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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "00ff462d",
   "metadata": {},
   "source": [
    "## Machine Learning\n",
    "### Radial basis functions (RBFs)\n",
    "A **radial basis function** (RBF) is a **radial function** which is **positive definite**. It means that the **interpolation** matrix is invertible (nonsingular). A radial function $\\phi$ is only dependent on the distance from a center point $\\boldsymbol{c}$ and not on the direction:\n",
    "<br>$\\large \\phi(\\boldsymbol{x},\\boldsymbol{c})=\\phi(r)$ where $r=||\\boldsymbol{x}-\\boldsymbol{c}||$\n",
    "<br> The radial basis function $\\phi$ is **stricly positive definite** if for any set of distinct numbers $\\boldsymbol{x}_1, \\boldsymbol{x}_2,...,\\boldsymbol{x}_N$; the interpolation matrix defined below is **nonsingular** (all its **eigenvalues** are positive):\n",
    "<br>$\\phi_{ji}=\\phi(||\\boldsymbol{x}_j-\\boldsymbol{x}_i||)$\n",
    "<br> In the following we display three strictly positive definite RBFs.\n",
    "<hr>\n",
    "The Python code at: https://github.com/ostad-ai/Machine-Learning\n",
    "<br> Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning//background-knowledge/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f1b89b47",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the required modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6526c664",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define strictly PD RBFs\n",
    "# The epsilon > 0 in these functions are called the shape parameter\n",
    "def gaussian(r, eps=1.0):\n",
    "    return np.exp(-(eps * r)**2)\n",
    "\n",
    "def inverse_quadric(r, eps=1.0):\n",
    "    return 1 / (1 + (eps * r)**2)\n",
    "\n",
    "def matern32(r, eps=1.0):\n",
    "    return (1 + np.sqrt(3) * eps * r) * np.exp(-np.sqrt(3) * eps * r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6fe62a96",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the three RBFs\n",
    "\n",
    "# Generate distance values\n",
    "r = np.linspace(0, 5, 500)  # Distance from center\n",
    "\n",
    "# Compute RBF values\n",
    "phi_gaussian = gaussian(r)\n",
    "phi_inverse_quadric = inverse_quadric(r)\n",
    "phi_matern32 = matern32(r)\n",
    "\n",
    "# Plot\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(r, phi_gaussian, label=\"Gaussian: $e^{-(\\\\epsilon r)^2}$\", linewidth=3)\n",
    "plt.plot(r, phi_inverse_quadric, label=\"Inverse Quadric: $1/(1 + (\\\\epsilon r)^2)$\", linestyle=\"--\")\n",
    "plt.plot(r, phi_matern32, label=\"Matérn (ν=3/2): $(1 + \\sqrt{3}\\\\epsilon r)e^{-\\sqrt{3}\\\\epsilon r}$\", linestyle=\"-.\")\n",
    "\n",
    "# Customize plot\n",
    "plt.title(\"Strictly Positive Definite (PD) Radial Basis Functions\", fontsize=14)\n",
    "plt.xlabel(\"Distance from center ($r$)\", fontsize=12)\n",
    "plt.ylabel(\"$\\\\phi(r)$\", fontsize=12)\n",
    "plt.legend(fontsize=10)\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.ylim(-0.1, 1.1)  # Adjust y-axis limits\n",
    "\n",
    "# Highlight key properties\n",
    "plt.annotate(\n",
    "    \"All functions are positive definite\\n(guarantee invertible interpolation)\",\n",
    "    xy=(2.5, 0.5), xytext=(3, 0.7),\n",
    "    arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "    fontsize=10,\n",
    ")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f0be7c5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}