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   "cell_type": "code",
   "execution_count": null,
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     "end_time": "2019-02-20T12:55:25.150873Z",
     "start_time": "2019-02-20T12:55:24.620811Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from random import sample\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## exercise 1.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:55:26.077169Z",
     "start_time": "2019-02-20T12:55:26.067921Z"
    }
   },
   "outputs": [],
   "source": [
    "def fx(x): # target line\n",
    "    return(-0.7 * x + 1)\n",
    "# build random data x_i in [0,1] with bias term\n",
    "xi = np.column_stack((np.ones(20), np.random.rand(20,2)))\n",
    "yi = (fx(xi[:,1]) > xi[:,2]) # T/F vector\n",
    "# xi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:55:26.761259Z",
     "start_time": "2019-02-20T12:55:26.755219Z"
    }
   },
   "outputs": [],
   "source": [
    "yp = np.zeros(20) # build target vec in {-1, 1}\n",
    "yp[yi] = 1\n",
    "yp[np.logical_not(yi)] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:55:27.619844Z",
     "start_time": "2019-02-20T12:55:27.284779Z"
    }
   },
   "outputs": [],
   "source": [
    "# plot data with f(x)\n",
    "plt.scatter(xi[:,1], xi[:,2], c=yp)\n",
    "plt.plot(np.arange(0,1,.1), fx(np.arange(0,1,.1)))\n",
    "plt.savefig(\"aml_e1.4_fx.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:55:38.064284Z",
     "start_time": "2019-02-20T12:55:38.056503Z"
    },
    "code_folding": [
     0
    ]
   },
   "outputs": [],
   "source": [
    "def fwd(x, y, w):\n",
    "    ''' predict function \n",
    "        in: x, y, current weights \n",
    "        out: vector w/ True for misses '''\n",
    "    yh = x @ w\n",
    "    yh[yh > 0] = 1\n",
    "    yh[yh < 0] = -1\n",
    "    \n",
    "    return(yh.T != y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:55:46.651852Z",
     "start_time": "2019-02-20T12:55:46.631850Z"
    }
   },
   "outputs": [],
   "source": [
    "w = np.random.rand(xi.shape[1],1) * 2 - 1 #random init weights [-1,1]\n",
    "neq = fwd(xi, yp, w)\n",
    "while np.sum(neq): # while some misses\n",
    "    # randomly choose a datapoint where x misclassified\n",
    "    ud = np.random.choice(np.where(neq==True)[1], 1) \n",
    "    w = w + yp[ud] * xi[ud].T # update w\n",
    "    neq = fwd(xi, yp, w) # get new miss vector\n",
    "    print(np.sum(neq)) # show improvement\n",
    "print(w) # final weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T12:59:46.858343Z",
     "start_time": "2019-02-20T12:59:46.850840Z"
    }
   },
   "outputs": [],
   "source": [
    "print(w[1] / w[2]) # get slope\n",
    "print(w[0] / w[2]) # get bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T13:00:51.666033Z",
     "start_time": "2019-02-20T13:00:51.661232Z"
    }
   },
   "outputs": [],
   "source": [
    "## b + w1x1 + w2x2 = 0 ##\n",
    "wfxn = -((np.arange(0,1,.1) * (w[1])) + w[0])/w[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-20T13:00:52.706379Z",
     "start_time": "2019-02-20T13:00:52.433112Z"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "plt.scatter(x=xi[:,1], y = xi[:,2], c=yp)\n",
    "plt.plot(np.arange(0,1,.1), wfxn)\n",
    "plt.savefig(\"aml_e1.4_gx.png\")"
   ]
  }
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