L1a.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zasady zaliczenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Na kazdych zajeciach notebook do oddania do konca zajec T+1 (mailowo jako pdf, lub link do repozytorium na githubie), lub za polowe punktow do konca zajęć T+2\n",
    "\n",
    "* Ocena z ćwiczeń na podstawie typowych progów 90%, 80%, etc.\n",
    "\n",
    "* 2 nieobecnośći"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Praktyczny Machine Learning w Pythonie\n",
    "\n",
    "Cel: \n",
    "\n",
    "1. zobaczyc jak w praktyce uzywa sie machine learningu w wielu firmach. Potem bedzie duzo mniej praktyki :)\n",
    "\n",
    "2. zapoznanie z pakietami scikit-learn, numpy, matplotlib z zastosowaniem do rozpoznawania cyfr. Konkurs pod koniec: jeszcze więcej rozpoznawania cyfr:)\n",
    "\n",
    "(Tak, to nie jest tak ze wielkie firmy uzywaja duzo trudniejszych modeli niż to co Państwo poznają na tych zajęciach, niestety)\n",
    "\n",
    "Następne zajęcia: teoria za regresją logistyczną, którą omówimy dzisiaj\n",
    "\n",
    "<br>\n",
    "<img src=\"figures/L1/python-comic-2.png\">\n",
    "\n",
    "## Przydatne pakiety\n",
    "\n",
    "Python to język wysokiego poziomu z ogromną ilością pakietów. \n",
    "\n",
    "Najpierw skupimy się na tym jak w praktyczny sposób wykorzystać pakiet scikit-learn do rozwiązywania problemów machine learningowych, które mogą się pojawić przy okazji inych projektów. Scikit-learn jest używany w takich firmach jak Microsoft, Evernote czy Spotify. Zawdzięcza to świetnemu API, dobrej wydajności i bardzo aktywnej społeczności.\n",
    "\n",
    "Uwaga: nie uczymy pythona, ale mam nadzieję, że składnia jest intuicyjna\n",
    "\n",
    "W tej części poznamy przydatne pakiety i narzędzia, które obecnie stanowią podstawę machine learningu w Pythonie:  IPython Notebook, numpy oraz matplolib.\n",
    "\n",
    "Pakietów jest duzo więcej: Scipy, Pandas, Sympy, PyTables, Cython, Blaze, NLTK i inne. Większość z nich jest dostępna w Anacondzie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  IPython Notebook\n",
    "\n",
    "* \"Mathematicowy\" notebook - możliwość ewaluacji komórek, podpowiadanie składni (tab) i inne\n",
    "* Właśnie go używamy :)\n",
    "* Dużo magicznych rzeczy (wyświetlanie wykresów, równoległe obliczenia)\n",
    "* Bardzo wygodne do zdalnego odpalania kodu na swoim serwerze\n",
