{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modified from https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_noisy_targets.html\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, c = (6, 1)\n",
    "def f(x):\n",
    "    phi = np.array([np.sin(a*x[0]), np.sin(a*c*x[1]), 2*x[0], 2*c*x[1]])\n",
    "    return phi.T@phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# visualize the real function, f\n",
    "%matplotlib notebook\n",
    "%matplotlib notebook\n",
    "\n",
    "nx1, nx2 = (50, 50)\n",
    "x1 = np.linspace(-1, 1, nx1)\n",
    "x2 = np.linspace(-1, 1, nx2)\n",
    "x1v, x2v = np.meshgrid(x1, x2)\n",
    "\n",
    "fx_s = np.zeros_like(x1v)\n",
    "for i in range(nx1):\n",
    "    for j in range(nx2):\n",
    "        x = np.array([x1[i], x2[j]])\n",
    "        fx_s[i,j] = f(x)\n",
    "\n",
    "fig = plt.figure(figsize=(8,4))\n",
    "ax1 = fig.add_subplot(121, projection=\"3d\")\n",
    "surf = ax1.plot_surface(x1v,x2v,fx_s,cmap=cm.coolwarm)\n",
    "fig.colorbar(surf)\n",
    "ax1.set_xlabel('x1')\n",
    "ax1.set_ylabel('x2')\n",
    "ax1.set_zlabel('f')\n",
    "ax2 = fig.add_subplot(122)\n",
    "surf2 = plt.contour(x1v,x2v,fx_s,levels=20,cmap=cm.coolwarm)\n",
    "fig.colorbar(surf2)\n",
    "ax2.set_xlabel('x1')\n",
    "ax2.set_ylabel('x2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Instantiate a Gaussian Process model\n",
    "l = .3\n",
    "kernel = RBF(l, (1e-2, 1e2))\n",
    "gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=9)\n",
    "\n",
    "X = np.expand_dims(np.random.rand(2)*2-1, axis=0) # uniformly sample from [-1,1]^2\n",
    "y = np.expand_dims(f(X[0]), axis=0)\n",
    "gp.fit(X, y)\n",
    "y_opt_old = np.inf\n",
    "X_candidate = np.stack([x1v.reshape(-1), x2v.reshape(-1)], axis=1)\n",
    "for i in range(300):\n",
    "    y_pred, sigma = gp.predict(X_candidate, return_std=True)\n",
    "    UCB = -y_pred+sigma\n",
    "    max_ind = np.argmax(UCB)\n",
    "    x_opt = X_candidate[max_ind,:]\n",
    "    y_opt = f(x_opt)\n",
    "    \n",
    "    X = np.concatenate([X, np.expand_dims(x_opt, axis=0)], axis = 0)\n",
    "    y = np.append(y, y_opt)\n",
    "    # Fit to data using Maximum Likelihood Estimation of the parameters\n",
    "    gp.fit(X, y)\n",
    "    \n",
    "    if (y_opt_old- y_opt)**2 < 1e-7 and i > 10:\n",
    "        break\n",
    "    \n",
    "    y_opt_old = y_opt\n",
    "    \n",
    "    if (i+1)%10 == 0:\n",
    "        fig = plt.figure(figsize=(8,4))\n",
    "        ax1 = fig.add_subplot(121)\n",
    "        surf1 = plt.contourf(x1v,x2v,y_pred.reshape(nx1,nx2),levels=20,cmap=cm.coolwarm)\n",
    "        fig.colorbar(surf1)\n",
    "\n",
    "        ax2 = fig.add_subplot(122)\n",
    "        surf2 = plt.contourf(x1v,x2v,sigma.reshape(nx1,nx2)**2,levels=20,cmap=cm.coolwarm)\n",
    "        plt.clim([0,1])\n",
    "        fig.colorbar(surf2)\n",
    "\n",
    "        ax1.plot(X[:,0], X[:,1], 'ro', ms=5)\n",
    "        ax1.set_xlabel('x1')\n",
    "        ax1.set_ylabel('x2')\n",
    "        ax1.plot(x_opt[0], x_opt[1], 'y*', ms=10)\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(8,4))\n",
    "ax1 = fig.add_subplot(121)\n",
    "surf1 = plt.contourf(x1v,x2v,y_pred.reshape(nx1,nx2),levels=20,cmap=cm.coolwarm)\n",
    "fig.colorbar(surf1)\n",
    "\n",
    "ax2 = fig.add_subplot(122)\n",
    "surf2 = plt.contourf(x1v,x2v,sigma.reshape(nx1,nx2)**2,levels=20,cmap=cm.coolwarm)\n",
    "plt.clim([0,1])\n",
    "fig.colorbar(surf2)\n",
    "\n",
    "ax1.plot(X[:,0], X[:,1], 'ro', ms=5)\n",
    "ax1.set_xlabel('x1')\n",
    "ax1.set_ylabel('x2')\n",
    "ax1.plot(x_opt[0], x_opt[1], 'k*', ms=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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