SU-2020-LAB00-Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fakultet u Zagrebu  \n",
    "Fakultet elektrotehnike i računarstva  \n",
    "  \n",
    "## Strojno učenje 2020/2021  \n",
    "http://www.fer.unizg.hr/predmet/su"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------\n",
    "\n",
    "### Laboratorijska vježba 0: Uvod u Python\n",
    "\n",
    "*Verzija: 1.1  \n",
    "Zadnji put ažurirano: 5. 10. 2020.*\n",
    "\n",
    "(c) 2015-2020 Jan Šnajder, Domagoj Alagić \n",
    "\n",
    "Rok za predaju: **N/A**\n",
    "\n",
    "------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1. Liste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6, 2, 3]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = [5, 6, 2, 3]\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 6, 10, 3]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[2] = 10\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', 6, 10, 3]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[0] = \"a book\"\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10, 3]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[1] = [3, 4]\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10, 3, 99, 100]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs += [99, 100]\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10, 3, 99, 100, 22, 33]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs.extend([22, 33])\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10, 3, 99, 100, 22]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4]]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 3, 99, 100, 22]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a book', [3, 4], 10, 3, 99]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs[:-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a book\n",
      "[3, 4]\n",
      "10\n",
      "3\n",
      "99\n",
      "100\n",
      "22\n"
     ]
    }
   ],
   "source": [
    "for el in xs:\n",
    "    print(el)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 a book\n",
      "1 [3, 4]\n",
      "2 10\n",
      "3 3\n",
      "4 99\n",
      "5 100\n",
      "6 22\n"
     ]
    }
   ],
   "source": [
    "for idx, el in enumerate(xs):\n",
    "    print(idx, el)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "for idx in range(len(xs)):\n",
    "    print(idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "for idx in range(2, len(xs)):\n",
    "    print(idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "2\n",
      "4\n",
      "6\n"
     ]
    }
   ],
   "source": [
    "for idx in range(0, len(xs), 2):\n",
    "    print(idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = []\n",
    "for x in range(10):\n",
    "    xs.append(x ** 2)\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x ** 2 for x in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 4, 16, 36, 64]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x ** 2 for x in range(10) if x % 2 == 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 512, 4, 512, 16, 512, 36, 512, 64, 512]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x ** 2 if x % 2 == 0 else 512 for x in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 4\n",
      "2 5\n",
      "3 6\n"
     ]
    }
   ],
   "source": [
    "for a, b in zip([1, 2, 3], [4, 5, 6]):\n",
    "    print(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 4\n",
      "2 5\n",
      "3 6\n"
     ]
    }
   ],
   "source": [
    "for a, b in zip([1, 2, 3], [4, 5, 6, 7]):\n",
    "    print(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 2, 5)\n",
      "(4, 3, 6)\n"
     ]
    }
   ],
   "source": [
    "a_list, b_list = zip(*[(1, 4), (2, 3), (5, 6)])\n",
    "print(a_list)\n",
    "print(b_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2. Stringovi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Miyazaki'"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cool_name = \"Miyazaki\"\n",
    "cool_name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Miyazaki is great'"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cool_name + \" is \" + \"great\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_people = 200000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can only concatenate str (not \"int\") to str",
     "output_type": "error",
     "traceback": [
      "\u001B[1;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[1;31mTypeError\u001B[0m                                 Traceback (most recent call last)",
      "\u001B[1;32m<ipython-input-32-e40dee72ca0e>\u001B[0m in \u001B[0;36m<module>\u001B[1;34m\u001B[0m\n\u001B[1;32m----> 1\u001B[1;33m \u001B[0mcool_name\u001B[0m \u001B[1;33m+\u001B[0m \u001B[1;34m\" has \"\u001B[0m \u001B[1;33m+\u001B[0m \u001B[0mnum_people\u001B[0m \u001B[1;33m+\u001B[0m \u001B[1;34m\" citizens\"\u001B[0m\u001B[1;33m\u001B[0m\u001B[1;33m\u001B[0m\u001B[0m\n\u001B[0m",
      "\u001B[1;31mTypeError\u001B[0m: can only concatenate str (not \"int\") to str"
     ]
    }
   ],
   "source": [
    "cool_name + \" has \" + num_people + \" citizens\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Miyazaki has 200000 citizens'"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cool_name + \" has \" + str(num_people) + \" citizens\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(cool_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Miyazaki has 200000 citizens\n"
     ]
    }
   ],
   "source": [
    "print(\"{0} has {1} citizens\".format(cool_name, num_people))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Miyazaki has 200000 citizens\n"
     ]
    }
   ],
   "source": [
    "print(f\"{cool_name} has {num_people} citizens\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3. Razredi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Product:\n",
