SU-2016-LAB0-Python-solved.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sveučilište u Zagrebu<br>\n",
    "Fakultet elektrotehnike i računarstva\n",
    "\n",
    "## Strojno učenje 2016./2017.\n",
    "\n",
    "<a href=\"http://www.fer.unizg.hr/predmet/su\">http://www.fer.unizg.hr/predmet/su</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Laboratorijska vježba 0: Uvod u Python\n",
    "\n",
    "(c) 2015-2016 Domagoj Alagić\n",
    "\n",
    "<i>Verzija: 0.1</i> <br/>\n",
    "<i>Zadnji put ažurirano: 7. listopada 2016.</i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Kreirajte dvije liste: $a = [2, 4, 5, 6, 8, 13]$ i $b = [1, 3, 10, 13, 15]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 4, 5, 6, 8, 13] [1, 3, 10, 13, 15]\n"
     ]
    }
   ],
   "source": [
    "a = [2, 4, 5, 6, 8, 13]\n",
    "b = [1, 3, 10, 13, 15]\n",
    "print a, b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(b)__ Napišite kôd koji konkatenira liste $a$ i $b$ u listu $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 4, 5, 6, 8, 13, 1, 3, 10, 13, 15]\n"
     ]
    }
   ],
   "source": [
    "c = a + b\n",
    "print c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(c)__ Sortirajte listu $c$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 8, 10, 13, 13, 15]\n"
     ]
    }
   ],
   "source": [
    "c = sorted(c)\n",
    "print c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(d)__ Izbacite duplikate iz liste c:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 8, 10, 13, 15]\n"
     ]
    }
   ],
   "source": [
    "c = list(set(c))\n",
    "print c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(e)__ Dohvatite i ispišite (pazite na indeksiranje od 0):\n",
    "* treći element,\n",
    "* zadnja dva elementa,\n",
    "* sve elemente između trećeg i šestog (uključujući treći element, isključujući šesti)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "[13, 15]\n",
      "[3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "print c[2]\n",
    "print c[-2:]\n",
    "print c[2:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(f)__ Generirajte interval brojeva `ran` s elementima iz $[2, 20]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n"
     ]
    }
   ],
   "source": [
    "ran = range(2, 21)\n",
    "print ran"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(g)__ Ispišite sve generirane brojeve iz intervala skupa s njihovim indeksima u listi:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 2\n",
      "1 3\n",
      "2 4\n",
      "3 5\n",
      "4 6\n",
      "5 7\n",
      "6 8\n",
      "7 9\n",
      "8 10\n",
      "9 11\n",
      "10 12\n",
      "11 13\n",
      "12 14\n",
      "13 15\n",
      "14 16\n",
      "15 17\n",
      "16 18\n",
      "17 19\n",
      "18 20\n"
     ]
    }
   ],
   "source": [
    "for ind, val in enumerate(ran):\n",
    "    print ind, val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(h)__ Korištenjem sažetog zapisa liste (engl. _list comprehension_) transformirajte listu `ran` tako da sve elemente zamijenite njihovim prirodnim logaritmom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.69314718055994529, 1.0986122886681098, 1.3862943611198906, 1.6094379124341003, 1.791759469228055, 1.9459101490553132, 2.0794415416798357, 2.1972245773362196, 2.3025850929940459, 2.3978952727983707, 2.4849066497880004, 2.5649493574615367, 2.6390573296152584, 2.7080502011022101, 2.7725887222397811, 2.8332133440562162, 2.8903717578961645, 2.9444389791664403, 2.9957322735539909]\n"