    "* ctrl + enter - odpal kod w komórce\n",
    "* ctrl + m + b - wstaw komórke poniżej (w command mode wystarczy b)\n",
    "* Inne przydatne skróty pod ctrl + m + h (lub w Help -> Keyboard Shortcuts).\n",
    "* Alternatywą jest collaboratory (nastawiony na jednoczesną pracę nad jednym notebooiem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy\n",
    "* Wygodne operacje na macierzach, wektorach itp.\n",
    "* Podstawa praktycznie wszystkich pakietów machine learning\n",
    "* Pod spodem wydajny kod C, BLAS (można podpiąć np. szybszy OpenBLAS). \n",
    "\n",
    "Zamiast teorii spróbujmy zrobić pare rzeczy w numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:  [1 2 3 4]\n",
      "Pierwszy element:  1\n",
      "Drugi element!:  2\n",
      "a+1: [2 3 4 5]\n",
      "2*a: [2 4 6 8]\n",
      "b:  [1 2 3 4]\n",
      "Iloczyn skalarny <a,b>:  30\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([1, 2, 3, 4])\n",
    "print \"a: \", a\n",
    "print \"Pierwszy element: \", a[0]\n",
    "print \"Drugi element!: \", a[1]\n",
    "print \"a+1:\", a + 1\n",
    "print \"2*a:\", 2*a\n",
    "b = np.array([1, 2, 3, 4])\n",
    "print \"b: \", b\n",
    "print \"Iloczyn skalarny <a,b>: \", np.inner(a,b) # Iloczyn skalarny"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  [[ 1.  0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0.  0.  1.]]\n",
      "\n",
      "b =  [[ 0.06155327  0.37632435  0.70935316]\n",
      " [ 0.40236883  0.37323993  0.99941991]\n",
      " [ 0.21685251  0.85573161  0.03489185]]\n",
      "\n",
      "a*b = [[ 0.06155327  0.          0.        ]\n",
      " [ 0.          0.37323993  0.        ]\n",
      " [ 0.          0.          0.03489185]]\n",
      "\n",
      "np.dot(a,b) =  [[ 0.06155327  0.37632435  0.70935316]\n",
      " [ 0.40236883  0.37323993  0.99941991]\n",
      " [ 0.21685251  0.85573161  0.03489185]]\n"
     ]
    }
   ],
   "source": [
    "a = np.eye(3) # Macierz identyczności (jedynki na diagonali) 3x3\n",
    "b = np.random.uniform(size=(3,3)) # Losowa macierz 3x3\n",
    "print \"a = \", a\n",
    "print\n",
    "print \"b = \", b\n",
    "print\n",
    "print \"a*b =\", a*b # Mnozenie kazdy element razy kazdy\n",
    "print\n",
    "print \"np.dot(a,b) = \", np.dot(a,b) # Mnozenie macierzowe "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suma elementow od 1 do 3 włącznie:  9\n"
