gaussian_process_demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import copy as cp\n",
    "import numpy as np\n",
    "import GPy\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fcabf105b50>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def test(a=1, b=1, x = np.linspace(0, 10, 100)):\n",
    "    return np.sin(a*x) + np.sin(b*x)\n",
    "\n",
    "plt.plot(test(a=0.2, b=0.8))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.74554342 0.93848961 2.17995315 9.75503157 0.88363739]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fcabf093ac0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Training data\n",
    "training_data = np.random.uniform(low=0., high=10., size=5)\n",
    "print(training_data)\n",
    "training_data_y = test(a=0.2, b=0.8, x=training_data)\n",
    "plt.scatter(training_data, training_data_y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernal = GPy.kern.RBF(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "gp = GPy.models.GPRegression(training_data.reshape(-1, 1), training_data_y.reshape(-1, 1), kernel=kernal, noise_var=1.e-10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "66c4b0429b764c26ab45ad4233b2b019"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<paramz.optimization.optimization.opt_tnc at 0x7fcabf055340>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp.optimize(messages=True, optimizer='tnc')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.1010101   0.2020202   0.3030303   0.4040404   0.50505051\n",
      "  0.60606061  0.70707071  0.80808081  0.90909091  1.01010101  1.11111111\n",
      "  1.21212121  1.31313131  1.41414141  1.51515152  1.61616162  1.71717172\n",
      "  1.81818182  1.91919192  2.02020202  2.12121212  2.22222222  2.32323232\n",
      "  2.42424242  2.52525253  2.62626263  2.72727273  2.82828283  2.92929293\n",
      "  3.03030303  3.13131313  3.23232323  3.33333333  3.43434343  3.53535354\n",
      "  3.63636364  3.73737374  3.83838384  3.93939394  4.04040404  4.14141414\n",
      "  4.24242424  4.34343434  4.44444444  4.54545455  4.64646465  4.74747475\n",
      "  4.84848485  4.94949495  5.05050505  5.15151515  5.25252525  5.35353535\n",
      "  5.45454545  5.55555556  5.65656566  5.75757576  5.85858586  5.95959596\n",
      "  6.06060606  6.16161616  6.26262626  6.36363636  6.46464646  6.56565657\n",
      "  6.66666667  6.76767677  6.86868687  6.96969697  7.07070707  7.17171717\n",
      "  7.27272727  7.37373737  7.47474747  7.57575758  7.67676768  7.77777778\n",
      "  7.87878788  7.97979798  8.08080808  8.18181818  8.28282828  8.38383838\n",
      "  8.48484848  8.58585859  8.68686869  8.78787879  8.88888889  8.98989899\n",
      "  9.09090909  9.19191919  9.29292929  9.39393939  9.49494949  9.5959596\n",
      "  9.6969697   9.7979798   9.8989899  10.        ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fcabcf84bb0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Test data\n",
    "test_data = np.linspace(0., 10., num=100)\n",
    "print(test_data)\n",
    "test_data_y = test(a=0.2, b=0.8, x=test_data)\n",
    "plt.scatter(test_data, test_data_y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predict, err_predict = gp.predict(test_data.reshape(-1, 1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.35728899e+00]\n",
      " [2.75047451e-01]\n",
      " [1.15090733e-01]\n",
      " [5.61148650e-02]\n",
      " [2.83225509e-02]\n",
      " [1.39054819e-02]\n",
      " [6.24585896e-03]\n",
      " [2.32506792e-03]\n",
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      " [2.29030373e-01]\n",
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      " [1.35893063e-01]\n",
      " [1.05770774e-01]\n",
      " [7.59561703e-02]\n",
      " [4.63621339e-02]\n",
      " [1.69039364e-02]\n",
      " [1.25018666e-02]\n",
      " [4.19370766e-02]\n",
      " [7.14841603e-02]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fcabcee1430>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(np.sqrt(err_predict)/y_predict)\n",
    "plt.errorbar(x=test_data.flatten(), y=y_predict.flatten(), yerr=np.sqrt(err_predict).flatten(), ls='', marker='o')\n",
    "plt.scatter(training_data, training_data_y, color='red', s=100)\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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}