     ]
    }
   ],
   "source": [
    "ran_ln = [np.log(elem) for elem in ran]\n",
    "print ran_ln"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Napišite funkciju `make_3sg_form(word)` koja vraća glagol u trećem licu jednine za dani glagol u infinitivu, npr. _try_ -> _tries_. Slijedite sljedeća pravila:\n",
    "* Ako glagol završava na _y_, odbaci _y_ i dodaj _ies_.\n",
    "* Ako glagol završava na _o_, _ch_, _s_, _sh_, _x_ ili _z_, dodaj _es_.\n",
    "* Inače samo dodaj _s_.\n",
    "\n",
    "NB: Znakovni niz je zapravo polje znakova tako da vrijede \"trikovi\" za indeksiranje polja.\n",
    "\n",
    "__(b)__ Isprobajte implementiranu funkciju za _fix_, _brush_, _cry_, _play_ i _echo_. Primjetite da je ovo složen problem i da tri jednostavna pravila neće uspjeti pokriti sve slučajeve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fix -> fixes\n",
      "brush -> brushes\n",
      "jump -> jumps\n",
      "cry -> cries\n",
      "echo -> echoes\n"
     ]
    }
   ],
   "source": [
    "def make_3sg_form(word):\n",
    "    ret_word = word\n",
    "    if ret_word.endswith(\"y\"):\n",
    "        ret_word = ret_word[0:-1] + \"ies\"\n",
    "    elif ret_word.endswith(\"o\") or ret_word.endswith(\"x\") or ret_word.endswith(\"s\") or \\\n",
    "        ret_word.endswith(\"ch\") or ret_word.endswith(\"sh\"):\n",
    "        ret_word += \"es\"\n",
    "    else:\n",
    "        ret_word += \"s\"\n",
    "    return ret_word\n",
    "\n",
    "print \"fix\", \"->\", make_3sg_form(\"fix\")\n",
    "print \"brush\", \"->\", make_3sg_form(\"brush\")\n",
    "print \"jump\", \"->\", make_3sg_form(\"jump\")\n",
    "print \"cry\", \"->\", make_3sg_form(\"cry\")\n",
    "print \"echo\", \"->\", make_3sg_form(\"echo\")\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Napišite funkciju `filterShortWords (word_list, min_length)` koja prima listu riječi i minimalnu dopuštenu duljinu riječi te vraća __novu__ listu riječi koja sadrži samo one riječi čija je duljina veća od minimalne dopuštene. Obavezno provjerite da je dana duljina riječi pozitivan broj veći od 1. Ako nije, bacite iznimku. U slučaju da korisnik nije zadao duljinu, funkcija radi jednako kao da je korisnik zadao duljinu od dva znaka (koristite podrazumijevane argumente, engl. _default arguments_). \n",
    "\n",
    "Zadatak riješite na dva načina: \n",
    "\n",
    "* __(a)__ korištenjem `for` petlji,\n",
    "* __(b)__ korištenjem sažetog zapisa liste,\n",
    "* __(c)__ korištenjem metode `filter` u kombinaciji s lambda-izrazom. \n",
    "\n",
    "__(d)__ Pokažite na primjeru da su izlazi implementiranih funkcija jednaki.\n",
    "\n",
    "NB: Podrazumijevani elementi (ili grupa istih) uvijek dolaze na kraju liste argumenata u definiciji funkcije."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def filterShortWordsLoop(word_list, min_length=2):\n",
    "    if min_length < 1:\n",
    "        raise ValueError(\"Length must be >= 1.\")\n",
    "    filtered_list = []\n",
    "    for word in word_list:\n",
    "        if len(word) >= min_length:\n",
    "            filtered_list.append(word)\n",
    "    return filtered_list\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def filterShortWordsLambda(word_list, min_length=2):\n",
    "    if min_length < 1:\n",
    "        raise ValueError(\"Length must be >= 1.\")\n",
    "    return filter(lambda elem: len(elem) >= min_length, word_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def filterShortWordsCompr(word_list, min_length=2):\n",
