{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:42.010560Z",
     "start_time": "2017-09-18T00:02:41.245299Z"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cmap\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(206)\n",
    "\n",
    "import theano\n",
    "import theano.tensor as tt\n",
    "import pymc3 as pm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean and Covariance Functions\n",
    "\n",
    "A large set of mean and covariance functions are available in PyMC3.  It is relatively easy to define custom mean and covariance functions.  Since PyMC3 uses Theano, their gradients do not need to be defined by the user.  \n",
    "\n",
    "## Mean functions\n",
    "\n",
    "The following mean functions are available in PyMC3.\n",
    "\n",
    "- `gp.mean.Zero`\n",
    "- `gp.mean.Constant`\n",
    "- `gp.mean.Linear`\n",
    "\n",
    "All follow a similar usage pattern.  First, the mean function is specified.  Then it can be evaluated over some inputs.  The first two mean functions are very simple.  Regardless of the inputs, `gp.mean.Zero` returns a vector of zeros with the same length as the number of input values.\n",
    "\n",
    "### Zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:05:07.845415Z",
     "start_time": "2017-09-18T00:05:07.816687Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "zero_func = pm.gp.mean.Zero()\n",
    "\n",
    "X = np.linspace(0, 1, 5)[:, None]\n",
    "print(zero_func(X).eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default mean functions for all GP implementations in PyMC3 is `Zero`.\n",
    "\n",
    "### Constant\n",
    "\n",
    "`gp.mean.Constant` returns a vector whose value is provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:05:09.813946Z",
     "start_time": "2017-09-18T00:05:09.779518Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 25.2  25.2  25.2  25.2  25.2]\n"
     ]
    }
   ],
   "source": [
    "const_func = pm.gp.mean.Constant(25.2)\n",
    "\n",
    "print(const_func(X).eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As long as the shape matches the input it will receive, `gp.mean.Constant` can also accept a Theano tensor or vector of PyMC3 random variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:05:11.974290Z",
     "start_time": "2017-09-18T00:05:11.939523Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "const_func_vec = pm.gp.mean.Constant(tt.ones(5))\n",
    "\n",
    "print(const_func_vec(X).eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear\n",
    "\n",
    "`gp.mean.Linear` is a takes as input a matrix of coefficients and a vector of intercepts (or a slope and scalar intercept in one dimension)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:05:14.707255Z",
     "start_time": "2017-09-18T00:05:14.625750Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.21615117  0.18483208 -0.13889476 -0.8641522  -1.89552731]\n"
     ]
    }
   ],
   "source": [
    "beta = np.random.randn(3)\n",
    "b = 0.0\n",
    "\n",
    "lin_func = pm.gp.mean.Linear(coeffs=beta, intercept=b)\n",
    "\n",
    "X = np.random.randn(5, 3)\n",
    "print(lin_func(X).eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining a custom mean function\n",
    "\n",
    "To define a custom mean function, subclass `gp.mean.Mean`, and provide `__call__` and `__init__` methods.  For example, the code for the `Constant` mean function is\n",
    "\n",
    "```python\n",
    "import theano.tensor as tt\n",
    "\n",
    "class Constant(pm.gp.mean.Mean):\n",
    "    \n",
    "    def __init__(self, c=0):\n",
    "        Mean.__init__(self)\n",
    "        self.c = c \n",
    "\n",
    "    def __call__(self, X): \n",
    "        return tt.alloc(1.0, X.shape[0]) * self.c\n",
    "\n",
    "```\n",
    "\n",
    "Remember that Theano must be used instead of NumPy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Covariance functions\n",
    "\n",
    "PyMC3 contains a much larger suite of built-in covariance functions.  The following shows functions drawn from a GP prior with a given covariance function, and demonstrates how composite covariance functions can be constructed with Python operators in a straightforward manner.  Our goal was for our API to follow kernel algebra (see Ch.4 of Rassmussen + Williams) as closely as possible.  See the main documentation page for an overview on their usage in PyMC3.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponentiated Quadratic\n",
    "\n",
    "$$\n",
    "k(x, x') = \\mathrm{exp}\\left[ -\\frac{(x - x')^2}{2 \\ell^2} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:48.083350Z",
     "start_time": "2017-09-18T00:02:47.649571Z"
    }
   },
   "outputs": [
    {
     "data": {
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k7CfkqZ/99EcIIYSoSCShEaISOhV9ilU3VzGo3iD61ulbrLW/XX7AvqCHvNe9Pp3qu5RQ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WAAAD\nDElEQVRuS3LHNlYUpRXwDVoyk3LL9hqKotiXfl0L6AJcqrTILUdZ2tjvlm+HoI2LBdgG9C9t6xpA\n/9Jt4jdl+ZxAUZQwtImQh2/ZJudw+dkITCxdYacjkK2qaiJyDpcLRVHqAmuBCaqqRtyy3VlRFNdf\nvkZr39uuMCX+v737d/UpjuM4/nzl2pRIYcBKGShJGUyURSmDxWAwiMRgMVAst8joV7EoxCAGiX+B\nUpLlllzKxIbi5m04R3FDx+L4XM/Hds73+63P+Xw/vc95fc/nfL6/l2RZ/wwuSTbSXV+9ZWCN0TBJ\nFtLN9Ljz3T7H8QD9+LwMPK+qs794W7O1eM5OOauqmSQH6Tp8Ht3KRM+SnAQeVdVdui/2apIpujsz\nu/vPPktyk+7iZAY4MGuaiRjcx6eBBcCtvtZPV9UOYA1wMckXusI/WVVeDM4ysI8PJdlBN1bf0a16\nRlW9S3KK7oQKcHLWLfr/3sD+he4B1Bv9Dx7fOIYHSnKdbhWoJUleAyeA+QBVdQG4R7e6zhTwAdjb\nv+YYHmBA/x6nez70XF+HZ6pqA7AUuN3vmwCuVdX9v34ADRjQx7uA/UlmgI/A7r5e/LTGjHAI/7wB\nfQywE3hQVe+/+6jjeJjNwB7gaZIn/b5jwEpovxbnx/OzJEmSJLVjLk85kyRJkjTHGWgkSZIkNctA\nI0mSJKlZBhpJkiRJzTLQSJIkSWqWgUaSNIokK5K8SLK4317Ub68au22SpHYYaCRJo6iqV8B5YLLf\nNQlcqqqX47VKktQa/4dGkjSaJPOBx8AVYB+wvqo+jdsqSVJLJsZugCTp/1VVn5McBe4D2wwzkqQ/\n5ZQzSdLYtgNvgLVjN0SS1B4DjSRpNEnWAVuBTcCRJMtHbpIkqTEGGknSKJKEblGAw1U1DZwGzozb\nKklSaww0kqSx7AOmq+phv30OWJ1ky4htkiQ1xlXOJEmSJDXLOzSSJEmSmmWgkSRJktQsA40kSZKk\nZhloJEmSJDXLQCNJkiSpWQYaSZIkSc0y0EiSJElqloFGkiRJUrO+AvJ4E/0j1ixjAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0890d41470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lengthscale = 0.2 \n",
    "eta = 2.0\n",
    "cov = eta**2 * pm.gp.cov.ExpQuad(1, lengthscale)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two (and higher) Dimensional Inputs\n",
    "\n",
    "#### Both dimensions active\n",
    "\n",
    "It is easy to define kernels with higher dimensional inputs.  Notice that the ```ls``` (lengthscale) parameter is an array of length 2.  Lists of PyMC3 random variables can be used for automatic relevance determination (ARD)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:48.452193Z",