    "\n",
    "    def __init__(self, product_name=None, tags=None, price=0.0):\n",
    "        self.product_name = product_name\n",
    "        self.tags = [] if tags is None else tags\n",
    "        self.price = price\n",
    "        \n",
    "    vat = 0.25 \n",
    "\n",
    "    def product_price(self, with_pdv=False):\n",
    "        if with_pdv:\n",
    "            return self.price * (1 + self.vat)\n",
    "        else:\n",
    "            return self.price\n",
    "    \n",
    "    def contains_tag(self, tag):\n",
    "        return (tag in self.tags)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.5\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "prod = Product(product_name=\"toilet paper\", tags=[\"health\", \"toilet\", \"fresh\"], price=10)\n",
    "print(prod.product_price(with_pdv=True))\n",
    "print(prod.product_price(with_pdv=False))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod.contains_tag(\"fresh\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod.contains_tag(\"money\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "prod1 = Product(product_name=\"toilet paper\", price=10)\n",
    "prod2 = Product(product_name=\"toothbrush\", price=10)\n",
    "Product.vat = 0.5\n",
    "prod1.vat = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod1.product_price(with_pdv=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prod2.product_price(with_pdv=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1. Polja"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1, 2, 3])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([1, 2, 3], dtype=np.float64)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 4],\n",
       "       [2, 3, 5]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[1, 3, 4], [2, 3, 5]])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0:1, 2] # Primijetite razliku!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6, 1])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(d, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6, 1, 2])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(d, [1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_add = np.array([[1], [2]])\n",
    "to_add"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d + to_add"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 1],\n",
       "       [4, 5, 6, 2]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack([d, to_add])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "all the input array dimensions for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 3 and the array at index 1 has size 1",
     "output_type": "error",
     "traceback": [
      "\u001B[1;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[1;31mValueError\u001B[0m                                Traceback (most recent call last)",
      "\u001B[1;32m<ipython-input-60-d1a30321b432>\u001B[0m in \u001B[0;36m<module>\u001B[1;34m\u001B[0m\n\u001B[1;32m----> 1\u001B[1;33m \u001B[0mnp\u001B[0m\u001B[1;33m.\u001B[0m\u001B[0mvstack\u001B[0m\u001B[1;33m(\u001B[0m\u001B[1;33m[\u001B[0m\u001B[0md\u001B[0m\u001B[1;33m,\u001B[0m \u001B[0mto_add\u001B[0m\u001B[1;33m]\u001B[0m\u001B[1;33m)\u001B[0m\u001B[1;33m\u001B[0m\u001B[1;33m\u001B[0m\u001B[0m\n\u001B[0m",
      "\u001B[1;32m<__array_function__ internals>\u001B[0m in \u001B[0;36mvstack\u001B[1;34m(*args, **kwargs)\u001B[0m\n",
      "\u001B[1;32m~\\anaconda3\\lib\\site-packages\\numpy\\core\\shape_base.py\u001B[0m in \u001B[0;36mvstack\u001B[1;34m(tup)\u001B[0m\n\u001B[0;32m    281\u001B[0m     \u001B[1;32mif\u001B[0m \u001B[1;32mnot\u001B[0m \u001B[0misinstance\u001B[0m\u001B[1;33m(\u001B[0m\u001B[0marrs\u001B[0m\u001B[1;33m,\u001B[0m \u001B[0mlist\u001B[0m\u001B[1;33m)\u001B[0m\u001B[1;33m:\u001B[0m\u001B[1;33m\u001B[0m\u001B[1;33m\u001B[0m\u001B[0m\n\u001B[0;32m    282\u001B[0m         \u001B[0marrs\u001B[0m \u001B[1;33m=\u001B[0m \u001B[1;33m[\u001B[0m\u001B[0marrs\u001B[0m\u001B[1;33m]\u001B[0m\u001B[1;33m\u001B[0m\u001B[1;33m\u001B[0m\u001B[0m\n\u001B[1;32m--> 283\u001B[1;33m     \u001B[1;32mreturn\u001B[0m \u001B[0m_nx\u001B[0m\u001B[1;33m.\u001B[0m\u001B[0mconcatenate\u001B[0m\u001B[1;33m(\u001B[0m\u001B[0marrs\u001B[0m\u001B[1;33m,\u001B[0m \u001B[1;36m0\u001B[0m\u001B[1;33m)\u001B[0m\u001B[1;33m\u001B[0m\u001B[1;33m\u001B[0m\u001B[0m\n\u001B[0m\u001B[0;32m    284\u001B[0m \u001B[1;33m\u001B[0m\u001B[0m\n\u001B[0;32m    285\u001B[0m \u001B[1;33m\u001B[0m\u001B[0m\n",
      "\u001B[1;32m<__array_function__ internals>\u001B[0m in \u001B[0;36mconcatenate\u001B[1;34m(*args, **kwargs)\u001B[0m\n",
      "\u001B[1;31mValueError\u001B[0m: all the input array dimensions for the concatenation axis must match exactly, but along dimension 1, the array at index 0 has size 3 and the array at index 1 has size 1"
     ]
    }
   ],
   "source": [
    "np.vstack([d, to_add])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_add2 = np.array([2, 3, 4])\n",
    "to_add2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [2, 3, 4]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = np.vstack([d, to_add2])\n",
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 1.41421356, 1.73205081],\n",
       "       [2.        , 2.23606798, 2.44948974],\n",
       "       [1.41421356, 1.73205081, 2.        ]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12],\n",
       "       [ 4,  6,  8]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12],\n",
       "       [ 4,  6,  8]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result + result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n",
      "[[5 6]\n",
      " [7 8]]\n",
      "[1 2]\n",
      "[5 3]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "y = np.array([[5,6],[7,8]])\n",
    "v = np.array([1,2])\n",
    "w = np.array([5,3])\n",
