{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e691d848",
   "metadata": {},
   "source": [
    "# Crash Course for Python 3\n",
    "- Börge Göbel Jan. 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c90d914a",
   "metadata": {},
   "source": [
    "Import numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d94bfe5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff755547",
   "metadata": {},
   "source": [
    "## Basic mathematic operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cb28ade3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2+2 #Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "706001de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "8-5 #Subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ee8e8473",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4*4 #Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d00b776",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5/2 #Division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "670f94df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5//2 #Integral division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "71da8f4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5%2 #Modulus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b75d7b8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3**2 #Exponent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ae937539",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "9**0.5 #sqrt command does not exist. It has to be imported."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a120579b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6e265fa",
   "metadata": {},
   "source": [
    "Constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3465d3f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1019aab3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.718281828459045"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.e"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26ba4432",
   "metadata": {},
   "source": [
    "Define variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "11d6e783",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "20be76cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4*a-5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d04a6a5",
   "metadata": {},
   "source": [
    "## Working with different data types"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "683f8b6e",
   "metadata": {},
   "source": [
    "### Numbers (integer, float and complex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7559d4d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "55d0d1a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "52bd4433",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "553c21fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1582566",
   "metadata": {},
   "source": [
    "There is no need to define the data type. Python does it automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9acc3a58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5+5.0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7aa92f1",
   "metadata": {},
   "source": [
    "but of course it is possible to transform data types"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4f2ca0c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2c3ea505",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(5.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8017d1bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(5.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5e604856",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(5.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef199bdb",
   "metadata": {},
   "source": [
    "Complex numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "da788ef1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1j"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "78fbf462",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1+0j)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1j**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "354d282a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(3+1j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3636475b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-7+11j)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(3+5j)*(1+2j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5c22c89",
   "metadata": {},
   "source": [
    "### Strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "84144ad5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Hello'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'Hello'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d52f87ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Hello'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"Hello\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "124cba91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Let's get started!\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"Let's get started!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e58deecb",
   "metadata": {},
   "outputs": [],
   "source": [
    "string = \"This is a test\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d9120518",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(string)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "1b72b4ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'The answer is: 5.0'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"The answer is: \"+\"5.0\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ee251515",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 5+8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f8f77703",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'The answer is: 13'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"The answer is: \"+str(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63de019a",
   "metadata": {},
   "source": [
    "## Lists, Arrays & More"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42c377b",
   "metadata": {},
   "source": [
    "### Lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f131e6ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "list1= [1,4,9]\n",
    "list2= [1,\"a\",3]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b518ba6",
   "metadata": {},
   "source": [
