QML_Tutorial_sklearn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QML Tutorial 2\n",
    "\n",
    "by Anders S. Christensen and Michael S. Marshall"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial is a general introduction to kernel-ridge regression with Quantum Machine Learning (QML).\n",
    "\n",
    "QML is freely available under the terms of the MIT open-source license. However, we ask that you properly cite the relevant, underlying work in your published work (provided below).\n",
    "\n",
    "##### QML Citation: \n",
    "AS Christensen, FA Faber, B Huang, LA Bratholm, A Tkatchenko, KR Müller, OA von Lilienfeld (2017) \"QML: A Python Toolkit for Quantum Machine Learning\" https://github.com/qmlcode/qml\n",
    "\n",
    "##### Theory Citation:\n",
    "[Rupp et al, Phys Rev Letters, 2012](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.058301)\n",
    "\n",
    "[Montavon et al, New J Phys, 2013](http://iopscience.iop.org/article/10.1088/1367-2630/15/9/095003/meta)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theory \n",
    "Regression model of some property, \n",
    "\n",
    "\\begin{equation*}\n",
    "y\n",
    "\\end{equation*}\n",
    "\n",
    "for some system, \n",
    "\n",
    "\\begin{equation*}\n",
    "\\widetilde{\\mathbf{X}}\n",
    "\\end{equation*}\n",
    "\n",
    "this could correspond to e.g. the atomization energy of a molecule:\n",
    "\n",
    "\\begin{equation*}\n",
    "y\\left(\\widetilde{\\mathbf{X}} \\right) = \\sum_i \\alpha_i \\  K\\left( \\widetilde{\\mathbf{X}}, \\mathbf{X}_i\\right)\n",
    "\\end{equation*}\n",
    "\n",
    "E.g. Using Gaussian kernel function with Frobenius norm:\n",
    "\n",
    "\\begin{equation*}\n",
    "K_{ij} = K\\left( \\mathbf{X}_i, \\mathbf{X}_j\\right) = \\exp\\left( -\\frac{\\| \\mathbf{X}_i - \\mathbf{X}_j\\|_2^2}{2\\sigma^2}\\right)\n",
    "\\end{equation*}\n",
    "\n",
    "Regression coefficients are obtained through kernel matrix inversion and multiplication with reference labels\n",
    "\n",
    "\\begin{equation*}\n",
    "\\boldsymbol{\\alpha} = (\\mathbf{K} + \\lambda \\mathbf{I})^{-1} \\mathbf{y}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load QML into Jupyter Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing version info for help reporting bugs\n",
      "Python version: 3.6.5 (default, Apr 26 2018, 00:14:31) \n",
      "[GCC 4.8.5 20150623 (Red Hat 4.8.5-11)]\n",
      "QML version: 0.4.0\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import sys\n",
    "print(\"Printing version info for help reporting bugs\")\n",
    "print(\"Python version:\", sys.version)\n",
    "\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn import metrics\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.kernel_ridge import KernelRidge\n",
    "\n",
    "try:\n",
    "    import qml\n",
    "    from qml.kernels import gaussian_kernel\n",
    "    from qml.kernels import laplacian_kernel\n",
    "    from qml.math import cho_solve\n",
    "    from qml.representations import get_slatm_mbtypes\n",
    "    \n",
    "    print(\"QML version:\",qml.__version__)\n",
    "except ImportError:\n",
    "    print(\"Failed to find QML\")\n",
    "    print(\"Please follow instructions here: http://www.qmlcode.org/installation.html\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tutorial exercises\n",
    "\n",
    "If you got this notebook without the repo, please clone the following GIT repository to access the necessary scripts and QM7 dataset (atomization energies and relaxed geometries at PBE0/def2-TZVP level of theory) for ~7k GDB1-7 molecules. \n",
    "[Ruddigkeit et al, J Chem Inf Model, 2012](https://pubs.acs.org/doi/abs/10.1021/ci300415d)\n",
    "[Rupp et al, Phys Rev Letters, 2012](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.058301)\n",
    "\n",
    "git clone https://github.com/qmlcode/tutorial.git\n",
    "\n",
    "Additionally, the repository contains Python3 scripts with the solutions to each exercise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import QM7, already parsed to QML\n",
    "from tutorial_data import compounds\n",
    "from tutorial_data import energy_pbe0\n",
    "\n",
    "# Assume 'qm7' is a list of Compound() objects.\n",
    "mbtypes = get_slatm_mbtypes([mol.nuclear_charges for mol in compounds])\n",
    "\n",
    "\n",
    "# For every compound generate a coulomb matrix or BoB\n",
    "for mol in compounds: #can lower this if you need to via compounds[:1000] to just use first 1k molecules\n",
    "    # you can select other descriptors here\n",
    "    # full list here http://www.qmlcode.org/qml.html#module-qml.representations\n",
    "    mol.generate_coulomb_matrix(size=23, sorting=\"row-norm\")\n",
    "    # mol.generate_slatm(mbtypes, local=False)\n",
    "    # mol.generate_bob(size=23, asize={\"O\":3, \"C\":7, \"N\":3, \"H\":16, \"S\":1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we start fitting data, let us take a moment to examine the data we are working with.\n",
    "For this, we use seaborn to look at the range of values we are trying to predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f548140c8d0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(energy_pbe0, shade=True, cut=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we will be using sklearn model to do\n",
    "test/train splitting of our data\n",
    "\n",
    "The example below will randomly select 33 percent of the given data\n",
    "to be used as a test, the rest will be assigned to be used as training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# observable we are trying to predict\n",
    "y = energy_pbe0\n",
    "# molecular descriptor from qml\n",
    "X = np.array([mol.representation for mol in compounds]) \n",
    "\n",
    "# split our data into testing data and training data with sklearn\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With our data now in good form, we are ready to find the fitting \n",
    "parameters. We are going to use Kernel Ridge Regression as implemented\n",
    "in the sklearn package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# select the kernel you wish to use for fitting\n",
    "# and any preprocessing can be done here\n",
    "# I only introduce this approach so others can play with \n",
    "# different kernels as a learning exercise\n",
    "# KRR shown here\n",
    "\n",
    "sigma = 4000\n",
    "gamma = 1.0/(2*sigma**2)\n",
    "alpha = 1e-8\n",
    "kernel = KernelRidge(gamma=gamma, kernel=\"rbf\", alpha=alpha)\n",
    "\n",
    "\n",
    "# find the fitting coeffecients\n",
    "kernel.fit(X_train, y_train)\n",
    "\n",
    "# and make predictions on test data\n",