    "print(x)\n",
    "print(y)\n",
    "print(v)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(v, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5, 11])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2. ,  1. ],\n",
       "       [ 1.5, -0.5]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.0000000000000004"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.det(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.477225575051661"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(x, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(x, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.array([2, 3, 1, 6, 4, 5])\n",
    "b = [\"a\", \"b\", \"c\", \"d\", \"e\", \"f\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'d'"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[np.argmax(p)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9166666666666665"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  1.09090909,  1.18181818,  1.27272727,  1.36363636,\n",
       "        1.45454545,  1.54545455,  1.63636364,  1.72727273,  1.81818182,\n",
       "        1.90909091,  2.        ,  2.09090909,  2.18181818,  2.27272727,\n",
       "        2.36363636,  2.45454545,  2.54545455,  2.63636364,  2.72727273,\n",
       "        2.81818182,  2.90909091,  3.        ,  3.09090909,  3.18181818,\n",
       "        3.27272727,  3.36363636,  3.45454545,  3.54545455,  3.63636364,\n",
       "        3.72727273,  3.81818182,  3.90909091,  4.        ,  4.09090909,\n",
       "        4.18181818,  4.27272727,  4.36363636,  4.45454545,  4.54545455,\n",
       "        4.63636364,  4.72727273,  4.81818182,  4.90909091,  5.        ,\n",
       "        5.09090909,  5.18181818,  5.27272727,  5.36363636,  5.45454545,\n",
       "        5.54545455,  5.63636364,  5.72727273,  5.81818182,  5.90909091,\n",
       "        6.        ,  6.09090909,  6.18181818,  6.27272727,  6.36363636,\n",
       "        6.45454545,  6.54545455,  6.63636364,  6.72727273,  6.81818182,\n",
       "        6.90909091,  7.        ,  7.09090909,  7.18181818,  7.27272727,\n",
       "        7.36363636,  7.45454545,  7.54545455,  7.63636364,  7.72727273,\n",
       "        7.81818182,  7.90909091,  8.        ,  8.09090909,  8.18181818,\n",
       "        8.27272727,  8.36363636,  8.45454545,  8.54545455,  8.63636364,\n",
       "        8.72727273,  8.81818182,  8.90909091,  9.        ,  9.09090909,\n",
       "        9.18181818,  9.27272727,  9.36363636,  9.45454545,  9.54545455,\n",
       "        9.63636364,  9.72727273,  9.81818182,  9.90909091, 10.        ])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(1, 10, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.array([[1, 2, 3], [4, 5, 6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False,  True],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w > 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 5, 6])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w[w>2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
    "y = np.array([0, 0, 0, 1, 0, 0, 1, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 7])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w[y==1] # Jako korisno!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 1, 6, 4, 5]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 1, 6, 4, 5]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.tolist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20cc2eca220>]"
      ]
     },
     "execution_count": 92,
     "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.plot([1,2,3,4,5], [4,5,5,7,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20cc2f70e20>]"
      ]
     },
     "execution_count": 93,
     "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.plot(np.array([1,2,3,4,5]), np.array([4,5,5,7,3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20cc2fd7880>]"
      ]
     },
     "execution_count": 94,
     "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.plot([4,5,5,7,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "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.plot([4,5,5,7,3], 'x');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x): return x**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.        ,   2.04081633,   4.08163265,   6.12244898,\n",
       "         8.16326531,  10.20408163,  12.24489796,  14.28571429,\n",
       "        16.32653061,  18.36734694,  20.40816327,  22.44897959,\n",
       "        24.48979592,  26.53061224,  28.57142857,  30.6122449 ,\n",
       "        32.65306122,  34.69387755,  36.73469388,  38.7755102 ,\n",
       "        40.81632653,  42.85714286,  44.89795918,  46.93877551,\n",
       "        48.97959184,  51.02040816,  53.06122449,  55.10204082,\n",
       "        57.14285714,  59.18367347,  61.2244898 ,  63.26530612,\n",
       "        65.30612245,  67.34693878,  69.3877551 ,  71.42857143,\n",
       "        73.46938776,  75.51020408,  77.55102041,  79.59183673,\n",
       "        81.63265306,  83.67346939,  85.71428571,  87.75510204,\n",
       "        89.79591837,  91.83673469,  93.87755102,  95.91836735,\n",
       "        97.95918367, 100.        ])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = linspace(0,100); xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00000000e+00, 4.16493128e+00, 1.66597251e+01, 3.74843815e+01,\n",
       "       6.66389005e+01, 1.04123282e+02, 1.49937526e+02, 2.04081633e+02,\n",
       "       2.66555602e+02, 3.37359434e+02, 4.16493128e+02, 5.03956685e+02,\n",
       "       5.99750104e+02, 7.03873386e+02, 8.16326531e+02, 9.37109538e+02,\n",
       "       1.06622241e+03, 1.20366514e+03, 1.34943773e+03, 1.50354019e+03,\n",
       "       1.66597251e+03, 1.83673469e+03, 2.01582674e+03, 2.20324865e+03,\n",