    "Select elements of a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "68148709",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "21c2da36",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1[0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39712715",
   "metadata": {},
   "source": [
    "Manipulate lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "f4b79e30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 3]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1.append(3)\n",
    "list1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "44fe385c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list2.remove(\"a\")\n",
    "list2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ffd37337",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 9]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1.sort()\n",
    "list1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "30a99c99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 10]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1[3]=10\n",
    "list1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d03440e",
   "metadata": {},
   "source": [
    "Multi-dimensional lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "91c8d48c",
   "metadata": {},
   "outputs": [],
   "source": [
    "list3=[[1,2,3],[1,4,9]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "ef7a59c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list3[1][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9f43b0e",
   "metadata": {},
   "source": [
    "Problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ddf17ae2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 10]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "628fcd53",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 10, 1, 3, 4, 10]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "5abf2c93",
   "metadata": {},
   "outputs": [],
   "source": [
    "#list1+2 gives an error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7e953b91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 10, 2]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list1+[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01a4950",
   "metadata": {},
   "source": [
    "### Arrays (import numpy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "7f511d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "array1=np.array([1,4,9])\n",
    "array2=np.array([1,\"a\",3])\n",
    "array3=np.array([[1,2,3],[1,4,9]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff2f03fa",
   "metadata": {},
   "source": [
    "Select elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d98bbcc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "7fa5b0c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "9fa99b2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['1', 'a'], dtype='<U11')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array2[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "2d155c2b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array3[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "d26b7a6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array3[0,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2730874",
   "metadata": {},
   "source": [
    "Manipulate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "6dcebe98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 9, 5])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(array1,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "18d7620d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 9, 5, 6])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(array1,np.array([5,6]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "9e60e26a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 9])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a76fc173",
   "metadata": {},
   "outputs": [],
   "source": [
    "array1=np.append(array1,np.array([5,6]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "39aba4c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 9, 5, 6])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0761b8b1",
   "metadata": {},
   "source": [
    "Manipulate multi-dimensional arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "b3496455",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [1, 4, 9]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f2fd2cfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  1,  4,  9,  1,  8, 27])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(array3,np.array([1,8,27]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "0717cbe5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 1,  4,  9],\n",
       "       [ 1,  8, 27]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(array3,np.array([[1,8,27]]),axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "5ff9ccba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 1,  4,  9, 16]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(array3,np.array([[4],[16]]),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d6e46aa",
   "metadata": {},
   "source": [
    "Maths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5c427511",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  8, 18, 10, 12])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "0cec785d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 10,  6,  7])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array1+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6dc3163c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 2,  8, 18]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array3*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "fc941934",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4],\n",
       "       [ 2,  5, 10]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array3+1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74215be2",
   "metadata": {},
   "source": [
    "### Vectors and Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d06dbec0",
   "metadata": {},
   "source": [
    "### Vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "50e6d85b",
   "metadata": {},
   "outputs": [],
   "source": [
    "vec1 = np.array([1,1,1])\n",
    "vec2 = np.array([2,3,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a66c5e",
   "metadata": {},
   "source": [