    "predictions = kernel.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have now predicted the energies for the test set, let us now see how well the model worked"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x7f54813d0208>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GsHu6E1z336tIpBwD3jGxipqKKB09CRYuae63BF3ySzMoERm1slmyvSue5Mr7nqW9J73u04wgOUH2LZAkP5SgRGTUGqwxbDyZ4nMPPcczzeln/ifXlDEho09fNi2QJH+UoERk1BpoyfZUyvnyo6v49dr0bOriU2dQGY0cUAskyS8lKBEZtfpbsn1abSU3/mINjz2f7it9zXtm860PnsBN5x1LfU0FrZ1x6msquOm8Y3X/qYBUJCEio9aCebO4YdEaOnoSVEbDdMaTxJPO5Jpy7v/TawBc/u7DOGn6BC6+45m9hRTfOP84JaYioBmUiIxa8+fUv21W9K5Zk/jFqjcBuPCkacybfRD/9Is/D1hIIYWhGZSIjGqZS7Y/8uzrXPezFwE4+5iD+faHTuDSu5cRDRuJpLOhtZ2eZPoh3ZufXKtZVIFpBiUiY8ITq97kK/+dTk7vmjWJ7118EpFwiI0tHSSSKd5o7SSRdMJmpFLOy9v2aBZVYJpBiciodNviddz1hw209yQpDxtdiRQphxNn1HLnJxqoCKr7ZtRV8fzGFkLY3kUIDYia6SHdAtMMSkRGndsWr+O7v1mfruBzpyOeTk6RkHHlX8ykuvytv5v3rrDb+7+UO+5w8PhyPaRbYEpQIjLq3PWHDYATTzrJjDVZkynn20+/tM+lu/lz6jmyvpqQGcmUEwkZh9RWEAmH9JBugekSn4iUtL567e3pTpDqY7Fwh72dJDIv3V13zhxuWLSGaNj2KUfXQ7qFpQQlIiWrt9deNGz7lIj3lZx69dVfb/6cem4i3RppU0sH0/tpKisjSwlKREpWZq89gKqyCLu74gMe019/vcxydCkOugclIiVr/157yZSztbVr72fL2NeAimhIl+5KiGZQIlKyZtRVEWvroqosQirlvLqjna5ECoCDqtOdyRPJFFt3dxNPpThsYhXXn3u0ZkolQglKREpWb6+99u44sbZuOoI1na46YybvPvygvfeUTjq0TveUSpASlIiUrPlz6rkx5XzpZ6vY051OTh+feyj/+L5j9m6X0qUEJSIly935VdNWdrT3APAPZx/J371ndoGjklxRkYSIlCR35+Ynm/jJso0AfPqMmXz+zCMKHJXkkhKUiJSkHzS+snfp9o82zOAf/+ZozGyQo6SUKEGJSMn58TOv8Z2nXwLgfcdP5V8uPF7JaRRSghKRkvL4ys18/fHVAMybfRC3fvREwiElp9FICUpESsZvmrbyDz99AXc45dA6br/0FMoi+mNstFIVn4gUVGaz1+qyMGZGW3dib+PX3lLxZ5p38JkfP0ci5Rw9tYYfffLUvS2OZHTSv10RKZjMZq9hg/Xb2gGYVluxt/HrTcCk6nKuuO9ZuhMpDptUxf2fmsuEymhhg5e8U4ISkYJobIpxzcPP09GTpDwSIpFMETYDg+17epg1uZqOngS3Ll7HK9v20N6dJGwwsaqMNZtb9RDuGNDvxVsz2z3Iq83M1o1ksCIyOvTOnNp7EoRDkEg63Ukn5SnMoCeZ7qcXNuPFza3s6U4SMph10Dhau+LcsGjNPosOyug00N3FV9x9/ACvGqB9pAIVkdGjd5mMikgYMEIhw4BECtyhLBwinkzRvL2dlIMZzDqomoqyCFVlkb2LDsroNlCC+mAWx2ezj4jIPnqXyZhcU447pNyJhNIr3sYTKeLJFE1b2kgEKw8eNrGKyrK3ltXoa9FBGX36TVDuPuhfT7LZR0RkfzPqquiMJ6mpiHJIbQWRkJECykJGKAQ9ybeWxI2EjK5Ecp/j+1t0UEaXge5BtfVxz2nvz5EMUkRGlwXzZhFPOh09CarLI0yZUMG02ipmTh5HNPzWH0sz6io5qLqMne1xOnoSuKeP0aKDY8NAM6ia/e85Zf4c7heb2YfNbI2ZpcysYb9tXzGz9Wb2kpm9N2P8nGBsvZldnzE+08yWBuOPmFnZcOMTkfyZP6eem847lvqaClo749TXVPBPf3sMr+/soDPeWyABO9t7KI+EqCkP77PvTecdqyq+MSCrMnMzeydwRvBxibuvysF3rwYuBBbu913HABcBxwKHAIvN7Mhg8/eBs4FNwLNmtsjd/wzcAtzq7g+b2e3AFcAPcxCjiOSZk+5Mfu//vvpWcgoZ0bCRSDmbd3Uxu76an1x1emEDlRE3aIIys2uBTwP/HQw9aGZ3uPv3hvPF7r42OP/+m84HHnb3bmCDma0HTgu2re+972VmDwPnm9la4EzgY8E+9wE3ogQlUpQam2Lc/ORaXt62h2goRH1NGas2t+5dDRfAIMhc6c/u3tepZJTLZgZ1BTDX3dsBzOwW4E/AsBLUAKYBz2R83hSMAWzcb3wuMAnY5e6JPvYXkSLS+/xTrK2LsBkObGzpIjP9hIBkynGgIhJiSnU57T3Jvk8oo1o2CcqAzN8dyWBs8APNFgNT+tj0VXd/PJtz5JKZXQVcBXDooYeO9NeLjGm9nSP2dCVIBWOG701OIYOUQzSoN4+EbW83ifqaikKFLQWUTYK6B1hqZo8Fnz8A3J3Nyd39rCHEtBmYkfF5ejBGP+M7gFoziwSzqMz994/nDuAOgIaGBl0zEBkhjU0xvvjoC+zuSuwznvkfYSRkhMxIP/rk9CRVsTfWDdqn3t3/HfgksDN4fdLd/yOPMS0CLjKzcjObCcwGlgHPArODir0y0oUUizx9cfq3wIeC4z8BjPjsTET6d/OTa9m5p2fAfZIpZ8qECg6prSBk6WSlir2xLdtmsRuARLC/mdnJ7v7ccL7YzC4gfR9rMvCEma109/e6+xoz+ynw5+A7P+fuyeCYzwNPA2HgR+6+JjjddcDDZvZN4HmynOGJyMjYsKNj72W9/iQ9XQwRCYeoH6/EJGCDVceY2TeAy4FXeGtG7u5+Zn5Dy6+GhgZfvnx5ocMQGROO+tqTdCcGS1EQDRkNh03cZx0oGZWyqmPIZgb1EeBwdx94fi4i0o9ZB41j7Za2QfcLhUzPO8le2SSo1UAtoN72IpK13pVy123dnVWZeFZ/pZYxJZsE9S3geTNbDXT3Drr7eXmLSkRKWu/zTrs7e9jVmRj8ANIJauYkNYCVt2SToO4j3UroRRj0PqeIjHF9Pe80mLBB3bgyrj/36LzGJqUlmwTV4e635T0SESl5mSvl9pecyiPpp1tqysP0JJ2ySIjZ9TUqjJC3ySZB/d7MvkX6+aTMS3zDKjMXkdHltsXr+O5v1pNMDVwZHE+mmDtzkoohZFDZJKiTgp+Zv5ucdINWEZGskxOk2xm9a9bEEYhKSl2/CcrM3gU84+5/NYLxiEgJuusPG9K99Ni3fVFfwgZ/at7JNSMRmJS0gWZQlwHfN7N1wFPAU+6+ZWTCEpFi1Fs6vrGlgxl1VXvvG7X3JAmbYwb9PftvQCQEmLGppWMkw5YS1W+CcvfPAJjZHOBc4F4zm0C6791TwB97WxCJyOjXWwARDRthg+dfb+GK+59l9uRqysMhOuL9/3FggBmELISFYHqdysllcNk0i21y91vd/RzS953+AHwYWJrv4ESkeCxc0kw0bCRTzput3QRNx1kX2zNgcgp2I+WQdKe6PKLu5JKVge5B9XcX8xnS