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Revision 1db48f3a735eb0fba06a7d503f080a7ead512604 authored by Artem Artemev on 11 July 2018, 12:50:44 UTC, committed by GitHub on 11 July 2018, 12:50:44 UTC
Update version.py file to 1.2.0 (#812)
1 parent 707b195
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kernels.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using kernels in GPflow\n",
    "--\n",
    "\n",
    "*James Hensman  2016*\n",
    "\n",
    "GPflow comes with a range of kernels that can be combined to make new kernels. In this notebook, we examine some of the kernels, show how kernels can be combined, discuss the active_dims feature and show how one can build a new kernel. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import gpflow\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "import tensorflow as tf\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plotkernelsample(k, ax, xmin=-3, xmax=3):\n",
    "    xx = np.linspace(xmin, xmax, 100)[:,None]\n",
    "    K = k.compute_K_symm(xx)\n",
    "    ax.plot(xx, np.random.multivariate_normal(np.zeros(100), K, 3).T)\n",
    "    ax.set_title(k.__class__.__name__)\n",
    "\n",
    "def plotkernelfunction(K, ax, xmin=-3, xmax=3, other=0):\n",
    "    xx = np.linspace(xmin, xmax, 100)[:,None]\n",
    "    K = k.compute_K_symm(xx)\n",
    "    ax.plot(xx, k.compute_K(xx, np.zeros((1,1)) + other))\n",
    "    ax.set_title(k.__class__.__name__ + ' k(x, %f)'%other)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernel choices\n",
    "GPflow comes with lots of standard kernels. There are a couple of very simple kernels which produce constant functions, linear functions and white noise functions: \n",
    "\n",
    "gpflow.kernels.Constant     \n",
    "\n",
    "gpflow.kernels.Linear      \n",
    "\n",
    "gpflow.kernels.White     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And some stationary functions which produce samples with varying degrees of smoothness:\n",
    "\n",
    "gpflow.kernels.Matern12   \n",
    "\n",
    "gpflow.kernels.Matern32   \n",
    "\n",
    "gpflow.kernels.Matern52   \n",
    "\n",
    "gpflow.kernels.RBF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and finally two kernels which produce periodic samples. \n",
    "\n",
    "gpflow.kernels.Cosine   \n",
    "\n",
    "gpflow.kernels.Periodic   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are some samples of GP functions from some of the default kernels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/Artem/anaconda3/lib/python3.6/site-packages/ipykernel/__main__.py:4: RuntimeWarning: covariance is not positive-semidefinite.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-3, 3)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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VswiEJY/vborqtYRmeIs72sK0t0bX4J5Mjrd4+M83akiym/jezbOZlzqxGTWU\nUTyBuLvDmMznZ4IAY7PdYJ7iYEDH55UkR9koNpkEV9+cwIKScwoVF298/T1xxT0yWW2CUNBo43Xr\nBPw6+3e6hwz5UFx63DQvCZOAl06NfsevPH4A5i1EWKKj52L5FXDqGLI7etX2FArF9EfExKJ98muI\nleuRTz2BvvH53vf8IZ1t1d2sy4/HNoa87aOh2xmmoSZIwXwbFuu5a2UnWLnvsjS213SzrdoZ1Wvm\nFVixWASV07SYx9lOP9/cVEuyw8x/3Tib9FjL8CeNE2UUTyBul05snOmCnIdDGcXdXYbhGW1PMUBM\nrHZekvC4BCOsw9VtXLNHpoSkc+EeXo9OS1OI2qogbS3Ka6w4R7LDzOrceDZXOUdV7EV2dUDdWcTC\nZVGTRSxfC1JHHtwVtT4VCsXMQJgtiAc+B8uuQP7ll8i92wDYUdONL6RzbeHEh05UHPehmYywxv7c\nvTCFuSk2frGriU5f9Ly6Zosgf66Vhtpg7wb+6UKHN8Q336jBatL4+nV5pDgmZwucMoonEMMovvAW\nW61i0PAJZyRvcLQ9xQNhdwhM5nOe4h6ZEiMp5ExmI7SiJ5exx6WMYsX5rMqJpdMX7k2NMxLksQMA\niEVLoydI/hxIzUDu2x69PhUKxYxBmM1oD34O5hSj//rHyLMVvFnlJD3GzKKMkZe7HwtuV5i6s0Fm\nz7WdV7egB7Mm+PTabDxBnZ/vbIxqRdnC+TYEUHVq+niLg2Gd72yuxekP89VrcsmMm7yNgsooniCk\nLvG4dWLjL7zFQ3mKXU4j5CI2fuJnRUIIIwNFP09xWoYZTYPZc4wZbWuTMXOdbjNNxcSzLCsWgH3V\nbqSUNNZ7h41fkwd3QmIK5M2JmhxCCMNbfPwA0uuJWr8KhWLmIKw2tI99GeIT6XjsJ+xvcHNVQQLa\nBFawA6g45kcImLdg8JzB+Uk27l+Wzs5aFy+d6ozatR0xGlm5Fs5W+gkFp0dWqcf3NFHe6uPT67KY\nG+UczsMxo4xiV59MClONz2eUSx4o13CPUdwjq8etc3ivh3BY0tURJiHxwpCLiSIuXrsgpjg13cyt\n9ySSmW0Y5p3tEU9xh1cZHIrziMHEXbYULCdMvPjXLl76Wx1vbXRxaI+hz/2RwSAc2Y9YuirqZZnF\nyrUQCiEP7Y5qvwqFYuYg4hPRPvolttvy0CVsmOANdh53