    "    if min_length < 1:\n",
    "        raise ValueError(\"Length must be >= 1.\")\n",
    "    return [elem for elem in word_list if len(elem) >= min_length]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sam', 'mali', 'Mate', 'mame', 'tate']\n",
      "['sam', 'mali', 'Mate', 'mame', 'tate']\n",
      "['sam', 'mali', 'Mate', 'mame', 'tate']\n"
     ]
    }
   ],
   "source": [
    "word_list = [\"Ja\", \"sam\", \"mali\", \"Mate\", \"od\", \"mame\", \"i\", \"tate\"]\n",
    "print filterShortWordsLoop(word_list, min_length=3)\n",
    "print filterShortWordsLambda(word_list, min_length=3)\n",
    "print filterShortWordsCompr(word_list, min_length=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dana vam je mapa koja za ključeve sadrži nazive programskih jezika, a za vrijednosti liste programskih paradigmi koje određeni jezik pokriva."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "langs_paradigms = {\n",
    "                  \"Java\" : [\"object-oriented\", \"imperative\"],\n",
    "                  \"Haskell\" : [\"functional\"],\n",
    "                  \"Lisp\" : [\"functional\", \"procedural\"]\n",
    "                  }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Napišite razred `ProgLanguageRepository` uzimajući u obzir sljedeće stvari:\n",
    "* Konstruktor ovog razreda prima početnu mapu koja sadrži programske jezike i njihove paradigme.\n",
    "* Dana mapa sprema se kao član klase imena `data`.\n",
    "* Razred sadrži metodu `count` koja vraća broj programskih jezika dostupnih u repozitoriju.\n",
    "* Razred sadrži metodu `get_langs_paradigms (lang)` koja za dano ime programskog jezika vraća listu njegovih paradigmi ili vraća `None` ako taj jezik ne postoji u repozitoriju.\n",
    "* Razred sadrži metodu `add_lang_paradigm (lang, paradigm)` koja danom programskom jeziku dodaje paradigmu (ako je već nema).\n",
    "* Razred sadrži metodu `remove_lang_paradigm (lang, paradigm)` koja danom programskom jeziku miče danu paradigmu (ako je ima).\n",
    "* Razred ima nadjačanu metodu za znakovnu reprezentaciju koja samo ispisuje znakovnu reprezentaciju člana `data`.\n",
    "\n",
    "Pokažite na par primjera da vaša implementacija radi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ProgLanguageRepository:\n",
    "\n",
    "    # Konstruktor\n",
    "    def __init__(self, data):\n",
    "        self.data = data\n",
    "    \n",
    "    def count(self):\n",
    "        return len(self.data.keys()) # len(self.data)\n",
    "    \n",
    "    def get_langs_paradigms(self, lang):\n",
    "        if lang in self.data:\n",
    "            return self.data[lang]\n",
    "        else:\n",
    "            return None\n",
    "    \n",
    "    def add_lang_paradigm(self, lang, paradigm):\n",
    "        if paradigm not in self.data[lang]:\n",
    "            self.data[lang].append(paradigm)\n",
    "    def remove_lang_paradigm(self, lang, paradigm):\n",
    "        if paradigm in self.data[lang]:\n",
    "            self.data[lang].remove(paradigm)\n",
    "    \n",
    "    def __str__(self):\n",
    "        return self.data.__str__()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Lisp': ['functional', 'procedural'], 'Haskell': ['functional'], 'Java': ['object-oriented', 'imperative']}\n"
     ]
    }
   ],
   "source": [
    "prog_repo = ProgLanguageRepository(langs_paradigms)\n",