       "       2.39900042e+03, 2.60308205e+03, 2.81549354e+03, 3.03623490e+03,\n",
       "       3.26530612e+03, 3.50270721e+03, 3.74843815e+03, 4.00249896e+03,\n",
       "       4.26488963e+03, 4.53561016e+03, 4.81466056e+03, 5.10204082e+03,\n",
       "       5.39775094e+03, 5.70179092e+03, 6.01416077e+03, 6.33486047e+03,\n",
       "       6.66389005e+03, 7.00124948e+03, 7.34693878e+03, 7.70095793e+03,\n",
       "       8.06330696e+03, 8.43398584e+03, 8.81299459e+03, 9.20033319e+03,\n",
       "       9.59600167e+03, 1.00000000e+04])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20cc309b4f0>]"
      ]
     },
     "execution_count": 99,
     "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.plot(xs, f(xs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "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.plot(xs, f(xs), 'r+');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "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.plot(xs, 1 - f(xs), 'b', xs, f(xs)/2 - 1000, 'r--');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "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.plot(xs, f(xs), label='f(x)')\n",
    "plt.plot(xs, 1 - f(xs), label='1-f(x)')\n",
    "plt.legend(loc=\"center right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "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.plot(xs, f(xs), label='f(x)')\n",
    "plt.plot(xs, 1 - f(xs), label='1-f(x)')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "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.plot(xs, f(xs), label='f(x)')\n",
    "plt.plot(xs, 1 - f(xs), label='1-f(x)')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlim([20, 80])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "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.plot(xs, f(xs), label=r'$\\lambda^{3}$')\n",
    "plt.plot(xs, 1 - f(xs), label=r'$\\mathcal{N}$')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.xlim([20, 80])\n",
    "plt.xlabel(\"hello\")\n",
    "plt.title(\"woohoo\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iQefOtuhv5Mg9l40caSuQzz8/XFwuMt27w8KF8NVXoSOJHZ404tA770DRotChQ+hI3MGUK2fJ4a23rItqxw4bizr/fFuf4WJb167WDTx2bOhIYocnjTj0zjtw+uk+6yZenHuulQlZutQWjP36qyf8eFGlik25nTw5dCSxw5NGnPnhB2sqn3de6EhcpNq1s59Tp9rq/ZQUG49y8aFdO5g50wpLOk8acWfXgOqpp4aNw0Wudm1b6PfhhzBjBjRubGMaLj60aWPdijNmhI4kNnjSiDMzZtiObieeGDoSlxennGJdU7Nmwcknh47G5cWu/7V588LGESs8acSZ2bOhSRObkePix0kn2Yy3tWsh7aCFGlwsqVgRatWCuXNDRxIbPGnEmW++sUVjLr402msj4+OPDxeHy58TT/SWxi6eNOLI1q22R0O9eqEjcXlVq1bOv7v4cMwxtkhz587QkYTnSSOOfP+9zfWvUyd0JC6v9i4XUq1auDhc/tSqZXXEcio+mWw8acSRdevsp8+8iT9ly+75vUiRcHG4/Dn8cPvp024DJw0RaS8iS0UkQ0RuzeF6EZHB2dcvEJGTQsQZKzZssJ97fwC5+PHGGzBxYugoXH7s+p/buDFsHLGgaKgHFpEiwDPA2dh+4bNEZIKqfr3XYecB9bNPLYAh2T+T0q43rCeN+HTxxaEjcPnlSWOPkC2N5kCGqn6nqtuA14FO+xzTCXhVzQzgcBFJ2h7hSpNH8TOpHL55dehQnEsqldcu5WdSKTXVm4ohk0Z1YNVe5zOzL8vrMQCISG8RSReR9DVr1hRooLGiShVI5RcqFdsQOhTnkkrVUutJ5RcqH+HDwCH/ApLDZftuWB7JMXah6lBVTVPVtNTU1EMOLhYd08zayOVTvI3sXGGqXHITAPVO9L7hkEkjE9h737IawL79LpEckzwOO8x+btoUNg7nks2uwYxd/4NJLGTSmAXUF5HaIlIc6A5M2OeYCcCV2bOoTgHWq2ry7tjro3HOhbHri5rPQgk3e0pVs0SkL/ABUAQYrqpfiUif7OufA94DOgAZwGbg6lDxxoRdG2j8739h43Au2exaJFWuXNg4YkCwpAGgqu9hiWHvy57b63cFrivsuGJWzZogAitWhI7EueSyapWVl07Q8dK88KkA8aRECaheHb77LnQkziWXb7+1WiIp/pHpf4F4U6cOZGSEjsK55LJwoZcnzuZJI94cfzwsWODlNp0rLL//bnsSeNIAPGnEn7Q0m8mxbFnoSJxLDl9/bV/SmjQJHUlM8KQRb3Zt+zZrVtg4nEsWX35pP32PZcCTRvxp2NCm/U2fHjoS55LDJ59AjRpQu3boSGKCJ414U7QonHkmTJ5sOzI556JH1ZLGGWfYdHfnSSMunXMOrFxpg3POueiZMwd++gnOPjt0JDHDk0Y8Ovdc+/nOO2HjcC7RTZhgazPOPz90JDHDk0Y8qlMHmjaFMWNCR+JcYhs/Hlq1gsqVQ0cSMzxpxKtu3WxWh5cUcS46Fi60NVFdu4aOJKZ40ohX3brZz1GjwsbhXKIaMcImnvToETqSmOJJI17Vrm0zOl54wVeHO1fQtm+HkSPhvPO8SOE+PGnEsz59YPlymDIldCTOJZZx42D1arjmmtCRxBxPGvHsoovsW9Czz4aOxLnEMniwTTjxWVP7CZI0RKSiiEwRkW+yf1bI5bgVIrJQROaJSHphxxnzSpSAv/wFJk6ExYtDR+NcYpg9G/7zH7j+eihSJHQ0MSdUS+NWYJqq1gemZZ/PTVtVbaqqaYUTWpy54QYoWRIefjh0JM4lhkcesb3Ar07ujUJzEyppdAJeyf79FaBzoDjiX2oq9O4N//63T7917lAtWgRjx9qXsV3bK7s/CJU0qqjqDwDZP4/I5TgFJovIbBHpfaA7FJHeIpIuIulr1qwp4HBjXL9+tmp14MDQkTgX3+67z1oZf/976EhiVtSShohMFZFFOZw65eFuTlXVk4DzgOtE5PTcDlTVoaqapqppqck2Ra5GDRvbGDYMliwJHY1z8WnBgj2tjEqVQkcTs6KWNFS1nao2zuH0NvCTiFQDyP75cy73sTr758/AOKB5tOKNe3feCaVLw223hY7EufijCv/3f1ChgrcyDiJU99QEoGf27z2Bt/c9QETKiEjZXb8D5wCLCi3CeHPEEXDLLVYr57PPQkfjXHyZOBGmToV77oGKFUNHE9NEA+zJICKVgDHAUcD3QFdV/VVEjgReVNUOIlIHa10AFAVeU9UHI7n/tLQ0TU9Pwhm6mzdD/fpQtSrMnOnTBZ2LxNat0LgxFCsG8+fbzyQkIrMjmaVatDCC2ZeqrgXOyuHy1UCH7N+/A04o5NDiW+nS8PjjVpfq2Wdtnrlz7sCeeAIyMuD995M2YeSFrwhPNF272n4bd9xhZRCcc7nLyLAuqU6d9uxT4w7Ik0aiEYFnnoFt2+DGG0NH41zsUrU1TsWL2/+Mi4gnjURUty7cfTe88QaMHh06Gudi07Bh8NFHMGgQVK8eOpq4EWQgPNqSdiB8b1lZ0Lq17SO+cCEceWToiJyLHd9/D02a2A6YH35oi2OTXKQD4f6XSlRFi8Irr8Dvv1t55wT8cuBcvuzYAZdfbj+HDfOEkUcH/WuJSN/cqtC6GNeggRUynDQJnn8+dDTOxYaBA2H6dJthWLdu6GjiTiQptiowS0TGiEh7EZFoB+UK0HXXwTnnwE03wbx5oaNxLqwZM2y2VI8e1tpweRbRmEZ2ojgHuBpIwxbmDVPVb6MbXv74mMY+1qyxvtvSpW2vgHLlQkfkXOH73/+gWTPbHnn+fK9iu48CHdNQyyw/Zp+ygArAGyLyyCFF6QpHaiq8/rptDXvttT6+4ZLPzp3WssjMtP8FTxj5FsmYxg0iMht4BPgPcLyq/hVoBlwc5fhcQTntNHjgARgzxueku+Rz333w3nvw5JNwyimho4lrkZQRqQx0UdWVe1+oqjtF5ILohOWion9/28by5put1k6bNqEjci763n0X7r0XevaEPn1CRxP3fJ1Gstmwwb5p/fQTzJoFdeqEjsi56PnmG2jeHGrXti9MpUqFjihm+ToNl7Ny5WDCBBvX6NgRNm4MHZFz0bF2LZx/vq1ZevNNTxgFxJNGMqpXz3YoW7IELrvMFjk5l0i2boUuXWDlSttjpnbt0BElDE8ayeqss6wk9MSJtmNZAnZTuiSlarMEP/0UXn4ZTj01dEQJJUjSEJGuIvKViOwUkVz70LIXEy4VkQwRubUwY0wK111ni/6efBL+9a/Q0ThXMB54AEaMsMHvHj1CR5NwQrU0FgFdgE9zO0BEigDPAOcBjYAeItKocMJLEiLw2GNw6aXQrx+MGhU6IucOzbBhcNddcMUVcOedoaNJSKF27lsMcJCKJM2BjOwd/BCR14FOwNdRDzCZpKRYYcOffrIpiVWqwJlnho7KubwbN872xzjnHHjxRftS5ApcLI9pVAdW7XU+M/uyHIlIbxFJF5H0NWvWRD24hFKypA0WNmgAnTvDnDmhI3Iubz76CLp3t+m1b71lGyu5qIha0hCRqSKyKIdTp0jvIofLch2tVdWhqpqmqmmpqan5CzqZHX64VcOtWNG+qX31VeiInItMerpNH69f3xbylSkTOqKEFrXuKVVtd4h3kQnU3Ot8DcA3vY6mGjVg6lQ4/XQ4+2ybfVKvXuionMvdkiVw3nlQqRJ88