mJqqALPnWrE7hh7z7liQzMrsWJ7Y28zp\n9uhlfpqSqosOAAAgAElEQVRTZCMUhJozo98UPdlsPN3JKxVd3LMoZUzpPsfLjDGKPa4wb7zUTWNd\ncKpFAc6Vah7IKLZaBVJCOOJQq670U1URoKUxRGd7mOTUyUsfHROn4fVKdN3IUayZwGQWCE30yt4z\nz3DXNCOf+9Okyaa4uOnqCLPl1W7SdAuHpIucAgvrr81gTrGNs6cD7Njkwu/vt7pQfhgvDprmXEtn\neyi6k9g5CyAxWYVQKBSKIRGz57Jl0c3kuRvJ3/XihF7r5FHDSzx3wfAeT00IPrU2i0S7iW+/WRu1\n+OLkNLNRzOOUH6lfHI7Dgajq8PGL3U2UZMbw3qVjL+o0HmaMUezs0kEa2RIuBnqMYrvjQo9vT6nn\nHoOhJzyh4oQPXYeU9OhVZxmOmFjNuG8e3fBea/DznY0A2PsY9JoGXksyev3ZSZNNcfHS7Qyz7Y1u\nhIBZKyzsCrvwZ+oULUpg8TIHK9bG0NkeZvcWd6/HOByS7D1s5o0NP2FPbTZbXnVxdL83ajIJTTNy\nFh/Ziwxe/B4RhUIxNbS4gxwP2Nlgboe//x559vSEXMflNLzEBfNsI65Qm2g388WrcnH6w3z7zVr8\noejYNHOKbXhcOo31F4fjsD++kM4PttYTY9H43PrsCctDPBwzxijuv1lsqvFFKsINtFwSFx/J+uDU\nCQZ0OiLhCR2tkU12k+kpjjXk87h0AgGJT+q8erqTQNioqteTTi4lBcJmO9Xh2ex400X5Ed+Ay+OK\nmU8wINm91Y2mCdZfH8eKObHEWTW213T3tsnJt7JibQwdbWH2bffQ7QyzfZOLBpHLXNdO1l8fR26B\nhTMVAZyd0dvAKUpWQcBvFAdRKBSKAdhWbYxVG267FuIT0X/1I2Qg+hvRyo/4MJlg3sLBY4kHYl6q\nnc+uy+Zkq4/vb6kjGB6/YTwrx4LjIi7m8fjuJuqcAT67PpvkSco0MRAzxyiObBYL+C8OQ83n1dE0\nI+dvf+ITDaPY2RmmtTkEEtJnGUoQE6sNG3cUTXqq7XncOsGgJCB0dAk1XYanrWd2m55ozC6PZ99O\nW3OIk0d9vR5uxaXFqeM+3N06l6+LJSbWhFkTrM6NY1ed67zBOyvXyuLlDhrrg2x6qRtnZ5jlh3/G\nguxuUtLMLF7mwGIRHDsYPW8xC0rAbEYe3he9PhUKxYxi61knc1NsZGcmo33wU9BYi3z291G9Rkdr\niPqaIHOKBs44MRxr8+P58KpM9tS7+d6WunF7jDVNMGe+lfbWMB1tF9eze3OVk42VXbxzcSpLZ8VO\nqSzT2ij2uM9trOv1FE+xUfzyqU5eKO/A69WxObQBN8xZrAJHjKC7K0xLYwiTGYoWGfFGKWmTFzoB\n4HAIhIgYxQEdf+R+VnUYQf6OGA0hINXuAkA32SgqMAzmnop9iksHv1+nqsJPTr6F1Ixzs/m1efG4\nAzr7as8vnjGnyMa6a+PIK7CyIbeCrObdiPmLAbDaNArnW2lpDOH3RUeXhM1uVK86sjcq/SkUiplF\nkyvAyTYf6yObuMSi5Yir34Z87TnkqWNRuYaUkqMHvdjsgnkjiCUejFuKkvnIqkz21Ln56sZqOsdZ\nCjp/jg2LRXD6xMXjLW7sDvDznY0sTHfw7svSplqc6BjFpaWlT5SWljaXlpYeiUZ/Q6FLyeuVXfx5\nTwsbn+/m6H4vUspznuIJDp9ocgVocg0crxjWJb872MILJzvweeWA8cQ9JCSZ6OoM01QfJD3TQnKq\nicxsM7kFk5ePD+jdUOdx94RPGJOLqkje2ex8CwXzrMSFjRQxppCXAmstJrPKW3wpUlnuJxyC+YvO\nH+iXZcXiMGu8Vt5ywTmp6WaWrYkhtmq/Udq5YF7ve7NyjApFTVGMcxNLVhqen5bGqPWpUChmBj2h\nE+v7ZJ0Q7/wgpKSj//bRqIRR1J0N0tEapniJHbNlfLGxtxQl8x8bcjjT4edTL55hT51rzH2ZLYLZ\n84xiHq7uqX9+B8OSH2ytR9Pgs+umLo64L9HyFD8JvC1KfQ3Jz3Y28sj2BracNBT7zKkAFcf9venE\nAv13u0eZH71Vz6M7Bn7YHm320O0P0+QK4vPoOIYIg4hPNOFyGiWdZ+VYEJpg9YY40mdNfBnD/sTE\naTg7wwR8Epdu3L9eozjPypIVMZh8TmI8TeQ2bMXU3kBsnKY8xZcYPq9O5Uk/2fmW3hCgHqwmjStn\nx/NGRSve4MB6IU8dgznFCPM5HU9IMmGPEVHd/CGWrTGut/PNqPWpUChmBm9VdzM3xc6s+HMOKGF3\noL3/49BUh3zuj+PqPxjQOXrAS1KKifw50XFyrc2P54dvKyDBZuKbm2r5zubaURVM6kvhfBuaxkXh\nLf7dgWYq2n18Yk0WGXGTb/sMRFSM4rKyss1AezT6Go5DjR4SbSbiMB7KickmThw2lvrtjsGLYkQD\nf0inos1Hk2vgB3jPRqOQLvF69SFjg3tKKQtBbz7gqSImVsPl1NF1OBUy4jurOvyEy36DPBxZhva4\nWb/rYRae/CM0NxITZ1JG8SVG+REfUsKCkoGXA6+fk4g3qLOt2nnBe7LbCTVnEEVLzjsuhGBWtoWW\nxhDhUHR+uyJ9Fixcitz6KlJXOqqYmehdHejbXkd/8hHC3/os4W99Fv2Pj6kVkiFodgU51eZj3QC5\nicWiZYgNNyFf+TvBiuNjvsbRAz4CAUnJSkdU6w3MTrLx41sKuH9pOgcaPHzyhTN8dWM1G0930u4e\nebYdu0Mjr9BKTVUAr2fqxsedNd38/UQHtxYlsXaCc0WPhkmzxkpLSx8CHgIoKysjLW1ssSOe4CmW\n5SbirwqAgJvuyOXZP9cQDOjMyomlutJFamrqBcpoNpvHfM0eDtR1EZbQ4QtdcA1dSnbVVZLksODx\nhtDDkJoWR1pa8oB9mYSffds9ZOU6yM7JuOD9aMg7UtIz2qmubCcx2UJTS5D0OCstrgAd215llsdJ\n0rU34yKMDHkw5eRj7mojbXkszfWdpKSkomliUuWdbKKlu2PhYrmv3c4gNWc6WbAkkdkFA+ePvDJV\nkrenhS21Xt61Zt5573mP7MEpdZI3XI+l3+dZsNhDVUU9Xe02ihZFJ1m775Z30PXjh0mor8K2bPWQ\nbS+WexxtplJvYfrd14tdXhkMEji0B//+HQSPH6Sl8iRgFKOwzikCILDlZeTWV4l/4NM4brxr0opA\nRZuJ0t3XqusAuH1pPmlJF5Z21j/8OdqO7MP5s++Q+oMnEObRmUg1VW5qznRy2Ypk5hWlRkXm/nwk\nM4P3XBHkmUMNvHC0iZ/uaOSnOxrJTbRTlBHH7GQHOUl2shKMV1qs9YKwhFXrglRXnqX+rGDNhsnX\n+UZXkEd3NlKcEcfnb1yE1XzxbG+bNKO4rKzsceDxyJ+ytbV11H3oUuIOhMlyCNqFmZBZ4vN3UbLS\nTnVlAHtMCF2HpsbWC+J40tLSGMs1+7Krog0w4mDO1DeTYDu3hNzqCdLqDnD3whQ2HTc8ZWHppbV1\n4LgdXZckp5rIzhcDytVXXhkMgseFSBzYwB4vUhizzKQsAS2wMM1OiytAVWw2yWdP09rait7cDDYH\n4fRswrVn0Ux+dB1qa1qIidWicn9HS3Z29qRcJxq6O1am4r4OxJF9HhCQUyCHlOeauan8YW8t1Q1N\nxFjO/T70bW9AQhKdiWmIfuebbZKEJBMH9rSSnO6PyoNczlsC8Yl0/uExtOyCIavnTfY9vhT0Foz7\nWlXXBECcbXI3EI8GeWAH+kt/RbQ2IecsQLvjPkR+9EqQjxcpJXLXZuTTT0JnG1htUFhE7HsexFu4\nAPLnEo7ot9bRhv7kT+n+3+/jqq1Bu/PdUZVluuvuK8cbKUy2YQ+5aW11D9zoPQ8R+tm3afn9Y2i3\nv2vEfXs9Optf6yY+USN3jj7hY8rtc2K4rbCAMx1+Tjph39lWjjV08capVvquuZk1QXa8hdlJNuan\nOliU4WBuip3c2VZOHO0ip0BOasYrf0jnSxtrkVLyubUZODsnJchgxLo7tev2o8QT1JFAvM0EJoEX\nw+DMybeSk2+lutKIkQkEdMyW6A/C5W3nUke1e4LnGcVtHmNX6KJ0B3tOGIHwvz3czK2WZJZlXZhi\nRNMEV94w9JKBDIeRf/4lcusrENbRvvNLRGr0q7ykzzJTWGTDPgs4BCWZMWyucnImPpvl9W/R7Qvw\ne38e98cnE5NbgDy4ixiTEbLicYV7cx0rZiYBv051ZYCcfMuwCejXzE7md3tqOdzoYU2eod8yFEIe\n2YdYsXZA41QIwbyFNvZt99BYFyQrd/xxeMJiQbzzA8jfPILc9CLiutvH3adi5NR0+Xls30leKW8B\nJOvzE/j4FbOwmi6esULqOvJPjyM3vQhZedhWrMW3awv6dz6P9sBnESvXT7WISGcH+v/9DA7ugtnz\n0N73b7BoOcJiIS4tDV8/w0skp6J96mHkbx9F/uNP6HHxaEr3AWjzBClv9fLepUN7RsWyK7BdeT3+\nF/6CXLEWkZ0/bN+hkGTPW270sOTydXGYTJPjoRdCMCfFzuqiNN5WYIS1BcM6ze4Qze4gza4gDd0B\nap1+jrd42XLWCPFMtJm4clYCWbqNiuM+lqyImRR5dSn5yfYGKts8fPWaXDLjJjexwEiYVkaxO2AY\nwbFWDR2oC58fR2O1GQNuwC+JiXKqOykl5S1eMuMsNLmCtHtDFPRx3LZ6jDjjzDgLs2xWCMGxTi85\njdYBjeIRXfPXP0bu3gKLlsGxA9BUCxNgFFutGkuWOzjcZMycZ8VZyMBHZVwOhILsPdnIP035LEsp\n5oqlq5DP/xlH9SGgBLdLJy0z6iIpLiIqT/oJh2Fu8fCphZZkxWM3C/Y3uHuNYiqOgdeNuGzVoOdl\n5VqIidU4fcIfFaMYQKy9zvCwPft75NrrEI7JGfgvNbxBncp2H05/mKpOHwcaPJS3erGZNW6cm4hJ\nEzxf3kGczcRDl18cg4XUdeSTP0Vufx1x092It99P4qwsAlWV6P/zLfTHvo/4wKfQ1l03dTIe2IH+\n2/8Bvw/xrn9FXHc7Qhve2SM0Dd7/caTHhfzT4+ix8Whrrp4EiS9uevb8rMsbPn414V8/Q8uBXehP\n/hTt/31vyPuu65K929x0toe5fH0McQlTuypiMWnkJFjJSbhwHG3zBDnc5GFPnYuNdZ2s1uMJn5LU\n2wNcW5yAZYInrX842Mq26m4+saGQFdmjK2gyWUQrJdufgO1AcWlpaW1paem/RqPf/rgDRlB4jFnD\nrGu0BoPnJbTuKZQxEbmKO31hOnxhVufGAdDeL19gj6c4NcZCnmbDI8N0Ex50U95w6G4XcvcWxPV3\noN3/MQBk24XprqKJK3J/46wmCn3NnInPAeBMg5GOrTk2DWbPg6RU7Ie3ItDpqOkatD/F9Cfg1zlz\n0k9WrqV3c+hQWEwaJZkxHGg8tzQp92w1lnwXLRv0PE0TzCmy0dEWpqM1OonlhRBod70PvB7kW69F\npU/FOao6fPz3W/W8/6+n+NJr1Xx3Sx1/OdxGIKzznsvS+OuHVvGR1bN48PJM7lyQzAvlHewdRzqp\naCGlRP7xF4ZBfOd70O79UG9GFBGXgPaZb8KCy5BPPoI+BRlMpJToL5Sh/+zbkJKO9pUfo91w14gM\n4h6EyYT20OehuAT5xH+jb311ZNduaUR/5W9jFf2iZvvZbuYl2EgxW/B5dXR9cDtBS0pB3PcQnDmJ\nfPW5QduFgkZ1z+aGECUrHVGb0E8UqTEWrilM5N+vzOG398ynZGkMAjh00MNHnqvkn6c6CA1xX8bD\nP0608/TRNm6el8S7lk9OGM5YiIqnuKysLLqBS4PginiK7boG6HQTpr47QGGy4cGyWifOKO6IGMFF\nqQ6gg3bPhUax1SSINQuSQmYqpRFe0Oweo1HcacQvUzAfklKNNBUdExuj1NcTX9h2hp05V+M12TjT\nFQCsNNmTEUIglq+BN14kZ9FiargKdnkonNtNfLJEuwjyDCqiR8UJP6EQFC8ZeQL6ZVmx7K5zU93p\nJy/OhNy7DbF0NcJ+4caWvuQVWjlxxMvpcj+Xp0VnEUsUzod5C5Eb/4G87rZRGRaKC3H6Qmyt7mbT\nmS7KW33YzRrXz0lkVU4cSQ4z2fFWHBbD15LksNATtvn+ZRnsqXPzm/3NLMuKnbJ8pEbIxGPIN/+J\nuOUetDvuu6CNsNnQPvYV9Ee/gXziv5Fm86SFUshQyDDYt7yCWH014gOfRFjGlqpKWKxoH/8K+v9+\nF/nbR9GP7EPc+e5BwwHkmZPoj34TwmHk6qsQSROzUWyyCIclzQ1BmhtCtLaEWO1MQBOCjc+fy44T\nE6uRkGQiOc1EWrqZxGQTIqKbYvVVyD1vGStNJSsvuG9dHSH27/TQ7dQpWemgYN7F6fkcDLtZ46ZF\nSRzxe9BOCty2MP+7q4m/H2/n/csyuCIvLmobNV862cGv9jazJjeOD6/KvKg3gF48AV4jwB3Jf2oO\nGTe0W4b53YEWOn2GgdrrKZ6AtGw9RnFGrIV4m4laZ4AP//10byLtVk+QtBgzzk4dky6olX6SHWaa\nx+op7jCMYpGYbOyATUiG9lb0v/ya8E+/EZ0P1Y8eT3ysv5s57ZUAVKXP40zAmP02WxMNmVZdBUJQ\nUvcMsxvfpLYqwObXmmhvubhKRyrGh7MzTGW5n9yCC/MSD8WG2QnYTIKnj7bBiUPgciJWbxj2PLNF\nUDDXRkNddBPLazfcCa1NcGhP1Pq81JBS8kJ5Bx9+rpLHdjfhDep8YHk6v7p7Lh9ZPYuVOXHMTbH3\nGsT9sZgE9y9Lo6YrwBtnpmZ1SYZChpG76SXEzW9HvP39g7YVNhvax78ChUXoj/0A/c1/Trx8jXXo\nP/ySYRDfVop44LNjNoh7EHYH2ie+grj9PuSRvegPf5zwD7+MvvmfyOrTyOYGZPkR9D8+hv7dL4DN\njvb/vj+tDWKvR+fYAS+vPudkz1se6msCeIXOIekme4GZpasclKxwMH+RjaQUE91dYY4f9LHlNRcv\nP+tk91tujh/uxNmpw3v/Dex29Cd+YuiPLmlrCbFvh5vNr7oI+CVrroqddgZxX4oW2bFYBTc5kvjy\nVTmYNMF3t9TxpVerOdVnH9VYkFLy9NE2frG7iVU5sXz+youjQMdQTMuYYhE0buodJcn89mgLv9nb\nzGfWZ2Ox9HiKdYJB2ft3X54+2oY7EOZ9S9NH9eV0RAzvJLuJFIeZHTXd+MOSynYfl+fE0eYJkRpj\nobnRaJedbWFlcixlR9rwhXTso0w5Eu7xCielGP+mpCE7WqHqFLgnZgnSFQijCbAf3k1ht5G6Zm/O\nCpwiYhRrRkymmL8I7b9/jzy4i8W/eYTCW5axaX8iPu/UlthWGFRX+jl+yEdGlplFSx3Y7KOf+0op\nObDLg8UqWLxsaA9vfxLtZm4rTubZ4+3c4D/MQkcs2uKVIzq3sMhG5Uk/p0/4WboqSjHAS9dAYgr6\nllcwRQp7KEZOIKzz6PZGNp91snRWDB9ckdG7Ojca1ubFU5Rq54+HWrmqIGFSN93JYBD9F9+FQ7sR\nb78f7dZ7hz1H2B1on/46+uM/QP7+54SP7kO7+30j2ng1KtnOnEK+8jfkvm1gj0E88LmoxgALswVx\n13uQ192G3PwycttG5O9+fl6GAoSG2HAT4h33I2Ivnpyxo8Hv1zl11MfZ0wGkNPYp5M2xkpZh5utv\n1NAUG2TFZbEDein9Pp3W5hAtjSFam4LsqDWev0ITODb8GHNbPfozDXi0ePQwmExGCfv5C229e5mm\nK1abRvFiO0f2e7l8fgyP3FrIq6c7+eOhVv79n2fZMDue9y5NJyt+dKEh3qDOY7sbeeOMk6tmJ/DJ\ntbMmPGY5Gkwzo9jwZMqAEU1w25Jkdre4aIiUXRaawGIVnC73c+akn5vuTsRkEoR1SYfHaPNCeQft\n3hCt7hCfu3LkcS3tTmPGlFS+hxRHHjWdfm7RkvF2GTK1eYIsyoihsS5IYrKJf78mh81VxjJNsztI\nfuLoZpJ6eyR8IiGymy85DWoqob3F+EVOAK5AmFgTiKd+TcqcYjJizbzIIgAKu+toiJ+FlNIIoYiN\nh6IlSMBafQxYi9+nCiVMNc7OMIf3eXE4NOqrjVWK5WtGv9GzrSVMV0eYpascYxr0716YwiunOvmq\nXEPq6qXcdLyLdy5JxTzMRLQnsXz1mQDzF9mjktlEmM2I9TcgX3oa2d6CSBl6s6rctx297NeINVcj\nrnobJKdcsmEXFW0+HtleT3VXgPuXpnPP4pQxL30KIXjfsnS+trGGl091cseClChLOzAy1Mcgfu9H\n0K65dcTnCrsD7WNfRr7yLPL5P6Hv3wHZ+UbKtnAY2d0FHpdhVGbnGZkhlq0ZNlQIQLa3oP/pcTiw\nExyxiBvvQtx494Sl3hTxiYjbSpG33guNtVBfjQwEEHHxRqXJaWoM67qkqiJA+REvoRDkF1qZv8hG\nTKzxm+32hznc5OGuhYPrrs2u9WaxklJityVx+lQL3Z1hvB4LAa8ZramcjCULSJqbQWaWZdzlm6OJ\n7nEjyw8jG2qNMEuPG6QONgckJiMyc6BwHiJhYN2aPc/K2Uo/R/Z5uSbTwtvmJ3NVQQLPHG3nuRPt\nvFXdzdUFCdy9MIWCYSbEUkr21bv55d4mGruDvLskjdKSVLSLOGSiL9PKKHYFwggg7JfY7AKhCZLt\nZo61nHPxW20Cd7dEB9zdOglJJl493cmT+yt49LYC2r0hEu0mNp918q+XZ5BkH9kt6GztICbkx1pT\nScqsQmIxkaPZaHcG0aWkzRMiU7PQ1RFm8XJjQMyINZa+ml1jMIo72sBsoSeNhkhJMzwJYAzGwQDC\nEt2gfpc3QKynE2x2TP/6WT7qtfGfr9cAsKb1KH+Oz6HbHyah556lZkBKGqaKg2ipa/GPMZbbH9L5\n+/F2bitOJtZ6aRof0eLIPg8Wi2D99XGcOu6n6pSf4iXh3gfESKk548dshuz8selYot3Mo3nN7Hth\nI2+tuZc/HW7FbBK8c/Hwy7LzFtqpqQpw9ICXVeujk0ZGXHkD8qWnkFtfRdz5nkHb6dteRz75CCSn\nIl98CvniU5CagfbZb0BKBnLbRmhvQdz5niFzH08Xvru5Fm9IUpBkY06yrTdFUq3Tz/bqbvbUu0m2\nm3j42lxWZMeN+3pLZ8VSkhnDU0fbuGFu0qDhFtFChkLoj30/YhD/G9o1t4y6D2EyIW65B7n+euTO\nN5FH9yHLj4DFAvGJxp6PSNpBtr+BtFqh5HLDOJ5TDKmZiD6ODNndhdz6GvKFv4CUiLffj7j2tknL\njiKEgKw8yMpjepgpg9PRFuLQHg/OTp30WWYWL3NcEOq1q7absGTAKnYDIYQgPsFC7mwrzDaOyeVz\n0b/xKFQH0b72SNSfvWNBNjcgd29BHtxFy9kK6KneqWmG3SA08HkhGDi3KpCVZ+jl2msRWXm9fWma\nYOmqGLa+5uLEIS8lK2OIsZh437J0bitO5q/H2nj5VCdvnHFSnOZgfX48JZkx5CVasZg0dClpcgU5\n2OjmtdNdnGrzkR1v5Zs35FGSGeVUYBPMtDKK3YEwMVYNn/dcsukkh5lOX6jXgzm32IbLqVN50o/b\nFSYhyURtVwBvMNzruV2RFcsbZ5x0eEMk2c3Ilkbkrs2IW+8ddCbZ7vSQ7HdDZxsphWbskXBsETAy\nU4QlJLjNCA1yZxvGcE8t77FsttM7Wo0ZXo88yf1yK7pd50IrooSrqopYfwDtwX9HJKWwPAnuXZzK\nqV37KHDVA9DkDvYaxUIIo2zv0f04rjfj9+q938No+OepTv5wqJX0WAvXzkmM6me6lPB6dNpawhQv\nsWOza8wttlFV4adiWz2LDz+Odss7EQuXDttPKChpqA2Sk2/FbB77YzNxzxtcGzjL9bct4Htb6/nz\noVbW5cWTPUCqoL7ExGoULbJz4rCPA7s8pKabyS2wjGtzRm/p522vI2+/b0CDVjY3IP/4CyhagvbJ\nr0FTPfL0ceTf/4j+nc8DAlyRTTpCIO5675jluVhIcZg53uLl+XLPBbvOkx1m3l2Sxu3FyVEtvnH/\nsnS+8PJZ/nGindKSiaumJcNh5K9+BAd2It79EGMxiPsiEpIQN94FN9418PV0HU6fQO7ejNy3Hbl3\nm2GMCAFxCUYGllAQnJ0gJSxdjXbfgwiV03LUBAI6Jw4ZoRJ2h2DluhiycgceI7bXdJMeY2ZeyuhD\nfnoQ9hi0j/wH+nc+j/7rH6F98mtTsnok9TAc2In++gtQftg4WFhE7D3/gjc7H7JnQ1LKeeObdDmh\noRZZeQJ5ZB/y5WeQLz0NCy5De9s9sGgZQgiSU416BWdO+snMsZAxy7Bfkh1mHliZSemSNDae7mTT\nGSdP7Gvu7d9uFgTDknBk+MhJsPKRVZncMDdxWoRL9GeaGcU6sRYTPq/emwswyW4iEJZ4QzoxFhOz\n59oIBiWVJ/24uo2ZU0/6tE2RDR6XzTpnFBcmg9z+BvIff0KsvRYGWVrt9IVIDriQrlZyTH7iIr89\nc0jQ5gkaJnKHICvX0rvcnGQ3YdHEmDbb6R1t5xm9IjX9/BiwKBnFW886Odvp5z0lqbjcPuIS4s4z\nnN63LB29LUjlsQ4AmlxB5qf2WRqcvwh2bMJmDuM/Wo5sOIl4+/tGfP1gWOfZ40ZFmzrnyOu3Ky6k\nodbQs+w8YzBzxGjk5+icrY4lp95F0o+/ili1AfHODwwZQtBYFyQcgryCsXtDpLMDju5D3HAnQtN4\n8PJM9tVX8uzxdj66Ztaw588tttHeGqKhNkDNmQCNdRZWrI0ZV1J8se56w0g6dRSKS86XNxRE/81P\nQNPQPvRphNUGeYWIvELkvIXoT/0GkZiCuHw9ct825PN/QRYtGdEk42LmoVXGdxHSJXXOAC3uIJqA\ntFgLeQnWCdklXpzmYE1uHM8ca+dt85POrTxFEamHkf/3P8i9byHu/eCkFLAQmgbzFyHmL0Le9xDU\nVL8WogAAACAASURBVCJrq4xNns5OCAQM73JKOqJkJWL2vGH7VAxMwC+pPRtgTpGN4iX2QUMZ3IEw\n+xs83FaUNG5dFvlzEe9+yIjH/tvvEff8y7j6Gw0yHEbu2IR8sQyaGyA1w1hhuOIaREr6gIVceuWO\nS+jVS25+B7Krw4grf/0F9J88DPMXob3rAcTseSwssdPaGOTATg9X3xx/3n6UBJuJty9K5e2LUmly\nBTjR4qXRFcQVCGM1aWTGWViQ5iAvcWLGjcliehnFwTBxVg2fVyc90xA9KfIJ/j975x0Yx1Wu/d+Z\nme1Vu6te3XtvieM4TnNCCCUUQyABLvCFEMolcAm9hAuEHsqlXPoNgYAhhISQ3hyX2LGduHdbvUsr\naXud8/0xK8myZUm2ZEcJev6xtTvlzOyZM895z/M+b1c821dW1mQSWKyCaI4U9zpH1PWkMCmCWfkG\nqevzGg62kRUKP9/RwZsvclPm7pc6ZH/6TYSm0WVdw9RUGLqDrKrdQv7xdqqnvxtrVqE9msaNhsxC\nQXF/trAiBAVO0zlFirNdnVBQ3P/BaZHi8Fkf81TE0ll+sb2VaCrLW8pVopqVgPX0bGexei1Figma\nOI3giymzDV1xuJWYbkK+tBnOghRvqAkRjGfQFEFjeIIUjwZNdSncHqVvwiilZPq2n9Lqfzd7Vn+R\nS+WT8MTfkAd3o3zsS8bS7iBob01jtgjyAuceCZEvPAvZLOKSqwHDH3NxiZPtjRF0KYfVlymqYMVq\nJ1JKThxOcmB3groTKSZNO/csb7HwIqTNjtz8NOIkUiylRP75V3DsIOKDnzptwiDKJqHefpLjy6wF\nRsb++t+gfOnu14TeWFMElV4Lld4Lk0V/88J8Pv6vau7b28GHlg0/STobyGTCmODs3GL4EK+9YUyP\nPxIIRYHKqQOIr5Syzy70XJJfJ9APp0vlyuvdWIbJd9jeGCGjS1ZWuMfkvMrqa9FrTyAfux+9qBTl\nkqvG5LhngpQSXn4B/YE/QEsjVExGufWzsGjFOY87wpOHeN3bkFe9CbnpSaPy4Tc+hVjzOpQb3sPi\nix1sfCrM9s1RLl4zeHW+Qqd5XFajGwu8qp7MSErHZVLJpOmTT3ge/RMAwacGWuY4XEqfrdPJhTZK\n3Gb8dm3A57KjjWabnyfbBVvrI8gj+8ne/RVk7XHYtRX50ha6hYW8VAi6OlDbGjEpRocwodAZzuAV\nRgd1ugfe0nzHyEmx7O5EZow26V2dAxMufDlSXGgU1CA2elL88OEuwsksuoSjDUEimg3nYKTYZMZ5\n+TV4rSrHgomBXxaXgd2J2niUlNkNLY3IYIeRgDICHOlI4LKoLCq2T0SKR4FYVKerM0tx+UkD1f6X\nMR3YzqxAK5G4SteKt6J8+cdgs6N/7wvoD/4JmRz4e0op6WjNECjQznm2L6VEbnwSps5CFJf1fb68\nzEkwnuH4qX1oCAghmDLTSp5f5fjh5JCG+8Mey2JBLLsUuWMTMmhEVeTxQwTv+KDhW3vtW0eU9S9M\nZsRb3gsNNcgtz5xze/6dUe6xcO00L48d7aama+T9YSjISAj9qQfRv3CrQYjXfWBQH+ILhe5ghqMH\nEuzYHGXD4yEeub+HJx4M8cSDIZ78Zw/HDyfIZicce84VwxFigC11Yfw2jemBc5dOnApx4y0we6Gx\nErF7+5gd91TI2mPo3/kc+s+/BUJBue3zKF+8G7Fk5ZhMxIXJhHL5dShf/wXiiuuRzz2KfufHcbUd\nZOFyO10dWXZvjxnE/DwhkzG8pA/vi7NjS5Qtz0bY/HSYFzdFOLQ3Tkdb+ryefzC8qkhxNJXFk0tY\n6NMUtxwHoGvHi8hwvym306USDRsa1654ps9+rdxjxqwqOMxKXwSZYDtdZmMm2RpJIV/cAAdeNpYW\nhCAuNBKqBa+qQyKOrDlmEMAcunuy+ITWd96TEbBrfdXuToZMJgf+3dGK/vkPIZ9+CJlKIqNh8Jwk\nj3B7IVDYZyIvx8CW7eHDXczORc2faYjTY3ZR5jnz4LGywsWLDREiyX4PWaEoMHUWlkQXKbMbCeh/\n+TX6J282klGGQTCeIWDXKHVbaA6n0C/wA/BaQWOtMaEozenZZTqNfv//QaCQoiuXoGrQVJ9GFJYY\nPqQLVyAf/jP6l24zEoRyiIR1EnFJoHAUi0hHD0BrI2LV2gEfLy1xoAh4seHs++7UWVbiUZ3m+nPz\n/e6FuO7tICXy/t+jP/UQ+nc/j94TRLzno4gbbh75cZZeAmVVyBFWCpvA6XjX/HwcJoVfbG8d1XMv\nYxH0v/0e/TPvR/7lN5BfhPKZb6GcQft7vhGP6WzdEGHjkxEO7U0Q6s5itSlUTbEwd5GN2QutOF0q\nB3Yl2PhEmFD32HlyT6AfsXSWl5qiXFzhGlPnA6FpKB/+LJRPRv/FXci9Y+t/LruD6L/7EfrXP2mM\nozffhvKVHyMWXXReZAnC7kB55/9DueNboCjo3/sixbvuZ8YcM421afbujI8pMc1mJdXHIry4KcLj\n/+hh2/NRjhxIEurKGjlJirHKf+xgkheejfL0wyFqjo0uIHI2eHXJJ1I6bofRZKtdIJNJ8npaAOg2\nu6CtCVwGWXW4FFJJSSiWJZmVLC33sqO+m/KcNCLPqtEVzxjC9WAHwYAhVWiNpJHHDxnJEZEQLFhO\nVy6C6SsMwBGguZ6k341EIhAEuzPkayasFnGatsmXSwTM6rKPmOvbNiD/7yco3/wlIqcLlo/81cgS\nPbQHsXilsfNJkWKhqKh3/QoZixq6olGS4lRWpyeR5foZDiKpLM92gZA6qyadWad81RQvjxzp5vna\nENdNP6ltU2dh3tGGrpjIeIsw5Vwy5J4XYdos9GSaY8cNneip9ycYz5Bn1Sh1m0llJe3R9Gt2WeZ8\nQUpJfU0KX76Kw6kiEzH0n90FDdUot34WYTFTWJKmpTHNvCUSxe1F3PJp5OWvR7/nJ+i//zHKd36L\nUBQ6Wo0J3GhIsXz+MbDZDeJ4EtxWjZkBG5vrwrxzXuCsfMILSzSsNkFLU5rSynPvH8JfgLj6jchH\n74cXn4fZi/B/7i6CibNbpRBCGBOLf/0VGY0gHKN3Zvh3g8ui8h+LC/jx1hb+eaiLN806uxwJqWeR\nWzcg7/89hHsQK9YgrnkzomzS+WnwCBDuybJ1Q4RMWjJrgZXySeZBI5pTZkBrU5rd22NseirMkksc\nFBaPrlDHBAZie0OEtC5ZNULXibOBsNpRbv8a+g++hP7TbyDe8zGUlVeM6pgymUQ+9aCRBJfJIK55\ni1HE5UK5kkydhfLlHyH/+HPkP+9j8pxDZFZ9kuPHU6RSkoXL7aNKvI6Gs9QcN3JE0qkerDZB5WQz\nhSUm8gLaacfOpCWtzWmqjyTZuzNOfXWKRSvsffLA84VxHyluDqf6IrrRdBZ7rslWmwLdnTjTcRQk\nXWYXsq25b7/eiG1LpxFZWjPVz1SflcUlhj2Iz6YRjGehuwuymb5IcUs4BY21iCvfCHMWobzubfQs\nNKpx5VX1m7anzG5UxVj2i0V18hQNh+v0H8tn09AlfVX3pJTIf62HdApqjhiftbcgNz8FmgbHD0O3\nkXg2qF+lzW5YroySFIdz0V6PRWNWvvHQzes6hq/gzJZZk/MsTMqz8MyJgdIIMWcRlrQh50jNWGp8\n6C9AHtiNvP//6Pzu9ziyP0Fb8+lRvmA8g8+uUZozBt9SF+bxo92jurZ/F0gpkc0NdDVGiIZ1yirN\nyK5O9G9/Dg7vRfzHJxBLjAlWSbmJVNKoxtQLMW024vp3Qk8Qjh8CoL0ljc2h4HCe28Cjh7qN5KaL\n1iAsp686XD8jj8bQ2Vc1682O7u4cfVRNXLcO8YYbUT79TZRPfBXFeW56QzFnseEFenDXqNv074or\nJntYVurg3t3t1PUkh91e5gIH+gP3on/lo8jf/RB8+Shf+AHKB25/RQlxNivZsTmKlHDJlS6mzrQO\nucRfWGJi9VoXDpfK9o1RWgcZHydw7tick07MyD+74kMjhXA4UT71dcOv/3c/RP/zr5Dps/8NZSaN\nvuEx9C/eivzHvTB7IcrX/gflbe+7YIS4F8JqQ7z/dsTNtyEO72XG3z/N7EkJmuvTbHwyTHfn2VWt\n1bOSpvoULzwX4ZlHwlQfSRIo0Fj7hmKuut7N3MV28otMg5JtzSQorTBzyZVOFl9sJxrR2fhUmLaW\n8/ucjFtSnMlI6k4kufPper7yTD3JjE4iI/us0Kw2BYLtKEi8mqTH7DKyMnNwuIztOoPGj1jutfKh\nyiKKNIN85dmMSDFBw1okaDMIaEc0TRaBmLcE9RN3IqbMpHv2cgC8pf3FPpJmNybiRGUWc0bBllVx\nuk6/nafql9n3EjQb3r+yrtr49+Au0HXENW+BeBS5b6ex7SCkWAgBdueoNcU9CYNcuC1qX+LhZT0H\nhywrKoRgUbGD6q7EgOVOUTGFgk9+DoDU6jehfOTziEvXQkM18rlHSOXedbHowOIeWV3Sk8jgsxmR\nYoDfv9zOz15sIZF5bRcCkfGYsWKQOLcymrKjFf0LH0L/8m3UPrAJRZEUB1Lo3/sCdLSgfOzLAyIX\n+UUmQ0JRd0qi5IJloJmQOzeTSUvaWzMUlZx7lDj+7CNGlGP1tYN+v7LCxYyAlXt3dxBLnx3B9fpU\nYlGdZHJ0fUNYbShvvBExfe7oliMnTQe7Y4D8ZAJnByEEH1lRjFVT+MHmJtLZwX9bGYug/+Fn6J+8\nGf37X0Q+9jdwexG33IHyue8iKqdc4JafjmMHE0TCOguX23F7RzaptNoUVl7hxOVReWlLdEJKMUbo\nlU6sHGPpxKkQdodhz3bVm5BP/xP9zo8j9+4YkdxARiPoT/zDkE3e+zPw56N8+i7U2z6PKBh5YbGx\nhhACZfW1KP/1TUglqfrDf3JRZRPplGTjUxF2vhAl2JE54zX26oT37IjxxEMhdm6JEQkZVqFXvcHN\n0ksclFY4ECNcKRTCIMer17qw2xVefD5KS+PpxFh/7H707ZtGde0wTuUT8ZjOixsjhLp1fFkT+2WM\n+/YYiTFmXcGkSdQju5Ddhk2Y16bR5fBD24G+YzidCqoGoS5jkDEnBXv3Jjh2MMGyVY4+Uqx3tAPQ\n5TM6YRZBpyWPoknT+451LJhEAIGi/ihqyuTGqofpkQ5KhRlVikFJsc9mkMzOWIZpftA3PWmQXbMF\nWX/C2Ch3HWLFZch/rUc+/gBKoBCKz1BO1OEadaQ4lOwnxYtLHISffpRVmaZh98t3mMjohjezz9bf\nfexeBxAkZctDTC8Ej9+Y9aZSJB1GkuCppLgnl+Tns2l4rCoOk0I0bWzTGEpxpCNOvsPE0tLX1tK0\nPLgb/RffNiphXXIV4n0fNz7PpEEdPsFNplPG/pEwqXfcRlP7EkobNqB+93HobEX55NcR0+cM2EfT\nBEWlJpob0sxbLFFyGcXCaoe5i5E7N9O68j3oWSgqO3d5QmLjUzBpOqKsatDvhRB8YEkhn3m8ll/v\naOPjFxcPut1g8PqN/tbdmaWw5JWfzwtVRcxaiNyzHRkOIVxjk+H+74Y8m8ZHLyrimxsa+d1LbX02\ncb2QTXXoP/4adHcaEoklK40kTvv4GRcScUMDWVphGuBANBKYTILllzrY+GSYnS9EWX21C3UUy9QT\ngG31hnTiksrzX6VPaCbEOz6AnLsY/Y8/N/pq2STExWsQM+ZDYQlYrIYlX3sT8sQR5N6dsG+n4Vs9\nfQ7Kez4CcxaPKyszMWUmyue/j/4//43vt5/nsnfexolJl1JzNElTneFQ5PWpWG0KQkA6JYmEdcKh\nLFIHVTNWQ8oqzRQUaSMmwWeC3aGw8koXW5+LsGNLlBWXOsjPeSnLvTuQf78HcdEaWLZqVOcZl6T4\nwK440YgOGlToFuLeLA/kvGzVngiWnh70H34VcdUbAchzWOiyeZCN/ZFioQi8eSodYSNCm1M6oCiC\no/sT+Io10rrkz42QX7SULkcALZ0ho2i0ls+kOLdsEU5mefRoN5dUunA5bGSdLmQ8TsrswpdpYrew\n8zrF0MI5BtG6nBYpbmkwSIPJjDxx2PisJ2hURioqM/4N9+B8x/uJnilq63AaiXijQB8ptqpYNIXX\nt20Hr3fY/fLtRpvao+kBpNhqM649lcjNHisnG4b1VdNIFy8ACbGeJNC/HBTMJSD6bAYRfPeCfGLp\nLPfu7qC+J8mf9nSwrNT5miLFUtfR//JrcDgRC5YhNz+FPnMeBDuQD/3JqH616mrEmtedtnQm02mo\nPoK+/jdQewzlo1+kwTQfvTPBpEAYGqKId3/4NELci9IKI3GirSVDUWl/3xLLVyN3baNlfxtmixv/\nOVqxye5OsscPDZuwNiNg421z/Px1fydLSx0jtkvy5qkgjKz+wpLxob8UV70BuWc7+ve/gJi31PCf\nnT73lW7Wqw4ryly8aWYeDx7qYqrfxhW5Ij6ysx397q+A1FE+fRdiysxXuKWD4/jhJFLCjHnn5nJg\nsyssXGFn24YoB/fEmbv4wi6bv9awqTZEvl1jRuD8SCcGg5izCOXOnyK3PYd89hHkX3/XX1tACKNg\nSy+8PsRl1yIuuQpR/spJfoaD8AVQ7vgW+i+/i3bf/zDj2mamXn8TLU1Z2lvThHt0errSSGlM7uxO\nhYIiC/4CDX++NuaTO5NJcNFlDjY/E2HnlhirrnLiSLaj//oHUFqFePdtoz7HuCLFmYzh49jckGby\nDAvbGyIUZ8zceKmXzc0xWiNpbLtasWYiRgb5rm3gcJHnMFNtckJb04CKal6/RkdHBqsqiIcyKAoU\nFGt0tmXIyxG69YlCSiuvIKvYmBxu4IinkrYZy/ra9M/DQRIZnbf3lqf1Bkh5TCAUHMkuGi15HNXj\nTFNsuAYhxR6riiqMSLGUEjpaEbMXgjsPtm9ERiPInq6+6nVi9kJkQw3Wy19HtOsM2lqHyzCDHwVC\nSYOQunsrVXUHEaVniEyfhEAu0bEjmh4w4PSS4t6lbaGoKJ/5NrjcpF6KQxPEmoPIrLuv5GkwbiyB\n+HITh9fPyCOd1fnTng5eaooSSmaZ5h87K51xgV3bDM36B25HLFqJPH4Y+Zu7je8WLDfcTf7+f4bu\nfPYCovOXoisa1B1HbnoKknFwulE+/DnkvGXUPBwiUKjhWXMz3Dw0Gc0v0jCZBYf2xIlGspRXmTFb\nFMSii0j4K2nttlA61XTOM3q5x7AnEvOXDbMlvHN+gO2NEe7Z1c6KMteIku40k8DlVugOjp8lZjF1\nNspHv4j+q+8hn3gA+cQDiLe8F3HZNUYUfgIjxnsXFVDdleR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2p0IsrCOtxgC4usKDEvIS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\n56RYkiRJTe9ftlWl4w5FdIEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x126f6fcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(2, 4, figsize=(12, 6), sharex=True, sharey=True)\n",
    "plotkernelsample(gpflow.kernels.Matern12(1), axes[0,0])\n",
    "plotkernelsample(gpflow.kernels.Matern32(1), axes[0,1])\n",
    "plotkernelsample(gpflow.kernels.Matern52(1), axes[0,2])\n",
    "plotkernelsample(gpflow.kernels.RBF(1), axes[0,3])\n",
    "plotkernelsample(gpflow.kernels.Constant(1), axes[1,0])\n",
    "plotkernelsample(gpflow.kernels.Linear(1), axes[1,1])\n",
    "plotkernelsample(gpflow.kernels.Cosine(1), axes[1,2])\n",
    "plotkernelsample(gpflow.kernels.Periodic(1), axes[1,3])\n",
    "axes[0,0].set_ylim(-3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combining kernels\n",
    "Valid kernels can be made by adding and multiplying kernels. To do this in GPflow, you can add or multiply intances of kernels, which creates a new kernel with the parameters of the old ones. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "k1 = gpflow.kernels.Matern12(input_dim=1)\n",
    "k2 = gpflow.kernels.Linear(input_dim=1)\n",
    "\n",
    "k3 = k1 + k2\n",
    "k4 = k1 * k2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kernels on multiple dimemensions\n",
    "The first, obligatory argument to every kernel is *input_dim*, which in the above has been 1. to make a kernel which works on more inputs (columns of X), simply specify a different input_dim. \n",
    "\n",
    "Stationary kernels all have ARD options, which allows the user to have one lengthscale parameter per input. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>prior</th>\n",