     ]
    }
   ],
   "source": [
    "# Możemy wziąć część wektora i wykonać na nim jakąś operację\n",
    "a = np.array([1,2,3,4,5])\n",
    "print \"Suma elementow od 1 do 3 włącznie: \", a[1:4].sum()\n",
    "# Jest bardzo dużo różnych operacji. Można zobaczyć przez wpisanie \"a.\" i tab (autocompletion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n"
     ]
    }
   ],
   "source": [
    "# Oczywiście obiekty numpy są iterowalne\n",
    "for x in a:\n",
    "    print x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ćwiczenie 1 (1 pkt)\n",
    "    a) znajdź największą i najmniejszą wartość w wektorze c. \n",
    "    b) stworzyć analogicznie wektor d i policzyć unormowany iloczyn skalarny. Ile wynosi jak zwiększymy ilość wymiarów?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c = np.random.uniform(size=(5,)) # wektor 5 pseudolosowych liczb\n",
    "d = np.random.uniform(size=(5,)) # wektor 5 pseudolosowych liczb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Matplotlib\n",
    "\n",
    "Podstawowy pakiet do rysowania. Istnieje dużo nakładek na matplotlib, najciekawsza to prawdopodobnie seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pylab as plt # Import podpakietu jako plt\n",
    "# Magia IPython Notebook :) Pokazuje wykresy w konsoli\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.05263158  0.10526316  0.15789474  0.21052632  0.26315789\n",
      "  0.31578947  0.36842105  0.42105263  0.47368421  0.52631579  0.57894737\n",
      "  0.63157895  0.68421053  0.73684211  0.78947368  0.84210526  0.89473684\n",
      "  0.94736842  1.        ]\n"
     ]
    },
    {
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du8JZZ8GaNWrsIqnQyF2yzqFDMGIEvPkmzJoFvXv7XZFI8GjkLlmlvBwuvRT27oWNG9XY\nRRpKI3fxTXwuzJln5tGpU4TS0gJ+8xv45S/BUlo+EpF4au7ii0S5MK1aRXn33SKuvlpbGUUaS9My\n4otEuTCHD5fw7LOlPlYlEh5JNXcz62tmW83sIzMbcZLjLjOzI2Z2a/pKlDD69FPlwohkUr3N3czy\ngClAH+BCYICZnV/HceOBZekuUsJl+XJYv165MCKZlMxvUk9gu3Ouwjl3BJgH3JLguCJgAbA3jfVJ\niBw+7H1R9R13wLRpyoURyaRkFlQ7ApVxj3fhNfxjzCwf+KlzrpeZnfCaCMCmTTBwIJx3nrfF8Ywz\nCrjmmiLGjJkYlwtTpFwYkTRJ126Zp4D4uXhtYhMAamrgqafgiSdg4kQYPPj4Fsezzy5gzpyovwWK\nhFQyzf0z4EdxjzvFnovXA5hnZgb8BXCjmR1xzi2ufbLi4uJj9wsLCyksLEyxZAmKykqIRKCqClav\nhs6d/a5IJBjKysooKytr1DnqTYU0s2bANqA38DmwBhjgnPuwjuNfBP7NOfdGgteUCpkj5s+HoiIv\nwXHECGjWzO+KRIIrI6mQzrmjZjYMeAdvAXamc+5DMxvqveym1/4jqRQg4fLVVzBsGKxdC0uWQI8e\nflckkpuU5y5ps2KFtxPmppvgySfh1FP9rkgkHJTnLk0mPhemQ4c82raNsHhxAc8/730Fnoj4S81d\nUpYoF+bUU6OsWFFEjx7ayiiSDXQ5oKQsUS7MN9+U8NRTpT5WJSLx1NwlZTt2KBdGJNupuUtKXn8d\nysuVCyOS7fTbKEn5+mu4804YORLmzlUujEi201ZIqdfvfge33w7XXw+TJsH3vnd8t8zxXJiIcmFE\nMqQhWyHV3KVOR45ASQnMnAnPPQc33+x3RSK5SfvcJW22bYNBg+AHP/C+tLpDB78rEpFUaM5dTuAc\nTJsGV18NQ4bAW2+psYsEkUbucswXX3gNfc8eWLnSy14XkWBSc89R8fEBHTvm8ZOfRCguLmDIEIhG\noUULvysUkcbQgmoOShQf0Lx5lJdfLuIXv9COF5Fs05AFVc2556BE8QHV1SUsWlTqY1Uikk5q7jlo\n1y7FB4iEnZp7jtm+HX7/e8UHiISdfptzhHMwYwZceSXcd1+Ezp0VHyASZlpQzQF798Jdd8HOnTB3\nLlxwgeIDRIJE8QPyJ95+22vsgwfDo4/CKaf4XZGIpErxA3LMwYPw8MPel1S/8gpce63fFYlIU9Kc\newitWweXXAIHDsCmTWrsIrlII/cQqa6GCRPg6afhmWegf3+/KxIRv6i5h8SOHV7meqtWsH49dOrk\nd0Ui4ic19wCKz4XJz8+ja9cITz5ZwKhRMHw45GmyTSTnabdMwCTKhWnRIsqbbxbRr5+2MoqEkbJl\nckCiXJgjR0p4+eVSH6sSkWyj5h4wlZXKhRGR+qm5B0h5OWzYoFwYEamfOkIAHD3qbXHs0weKiyN0\n6aJcGBE5OS2oZrmKCi86wAxmzYKCAuXCiOQaZcuEiHNeyNeDD3oxAg89BM2a+V2ViPhB2TIh8eWX\ncM89sHkzLFsG3bv7XZGIBI3m3LPM8uVw8cXQvr2XEaPGLiINoZF7ljh8GEaPhvnz4YUX4IYb/K5I\nRIJMzT0LbN4MAwfCuefCxo1wxhl+VyQiQafm3sRq58KcdVaE6dMLmDjx+K4YEZHGSqq5m1lf4Cm8\nOfqZzrkJtV7/JTAi9vCPwD3Ouc3pLDQMEuXCtGoVZdmyIq65RlsZRSR96l1QNbM8YArQB7gQGGBm\n59c6bAdwjXOuK/AYMCPdhYZBolyYw4dLmD691MeqRCSMktkt0xPY7pyrcM4dAeYBt8Qf4Jxb5Zz7\nKvZwFdAxvWWGQ0WFcmFEpGkk09w7ApVxj3dx8ub998DSxhQVRitWQHm5cmFEpGmkdUHVzHoBdwJX\n13VMcXHxsfuFhYUUFhams4SsU1UFY8fC7NkweXKEf/qn6Alz7l4uTJHfZYpIFikrK6OsrKxR56g3\nfsDMrgCKnXN9Y49HAi7BourFwOtAX+fcx3WcK6fiB7ZsgUGDvDyYGTOgXTvlwohI6jKSLWNmzYBt\nQG/gc2ANMMA592HcMT8ClgO3O+dWneRcOdHca2pgyhR49FEYPx6GDNEWRxFpuIxkyzjnjprZMOAd\njm+F/NDMhnovu+nAGOD7wFQzM+CIc65n6n+F4Nu9G+68E776ClatgnPO8bsiEclFSoVMo9dfh3vv\n9W6jR0NzXSImImmgVEiffP01DB8OK1fC4sVw+eV+VyQiuU578Bpp5Uro1g1atPC+Bk+NXUSygUbu\nKYjPhenQIY/vfz/CG28U8NxzcPPNflcnInKcmnuSEuXCtG4dpaysiJ49tZVRRLKLpmWSlCgX5tCh\nEiZPLvWxKhGRxNTck/TJJ8qFEZHgUHNPwqJFsH69cmFEJDjUmU7iwAG46y741a/gpZcidOkS5XiD\n/y4XJuJfgSIiddBFTHVYtcrLhfnJT+Dpp+G005QLIyL+yEi2TDoFoblXV8Njj8G0aTB1KvzsZ35X\nJCK5TleoNtL27XD77dC2rXdBUn6+3xWJiDSM5twB57xI3iuvhIEDYelSNXYRCbacH7nv3estmu7c\n6X1b0oUX+l2RiEjj5VRzj48P6Ngxj169IowZU8DgwfDqq9Cypd8VioikR84sqCaKD2jePMpLLxUx\nYIB2vIhI9mrIgmrOzLknig+ori7h7bdLfaxKRCQzcqa579ql+AARyR050dx37IAtWxQfICK5I9Sd\nzTkoLfW+QOPuuyN07qz4ABHJDaFdUN23D+6+27swac4cuPhixQeISDApfiBm2TIYMgT694fHH4dW\nrTL+I0VEMibn4wcOHYIRI+DNN2HWLOjd2++KRET8EZo59/JyuPRS74rTjRvV2EUktwW+uR89ChMm\nQJ8+MHo0vPIKnH6631WJiPgr0NMyFRUweDCYwdq1UKC1URERIEDNPT4XJj8/j0svjTB+fAEPPwwP\nPQTNmvldoYhI9gjEbplEuTAtWkRZuLCIm27ScF1Ewi202TKJcmGOHCnhlVdKfaxKRCR7BaK5V1Yq\nF0ZEJBVZ39w3b4aNG5ULIyKSiqztjjU1MGkSXHcdjB4doUsX5cKIiCQrKxdUKyshEoGqKpg9G84+\nW7kwIpK7QpEtM28e3H8/PPCAFyWgLY4ikusCnS2zfz8MGwbr1sGSJdCjh98ViYgEV1bMua9YAd26\nQdu2sH69GruISGMl1dzNrK+ZbTWzj8xsRB3HTDaz7Wa2wcy6JXPeqipv6mXAAJg6Ff71X+HUU1Mp\nX0REEqm3uZtZHjAF6ANcCAwws/NrHXMj0MU595fAUODZ+s67ZQtccQVs2+alOPbr16D6c1pZWZnf\nJYSK3s/00Xvpv2RG7j2B7c65CufcEWAecEutY24BXgJwzq0G2ppZ+0QnGziwhLFjK7j2WrjvPli4\nENq1a8TfIIfpFyi99H6mj95L/yWzoNoRqIx7vAuv4Z/smM9iz+2pfbKXX36Yli2jLF1aRK9e2soo\nIpIJPiyotqGqqoSZM0ub/keLiOSIeve5m9kVQLFzrm/s8UjAOecmxB3zLPBb59z82OOtwLXOuT21\nztV0m+pFREIkE/vc1wLnmFkB8DlwGzCg1jGLgfuA+bF/DPbXbuwNKU5ERBqm3ubunDtqZsOAd/Cm\ncWY65z40s6Hey266c26JmfUzsz/gBcDcmdmyRUTkZJo0fkBERJpGky2oJnMhlCTPzD41s41mVm5m\na/yuJ0jMbKaZ7TGzTXHPnW5m75jZNjNbZmZt/awxSOp4P6NmtsvM1sduff2sMSjMrJOZvW9mW8xs\ns5ndH3s+5c9nkzT3ZC6EkpTVAIXOue7OudpbU+XkXsT7LMYbCbznnDsPeB94pMmrCq5E7yfAJOfc\nJbHbvzd1UQFVDTzonLsQuBK4L9YrU/58NtXIPZkLoSQ1RpZkAwWNc24l8GWtp28BZsXuzwJ+2qRF\nBVgd7yd4n1FJgXPuC+fchtj9A8CHQCca8PlsquaQ6EKojk30s8PKAe+a2Vozu8vvYkLgB9/t8HLO\nfQH8wOd6wmBYLGvqeU1zpc7MzgK6AauA9ql+PjXyC66rnHOXAP3w/q/b1X4XFDLaadA4U4HOzrlu\nwBfAJJ/rCRQz+x6wABgeG8HX/jzW+/lsqub+GfCjuMedYs9JAznnPo/97/8AC/nTSAhJzZ7v8pDM\nrAOw1+d6As059z9x38wzA7jMz3qCxMya4zX22c65RbGnU/58NlVzP3YhlJmdgnch1OIm+tmhY2an\nxv5lx8zaADcAv/e3qsAxTpwTXgxEYvfvABbV/gNyUie8n7EG9J1b0eczFS8A/+2cezruuZQ/n022\nzz22Feppjl8INb5JfnAImdnZeKN1h3ch2ly9n8kzs5eBQuAMvHC7KPAm8BrwQ6AC+Dvn3H6/agyS\nOt7PXnjzxTXAp8DQRFety4nM7CrgA2Az3u+3A0YBa4BXSeHzqYuYRERCSAuqIiIhpOYuIhJCau4i\nIiGk5i4iEkJq7iIiIaTmLiISQmruIiIhpOYuIhJC/w++ajPO6dG1bQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a518a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,1,20) # Tworzy wektor z 20 wartosciami w równych odstępach od 0 do 1\n",
    "print x\n",
    "_ = plt.plot(x, 'o-') # matplotlib naśladuje składnie matlaba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2jTHG/7jXnJk/HxYtKvm6M/kZtWwUyWnJ/Pvuf/tlj4JHM169trM8ZrwaY/xf\nfrNWXaNr9u/PpEGDIMaOjaRx45Lv8ntn3TtMWj+J7x7+jlpVapX4/oqqODNeLckbY0qc+7j3adNK\nb9x7fhZtX8SQhUP49uFvaVKria/DyVdxkrx11xhjSowvZq16YsOBDTw0/yHm/WlemU/wxVXmLxpi\njCmfXK33zZtLd9ZqQfYe28s9H93Dez3e48bLykhQJcha8sYYr3JvvYeHw8aNZSfBHz99nB6zevD3\ndn/nvivu83U4pcL65I0xReZejiAkJIjhwyMZNy