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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#!/usr/env/python\n",
    "\n",
    "# Python version of RBF fitting\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate noisy sine wave\n",
    "x = np.linspace(0,10,100)\n",
    "y = np.sin(3*x) + np.random.randn(x.size)*.5\n",
    " \n",
    "# Define RBF atom\n",
    "# two options:\n",
    "#   inline function definition (not available in matlab)\n",
    "#   lambda : like @ in matlab\n",
    "\n",
    "sig = 2\n",
    "# option 1\n",
    "# def rbf(x,c):\n",
    "#     return np.exp(-(x-c)**2/sig**2)\n",
    "# option 2\n",
    "rbf = lambda x,c : np.exp(-(x-c)**2/sig**2)\n",
    "\n",
    "# create design matrix\n",
    "# (use list comprehension to show off)\n",
    "xi     = np.linspace(0,10,15)\n",
    "desmat = [rbf(x,c) for c in xi] \n",
    "desmat = np.asarray(desmat).T\n",
    "\n",
    "# invert model\n",
    "beta   = np.linalg.pinv(desmat)@y.T\n",
    "\n",
    "# plot fit\n",
    "plt.figure()\n",
    "plt.plot(x,y,'.')\n",
    "plt.plot(x,desmat,'k') \n",
    "plt.plot(x,desmat@beta)\n",
    "\n",
    "\n",
    "# make it pretty\n",
    "plt.grid()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title('RBF fitting')\n",
    "plt.savefig('/Users/saad/Desktop/RBF.pdf')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}