       "      <th>transform</th>\n",
       "      <th>trainable</th>\n",
       "      <th>shape</th>\n",
       "      <th>fixed_shape</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Matern52/variance</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Matern52/lengthscales</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           class prior transform  trainable shape  \\\n",
       "Matern52/variance      Parameter  None       +ve       True    ()   \n",
       "Matern52/lengthscales  Parameter  None       +ve       True    ()   \n",
       "\n",
       "                       fixed_shape value  \n",
       "Matern52/variance             True   1.0  \n",
       "Matern52/lengthscales         True   1.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = gpflow.kernels.Matern52(input_dim=5)\n",
    "k.as_pandas_table()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>prior</th>\n",
       "      <th>transform</th>\n",
       "      <th>trainable</th>\n",
       "      <th>shape</th>\n",
       "      <th>fixed_shape</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Matern52/variance</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Matern52/lengthscales</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>(5,)</td>\n",
       "      <td>True</td>\n",
       "      <td>[1.0, 1.0, 1.0, 1.0, 1.0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           class prior transform  trainable shape  \\\n",
       "Matern52/variance      Parameter  None       +ve       True    ()   \n",
       "Matern52/lengthscales  Parameter  None       +ve       True  (5,)   \n",
       "\n",
       "                       fixed_shape                      value  \n",
       "Matern52/variance             True                        1.0  \n",
       "Matern52/lengthscales         True  [1.0, 1.0, 1.0, 1.0, 1.0]  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = gpflow.kernels.Matern52(input_dim=5, ARD=True)\n",
    "k.as_pandas_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Active dimensions\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When combining kernels, it's often helpful to have bits of the kernel working on different dimensions. For example, to model a function that is linear in the first dimension and smooth in the second, we could  use a combination of Linear and Matern52 kernels, one for each dimension. \n",
    "\n",
    "To tell GPflow which dimension a kernel applies to, one specifies the *active_dims*, which is a list of integers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "k1 = gpflow.kernels.Linear(1, active_dims=[0])\n",
    "k2 = gpflow.kernels.Matern52(1, active_dims=[1])\n",
    "k = k1 + k2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making new kernels\n",
    "\n",
    "It's easy to make new kernels in GPflow. To demonstate, we'll have a look at the Brownian motion kernel, whose function is \n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\text{min}(x, x')\n",
    "$$\n",
    "where $\\sigma^2$ is a variance parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "class Brownian(gpflow.kernels.Kernel):\n",
    "    def __init__(self):\n",
    "        super().__init__(input_dim=1, active_dims=[0])\n",
    "        self.variance = gpflow.Param(1.0, transform=gpflow.transforms.positive)\n",
    "        \n",
    "    def K(self, X, X2=None):\n",
    "        if X2 is None:\n",
    "            X2 = X\n",
    "        return self.variance * tf.minimum(X, tf.transpose(X2))\n",
    "    \n",
    "    def Kdiag(self, X):\n",
    "        return self.variance * tf.reshape(X, (-1,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a new kernel class, we inherit form the base class `gpflow.kernels.Kernel` and implement three functions.\n",
    "\n",
    "#### `__init__`\n",
    "The constructor takes no argument in this simple case (though it could, if that was convenient). It *must* call the constructor of the super class with appropriate arguments. In this case, the input_dim is always 1 (Brownian motion is only defined in 1D) and we'll assume the active_dims are [0], for simplicity.\n",
