{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exploring One-Dimensional Data\n",
    "one-dimensional dataset is usually a collection of numbers. An obvious first step is to compute a few summary statistics, like how many data points you have, the smallest, the largest, the mean, and the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 3, 2, 0, 123, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n",
      "26\n",
      "123\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "L = [1,3,2,0,123,23]\n",
    "for i in range(20):\n",
    "    L.append(i)\n",
    "print(L)\n",
    "print(len(L))\n",
    "print(max(L))\n",
    "print(min(L))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A good next step is to create a histogram, in which you group your data into discrete buckets and count how many points fall into each bucket"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import List, Dict\n",
    "from collections import Counter\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "def bucketize(point: float, bucket_size: float) -> float:\n",
    "    \"\"\"Floor the point to the next lower multiple of bucket_size\"\"\"\n",
    "    return bucket_size * math.floor(point / bucket_size)\n",
    "\n",
    "def make_histogram(points: List[float], bucket_size: float) -> Dict[float, int]:\n",
    "    \"\"\"Buckets the points and counts how many in each bucket\"\"\"    \n",
    "    return Counter(bucketize(point, bucket_size) for point in points)\n",
    "\n",
    "def plot_histogram(points: List[float], bucket_size: float, title: str = \"\"):    \n",
    "    histogram = make_histogram(points, bucket_size)    \n",
    "    plt.bar(histogram.keys(), histogram.values(), width=bucket_size)    \n",
    "    plt.title(title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Consider the following two datasets: uniform and normal, what is there mean and statndard deviation?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "random.seed(233)\n",
    "\n",
    "# uniform between -100 and 100\n",
    "uniform = [200 * random.random() - 100 for _ in range(10000)]\n",
    "\n",
    "# normal distribution created by numpy\n",
    "normal = list(np.random.normal(0, 57, 10000))\n",
    "#normal = [57 * inverse_normal_cdf(random.random())          \n",
    "#          for _ in range(10000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## However, they have very different distributions, let's take a look at them by ploting it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "plot_histogram(uniform, 10, \"Uniform Histogram\")\n",
    "plot_histogram(normal, 10, \"Normal Histogram\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Two dimensional data\n",
    "What kind of data is two dimensional? Let's create it by ourself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_normal(mean, std, total=1) ->float:\n",
    "    \"\"\" return random draw from normal distribution \"\"\"\n",
    "    return np.random.normal(mean,std,total)\n",
    "\n",
    "xs = list(random_normal(0,10,1000))\n",
    "ys1 = [x + random_normal(0,10).item() for x in xs]\n",
    "ys2 = [-x + random_normal(0,10).item() for x in xs]\n",
    "\n",
    "#print(ys1)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "plot_histogram(ys1,10, \"ys1\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": [
    "plot_histogram(ys2,10, \"ys2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "plot_histogram(ys1,10, \"ys1\")\n",
    "plot_histogram(ys2,10, \"ys2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## It seems they have similar distribution, but actually they are different"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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(xs, ys1, marker='.', color='black', label='ys1')\n",
    "plt.scatter(xs, ys2, marker='.', color='gray',  label='ys2')\n",
    "plt.xlabel('xs')\n",
    "plt.ylabel('ys')\n",
    "plt.legend(loc=9)\n",
    "plt.title(\"Very Different Joint Distributions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.50820192],\n",
       "       [-0.50820192,  1.        ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(ys1,ys2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Many dimensions\n",