    "Dot and cross product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "b477808b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(vec1,vec2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "eee266b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1, -2,  1])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(vec1,vec2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "5338c5a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  2, -1])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(vec2,vec1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50850406",
   "metadata": {},
   "source": [
    "Norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "e24f2c26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.385164807134504"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(vec2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "a0a79910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.385164807134504"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(vec2[0]**2+vec2[1]**2+vec2[2]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "68336507",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.385164807134504"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.sum(vec2**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cfcf2a6",
   "metadata": {},
   "source": [
    "### Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "f563532d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mat1 = np.array([[1,-2,3],[-4,5,-6],[7,-8,9]])\n",
    "mat2 = np.array([[1,1,1],[0,2,2],[0,0,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "23d7fec0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2,  3],\n",
       "       [-4,  5, -6],\n",
       "       [ 7, -8,  9]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "ab64f102",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [0, 2, 2],\n",
       "       [0, 0, 3]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e637cfb5",
   "metadata": {},
   "source": [
    "Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "6ddb3a60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,  -2,   3],\n",
       "       [  0,  10, -12],\n",
       "       [  0,   0,  27]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat1*mat2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "04735e23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,  -3,   6],\n",
       "       [ -4,   6, -12],\n",
       "       [  7,  -9,  18]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(mat1,mat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "1f7968be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  4,  -5,   6],\n",
       "       [  6,  -6,   6],\n",
       "       [ 21, -24,  27]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(mat2,mat1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34cc24c1",
   "metadata": {},
   "source": [
    "Determinant and inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "c1c8af5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.det(mat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "fade967f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.5       ,  0.        ],\n",
       "       [ 0.        ,  0.5       , -0.33333333],\n",
       "       [ 0.        ,  0.        ,  0.33333333]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(mat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "7edd1f23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(np.linalg.inv(mat2),mat2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c83d463",
   "metadata": {},
   "source": [
    "### Dictionaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "bc1de240",
   "metadata": {},
   "outputs": [],
   "source": [
    "dict1 = {\n",
    "    \"brand\": \"Mercedes\",\n",
    "    \"model\": \"Sprinter\",\n",
    "    \"year\": 1995\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "9ba54534",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'brand': 'Mercedes', 'model': 'Sprinter', 'year': 1995}"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fce0d30",
   "metadata": {},
   "source": [
    "Select entries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "e93fd455",
   "metadata": {},
   "outputs": [],
   "source": [
    "#dict1[1] not working"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "bbeec0d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Sprinter'"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1[\"model\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "d7cda642",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['brand', 'model', 'year'])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "6823202c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_values(['Mercedes', 'Sprinter', 1995])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1.values()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad5b9d7b",
   "metadata": {},
   "source": [
    "Manipulate entries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "d58dd19a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dict1[\"year\"] = 1996\n",
    "dict1[\"country\"] = \"Germany\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "ec3d849d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'brand': 'Mercedes', 'model': 'Sprinter', 'year': 1996, 'country': 'Germany'}"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "898f34a9",
   "metadata": {},
   "source": [
    "## Loops & If statements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0223b044",
   "metadata": {},
   "source": [
    "### While loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "61241f58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "i = 1\n",
    "\n",
    "while i <= 10:\n",
    "    print(i)\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22a7713e",
   "metadata": {},
   "source": [
    "### While loop with if statement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "cd68d950",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odd\n",
      "2\n",
      "odd\n",
      "4\n",
      "odd\n",
      "6\n",
      "odd\n",
      "8\n",
      "odd\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "i = 1\n",
    "\n",
    "while i <= 10:\n",
    "    if i%2 == 0:\n",
    "        print(i)\n",
    "    else:\n",
    "        print(\"odd\")\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25679e12",
   "metadata": {},
   "source": [