    "print prog_repo\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['functional', 'procedural']\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "print prog_repo.get_langs_paradigms(\"Lisp\")\n",
    "print prog_repo.get_langs_paradigms(\"d\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Lisp': ['functional', 'procedural'], 'Haskell': ['functional', 'object-oriented'], 'Java': ['object-oriented', 'imperative']}\n"
     ]
    }
   ],
   "source": [
    "prog_repo.add_lang_paradigm(\"Haskell\", \"object-oriented\")\n",
    "prog_repo.add_lang_paradigm(\"Haskell\", \"object-oriented\")\n",
    "print prog_repo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Lisp': ['functional', 'procedural'], 'Haskell': ['functional'], 'Java': ['object-oriented', 'imperative']}\n"
     ]
    }
   ],
   "source": [
    "prog_repo.remove_lang_paradigm(\"Haskell\", \"object-oriented\")\n",
    "prog_repo.remove_lang_paradigm(\"Haskell\", \"object-oriented\")\n",
    "print prog_repo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Napišite kôd koji stvara sljedeća tri vektor-stupca, jedan vektor-redak i kvadratnu matricu ranga 2 (koristite `numpy` za cijeli zadatak):\n",
    "\n",
    "$ x_{1} = \\begin{pmatrix}\n",
    "1\\\\\n",
    "2\\\\\n",
    "\\end{pmatrix}$,\n",
    "$ x_{2} = \\begin{pmatrix}\n",
    "3\\\\\n",
    "5\\\\\n",
    "\\end{pmatrix}$,\n",
    "$ x_{3} = \\begin{pmatrix}\n",
    "-3\\\\\n",
    "4\\\\\n",
    "\\end{pmatrix}$,\n",
    "$ x_{4} = \\begin{pmatrix}\n",
    "4\\\\\n",
    "0\\\\\n",
    "\\end{pmatrix}^T$,\n",
    "$ A = \\begin{pmatrix}\n",
    "5 & 3 \\\\\n",
    "10 & 6 \\\\\n",
    "\\end{pmatrix}\n",
    "$\n",
    "\n",
    "__(b)__ Zatim napišite naredbe koje stvaraju dvije nove matrice: matricu $C$ dimenzija $2\\times3$ koja se dobije tako da se vektor-stupci poredaju horizontalno jedan kraj drugog te matricu $D$ dimenzija $3\\times2$ koja se dobije tako da se matrica $A$ postavi ispod danog vektor-retka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1]\n",
      " [2]]\n",
      "[[3]\n",
      " [5]]\n",
      "[[-3]\n",
      " [ 4]]\n",
      "[4 0]\n",
      "[[ 5  3]\n",
      " [10  6]]\n"
     ]
    }
   ],
   "source": [
    "# stvaranje svih danih vektora i matrica\n",
    "x_1 = np.array([[1], [2]])\n",
    "x_2 = np.array([[3], [5]])\n",
    "x_3 = np.array([[-3], [4]])\n",
    "x_4 = np.array([4, 0])\n",
    "A = np.array([[5, 3], [10, 6]])\n",
    "print x_1\n",
    "print x_2 \n",
    "print x_3\n",
    "print x_4\n",
    "print A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  3 -3]\n",
      " [ 2  5  4]]\n"
     ]
    }
   ],
   "source": [
    "# stvaranje matrice C\n",
    "C = np.hstack([x_1, x_2, x_3])\n",
    "print C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4  0]\n",
      " [ 5  3]\n",
      " [10  6]]\n"
     ]
    }
   ],
   "source": [
    "# stvaranje matrice D\n",
    "D = np.vstack([x_4, A])\n",
    "print D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(c)__ Izračunajte umnožak matrica $C$ i $D$ te ga pohranite u matricu $U$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-11  -9]\n",
      " [ 73  39]]\n"
     ]
    }
   ],
   "source": [
    "U = C.dot(D)\n",
    "print U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(d)__ Nadalje, napišite kôd koji izračunava inverz matrice $U$ (spremiti u matricu $I$) kojeg zatim transponira (i sprema u matricu $R$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.17105263  0.03947368]\n",
      " [-0.32017544 -0.04824561]]\n",
      "[[ 0.17105263 -0.32017544]\n",
      " [ 0.03947368 -0.04824561]]\n"
     ]