     "start_time": "2017-09-18T00:02:48.085342Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0891bebf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1, x2 = np.meshgrid(np.linspace(0,1,10), np.arange(1,4))\n",
    "X2 = np.concatenate((x1.reshape((30,1)), x2.reshape((30,1))), axis=1)\n",
    "\n",
    "ls = np.array([0.2, 1.0])\n",
    "cov = pm.gp.cov.ExpQuad(input_dim=2, ls=ls)\n",
    "\n",
    "K = theano.function([], cov(X2))()\n",
    "m = plt.imshow(K, cmap=\"inferno\", interpolation='none'); plt.colorbar(m);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### One dimension active"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:48.797628Z",
     "start_time": "2017-09-18T00:02:48.454837Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0890d79a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls = 0.2\n",
    "cov = pm.gp.cov.ExpQuad(input_dim=2, ls=ls, active_dims=[0])\n",
    "\n",
    "K = theano.function([], cov(X2))()\n",
    "m = plt.imshow(K, cmap=\"inferno\", interpolation='none'); plt.colorbar(m);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-01-16T15:54:27.610520",
     "start_time": "2017-01-16T15:54:27.607345"
    }
   },
   "source": [
    "#### Product of covariances over different dimensions\n",
    "\n",
    "Note that this is equivalent to using a two dimensional `ExpQuad` with separate lengthscale parameters for each dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:49.180865Z",
     "start_time": "2017-09-18T00:02:48.803617Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0890d79a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls1 = 0.2\n",
    "ls2 = 1.0\n",
    "cov1 = pm.gp.cov.ExpQuad(2, ls1, active_dims=[0])\n",
    "cov2 = pm.gp.cov.ExpQuad(2, ls2, active_dims=[1])\n",
    "cov = cov1 * cov2\n",
    "\n",
    "K = theano.function([], cov(X2))()\n",
    "m = plt.imshow(K, cmap=\"inferno\", interpolation='none'); plt.colorbar(m);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-01-25T18:43:14.006448",
     "start_time": "2017-01-25T18:43:14.003695"
    }
   },
   "source": [
    "### White Noise\n",
    "\n",
    "$$\n",
    "k(x, x') = \\sigma^2 \\mathrm{I}_{xx}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:49.555483Z",
     "start_time": "2017-09-18T00:02:49.186642Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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a1QU+gXvEG5sMhAqNNmB/AIN52bdAaLh/uxFjf2m49Ht8wp0azDJdAZNT7e9N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27LmWzbg+2Fv+NHCQfD4FiGJgM0jcd/WbJkb/2v5A8e/DYY3JQSrnL0dhCawT6rbLUqNFyTVE9w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Alo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f088bbd8198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sigma = 2.0\n",
    "cov = pm.gp.cov.WhiteNoise(sigma)\n",
    "    \n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant\n",
    "\n",
    "$$\n",
    "k(x, x') = c\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:49.970346Z",
     "start_time": "2017-09-18T00:02:49.557189Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BAABGT/ABAABGT/ABAABGT/ABAABGT/ABAABGT/ABAABGT/ABAABGT/ABAABGT/ABAABG\nb6rgU1Uvqqpbqur+qpo5SN1jq+ryqvpsVe2tqtOm6RcAAGAlpj3jc3OSFyT5yDJ1v5Pk/d39w0l+\nNMneKfsFAACY2LZpXtzde5OkqpasqapHJ3lWkguH13w7yben6RcAAGAl1uMzPk9KciDJf6mqT1XV\npVX1yHXoFwAAIMkEwaeqrq2qmxd57Jywj21JnpHkD7r75CR/m+Sig/S3q6pmq2r2wIEDE3YBAACw\ntGUvdevuM6fsY1+Sfd19/bB+eQ4SfLp7d5LdSTIzM9NT9g0AALD2l7p1918mubOqfmhoOiPJrWvd\nLwAAwAOmvZ31eVW1L8lpSd5bVVcP7Y+vqqvmlf5KkrdV1Y1Jnp7kP0zTLwAAwEpMe1e3K5JcsUj7\nXUnOmbf+6SRL/p0fAACAtTRV8HmoeN2fvS4fveujGz0MAADYFN517ruy7WFbK0psrdFukO2P3J4n\nP/bJGz0MAADYFCpL/x3PzUrwmcBLn/rSjR4CAAAwhfX4A6YAAAAbSvABAABGT/ABAABGT/ABAABG\nT/ABAABGT/ABAABGT/ABAABGT/ABAABGr7p7o8ewpKo6kORLGz2OwZFJ/mqjBzFy5njtmeO1ZX7X\nnjlee+Z47ZnjtWV+195mm+MndvdRyxVt6uCzmVTVbHfPbPQ4xswcrz1zvLbM79ozx2vPHK89c7y2\nzO/a26pz7FI3AABg9AQfAABg9ASfye3e6AE8BJjjtWeO15b5XXvmeO2Z47VnjteW+V17W3KOfcYH\nAAAYPWd8AACA0RN8klTV2VX1uaq6vaouWmT7w6vqncP266vq+Hnbfn1o/1xV/dR6jnurmGB+f62q\nbq2qG6vquqp64rxt36mqTw+PPes78q1jgjm+sKoOzJvLl83bdkFV3TY8LljfkW8dE8zxf543v5+v\nqr+Zt81+vIyqenNV3VNVNy+xvarqd4f5v7GqnjFvm314AhPM8c8Nc3tjVX20qn503rYvVtVNwz48\nu36j3lommOPnVNVX5x0PXjNv20GPMUw0v6+eN7c3D8feI4Zt9uEJVNVxVfWhqtpbVbdU1SsXqdm6\nx+Pufkg/khyS5AtJnpTksCSfSXLSgpqXJ/nDYfn8JO8clk8a6h+e5IThfQ7Z6K9pMz0mnN+fSPJ9\nw/IvPTC/w/o3Nvpr2OyPCef4wiS/t8hrj0hyx/B8+LB8+EZ/TZvtMckcL6j/lSRvnrduP15+jp+V\n5BlJbl5i+zlJ3pekkpya5Pqh3T68enP8Yw/MXZLnPTDHw/oXkxy50V/DZn9MMMfPSfLfF2lf0THm\nofpYbn4X1P5Mkg/OW7cPTzbH25M8Y1j+/iSfX+Rnii17PHbGJzklye3dfUd3fzvJO5LsXFCzM8ll\nw/LlSc6oqhra39Hd3+ruP09y+/B+/H/Lzm93f6i7vzmsfjzJses8xq1ukn14KT+V5Jru/kp3/3WS\na5KcvUbj3MpWOsc/m+Tt6zKykejujyT5ykFKdiZ5S8/5eJLHVtX22Icnttwcd/dHhzlMHIsflAn2\n46VMcxx/yFjh/DoOPwjdvb+7Pzksfz3J3iRPWFC2ZY/Hgs/cN/POeev78r3f4L+r6e77knw1yQ9M\n+NqHupXO0S9k7rcID3hEVc1W1cer6vlrMcARmHSO/+FwSvryqjpuha99qJt4noZLNU9I8sF5zfbj\n6S31PbAPr42Fx+JO8oGquqGqdm3QmMbitKr6TFW9r6qeOrTZj1dRVX1f5n7gfte8ZvvwCtXcRztO\nTnL9gk1b9ni8baMHsAnUIm0Lb3W3VM0kr32om3iOqurnk8wkefa85h3dfVdVPSnJB6vqpu7+whqM\ncyubZI7fk+Tt3f2tqvpnmTuD+ZMTvpaVzdP5SS7v7u/Ma7MfT89xeJ1U1U9kLvj8/XnNpw/78OOS\nXFNVnx1++87KfDLJE7v7G1V1TpI/TXJi7Mer7WeS/K/unn92yD68AlX1qMwFx1d199cWbl7kJVvi\neOyMz1waPW7e+rFJ7lqqpqq2JXlM5k61TvLah7qJ5qiqzkxycZJzu/tbD7R3913D8x1JPpy53zzw\n3Zad4+6+d968/lGSZ076WpKsbJ7Oz4LLK+zHq2Kp74F9eBVV1dOSXJpkZ3ff+0D7vH34niRXxGXd\nD0p3f627vzEsX5Xk0Ko6Mvbj1Xaw47B9eBlVdWjmQs/buvvdi5Rs2eOx4JN8IsmJVXVCVR2WuX8s\nC++6tCfJA3emeGHmPizXQ/v5NXfXtxMy91ubP1uncW8Vy85vVZ2c5I2ZCz33zGs/vKoePiwfmeT0\nJLeu28i3jknmePu81XMzd81uklyd5LnDXB+e5LlDG99tkuNEquqHMveBzo/Na7Mfr449SV463E3o\n1CRf7e79sQ+vmqrakeTdSV7S3Z+f1/7Iqvr+B5YzN8eL3lWLg6uqY4bPCKeqTsncz2H3ZsJjDMur\nqsdk7sqRK+e12YcnNOyfb0qyt7t/a4myLXs8fshf6tbd91XVKzL3jTkkc3diuqWqXptktrv3ZG4H\neGtV3Z65Mz3nD6+9par+OHM/xNyX5JcXXN7ykDfh/L4+yaOS/Mnw/8GXu/vcJE9J8saquj9z/zlc\n0t1+YFxgwjn+1ao6N3P76Vcyd5e3dPdXquo3MvefbpK8dsGlAWTiOU7mPkz7juEXIw+wH0+gqt6e\nuTteHVlV+5L82ySHJkl3/2GSqzJ3J6Hbk3wzyT8ZttmHJzTBHL8mc59f/f3hWHxfd88kOTrJFUPb\ntiT/rbvfv+5fwBYwwRy/MMkvVdV9Sf53kvOH48Wix5gN+BI2tQnmN0nOS/KB7v7beS+1D0/u9CQv\nSXJTVX16aPvXSXYkW/94XN/9/zMAAMD4uNQNAAAYPcEHAAAYPcEHAAAYPcEHAAAYPcEHAAAYPcEH\ngE2tqo6rqj+vqiOG9cOH9Sdu9NgA2DoEHwA2te6+M8kfJLlkaLokye7u/tLGjQqArcbf8QFg06uq\nQ5PckOTNSX4xycnd/e2NHRUAW8m2jR4AACynu/9vVb06yfuTPFfoAWClXOoGwFbxvCT7k/zIRg8E\ngK1H8AFg06uqpyc5K8mpSf55VW3f4CEBsMUIPgBsalVVmbu5wau6+8tJXp/kP27sqADYagQfADa7\nX0zy5e6+Zlj//SQ/XFXP3sAxAbDFuKsbAAAwes74AAAAoyf4AAAAoyf4AAAAoyf4AAAAoyf4AAAA\noyf4AAAAoyf4AAAAoyf4AAAAo/f/AA/8DzxxFv16AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f088b665860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 2.0\n",
    "cov = pm.gp.cov.Constant(c)\n",
    "    \n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rational Quadratic\n",
    "\n",
    "$$\n",