    "### For loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "a12a1450",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "5\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "for i in [1,2,5,10]:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "19f9e46b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t\n",
      "e\n",
      "s\n",
      "t\n"
     ]
    }
   ],
   "source": [
    "for i in \"test\":\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "7fceceb2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "odd\n",
      "2\n",
      "odd\n",
      "4\n",
      "odd\n",
      "6\n",
      "odd\n",
      "8\n",
      "odd\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "for i in range(1,11):\n",
    "    if i%2 == 0:\n",
    "        print(i)\n",
    "    else:\n",
    "        print(\"odd\")\n",
    "    i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "a1420b6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "storelist = []\n",
    "for i in range(1,6):\n",
    "    storelist.append(i**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "b3502799",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 4, 9, 16, 25]"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "storelist"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a42f405",
   "metadata": {},
   "source": [
    "## Work with files"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59fc0b05",
   "metadata": {},
   "source": [
    "### Save"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba81e7c0",
   "metadata": {},
   "source": [
    "Save the whole list at once"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "3e1138d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt(\"storelist1.dat\", storelist, fmt=\"%s\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "b23422e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savetxt(\"storelist2.dat\", storelist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2098a20f",
   "metadata": {},
   "source": [
    "Save each line one after another"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "595a4948",
   "metadata": {},
   "outputs": [],
   "source": [
    "file = open('storelist3.dat','w')\n",
    "\n",
    "for i in range(1,6):\n",
    "    file.write(str(i**2))\n",
    "    file.write(\"\\n\")\n",
    "    \n",
    "file.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "90fe8f73",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('storelist4.dat','w') as file:\n",
    "    for i in range(1,6):\n",
    "        file.write(str(i**2))\n",
    "        file.write(\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcfd7618",
   "metadata": {},
   "source": [
    "### Load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "11c057fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "loadlist = np.loadtxt(\"storelist1.dat\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "ef985acf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  4.,  9., 16., 25.])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadlist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "29c257e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadlist[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea05e2b0",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "546f29c8",
   "metadata": {},
   "source": [
    "def _name_(_arguments_):\n",
    "\n",
    "    commands"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f771f79",
   "metadata": {},
   "source": [
    "First function without arguments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "86d3a2a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sayHello():\n",
    "    print(\"Hello!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "38947cbd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello!\n"
     ]
    }
   ],
   "source": [
    "sayHello()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12767034",
   "metadata": {},
   "source": [
    "Create your own dot product function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "1539adb5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec1 = np.array([1,1,1])\n",
    "vec2 = np.array([2,3,4])\n",
    "\n",
    "np.dot(vec1,vec2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "2f3d6300",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dotProduct(a,b):\n",
    "    c = a[0]*b[0]+a[1]*b[1]+a[2]*b[2]\n",
    "    # print(c) not really useful\n",
    "    return(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "138f821b",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = dotProduct(vec1,vec2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "999de207",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6dadb70",
   "metadata": {},
   "source": [
    "Use argument keywords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "333a84f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def personaldata(number, name, age):\n",
    "    print(\"ID: \" + str(number))\n",
    "    print(\"Name: \" + name)\n",
    "    print(\"Age: \" + str(age))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "c45daa75",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ID: 49\n",
      "Name: Peter\n",
      "Age: 29\n"
     ]
    }
   ],
   "source": [
    "personaldata(49, \"Peter\", 29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "5ebed2f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ID: 49\n",
      "Name: Peter\n",
      "Age: 29\n"
     ]
    }
   ],
   "source": [
    "personaldata(age=29, number=49, name=\"Peter\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f84b488",
   "metadata": {},
   "source": [
    "## Plots (import matplotlib)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "6ccb52c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b12613a9",
   "metadata": {},
   "source": [
    "### Scatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "8a8b271b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1d1777fcd00>"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.scatter([1,2,3,4,5],[5,1,-1,0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "01cfa64b",
   "metadata": {},
   "outputs": [],
   "source": [
    "coords1 = np.array([[1,1,1],[2,4,8],[3,9,27],[4,16,64],[5,25,125]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "e7d4c01f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   1,   1],\n",