6MzZshNrbsJHeA9Ix07vroLsJrhfPOne+Uq5E0\nduLVGFPq4uMTuO22t91mq56kQoUoBg8exptvhpV6zZn8qCqPLXqMxJRE5v95PhWDyldPtZ14NcaU\nuuefP78cQUZGNCdPxpapBA/w2urXWL9/PbPvm13uEnxxBdZfa4zxmsRE35cj8MSczXN4Z/07rBm8\nhuoXVi94BT9jSd4YU2iHD8POnUE4Zqn6phyBJ77b+x1Dlwxl2cBlhNQI8XU4PlF2Xg1jTJnnPnLm\njjsiadLEd+UICrLj6A56f9yb6b2mc3X9q30djs/YiVdjjEfcx727Rs74qhxBQf449Qftp7RnRPsR\nPH79474Op9hsdI0xpsS415wZNMhRWKysnVh1vwD36bOnue3D27i63tV0b9q9XFeQdLHRNcaYEuGq\nGDlmjGPW6rhxZS/Bw7kLcCelJvHwgocJrhxMhmaU6wtwe4u15I0x5ykPrfecktOS6TK9C6pK25C2\njLttXLm+ALe74rTkbXSNMSabslpzpiBTNkzh2Olj7Eraxbw/z/ObBF9c1l1jjAHKds2Zgkz/aToT\nv5/IzQ1vJn54PONXjy/X12X1JuuuMSYAlaeaMwVZ8NsCHlnwCLc2uZV3e7xLcOVgktOSGb18NDFd\nY/yiRW+ja4wxHitPNWcKsiphFffNuY9nb36Wh655KFtCT05LLtcX4HZnffLGGI/lXXNmApUrR/ky\ntEL56eBP3D/nfj667yNubXLreb8v7xfg9hbrkzcmwJSXmjP52XF0Bz1m9eDdHu/mmuDNOZbkjQkg\n2WvOuCtbNWfycyDlALd/eDtRnaK4/4r7fR1OmVc+XlVjTLG4j5y5886yXXMmP0mpSXSb0Y3B1wxm\nyHVDfB1OuWAnXo3xc65x71u2wLRpZbvmTH5OpZ/i9g9v54YGN/B6t9fL1ZWdistG1xhjzuM+azUy\n0lGaoDyPO8IkAAAgAElEQVSNnHGXnpFOr497UbtKbab3mk6QBFYnhI2uMcZk4956L0+zVnOTqZk8\nvOBhBGHqPVMDLsEXlx0tY/yIe99706awYUP5TvCqyoivRhCfFM+cB+ZQqUIlX4dU7lhL3hg/4U+t\nd5eXv3mZ/8b/l1UPreKiShf5OpxyyVryxpRz/tZ6d3n/h/eZ+tNUvhrwlV+UJvAVa8kbU864152p\nXTuIU6ciSUgI85vWO8CnWz7lxVUvsjJyJZdWv9TX4ZRrluSNKUdyqzsTHBzFmjXDaNGibA+B9NTX\nu77micVPsHTgUprWburrcMo9664xphzJre5McnI0L70U68Ooimfx9sVZZYHXJ66n79y+TOs5jcTj\niT6OzD9YkjemnFCFjRvLf92ZnFyX7luXuI67P7qbN7u/yZLfl9il+7zEkrwx5YDrWqv79pXvujO5\nCa4czGPXP0bXD7oy8qaRrN6z2m/qwJcFHr0zRKS7iGwTke0i8nQey0SIyEYR+VVEVng3TGMCU86R\nM99/H0l4ePmsO5OXPcf20HN2T0a2H8moZaMY1WGUJXgvKrCsgYgEAduBrsB+YD3wZ1Xd5rZMTeA7\n4HZVTRSROqp6JJdtWVkDYzyUW80ZKJ91Z/Ky7/g+ImIjGHzNYPYd38eoDqMYv3q8teRzKNHaNSLS\nDohS1Tucj58BVFXHuS3zF+BSVX2hgG1ZkjemAP5UcyY/+1P20ym2Ew+2fpCDJw5mJXZ/u3SfN5R0\n7ZoQYK/b431A2xzLNAcqObtpqgFvqeqHRQnImEDmj7NWc3PwxEG6TO/C4GsGc1Xdq+gQ2iEroQdX\nDiama4zfXLrP17w1Tr4icC3QBcep/zUiskZVd3hp+8b4tZyt9xkz/LP1DnD45GG6TO/CgNYDeObm\nZ3Jdxi7d5z2eJPlEINTt8WXO59ztA46oahqQJiKrgKuB85L8mDFjsu5HREQQERFRuIiN8TOu1vvm\nzf7degc4cuoIXT/oygNXPMBzHZ/zdThlVlxcHHFxcV7Zlid98hWA33CceD0ArAP6qupWt2VaAG8D\n3YELge+BP6nqlhzbsj55Y5zcW++DBkF0tP+23gH+OPUHXT/oSo9mPXipy0sBddGP4irRPnlVzRCR\nocBSHEMup6jqVhF5zPFrnayq20TkK+BnIAOYnDPBGxPocqs5s3u3f9WcyUtSahK3fXgbt4ffbgm+\nlNmVoYwpBYFQcyYvyWnJ3PbhbdwSegv/vP2fluCLoDgt+fI7Tc6YcsQfa8544vjp43Sf0Z32l7W3\nBO8jluSNKWH+WnOmICmnU7hj5h1ce+m1vNn9TUvwPmJJ3pgS5M81Z/Jz8sxJeszqQatLWjHpzkmW\n4H3IP99hxviYe82Z8HD/rDmTl1Ppp7jro7toWrsp7931nl1428fsxKsxXuY+7j021j9rzuQlNT2V\ne2bfw6XVLmVaz2lUCKrg65D8QonWrvEmS/LGnwXauPec0s6m0Wt2Ly6+6GI+6PWBJXgvKunaNcaY\nAgTSrFWXxdsXZ9WcOX32NPfPuZ8qlarwp1Z/sgRfhlhnmTHFkLPvfePGwEjwcO6KTodPHqbPp30Q\nEepXrU/HsI6+Ds24se4aY4oor773QHLoxCHaTWlH09pNCa8Vzqu3vmrlgUuA9ckbU4LcyxGEhATx\n4ouRrF8fFrB97y4nz5zk3o/vpWJQRb7Y8QXxw+NpFNzI12H5JeuTN6aE5FaO4PPPo6hXbxjz54cF\nZOsd4FjaMXrM6kFozVBqVq5J/PB4u6JTGWV98sbkI7dyBCdPRtO2bWzAJvj/nfwfXT7oQqtLWhFc\nOZhXur5Co+BGxHSNYfTy0SSnJfs6ROPGkrwx+UhMzL0cwaFD/luOID+uS/Z1D+/O3c3v5uWuL+d6\nRSdTdlh3jTF5UIX0dFc5AvdE77/lCPITnxTPrR/eyqPXPmpXdCpHAu+daowHXDVnDh6MJCQkMMoR\n5GfbkW10iu3EiHYj8kzwpmyy0TXGuMl5rdUxY+DAAf8vR5Cfnw7+xJ0z7+SVrq8wqM0gX4cTkGwI\npTFe4Br3vmULTJsWmOPec1qzdw29Pu7Fu3e+y31X3OfrcAKWXTTEmGJwn7XatCls2GAJHmD5ruX0\nnN2T6b2mW4Ivx+zEqwlo7q33QKk544mFvy1k8ILBfNrnUytTUM5ZS94EJGu95232r7N5dOGjLO63\n2BK8H7CWvAk41nrP2382/IeouCi+fvBrrqx7pa/DMV5gSd74Nfe6Mw0aBHHjjZG8/HIYkZEwY0Zg\n1pzJy8S1E5m4diJxg+JodnEzX4djvMRG1xi/lVvdmUqVopg9exi9ewfOEMic3OvAA6gqzy5/lg82\nfcCaR9YQWjPUxxGanGx0jTG5yK3uTHp6NJ99FuvDqHzPVQc+OS0ZVeXJL55k8obJrBi0whK8H7Lu\nGuO34uNzrzuzf39g1p1xcdWYeXb5sxxLO8bX8V/zw6M/0LhWY1+HZkqAJXnjd1yzVjdssLozebmw\nwoXEJ8Xz5c4v+eXxXyzB+zF7txu/4qo5Ex0NM2dGEh5udWdyOnLqCBHTI9iZtJNtf93Gv374l5UH\n9mN24tX4hdxqzlSufG50TaDWnclp59GddJvRjZoX1mTZg8uoXaU2yWnJjF4+2i74UYZZ7RoT0Kzm\njGfWJa6j5+ye9G7R+7yEnpyWzOo9q61McBllSd4EpLxa7+Z8C35bwCMLHmFqz6nc1fwuX4djCsmu\n8WoCjqv1vnmzzVotyDvr3iHmmxgW91vMDSE3+DocU8rsxKspV9xrzoSHw8aNluDzkqmZ/GPZP3h7\n3dusfni1JfgAZS15U25Y691zaWfTiPw8ksSURFY/vJqLL7rY1yEZH7Ekb8qkvGrODBpkNWcKcjT1\nKL1m96J+tfosG7iMyhXtYAUyO/FqyhyrOVN0u5N3c8fMO+jRrAev3fYaQWI9sv7AatcYv2I1Z4rm\nx/0/0mFqB564/gkm3D7BErwBPEzyItJdRLaJyHYReTqf5W4QkXQR6e29EE2gsZozhbd4+2K6z+zO\nO3e+w7Abh/k6HFOGFJjkRSQImAR0A1oBfUWkRR7LvQp85e0gTWBwjZw5V3PGndWcycvkHyfzyMJH\nWNh3Ib1a9PJ1OKaM8eS/pi3wu6omqGo6MBvomctyw4BPgcNejM8ECFfNmTFjrOZMfhZvX5xVZyZT\nM3l2+bO8+u2rvBjxIu0ua+fj6ExZ5EmSDwH2uj3e53wui4g0AHqp6r+AIp0cMIEpt3HvvXuHsWzZ\nMPr3n0DnzlH07z+BZcuGBXTNGRdXLfhDJw4xcN5Alu1aRkSjCB5o9YCvQzNllLeGUE4E3PvqLdGb\nAuU37r1x4zBmzIjyXXBlVHDlYEa0H8G1k6/lykuu5Nr61zLutnFWWMzkyZMknwi4Xy7mMudz7q4H\nZouIAHWAO0QkXVUX5NzYmDFjsu5HREQQERFRyJBNeedec8bGvRfOpoOb6PVxL+5udjfvb3if+OHx\nluD9UFxcHHFxcV7ZVoHj5EWkAvAb0BU4AKwD+qrq1jyWnwYsVNXPcvmdjZMPcO6t99hYm7VaGB//\n+jFDvxjKuK7j+PHAj4zqMIr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UHmz9IH2v6ku7y9rZqBhjTLGV6e4a95EzMTEJ/OMf2fvk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\nekligKEAAAABSURBVPSS6EvtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a630cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, x, 'o-', label='liniowa')\n",