    }
   ],
   "source": [
    "I = np.linalg.inv(U)\n",
    "print I\n",
    "R = np.transpose(I)\n",
    "print R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(e)__ Izračunajte sumu svih elemenata u matrici $D$ (spremite u varijablu `D_total`), ali i sume po zasebnim dimenzijama (`D_x`, `D_y`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28\n",
      "[19  9]\n",
      "[ 4  8 16]\n"
     ]
    }
   ],
   "source": [
    "D_total = np.sum(D[:])\n",
    "print D_total\n",
    "D_x = np.sum(D, axis=0) # po x osi\n",
    "print D_x\n",
    "D_y = np.sum(D, axis=1) # po y osi\n",
    "print D_y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(f)__ Ispišite determinantu matrice $R$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00438596491228\n"
     ]
    }
   ],
   "source": [
    "print np.linalg.det(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(g)__ Isprobajte vrijedi li $R\\cdot R^{-1} = I$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.]\n",
      " [ 0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "RI = np.dot(R, np.linalg.inv(R))\n",
    "print RI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(h)__ Stvorite vektor-stupac $n$ dimenzija $4\\times 1$ čiji su svi elementi 0 (bez ručnog pisanja svih elemenata)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "n = np.zeros([4, 1])\n",
    "print n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Napišite kôd koji iscrtava sljedeće funkcije:\n",
    "\n",
    "$f_{1}(x) = \\sqrt{(1-(|x|-1)^2)}$ i $f_{2}(x) = -3 \\cdot \\sqrt{(1-\\sqrt{\\frac{|x|}{2}})}$\n",
    "\n",
    "pritom definirajući domenu funkcija kao $x \\in [-2, 2]$ (u 1000 točaka). Graf funkcije $f_{1}(x)$ prikažite plavom bojom, a graf funkcije $f_{2}(x)$ crvenom. Iscrtajte oba grafa na istoj slici tako da su vidljive točke iz intervala $x \\in [-3, 3]$ i $y \\in [-3, 1.5]$.\n",
    "\n",
    "__(b)__ Ostavite oznake osi jednostavno kao $x$ i $y$. Iscrtajte legendu u donjem desnom kutu tako da je naziv funkcije $f_{1}(x)$ _bolja polovica_, a naziv funkcije $f_{2}(x)$ _dobra polovica_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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kFSrAxx9DgwauhsDatb4jMsW1dasrQrV5M3z9tSWIOGVJwpS+smXh9dfdLqDN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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc101518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# funkcije\n",
    "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",
    "# domena u 1000 točaka\n",
    "x = np.linspace(-2, 2, 1000)\n",
    "# iscrtavanje prvog grafa plavom linijom\n",
    "plt.plot(x, f_1(x), 'b-', label=\"bolja polovica\")\n",
    "# iscrtavanje drugog grafa crvenom linijom\n",
    "plt.plot(x, f_2(x), 'r-', label=\"dobra polovica\")\n",
    "# postavljanje ograničenja prikaza\n",
    "plt.xlim([-3, 3])\n",
    "plt.ylim([-3, 1.5])\n",
    "# postavljanje oznaka osi\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "# iscrtavanje legende\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Učitajte skup podataka _Iris_. Ovaj skup podataka sadrži 150 instanci, 50 za svaku od tri klase (_Iris setosa_, _Iris virginica_ i _Iris versicolor_). Svaka instanca, to jest vektor, sadrži četiri značajke: širinu i dužinu latice te širinu i dužinu čašićnog listića. U polju _iris.data_ nalaze se instance, dok se u _iris.target_ nalaze oznake instanci (njihove stvarne klase).  Ispišite dimenzije polja instanci te polja njihovih stvarnih oznaka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150L, 4L)\n",