    "Once you have many dimensional data, what can you do to understand the relationship?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# One method is to calculate the pairwise correlation matrix of row[i] and row[j] or for each column. Another method is visualize them. Let's try"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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14.332687334693516, 30.520515916974865, 16.094692365214087, 24.749996051529617, 12.131711093270685, 16.20312787544825, 16.343873167601398, 21.758080711331576, 17.70166862930189, 14.660256521626376, 3.00024744662349, 28.04948352601104, 28.80390625205322, 21.148563544762773, 24.050437852938952, 7.64737112181621, 15.842123321867163, 29.43159283729942, 12.453569294226169, 34.457861144561136, 21.92464513261612, 25.097714782483358, 16.19810468426723, 13.289167801240094, 5.250399659674512, 14.094453034772691, 11.050774782507318, 10.479629620271368, 7.35052727793439, 11.00976722643226, 23.769764687532042, 23.083446299484603, 22.256340585006253, 9.980780544526805, 14.395411875893265, 27.786757570865817, -3.2547066847355275, 26.273568814682264, 19.348437768661928, 24.53353343364876, 18.652663920084287, 8.9856944709395, 34.868874389853225, 5.5669702895701185, 31.873807549208948, 27.639381905581246, 21.911898536561058, 25.469742668727186, 29.26170415733167, 21.09182775957343, 16.14054997729289, 19.00233866386112, 28.181281428034247, 13.767095807467616, 14.34365341984438, 38.72476619046191, 10.919082821933694, 17.6680882384536, 30.068042993406046, 20.01992380590582, -0.3655444420945777, 16.393057162788594, 20.93296677833516, -9.373996981672459, 9.005203643850756, 12.824573534096151, 28.16859205487556, 19.913799041890638, 17.828088414613507, 14.928355181628124, 24.659406189197163, 24.8926311373684, 3.4202252352286493, 6.104305858105031, 14.772667094865554, 30.299519318034637, 19.247345991290988, 24.048712243920573, 13.689312483547816, 21.20474949840462, 38.9254537826324, 20.256508185702426, 13.030737718121006, 37.714288651693124, 22.855703682319234, 9.993416702782778, 16.286395245003803, -9.772741783126794, -21.66428687461847, -10.304604725932265, 25.548237461724703, 20.9280642827227, -1.0276359656260468, 8.031622417040769, 29.7634717607702, 23.312012450389304, 19.46529222468142, 24.624988137489147, 32.82429942088913, 32.45500990174666, 25.79987530052188, 26.77346660188855, 21.80299488537627, 37.92460157938032, 22.501673095422724, 21.787799556662552, 20.99237151593337, 19.800062001854542, 18.59022517633146, 35.21507858108697, 21.425283999167437, 23.50155906000038, 20.208756062385348, 20.162910414366383, 6.738668856659668, 7.720108171447473, 28.281568203834375, 27.043364396939637, 23.189829950179103, 8.878060295543047, 12.053745645173791, 5.191667220691439, 17.07440776639067, 25.618078624272645, 12.932304189602403, 23.333941671988136, 15.879121454463217, 6.437083219920419, 22.797901167961456, 27.95483651063135, 10.173424595867598, 25.80527345881923, 25.74821374022312, 14.462492888565723, 6.489968732882863, 4.471372415961072, 13.678558635880012, 22.69218272989461, 25.082659490595994, 26.146226222458626, 31.541115193425423, 15.783771922651258, 5.007009531919193, 27.329841617121367, 12.388641221283544, 32.543200578669, 24.51791122630967, 34.938310468949695, 16.861605110907433, 25.370042114308013, 13.35434700805342, 4.31969312123625, 56.39681596823562, 21.8752347156651, 23.715674082224456, 9.172247003118372, 26.509830362230772, 32.493008932976856, 14.580834505326624, 25.014123047808738, 21.2835388481819, 21.97953923804592, 21.588550535650278, 21.0060969155311, 23.268908910045738, 28.934385916287717, 16.358914741476593, 40.115603555912735, 25.06970907759179, 39.51101396070887, 14.978768249543059, 23.667419065574, 16.891090916051887, 36.73003726387556, 18.34876642077084, 28.076913796476145, 28.210862942691534, 4.24633182807627, 27.864329559547784, 19.996825010452238, 25.486908180483812, 22.534712654983093, 23.931355666030445, 21.20539646153028, 1.8585546608940078, 28.818043346342343, 15.832624687033874, 18.412223773288133, 10.525381131896822, 18.841361310131543, 14.583694308900057, 32.1273625186406, 24.406889023052052, 29.270100807488117, 6.620641922496869, 14.277276033359323, 2.463761131437799, 37.91663468318508, 26.288040115947503, 17.369151247862646, 11.704197665303669, 14.093380906516433, 9.505702079853098, 24.210601868352278, 17.73472830544039, 30.488547046585772, 31.094917840304145, 19.30361945887205, 33.35767309669101, 19.13227974760672, 22.957523746571347, 18.921596071740094, 8.520539876563138, 41.08388704539968, 25.2136595844575, 26.140035539965766, 11.614101825283228, 19.564209867732966, 25.067902074305685, 0.8515259314536863, 30.691717719019362, 20.80962819260533, 28.458518358055805, 19.36500050510415, 15.18139367977055, 30.630844237819094, 44.547589169258444, 29.748192390005094, 25.50460892204581, 53.81347285941574, 40.98412410661027, 21.51080412988832, 17.777260749690708, 24.761212660456458, 19.170957624754884, 18.94289033474282, 29.190953900006523, 25.91102442663525, 21.77816467179297, 18.981880689411557, 