    "k(x, x') = \\left(1 + \\frac{(x - x')^2}{2\\alpha\\ell^2} \\right)^{-\\alpha}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:50.383983Z",
     "start_time": "2017-09-18T00:02:49.985945Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ELRNdK+NaKQ/m7ovg+BT8y/elq3dnQqMSWNq3Fi6VChnmuNLh3rN7jD05Fu8I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DAAAg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\nNCIiIiIiErNU0IiIiIiISMz6f9uRglSEEXu7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0889b533c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.1\n",
    "ls = 0.2\n",
    "tau = 2.0\n",
    "cov = tau * pm.gp.cov.RatQuad(1, ls, alpha)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponential\n",
    "\n",
    "$$\n",
    "k(x, x') = \\mathrm{exp}\\left[ -\\frac{||x - x'||}{2\\ell^2} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:50.770815Z",
     "start_time": "2017-09-18T00:02:50.385789Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wulpNLcCw6ljMxd3enRWhK7gh5gaUCuWwz4v3jEelUaHu6jsb/3nx5zgoHXjm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\noRx4arbR1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jS5uYfMBCCgcF/nBAG2/AUUjSgM5SVBWXOp+8Eug/Gy9+LTpE+pLZNV1dTQ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\nVLdMaCRJkiTVrf8HSgr6P7WgFccAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08896f0320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inverse_lengthscale = 5\n",
    "cov = pm.gp.cov.Exponential(1, ls_inv=inverse_lengthscale)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matern 5/2\n",
    "\n",
    "$$\n",
    "k(x, x') = \\left(1 + \\frac{\\sqrt{5(x - x')^2}}{\\ell} +\n",
    "            \\frac{5(x-x')^2}{3\\ell^2}\\right)\n",
    "            \\mathrm{exp}\\left[ - \\frac{\\sqrt{5(x - x')^2}}{\\ell} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:51.178581Z",
     "start_time": "2017-09-18T00:02:50.772671Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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M0ghRBVLQCJtVaihl0pZJlBpLmd1nNn4usgjVlvk4+zDrtlnY6eyYvHUypYZr77MjhNBI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\ncFj/D1KFtMOsvTTlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08894769b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls = 0.2\n",
    "tau = 2.0\n",
    "cov = tau * pm.gp.cov.Matern52(1, ls)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matern 3/2\n",
    "\n",
    "$$\n",
    "k(x, x') = \\left(1 + \\frac{\\sqrt{3(x - x')^2}}{\\ell}\\right)\n",
    "           \\mathrm{exp}\\left[ - \\frac{\\sqrt{3(x - x')^2}}{\\ell} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:51.585335Z",
     "start_time": "2017-09-18T00:02:51.180672Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GPW4lZODjZs9LDcvxUoPy+Lg//vswGlVWnb7FrB1Xyc4z4uftSmUvByp7OlKj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\nRCSyVNCIiIiIiEhk/T8V0BjMFvb6wwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0888f134e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ls = 0.2\n",
    "tau = 2.0\n",
    "cov = tau * pm.gp.cov.Matern32(1, ls)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Cosine\n",
    "\n",
    "$$\n",
    "k(x, x') = \\mathrm{cos}\\left( 2 \\pi \\frac{||x - x'||}{ \\ell^2} \\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:52.283608Z",
     "start_time": "2017-09-18T00:02:51.834720Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kBsDDzoNnej/D2lvW4mPvw4M7HuTTyE/Ry+LcnMZKJDQm9ltUFjZaFWPCms9y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0888e45518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "period = 0.5\n",
    "cov = pm.gp.cov.Cosine(1, period)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear\n",
    "\n",
    "$$\n",
    "k(x, x') = (x - c)(x' - c)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:53.047568Z",
     "start_time": "2017-09-18T00:02:52.743629Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2ybnH0nwsbGY1x9JWseX5Dp/7FYMk7UpLrDeIz6PQLSK/jAKNiMhhVKvaR9Oc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0888bc64a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 1.0\n",
    "tau = 2.0\n",
    "cov = tau * pm.gp.cov.Linear(1, c)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial\n",
    "\n",
    "$$\n",
    "k(x, x') = [(x - c)(x' - c) + \\mathrm{offset}]^{d}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:54.231474Z",
     "start_time": "2017-09-18T00:02:53.867141Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9BUSHh74Qscfv4XT36WDYaR9rB2B98npVYlshlupT9BLwScMwvodV1GBY83tEREREBGBo\nYpp/eL2RfzrSjGnCR+8r4HcfKsYZE9pKbSPTI7zR/gb7W/dzuO0wo55Rwm3h3Jt5Lx/f8HEezH6Q\n1OjUkLZRbt1ilbP+LrAHcBmG0QZ8HnAAmKb5VeDnWKWsG7DKWX90MV5XRERERFYut8fHt95o5h9e\nb2B0ysszW7L49GOlZCeFbvJ/22gbB9oOsL91P6e6TuE1vTgjnTyS9wh7cvawM0PFCVaqxarq9oGb\nPG4Cv7sYryUiIiIiK5vX5+eHp9r4m1/V0zXi5uHyVP7wHWWUp8cveVv8pp9LfZfY37qf19tep36w\nHoDChEI+XPlhHsp5iA2uDdhty39hVHlroR8wKSIiIiJrgmmavHypm798uYbG3nG25iby5Q9sYUeB\nc0nb4fa6ebPzTfa37udA2wH6JvuwG3a2pG7hM1WfYU/OHvLi85a0TXL3KfiIiIiIyF137Eo/f/HL\nGs60DFGcGsvXnt/G40tYmrpvso9DbYfY37qfox1HcfvcxDhiuC/zPvbk7GF31m4tJrrKKfiIiIiI\nyF1zrnWI//eVWg7V95EeH8lfPLuBZ7dmE3aXS1P7TT/VA9UcbDvIwdaDXOy/CEB6TDrvKX4PD+U8\nRFV6FeH20BZQkKWj4CMiIiIii662a5S/esVaiycp2sFn37mO53fmEem4e3NlJjwTHO08ysG2gxxq\nO0TvZC8GBhtSNvDJzZ/kgewHKHeWL7sFUGVpKPiIiIiIyKJp7hvnb35Vx4/PdRAbHsanH7PW4omN\nuDuXna0jrRxsP8iB1gOc7D6Jx+8h1hHLfVn38UD2A9yfdT/OyKWdQyTLk4KPiIiIiNyxzuFJvryv\ngX892YrDbvCfHijitx8sJDF6cYeSefwezvac5UDrAQ62H6RpuAmAgoQCPlj+QR7MeZDNqZtx2ByL\n+rqy8in4iIiIiMjb1jc2xd/vb+Q7b17FNE0+dE8uv/tQManxkYv2GgPuAQ63H+Zg20GOtB9h1DOK\nw+Zge/p23l/2fh7IeoCc+JxFez1ZnRR8REREROS2DU96+MeDV/jmG024PT6e3ZrNpx4pIcd554t7\nmqZJ7WBtsFfnQu8FTExSolJ4LP8xHsh+QAuJym1T8BERERGRWzYx7eVbbzTztQONjLi9PLkxg99/\ntJTi1Ng7+rmj06Mc6zzG4fbDHG4/TM9EDwAbXBv4nc2/w4PZD1LuLMdm3N1qcLJ6KfiIiIiIyE25\nPT6+c+wqXz3QSN/YNI+Up/Lpx0upzEx4Wz/PNE3qBus41H6Iw+2HOddzDq/pJc4Rx72Z9wYLE7ii\nXIv8TmStUvARERERkRtye3z8f2+28A8HGukdnWJXUTJfe76UbXm3XyltZHqEox1HOdx+mDfa36B3\nsheAdc51fHT9R7k/6342pmwkzKZLVFl8+lSJiIiIyDWmvD6+f6KVv9vfQPfIFPcWOvnKB7ZwT2Hy\nLf8M0zSpGagJDl8713sOn+kjLjyOXZm7uD/rfu7LvI+U6JS7+E5ELAo+IiIiIhI07fXzryetwNM5\n7GZHvpP/8/7N7Cq6tSFnw1PDHO04yqH2QxzpOELfZB8AFckVfGz9x9idvZsNrg3q1ZElp0+ciIiI\niODx+fnhqTa+8loD7UOTbMtL4i/fu4n7ipMxDOOGz/ObfqoHqjncZvXqnO87j9/0kxCRwK6MXdyf\nfT+7Mndpro6EnIKPiIiIyBrm8fn50el2vvxaPW2Dk2zOSeTPf20DD5S4bhh4+ib7ONpxlKMdRznS\ncYR+dz8AlcmV/NaG3+L+rPvZ4NqA3WZfyrci8pYUfERERETWIK/Pz4/OtPO3rzXQMjDBxuwE/vTp\n9ewpS7km8Ez5pjjTc4Yj7Uc40nGE2sFaAJyRTu7NuJf7s6xeneSoW5//I7LUFHxERERE1hCPz8+P\nz3bwd/sbaOobpzIznhc/XMUj61KDgcc0Ta4MX+GN9jc40nmEU12ncPvchNnC2Jq6ld/b+nvsytyl\ndXVkRVHwEREREVkDpr1+/u10G3//egOtA5Osy4jn689v47GKNAzDYNA9yLHOYxzpsHp1ZhYQLUgo\n4NnSZ9mVuYuqtCqiHdEhficib4+Cj4iIiMgq5vb4+MHJVv7h9UY6ht1syk7g809V8kBpEuf6zvG3\nZ/6VIx1HuNx/GROT+PB47s24l12Zu9iZuZPM2MxQvwWRRaHgIyIiIrIKTU77+O7xFr52sJHukSm2\n5iXyX59IxBtRy487vs9nzxxnwjuB3bCzKWUT/3nzf2ZX5i4qkytVlEBWJQUfERERkVVkfMrLd45d\n5R8PXaFvYoh1Bd1s29pO4/hp/vRcBwA5cTm8q+hd7MzcyY70HcSFx4W41SJ3n4KPiIiIyCow6vbw\nrSMNfOPEfibDakjKvkq80UwbfgYHYrgn/R4+VvkxdmXuIic+J9TNFVlyCj4iIiIiK5TP7+Nk50W+\n+ubLnOx5EzOiCSPdQ5Rhp8S1nnszfotdmbvYkLIBh80R6uaKhJSCj4iIiMgKYZomraOtHOs8xsHW\nIxzteJNpcwyAqKgsHsx5D0+WPEBVWhWx4bEhbq3I8qLgIyIiIrKM9U32cbzzOMc6j3Gs8xid450A\nmJ4EvONlrHdW8end72RXfmGIWyqyvCn4iIiIiCwj455xTnWf4mjHUd7sepP6wXoAYsLiiPGXMd19\nD+ZEMU9XbuK3ny6mKEU9OyK3QsFHREREJIQ8Pg/n+87zZuebHOs8xoXeC3hNL+G2cLakbeF9hf+J\n6qZUjlyIIsrh4Dd25PKbuwvITIwKddNFVhQFHxEREZEl5Df91A3WBYPOqe5TTHonsRk2KpwVvLD+\nBXak78A9msuLh1r5RkM/8ZFhfOrhfF64rwBnTHio34LIiqTgIyIiInIXmaZJw1ADx7uOc6LrBCe7\nTzI8NQxAfnw+7y56NzszdlKVXkWcI55Xq7v54o8aOdd6lpS4CP6fd5bzwXvyiI3QZZvIndC/IBER\nEZFFZJomTSNNnOg8wfGu45zsPsmAewCArNgsHsp5iB3pO9ievp30mHQAPD4/L53t4KsHzlLfM0au\nM5r/+cx6nt2aTaTDHsq3I7JqKPiIiIiI3IGZEtPHu45bQafrJL2TvQCkRqeyK3NXMOhkx2XPe+74\nlJfvn2jlG4ebaB+apDw9ji89t5knN2QQZreF4u2IrFoKPiIiIiK3qX2sneOd1tC1413H6Z7oBiA5\nMtkKORnb2ZG+g9y4XAzDuOb5PaNu/vlIM9851sLwpIft+Ul84elKHi5Pve75InLnFHxEREREbqJr\nvCsYck50naB9rB2ApIgkqtKr2JG+gx3pOyhIKHjL4NLQM8aLh67w76fb8fj97K1I5xMPFrI1N2mp\n3orImrUowccwjHcAXwLswIumaX5xweMvAH8JtAfu+oppmi8uxmuLiIiILLaZRUNngk7LaAsA8eHx\nVKVV8XzF82xP305xYjE2462HpJmmycmrg3ztwBV+Vd1NRJiNX6/K5jd3F1LgilmKtyMiLELwMQzD\nDvwd8BjQBpwwDOMl0zQvLzj1+6ZpfvJOX09ERERksXWNd3Gq+xQnu09ysuskzSPNAMQ6YtmWto33\nlb2PHek7KE0qxW67tWIDPr/Jq5e7+NrBK5xpGSIp2sGnHinhwzvzcMVG3MV3IyLXsxg9PjuABtM0\nrwAYhvE94GlgYfARERERCTnTNGkfa+dk90kr7HSdpG2sDbCCzpbULTxT8gw70ndQ7iwnzHZ7l0tu\nj48fnmrjG4ebaOobJ9cZzReeruS927KJDtcsA5FQWYx/fVlA65zjNuCe65z3rGEYDwB1wO+bptm6\n8ATDMD4BfAIgNzd3EZomIiIia51pmjSPNAd7dE51n6JrvAuAhIgEtqVu4wPlH6AqvYqypLJb7tFZ\naGB8mu8cu8o/H2mmf3yajdkJfOWDW3hHZboqtN0K0wxs/htsvps8HtgADNv8DWPBfUZge4vzbHbr\nHFk1FiP4XO8TYS44/gnwXdM0pwzD+G3gn4GHr3mSaX4d+DpAVVXVwp8hIiIiclN+00/jUGMw5Jzq\nPkXfZB9gVV3blraNj63/GFVpVRQlFt10js7N1HWP8s3DTfzoTDtTXj8PlaXwiQeKuLfQubwrtPl9\n4JkEr9vaPG7wTgZuZ+6bBO/UnPsDxzPP80yCbzqweazN7wkce61bv2f2Md80+L3XP38mtCwntjCw\nh4PNAfbANnd/3nG4dX5YBIRFWpsjEsKiArcz90Xd4PEoCI+BiFgIj7X2wzQkcjEtRvBpA3LmHGcD\nHXNPME2zf87hPwJ/sQivKyIiIoLP76NusC44P+d0z2mGpoYASItO456Me9iWto2qtCry4/MXJYyY\npsmBul6+cbiJQ/V9RITZ+LWt2XzsvnxK0uLu+Odfw+eBqVFwD1u30+OBbQw8E7P70+MwPTG775lY\ncP+c83xTb789trDZC3Z7xOyF/7wwEA7h0dcGh5mAsPB8mx0M+5weGdv1t5memOs9Fvw+/no9Q+aC\nW/9bn+f3Lghr1wluC0Oc1w0T/QvCZGDzTb+NP2eHFYBmgtDCYDTzWGTCgi1x/nF4jHqvWJzgcwIo\nMQyjAKtq23PAB+eeYBhGhmmanYHDdwPVi/C6IiIisgZ5/B6q+6uDQ9fOdJ9h1DMKQHZsNg9mP0hV\nehVVaVVkxWYtaq/L5LSPfz/TxrfeaKahZ4zUuAg+83gpH7wnD2dM+LVPME2rV2RqJBBcRmBqOHA7\nat3vHgk8Pmd/4ePeyVtsoRG4KI5ecGGcCPFZ8y+YHdGzvQ8zPQ5hEdfvkVh4v11zlW6b33dtGJrX\nozY5J6SOXxtwZx6bGoOJ1tn7psZu/vkw7NcJRwkQlQTRydfZAvdHxK+qwHTHn1rTNL2GYXwSeBmr\nnPU3TdO8ZBjGF4CTpmm+BHzKMIx3A15gAHjhTl9XRERE1oYJzwQX+i5wuuc0Z7rPcLb3LJOBC738\n+Hz2FuwN9uikx6TflTZ0D47ww8MX2He6FtzD7Hb5+eLOSDanGIRNHYcDQzA5aG3umf0ha9/vvfkL\nhMdaF5kRcRAZb12QJuVZxxHx1kXqzH5E3Pxv/R3Rc/ajVtWF6qpis8+GzsXmnQ6E5GHrM+cevvnW\n1219Tif6b/wZtYUtCERO6zY+Cx74zOK/j7vMMM3lOZWmqqrKPHnyZKibISIiIktswD3AmZ4znO4+\nzZmeM1T3V+M1vRgYlCaVsiV1C1XpVWxL24YrynV7P9zvty4MJ/qtbbxvdn8muEwOWheGk4NMjw1g\nTgwSYb7VN+rGbFiJTLRuo5IgKjEw5GgmrCTM2Y8P7AeO32ZBBZE7ZppWaJroh4mBwNZ/7TYTkib6\nrc/sp86EuuVBhmGcMk2z6mbnqZ9SREREQsY0TdrG2oIh53TPaZqGmwAIt4Wz3rWej67/KFtSt7A5\ndTNx4Qvmz0xPzLk467Mu2uaGmZn7ZkLO5MCNJ9HbIyDaiRmZyKAZQ+NoLM3jTsbtceRmZbKppIBk\nV5oVaOaGnMgEBRdZuQxjduibs/DWnrNMO05uRsFHRERElsxMIYLTPaeDYad3sheA+PB4trg28nTm\ng2yLzqLCHkP4xACM9UDPz2H829eGGc/E9V/IsM0fouMqhdyd1n6M67rzGoa8YXz/RCv/99hV2gYn\nyUqM4qN783nf9hziIx1L+Kckssyt0OGUCj4iIiJy17g9k1zoOsHp9jc403uOs0MNjPutamIZtki2\nE8k2XwJbJsYoGrmKrfbi9X9QeNzs/ILYNEitmB9cFoaZyESw3VqZ6ssdI/zzrxr4j7NWOep7Cpx8\n9p3reKwiTevviKwiCj4iIiJy+6ZGYbQbxrqsHpnxXhjrYWi0nTNjLZyZ7uO0f5JLYSbewLfDxdPT\nPOWeYot7iq3uKTLCEyA2FWJSIK0EigL7sakQkwqxKdZxTIo1aX8ReXx+Xr7UxT8faeZE8yCRDqsc\n9Ud25VGeHr+oryUiy4OCj4iIiFhM0xpCNtYFo10w1n3t7Vi3FXg845hAkyOMcxERnI2M4GxEBFfC\nrSFhDjusD4/jw5FpbIsvZJOzkoTEXCvQxKRYPTT2pR8+1jPq5nvHW/mXN6/SPTJFrjOazz25jl/f\nlkNCtIa93rqxAAAgAElEQVSziaxmCj4iIiKrnc8L4z0LQkxPIOB0z7ntBr/n2ueHx0FcGpOxqVxM\nK+JsVjFn/eOcm+pj2GdVO0sIj2dzymaeSt3M1rStrHetJ8K+PFadN02TM61DfPtIMz+70InHZ/JA\naQr/69fyeLA0FbttZc5XEJHbo+AjIiKyUvl91hCzkQ4Y7Zy9nRdmuqxqZlynClN0MsSmQ1wauMqs\n29h0a6hZXDpddhtnJ7s4O1jD2Z6z1A7U4nVb630UJhTySNYTbE7ZzKbUTRTEFyzqQqGLwe3x8dPz\nnXz7aDPn24aJjQjjN+7J4/mdeRSlxIa6eSKyxBR8REREliPP5JxA0wmjHdbxvPs6wfTNf55ht4JL\nbBokZEHWVohLt47j0meDTkwqhIXPvpzfQ+1ALWd7znK29whnq8/SPdENQFRYVLCs9ObUzWxK2URC\nRMJS/mnclqa+cb57vIUfnGxlcMJDcWosf/p0Jc9szSY2Qpc+ImuV/vWLiIgsJdO0FgIcaZ8TaDqt\n47khZ3Lw2ueGx0F8BsRlQMEDs/vxmYHbLGvuzC2sKTPkHuJc51HO9p7lbM9ZLvZdxO1zA5ARk8HW\n1K1sSt3E5tTNlCaV4rAt7/kvHp+ffdXdfOdYC4cb+rDbDB6vSOM37snjvuLkZdcbJSJLT8FHRERk\nsfg81vyZ0c7rBJsOa3+0C7zuBU80AsPLMiApD3LvtcJMMNAEbiPfXrUxv+mnebiZs71nOdNzhrM9\nZ2keaQYgzAij3FnOe0vfG+zNSY9Jv7M/hyXUMTTJ94638L0TrfSMTpGREMmnHyvl/dtzSIuPDHXz\nRGQZUfARERG5Fe6R+fNogsGmc3YI2ngv18ylsUdYPTPxWZBVFeilyZwfbOLSF7XC2dj0GBf7L3Ku\n5xzneq1tZHoEgMSIRDanbObp4qfZnLKZSlclUWGLWyr6bvP5TQ7W9/Ivx67yWk0PJrCnNIU/vyeP\nPWUpWntHRK5LwUdERNa2GxUIWDifZnr02udGJQVCTAZkbJzdnxtsopLu6irnPr+PK8NXON97nvN9\n5znfe57GoUbMQAArSijisbzH2JRiDVvLj89fscO+eken+NeTrXz3eAttg5O4YsP5nT1FPLc9lxxn\ndKibJyLLnIKPiIisXh73nKIAN5hPM9YFfu/85xn2wBCzDEgph6KHA70zmfPn1Szyopq3YsA9wIXe\nC5zrPcf5vvNc7LvIuGccgPjweDambOTx/MfZ5NrE+pT1xIev7MU4TdPk6JV+/uXNFl651IXHZ7Kz\nMJn//kQ5j1ekEx6m3h0RuTUKPiIisvIECwQsHHa2YD7NdQsExM4OMSvYPRti5s6niUm5pQIBd5vH\n56F2sHZeb07raCsAdsNOaVIpTxU+xaaUTWxwbSAvPm/F9uYs1DPi5gen2vjByVaa+ydIiHLw4Z35\nfGBHLsWpKkUtIrdPwUdERJaXeQUCbjCfZrTz+gUCYlKsHplggYDrzKd5mwUC7jbTNOme6LZ6cnqt\nkHO5/zLT/mkAUqJS2JSyiV8v/XU2pmykIrlixc3NuRmvz8/rtb1870Qr+2t78PlN7ilw8nuPlvDE\n+gwiHaEPoyKycin4iIjI0pkaXTDU7DrzacZ6uGGBgLhMa12aecPOZkLN4hYIuNsmvZNc7r8cDDnn\ne8/TM9kDQLgtnEpXJR8o/wAbUjawKWUTadFpq6Y3Z6HmvnH+9WQrPzzVRs/oFK7YCH5rdyHvq8qm\nUAuNisgiUfAREZE75/dZgWV0Qa/MvIU3b1AgIDLRqngWnwHpG+b0zswJNtHOu1og4G7zm36ujlzl\nQt+FYMipG6zDF1h8NCcuh+0Z29no2simlE3WujkrKMS9HW6Pj19e7OL7J1o5eqUfmwEPlaXy/u05\nPFSeikOV2URkkSn4iIjIW5sau7Z3ZmG4GeuGwEV8kGG3emHi5hQIWDifJi4DwldfNa6eiR4u9F3g\nYt9FLvZd5FLfJUY9VuiLccSwwbWBj2/4OBtdG9mQsgFnpDPELV46lztG+P6JFn50pp0Rt5dcZzR/\nsLeMZ7dmk56gdXdE5O5R8BERWauCvTQd186fGemYnWczNXLtcyMSZqubFZXPrkWzDAsE3G2j06Nc\n7r8cDDoX+i7QM2ENWQszwihJKuGJgidY71rPetd6ChMKsa+BP5e5Bsen+cn5Dn5wso0L7cOEh9l4\nR2U6z23P4d7CZGy2ldubJyIrh4KPiMhqNDOXZm6oue1emlIo3DNnHs2c2/CYULyrkJv2TVM3WDcv\n5DQNNwUfz4vPY3v6dja4NlCZXEm5s5zIsLXZi+EJFCr4t1Nt7KvpxuMzWZcRzx+/q4L3bMkiMTo8\n1E0UkTVGwUdEZCXxTlk9MWPdgTDTff1Qc725NNfrpVkYamJca6KX5lb4TT/NI81WwOm9wKX+S9QM\n1ODxewBIjkxmg2sDTxY8aQUdVyUJEQkhbnXoXeoY5t9OtfPjs+30j0+THBPOh3fm8+zWbCoyl2dF\nPRFZGxR8RESWg+kJayHN0e7Abde1AWes6/rr0tjCIDZ9/mKbM8PN4tLXfC/Nreoe77bm5PRbPTmX\n+i4x5hkDIDosmkpXJR+q+BAbXBvY4Nqwqqus3a7e0Sl+fLadfzvdTnXnCOF2G4+sS+XZrdk8WJai\nQgUisiwo+IiI3E1TY3PCy3WCzGgg7EwNX/tcm8MKLrFpkFwE+fdZAScuzQo2sWnW49EusOnC8nYM\nTw1zuf8yl/ovcaHXGrY2U0o6zAij1FnKk4VPUplcyQbXBgoSCtbcvJybmfL6eK26hx+eauP1ul58\nfpNN2Ql84elK3rUxk6QYDWUTkeVFwUdE5Hb5PDDeaxUGGO+1wszc/bmhZnrs2ufbIwI9MelWD03h\nQ1aYiU2fvT82HaKSFGgWwdj0GNUD1VzquxQMOy2jLcHH8+Lz2J5hzctZ71pPubOcCHtECFu8fJmm\nyZnWIX50up2XznUwPOkhLd5ac+fZrVmUpMWFuokiIjek4CMiAuDzwkRfIMT0wnjP7P5Yd+A4sD85\ncP2fER5rVTKLC6xHU/zYnCAT6KWJS7PWrdEQqbtiwjNBzUANl/ovWVvfJZpHmoOPZ8ZkUumq5JmS\nZ6hIrqAyWfNybkVDzxgvnW3nx+c6uNo/QUSYjb2V6Ty7LZv7i13YVZVNRFYABR8RWb2mx2G8zwo0\n4/2BYNMz21sz1j3bSzMxAJjX/gxHDMSmWpurGPJ2zR7HpM7fX4Xr0Sxnbq+bmoGaYC/O5f7LXBm+\ngt/0A5AanUplciVPFT5FpauSiuSKNbVezp3qHnHzk3Md/MfZdi62j2AzYFeRi08+VMze9enER67u\nBVZFZPVR8BGRlcE0rRLNc0NMMNT0wUT/tSHHM3H9n+WIng0rzkLIvffaEDOzr4IAy8JMGelLfZeC\nvTmNQ434AuW4kyOTWe9az+N5jwdDjivKFeJWrzwjbg+/vNDFj8+1c6SxH9OEjdkJfO7Jdbx7Uyap\n8WuzNLeIrA4KPiISGt4pq5dlctAaOjY5eG1wWXjsm77+zwqLssowRydbQ81SygP7Lmvif/A22Qo1\nEbFL+17ltnh8HhqGGuYNV6sfqsfr9wKQFJFEhauCPTl7qEyupDK5ktToVFVYe5vcHh+v1/bw47Md\n7KvpYdrrJy85mv/ycAlPb86kKEX/XkRkdVDwuRXH/xHcQ9YFVXBzWbfhsRqrL2ubdzoQXuYEmIWB\nJnjf0Ox9N+qNAQiPs0JKtAvisyB90+zx3BAzc6xemRXL6/fSONQYHK52qe8StYO1wbVy4sPjqUyu\n5IXKF6hMtnpyMmIyFHLukM9v8uaVfn58toOfX+xk1O3FFRvOB3fk8p4tWWzKTtCfsYisOgo+t+LC\nD6D1zes/FhY1PwjN7MemWvvRyVZlpmindRsRr6Aky4vPC1Mj4B62tuD+9e6bs80EmutVLZthC4Oo\nwGc/KgkScyBj4+zx3H8bUUlWkIlOBoeG06xGHp+HxuFGqvurudx/meqBamoHanH73ADEOmKpSK7g\nQ+s+RIXLKjyQHZutC/BF4vObnGge4KfnO/jlxS76xqaJCbezd30679mcxa6iZMK03o6IrGIKPrfi\n46+Axx0YctNrDb8Z751TzjZwPNoJXRes/cC3ldcw7BCVOP/Cb+6F4dwtMh4i4qywFBFn9S6ptK3M\n8Hms0DE1Nv924b57ZEFwGZkfZt4quMwIj4PIBOszGZlgLYyZtn5OYLnOZznaqR7RNWzKN0XdQB3V\nA7Mhp36wPtiTE+OIoSypjPeVvc8aruaqJCcuB5uh33GLye83OXl1kJ+d7+DnF7voHZ0iymHn4XWp\nPLUhgz1lqUSFa30iEVkbFHxulSMSErKt7WZM07qgnAlJwWFA19nGeqC3xhoCNDVykx9sBIJQ3PxA\nNC8gxVuVpRzR1vAfx8z+3PuiZvft4bowvVv8fvC6wTMJ3knr1jMx59Y953jOYzPnTo9bk/mnx68f\nbHxTt9YOW5gVViLiZ8OLqzhwX8L8QLPwvJljLdwob2HCM0HtYK0VcPqrqR6onld4ICEigXXOdXyo\n4kNUOCtYl7xOIecu8vtNTrcM8tPznfziYifdI1NEhNl4uDyVJzdm8HB5KtHh+u9fRNaeRfnNZxjG\nO4AvAXbgRdM0v7jg8Qjg28A2oB94v2mazYvx2suSYQR6dRLBVXLrz/N55g8hmvmmfmp0zu3o/Pvd\nQzDcOnu/Z/w222qfDUZhkRAWYW32iAX74de5b2Y/3Lq4Dm726xxf774wwJj9M5tt1IL7bnA89z6/\nD/xeMH3Wvum3jv2+2fvm7pu+OY/7Z5/vm7L+HrxT1kR63/SC/cCtb2rO/oLzvFOzAebtCIuygrYj\nxpqEHx5rhdSZOWURgePwuDn7sbO9guEzz4ubDboKt7JIRqZHqOmvmdeT0zzcjBkoBZ4cmUxFslV4\nYCbkaE7O3TezsOjPznfy8wuddA67CQ+z8VBZCk9uzOSR8lRiIhR2RGRtu+PfgoZh2IG/Ax4D2oAT\nhmG8ZJrm5TmnfRwYNE2z2DCM54C/AN5/p6+96tgdgblCd1CC1ecN9BxMWD0FMz0J0+OzPQoz+9fc\nNznngj5w6x6Z3fe6F1zgu62wsBrZw+cEvsA2E/Jm9sPCrbARFmH93c0NiDO9avNu525zHguLnD0O\ni9RwRlk2BtwDwR6cmd6ctrG24OPpMemsc67jiYIngiEnNTo1hC1eW/x+kzOtg/zyYhc/v9BF+9Ak\n4XYbD5Sm8N/eUc4j61KJ01o7IiJBi/H1zw6gwTTNKwCGYXwPeBqYG3yeBv44sP9D4CuGYRimaV5n\ntUC5I/YwsMdbw5SWgt9vBSP/nB4Uv3fBNrc3Zs6xb2Ye1JyPQfAjYd7keO59zPYqGXN6lwzbTe4L\nm7Nvs47tgRCjb6dlDTFNk56JHqoHqq3CAwNWyOme6A6ekxOXQ0VyBc+WPkuFs4Ly5HItBhoC014/\nx6708/KlLl653E3v6BQOu8HukhQ+/Vgpj1WmaWFREZEbWIzgkwW0zjluA+650TmmaXoNwxgGkoG+\nRXh9CSWbDWxRoW6FiNwiv+mnbbSNmoEaagZqgiFnwD0AgIFBQUIBVelVrHOuoyK5gjJnGfHhS/Rl\nilxjYtrLwbpeXr7Uzb7qbkbcXqLD7ewpS2FvZToPlacq7IiI3ILFCD7X+2p8YU/OrZyDYRifAD4B\nkJube+ctExFZw6Z90zQMNVA7UBssHV07WMt4YC6g3bBTlFjE7qzdVCRXUJFcQWlSKdGO6BC3XIYn\nPPyqupuXL3VxsL4Xt8dPYrSDxyvT2VuZzu4SF5EOFR0REbkdixF82oCcOcfZQMcNzmkzDCMMSAAG\nFv4g0zS/DnwdoKqqSsPgRERu0fDUMHWDdVT3V1M7WEvNQA1Xhq7gNa15eNFh0ZQ5y3hX4btYl7yO\nMmcZxYnFRNgjQtxymdE94uaVy928fLGLY1f68fpN0uMjeX9VDnsr09lR4NQ6OyIid2Axgs8JoMQw\njAKgHXgO+OCCc14CPgIcBd4LvKb5PSIit880TbrGu4I9ODND1jrGZ79vSolKocxZxoPZD1LmLKPc\nWa7y0cuQaZpc7hxhX3UP+2p6ONc6BEChK4bf3F3IO9anszErAZtNcw5FRBbDHQefwJydTwIvY5Wz\n/qZpmpcMw/gCcNI0zZeAbwD/1zCMBqyenufu9HVFRFY7j99D03DTvIBTM1DDyLS15peBQV58HhtT\nNvK+svdR7iynzFmGK+oOKkPKXeX2+Dja2M++mm5eq+6hY9iNYcCm7EQ+83gpeyvTKU6NVflvEZG7\nwFiuHS9VVVXmyZMnQ90MEZElMbMIaM1ATXBOTsNgA9P+aQAi7BGUJJZQnlxOeZIVcDQfZ2XoGXWz\nv6aHX1X3cLi+j0mPj+hwO7tLXDxSnsZD5amkxGnIoYjI22UYxinTNKtudp5WMxMRWWK9E71WwBms\nDc7JaRlpCS4CmhiRSLmznA+u+yBlzjLWOdeRF59HmE2/sleCeUPYqrs51zYMQFZiFL9elc3D5anc\nW5is4gQiIktM/4vegi/9qh7DgMcr0yhLi9MQBBG5JR6/h+bhZmoHa6kbqKNusI6agRr63f3Bc7Ji\ns1jnXMdThU9R7iyn3FlOWnSafs+sMKNuD0ca+zlQ18v+mh46A0PYNuck8gd7y3i4PJXydP3/ISIS\nSgo+t+Bc2xD7a3v461fryHFG8XhFOo9VpFGVl6QKOyICwKB7kLrBumDJ6LrBOhqHGvH4rYV6HTYH\nRYlF3J91fzDglDpLtT7OCuX3W706B+p6OVjXy6mrg3j9JrERYdxXnMzvP1bKQ2UawiYispxojs8t\n6hl1s6+6h1cudfFGQz/TPj9J0Q4eWZfGYxVpPFCSQlS4hi2IrHZev5erI1fnh5yBOnome4LnJEcm\nU+YsoyypjFJnKaVJpRQkFOCwaZHJlWxgfJpD9b2BsNNH39gUAJWZ8TxYmsKDpSlszUvCoS/ERESW\n1K3O8VHweRvGpqxVtF+51MW+mh5G3V4iHTbuL07h8co0fcsnskrMrI1TO2D14NQO1tI41MiUz7rg\nDTPCKEwspDSpdF7IUVW11cHnNznbOsSBOivsnG8bwjQhKdrB7hIr6OwudZEaFxnqpoqIrGkKPkvE\n4/NzvGmAVy518erl7mBp0o1ZCTxUnsrD5amsz9Q6DCLLmc/vo2W0Zd5cnNrBWrrGu4LnOCOd8wJO\nWVIZhQmFOOzqxVktTNPkav8EbzT2caShn8MNfQxPerAZsCU3Kdirsz4rAbt+p4uILBsKPiFgmiaX\nOkbYX9PDa7U9nG21vh10xUbwUFkKD5WnsrvERVykLpREQmVkeoT6wfrZXpyBWhqGGnD73ADYDTsF\nCQVWyAmUjC5LstbG0cT01adn1M2Rhn7eaOjjSGM/7UOTAGQkRHJ/sYs9ZancX+wiIVq/t0VElisF\nn2Wgf2zKqvBT28uB2h5G3F7CbAbb8508XJ7KQ+UpFKVooTqRu8Fv+mkdbb1mLk7HeEfwnISIBKsH\nJxByypLKKEwsJMKuoaqr1Yjbw5tXBgJBp4+67jEAEqIc7CxM5r4SF/cVJVPgitHvZhGRFULBZ5nx\n+vycbhnitZoeXq/toaZrFIDMhEh2l1jjxO8rcpEUEx7iloqsPDO9OHWDdVZvzmAt9YP1THqtb+9t\nho38+Px583DKkspIjU7Vxe0q5/b4OH11kDca+3ijoZ/zbUP4TYh02Nie7+S+Yut3b0VmvIaviYis\nUAo+y1z70CSv11qreL/R0MeI2xucG7S7JIXdJS625CYRHqbqQCIzPD4PTSNN80JO/VD9vLk4ceFx\nlCWVzRumVpRYRGSYJqCvBRPTXs60DPFm0wDHm/o50zLElNeP3WawOSeR+4qS2VXsYktuIhFhqsQp\nIrIaKPisIF6fn/Ptwxyq6+NQfS9nWofw+U1iwu3sLEpmd0kK9xW7KErR0AtZG0zTpHuiOxhu6gbr\nqB+qp2m4Ca/fC0CYLSw4F6ckscS6TSrR4p9rzPCkh1NXBwJBZ4ALbcN4/SY2A9ZnJbA938muomR2\nFDg1v1JEZJVS8FnBRtwejjb2c6i+l0P1fVztnwAgNS6CnUXJ7CxMZmdRMrnOaF3gyYo3Nj1Gw1DD\nNSFndHo0eE56THow4JQkWSEnPz5fFdXWoP6xKU40W0HnzSsDVHeNYJrgsBtsyk5kR4GTHQVOtuUl\nKeiIiKwRCj6rSEugvOrRxn6ONPYHF83LSozi3kAI2lmUTFZiVIhbKnJjXr+XlpEW6gbrguGmfrCe\n9rH24Dkxjph5vTczW3x4fAhbLqEyU176dMsgJ68OcrxpgIYeqxhBpMPG1twkdhQ4uacgmS25iUQ6\nNHRNRGQtUvBZpUzTpLF3LBiCjl3pZ3DCA0BecjQ7C5O5p9BJVZ6T7KQo9QjJkjNNk77Jvnm9N/WD\n9TQONTLtnwasktH58fnB3puZgJMZk6nP7Bo2Oe3jXNsQp1sGOX11iDMtg/SPW5+Z2IgwqvKTuKfA\nGra2IStBcyBFRARQ8Fkz/H6T2u5RjjT2c7Sxnzeb+hl1W3MgMhIiqcp3siM/iap8J2VpcVpIVRbV\nhGeCxqFG6ofmFBsYrGdwajB4TmpUajDYzIScwoRCwu2qYLiWmaZJ2+BkIOQMcqplkOrOUXx+6/+k\nQlcMW3KT2JqXyLa8JEpS41R1TURErkvBZ43y+U1qu0Y5edWa6HuieYDuEWtoXHxkGNvykthe4GR7\nvpON2QmqaiS3xOf30TbWNn8ezmA9raOtmFi/Q6LCooJzcIIhJ7GExMjEELdeloPxKS+XOkY40zLI\n6ZZBTl0dCg7bjQ63syk7ka15iWzNTWJLbhJOlfYXEZFbpOAjwOy3qieaBwLbYHCMfHiYjfWZ8WzO\nSWJLbiJbchPJStTwuLXMNE363f00DDUEe2/qButoHGrE7XMD1po4uXG5swEn0VoXJysuC5uhoUdi\nrZ1zuXOE861DnG8f5kLbMA29Y8z8d5OXHM3W3CS25iayJTeJ8vQ4wuz67IiIyNuj4CM3NDA+zcnm\nAU5eHeRsyxDn24dwe/wApMRFsCXHuhjZnJPIxuwEYiLCQtxiuRtGpkesYWqD9TQMNVjbYMO8YWrO\nSOe83pvSpFIKEwuJClMhDbFMe/3UdI1wvs0KOOfbh6nrnh2y5ooNZ2O29btkY3YCG7ISSYmLCHGr\nRURkNVHwkVvm8fmp7RrlTMsgZ1qHONsyxJW+cQBsBpSlx7M5J5ENWQlsyEqgLD1Ok4pXkEnvJFeG\nr9AwaIWb+qF6GgYb6J7oDp4T44ihKLGIksQSihOLKU4qpjixGFeUK4Qtl+XG7fFR1z3K5Y4RLrQP\nc6F9mJrOUaZ91hcnidEOK+RkJbAhEHTS4yPViywiIneVgo/ckcHxac62DXGmZYizrUOcax1ieNKq\nHuewG5Slx7EhazYMlabHar5QiHl8Hq6OXJ0XbhqGGubNwwm3hVOUWDQv3JQklpAek66LUwkyTZOe\n0Skud45Q3TlCdeco1Z0jXOkdI9CRQ1xEGBuyAwEny+rRUSVJEREJBQUfWVSmadI6MBn8lvdi4Pba\nMJRARWYCFRlxlKXHE6thcovO5/fRPtY+L9w0DDXQPNKM129V9LMbdvLi84IBZ6YnJzsumzCb/k5k\n1rTXT2PvWCDgWCHncucIA4Ey0mCtGbYuI56KjDjWZcSzLiOeXGe0qkSKiMiyoOAjd93NwhBArjOa\ndRlxlKfHsy5w0ZSTpAumW2GaJt0T3cG5N/VD1lycK0NXgoUGALJis6xgE+jBKU4spiChQOWiZR6v\nz8/VgQnqu8do6BmloWeM2sC+xxfoEQyzUZYWx7qMOCoCAac8I56EKEeIWy8iInJjCj4SEqZp0jHs\nprpjhJqu2SEyTf3jwYpOMeF2ytLjKM+IpzQ1ltK0OIrTYkmJjVizw2QG3YPBSmpzCw2MekaD56RG\npVKcVDxvLk5RYhHRjugQtlyWm2mvn+b+ceq7x6jvGaW+Z4yG7jGa+saDc3HA6sUpTo0N9OBYQafA\nFaPqaiIisuIo+MiyMjnto7Z7lJqZ4TRd1v5IYLFVgIQoByWpsZSkxVKcGhfcX02To8emx2gcbrym\n0EC/uz94Tnx4PCVJJcH5NzM9OQkRCSFsuSwnpmkyNOGhqX+c5r5xmvpmg05z/0SwopphWL2uJanz\n/00VpcSqWqOIiKwaCj6y7JmmSe/oFPU9Y9R3W99Mz+wPTswOl4uNCKMoNZaC5GgKXLHku6IpcMWQ\n74ohPnJ5DsFxe900DTcFw03jkBV2OsY7gudEhUUFh6bNnYvjinKtmqAnd2ZwfJrm/nGa+8dp6pvg\n6pygM/dLA7vNID85mpLUOIqDXx5YASfSoaIjIiKyuin4yIrWP2YFooY5W1PfOB3Dk8z9yLpiw60Q\nlGwFoUJXDLnJ0eQ4o5ckFHn9XlpGWoLzb2Z6clpGW/Cb1rAih81BQUKB1YMT6MkpTiwmMzZTC36u\ncT6/SdeIm/bBSdoGJ7jaPxEIOhM0943Pmy9nGNbwtAJXDHnJ0eQnxwT2Y8h1RqvEvIiIrFkKPrIq\nuT0+WgYmuNIb+Ba8dzw43KdndGreuQlRDnKcUeQkWUEoO2lmP4rspOjb+ibcb/rpGOsIzr+ZmYvT\nNNyEx29dnNoMG7lxudeUis6Jz8FhW549U3J3TXv9dA5PWsFmaJK2wclgyGkfmqRr2I3XP/s72DAg\nMyGKfNdssLFCvfUZVsl4ERGRa91q8NEgb1lRIh12StPiKE2Lu+axsSkvzf9/e/ceG9lZ3nH8+8zN\nM7O+zGy869317np37VGAhkBgFaAblRDSAAE2hUJJ1VKouAh6TYtQaZGoRP9ZlaqVKkRJ2iLRquVS\nyiWtgJISol5S0gYECdesd5O95LJXe+3xZa5P/zjH4/EtHsc7Hs/495FGc857ztl55/G7x/P4PeeZ\ni/VoiBMAABDPSURBVFOcvjzNmcvTnBmb5szlGX56bpJv/uQ8xXJ1wf47errYk0mxuzfJ7kyS3X1J\nBnqTbEtNM81ZLpVO8/iVE7VkZ6Y8Uzt2z7Y9jGRHuGnwptpMzsG+g3RF9Y30W0WxXOX85CznJmZ5\n5kqBcxPhcm0GZ4Zzk7MLZijNYKAnyd5sipcOZdmbTTGYSTOYTTGYSbE3m9KlaSIiIk2ixEc6RndX\njOsG+7hucGkRgGrVuZAv1BKis5dnOHH5PKcmTvLIxCn+a+w0ldgzRLvOYbHp+QMrPaR8kEzsJq5N\nHWB/9yFy2RH29mXZ0dPFjp4u+ru7dJlRh3B38oUyl/JFLuYLXMwXuJAvcilf4NzEfHJzbmKWi/ni\nkuMT0QgDfV3s6UtxZKSfwWyQzOzNBLOMu/qSGisiIiItosRHOt50aTooLlBXRW10fJQLMxeC/wHd\n0Bvv4WDfMAPJF9EX20eyuodKYYDxfIKnr8zyzKVZHs0X+M/pEnBiyWtk0nF2dAeJ0DXdXWxPx8mk\nE2zfliCTjrN9W4JsOkF2W4JsOk4qHlUBgw1QLFcZnykyPl1ifLrE2HSR8eliuFxibCpMcKaKXJwM\nEp3CopnBOddsSzDQm2RXX5Lr9/YFy71JBvqSDPQE7dl0XD9XERGRTUqJj3SMYqVYq6RW/6WfT+af\nrO2TjCY5lDnEK/a8YkGp6IH0QEMfWAvlCpfyRS5MFoJHvjC/HK4/cnacsanigqpbi3XFImTTCfpS\ncXqSMXqSMXpry/PPvckYveF6KhElnYiRTkRJxqOkE1HiHfqdK6VKlZlShdlihelihZlShXyhTH62\nzMRsiXyhzORsmcnZEvnZcLkQrE/OlsNEp8hUsbLiaySiETLpOP3dXfT3dDG8Y1uw3J2gvztIYPu7\nE+zo7iK7LdGxsRYREdkqlPhI26lUK5yZPLNkBufUxCkqHnzQjVmMA30HeGH/C3nTyJtqpaIHuweJ\nRp77PRRdsSh7Min2ZFKr7luuVBmfCT6AX56an224PDXXVuTKTPBB/UK+wMmLU0zOlpmYKS244f3Z\nxKNGKj6fEKXCpCgRjZCIRYhHIyRiRiI6txw8d4XPsagRMSNiYGZEI8FyxCxYN4hEgmXcqTpUw2d3\np1Kdb/OwvVJ1SpVq+HAK5WrdepViuUqx4pTKVQrlILGZLQXJzdxyqdLY+49GjO6uIHHs7gqSxF29\nSa7d1UM2nSCTipMJZ9kyqWD2LbstaE8nNOsmIiKylSjxkU3L3Xlm6pklpaJPXjlJoRJUcDOMfT37\nGMmMcOvQrcEsTmaEod4h4tHWVlKLRSPhDMLaCh64O7OlKpOzJSbCWY2J2TIzxQozpXIwAxI+pkvh\nc7HMTKnKTLHMTKlCqeyMz5QolasU6xKOUqVaS0SK5SoN5ldrf+8RqyVZ8WiERHThejwWoSsaIZ2I\ncU13V5i8zc9kpeJBEpeaW45H6Q5nwYIEJ0Z3MqZLBkVERKRh60p8zGw78DngAPAE8EvuPrbMfhXg\n0XD1tLsfXc/rSue5NHNpSano0fFRpkpTtX0G0gOMZEd42e6X1UpGH+o7RCq2+uxLOzGz2of+nb3N\nfS2vm8WpVB2vzeg41er8csU9nBmanx2amxmKmBGJzC8bwSyRiIiIyGay3hmfDwHfdPdjZvahcP0P\nltlvxt1fvM7Xkg4wUZzgxPiJBcnN6NgoY4X5fDnTlSGXzXF0+GitVPRwZpjeRJOzgC1o7nK2KIaq\nKIuIiEgnW2/icwdwc7j8aeABlk98ZIuZKc9w8srJ2uVpc/finJs+V9snHUszkh3hlv23LPjSz2uS\n1+jyJRERERG5qtab+Ay4+9MA7v60me1cYb+kmT0MlIFj7v7ldb6ubBKlaolTV04tKTRwZvIMTnAD\nSSKSYDgzzI27bmQ4M0wuG9yHs3vbbiU4IiIiIrIhVk18zOzfgV3LbPrwGl5nv7s/ZWaHgPvN7FF3\nX/JlKGb2XuC9APv371/DPy/NVvUqT04+uaDQwPHx4zwx8QTlalC2OWpRhnqHeN725/GG4TfUCg3s\n7dlLLKI6GiIiIiLSOqt+GnX3W1faZmbnzGx3ONuzGzi/wr/xVPh80sweAG5gmW+BdPd7gHsADh8+\n3KR6U/Js3J3z0+eXFBo4MX6C2cpsbb/B7kFymRw377s5uEwtM8LBvoMkookW9l5EREREZHnr/TP8\nvcA7gGPh81cW72BmWWDa3Qtm1g8cAf50na8rV8H47PiSUtHHx48zWZys7bMjtYORzAhvvfattRmc\n4cww6Xi6hT0XEREREVmb9SY+x4DPm9m7gNPAWwHM7DDwPnd/N/B84G4zqwIRgnt8frTO15U1mC5N\nc2L8BKPjozw29lhtNufizMXaPj2JHnKZHLcfvL2W3OQyOTLJTAt7LiIiIiJydawr8XH3S8Crl2l/\nGHh3uPwg8ML1vI40plQpBZXU6spEHx8/zpP5J2v7JKNJhjPDHNlzhFw2F8ziZEfYkdqhQgMiIiIi\n0rF0x3kbqlQrnM2frSU2c0nOqYlTlD0oNBCzGAf6DnB9//W8Offm4PtwMjkGewaJWKTF70BERERE\nZGMp8dnE3J1z0+cWzN4cHzvOySsnKVQKABjG3p69jGSC78OZKxV9oPcA8Wi8xe9ARERERGRzUOKz\nSYzNji2oojaX7EyW5gsN7EztZCQ7wtt2va12mdrBvoMqNCAiIiIisgolPhtsqjRVKzRQn+TUFxro\nTfSSy+a4/dDttXtwRjIj9HX1tbDnIiIiIiLtS4lPkxQrRR6/8viS78OpLzSQiqUY7hvmpsGbavfg\nqNCAiIiIiMjVp8RnneYKDRwfOx4UGgi/D+fUxCkqXgGWFhqYS3AGu1VoQERERERkIyjxadBcoYH6\ny9NWKjSQy+S4dejW2hd+DvUOqdCAiIiIiEgLKfFpwAce+AAPPvUg+VK+1rYzvZNcJseNu25kJDui\nQgMiIiIiIpuYEp8G7OvZx+sPvZ5cJkcum2M4M6xCAyIiIiIibUSJTwPueuldre6CiIiIiIisg+6s\nFxERERGRjqfER0REREREOp4SHxERERER6XhKfEREREREpOMp8RERERERkY6nxEdERERERDqeEh8R\nEREREel4SnxERERERKTjmbu3ug/LMrMLwKlW96NOP3Cx1Z3ocIpx8ynGzaX4Np9i3HyKcfMpxs2l\n+DbfZovxkLvvWG2nTZv4bDZm9rC7H251PzqZYtx8inFzKb7Npxg3n2LcfIpxcym+zdeuMdalbiIi\nIiIi0vGU+IiIiIiISMdT4tO4e1rdgS1AMW4+xbi5FN/mU4ybTzFuPsW4uRTf5mvLGOseHxERERER\n6Xia8RERERERkY6nxAcws9ea2U/NbNTMPrTM9i4z+1y4/SEzO1C37Q/D9p+a2Ws2st/tooH4/r6Z\n/cjMHjGzb5rZUN22ipl9L3zcu7E9bx8NxPidZnahLpbvrtv2DjM7Hj7esbE9bx8NxPgv6uL7mJmN\n123TOF6FmX3KzM6b2Q9W2G5m9pdh/B8xs5fUbdMYbkADMf6VMLaPmNmDZvaium1PmNmj4Rh+eON6\n3V4aiPHNZnal7nzwkbptz3qOkYbi+8G62P4gPPduD7dpDDfAzPaZ2bfM7Mdm9kMz+91l9mnf87G7\nb+kHEAVOAIeABPB94AWL9vkN4JPh8p3A58LlF4T7dwEHw38n2ur3tJkeDcb3VUA6XH7/XHzD9Xyr\n38NmfzQY43cCH1/m2O3AyfA5Gy5nW/2eNtujkRgv2v+3gU/VrWscrx7jnwNeAvxghe23A18DDHg5\n8FDYrjF89WL8s3OxA143F+Nw/Qmgv9XvYbM/GojxzcC/LtO+pnPMVn2sFt9F+74RuL9uXWO4sRjv\nBl4SLvcAjy3zmaJtz8ea8YEbgVF3P+nuReCzwB2L9rkD+HS4/AXg1WZmYftn3b3g7o8Do+G/J/NW\nja+7f8vdp8PVbwN7N7iP7a6RMbyS1wD3uftldx8D7gNe26R+trO1xviXgc9sSM86hLv/B3D5WXa5\nA/g7D3wbyJjZbjSGG7ZajN39wTCGoHPxc9LAOF7Jes7jW8Ya46vz8HPg7k+7+3fD5Ungx8Dgot3a\n9nysxCf4YZ6pWz/L0h9wbR93LwNXgGsaPHarW2uM3kXwV4Q5STN72My+bWa/0IwOdoBGY/yL4ZT0\nF8xs3xqP3eoajlN4qeZB4P66Zo3j9VvpZ6Ax3ByLz8UOfMPMvmNm721RnzrFK8zs+2b2NTP7mbBN\n4/gqMrM0wQfuf65r1hheIwtu7bgBeGjRprY9H8da3YFNwJZpW1zqbqV9Gjl2q2s4Rmb2q8Bh4JV1\nzfvd/SkzOwTcb2aPuvuJJvSznTUS438BPuPuBTN7H8EM5i0NHitri9OdwBfcvVLXpnG8fjoPbxAz\nexVB4nNTXfORcAzvBO4zs5+Ef32XtfkuMOTueTO7HfgykEPj+Gp7I/Df7l4/O6QxvAZm1k2QON7l\n7hOLNy9zSFucjzXjE2Sj++rW9wJPrbSPmcWAPoKp1kaO3eoaipGZ3Qp8GDjq7oW5dnd/Knw+CTxA\n8JcHWWjVGLv7pbq4/jXw0kaPFWBtcbqTRZdXaBxfFSv9DDSGryIzux74G+AOd7801143hs8DX0KX\ndT8n7j7h7vlw+atA3Mz60Ti+2p7tPKwxvAozixMkPf/g7l9cZpe2PR8r8YH/A3JmdtDMEgT/WRZX\nXboXmKtM8RaCm+U8bL/TgqpvBwn+avO/G9TvdrFqfM3sBuBugqTnfF171sy6wuV+4Ajwow3refto\nJMa761