      "(150L,)\n"
     ]
    }
   ],
   "source": [
    "# učitavanje dataseta\n",
    "iris = datasets.load_iris()\n",
    "print iris.data.shape\n",
    "print iris.target.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(b)__ Budući da ne možemo vizualizirati 4-dimenzijske podatke, iz svake instance izdvojite samo prve dvije značajke. Koristite indeksiranje poljem brojeva. Ispišite dimenzije dobivenog polja instanci."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150L, 2L)\n"
     ]
    }
   ],
   "source": [
    "data_2dim = iris.data[:, 0:2]\n",
    "print data_2dim.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(c)__ Logičkim indeksiranjem razdvojite primjere za svaku od tri klase. Ispišite dimenzije dobivenih polja."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50L, 4L)\n",
      "(50L, 4L)\n",
      "(50L, 4L)\n"
     ]
    }
   ],
   "source": [
    "class_1_samples = iris.data[iris.target == 0]\n",
    "class_2_samples = iris.data[iris.target == 1]\n",
    "class_3_samples = iris.data[iris.target == 2]\n",
    "\n",
    "print class_1_samples.shape\n",
    "print class_2_samples.shape\n",
    "print class_3_samples.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(d)__ Napišite kôd koji iscrtava četiri zasebna grafa (četiri podgrafa u 2x2 mreži), pri čemu tri grafa prikazuju instance određene klase (točke u 2-dimenzijskom prostoru), a četvrti ih prikazuje sve (u različitim bojama). Osigurajte da svi grafovi prikazuju isto područje grafa (npr. $x \\in [4,9]$ i $y \\in [1.5, 5]$).\n",
    "\n",
    "Proučite kako se postavlja veličina glavnog okvira (u koji se smještaju podgrafovi) te ju postavite na 10x8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2ERFZIxCz6eycscfZgqEvpLrzAO8z5FrSLjc3F4/ddx+Amg1/s7OzLb82EdVgdx75KhCz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\n7DwFw8qyaSSf+4s2/gCukaRSKhbACpKhd7RhZX1ZE2ufZWXJ+Mzdt7U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      "text/plain": [
       "<matplotlib.figure.Figure at 0x16e1acc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "# class 1\n",
    "plt.subplot(221)\n",
    "plt.scatter(class_1_samples[:,0], class_1_samples[:,1], c='r')\n",
    "plt.xlim([4, 9])\n",
    "plt.ylim([1.5, 5])\n",
    "# class 2\n",
    "plt.subplot(222)\n",
    "plt.scatter(class_2_samples[:,0], class_2_samples[:,1], c='g')\n",
    "plt.xlim([4, 9])\n",
    "plt.ylim([1.5, 5])\n",
    "# class 3\n",
    "plt.subplot(223)\n",
    "plt.scatter(class_3_samples[:,0], class_3_samples[:,1], c='b')\n",
    "plt.xlim([4, 9])\n",
    "plt.ylim([1.5, 5])\n",
    "# all three classes\n",
    "plt.subplot(224)\n",
    "plt.scatter(data_2dim[:,0], data_2dim[:,1], c=iris.target, cmap=plt.cm.Set1)\n",
    "plt.xlim([4, 9])\n",
    "plt.ylim([1.5, 5])\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(a)__ Napišite kôd koji u petlji iscrtava grafove normalnih distribucija definiranih s parametarima $\\mu$ i $\\sigma$:\n",
    "\n",
    "* $\\mu = 3$\n",
    "* $\\sigma \\in [1, 5]$ (korak 1)\n",
    "\n",
    "Dakle, generirat ćete pet grafova normalnih distribucija: $\\mathcal{N}_{1}(\\mu = 3, \\sigma = 1)$, $\\mathcal{N}_{2}(\\mu = 3, \\sigma = 2)$, ... , $\\mathcal{N}_{1}(\\mu = 3, \\sigma = 5)$.\n",
    "\n",
    "Grafove iscrtajte na istoj slici tako da su vidljive točke iz intervala $x \\in [-15, 15]$ i $y \\in [0, 0.5]$. Za svaki graf upotrijebite drugu boju. Za domenu koristite $[-50, 50]$ (uzorkujte 1000 točaka). Također napravite legendu u gornjem lijevom kutu koji će sve grafove nazvati onako kako su i u zadatku \n",