    "plt.plot(x, x ** 2, 'x-', label='kwadratowa') # Operacja na wektorze numpy ! x ** 2 podnosi każdy element do kwadratu\n",
    "\n",
    "plt.legend(loc='best')\n",
    "_ = plt.title('Funkcja liniowa vs funkcja kwadratowa')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pierwsze 10 z wylosowanej próby:  [ 1.36959209  0.26680805  0.95946403  1.02949203  0.41623119  1.70655422\n",
      "  0.49042707  1.33225522  0.85912304  0.15838457]\n",
      "Rozmiar próby:  (1000,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a5e3350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Są inne wykresy, np histogram\n",
    "samples = np.random.normal(loc=1.0, scale=0.5, size=1000) # 1000 liczb z rozkładu normalnego\n",
    "print \"Pierwsze 10 z wylosowanej próby: \", samples[0:10] # 10 pierwszych\n",
    "print \"Rozmiar próby: \", samples.shape # rozmiar\n",
    "_ = plt.hist(samples, bins=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a5df390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Inny przykład bez tłumaczenia \n",
    "samples_1 = np.random.normal(loc=1, scale=.5, size=10000) # Rozklad Gaussa\n",
    "samples_2 = np.random.standard_t(df=10, size=10000) # Rozklad studenta t (taki jakby Gauss :))\n",
    "bins = np.linspace(-3, 3, 50)\n",
    "_ = plt.hist(samples_1, bins=bins, alpha=0.5, label='samples 1')\n",
    "_ = plt.hist(samples_2, bins=bins, alpha=0.5, label='samples 2')\n",
    "_ = plt.legend(loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ćwiczenie 2 (1 pkt)\n",
    "\n",
    "Prosze narysowac wylosowac 100 punktow z np.random.uniform z 2 wspolrzednymi i narysowac za pomoc plt.scatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x107643e90>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a810110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([1,2], [1,2]) # Przyklad wywolania plt.scatter"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "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": "2.7.11"
  },
  "toc": {
   "toc_cell": false,
   "toc_number_sections": true,
   "toc_threshold": 6,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}