21.672646273334077, 15.233350134516655, 22.46792358743541, 25.6791163078585, 30.701363730872934, 18.112464764906612, 20.177576349974846, 10.670367690404266, 4.970263952505432, 21.633201003984563, 17.011804827508325, 16.112799791345118, 16.701778433176923, 31.13975878974835, 25.908647907294515, 29.16815760499363, 36.91699026760226, 10.0594371124645, 18.211664242412883, 1.3623073219519917, 35.00278314881551, 22.35847756051493, 29.97990464686631, 13.673631746828285, 29.697406332157325, 21.580581763438165, 14.73489156469082, 26.384859984435305, 19.500538948066488, 16.386826398838217, 18.966346269427913, 22.274138248385466, 32.5103971783909, 26.526695615314907, 17.28624000861138, 18.247656044630784, 13.00604878519649, 7.594651980659934, 16.782024887769605, 28.02123025144991, 29.189847980346443, 27.898568858908725, 27.442742647060268, 14.956008249489296, 20.8842971885263, 14.846464071572745, 42.63166761262368, 27.762723004859218, 27.707194041750636, 21.488244221167882, 21.337996952262124, 24.489081702719464, 26.04282009953721, 19.453957665507968, 23.38731523244711, 14.840908197861097, -2.3462718695811375, 27.103591861419186, 27.839751064926467, 29.46528326091332]]\n"
     ]
    }
   ],
   "source": [
    "corr_data = [[200 * random.random() - 100 for _ in range(1000)],list(random_normal(0,10,1000)), \n",
    "             list(-1*random_normal(0,10,1000)),list(20-random_normal(0,10,1000))]\n",
    "print(corr_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_vectors = len(corr_data)\n",
    "fig, ax = plt.subplots(num_vectors, num_vectors)      # plt.subplots would allow us to create subplots\n",
    "\n",
    "for i in range(num_vectors):\n",
    "    for j in range(num_vectors):\n",
    "\n",
    "        # Scatter column_j on the x-axis vs. column_i on the y-axis\n",
    "        if i != j: ax[i][j].scatter(corr_data[j], corr_data[i])\n",
    "\n",
    "        # unless i == j, in which case show the series name\n",
    "        else: ax[i][j].annotate(\"series \" + str(i), (0.5, 0.5),\n",
    "                                xycoords='axes fraction',\n",
    "                                ha=\"center\", va=\"center\")\n",
    "\n",
    "        # Then hide axis labels except left and bottom charts\n",
    "        if i < num_vectors - 1: ax[i][j].xaxis.set_visible(False)\n",
    "        if j > 0: ax[i][j].yaxis.set_visible(False)\n",
    "\n",
    "# Fix the bottom-right and top-left axis labels, which are wrong because\n",
    "# their charts only have text in them\n",
    "ax[-1][-1].set_xlim(ax[0][-1].get_xlim())\n",
    "ax[0][0].set_ylim(ax[0][1].get_ylim())\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now could you try to create another corr_data with different kind of data, and run your script to draw correlation pictures?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to understand multidimentional data like Stock? For example,\n",
    "AAPL,6/20/2014,90.91 <br>\n",
    "MSFT,6/20/2014,41.68<br>\n",
    "FB,6/20/3014,64.5<br>\n",
    "AAPL,6/19/2014,91.86<br>\n",
    "MSFT,6/19/2014,n/a<br>\n",
    "FB,6/19/2014,64.34<br>\n",
    "Any ideas to represent this data? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One way to represent this is by using dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime\n",
    "\n",
    "stock_price = {'closing_price': 102.06,\n",
    "               'date': datetime.date(2014, 8, 29),\n",
    "               'symbol': 'AAPL'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Issues: need a lot of memory, accessing things by dict key is error-prone:\n",
    "#oops, typo\n",
    "stock_price['cosing_price'] = 103.06"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Another solution: namedtuple class, tuple with named slots. Like regular tuples, namedtuples are immutable, which means that you can’t modify their values once they’re created. Occasionally this will get in our way, but mostly that’s a good thing. Let's see the following example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import namedtuple\n",
    "\n",
    "StockPrice = namedtuple('StockPrice', ['symbol', 'date', 'closing_price'])\n",
    "price = StockPrice('MSFT', datetime.date(2018, 12, 14), 106.03)\n",
    "\n",
    "assert price.symbol == 'MSFT'\n",
    "assert price.closing_price == 106.03\n",
    "\n",
    "# now let's solve the type annotation issue\n",
    "from typing import NamedTuple\n",
    "\n",
    "class StockPrice(NamedTuple):\n",
    "    symbol: str\n",
    "    date: datetime.date\n",
    "    closing_price: float\n",
    "\n",
    "    def is_high_tech(self) -> bool:\n",