    "definirani ($\\LaTeX$ kôd radi unutar znakovnih nizova koji definiraju oznaku unutar legende), npr. $\\mathcal{N}_{1}(\\mu = 3, \\sigma = 5)$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5bVU0RU40Ljft55yWBr6+kJFR87p++QVmz4Zdu2pel2gwrv3smLxllvTUhbAm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\nEGEpdQsLC4tBhKXULSwsLAYR/w/P25TFmJSDIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb45bcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.linspace(-50, 50, 1000)\n",
    "sigmas = range(1, 6)\n",
    "\n",
    "for sigma, color in zip(sigmas, \"rgbmy\"):\n",
    "    n_dist = stats.norm.pdf(xs, loc=3, scale=sigma)\n",
    "    label = \"$\\mathcal{N}_{1}(\\mu = 3, \\sigma = \" + str(sigma) + \")$\"\n",
    "    plt.plot(xs, n_dist, color, label=label)\n",
    "\n",
    "plt.xlim([-15, 15])\n",
    "plt.ylim([0, 0.5])\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sada pretpostavite da imate zadanu distribuciju ocjena na nekom kolegiju koja se pokorava normalnoj distribuciji $\\mathcal{N}_{G}(\\mu = 62, \\sigma = 13)$. Najprije je iscrtajte (nebitno kako), ali osigurajte da je domena $[0, 100]$ (raspon mogućih bodova na kolegiju) također uzorkovana u 1000 točaka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g7EjiaLT5yMzaAW8Cg4D3gJeBU919WUqZwcBEdx9sZv2B6929pLFzzewy4GN3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\nUuv/A8NhqNO3qNh9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18a99518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xsg = np.linspace(0, 100, 1000)\n",
    "n_g = stats.norm.pdf(xsg, loc=62, scale=13)\n",
    "plt.plot(xsg, n_g, 'b-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Međutim, vi polažete kolegij naknadno na roku, a profesoru se zaista ne da ispravljati vaš ispit. Kako bi tome doskočio, profesor često koristi tradicionalnu metodu stubišta (https://www.linkedin.com/pulse/20140414044726-2259773-a-guide-to-grading-exams) koju možemo aproksimirati nasumičnim odabirom broja iz distribucije bodova na ispitu. Napišite kôd koji iz distribucije bodova $\\mathcal{N}_{G}$ dohvaća slučajnu vrijednost koja predstavlja vaš broj bodova (zaokružite bodove na cijeli broj)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Na ispitu sam osvojio 59 bodova.\n"
     ]
    }
   ],
   "source": [
    "points = int(stats.norm.rvs(loc=62, scale=13))\n",
    "print \"Na ispitu sam osvojio\", points, \"bodova.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Iscrtajte konture 2-dimenzijske Gausove distribucije $\\mathcal{N} (\\vec{\\mu}, \\Sigma)$ sa sljedećim parametrima:\n",
    "\n",
    "* $\\vec{\\mu} = [1, 1]$\n",
    "* $\\Sigma = \\begin{pmatrix}\n",
    "1 & 1 \\\\\n",
    "0.5 & 3 \\\\\n",
    "\\end{pmatrix}$\n",
    "\n",
    "Za domenu uzmite $x_{1} \\in [-1, 2]$ i $y_{2} \\in [-2, 2]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p4m9JiBU/hFn1gyp/qabAP1LaFf+mHV2vgbQo1ANcunH1nLXBviZiqfJ7xRP8kTuwZl7X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\nRsEvIpIZBb+ISGb+H+KPWEZWdWjpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x16d67eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mnormal = stats.multivariate_normal([1, 1], [[1, 1], [0.5, 3]])\n",
    "x_1 = np.linspace(-1, 2)\n",
    "x_2 = np.linspace(-2, 2)\n",
    "\n",
    "X1, X2 = np.meshgrid(x_1, x_2)\n",
    "X1X2 = np.dstack((X1, X2))\n",
    "\n",
    "plt.contourf(X1, X2, mnormal.pdf(X1X2))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}