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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import Library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pylab import rcParams\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "%matplotlib inline\n",
    "rcParams['figure.figsize'] = 8, 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate Sin(x) Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define input array with angles from 60deg to 300deg converted to radians\n",
    "x = np.array([i*np.pi/180 for i in range(60, 300, 4)])\n",
    "np.random.seed(100)  # Setting seed for reproducability\n",
    "y = np.sin(x) + np.random.normal(0, 0.15, len(x))  # 加上雜訊\n",
    "\n",
    "data = pd.DataFrame(np.column_stack([x, y]), columns=['x', 'y'])\n",
    "plt.plot(data['x'], data['y'], '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate New Features with higher power \n",
    "自行產生新的feature，x^2～x^15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(2, 16):  # power of 1 is already there\n",
    "    colname = 'x_%d' % i      # new var will be x_power\n",
    "    data[colname] = data['x']**i\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 0. Function definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression, Lasso, Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def example_regression(data, power, plot_dict, reg_type, alpha = 0):\n",
    "    # define estimator object\n",
    "    type_dict = {'Linear':LinearRegression(),\n",
    "                 'Lasso':Lasso(alpha = alpha),\n",
    "                 'Ridge':Ridge(alpha = alpha)}\n",
    "    \n",
    "    # generate X in order\n",
    "    X = ['x']\n",
    "    if power >=2:\n",
    "        X.extend(['x_%d'%i for i in range(2, power+1)])\n",
    "    \n",
    "    # fit the model\n",
    "    if reg_type in type_dict:\n",
    "        model = type_dict[reg_type]\n",
    "    model.fit(data[X],data['y'])\n",
    "    y_pred = model.predict(data[X])\n",
    "    mae = mean_absolute_error(y_pred, y)\n",
    "    # check if a plot is to be made for the entered power\n",
    "    if power in plot_dict:\n",
    "        plt.subplot(plot_dict[power])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'], data['y'], '.')\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.title('Plot for power: %d'%power + '\\n' + 'mae:%.2f'%mae)\n",
    "        \n",
    "    # return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([model.intercept_])\n",
    "    ret.extend(model.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize a dataframe to store the results:\n",
    "col = ['rss', 'intercept'] + ['coef_x_%d' % i for i in range(1, 16)]\n",
    "ind = ['pow_%d' % i for i in range(1, 16)]\n",
    "\n",
    "perf_Linear = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "# define the powers for which a plot is required: {power:where}\n",
    "plot_dict = {1:231, 3:232, 6:233, 9:234, 12:235, 15:236}\n",
    "\n",
    "# iterate through all powers and assimilate results\n",
    "for i in range(1, 16):\n",
    "    perf_Linear.iloc[i-1, 0:i+2] = example_regression(data, power=i, plot_dict=plot_dict, reg_type='Linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "perf_Linear"
   ]
  }
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