    "        \"\"\"It's a class, so we can add methods too\"\"\"\n",
    "        return self.symbol in ['MSFT', 'GOOG', 'FB', 'AMZN', 'AAPL']\n",
    "\n",
    "price = StockPrice('MSFT', datetime.date(2018, 12, 14), 106.03)\n",
    "\n",
    "assert price.symbol == 'MSFT'               # so now you have to use price.symbol, this will avoid your typos.\n",
    "assert price.closing_price == 106.03\n",
    "assert price.is_high_tech()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cleaning and Munging.\n",
    "Real-world data is dirty. Often you’ll have to do some work on it before you can use it. For example, you may need to convert strings to floats or ints, check missing values and outliers and bad data:\n",
    "closing_price = float(row[2])\n",
    "Let's write a function to do the parsing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dateutil.parser import parse\n",
    "\n",
    "def parse_row(row: List[str]) -> StockPrice:\n",
    "    symbol, date, closing_price = row\n",
    "    return StockPrice(symbol=symbol,\n",
    "                      date=parse(date).date(),\n",
    "                      closing_price=float(closing_price))\n",
    "\n",
    "# Now test our function\n",
    "stock = parse_row([\"MSFT\", \"2018-12-14\", \"106.03\"])\n",
    "\n",
    "assert stock.symbol == \"MSFT\"\n",
    "assert stock.date == datetime.date(2018, 12, 14)\n",
    "assert stock.closing_price == 106.03"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How about bad data? Please try the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "could not convert string to float: 'oh my data'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-5e611a54abd8>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mstock\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparse_row\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"MSFT\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"2018-12-14\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"oh my data\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-34-6ca1c26ff5a7>\u001b[0m in \u001b[0;36mparse_row\u001b[0;34m(row)\u001b[0m\n\u001b[1;32m      5\u001b[0m     return StockPrice(symbol=symbol,\n\u001b[1;32m      6\u001b[0m                       \u001b[0mdate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mparse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m                       closing_price=float(closing_price))\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;31m# Now test our function\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: could not convert string to float: 'oh my data'"
     ]
    }
   ],
   "source": [
    "stock = parse_row([\"MSFT\", \"2018-12-14\", \"oh my data\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maybe it should return None instead of crash? Let's see this function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Optional\n",
    "import re\n",
    "\n",
    "def try_parse_row(row: List[str]) -> Optional[StockPrice]:\n",
    "    symbol, date_, closing_price_ = row\n",
    "\n",
    "    # Stock symbol should be all capital letters\n",
    "    if not re.match(r\"^[A-Z]+$\", symbol):\n",
    "        return None\n",
    "\n",
    "    try:\n",
    "        date = parse(date_).date()\n",
    "    except ValueError:\n",
    "        return None\n",
    "\n",
    "    try:\n",
    "        closing_price = float(closing_price_)\n",
    "    except ValueError:\n",
    "        return None\n",
    "\n",
    "    return StockPrice(symbol, date, closing_price)\n",
    "\n",
    "# Should return None for errors\n",
    "assert try_parse_row([\"MSFT0\", \"2018-12-14\", \"106.03\"]) is None\n",
    "assert try_parse_row([\"MSFT\", \"2018-12--14\", \"106.03\"]) is None\n",
    "assert try_parse_row([\"MSFT\", \"2018-12-14\", \"x\"]) is None\n",
    "\n",
    "# But should return same as before if data is good\n",
    "assert try_parse_row([\"MSFT\", \"2018-12-14\", \"106.03\"]) == stock"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try to create a CSV file \"comma_delimited_stock_prices.csv\" with the following data:<br>\n",
    "AAPL,6/20/2014,90.91 <br>\n",
    "MSFT,6/20/2014,41.68 <br>\n",
    "FB,6/20/3014,64.5<br>\n",
    "AAPL,6/19/2014,91.86<br>\n",
    "MSFT,6/19/2014,n/a<br>\n",
    "FB,6/19/2014,64.34<br>\n",
    "And then run the following function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "skipping invalid row: ['MSFT', '6/19/2014', 'n/a']\n"
     ]
    }
   ],
   "source": [
    "import csv\n",
    "\n",
    "data: List[StockPrice] = []\n",
    "\n",
    "with open(\"comma_delimited_stock_prices.csv\") as f:\n",
    "    reader = csv.reader(f)\n",
