{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from matplotlib import gridspec\n",
    "from mpl_toolkits.axes_grid.axislines import SubplotZero\n",
    "\n",
    "plt.xkcd()\n",
    "\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2290135f9e8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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G8p4jQojClAdPNptVXYIQosiUBk9+syMhRGlRGjwWi+WYF6UXQow9SoPHbrfr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\neIQQRff/AHsWW3H0takUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x229012f98d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(1)\n",
    "fig.set_size_inches(4,4)\n",
    "ax = SubplotZero(fig, 111)\n",
    "fig.add_subplot(ax)\n",
    "\n",
    "for k,v in [(\"xzero\", \"\"), (\"yzero\", \"\")]:\n",
    "    ax.axis[k].set_axisline_style(\"-|>\")\n",
    "    ax.axis[k].set_visible(True)\n",
    "    ax.axis[k].set_label(v)\n",
    "    ax.axis[k].set_zorder(-20)\n",
    "\n",
    "ax.xaxis.set_ticks((0,1))\n",
    "ax.yaxis.set_ticks((1,))\n",
    "\n",
    "for direction in [\"left\", \"right\", \"bottom\", \"top\"]:\n",
    "    ax.axis[direction].set_visible(False)\n",
    "\n",
    "ax.scatter((0,1), (1,0), marker=\"x\", s=250, lw=5, facecolor=\"#08519c\")\n",
    "\n",
    "ax.text(1.1, 0.4,\n",
    "        \"~0 = 1\\n~1 = 0\",\n",
    "        style=\"italic\",\n",
    "        bbox={\"facecolor\": 'grey', 'alpha':0.5, 'pad': 10})\n",
    "plt.title('NOT')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1. / (1 + np.exp(-z))\n",
    "\n",
    "activate = np.vectorize(sigmoid, otypes=[np.dtype('float64')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def threshold(a):\n",
    "    if a >= 0.5:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "h = np.vectorize(threshold, otypes=[np.dtype('int8')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def create_training_set(Truth, m):\n",
    "    rows, cols = Truth.shape\n",
    "    \n",
    "    train = np.ones(shape=(m, cols+1))\n",
    "    train[:, 1:cols+1] = np.vstack(Truth[np.random.randint(0, rows, size=m)])\n",
    "    X = train[:, 0:cols]\n",
    "    y = train[:, cols:cols+1]\n",
    "    \n",
    "    return X,y\n",
    "\n",
    "def predict(theta, X):\n",
    "    z = X.dot(theta.T)\n",
    "    a = activate(z)\n",
    "    return h(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost(theta, X, y):\n",
    "    theta = np.matrix(theta)\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    \n",
    "    z = X.dot(theta.T).sum(axis=1)\n",
    "    a = activation(z)\n",
    "    y_hat = h(a)\n",
    "    \n",
    "    cost_simple = np.add(np.multiply(y, np.log1p(y_hat)),\n",
    "                         np.multiply(1-y, np.log1p(1-y_hat)))\n",
    "    \n",
    "    reg = (LAMBDA/2) * np.square(theta[:, 1:X.shape[1]]).sum()\n",
    "    \n",
    "    cost = (-1./m) * (cost_simple.sum() + reg)\n",
    "    \n",
    "    return cost"
   ]
  }
 ],
 "metadata": {
  "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",
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