IF96XFRFcvdU7OA+iJSW0SKA92BCYFjSnz16lni2L7dpuV+/33oiJzL2Tff2PhbSgpMmeJbthaSUFNuLxKRTKAl8K6IfJB9+ZEi8h6AqmYBfYEPgMXAGFX1PpPC0KgRTJ4M69db4vjhh9AROfdHGRnQtq19uZk2zbqmXKHw2lMud198Yd1URx1l+yhXrRo6Iufgu+/gjDNsK+MPP7S9vt0h89pT7tC1bGnlpL//3irirvYhJRfYihXWwti82bpRPWEUOk8a7sBOPx3efx/++19LHJmZoSNyyWrlSksYGzbYGEbTpqEjSkqeNNzBtW5tYxw//mjdAj447gpbRoa999atsxbGSSeFjihpedJwkWnZ0r7drV1r/7wrVoSOyCWLr7+2Fu+mTZYwmjULHVFS86ThIteihf3Trltn/8TLloWOyCW6OXPsvQbwySeeMGKAJw2XN2lpNmNlyxbrtpo7N3RELlF9/rmNYZQpYwtNjzsudEQOTxouP048ET77zGpWtWljvztXkKZNs+neVarY+8srE8QMTxouf445xvZcrlbNalVNmhQ6Ipco3nnHtmmtU8daGDVrHvw2rtB40nD5V7Om/VM3bGgF40aPDh2Ri3cvvWSVlo8/Hj7+2BeUxiBPGu7QHHGElaVu1cp2SXv++dARuXikCgMGQK9eVrrmo4+sCKGLOZ403KErX94WAHboAH36wD33+J7jLnI7dsANN8Add8Bll9m+9YcdFjoqlwtPGq5glCplO6ddfbXtzXzttZCVFToqF+u2brUW6tNPw//9H7z6qm+gFOOCbPfqElSxYrZHc40acP/9Vh13zBjfFMflbP16uOgi64p69FFLGi7meUvDFSwRuO8+G9t4/32bZ//zz6GjcrHmhx+sssD06fDvf3vCiCOeNFx09O5t3VWLFtkgeUZG6IhcrFi8eM974t13bRzDxY1QmzB1FZGvRGSniORav11EVojIQhGZJyK+QUa86djRVo+vW2cfErNmhY7IhTZtmtUx+/13m1J7zjmhI3J5FKqlsQjoAnwawbFtVbVpJJuDuBh0yilWDuKww2z1+MSJoSNyobz4IrRvb+t7vvzSStK4uBMkaajqYlVdGuKxXQDHHGOJo1Ej6NQJBg8OHZErTDt3wi232Iy6du2skkCtWqGjcvkU62MaCkwWkdki0vtAB4pIbxFJF5H0NWvWFFJ4LmJVq1p3ROfOcOONcP31PiU3GWzeDF27wiOPwF//ai3NcuVCR+UOQdSShohMFZFFOZw65eFuTlXVk4DzgOtE5PTcDlTVoaqapqppqamphxy/i4IyZWDsWJsp8/TT1urYuDF0VC5afvzRuiTHjYPHH4dnnoGiPss/3kXtFVTVdgVwH6uzf/4sIuOA5kQ2DuJiVZEiNie/Xj3o2xdOO80K1NWoEToyV5AWLoQLLrBNu95+Gy68MHREroDEbPeUiJQRkbK7fgfOwQbQXSLo08emW373nW3uNGdO6IhcQXn/fTj1VOt+nD7dE0aCCTXl9iIRyQRaAu+KyAfZlx8pIu9lH1YF+ExE5gMzgXdV9f0Q8booOfdcGxQtUsR2Z/OZVfHv2WetrHndujZD6sQTQ0fkCphoAhaWS0tL0/R0X9YRN374wb6Nzp1rfd833BA6IpdXO3ZAv37wxBP2Wr72mhcdjDMiMjuSpQ0x2z3lkki1arb/c8eOPrMqHm3aZDWknngCbrrJBr49YSQsTxouNpQpA2+84TOr4k1mpk1mePddmx31+OPW3egSlicNFzt2zawaMgQ++ABat4ZVq0JH5XIzd65NYvj2W0saf/tb6IhcIfCk4WLPrplVK1ZA8+bg41OxZ8IES+pFi9pkhvbtQ0fkCoknDRebds2sKlHCZlaNHx86Ige2I+Pjj9vK/kaNbIbU8ceHjsoVIk8aLnY1bmwfSk2aQJcu1nWVgLP94kZWFlx3Hfz97zbw/cknVh7GJRVPGi62ValiO7tdcgn84x/WdbV9e+ioks+GDbbCe8gQ6N/fysGULh06KheAF4Jxsa9UKXj9dSs9MnCgrSIfOxYOPzx0ZMlh5UpLGEuWwNChVq3WJS1vabj4kJICAwbA8OFWLffUU2H58tBRJb6ZM22G1KpVMGmSJwznScPFmauvhsmTYfVq+zD74ovQESWuN9+0fbxLl7a/c7tDrkHqEoAnDRd/2raFGTNsX4a2bWH06NARJRZVGDTIxpGaNrW/9bHHho7KxQhPGi4+NWhgH2ZpadC9Ozz4oM+sKgjbt9tkg/794dJLbY/3I44IHZWLIZ40XPyqXBmmTYPLLoN//tO6rrZtCx1V/Fq/3irUDh0Kt98Oo0bZJATn9uKzp1x8K1ECRoyA+vXhnntsFflbb0HFiqEjiy8rV1rCWLoUhg2DXr1CR+RilLc0XK/N7lIAABXuSURBVPwTgbvvhn//2wZsTzkFvvkmdFTxY9Ysm1SQmWkbKHnCcAcQahOmQSKyREQWiMg4Eclxwr2ItBeRpSKSISK3FnacLs5cdpl1V/36qyWO6dNDRxT7xo2zGVKlSlnCPeus0BG5GBeqpTEFaKyqTYBlwG37HiAiRYBngPOARkAPEWlUqFG6+NO6tZUeSU21D8ARI0JHFJtU4bHH4OKL4YQT7G/mM6RcBIIkDVWdrKq7dtmZAdTI4bDmQIaqfqeq24DXgU6FFaOLY3Xr2rfm1q3hyivhrrt8ZtXeduywGlL9+tm0Wp8h5fIgFsY0egGTcri8OrD3ZgqZ2ZflSER6i0i6iKSvWbOmgEN0cadCBeufv/pquP9+67rasiV0VOFt3mytiyFD4JZbrDyLz5ByeRC12VMiMhXIqQTmHar6dvYxdwBZwMic7iKHy3L9uqiqQ4GhYHuE5zlgl3iKF7eZQMccA7fdZqvI334bypcPHVkYa9fa/t0zZsBTT0HfvqEjcnEoaklDVQ9Yc0BEegIXAGep5th3kAnU3Ot8DWB1wUXokoII3HorHHUUXHWV7c0xaRIceWToyArXypW2UdLy5Vbs8eKLQ0fk4lSo2VPtgVuAjqq6OZfDZgH1RaS2iBQHugMTCitGl2D+9CfbDfC776BVK1i2LHREhWfePGjZEn78EaZM8YThDkmoMY2ngbLAFBGZJyLPAYjIkSLyHkD2QHlf4ANgMTBGVb8KFK9LBGefbRVyN2+2KrkzZ4aOKPo+/NBaV0WKwGefwWmnhY7IxTnJuWcovqWlpWm67yvtcpORYdvJ/vijVXJN1P2tx4yByy+3Ol2TJkGNnCYpOmdEZLaqph3suFiYPeVc4apXz/YfP+YYGxhOxLUcL7xghRx3LXL0hOEKiCcNl5yqVrU9rk8/3dZyPPNM6IgKzmOPQe/e1oJ6/33f4dAVKE8aLnmVKwfvvQedOtn000GDQkd0aFRtIWO/ftC1K4wf7/t4uwLnScMltxIlbApq9+62h8Tdd8fn6vGdO+Gmm2wh45//bGXNixcPHZVLQF4a3blixaxCbqlScN998Ntv1uqQnNaXxqAdO6w7avhw+Pvf4dFH4yd2F3c8aTgHNiX1xRehTBkbE9i8GZ5+GlJivDG+Ywdccw28/LK1ku6+u9ATxvbt28nMzGSLl2mJCyVLlqRGjRoUK1YsX7f3pOHcLikpMHiwjQM88ghkZcFzz8Vu4tg7Ydx7r41nBJCZmUnZsmU5+uijEW/hxDRVZe3atWRmZlK7du183YcnDef2JgIPPQRFi8KAATYu8NRTsdfdEyMJA2DLli2eMOKEiFCpUiUOpairJw3n9iUCDzwAW7daV1Xx4vYzVj4U904Y99wTNGHs4gkjfhzqa+VJw7mciNhg+LZt8PjjNstqwIDwiUPV9sLYlTDuvjtsPC7pxGhnrXMxQASefBL+8hfrsrrvvtARwR13wPPP214YnjAAWLFiBY0bN87Tbdq0acOuUkMdOnRg3bp10QgNgHvuuYdHH300X7e95ppr+Prrrws4okPjLQ3nDkQEnn3Wuqruuce2kf3b38LE8uijMHCgTa8dODBMDAnovffeCx1Crl588cXQIezHk4ZzB5OSYrWc1q61leNVq0KXLoUbw7Bh8I9/wKWXWhIL3U2Wi5tuskrsBalpU3jiiQMfk5WVRc+ePZk7dy7HHHMMr776KqVLl2batGn069ePrKwsTj75ZIYMGUKJEiX+cNujjz6a9PR0KleuTOfOnVm1ahVbtmzhxhtvpHfv3vs91tFHH023bt346KOPAHjttdeoV68eK1eupFevXqxZs4bU1FReeukljjrqqD/cdt68efTp04fNmzdTt25dhg8fzo8//kjPnj2ZmV11ecWKFXTs2JEFCxbQpk0bHn30UdLS0nj//fe5/fbb2bFjB5UrV2batGnMnDmTm266id9//51SpUrx0ksv0aBBg0P4ax+cd085F4miRW1r1FNOsb05Pv208B773Xf31JIaMcLWlLg/WLp0Kb1792bBggWUK1eOZ599li1btnDVVVcxevRoFi5cSFZWFkOGDDng/QwfPpzZs2eTnp7O4MGDWbt2bY7HlStXjpkzZ9K3b19uuukmAPr27cuVV17JggULuOyyy7jhhhv2u92VV17Jww8/zIIFCzj++OO59957OfbYY9m2bRvfffcdAKNHj+bSSy/9w+3WrFnDtddey5tvvsn8+fMZO3YsAA0bNuTTTz9l7ty53Hfffdx+++15/tvlmaom3KlZs2bqXFT88otqw4aq5curLloU/cebN0/1sMNUmzVT3bQp+o+XD19//XXQx1++fLnWrFlz9/lp06Zpp06ddN68eXraaaftvnzq1Kl60UUXqarqGWecobNmzVJV1Vq1aumaNWtUVfXuu+/WJk2aaJMmTbRcuXL6xRdf7Pd4tWrV0m+//VZVVbdt26YVK1ZUVdVKlSrptm3bdl9eqVKl3fc5aNAgXbdu3R/izMjI0BNPPFFVVR988EEdOHCgqqqeeOKJumzZsj/EOWHCBP3Tn/60Xyzff/+9du7cWY877jht3LixNmjQIKK/WU6vGZCuEXy+htq5b5CILBGRBSIyTkRyLMMpIitEZGH2Rk2+QYYLr1Il+OADWwB44YXWZRUtq1fDBRdYldoJE2y1usvRvtNIRQTNYw2xjz/+mKlTp/LFF18wf/58TjzxxFxXue/9eLlNYc3L1NZu3boxZswYli1bhohQv379P1yvqjne35133knbtm1ZtGgREydOLJRV+aG6p6YAjVW1CbAMuO0Ax7ZV1aYaweYgzhWKo46CcePsQ71rV9i+veAf47ffLCmtWwfvvJN8e5rn0ffff88XX3wBwKhRo2jdujUNGzZkxYoVZGRkADBixAjOOOOMXO9j/fr1VKhQgdKlS7NkyRJmzJiR67GjR4/e/bNly5YAtGrVitdffx2AkSNH0rp16z/cpnz58lSoUIHp06fvF0/dunUpUqQI999/P926ddvv8Vq2bMknn3zC8uXLAfj11193x1y9enUAXn755QP8hQpOkIFwVZ2819kZwCUh4nAu31q0sMHxK6+Em2+2OlUFRdWm+c6dCxMnwgknFNx9J6hjjz2WV155hb/85S/Ur1+fv/71r5QsWZKXXnqJrl277h4I79OnT463FxHat2/Pc889R5MmTWjQoAGnnHJKro+3detWWrRowc6dOxk1ahQAgwcPplevXgwaNGj3QPi+Xnnlld0D4XXq1PnDMd26deMf//jH7sSwt9TUVIYOHUqXLl3YuXMnRxxxBFOmTKF///707NmTf/3rX5x55pl5/bPlTyR9WNE8AROBy3O5bjkwB5gN9