96Z25ickESlGL8faaOuM0508sJVqjHSCMoMjJo/j+nOPVjm5ZGWge1ArCH5f9bHNAf0VSGQMaGyK8fXHV7N9kOUy+uPAoROr1J1cDthA96BmjmQgIlJ8GptifOnRF9g2xOQE6b/hKjnJUGS1HpSZ1ZFeOHDvusvuviRfQYlIcVi4pJkd7cNbyKAiGlJykiEZNEGZ2ZXAtaSXUl9J+oHdP6EHdUVGvTVvtJLFs7cDGlee7bqoIvvK5nfOtcCpBA/tBmXn/5LfsESkUBqbYtz85FrWb2snkUV26i2C6EvYYHZ9TU7jk7EjmwTV5e5dZoaZlbt7k5kdlffIRCRv+nvgtrEpxhcffYGW9h6yLdaLho140tOdJIJjPBgPmamkXIYsmwS1ycxqgZ8DvzKzFuC1/IYlIvmS+cBtbWWUWFsXNyxaw02k7znt6ohnnZwAzIywOUmHcMj2zrpCZnxu/uG6/yRDNmiCcvcLgrc3mtlvgQmkO0mISAnqfeC2qiz9n39VWYSOngQLlzTz3Os7SBzgqm/JlBMKGamUEwkbDhxZX81158xRcpJhyaZI4nRgjbu3ufvvzGw86Q7n6iQhUoI2tnRQWxndZ6wyGmbNG610Z7f47T4iofSjktGwcdKMOq3rJDmTzSW+HwInZ3ze08eYiJSIGXVVxNq69s6gAN7Y1cnuriFkJyCeSjGtVg/iSu4N2osPMPe3+hO7e4osn58SkeKzYN4s4kln+54u1m3ZzYubW9nZER/y+caVRZScJC+ySVDNZnaNmUWD17VAc74DE5H8mD+nng+dPI3te3oOuK9eX2676CQlJ8mLbBLU1cC7gc3AJmAucFU+gxKR/PpT887+F246ADPqKpWcJG+yuVSXcPeLMgfMTH36RErYxpYO4gdYrdcrBJRFQtRURPjG+cflNC6RTNnMoH4RVO4BYGZHA7/IX0gikm/VZeEhHzutrpKTDq3jOx96p2ZPklfZzKD+hXSSeh9wFHA/cEleoxKRvGlsivF6S+eQjh1fEeH316kNp4yMbB7UfcLMosD/ADXABe6+Lu+RiUjO9PbX27Cjg55Eqt/eeYO58i90dV9GzkAr6n6PfXtATgBeAT5vZrj7NfkOTkQOTGYiAph10DjOPW4K9z/zGrs64oSs/8aug7ngxKlcc9aRuQtWZBADzaCW7/d5RT4DEZHhyWz0mvJ0Ilq7pY21W9oKHZrIkAy0ou59IxmIiAzPwiXN7O48sEavB+LnK9/k/BNjKoyQEdNvFZ+Z3THYwdnsIyIjY2NLB/F8ZSfSM7KFS/SMvoycgS7xfcDMugbYbsBf5TgeERmiGXVVbBpidV42DNjU0pG384vsb6AE9aUsjv99rgIRkeFZMG8Wf2rekbfz11VFmV5Xlbfzi+xP96BERon5c+r3WdU2lyZWRamuiGp1XBlR6kouMko0NsVylpxqKyNEwiEmV5ezpzvB9Ixl4UVGihKUSAlrbIqxcEkzG1s62No6/PtPRnoBwqOnTlBCkoLLZkXd4939xZEIRkSyd9vidXy/8RWSKSeRg6nT1AnlRMNhre0kRSObZrE/MLNlZvZZM5uQiy81sw+b2RozS5lZQ8b42Wa2wsxeDH6embGt0cxeMrOVwas+GC83s0fMbL2ZLTWzw3IRo0gxa2yK8f3GV0i5k8xBchpfEeGwSdVKTlJUsunFd4aZzQY+Bawws2XAPe7+q2F872rgQmDhfuPbgfe7+xtmdhzwNDAtY/sl7r5/h4srgBZ3P8LMLgJuAT46jNhEit7CJc0kUinwobcu6hUNmxYdlKKUzQwKd38Z+BpwHfCXwG1m1mRmFw7lS919rbu/1Mf48+7+RvBxDVBpZuWDnO58oLfi8FHgPWZmQ4lLpBTctngdz2zYQTLFsLtGRELGpHFlegBXitKgCcrMTjCzW4G1wJmkZzhHB+9vzWNsHwSec/fujLF7gst7X89IQtOAjQDungBagUl9ndDMrjKz5Wa2fNu2bXkMXSQ/blu8ju/+Zn0uFsMlGjam1VZyUHW5HsCVopRNFd/3gLuBf3T3vWVCwWW4r/V3kJktBqb0semr7v74QF9oZseSvlT31xnDl7j7ZjOrAX4GXEp6baqsufsdwB0ADQ0N+esJI5Int/+uedj3nMKhdNeJmoooAB09CT2AK0Upm3tQfznAtgcG2HbWUAIys+nAY8Bl7v5Kxvk2Bz/bzOwh4DTSCWozMAPYZGYR0suC5O9xepECuW3xOjriySEfb8Ck6jKqyiKEQ4a70xlPEk+6HsCVopRNmfmLvP0+bCvp5Ti+6e45SwZmVgs8AVzv7n/MGI8Ate6+PVg88W+BxcHmRcAngD8BHwJ+456LCyAihZX5jBPubNo1UGvMwdVVRZldX8OCebNYuKSZTS0degBXilo2l/ieBJLAQ8Hni4AqYAtwL/D+A/1SM7uA9KXDycATZrbS3d8LfB44ArjBzG4Idv9roB14OkhOYdLJ6c5g+93AA2a2HtgZxCdS0nqfcUqkUoSBntTwz9nbqmj+nHolJCmeLiFbAAAgAElEQVQJNthkw8yec/eT+xozsxfd/fi8RpgnDQ0Nvnz5/hXrIoXX2BRjwY9XkHLHgJ4cLaFx7+WnKjFJsciq0jqbMvOwmZ2296xmp5KexQAkhhCYiAxg4ZKgEMJzl5xChpKTlJxsLvFdQbq8uzr43AZcYWbjgG/lLTKRMSLzXtOMuirWbd1NeSREe8/QCyL2pwcDpRQNmKDMLATMcvfje9scuXtrxi4/zWdwIqNdY1OMGxatIRo2aiujxNq62NOdpDKa1TP0WcvjQrsieTPgfwXungK+HLxv3S85icgwLVzSTDRsVJVFMEv/nDguSmtn7q+eNzbFcn5OkXzK5hLfYjP7IvAI6Wo6ANx9Z96iEhkjNrZ00BNPsmF7e14WGsy0cEmz7kNJSckmQfU2Xv1cxpgDerJPZJgMiO3pyfv3lIVQOyMpOdl0kpg5EoGIjEXb93QPvlOWvnDWbJ5cvYW1W9reti0UCqmdkZScbJrFVpnZ18zsjuDzbDP72/yHJjK6NTbF6Izn4AlcoDwM15x1JG3dCd4xsZJo2CgPh6iIhCgLG/FUSu2MpORkUyp0D9ADvDv4vBn4Zt4iEhkDeqv3clX+vfDSU4F0E9hIOMQhEyqJhI2kO6GQMXtyte4/ScnJJkEd7u7fBuIA7t6BHqsQGZbe6r3xFdncBh7YnIPfSj4L5s0innQiYWPmQeM4dGIV9TUVXH/u0cP+HpGRlk2C6jGzSoKGsWZ2OJC7C+ciY9DGlg52d/bQ2jX8cvLM5DN/Tj03nXcs9TUVtHbGqa+p0DLuUrKy+evbPwFPATPM7EHg/wCX5zMokdGupjzC5pbOwXccxIy6yrclHzWDldEimyq+X5nZc8DppC/tXevu2/Memcgo1tYVf9saNgdqfHmYb5x/XE7iESlG2V4ArwBagv2PMTPcfUn+whIZvRqbYmwe5tpO02sr+OYHjtdMSUa1bBYsvIX0w7prgN6aWAeUoESG4JanmoY1e4qGjD9c/56cxSNSrLKZQX0AOMrdVRghMgSZ3cq37e6ke5hNyqdMqMhNYCJFLpsE1QxEUeWeyAFpbIrxtcdWsak1d//phA3GlYUH31FkFMgmQXUAK83s12QkKXe/Jm9RiZS4xqYYX3z0BbbnsM9eyGB6XWVO14kSKWbZJKhFwUtEsrRwSTO7O+M5O180BJgRCYeor9ElPhkb+k1QZjbe3Xe7+319bDs0v2GJlI79V8R916yJLG3eQW667EEkBGZGKGTEk66eejJmDNRJorH3TXB5L9PP8xKNSInp7akXa+uitjLKhu17+PfFL+csOZVHQkRCIZLuHDaxSl0hZEwZ6BJfZr+9iQNsExmzMlfE3d0ZJ9aWw4IIIJFyTjtsIgvmzVJikjFnoATl/bzv67PImLSxpYPayii7O+NsaunI2aq4k6vLGF8Zpb6mgp9cdXpuTipSYgZKUPVm9gXSs6Xe9wSfJ+c9MpESMKOuilhbF1t3d5HMQXKaWBXlkNpKOuNJ3W+SMW+ge1B3AjVAdcb73s935T80keLXu7xFV2L4d52+cNZsjpoyXl3IRQL9zqDc/Z9HMhCRUtXeNfxnnS44cSrXnHUkerhQ5C3DXy1NZIxqbIrxdz95jrZh9i664MSp3HrRyTmKSmT0yGbBQhHpw81Prh12chpfHub8E6fnKCKR0UUJSmQIblu8jqate4Z1jpDB5PEVLFzSnKOoREaXgTpJfKG/bQDu/u+5D0ek+N22eB3/vvjlYZ0jBBw6sYrKaJhNLR25CUxklBnoHlRN8PMo4FTe6sf3fmBZPoMSKTa97YxWb9417Mt6AIdOqqKmIkpHT4LpdVU5iFBk9Bm0is/MlgAnu3tb8PlG4IkRiU6kCDQ2xfjSoy+ws70nZ886VZdH6OhJ6FknkQFkU8V3MJBZR9sTjImMCbc81cT2PT05aZ8y5+Bx1I2rYFNLB9PrqtTCSGQA2SSo+4FlZvZY8PkDwNs6nIuMVuu2tuUkOZWFoG6cWheJZGvQBOXu/5+ZPQmcEQx90t2fz29YIsWhsSmWk8t6AEdOGa+CCJEDkG2ZeRWw292/C2wys5l5jEmkaNz85NqcnGdydRmd8aQKIkQOwKAJysz+CbgO+EowFAV+nM+gRIpBY1MsN886VUcZXxlVQYTIAcpmBnUBcB7QDuDub/BWCbrIqHXLU01DPvZdM+u49/JTmTtzEhXRiJq/igxBNkUSPe7uZuYAZjZuuF9qZh8GbgSOBk5z9+XB+GHAWuClYNdn3P3qYNspwL1AJfBL4NogronAI8BhwKvAR9y9Zbgxyth22+J1rN3SNqRjq8rC/GTBuwGUkESGIZsZ1E/NbCFQa2afBhYz/OU2VgMXAkv62PaKu58YvK7OGP8h8GlgdvA6Jxi/Hvi1u88Gfh18FhmSxqYYZ9zym2F1injn9NocRiQydmVTxfevZnY2sJt0V4kb3P1Xw/lSd18LYJbdyvFmNhUY7+7PBJ/vJ13u/iRwPjA/2PU+oJH0PTORfvV2htjY0sGMuireNWsiT67eQtOW4ZeU6z6TSG4MmqDM7BZ3vw74VR9j+TDTzJ4nnRC/5u6/B6YBmzL22RSMARzs7m8G77egh4hlEI1NMW5YtIZo2KitjLJh+x6WvbqTZI7Wa9dlPZHcyOYS39l9jJ072EFmttjMVvfxOn+Aw94EDnX3k4AvAA+Z2fgsYgTA3R36/wuwmV1lZsvNbPm2bduyPa2MMguXNBMNG1VlEWK7u9iyuztnyWlGXWVOziMiA3cz/wzwWeBwM1uVsakG+N/BTuzuZx1oMO7eDXQH71eY2SvAkcBmIHPRnOnBGMBWM5vq7m8GlwJjA5z/DuAOgIaGhhw9fimlZmNLB7WVUV7f0U5rVyIn5zRgfGWEb5x/XE7OJyIDz6AeIt25/PHgZ+/rFHe/JB/BmNlkMwsH72eRLoZoDi7h7Taz0y194+qyIC5Id1n/RPD+ExnjIn2aUVfFjvbunCWncMg4fdYkvvvRk3R5TySH+k1Q7t7q7q8C3wV2uvtr7v4akDCzucP5UjO7wMw2Ae8CnjCzp4NN84BVZrYSeBS42t13Bts+S7p6cD3wCukCCYCbgbPN7GXgrOCzSL8WzJvFm63dwz5PVcQ4fPI4TjtsIj+56nQlJ5Ecy+Y5qB8CJ2d83tPH2AFx98eAx/oY/xnws36OWQ687fqJu+8A3jPUWGTsWbVpV07OM7WuSt0hRPIomwRlQfEBAO6eMrNsjhMpOo1NMf7j18NbDbdXWTjE1983RzMnkTzJpoqv2cyuMbNo8LoWaM53YCK51tgU48r7l5OLgr2ysFFbVabkJJJH2SSoq4F3k66a2wTMBa7KZ1AiudbYFOPaR54nkYPsFAkZUydUaOkMkTzLppNEDLhoBGIRyZnMThGd3Ql2dMRzct7ysDG1tpJwyKivqcjJOUWkbwM9B/Vld/+2mX2PPh5+dfdr8hqZyBBldorY3dHN7u5UTs4bMph9cA2d8aSKI0RGwEAzqN6V2paPRCAiubJwSTM9iSRbW3voHuZyuCGDQydW0Z1I0t6dpLUzzvS6KhbMm6X7TyJ51m+CcvdfBD/vG7lwRIansSnGs6/uIDHMSZMBsyaPozIapjOeJBoOc9tFJygpiYyggS7x/YIB+tq5+3l5iUhkiBqbYnzx0ReGnZwAjjq4mrpx5Wxq6dCMSaRABrrE96/BzwuBKby1zPvFwNZ8BiUyFDc/uZYde3pycq7rzz1aCUmkwAa6xPc7ADP7N3dvyNj0CzPTfSkpKn//8HM0bd2Tk3NNqooqOYkUgWw6Qowzs1nu3gxgZjOBYS/7LpIrFy/8X/60oSVn5/u3j5yYs3OJyNBlk6D+Hmg0s2bS947fASzIa1QiWWpsiuU0OYXQgoMixSKbB3WfMrPZwJxgqClYt0mkYHofxH3u9dwlJ4D/e9bsnJ5PRIYumyXfq0ivbvsOd/+0mc02s6Pc/f/lPzyRt8t8ELcnFyV7QFVZmKvnzeKas47MyflEZPiyucR3D7CC9NpNkO7J91+AEpQURO+S7cmU9/8cxAGoKQ/z4j+fk4MziUguZZOgDnf3j5rZxQDu3hGsaisy4hqbYjz3egvJVConXcnDBsdNqx3+iUQk57LpZt5jZpUED+2a2eGA7kHJiOu9tGcGIbOcJKiJ48rUU0+kSGWToP4JeAqYYWYPAr8GvpzXqET60Htp7+CaCuLD7LEHMKOuku986J2q2hMpUgNe4gsu5TWR7iZxOuky82vdffsIxCayj40tHXTHE2zbM/ylMy44cSq3XnRyDqISkXwZMEG5u5vZL939eOCJEYpJpG/uw05O5ZEQn5t/uKr1REpANkUSz5nZqe7+bN6jERnAG61dwzr+3stP1eU8kRKSTYKaC3zczF4F2klf5nN3PyGfgYlAujDi5ifXsn7bnmEXRSg5iZSWbBLUe/MehUgfGptifOreZ8nFo7gz6ipzcBYRGUkDrQdVAVwNHAG8CNzt7omRCkxkwQO5SU5V0RDfOP+4HJxJREbSQGXm9wENpJPTucC/jUhEIqRnT93J4Z+nLGz84JJTdHlPpAQNdInvmKB6DzO7G1g2MiGJpJ95yoWDx1coOYmUqIFmUHvreXVpT0ZSbzujXJheV5WT84jIyBtoBvVOM9sdvDegMvjcW8U3Pu/RyZhz2+J1fO+363PSKaIiYmpjJFLCBlryPTySgcjY1tgU45anmli7pS0n56suC/GfH9O9J5FSlk2ZuUhe5XLJ9oPGRfnXD5+oxCQyCihBSUH9/cPP5Sw5qb+eyOiSTTdzkbxobIrx2Mo3c3Ku6bUVSk4io4xmUFIQjU0xvvjoC0M+vixsOBAOGdXlEb75geNzF5yIFAUlKCmIhUua2bGnZ0jHzjm4mrpx5Wxq6WB6XRUL5s3SPSeRUUgJSkbccIoiasrDXH/u0UpIImOAEpSMqFNuepodHUN/7vt7F5+s5CQyRqhIQkbMxQv/d1jJaUZdpZKTyBiiGZTkVWNTjIVLmnk51sb2Id5zgnT7ErUtEhlblKAkL3o7Q6yL7SEaNuLx4S2cUV0eVtsikTGmIJf4zOzDZrbGzFJm1pAxfomZrcx4pczsxGBbo5m9lLGtPhgvN7NHzGy9mS01s8MK8WuStzQ2xbj2kedZu6WNZMrpiqcYzsoZ0yeU696TyBhUqBnUauBCYGHmoLs/CDwIYGbHAz9395UZu1zi7sv3O9cVQIu7H2FmFwG3AB/NW+QyqC8++gKtncNvgP+Fs2ZzzVlH5iAiESlFBZlBuftad39pkN0uBh7O4nTnk15cEeBR4D1mZsOJT4ausSk2rHtNvQ4aF1VyEhnjirmK76PAT/Ybuye4vPf1jCQ0DdgIe9etagUm9XVCM7vKzJab2fJt27blK+4x7WuPrRr2OWorI8w+WKu5iIx1eUtQZrbYzFb38To/i2PnAh3uvjpj+JJghd8zgtelBxqTu9/h7g3u3jB58uQDPVyysKm1e1jH11VFGF9ZpoIIEcnfPSh3P2sYh1/EfrMnd98c/Gwzs4eA04D7gc3ADGCTmUWACcCOYXy3DNFti9cN+dhICMBIpuCm845VQYSIFF+ZuZmFgI+QniX1jkWAWnffbmZR4G+BxcHmRcAngD8BHwJ+4+7DX45VDtj3G18Z0nFmcPTUCbg7rZ1xJScRAQqUoMzsAuB7wGTgCTNb6e7vDTbPAza6e3PGIeXA00FyCpNOTncG2+4GHjCz9cBO0rMvKYDuxNCeder960RnPKmHcUVkr4IkKHd/DHisn22NwOn7jbUDp/Szfxfw4RyHKCMoZNDRkyCedN17EpG9iu4Sn5SmxqbYkI8dVxaivqZCy2aIyD6UoCQnFi5pHnynPoQMXvznc3McjYiMBsX8HJSUkGUbhlY4edTBNTmORERGCyUoGbbbFq8jOYS6ycnVZVx3zpzcByQio4ISlAzbD383tPLy73zonbrnJCL90j0oyVpjU4yv/fxFNrd24Q5V0TBX/+UsOoewlMb02golJxEZkBKUZKWxKcZnH1xBR0Yy6ognuXXxywd8rrKw8c0PHJ/L8ERkFNIlPsnKF/9r5T7JqdeB3nqaUVfJHZc2aPYkIoPSDEoGdNvidfznb9fTM0gVRFnY+t0nBEysLuNfdc9JRA6AEpT06+8ffo7HVr6Z1b711WXUVJbxcqyNZCo9szIgHIIjJldz/blHKzmJyAFRgpI+NTbFsk5OAG+0dtP8leE0sBcR2ZfuQUmfbnmq6YD2H1qbWBGR/ilBSZ+at7cXOgQRGeN0iU9obIqxcEkz67buJp50yiIheoa4dIaISK4oQY1xjU0xvvjoC+zujNOTdIx0cYNWfBSRQlOCGuNufnIt2/f07P3sDC05zairzFlMIiKge1BjXtPWPTk5zzfOPy4n5xER6aUZ1BjUe8/p+dd35uR8NeUhPeMkIjmnBDXGNDbF+NKjL7BjT8+wS8PLIyHqqqLMPKg6J7GJiGRSghpjvvbzF9m+p+eA7jOFgOqKCO4pepIwcVyUSePK6YwniSedBfNm5StcERnDlKDGkMamGJt2dR3wceGwserG9+49x8IlzWxq6WB6XRUL5s3S5T0RyQslqDFk4ZLmIR2XyGgCO39OvRKSiIwIVfGNIRtbOogM4d94JGS5D0ZEZBBKUGPIjLqqIT3jdPjkcTmPRURkMEpQY8iCebNIHmDpXk15mOvPPTo/AYmIDEAJagw50HtHIeB7F5+se04iUhAqkhhDblu8Lut9y8Nw8jsmKTmJSMFoBjWG3P67A6jis5CebxKRglKCGkM64sms962piGj2JCIFpQQ1RrR2xLPed2JVlNn1NXmMRkRkcEpQY0BHT4JP3rss6/2rK6K6vCciBacENcp1J5IseGAFz72+K6v9q6JhbjrvWF3eE5GCU4IaxZIp5+8fWcnvX94OQHSQjhAG/OASlZWLSHFQghql3J2v/PcqfvniFgCuO2cOE6qi/f4LLwsbRx1creQkIkVDz0GNEr1dxje2dDC9tpIJVVGeXrMVgM/MP5zPzD+cJeu20ZRqpaUj8bbjJ1RG1TFCRIqKEtQo0NgU44ZFa4gnk7R2xNm8qxMPmu59bO6hfPm9RwHpVkcLfryCaNjAnYSDe3r2NGlcmWZPIlJUlKBGgZufXMuW1k56kvu2gjWDs46qxyx972n+nHpqKiJ0dCeIp6AqEmJyTTnV5RFaO7MvQxcRGQlKUCWusSnGutgeUn20KXeH7/zPS5x5zMF7x2bX1xBr66Kq7K1/9R09CabXVY1EuCIiWStYkYSZfcfMmsxslZk9Zma1Gdu+YmbrzewlM3tvxvg5wdh6M7s+Y3ymmS0Nxh8xs7KR/vUUyi1PNfWZnHqtj+3Z5/OCebOIJ52OngTu6Z9atl1EilEhq/h+BRzn7icA64CvAJjZMcBFwLHAOcAPzCxsZmHg+8C5wDHAxcG+ALcAt7r7EUALcMWI/kry5LbF6zjhxqc5/B9/yQk3Pt1ns9fm7e0DniO+X/aaP6eem847lvqaClo749TXVOi5JxEpSgW7xOfu/5Px8RngQ8H784GH3b0b2GBm64HTgm3r3b0ZwMweBs43s7XAmcDHgn3uA24EfpjfX0F+3bZ4Hd/9zXrcHQd2dyX498Uvs2H7Hm696OS9+6V88CUIG5ti+yQgLdsuIqWgWJ6D+hTwZPB+GrAxY9umYKy/8UnALndP7Dde0u76wwbcnVRQadfr5yvfpLEpBsC6rW0kB7q+F1i45AC6mIuIFIm8zqDMbDEwpY9NX3X3x4N9vgokgAfzGUvwXVcBVwEceuih+f66YWnvSfa5PLuTTjizJlfz8buWkvJ0B4j+0lRZCDa1dOQvUBGRPMlrgnL3swbabmaXA38LvMd97zxhMzAjY7fpwRj9jO8Aas0sEsyiMvffP547gDsAGhoaBp96FNC4sjC7u97+QC1A05bdfPzupcTauqmpiPClvz6KO3/fzMaWzr37GBAymFRTrgo9ESlJhaziOwf4MnCeu2f+FX8RcJGZlZvZTGA2sAx4FpgdVOyVkS6kWBQktt/y1j2sTwCPj9SvI1+u/IuZ/W7b1RHn9Z0dVEbD3PvJU7ns3Yfx++vO5IITpxI88oQZjK+MEA2HVaEnIiWpkPeg/hOoAX5lZivN7HYAd18D/BT4M/AU8Dl3Twazo88DTwNrgZ8G+wJcB3whKKiYBNw9sr+U3GpsivGn5p39bncgGjZuv/QUTnnHxL3HrHi9lSnjy6mKhjCDjp4UHzp5mgoiRKQkmWdRBTYaNTQ0+PLlywsdxttkti16s7W73/1+cMnJ/M3xU/d+vviOZ/p8ALe+poKfXHV6XmMWETlAAy+tECiWKj4JLFzSTDyZZMeegVsPZSYngI0t6Ut+mSqjYRVIiEjJUoIqMhtbOmjtiJPy1AEdN6Ouis54cp+xznhSBRIiUrKUoIrMjLoqOuIpEgeWn9TCSERGHSWoIvOuWROHdJxaGInIaKNu5kVmoOq9Xv3dXVQLIxEZTTSDKjIvx9oG3aciqn9tIjL66U+6ItPe3Xf3iEyRUFYVmiIiJU0Jqoj8bt02OuODV0f0rpArIjKaKUEViRWv7eTqB1ZktW9ZWAlKREY/Jagi8Oc3dnP5Pc/SGU8yubpswARUWxlh9sHjRzA6EZHCUIIqsA3b27n07qW0dSWYXFPOo595N5//qyMoj4T2qdYz0slpfGWZnm0SkTFBZeYF9GZrJ5fc9Qw72nuYUBnlx1fM5R2TxnHNWUdywvRaFi5p5uVYGz2JFGVhY/bB41kwb5ZKyUVkTFCCKpAde7r5+F1LeWNXF1Vl6WUzjppSs3e7nmkSkbFOl/gKYHdXnE/8aBmvbGsnGjbuvKyBkw6tK3RYIiJFRQlqhHXFk1x533JWv7GbcMj4z4+dzP854qBChyUiUnSUoEZQTyLFZ368gmUb0u2Mvv3BE3jvsVMKHJWISHFSghohyZTzD//1Ar99aRsAN77/GD54yvQCRyUiUryUoEaAu/P1x1fzixfeAOALZx/J5f9nZoGjEhEpbkpQI+DbT7/EQ0tfB+CKv5jJ3515RIEjEhEpfkpQeXb7717hh42vAPDhU6bztfcdrV56IiJZUILKoweXvsbNTzYBcO5xU/jWhccrOYmIZEkJKk8WvfAGX/v5agDOmH0Q/3HRiUTC+sctIpIt/YmZB79tivGFR1biDqe8o46Fl55CeSRc6LBEREqKElSOLW3ewdU/XkEi5cyZUsOPPnEqVWXqKCUicqCUoHJo9eZWrrhvOd2JFO+YVMUDV8xlQlW00GGJiJQkJagcWR/bw6V3L2VPd4IpEyp48Mq5TK4pL3RYIiIlS9eehqGxKcbCJc1s2L6Hne1xepIp6qrSy2ZMr6sqdHgiIiVNCWqIGpti3LBoDWaws72HnqRjwLVnzuaI+upChyciUvJ0iW+IFi5pJmSwtbVrb3KaOqGCp/+8tdChiYiMCppBDdHGlg52tvfQlUgBUBYJEQ0bm1o6ChyZiMjooBnUEFWXhemOJzEgGjJw2Lyri3Flet5JRCQXNIMaot6WRQ4kUg7mhDLGRURkeDSDGqJte7oBMNJJKv1/b42LiMjwaAY1RD2JFKGQURZ6K8cnUil6gntSIiIyPJpBDVE0nL6Ul0o57k4qlZ5ClYV1iU9EJBeUoIboyIPHM2lcGZGwkXQnEjYmjStj9sHjCx2aiMiooAQ1RAvmzaIsEmbKhAqOOriGKRMqKIuEWTBvVqFDExEZFZSghmj+nHpuOu9Y6msqaO2MU19TwU3nHcv8OfWFDk1EZFRQkcQwzJ9Tr4QkIpInBZlBmdl3zKzJzFaZ2WNmVhuMn21mK8zsxeDnmRnHNJrZS2a2MnjVB+PlZvaIma03s6Vmdlghfk0iIpJbhbrE9yvgOHc/AVgHfCUY3w68392PBz4BPLDfcZe4+4nBKxaMXQG0uPsRwK3ALfkPX0RE8q0gCcrd/8fdE8HHZ4Dpwfjz7v5GML4GqDSzwRZVOh+4L3j/KPAeUzsHEZGSVwxFEp8Cnuxj/IPAc+6e2ZrhnuDy3tczktA0YCNAkPRagUl9fZGZXWVmy81s+bZt23L3KxARkZzLW4Iys8VmtrqP1/kZ+3wVSAAP7nfssaQv1S3IGL4kuPR3RvC69EBjcvc73L3B3RsmT548lF+WiIiMkLxV8bn7WQNtN7PLgb8F3uPunjE+HXgMuMzdX8k43+bgZ5uZPQScBtwPbAZmAJvMLAJMAHbk9lcjIiIjrVBVfOcAXwbOc/eOjPFa4Angenf/Y8Z4xMwOCt5HSSe21cHmRaQLKgA+BPwmM+GJiEhpKtRzUP8JlAO/Cm4lPePuVwOfB44AbjCzG4J9/xpoB54OklMYWAzcGWy/G3jAzNYDO4GLRuxXISIieWNjdbLR0NDgy5cvL3QYIiJjUVaV1sVQxSciIvI2SlAiIlKUlKBERKQojdl7UGa2DXhtgF0OIt16qVQo3vxSvPmlePOr2OLd7u7nDLbTmE1QgzGz5e7eUOg4sqV480vx5pfiza9Si7eXLvGJiEhRUoISEZGipATVvzsKHcABUrz5pXjzS/HmV6nFC+gelIiIFCnNoEREpCgpQYmISFEakwnKzL5jZk1mtsrMHgu6qGNmZ5vZCjN7Mfh5ZsYxjWb2UrBg4kozqw/Gy83sETNbb2ZLzeywkYo32PaV4LtfMrP3ZoyfE4ytN7PrM8ZnBnGuD+Iuy0O8HzazNWaWMrOGjPFLMv75rQy2nxhsK+Q/3/7iPczMOjNiuj1j2ynB75P1ZnZb7wKaZjbRzH5lZi8HP+tGMN6i/P07UMzBtqL7PbxffI9k/HN71cxWBuMH/PtjJJjZjWa2OSOuv8nYdkD/rAvO3cfci3SH9Ejw/hbgluD9ScAhwfvjgM0ZxzQCDX2c67PA7cH7i4BHRjDeY/7/9vrJCcoAAAk1SURBVM492OqqiuOfr1wVLMNAUwqJR0RJJAyg5siMBjFSEwhBcmUkzF5OOT2GrBmKNKfHMDmjM6aMMAqaxYAMRTRehAKHLJK34APkigpENFEgofFy9cdeh/u7x/s493XOufeuz8yZ8zvrt/f+rbPOPmftvX/7rAVsI0WG7wdUk6K9d/Hj/sA5XuYyr7MYmOrHc4Hb2kDfjwKD6rOZlxkCVJeJfevUF+gL7KinzrPAVaSgl08C41w+h5QuBuD7uc+qSPqWZf9tROey7MMNvI97gNnN7R9F0vFOYGYd8ibbutSPTjmDMrOnLKWHB1gP9Hb5FjP7u8ufB7pJOreR5iYAC/34CWB0a4+W6tPXr73IzI6b2R5gNymR4xXAbjN7xcxOAIuACa7XJ11PXO8bWlNX1/dFM9vZSLFK16sximHfQvQ9g6RewHvMbL2lb/6j1Ngxq29R7Vuu/dd1q8/GZdmH68Kv/XngN42Ua6h/lJIm2bqEep6hUzqoPL5IGuHk8zlgs5kdz8ge8SnzDzNf4g8AewHciRwBehZJ3zPXdva5rD55T+Bwxtnl5KXgRt75RS8H++bTT9IWSU9LGpXRaV+mTNaOF5vZAT/+B3BxkfTMp1z7bz7tqQ+PAg6a2csZWVP7R7H4htItgYczy8xNtXXJKVXCwjZH0mrgkjpOzTKz33mZWcAp4PG8uoNJS2ljM+JpZrZf0vnAUuBm0sio5PqWgkL0baDulcCbZrYjIy65fevgANDHzA5JGg781vtGQZiZSWrW/zhaaN+i91+/brN1LjUF6l5J7UFVi/pHS2hIX+BB4G7A/Pke0sC23dFhHZSZjWnovKQZpNTxo30anpP3BpYB082sOtPefn8+KunXpGnxo8B+4FJgn6QKoDtwqEj65q6do7fLqEd+CLhAUoWPQLPlW1XfRphK3uyp1Patp85x4Lgfb5JUDXzYdeqdKZq140FJvczsgC/1/LOp122uvlC6/tsCnUvWh7MU8P2rACYBwzN1mtM/WoVCbS1pHrDCXzbV1iWnUy7xSboeuAMYb2ZvZuQXAH8g3eR+JiOvkHShH59NchS50f9y4At+PBn4U9bhtaW+fu2pSjux+gEDSTdnNwADfbfTOSSHsNz1WuN64noXdWQr6SzSOv6ijKyk9m1A14skdfHj/iT7vuJLeG9IusqXyqZTY8esvkW1b7n230ZoL314DPCSmZ1Zumtm/2hzfGCUYyK1P+uCbV0sfRukWLsxyulBujm4F9jqj9wuph8AxzLyrcD7gHcBm4DnSDef7wO6eJ2uwBJv81mgf7H09XOzSDtwdpLZKQR8Gtjl52Zl5P1dz92u97ltoO9E0jr2ceAgsDJz7lpgfV75Utu3Tn1J93Ged5tvBj6bqTOC9MWvBu6nJipLT+CPwMvAaqBHEfUty/5bQJ8ouz5ch/4LgK/lyZrcP4rxAB4DtvvnvRzo1Vxbl/oRoY6CIAiCsqRTLvEFQRAE5U84qCAIgqAsCQcVBEEQlCXhoIIgCIKyJBxUEARBUJaEgwo6DJJukGSSPlJA2RmS3t+Ca10raUU98iOqHbW9JX9qbhWUibydeb2jsXoFtLtA0uTM66ke8aSl7a6VRz2XtEbSf5UXBT3o+ISDCjoSlcCf/bkxZgDNdlCNsM7MhmYeq1vaoEcyaCnVZja0FdppiHFAVWs2aGbXARtbs82gfRAOKugQSHo3cA1wK+mf8Nlz31PKzbNN0s99xD8CeNxnON2U8vzkoi2MkLTWj6+Q9FelgKB/kTSomfr1lfSipHlKeZGektTNzw2QVKWUw2ldbgbos5O5kv4GzPHIBau8/nxJr0m6UNKPJX0rc62fSPpmE3Tr7+9vpKQukn4haYdSsNHbvcxsSRtc/pBHSMhvR8BQYLNSTqKF/n5ekzRJ0hz/HKo8ogWSRvu1tysFNm0s+nrQiQgHFXQUJgBVZrYLyAXvRNI4P3elmV0OzDGzJ0gj8mk+w3mrgXZfAkaZ2TBgNvDTAnQZlbfEN8DlA4Ffmtlg4DApEgHAQ8DtZjYcmAk8kGmrN3C1mX0H+BEpFNFgUrqJPl7mYVI4nVwoqanArwrQE3e4S4EZZrYB+Aopz9FQM/s4NYGJ7zezkWb2MaAbKVxSPsOAbVbz7/8BpNQY412fNWY2BHgL+IykrqQIDTe6vAK4rRC9g85Bhw0WG3Q6KkkhfCDF+askhfcZAzxiHsPQzP7dxHa7AwslDSRFhz67gDrrzKzWD7hSpto9ZrbVRZuAvj7zuxpYkpmUZGcRS8zstB9fQwoZhJlVSfqPH78q6ZCkYaT0HlvMrJCArxeRYsRNMrMXXDaGFErrlLeds9d1ku4AzgN6kEL8/D6vveupnbrmSTM7KWk7KSlebulvO8kJDnKb7HL5QuDrwL0F6B50AsJBBe0eST1II/UhSuktugAm6btNaOYUNSsKXTPyu0kj/4nuZNa2QNVsbqbTpJnIWaT8RvXdGzpWYNvzSffVLiHNqArhCPA6yfG9UF8hn+k8QMqEu1fSndS2UY6x1MwKoSbS99uSTmZmVm8Tvz1BAcQSX9ARmAw8ZmYfNLO+ZnYpsIeUYG4VcIuk8+CMMwM4CpyfaeNValIpZH9ku1OTemBGaytuZm8AeyRNcf0k6fJ6ij9DigSPpLHAezPnlpFmMCOBlQVe/gRpRjZd0k0uWwV8Nbcpw+2Vc0b/8hnf5PyGJHUHKgqcueXYSZpFfshf3ww83YT6QQcnHFTQEagk/UBnWQpUmlkVKaLzRqUt1jP9/AJgbm6TBHAXcJ+kjaTZTY45wM8kbaHwUX/+Pah3/KDnMQ24VdI20tJZfem27wLGKm0Pn0LK2HsUwFKq7jXA4sySYKOY2THS/aRvSxpPmom9Djzn+txkZoeBeaTo3CtJ6Rny+RQpenvBmNn/gFtIy5vbSTOruU1pI+jYRDTzIGgn+A6302Z2StIngAdzS4O+OWIzMMVqpyTP1e0LrPBNDm2h23xgvpmtb6P21wIzzSy2m3ciYh04CNoPfYDF7oxOAF8GkHQZKWvqsrqck3Ma6C5pa1v8F8rMvtTabeaQtIaUA+pkW10jKE9iBhUEQRCUJXEPKgiCIChLwkEFQRAEZUk4qCAIgqAsCQcVBEEQlCXhoIIgCIKy5P+qtkS88jXB/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data=pd.DataFrame(data={'Actual Energy [kcal/mol]': y_test, 'Predicted Energy [kcal/mol]': predictions})\n",
    "sns.lmplot(x=\"Actual Energy [kcal/mol]\",y=\"Predicted Energy [kcal/mol]\", truncate=True, data=data, size=6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE: 11.388102777477823 kcal/mol\n",
      "MSE: 232.25021739772032 kcal/mol\n",
      "RMSE: 15.239757786714339 kcal/mol\n"
     ]
    }
   ],
   "source": [
    "print('MAE:', metrics.mean_absolute_error(y_test, predictions), \"kcal/mol\")\n",
    "print('MSE:', metrics.mean_squared_error(y_test, predictions), \"kcal/mol\")\n",
    "print('RMSE:', np.sqrt(metrics.mean_squared_error(y_test, predictions)), \"kcal/mol\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can go back to the top and play with using different molecular descriptors, training set size, or kernels inside of QML to see how they impact performance. \n",
    "\n",
    "Enjoy!"
   ]
  }
 ],
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