dataHacker_Blog_002.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kratak uvod u NumPy - Numerical Python biblioteku"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# \"#\" Ovo je znak za komentar. \n",
    "# Uvezli smo biblioteku numpy kao instancu np koristeci komandu import\n",
    "\n",
    "import numpy as np "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# np sada mozemo koristiti u velikom broju primera.\n",
    "# ukoliko otkucamo np. i pritisnemo TAB dobićemo listu mogucih funkcija\n",
    "\n",
    "# kreiramo niz od 6 elemenata\n",
    "a= np.array([0, 1, 2, 3, 4, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# a * 3 u slucaju da je a numpy instanca, mnozi se svaki element sa 3\n",
    "a = a * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ovo je vazan koncept u NumPy-ju  (slican kao i u Matlabu).   \n",
    "### Vectorization:: moguce je procesirati nizove na brz nacin bez koriscenja loop petlji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  3  6  9 12 15]\n"
     ]
    }
   ],
   "source": [
    "print (a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ovim smo generisali numericki niz od 6 elemenata. \n",
    "# mozemo proveriti dimenzije niza. U ovom slucaju rezultat 1 nam \n",
    "# govori da se radi o vektoru. \n",
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sam oblik visedimenzionalnog numpy niza (ndarray) moguce je proveriti naredbom shape\n",
    "a.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  3,  6],\n",
       "       [ 9, 12, 15]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# komandom reshape mozemo promeniti oblik niza. Od 1D niza (1x6), mozemo kreirati matricu, 2D niz, dimenzija (2 x 3)\n",
    "a.reshape(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.zeros((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([[1., 2., 3.], [4., 5., 6.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.]\n",
      " [ 4.  5.  6.]]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  3.,   6.,   9.],\n",
       "       [ 12.,  15.,  18.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Indeksiranje"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 10\n",
    "x  = np.arange(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ovom naredbom type mozemo proveriti koji je tip podataka x. --> numpy.ndarray\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indeksiranje pocinje od 0, do N-1\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 5 9\n"
     ]
    }
   ],
   "source": [
    "print(x[1], x[5], x[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4]\n"
     ]
    }
   ],
   "source": [
    "print(x[2:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# # Funkcije za brzo procesiranje pojedinacnih elemenata niza"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# # \"Element-wise processing\". U Matlabu se za ovo koristila tacka, npr. \".*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# komandom range(N) mozemo definisati intervale od nula do N-1\n",
    "x = np.array(range(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print (x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.        ,  1.41421356,  1.73205081,  2.        ,\n",
       "        2.23606798,  2.44948974,  2.64575131,  2.82842712,  3.        ])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# naredba kvadratni koren primenjuje se na svaki element niza pojedinacno. \n",
    "np.sqrt(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          1.          1.18920712  1.31607401  1.41421356  1.49534878\n",
      "  1.56508458  1.62657656  1.68179283  1.73205081]\n"
     ]
    }
   ],
   "source": [
    "# Obratiti paznju da se ovde vrednost vektora x ne menja !!\n",
    "# trebalo bi pipsati x = np.sqrt(x)\n",
    "\n",
    "x = np.sqrt(x)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# naredbom arange mozemo kreirati prvih 1000 celih brojeva pocevsi od nule.\n",
    "# dodatni komentar oznacava da ove brojeve zelimo da sacuvamo kao tip podataka 'float'\n",
    "t = np.arange(1000, dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mozemo kreirati vremensku osu u trajanju od 1 sekunde\n",
    "# odbirci ce u ovom slucaju biti na odstojanju od 1 mili sekunde\n",
    "t = t / 1000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mozemo definisati novu vrednost x, kao kosinusnu funkciju sa frekvencijom od 3 Hz\n",
    "x = np.cos(2*np.pi*3*t )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ukoliko zelimo da iscrtamo grafike potrebno je da uvezemo biblioteku matplotlib.pyplot\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# komentar koji je potreban za iscrtavanje grafika\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x9e1e940>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bLkLfOThFMKQs97DnZ6dTlpdp2xBf28Ak+dnWUSQZ1Jd6CKnwc2U3DEWSFSYc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\nsV8QVxSKEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9c4d5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# iscrtavanje nizova, narocito vremenskih serija radimo uz pomoc naredbe plot\n",
    "plt.plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}