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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit 3rd order Polynomial to graph data using scikit-learn, more infos\n",
    "https://www.datatechnotes.com/2018/06/polynomial-regression-fitting-in-python.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.rcParams[\"font.size\"] = 20\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], dtype='d')\n",
    "dx =  np.array([0.1,0.1,0.5,0.1,0.5,0.1,0.5,0.1,0.5,0.1], dtype='d')\n",
    "y = np.array([1.1 ,2.3 ,2.7 ,3.2 ,3.1 ,2.4 ,1.7 ,1.5 ,1.5  ,1.7 ], dtype='d')\n",
    "dy = np.array([0.15,0.22,0.29,0.39,0.31,0.21,0.13,0.15,0.19,0.13], dtype='d')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " building polynomial model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "polyModel = PolynomialFeatures(degree = 3)\n",
    "xpol = polyModel.fit_transform(x.reshape(-1, 1))\n",
    "preg = polyModel.fit(xpol,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Building linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "linearModel = LinearRegression(fit_intercept = True)\n",
    "linearModel.fit(xpol, y[:, np.newaxis])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_plot = np.linspace(0.1,10.1,200)\n",
    "polyfit = linearModel.predict(preg.fit_transform(x_plot.reshape(-1, 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " plot data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.errorbar(x, y, dy , dx, fmt=\"o\")\n",
    "plt.plot(x_plot, polyfit )\n",
    "plt.title(\"scikit-learn Fit Test\")\n",
    "plt.xlim(-0.1, 10.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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