    "\n",
    "We've added a parameter to the kernel using the Param class. Using this class lets the parameter be used in computing the kernel function, and it will automatically be recognised for optimization (or MCMC). Here, the variance parameter is initialized at 1, and constrained to be positive. \n",
    "\n",
    "#### `K`\n",
    "This is where you implement the kernel function itself. This takes two arguments, X and X2. By convention, we make the second argument optional (defaults to None). \n",
    "\n",
    "Inside K, all the computation must be done with tensorflow -- here we've used `tf.minimum`. When GPflow executes the `K` function, X, X2 and self.variance will be replaced with tensorflow tensors. \n",
    "\n",
    "#### `Kdiag`\n",
    "This convenience function allows GPflow to save memory at predict time. It's simply the diagonal of the `K` function, in the case where X2 is None. It must return a 1D vector, so we use tensorflow's reshape command.\n",
    "\n",
    "#### Using the kernel in a model\n",
    "\n",
    "Because we've inherited from the `Kernel` base class, this new kernel has all the properties needed to be used in GPflow. It also has some convenience features such as\n",
    "\n",
    "`k.compute_K(X, X2)`\n",
    "\n",
    "Which allow the user to compute the kernel matrix using (and returning) numpy arrays. \n",
    "\n",
    "To show that this kernel works, let's use it inside GPregression. We'll see that Browninan motion has quite interesting properties. To add a little flexibility, we'll add a Constant kernel to our Brownian kernel, and the GPR class will handle the noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Optimization terminated with:\n",
      "  Message: b'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'\n",
      "  Objective function value: 3.920244\n",
      "  Number of iterations: 24\n",
      "  Number of functions evaluations: 27\n"
     ]
    },
    {
     "data": {
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4p6wcjh+bgGR80feFQiGam5tPPJYrP8pMSyuzP3oQue/b1CBU/+5b8lbvU4nvY+amiXTk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\nxwOPPHqiz9/dcD0A9rrPsPv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1276da9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.random.rand(5, 1)\n",
    "Y = np.sin(X*6) + np.random.randn(*X.shape)*0.001\n",
    "\n",
    "\n",
    "k1 = Brownian()\n",
    "k2 = gpflow.kernels.Constant(1)\n",
    "k = k1 + k2\n",
    "\n",
    "m = gpflow.models.GPR(X, Y, kern=k)\n",
    "opt = gpflow.train.ScipyOptimizer()\n",
    "opt.minimize(m)\n",
    "\n",
    "xx = np.linspace(0, 1.1, 100).reshape(100, 1)\n",
    "mean, var = m.predict_y(xx)\n",
    "plt.plot(X, Y, 'kx', mew=2)\n",
    "line, = plt.plot(xx, mean, lw=2)\n",
    "_ = plt.fill_between(xx[:,0], mean[:,0] - 2*np.sqrt(var[:,0]), mean[:,0] + 2*np.sqrt(var[:,0]), color=line.get_color(), alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Brownian kernel can be displayed in the same way as the built-in kernels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>class</th>\n",
       "      <th>prior</th>\n",
       "      <th>transform</th>\n",
       "      <th>trainable</th>\n",
       "      <th>shape</th>\n",
       "      <th>fixed_shape</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GPR/kern/brownian/variance</th>\n",
       "      <td>Parameter</td>\n",
       "      <td>None</td>\n",
       "      <td>+ve</td>\n",
       "      <td>True</td>\n",
       "      <td>()</td>\n",
       "      <td>True</td>\n",
       "      <td>2.246233562768178</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                class prior transform  trainable shape  \\\n",
       "GPR/kern/brownian/variance  Parameter  None       +ve       True    ()   \n",
       "\n",
       "                            fixed_shape              value  \n",
       "GPR/kern/brownian/variance         True  2.246233562768178  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k1.as_pandas_table()"
   ]
  }
 ],
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