I70Pn1MwxWafv1UQfWFFwruPp95xu7z/vsL7j6jKPSYxqHIysrSihUr7h6LiMTeYyDx6lDGNKLW0hCRqUDVHK66Q1Xfzj7mDiALGJnL3ZyqqqtF5AhgiogsUdUcp62ISG+gN7DfNDfnouahh2D+fLj+eptZlcdFZvuZMcPmrZ5/PhTGTJgkd9xxx3HNNdfku+JrMhINtOGMiPQE+gBnqermCI6/B9ikqgddWpmWlqa7Vns6F3U//WRdSJUqwaxZ+d8tb906aNLEptTOmQMVKhRsnFGyePFijj322NBhuDzI6TUTkdkawdhxqNlT7YFbgI65JQwRKSMiZXf9DpwDLCq8KJ2LUJUqtonT4sWQw9z8iPXta4PrY8bETcJwySfU7KmngbJYl9M8EXkOQESOFJFda/qrAJ+JyHxgJvCuqr4fJlznDqJdO7j1Vlu5/e67eb/96NEwcqRVrD355IKPz7kCEqx7Kpq8e8oFsW0bNGsG//sffPUVlC8f2e1+/BEaNYL69eE//7HV53HEu6fiT9x1TzmXkIoXt326f/jB6kRF6v/+z9ZlvPpq3CUMl3w8aThXkE4+Gf7+d1vD8eWXBz/+ww/htdesayvKheaSRSSlyPcujR7CoTx+q1atCjiavPGk4VxBu+suq4R78822UC8327fbhkp161rScDElKysrdAg5+vzzz4M+vreFnStoZcvadrHXXGMD3N2753zcK6/AkiUwfjyUKlW4MUZLoNroDz74IK+++io1a9YkNTWVZs2aATmXIq+QPTPt3//+NzfccAMbNmxg+PDhNG/enHvuuYfVq1ezYsUKKleuzIABA7jiiiv47bffAHj66af3+6a/YsUK2rdvT4sWLfJVmn3UqFEMGDAAVeX888/n4YcfZsiQISxfvpxHHnkEsBIhs2fP5qmnnuKwww5j06ZNADzyyCOMGDGClJQUzjvvPB566CFeeOEFhg4dyrZt26hXrx4jRoygdH6ngefAWxrORcNVV9mH3e23Q07fWLdsgXvvtQWBHTsWeniJZPbs2bz++uvMnTuXt956i1mzZu2+LqdS5Lv89ttvfP755zz77LP06tXrD/f39ttv89prr+0u1zFnzhxGjx6dY7lzyH9p9tWrV3PLLbfw4YcfMm/ePGbNmsX48eO55JJLeOutt3YfN3r06P1qUk2aNInx48fz5ZdfMn/+fPr37w9Aly5dmDVrFvPnz+fYY49l2LBh+f/j5sBbGs5FQ5EittNf587W2rjssj9eP3QoZGba4HeMbqiULwfbLSkKpk+fzkUXXbT723TH7CS8fv161q1bt7soYM+ePenatevu2/Xo0QOA008/nQ0bNuze8rVjx46Uym75bd++nb59+zJv3jyKFCnCsmXLcoyhZs2anHrqqQBcfvnlDB48mLPPPpvatWtzzDHH7H78Z555Zvf+GwCzZs2iTZs2pKamAnDZZZfx6aef0rlzZ+rUqcOMGTOoX78+S5cu3X3/u0ydOpWrr7569/OuWLEiAIsWLeKf//wn69atY9OmTZx77rn5+rvmxpOGc9Fy4YVw3HG2NWuPHrYDIMCOHfD449C6NbRtGzbGBJGXMuS53WbX+TJ7laB//PHHqVKlCvPnz2fnzp2ULFky4vuKZDnDgY7ZVS69YcOGXHTRRfs9huZSLv2qq65i/PjxnHDCCbz88st8/PHHB40jL7x7yrloSUmBW26xNRvTpu25fMIEWLHCBsrdITv99NMZN24cv//+Oxs3bmTixInAgUuRw57y5p999hnly5enfA7ratavX0+1atVISUlhxIgR7NixI8cY8luavUWLFnzyySf88ssv7Nixg1GjRu0+pkuXLowfP55Ro0blWC79nHPOYfjw4WzebEU1dpVL37hxI9WqVWP79u2MHJlbWb/885aGc9HUtauVFnnpJTj7bLvsuedsTw4fyygQJ510Et26daNp06bUqlWL0047bfd1BypFXqFCBVq1arV7IDwnf/vb37j44osZO3Ysbdu2/UMrZG/5Lc1erVo1Bg4cSNu2bVFVOnToQKdOnXbH16hRI77++muaN2++32O2b9+eefPmkZaWRvHixenQoQMDBgzg/vvvp0WLFtSqVYvjjz+ejRs35vlveiC+Ity5aOvb18qL/PADbN1qGyrddpvNsEoAyb4ifMWKFVxwwQUsWhQ/pfF8RbhzsaxnT5stNWECjB0LO3faGIdzcci7p5yLtmbNbLHfpEmwYQMcc4wNkLuEcPTRR8dVK+NQedJwLtpSUqB9e3jzTWtlXHll6IgKXG4zeVzsOdQhCe+ecq4wnHoqbNxohQnbtAkdTYEqWbIka9euPeQPIxd9qsratWtznTocCW9pOFcY9t4j44QTwsURBTVq1CAzM5M1a9aEDsVFoGTJktSoUSPft/ek4Vxh2LuCbZ064eKIgmLFilG7du3QYbhCEmq71/tFZEH2rn2TReTIXI5rLyJLRSRDRLwMqItfJUvaFq7Vq0OxYqGjcS7fQo1pDFLVJqraFHgHuGvfA0SkCPAMcB7QCOghIo0KN0znCtDChbBXMT3n4lGQ7ilV3bDX2TJATiNozYEMVf0OQEReBzoBX0c/QueioHr10BE4d8iCjWmIyIPAlcB6IKeqbdWBVXudzwRaHOD+egO9s89uFZFEnThdGfgldBBR5M8vvvnzi18RbR0ZtaQhIlOBqjlcdYeqvq2qdwB3iMhtQF/g7n3vIofb5jqnT1WHAkOzHzs9kuXw8SiRnxv484t3/vzil4hEVHspaklDVdtFeOhrwLvsnzQygZp7na8BrC6A0JxzzuVTqNlT9fc62xFYksNhs4D6IlJbRIoD3YEJhRGfc865nIUa03hIRBoAO4GVQB+A7Km3L6pqB1XNEpG+wAdAEWC4qn4V4f0PjUbQMSKRnxv484t3/vziV0TPLSFLozvnnIsOrz3lnHMuYp40nHPORSwhk0akZUrilYgMEpEl2c9xnIgcHjqmgiQiXUXkKxHZKSIJMb0x0UviiMhwEfk5EddHiUhNEflIRBZnvy9vDB1TQRKRkiIyU0TmZz+/ew94fCKOaYhIuV2rzkXkBqCRqvY5yM3ihoicA3yYPVngYQBVvSVwWAVGRI7FJkk8D/RT1bjeuze7JM4y4GxsKvksoIeqJkx1AxE5HdgEvKqqjUPHU5BEpBpQTVXniEhZYDbQOVFeP7GNUMqo6iYRKQZ8BtyoqjNyOj4hWxoRlimJW6o6WVWzss/OwNawJAxVXayqS0PHUYB2l8RR1W3ArpI4CUNVPwV+DR1HNKjqD6o6J/v3jcBirGJFQlCzKftssexTrp+ZCZk0wMqUiMgq4DJyKIiYQHoBk0IH4Q4op5I4CfOhk0xE5GjgRODLsJEULBEpIiLzgJ+BKaqa6/OL26QhIlNFZFEOp04AqnqHqtYERmJlSuLKwZ5f9jF3AFnYc4wrkTy/BJKnkjguNonIYcCbwE379GbEPVXdkV11vAbQXERy7WKM202YCqBMSUw72PMTkZ7ABcBZGocDU3l4/RKBl8SJc9l9/W8CI1X1rdDxRIuqrhORj4H2QI6TGuK2pXEgEZYpiVsi0h64BeioqptDx+MOykvixLHsgeJhwGJV/VfoeAqaiKTumoEpIqWAdhzgMzNRZ0+9iZX53V2mRFX/GzaqgiMiGUAJYG32RTMSbHbYRcBTQCqwDpinqueGjerQiEgH4An2lMR5MHBIBUpERgFtsNLhPwF3q+qwoEEVEBFpDUwHFmKfKQC3q+p74aIqOCLSBHgFe2+mAGNU9b5cj0/EpOGccy46ErJ7yjnnXHR40nDOORcxTxrOOeci5knDOedcxDxpOOeci5gnDeeccxHzpOGccy5injScizIROTl775OSIlIme8+ChCof7pKHL+5zrhCIyANASaAUkKmqAwOH5Fy+eNJwrhBk15yaBWwBWqnqjsAhOZcv3j3lXOGoCBwGlMVaHM7FJW9pOFcIRGQCtmNfbWzr0Ljb48U5iOP9NJyLFyJyJZClqq9l7xf+uYicqaofho7NubzyloZzzrmI+ZiGc865iHnScM45FzFPGs455yLmScM551zEPGk455yLmCcN55xzEfOk4ZxzLmL/D+H7+0d8Kg4XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_1(x):\n",
    "    return np.sqrt((1 - (np.abs(x) - 1)**2))\n",
    "def f_2(x):\n",
    "    return -3 * np.sqrt(1 - np.sqrt((np.abs(x)/2)))\n",
    "\n",
    "x = np.linspace(-2, 2, 1000)\n",
    "plt.plot(x, f_1(x), 'b-', label=\"bolja polovica\")\n",
    "plt.plot(x, f_2(x), 'r-', label=\"dobra polovica\")\n",
    "plt.xlim([-3, 3])\n",
    "plt.ylim([-3, 1.5])\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "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.scatter([0, 1, 2, 0], [4, 5, 2, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "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.scatter([0,1,2,0], [4, 5, 2, 1], s=200, marker='s');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "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": [
    "for c in 'rgb':\n",
