 und 4\n",
    "print(a[:, 2:4])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "[4 5 6]\n",
      "[1 2 3]\n",
      "[4 5 6]\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "# Iterieren über Matrizen\n",
    "\n",
    "a = np.array([[1,2,3], [4,5,6]])\n",
    "\n",
    "# Zeilen und Spaltenweise iterieren\n",
    "for row in a:\n",
    "    for column in a:\n",
    "        print(column)\n",
    "\n",
    "# Über alle Elemente iterieren\n",
    "for element in a.flat:\n",
    "    print(element)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.  2.  3.5]\n",
      " [4.  5.  6. ]\n",
      " [7.  8.  9.3]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix aus Datei lesen\n",
    "\n",
    "m = np.loadtxt(\"matrix.txt\")\n",
    "\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 1.]\n",
      " [1. 1.]]\n",
      "[[1. 1. 1.]\n",
      " [1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix-Operationen\n",
    "\n",
    "a = np.ones((3,2))\n",
    "\n",
    "b = a.T # Transponierte Matrix\n",
    "\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 7 9]\n",
      "[ 6 15]\n",
      "21\n",
      "[[1 2 3]\n",
      " [5 7 9]]\n",
      "[[ 1  3  6]\n",
      " [ 4  9 15]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix-Operationen\n",
    "\n",
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "\n",
    "# Spalten und Zeilensumme\n",
    "print(a.sum(axis=0))\n",
    "print(a.sum(axis=1))\n",
    "\n",
    "print(a.sum())\n",
    "\n",
    "# Kumulative Summe\n",
    "print(a.cumsum(axis=0))\n",
    "print(a.cumsum(axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "6\n",
      "[1 4]\n",
      "[3 6]\n"
     ]
    }
   ],
   "source": [
    "# Matrix-Operationen\n",
    "\n",
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "\n",
    "#Maximum und Minimum\n",
    "print(a.min())\n",
    "print(a.max())\n",
    "\n",
    "#Maximum und Minimum entlang einer Achse\n",
    "print(a.min(axis=1))\n",
    "print(a.max(axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n",
      "14\n"
     ]
    }
   ],
   "source": [
    "# Matrix-Operationen\n",
    "\n",
    "# 3x3 Identitätsmatrix\n",
    "id = np.eye(3)\n",
    "\n",
    "print(id)\n",
    "\n",
    "# Spur berechnen\n",
    "\n",
    "a = np.array([[1,2,3],[4,5,6],[7,6,8]])\n",
    "print(a.trace())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 4]\n",
      " [2 5]\n",
      " [3 6]]\n",
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix Operationen\n",
    "\n",
    "a = np.array([1,2,3])\n",
    "b = np.array([4,5,6])\n",
    "\n",
    "print(np.column_stack([a,b]))\n",
    "\n",
    "print(np.row_stack((a,b)))"
   ]
  }
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