    "    for row in reader:\n",
    "        maybe_stock = try_parse_row(row)\n",
    "        if maybe_stock is None:\n",
    "            print(f\"skipping invalid row: {row}\")\n",
    "        else:\n",
    "            data.append(maybe_stock)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Think about what else error in your data? Any outliers? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Manipulating Data\n",
    "One of the most important skills of a data scientist is manipulating data. It’s more of a general approach than a specific technique, so we’ll just work through a handful of examples to give you the flavor of it. <br>\n",
    "Continue the stock data example, now I want to know the highest-ever closing price for AAPL, what can we do? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "91.86\n"
     ]
    }
   ],
   "source": [
    "max_aapl_price = max(StockPrice.closing_price\n",
    "                     for StockPrice in data\n",
    "                     if StockPrice.symbol == \"AAPL\")\n",
    "print(max_aapl_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More generally, how to find the highest-ever closing price for each stock? \n",
    "Idea: Create a dict to keep track of highest prices (we’ll use a defaultdict that returns minus infinity for missing values, since any price will be greater than that).<br>\n",
    "Iterate over our data, updating it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "defaultdict(<function <lambda> at 0x1199ea598>, {'AAPL': 91.86, 'MSFT': 41.68, 'FB': 64.5})\n"
     ]
    }
   ],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "max_prices: Dict[str, float] = defaultdict(lambda: float('-inf'))\n",
    "\n",
    "for sp in data:\n",
    "    symbol, closing_price = sp.symbol, sp.closing_price\n",
    "    if closing_price > max_prices[symbol]:\n",
    "        max_prices[symbol] = closing_price\n",
    "\n",
    "print(max_prices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now we coud do some more complicated things\n",
    "Such as the largest and smallest changes? The per-day change could be calculated by: price_today / price_yesterday - 1. Ideas?  <br>\n",
    "\n",
    "1. Order the prices by date. <br>\n",
    "\n",
    "2. Use zip to get (previous, current) pairs. <br>\n",
    "\n",
    "3. Turn the pairs into new “percent change” rows. <br>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import List\n",
    "from collections import defaultdict\n",
    "\n",
    "# Collect the prices by symbol\n",
    "prices: Dict[str, List[StockPrice]] = defaultdict(list)\n",
    "\n",
    "for sp in data:\n",
    "    prices[sp.symbol].append(sp)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Order the prices by date. \n",
    "prices = {symbol: sorted(symbol_prices)\n",
    "          for symbol, symbol_prices in prices.items()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[DailyChange(symbol='AAPL', date=datetime.date(2014, 6, 20), pct_change=-0.0103418245155672), DailyChange(symbol='FB', date=datetime.date(3014, 6, 20), pct_change=0.0024867889337891746)]\n"
     ]
    }
   ],
   "source": [
    "# compute a sequence of day-over-day changes\n",
    "def pct_change(yesterday: StockPrice, today: StockPrice) -> float:\n",
    "    return today.closing_price / yesterday.closing_price - 1\n",
    "\n",
    "class DailyChange(NamedTuple):\n",
    "    symbol: str\n",
    "    date: datetime.date\n",
    "    pct_change: float\n",
    "\n",
    "def day_over_day_changes(prices: List[StockPrice]) -> List[DailyChange]:\n",
    "    \"\"\"\n",
    "    Assumes prices are for one stock and are in order\n",
    "    \"\"\"\n",
    "    return [DailyChange(symbol=today.symbol,\n",
    "                        date=today.date,\n",
    "                        pct_change=pct_change(yesterday, today))\n",
    "            for yesterday, today in zip(prices, prices[1:])]\n",
    "\n",
    "# now get all of them\n",
    "all_changes = [change\n",
    "               for symbol_prices in prices.values()\n",
    "               for change in day_over_day_changes(symbol_prices)]\n",
    "print(all_changes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FB\n",
      "3014-06-20\n",
      "0.0024867889337891746\n",
      "AAPL\n",
      "2014-06-20\n",
      "-0.0103418245155672\n"
     ]
    }
   ],
   "source": [
    "# now we could find the largest and smallest\n",
    "max_change = max(all_changes, key=lambda change: change.pct_change)\n",
    "print(max_change.symbol)\n",
    "print(max_change.date)\n",
    "print(max_change.pct_change)\n",
    "\n",
    "min_change = min(all_changes, key=lambda change: change.pct_change)\n",
    "print(min_change.symbol)\n",
    "print(min_change.date)\n",
    "print(min_change.pct_change)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-54-460953c9d575>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      8\u001b[0m avg_daily_change = {\n\u001b[1;32m      9\u001b[0m     \u001b[0mmonth\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchange\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpct_change\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchange\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchanges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchanges\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m     \u001b[0;32mfor\u001b[0m \u001b[0mmonth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchanges\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchanges_by_month\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m }\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-54-460953c9d575>\u001b[0m in \u001b[0;36m<dictcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      8\u001b[0m avg_daily_change = {\n\u001b[1;32m      9\u001b[0m     \u001b[0mmonth\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchange\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpct_change\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mchange\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchanges\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchanges\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m     \u001b[0;32mfor\u001b[0m \u001b[0mmonth\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchanges\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchanges_by_month\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     11\u001b[0m }\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "# Now we could try to use this to find out which month is the best to invest? \n",
    "# Let's just check the average daily change by month\n",
    "changes_by_month: List[DailyChange] = {month: [] for month in range(1, 13)}\n",
    "\n",
    "for change in all_changes:\n",
    "    changes_by_month[change.date.month].append(change)\n",
    "\n",
    "avg_daily_change = {\n",
    "    month: sum(change.pct_change for change in changes) / len(changes)\n",
    "    for month, changes in changes_by_month.items()\n",
    "}\n",
    "\n",
    "# If October is the best month, we could find it now\n",
    "#assert avg_daily_change[10] == max(avg_daily_change.values())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rescaling\n",
    "Many techniques are sensitive to the scale of your data. For example, imagine that you have a dataset consisting of the heights and weights of hundreds of data scientists, and that you are trying to identify clusters of body sizes. \n",
    "Like A has height and weight 63, 120, B has height and weight 67, 200, etc. You could directly compare but maybe height is in the range of 0 and 100, but weight in the range of 0 and 300, they are not in the same scale, the general idea is to rescale each data so they are all in the distribution of mean 0 and standard deviation 1, please read book for example of details. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# tqdm\n",
    "Frequently we’ll end up doing computations that take a long time. When you’re doing such work, you’d like to know that you’re making progress and how long you should expect to wait. <br>\n",
    "You should first install: python -m pip install tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:12<00:00,  8.38it/s]\n"
     ]
    }
   ],
   "source": [
    "import tqdm\n",
    "\n",
    "for i in tqdm.tqdm(range(100)):\n",
    "    # do something slow\n",
    "    _ = [random.random() for _ in range(1000000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "6802 primes:  68%|██████▊   | 68375/99997 [00:48<00:24, 1306.79it/s]"
     ]
    }
   ],
   "source": [
    "# Practice the following example\n",
    "from typing import List\n",
    "\n",
    "def primes_up_to(n: int) -> List[int]:\n",
    "    primes = [2]\n",
    "\n",
    "    with tqdm.trange(3, n) as t:\n",
    "        for i in t:\n",
    "            # i is prime if no smaller prime divides it\n",
    "            i_is_prime = not any(i % p == 0 for p in primes)\n",
    "            if i_is_prime:\n",
    "                primes.append(i)\n",
    "\n",
    "            t.set_description(f\"{len(primes)} primes\")\n",
    "\n",
    "    return primes\n",
    "\n",
    "my_primes = primes_up_to(100_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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