    "    plt.scatter(np.random.random(100), np.random.random(100), s=200, alpha=0.5, marker='o', c=c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5GQs2LWDSykm8l/keP+7/kfiYeG7vdDs3n3sz3ZO71/q6cFOzLCAYU4uoKuk/pPPOynd4N/NdcgtziYmIYVDrQdzc4WYua3mZzS5qqswCgjEBTlVZtnUZk1dNZvKqyWTvzKZuWF2ubHUlv2z3SwacPYDT6p7mdTZNELCAYEwAqugm+l7me7yf+T7rd6wnTMLo17IfT/R8gsHnDA7p8QKmelhAMCZAqCpLtizhvVXv8f7q99mwYwNhEkafM/sw/OLhDD5nMPEx8V5n0wQxCwjGeKiiYfjD1R8y5bspbN69mfA64fQ9sy+PXfIYg1oPIi4mzutsmhBhAcGYGlZUWsTsDbOZ8t0Upq6ZSv6+fKLCo7i85eU8eemTXN36ahpFNzr+FxnjZxYQjKkB+fvy+WTtJ0xdM5WZ62eyt2QvDSIbMODsAfzinF/Q/6z+1jBsPGcBwZhqsrZgLR+v+Zhpa6exYNMCyrWcpPpJ3NrxVga1HkSvlF5Ehkd6nU1jDrKAYIyfHCg7wLzv5/HJ2k+Yvm46WT9mAXBuk3MPtgd0btbZBouZgGUBwZhTkLM7h8+zPmdG1gxmrp9J4YFCosKj6J3am/svuJ+rWl3FGQ3P8DqbxpwQCwjGnIQDZQf4atNXzMiawWdZn7Fi+woAkhskc1OHmxhw9gB6p/YmJiLG45wac/IsIBhzDKrK2oK1zFw/k1kbZjE3ey57Duwhok4El5xxCf/b73/pf1Z/2jVuZ1VBptazgGDMIfL35TN7w2xmbZjFzPUz2bx7MwAtY1sytMNQrmh1Bb1Te1uvIBN0LCCYkLe7eDfzv5/PnI1zmL1xNsu3LQegYVRDeqf25rFLHqNfy36cGXumxzk1pnpZQDAhZ8+BPXy9+Wu+zP6SOdlzWPzDYsq0jMiwSC5qcRF/u/Rv9DmzD2mJafZGMRNS7LfdBL3dxbv5atNXfPn9l3z5/Zdk5GZQWl5KmITRNakrwy8eTp/UPnRv3p2o8JN7B60xwcQCggk6W/dsZcGmBSzYtID5m+azbOsyyrWc8DrhdE3qyh8v/CM9z+jJhc0vpH5kfa+za0zAsIBgarVyLSczL5OFmxfydc7XLNi04OCAsOjwaLold+PRix+lZ0pPuid3p17deh7n2JjAZQHB1Co79u9g0Q+LWLh5IQtzFrLoh0XsLt4NQHxMPBe3uJhhXYZxcYuLOa/ZedQNq+txjo2pPSwgmIC1v2Q/y7YuY3HuYtJ/SCf9h3TW/bgOgDpShw4JHbip/U10b96d7sndOavRWTYWwJhTYAHBBISi0iJWbFvBki1LWJK7hCVblrBi+wpKy0sBSKyfSLekbtx+3u10TerK+YnnW/2/MX5mAcHUuN3Fu/l227cs27qMZVuXsWTLElZuX3nw5h8bFUuXxC482P1BuiV1o2tSV5IaJHmca2OCnwUEU23KtZyNOzayYvsKVmxbwbJty1i+dTnrd6w/eExcdBxdErvwUPeH6JLYhS7NupDSMMWqfozxgAUEc8pUlR8KfyAzL5PMvExWbFvBiu0rWJW3in0l+w4e16pRKzo368zt591OxyYd6dS0E4n1E+3mb0yAsIBgTlhJWQkbdmxgbcFaVuevZnX+ajLzMlmdt5rCA4UHj2sc05gOTTpwZ+c7aZ/Qng4JHWiX0M7m/jEmwFlAMD9TVl5Gzu4c1u9YT9aPWawtWMuagjWsLVjLhh0bDtbzAzQ9rSltG7fl1o630rZxW9o2bkub+DY0Oa2JhyUwxlSVBYQQtKtoFxt3biR7ZzYbd2xk486NrN+xnvU/rmfjzo0cKDtw8Nio8ChaNWpFh4QOXNfmOs6OO5vW8a1pHdea2OhYD0thjPE3CwhBpqSshNzCXDbv3szmXZvZtGuT297ttrN3ZrOzaOfPzqlftz4tG7WkfUJ7Bp8zmJaxLWnZqCUtY1vS/PTm1JE6HpXGGFOTLCDUEnsP7GXb3m1s27Pt4HrLni3kFubyQ+EP5BbmkluYy/a92w87t2FUQ5o3aE7z05tzUfOLSGmYQmrDVLeOTSU2KtYado0xgRMQRKQ/8AIQBryhqs94nKVqUa7l7C7ezY79O9hRtONn6/x9+W7Zn39wO29vHtv3bmdvyd7DvksQEuolkFg/keQGyXRN7Epi/UQS6yfS4vQWND+9Oc0bNLcBXMaYExIQAUFEwoBXgH5ADrBYRKapaqa/r3Wg7ADFpcWUazmKoqoHt8u1nJKyEkrLSykpL/nZdnFpMUWlRRSXuXXFsr9kP3tL9rL3wN6D632l+9hzYA+7i3f/bCksLmR38W4UPWr+YiJiiI+Jp3FMY+Jj4jmr0VkkxCTQ9LSmNDmtCU3qNTm4TqiXQERYhL//iYwxISogAgLQFchS1Q0AIvIOMAjwe0AY/c1oHv7Pw/7+WgAiwyKpV7ce9SLqUa9uPU6PPJ0GkQ1Iqp9Eg8gGB5fYqFhio2NpGNXw4HZsVCxxMXH2cnZjjGcCJSAkAZsrfc4Buh16kIjcBdwF0KJFiypdqFdKL57v9zwigiDUkTqI+NYIEWERhNcJJ6JOxM+2I8MjiQqPIio8isgwtx0ZHklMRAz1IuoRExFDWJ2wKuXJGGMCQaAEhCO1aB5Wr6KqY4GxAGlpaUevdzmGrkld6ZrUtSqnGmNMUAuU/oQ5QPNKn5OBXI/yYowxISlQAsJioJWIpIpIXWAIMM3jPBljTEgR1SrVvPidiFwJjMZ1Ox2nqk8d5/g84PsqXi4eyK/iubWVlTk0WJlDw6mU+QxVbXykHQETEGqSiGSoaprX+ahJVubQYGUODdVV5kCpMjLGGOMxCwjGGGOA0A0IY73OgAeszKHByhwaqqXMIdmGYIwx5nCh+oRgjDHmEBYQjDHGACEYEESkv4isEZEsERnudX6qg4g0F5G5IrJaRFaJyB986Y1EZJaIrPOtg+qVZyISJiJLRWS673Owl7ehiLwvIt/5ftbdQ6DM9/t+p1eKyCQRiQq2MovIOBHZLiIrK6UdtYwi8ojvfrZGRC4/lWuHVECoNM32FUBb4EYRaettrqpFKfCgqrYBLgB+5yvncGC2qrYCZvs+B5M/AKsrfQ728r4AfKaq5wAdcWUP2jKLSBJwL5Cmqu1xg1iHEHxl/ifQ/5C0I5bR9/96CNDOd86rvvtclYRUQKDSNNuqegComGY7qKjqFlX9r2+7EHejSMKVdYLvsAnAYG9y6H8ikgxcBbxRKTmYy9sA6AG8CaCqB1R1J0FcZp9wIFpEwoEY3JxnQVVmVZ0H/HhI8tHKOAh4R1WLVXUjkIW7z1VJqAWEI02zneRRXmqEiKQA5wGLgCaqugVc0AASvMuZ340G/gSUV0oL5vKeCeQB433VZG+ISD2CuMyq+gPwPLAJ2ALsUtWZBHGZKzlaGf16Twu1gHBC02wHCxE5DfgAuE9Vd3udn+oiIgOA7aq6xOu81KBwoDPwmqqeB+yl9leVHJOv3nwQkAokAvVEZKi3ufKcX+9poRYQQmaabRGJwAWDiar6oS95m4g08+1vBmz3Kn9+dhEwUESycdWAvUXkbYK3vOB+l3NUdZHv8/u4ABHMZe4LbFTVPFUtAT4ELiS4y1zhaGX06z0t1AJCSEyzLSKCq1teraqjKu2aBtzm274NmFrTeasOqvqIqiaragruZzpHVYcSpOUFUNWtwGYRae1L6oN75WzQlhlXVXSBiMT4fsf74NrHgrnMFY5WxmnAEBGJFJFUoBWQXuWrqGpILcCVwFpgPfCY1/mppjJejHts/BZY5luuBOJwPRTW+daNvM5rNZS9FzDdtx3U5QU6ARm+n/NHQGwIlPmvwHfASuBfQGSwlRmYhGsjKcE9AdxxrDICj/nuZ2uAK07l2jZ1hTHGGCD0qoyMMcYchQUEY4wxgAUEY4wxPuFeZ6Cq4uPjNSUlxetsGGNMrbJkyZJ8Pco7lY8bEERkHFAx8Ke9L60RMBlIAbKBG1R1h2/fI7hW8TLgXlX93JfeBTdHRzTwKfAHVVURiQTeAroABcAvVTX7ePlKSUkhIyPjeIcZY4ypRES+P9q+E6ky+if+mWjpNeAuXD/ZVpW+8w5gh6qeBfwDePYE8mSMMcbPjhsQ1A8TLflG1jVQ1YXq+rm+dcg5Fd/1PtDHN+jEGGNMZaowZQrs2lUtX1/VRuWTnWgpybd9aPrPzlHVUmAXbhDGYUTkLhHJEJGMvLy8KmbdGGNqoZUroW9fuOYaGDOmWi7h715GR5to6VgTMJ3w5EyqOlZV01Q1rXHjI7aJGGNMcNmxA+69Fzp1gqVL4eWX4cEHq+VSVQ0IJzvRUo5v+9D0n53jm+P8dA6vojLGmNBSVgavvw6tWsErr8BvfgPr1sHvfgfh1dNBtKoB4aQmWvJVKxWKyAW+9oFbDzmn4ruuw01MZvNpGGNC17x5cP75MGwYtG8P//2vCwpxR6xN95sT6XY6CTdhWLyI5ACPA88A74rIHbgZCK8HUNVVIvIubtbFUuB3qlrm+6q7+anb6QzfAm5Wzn+JSBbuyWCIX0pmjDG1zcaN8Kc/wfvvQ/PmMHkyXH891FA/m1o7uV1aWpraOARjTFAoLIS//x1GjYKwMBg+3LUTxMT4/VIiskRV0460r9aOVDbGmFqvvBwmTIBHH4WtW+GWW1xgSPLmzb4WEIwxxgtz57qngKVLoXt3mDoVunb1NEs2uZ0xxtSkNWtg0CDo3RsKCmDiRPjqK8+DAVhAMMaYmlFQ4MYTtG/vng7+/nf47ju46aYaazQ+HqsyMsaY6lRU5LqM/u1vsHs33HUX/PWvkJBw/HNrmAUEY4ypDuXlMGkSPPYYfP899O8Pzz8P7dp5nbOjsiojY4zxtzlz3MCyoUOhUSOYNQtmzAjoYAAWEIwxxn9WroQrr4Q+fSA/H/71L8jIcJPS1QIWEIwx5lR9/z386ldw7rmwcCH87/+63kRDh0Kd2nObtTYEY4ypqvx8ePpp12gs4sYVDB9e7XMOVRcLCMYYc7L27oXRo+G552DPHrjtNtdzqHnz458bwCwgGGPMiTpwAN54A5580k01MWgQPPVUwDcWnygLCMYYczxlZW5E8eOPQ3Y2XHIJfPABXHih1znzq9rT2mGMMTWt4h3G557rqoUaNYLPPoMvvwy6YAAWEIwx5nCq8Pnn0K2be4dxWRm8957rQnr55QEz1YS/WUAwxpjK5s51VUL9+8O2bTBunBtfcN11QRsIKlhAMMYYcDOO9u7tlo0b4dVX3TuM/+d/qu0dxoHGAoIxJrSlp7ungYsvhlWr4B//gKwsuPtuqFvX69zVKAsIxpjQlJ4OV13l2gkyMuDZZ2HDBrjvPoiO9jp3ngiN5yBjjKmQnu4GkX36qes19PTT8PvfQ/36XufMcxYQjDGhYdEiGDHCAsExWEAwxgS3+fPdyOJZsywQHIcFBGNM8FF13UeffBK++MK9nezZZ11DsQWCo7KAYIwJHhUDyp58Er7+Gpo1c72G7roLYmK8zl3As4BgjKn9ysrcFBNPPw1Ll0KLFm4cwf/8D0RFeZ27WsO6nRpjaq+SEvjnP91so9df76alHjfODSi7+24LBifJnhCMMbXPvn3w5pvupfWbNkGnTvDuu27eobAwr3NXa1lAMMbUHgUF8PLL8NJLbvuSS+D114N6wrmaZAHBGBP4vv8eRo50TwX79sHVV8Of/uSmmzB+YwHBGBO4li93L6x/5x33BHDzzfDHPwbNG8oCjQUEY0xgqeg6OnIk/Oc/UK8e3Hsv3H9/tb6zuKSkhJycHIqKiqrtGjUpKiqK5ORkIiIiTvgcCwjGmMBQXAyTJrlAsHKlG0PwzDNuDEFsbLVfPicnh/r165OSkoLU8vYIVaWgoICcnBxSU1NP+DwLCMYYbxUUuIbhl1+GLVugQwfXlfTGG2t0+umioqKgCAYAIkJcXBx5eXkndZ4FBGOMN1avhhdegLfegv37oV8/Fwj69fOsx1AwBIMKVSmLBQRjTM1RdZPM/eMf7mX1kZEwdKh7B0H79l7nLuRZQDDGVL89e+Bf/3LVQpmZ0LSpm2/oN7+Bxo29zp3xOaWpK0QkW0RWiMgyEcnwpTUSkVkiss63jq10/CMikiUia0Tk8krpXXzfkyUiL0owPbcZE8rWrytrYG4AAA64SURBVIcHHoDkZPjtb92byCZMgOxs+POfLRgc4sUXX6RNmzbcfPPNfPTRR4wYMeKYxz/00EPMmTPHfxlQ1SovQDYQf0jac8Bw3/Zw4FnfdltgORAJpALrgTDfvnSgOyDADOCK4127S5cuaowJQGVlqjNnqg4YoCqiGh6uOmSI6tdfq5aXe527o8rMzPQ6C9q6dWvdsGGDqqp2795d8/Lyjnl8dna29uvX76j7j1QmIEOPcl+tjiqjQUAv3/YE4AvgYV/6O6paDGwUkSygq4hkAw1UdSGAiLwFDPYFBmNMbbFjh/vr/7XXYO1a9w6CP/8Zhg2DxESvc3dy7rsPli3z73d26gSjRx9197Bhw9iwYQMDBw5k6NChREZGEh8fD8CgQYO49tprufXWW3n99deZN28eEydO5IwzzqCgoICtW7fStGnTU87iqc52qsBMEVkiInf50pqo6hYA3zrBl54EbK50bo4vLcm3fWj6YUTkLhHJEJGMk+1OZYypJkuXwp13QlKSGzwWF+faCzZtcq+srG3BwCNjxowhMTGRuXPnkpCQQOfOnQ/uGzt2LCNGjGD+/PmMHDmSl1566eC+zp0789VXX/klD6f6hHCRquaKSAIwS0S+O8axR2oX0GOkH56oOhYYC5CWlnbEY4wxNWD/fje76Jgx8M03rm3g5ptdO8F553mdu1N3jL/ka8KWLVtoXKl9pUmTJowYMYJLL72UKVOm0KhRo4P7EhISyM3N9ct1TykgqGqub71dRKYAXYFtItJMVbeISDNgu+/wHKDyuPNkINeXnnyEdGNMoPnuOzeIbMIEV0V09tmuC+mvfgUNG3qdu6ARHR3Nrl27fpa2YsUK4uLiDrv5FxUVER0d7ZfrVrnKSETqiUj9im3gMmAlMA24zXfYbcBU3/Y0YIiIRIpIKtAKSPdVKxWKyAW+3kW3VjrHGOO1iiklevWCNm3glVfgsstgzhwXIO67z4KBn7Vp04asrKyDn9PT05kxYwZLly7l+eefZ+PGjQf3rV27lvZ+GsNxKm0ITYAFIrIc10voE1X9DHgG6Cci64B+vs+o6irgXSAT+Az4naqW+b7rbuANIAvX+8galI3x2qpVrk0gMRFuugk2b3Yvqs/JcbOPXnqpvYOgmvTo0YOlS5eiqhQXF3PnnXcybtw4EhMTGTlyJLfffjuqSklJCVlZWaSlpfnlulWuMlLVDUDHI6QXAH2Ocs5TwFNHSM8AbJiiMV7bswcmT4Y33nBtAxER8ItfwK9/DX36QB176251ys7OPrjdt29fZs+eTd++fVm+fPnB9IEDBzJw4EAApk+fznXXXUd4uH86jNpIZWNCnSp8/TWMH++CwZ49rmpo5Ei45RYbPOaRRx99lEWLFh3zmNLSUh588EG/XdMCgjGhKjfXTSw3frwbNxATAzfc4LqQdu8ektVBqhowE9w1adLk4JPA0Vx//fVH3efGoJ0cCwjGhJKiIvj4YxcEPv8cysvdaygffhiuvx7q1/c6h56JioqioKCAuLi4gAkKVaW+9yFERUWd1HkWEIwJdqqwcKF7Gpg8GXbudIPIhg933UVbtfI6hwEhOTmZnJyck36HQKCqeGPaybCAYEyw2rjRjRh+6y03yVxMDFxzDdx6K/TuDWFhXucwoERERJzU28WCkQUEY4JJfr4bQTxxomsoFnHdQ//yFxcMQrhKyByfBQRjart9+2DaNBcEPvsMSkuhXTt4+mk3nUSLFl7n0NQSFhCMqY0OHICZM90AsalTXVfR5GQ3kOzmm+Hcc0Oyl5A5NRYQjKktSkth7lzXMPzBB65xuFEjGDLEBYEePWzgmDklFhCMCWSlpTBvHrz/vlvy8lw7wODBLhD07Qt163qdSxMkLCAYE2hKS+HLL+G99+DDD10QiImBq66CG2+EK66Ak+xfbsyJsIBgTCAoLnazh06Z4pb8fKhXDwYMcAPGrrjCBQVjqpEFBGO8smeP6xU0ZQpMnw67d7vqoKuu+ikI+Gmee2NOhAUEY2rS9u3u5j91quslVFQE8fEuAFxzjZtRNDLS61yaEGUBwZjqtmaNCwBTp7opJFSheXM3pfS117q5hPw0fbExp8J+C43xt5ISWLDAPQlMn+5mEgX3ruHHH4eBA6FTJxsnYAKOBQRj/CEvD2bMcAHg889de0DdutCzJ9xzjwsCNmLYBDgLCMZURVkZLF7sGoVnzHDbqtC0qWsPGDDAjRE47TSvc2rMCbOAYMyJ2rrVNQTPmOHWP/7oqn26dXNVQQMGuGohGy1saikLCMYczb59MH++u/nPmgUrVrj0Jk3g6quhf3/o1w/i4rzNpzF+YgHBmAplZbBkiRsgNmuWaxg+cMC1BVx8MTzzjAsAnTrZU4AJShYQTOhShVWrXACYPdtNF7Frl9vXvj38/vcuAPToYaOETUiwgGBCR3k5ZGa6G/8XX7hJ47Zvd/tatnQvmO/d271QpkkTT7NqjBcsIJjgVVoK337r2gG+/NIFgIICt69FC7j8cnfz790bzjjD27waEwAsIJjgsXcvpKe7uv8FC9yo4MJCty811TUE9+wJvXpBSoqXOTUmIFlAMLWTKnz/vbvpVyzLlrmnAhHo0AFuucU1Bl98sZsqwhhzTBYQTO1QWOh6AKWnwzffuACwdavbFxMDXbvCH/8Il1wC3btDw4be5teYWsgCggk8xcWwcqUb/Zue7pbMTPdUAK4BuG9fd+Pv3t09DdjkcMacMvtfZLxVXOwGfC1Z8tOyYoWbIA7c1NDdurkeQF27QlqaSzPG+J0FBFNzCgpg+XJX179smdvOzHT1/gCxsdClCzzwgFunpbnGX5sV1JgaYQHB+F9xMXz3nftLv/KSk/PTMYmJ0LEjXHmlu/l36WI3f2M8ZgHBVF1RkZvrf/Vq95d+ZqYb+bt2rZsGAiAiAtq0cd09O3Z00z507AgJCd7m3RhzGAsI5thUYds299avtWt/Wq9eDRs2uNG/4Ob2adnS3fyvucY19HboAK1auaBgjAl4FhCMu6lv2QLr10NWlltXbK9b5172UiEqyt3kO3WCm26Ctm1dEDj7bLfPGFNrWUAIBapuzp5NmyA72y0bN/58XVT00/FhYa4+v2VL162zdWt3w2/d2g3wspk+jQlKFhBqu9JSd7PPzf1pycmBzZtdANi82X0uLv75ebGxbjqHtm1dw27LlnDWWW7dooVV8xgTggImIIhIf+AFIAx4Q1Wf8ThL3ikudl008/Pdu3q3b3f1+Fu3unXFsmWLW1fU41cIC3O9eFq0gPPPd3X6LVq4v+5TU91Ebqef7k3ZjDEBKyACgoiEAa8A/YAcYLGITFPVTG9zVkWlpbBnj6t7r7wUFrr59nfscMuPP/60vWPHT0GgYkK2Q4WHu2mZK5aOHSEpyd38K9aJia4Hj43cNcacpEC5a3QFslR1A4CIvAMMAvwfEDIy3DTI5eWubr28/OfbJSXuhl5S8vPt4mK3FBW5pWJ7/343y2blpWKU7bGEh7tqm4olPh7OOcetKy9xce4G37SpO8766RtjqkmgBIQkYHOlzzlAt0MPEpG7gLsAWrRoUbUrzZkDDz987GPCwlwdekSEu3FHREBkpOtFExX103Z0tLth16vnlpiYn7br1XPVMg0aQP36bl2xxMa6/XZzN8YEkEAJCEe6M+phCapjgbEAaWlph+0/IffeC8OGuZtxnTpuqdgWcQHAbtTGmBAUKAEhB6g8YX0ykFstV6r4K98YY8zPBEqH8sVAKxFJFZG6wBBgmsd5MsaYkBIQTwiqWioivwc+x3U7HaeqqzzOljHGhBRRrVpVvNdEJA/4voqnxwP5fsxObWBlDg1W5tBwKmU+Q1UbH2lHrQ0Ip0JEMlQ1zet81CQrc2iwMoeG6ipzoLQhGGOM8ZgFBGOMMUDoBoSxXmfAA1bm0GBlDg3VUuaQbEMwxhhzuFB9QjDGGHMICwjGGGOAEAwIItJfRNaISJaIDPc6P9VBRJqLyFwRWS0iq0TkD770RiIyS0TW+daxXufVn0QkTESWish03+dgL29DEXlfRL7z/ay7h0CZ7/f9Tq8UkUkiEhVsZRaRcSKyXURWVko7ahlF5BHf/WyNiFx+KtcOqYBQ6b0LVwBtgRtFpK23uaoWpcCDqtoGuAD4na+cw4HZqtoKmO37HEz+AKyu9DnYy/sC8JmqngN0xJU9aMssIknAvUCaqrbHzWowhOAr8z+B/oekHbGMvv/XQ4B2vnNe9d3nqiSkAgKV3rugqgeAivcuBBVV3aKq//VtF+JuFEm4sk7wHTYBGOxNDv1PRJKBq4A3KiUHc3kbAD2ANwFU9YCq7iSIy+wTDkSLSDgQg5sEM6jKrKrzgB8PST5aGQcB76hqsapuBLJw97kqCbWAcKT3LiR5lJcaISIpwHnAIqCJqm4BFzSABO9y5nejgT8Bld8nGszlPRPIA8b7qsneEJF6BHGZVfUH4HlgE7AF2KWqMwniMldytDL69Z4WagHhhN67ECxE5DTgA+A+Vd3tdX6qi4gMALar6hKv81KDwoHOwGuqeh6wl9pfVXJMvnrzQUAqkAjUE5Gh3ubKc369p4VaQKi59y54TEQicMFgoqp+6EveJiLNfPubAdu9yp+fXQQMFJFsXDVgbxF5m+AtL7jf5RxVXeT7/D4uQARzmfsCG1U1T1VLgA+BCwnuMlc4Whn9ek8LtYAQEu9dEBHB1S2vVtVRlXZNA27zbd8GTK3pvFUHVX1EVZNVNQX3M52jqkMJ0vICqOpWYLOItPYl9cG9gzxoy4yrKrpARGJ8v+N9cO1jwVzmCkcr4zRgiIhEikgq0ApIr/JVVDWkFuBKYC2wHnjM6/xUUxkvxj02fgss8y1XAnG4HgrrfOtGXue1GsreC5ju2w7q8gKdgAzfz/kjIDYEyvxX4DtgJfAvIDLYygxMwrWRlOCeAO44VhmBx3z3szXAFadybZu6whhjDBB6VUbGGGOOwgKCMcYYwAKCMcYYHwsIxhhjAAsIxhhjfCwgGGOMASwgGGOM8fn/Q6bnRUI8oFcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,1,1)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"g\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,1,2)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"r\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,3,1)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"g\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,3,2)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"r\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,3,3)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"m\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,3,4)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"c\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,3,5)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"y\")\n",
    "plt.legend(loc=\"center right\")\n",
    "\n",
    "plt.subplot(2,3,6)\n",
    "plt.plot(xs, f(xs), label='f(x)', c=\"w\")\n",
    "plt.legend(loc=\"center right\")\n",
    "plt.show()"
   ]
  }
 ],
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