       "       [  2,   4,   8],\n",
       "       [  3,   9,  27],\n",
       "       [  4,  16,  64],\n",
       "       [  5,  25, 125]])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coords1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "2c3adedd",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1, y1, z1 = coords1.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "f556c1d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1d17797fe50>"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xlabel('x')\n",
    "plt.ylabel('y, z')\n",
    "plt.scatter(x1, y1)\n",
    "plt.scatter(x1, z1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c87de0e",
   "metadata": {},
   "source": [
    "### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "d27c3a51",
   "metadata": {},
   "outputs": [],
   "source": [
    "#data points\n",
    "x1 = np.linspace(0,4,101)\n",
    "y1 = 1 + 2*np.cos(3*x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "3d815922",
   "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": [
    "plt.xlim([0,8])\n",
    "plt.plot(x1, y1)\n",
    "\n",
    "x2 = np.linspace(4,8,101)\n",
    "y2 = 1 + 2*np.cos(3*x2)\n",
    "plt.scatter(x2, y2)\n",
    "\n",
    "plt.savefig('testplot.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1533152",
   "metadata": {},
   "source": [
    "### Density plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "47ed9e3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5.])"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0,5,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "a9b064ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.,  6.,  7.,  8.,  9., 10.])"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(5,10,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "21850114",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0., 1., 2., 3., 4., 5.],\n",
       "        [0., 1., 2., 3., 4., 5.],\n",
       "        [0., 1., 2., 3., 4., 5.],\n",
       "        [0., 1., 2., 3., 4., 5.],\n",
       "        [0., 1., 2., 3., 4., 5.],\n",
       "        [0., 1., 2., 3., 4., 5.]]),\n",
       " array([[ 5.,  5.,  5.,  5.,  5.,  5.],\n",
       "        [ 6.,  6.,  6.,  6.,  6.,  6.],\n",
       "        [ 7.,  7.,  7.,  7.,  7.,  7.],\n",
       "        [ 8.,  8.,  8.,  8.,  8.,  8.],\n",
       "        [ 9.,  9.,  9.,  9.,  9.,  9.],\n",
       "        [10., 10., 10., 10., 10., 10.]])]"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.meshgrid(\n",
    "    np.linspace(0,5,6),\n",
    "    np.linspace(5,10,6)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "2063530d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.,  5.],\n",
       "        [ 0.,  6.],\n",
       "        [ 0.,  7.],\n",
       "        [ 0.,  8.],\n",
       "        [ 0.,  9.],\n",
       "        [ 0., 10.]],\n",
       "\n",
       "       [[ 1.,  5.],\n",
       "        [ 1.,  6.],\n",
       "        [ 1.,  7.],\n",
       "        [ 1.,  8.],\n",
       "        [ 1.,  9.],\n",
       "        [ 1., 10.]],\n",
       "\n",
       "       [[ 2.,  5.],\n",
       "        [ 2.,  6.],\n",
       "        [ 2.,  7.],\n",
       "        [ 2.,  8.],\n",
       "        [ 2.,  9.],\n",
       "        [ 2., 10.]],\n",
       "\n",
       "       [[ 3.,  5.],\n",
       "        [ 3.,  6.],\n",
       "        [ 3.,  7.],\n",
       "        [ 3.,  8.],\n",
       "        [ 3.,  9.],\n",
       "        [ 3., 10.]],\n",
       "\n",
       "       [[ 4.,  5.],\n",
       "        [ 4.,  6.],\n",
       "        [ 4.,  7.],\n",
       "        [ 4.,  8.],\n",
       "        [ 4.,  9.],\n",
       "        [ 4., 10.]],\n",
       "\n",
       "       [[ 5.,  5.],\n",
       "        [ 5.,  6.],\n",
       "        [ 5.,  7.],\n",
       "        [ 5.,  8.],\n",
       "        [ 5.,  9.],\n",
       "        [ 5., 10.]]])"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.transpose(\n",
    "    np.meshgrid(\n",
    "        np.linspace(0,5,6),\n",
    "        np.linspace(5,10,6)\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "570df1c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "x2, y2 = np.meshgrid(np.linspace(-10,10,201),np.linspace(-10,10,201))\n",
    "z2 = x2 + y2**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "446208ec",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<a list of 15 text.Text objects>"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "contourplot = plt.contour(x2,y2,z2)\n",
    "plt.clabel(contourplot, inline = 1, fontsize = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "db932391",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1d178fead60>"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x3, y3 = np.meshgrid(np.linspace(-10,10,201),np.linspace(-10,10,201))\n",
    "z3 = np.cos(x3+y3) + 0.05*(x3-y3)\n",
    "\n",
    "plt.contourf(x3,y3,z3)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75d4f04e",
   "metadata": {},
   "source": [
    "### 3d plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "fcaf23b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x1d17fc289d0>"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plotproj = plt.axes(projection='3d')\n",
    "plotproj.view_init(70,30)\n",
    "plotproj.contour3D(x3,y3,z3,100,cmap='binary')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627ab7c9",
   "metadata": {},
   "source": [
    "### 3d plots - lines & scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "059c74c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<mpl_toolkits.mplot3d.art3d.Line3D at 0x1d102433910>]"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt3D = plt.axes(projection='3d')\n",
    "z1 = np.linspace(0,30,301)\n",
    "x1 = np.sin(z1)\n",
    "y1 = 2*np.cos(z1)\n",
    "plt.xlim([-2,2])\n",
    "plt.ylim([-2,2])\n",
    "plt3D.plot3D(x1, y1, z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "3173e200",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x1d1025d4760>"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt3D = plt.axes(projection='3d')\n",
    "z1 = np.linspace(0,10, 51)\n",
    "x1 = np.sin(z1)\n",
    "y1 = 2*np.cos(z1)\n",
    "plt.xlim([-2,2])\n",
    "plt.ylim([-2,2])\n",
    "plt3D.scatter3D(x1, y1, z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9cce0cf6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}