aPElyzC/BvwG1hrLPAbWGbLNTIeQIzu5bghs7/qWvTOL467gV+Lawm9HLgirs/jcbwVWNm\n+4EvAm9398fq2reZWc/cMkGMl62qJc/OzHaF9whjZjcSfA67RIPnGFmdmfURXDnylbo2jeEGhePz\nb4Efu/ufr7Bb256Pt/ylbu5eNrPfIvjBRAkqMf3QzD4KPOzu9xIMgL83s1GCmZ47w2N/aGafJ/gQ\nUwZ+c9HlLVteg/H9GNAN/FP4++C0ux8Fng/cbWZVgl8Ox9xdHxgXaTDGv2NmRwnG6WWCKm+4+2Uz\n+xOCX7oAH110aYDQcIwhuJn2s+EfRuZoHDfAzD5DUPGq38zOAn8MxAHc/ZPAVwkqCY0C08Cvh9s0\nhhvUQIw/QnD/6ifCc3HZ3Q8DA8CXwrYY8I/u/vUNfwNtoIEYvwV4v5mVgRngzvB8sew5pgVvYVNr\nIL4AbwK+4e5TdYdqDDfuCPB24FEz+17Y9kfAfmj/87Et/P0sIiIiIiLSeXSpm4iIiIiIdDwlPiIi\nIiIi0vGU+IiIiIiISMdT4iMiIiIiIh1PiY+IiIiIiHQ8JT4iIrKpmdk+M3vczLaH69lwfajVfRMR\nkfahxEdERDY1dz8D/BVwLGw6Btzj7qda1ysREWk3+h4fERHZ9MwsDnwH+BTwHuAGdy+2tlciItJO\nYq3ugIiIyGrcvWRmHwS+DtympEdERNZKl7qJiEi7eB3wNHBdqzsiIiLtR4mPiIhsemb2YuDngZcD\nv2dmu1vcJRERaTNKfEREZFMzMyMobnCXu58GPgb8WWt7JSIi7UaJj4iIbHbvAU67+33h+ieA55nZ\nK1vYJxERaTOq6iYiIiIiIh1PMz4iIiIiItLxlPiIiIiIiEjHU+IjIiIiIiIdT4mPiIiIiIh0PCU+\nIiIiIiLS8ZT4iIiIiIhIx1PiIyIiIiIiHU+Jj4iIiIiIdLz/B+/gFgtoU4y5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0888bdd6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 1.0\n",
    "d = 3\n",
    "offset = 1.0\n",
    "tau = 0.1\n",
    "cov = tau * pm.gp.cov.Polynomial(1, c=c, d=d, offset=offset)\n",
    "\n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiplication with a precomputed covariance matrix\n",
    "\n",
    "A covariance function ```cov``` can be multiplied with numpy matrix, ```K_cos```, as long as the shapes are appropriate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:56.399060Z",
     "start_time": "2017-09-18T00:02:55.884808Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aiTmJIeRW2knQyLKSIhY7R53xJrgxgBA0ZrKtchtvnXqLuzLu4obUGy54T5Ik\nvjPzO1R0VvBF+RdOWqFjKG4r5kDdAe7MvBNPzei1HxG+EXxt6tdYX7qeqk7henY+gwYje882szIj\n0iZb3pnxSj+O/Br3TDurGRY0PqqPbRJJ7uh0VtbcrWq6GSg1NAAVblpHo2aj0fOZFjPxjAHe2F9O\nSoQ/y6eMHP2VJIkfrkmntqOffx5Sqf6zZDt4+FjmVpV+vSKE+uy4u+1Mzn4JstFyu+aLSVmuvJbt\nsX1NroSpf4yl/WcuxnR+1SGzT9lf0kyAtwdzEkNsmxsl7exMQzcdfXbYWGwtVZqOxs5WZzzTOGMY\nA3QP6Fn0u23853itOnM6ECFozOTNk2+SEpzCE/OeGPH9lYkrmRI6hZdOvIRhAjcNe6fwHby13tw2\n5bZxj71/xv1oJS2vFLzigJW5DzkVbXQN6Fkx1br6GRMzh4wBjrtp2lltex9eHhoi/M1IUbGQUD9P\nfD21bpliVdbco3pqVWSAe1s3lw1FUNQWeikR/nhpNRPGGOB4VTt5le3csygJzRjmCUsmR7AoNZy/\n7yimV6dCVkHJdsVxytOCzYn060E2wNktts/vihRtgKC4c+5S1hKZoTQkVTHtrGdAb58HcEuo2A9+\nERAxxbZx4uaC1suiOprcynZmJYTgobX9EXjOUB1Nnj2iNLVDwkMtQWOGMcCJqnbqOvoJssLK2tkI\nQWMGDT0N5DXmsTZlLZ7akf+RNZKGb8/8NmUdZWypmJg36Lb+NtaXrueG1BsI8Rl/ZyPKL4rbpt7G\n58WfU9Nd44AVugc7TjfiqZVYMtnCRmIXEeznSXK4H/luagxQ095HbLDPmA9e1iJJklv2omnr0dHW\nO6h6apXJurncTa2bS5t7CPTxICLAS9VxPbQa0qICONswMQTNm/vL8ffSctvc8Yusn1iTTnO3jtf3\nlds2aUc1NJ+GtFWWnRc3FwImTcy0M8OgIvKmXqtYVduCJClRmrJdSgqSjVS39XLdc3tY8Jut/OTT\nfIobnfS7X7FfSRez9fp4+igpWWbW0fQM6Dld36lKdAYgOz4ErUayTx1N3THQekNUpjrj+QSPawyQ\nV6VskM6KV+f6OBIhaMxga+VWAK5JvmbM41YnrSYtOI0XT7yIUZ44RaYmPj7zMQOGAe7OvNvsc+6f\ncT9GjHx69lM7rsy92HW6iXlJYQRaYdd8MVnxIW5r3WyvHjQmYkPcrxdNWYv6DmcmUiL83TblrKxZ\ncTizJUUyIGgCAAAgAElEQVRzNFIj/N02cnU+zd0DrD9Rx21z4826t8xNCuWqjChe3FVi2269qbGh\npYJGM9Rs8uxW0A9YP78rUn8CBnvPpYvZSspy6G6A5jM2DVPR0sMdLx6kvVfHjdmxfJpbzdV/2s39\nrx+msatfnbWaQ0eNUheUtESd8ZIWKdEMM/r1HK9uxyjD7CQViuwBf28PMqIDybFLhOYYRM+AUTbS\nrSJm1pgRmrzKdlIj/An2ExGaCcnm8s1MCZ1CSvDYTiUaScNDMx+iuL2YrRVbHbQ6xzBoGOT9ovdZ\nFLOIyaGTzT4v2j+aWZGz2FN9af5vbXsf1/5lN197YT8f51TTp7MgVa9kO+S+pTSdciPqOvooqu+y\nyd3sfLLjg6nt6Kepy/0eCGrb7dODxkRciNKLxp0oa7KfoEmO8HNb6+bSph67XBOA1Eh/qtr63N7p\n7L1DlegMRu4ZwQxgNB6/Jp3Ofj0v77ahZ1jJdsWu2Zpd5PTrlT4r5ROsPqTqsPKacIU646UMNVW0\nIe2spKmbO148SK9Ozz+/tZBnv5bN/h+v4rHVU9lX0sIzm06rs1ZzMEVTLKm5GovExWDUKz1bxiGv\nUtkAnJOgjqABZXPgWGW7uvdWo3HIEECldDMTsbOho2pEYwBZljlWpaTjuSNC0IxDY28jeY15rE4a\n3dHrfNYkryEuIG7CRSR2Vu+ksa+Ru6eZH50xsTx+OYWthTT0NAz/rKa9jzteOkBNWx/N3Tqe+Og4\nC367lV+vP8XgWDeFwT7Y+AN4+xb4/Lvw9/mQ/7Hy4XcDDpQoN5Glk9URNFlxijFAQVWTYp3qJuj0\nRhq7BuwaoYkL8aGlR0f/oPvUtJU196DVSCSE+ak+dlK4Yt3sbs5v/YMGajv6VDcEMJES4Y/BKFPZ\nasfoVU8LDNpvB1yWZd4/UsWyKRGkRZp/nabFBrE2K4Y3D5Rb53hmNEDpDiU6Y030LHUFePpNPPvm\nqkNKf5WgGHXGC01WxivbZdXpNe19fP2lg+iNRt57aCEzhr43wgO8+d5VU7hvcTKf5lVzut5B6WeV\nB5T+MdFZ6oyXsACQFBvoccitaCMtUt0IxNykUHp0Bk6rmbraWqKIfdUFzVBN1wjGADXtfTR3DzBb\npXQ8RyMEzThsqdiCjMyapDVmHa/VaFmZsJIj9Ufo07vXg8NY7KzaSbB3MEtiLQ8Rr4hXdpd21yi7\nS9VtvXz9pQO09w7y9oNXsP3xFbz/0EJWTI3k1b1lozvvNJyCl1fB4Zfgiv+CO98HrwD45AF4aYVi\nA+ni5Fa2EejtQXq09XbN5zMjLpjJmhrmf3Yl/C4BXlwOG56AU/9WJd/aXtR39CPL2DdCE+p+vWjK\nWnpICPXFU4Vi1YsxRTjcrY6moqUXWUZ1owQTputit7Szoo3w3Ex46Uol1cYOlLf0UtPex7Uzoi0+\n9/b5CXT169l5usnyieuOKy5llqabmfD0Vc49vcml71cWU3V46CFbJYbraPZYtXn39x3FdPQO8t63\nFpIRHXTJ+/+1Io0ALw/+70sHRWnqTigF6hqtOuP5hsCk6eec00ZBlmXyqtqZk6hedAYYHk/VOhq1\nDQFMDBsDXCpojpnqZ1SMXjkSIWjGYXP5ZiaHTB6xgeRoLItbhs6o40j9ETuuzHEYjAb2VO9hadxS\ntFbcgNJC0ogLiGN31W5qh3aKOnoHeffBK5iVEIIkSSxMDeevd85mcVo4f9l65tKc7rrj8PJK6GmG\nb3wC1/1eac727T1wy0vQVgGbfqTS39h+5FS0MytRKSJUA//OEj70/g0GvR6WfE8p+jv+Hnx4Dxx2\n3R5A9myqaSIuRIlyuFPaWXVbn12iM3CuF025m9WLlDUrDmdqGyWYSB2K/JjmUQ1Zhj1/gvfvUnbY\nO6rh1dXQWKjuPMChUiXye0WK5UYjS9LCCff34nNrbFpLtiuvqVdafq6JtFXQOVRTMRHoqFb+Pmql\nm5lIWQ797dCQb9FpDZ39fHy0mtvmxTNllL5nof5efOfKNLYWNpBTYX4/F6swGqDhpHrRGROJi6Dq\nCBhGd+2raOmltUfHbJUFTXyoL1GB3uSoKmiOgYcvRKSrNyacMwYYoY7mWGU73h4aMmLU2XB1NELQ\njEFTbxN5jXlckzS2GcDFzI2ei6+HL3tr9tppZY4lvzmftoG24UiLpUiSxPL45RysO8jTG0/Q1qPj\n3QcXMvMiFw1JkvjZ2kza+wb5+47ic2/IMmz6sRKN+c5emHL1ufc0Gsi+A5Y/DsVbXLqjcvewu4pK\nN9PGInjjBjw0Gh6QnkK+6im49z/w40qlwd22X0K7a/YAqrFjU00Tpv427uR0VtNmv7qiiAAv/L20\nlLuZMUCJHeuKQHELDPf3UjdCM9gPnz6kfAZnfBUe3Arf3KQ8zL22xiKLWXM4WNpCRIA3aVZEsTy0\nGq7PimHrqQa6Byy0cC7Zoez4+kdYPO8w8fOU1+rx6x/cAlM/FDUjNAApy5RXC7/jXtlTit5o5DvL\n08Y87v4lyUQEePPMptPI9oyWtZbBYI/6giZpkTJu/fFRDzE1wJyTpG5KlSRJzE0KVdcYoDZPuUZa\n9RosDxM7W9kkvoi8qnZmxAXbJUPAEbjnqh3E1sqtyMjjuptdjLfWm/nR89lTvce+NwYHsbt6N1pJ\ny+JY6xtgLY9fTr+hny1l+7jrikSyhppCXsz02GBumxPPG/vKqTQ9eJ36txJKXvUkBI7S2XfBtyEo\nHrY85bKpC8erFHeVOWq4q7SUwJs3ArBj4asc7YmirmMoR1+jhRv+rFyH9d93yethEhkxweo31TQR\nHeSDViO5TcpZ/6CB5u4B4u0UtZIkieQI97NuLmvuYVKQN/7edvhiHyIlwn9YOKnCnj9C/ofKPevW\nV5XUqugseGAz+EfBW19RLUVWlmUOlrZyRWqY1S5wN82KZUBvZMupevNPGuhSHt6tTTczETVd2Yme\nMILmsFIXNGmGuuMGxUL4FIsETXuvjncPVXJTdiyJ4WNHfv28PHjkqskcLm9l5xkr0g/Npf6E8qq2\noDFFxGpyRz0kt7KNAG8PpkSpH4GYmxRKVWsfjZ0q1MoZDYrgUDvdzETMrCFjgObhHw0ajBTUdJAd\nH8Qzh5/hTJttjnrOQAiaMdhcvpm04DTSQsbe2RiJpXFLqe6upqLT/cPou6t3MytqFsHeI4sQc5gf\nPR8t3mj9C7l3HBeeJ9ako9VIPPNFkbLTueXnypfDnHtGP8nTB1b+FGpz4dRnVq/TnuRUtCFJqOMg\nsv1pxSDhvg0kpis3vQvsm0OT4KqfK1Gr/I9sn09latv7iAjwxsdTpRzqEfDQaogO8nEbQeOINLzk\nCH83TDmzn8OZiRQ1rZv1Osh5Q7EkXv6DC4vlQ5Pgnn8rjkx5b6syXWVrL/Wd/SxMtb6v1dzEUOJC\nfPn8mAVpZxX7wTgIqSutnhdQdqBjZ0P1xEjRpurQULNHOwjwlGVK4buZdTRv7C+nV2fgv640z5n0\njvmJJIb58cfNdqylqc8HjafSMFRNguKURp0j1IaYyK1QHLzUSvk+H9NGpSppZ81nlWiT3QTNUB3N\neVGaorouBvRGvIJP8U7hO5S0u35N8sUIQTMKLX0t5DTkWBydMbE0bimA26ed1ffUc7rttNXpZiYM\nBi2G3skEhJ4dN6VmUpAP316Ryob8Oqo3PQvtlbDmt+MXEGZ/HSIzYduvlMZmLkZORRtTowIJtrUD\nb0uJItrmPwCRU8mMCcJDI3H84gabCx6CuHlKbdF5OzGuQE17H3Eh9ovOmIgN8XGbGhqT+1h8qH1q\naACSw/2obusb20nQxVAEjX0czkykRgbQ1DVAV78K943TG6CnEeZ9c+T3g+NgyjVw7L0x8/3N5eBQ\n/cyi1DCrx9BoJG7IjmHP2Wbaesy0wq86DBoPdVKr4ucpO/fu3o9G16MUvKtdP2Mibq7ifNU6vs12\nz4Ce1/eVc3XmJLNNaLw8NDywNIWCmk77Ndysz4fIdPBQt0kukqQIgFF6rPTq9BSp2FDzYqbHBqHV\nSBTUqtDo2l6GACZMFuvn9TU6VtUGyBxu+5j4gHiznX1dCVUEjSRJr0mS1ChJUoEa47kCRxqOICOz\nLG6ZVecnBCaQHJTs9oJmd7US3rZV0HySU01/RzoDtHC2/ey4xz+0PJVpgb2E5/0N0tcq9p7jodHC\n1f+r3Oxz37RpvWpjNMrkVbapk7u7/6/Kg8TC/wLAx1PLlEmBFNZ1XnicRgs3/01JDdnyC9vnVZGa\n9j67RiJMxLlRc02T8LKn81vykHWzu4i89l4drT06uxkCmBh2gGtWob7oyKuKxe7kq0c/Zvbd0F0P\nJdtsnu5QaSsRAV4W2TWPxE3ZseiNMhsL6sw7oSZHeTDyVOH3NX4eGHRQ7+aPELV5IBvsJ2iGd9ZH\nb4xo4r3DlXT0DfLfKy3LMFkzXXHK+6LAgvRDS6jPVz/dzETsLGgqUrIXLuJ4VYdZDTW7dF0cazyG\nwWiZjbm3h5a0SH8K61QQgnXHwNMfIqbYPtZI+EeCb6hyrYbIq2wnLLySs+2F3D/jfjw09kvxtRdq\nRWjeAK5VaSyXIKc+B18PXzLDrWgWNsTSuKVub9+8u3o3cQFx4zYVHQujUeb1feVMDZw/POZ4+Hl5\n8EzYf9AaddQv/Jn5k01do3Qf3vUHl4rSlDR109mvt90QoKsejr0Ls+6CwHMWrZOjAihpGsGlKSpT\n2SnO/0ixV3UBZFmmtr2P2GD7C5rYEF/qO/oxGF2vjuhiatp78dBITAqyX+Rq2KLYTepoSpvtawhg\nInWomL7UVqezpjNKk8h5940dUZ66RnmosDHtTKmfaeGKlHCr62dMTIsJIi3S37y0M1lWHt7j5to0\n5zDxyneD26edmQwBTEYHahOZAVqvEQu6z8f0nbsoNdzi75zoYB/mJIawyR6CprtJEfL2EjQxsxRB\nOYIwNhkCzB4h5VuWZfIa83hy75Nc9dFVrNu0jpv/fTOfFX/GoNH854jMmCCKLt5YtIbaPHVtrS9G\nkhT3tKbzIzTt+EbtIsI3gpsn32yfee2MKoJGluXdgJ29/hxLTmMOs6Nm26RS3d2+uV/fz6G6Q6yI\nX2HTl+XOM42UNvfw0JLZTAufZpagoa+NGc1f8KHhSj4usyA0LUmw6GHoboBS65qQ2QNTXu1cWw0B\nDv5Dyb9f/L0LfpwW6U91W9/ITSRn3ansfp50jdqi1h4d/YNGuzqcmYgL9UVvlGnssl9TQ7Wobusj\nJsTHLvndJpKGrJsr3KSOpmyoUD/VTj1oTCSG+SFJUGqrMUDO60p9wOx1Yx+n9YSZdyj9V2xIB61u\n66O2o58rbEg3MyFJEjfPiuNweSt1HeNswrWWKhbCsXNsnhdQCt4DY83q9O7SVB1WHhT9bP/3GBGt\np9JvZRxBk1fVpjSvnp9g1TTXzojmZG0nVWo3mzVZTtszQgMjRrDyKttIjfQnxO/C54kBwwD3fXEf\n92y6hy0VW1ibupZfLf4Vfh5+/Hzfz7nh0xvYUbnDrOkzY4Ko7einvdfMtM2RMOiVtEXT38VeRKZD\ns1Ir1dE7SHl3EZ2c4p5p9+Ct9bbv3HbCYTU0kiQ9JEnSUUmSjjY12dFBQwU6Bjoobitm7iTbdp/c\n3b75cP1h+g39Nqebvba3nOggH67PimFZ3DKONx2nWzfOTmj+x0iGAU5E38InuTWWucVNvgq8g+Hk\npzatW01yK9sI9fO0bae5vwOOvgbTbobwC9MI0iIDkOVRmgPGzFK+ZE98YP3cKlLbrogLR6WcKXO6\nfpTUnpbNJiICvAjw9nAb6+ay5h60GsluvXlM+HhqiQ/1tc0YYLBPiZ5m3ggBUeMfP/tuZXPChs/l\ngaH6GVsMAc7npuxYZBk25o+zO29ykopTSdCAEtVw5wiNLCsRGrXtmi8mJlsRNGN8J64/UYeXh4ar\nMs34PRyB62bEAHZIO6sfEjRqO8CZGMUYQJZl8ipHbqj5XO5z5Dbm8qP5P2LH7Tt4atFT3DLlFj64\n4QP+ftXfCfAK4Ie7f0hZR9m402cM1SrZlHbWfBr0fcr3tj2JTIfeFuhp5lh1O17hO/HTBnB7+u32\nndeOOEzQyLL8kizL82RZnhcZGemoaa0irzEPGZk5UbbdrN3dvnl39W58PXyZF219+LyypZe9xc2s\nW5SEp1bDnKg5GGUj+c3jNAfLeweis5h3xZWUNfeQW9k+9vHn4+ENmTdA4XqXKTLNqWhjTmKobWkh\nR1+DgU5Y8uglb02OUvLnixtHEIqSpPTqqTwAbeXWz68SNe3Kw7S9H97Pn6PaDWpGqtv67GoIACbr\nZj91e67YkbLmHhLD/BzSFyElIsC2lLOCT5VNh/kPmHd8VKZi2pH7ttXW6gdLWwjz92JKlDqmCckR\n/kyOCmDXeLa9tbmK1XKk9SnZlxA/T7k/uZiBidm0FCtpvfaqnzERk61Ex9orR3zbaJTZmF/HlVMj\nCfQZ2YCmrruOqq7Re5QlhPkxPTaITebWU5lLfT4EJ9gvgjWKMUB1Wx8tPbpLHEb31+zn7VNvc2fG\nndw97W78PP3OG0rpn/fC1S/g7eHNT/f8dNz0s2kxQQAU1duQdmZKl4uZaf0Y5hA51LCz6TQ7Sgrw\nDDrJ7elfx9/TvtFweyJczkYgpyEHT40nWZG2h0VN9s1j3TxclT3Ve1gYsxAvrfVuJJuH+hrcMFPZ\n8cmKzEJC4ljTGEWN9flKyHj2Oq7LisbHU8MnudWWTTz9qzDQAcW2F93aSnuvjpKmHtv6zxj0SrpZ\n6soRQ9EpEf5IEiPX0QBkDe26nHC+hXONKULjAEFjSmtzdWMAnd5IQ1e/Q65JUrg/FW5UQ5M8Tv8M\ntUiN8Kesqcf6zaejrymR0KQl5p8z+25oKlQEghUcKm3lihTr+8+MxIqpkRwqbRk5fdVETY7yYK2m\nNfFwHY2bpp0NN9R0gKCBUdPOcirbaOgcYO3Qd64Jo2xkX80+Ht72MGs+WcP1n17Pg18+yJflXzI4\nQr3pdTOiya1sp75DxXRdexoCmBjBGKCgRnEem3le/7u2/jZ+tu9npAWn8djcx0YdLtIvkqcWPUVB\nSwEvnXhpzKkjA70J9/e61KDHEhpPKmmr4eZZbVtNhEnQFLG74WOQPbk/a5xUWRdHCJoRyGnIISsi\nS5U8wnmTlOjGmA/wLkhddx21PbUsjFlo0zhbTjWQPilwOHc/0CuQtJA0jjeNkQOc965S+Jj1NQJ9\nPLl2ejTrj9eO/QV7MakrwDcMCj6xaf1qkDcUXbLJEKDygFIXNPe+Ed82pcyMGKEBCEmA5GVw4n2n\nN9qsbe/D11NLiJ+N9tVm4O/tQYifp8unnNV39CPLjknDSwzzo6a9z+WNEmRZprKlZ/jeYW9SI/3p\n0Rlo6rIiqttWrtR/zFl3Yd+Z8ZjxVSXSkfeOxVNWtfZS096nWrqZiRVTIxnQG4ftoC/BlOOvliGA\niZhZIGndt46m+ij4BNv/QTRqunKdRnE6W3+8Fm8PDVdlnmtCXdpeys2f3cx3tn6H/OZ8Hpr5EI/M\neYTq7mqe2PUE13xyzSXfydfOUExnNlvSbHUsBvsUm2B7C5oRjAHyazrw0EjD9tWyLPPU/qfoGOjg\nmeXP4OMxthHL6qTV3JR2Ey+feHnMZxdJksiICaSo3oaUs4ZTSvREa+fvx+B48ApA11RIk3yYSdor\nCPOxU+TMQahl2/wecABIlySpWpIkM2PurkfvYC+nWk7ZXD9jIjU4FT8PP040nVBlPEeR26jsGM6Z\nZH3aXVuPjiPlrayeNumCn8+KmsWJxhMY5RF6YegHlJzyjLXDYelb58bT2a9na2GD+ZNrPWHaTUrR\nrc659QI5FW1oNRLZCdY3JqVoA2i9x7SCnRwZMHa385l3KGkRY3RSdgQ1bX3Ehviouqs8FnEhvi5v\nU1zdpvyOxjtI0AwaZOrV6GhtR9p6B+nRGUi0c/2MCVN9W6k16XhntyivU6+z7DyfYMXx7PQXFm80\nHCpTfHjUMAQ4nwUpYfh4akZPO2sqVHL81ayfAfDyUwre3bWOpj4fomeCxs77xJ4+SrriCBEag1Fm\nY0E9K9OjCPBWomc9gz08suMROnWd/H7Z79ly2xYenv0wD2Y9yIZbNvD8Vc/jrfXmiV1P0DFwrofK\n5KhAJkcFsGm8eipzaTwFstF+9TMmRjAGyK/pYOqkQLw9FNew9aXr2VG1g0fmPEJ6WLpZw/54wY+Z\n5DeJn+75Kb2Doz9TZEYHcbq+C721vb4aT0HUNOvOtQRJgogp7GrMA00/88JX2X9OO6OWy9mdsizH\nyLLsKctyvCzLr6oxrjM41nQMg2wYjqzYilajJSsiy+0ETV5jHv6e/kwJsd4HfXtRI0aZSwRNdmQ2\nXYNdIxfZnd4Efa1KKsYQi9MiiA7y4ZMcK9LOBnvg7JfWLN9iZFkmtyGXXx74Jes2ruPjMx+jM+jI\nqWhjWkwQfl5WpmfIMhSth7SV4D16rnxaZAClTd0YR9t5n3YTePgoURonUtvRR5yda0XOxx160VQP\nrS8+xP7XxSQQKl3cGKByyGHJ3oYAJoYFjTVOZ8XbIDT5ErMO8yZeDl21ZjVLPJ/jVe0EenswNcq8\nponm4uOpZWFq+OiCpiZHebVH07/4ecqGi9F9Gr8CYDQoD6L2jj6YiMlW6kQuEsFHyltp6jqXbibL\nMr/Y9wuquqp4dsWzrE1de0EKuVajZVn8Mv644o809zXz5L4nL0i5vG5GNIfKWmjpVqEWtd7ODmcm\nLjIGkGWZgpoOsuKUDUWjbOTl/JfJDMtk3TTzU6wCvQL59ZJfU9lVyadnRzccyogJYkBvpNyatN6+\nNuisgUkOEDQAEel8OVCHUe/PlYmLHTOnHREpZxeR05CDRtKQHZWt2phZkVmcbTtLv961d0TPJ68x\nj+zIbLQ2+KBvOdXApCDv4RuJiVmRyg7KscYRQuZ57yg3pNSVwz/SaiRumRPH7rPNNFqyq5y8FPyj\nlGJdOyLLMm+efJPrPr2Oe7+4lw2lG+jUdfLLA7/k2k+uJb/730yPtyF9sf4EdFRBxg1jHpYWFcCA\n3jj6w7tPMKRfp6ThObFHj+LmpUKvFf0AVOfA4Zfhs/+Gz793ga++idihCI0rG3NUt/WhkZQeEPbG\nJGhUt2RVGdP6HBWhiQ32xdtDQ5mlxgD6ASjbrURPrYk6pixXXsvMsLM/j5O1HWTGBqGxg833iqmR\nlDb1jPw7UpMLPiEQlqr6vMTPV4xPmi/9HLs0raUw2Gv/6IOJmGzobYauC4v2N5yow8dTw6oMxd3s\nncJ32Fyxme/N+R7zo+ePOtz0iOl8f8732Vm1k38W/XP452umR2OUsSw7YjTq88E7CEKSbB9rLC4y\nBqhp76Otd5AZQ/Uze6r3UNZRxr3T70UjWfYIvCBmATMjZvLhmQ9H/T7JjLHB6ayxUHmNmm75uVbQ\nG57Kbi8JqSuDaTE2tpRwAYSguYjchlwywzJVdXrIishCL+spbC1UbUx70qnr5GzbWWZHWb8D1z9o\nYNeZJlZPm3TJF25SUBIh3iGX5qJ21Cids2fddUlDqVtmx2Ewymw+ZcGNVaOF6V+Bs5thQIXuvaPw\n0ZmPePbos8T4x/Dbpb9l5+07+ezmz3hp9UvE+iUhha8nV/c76wVt0QaQNIoYGYNhp7PRjAEAZn5d\nsWos2W7dWmykf9BAS4/O9qaapTvhD2nwyirY+ASc+VJpHvr8FfDJty4QNnEhvvToDHT2622b047U\ntPUxKcgHLw/735JjgpVeN1VtThA09QXwn0fgg7uhsWjMQ00RGkek4QFoNBIpEf6WO8BV7FciwZNX\nWzdx+GQIjFEacpqJwShTWNc17KqkNiumKk6kO0eK0tTmKulm9kgZjRvKjHC3Opr6oQwMR0Zo4IK0\nM4NRZlNBHasyovD39iCvMY8/Hf0TqxJWcf/0+8cdct20dayIX8Efj/6RUy2nAJgeG0RMsA+7z6jg\nPFefrwg+e6fkwQXGAAU1SoG+aWP1jZNvEO0fzTXJ11g19O3pt1PWUTZqf8HJUQF4aCTrjAEaTiqv\nDorQ7PYw0KfRkNIb47D7rD0RguY8dAYdJ5pOqFY/Y2JmpGK/5y5pZ8cbj9tsW72vuJm+QQOrp0Vf\n8p4kSWRHZl9qlFDwiZJjO+uuS86ZEhVAfKgvO4oaLVvIjFtB36+kstmBUy2n+P3h37MkdgmvrnmV\nG9NuxM/TD0mSWBS7iNsTfkNf9Teo7y/mF/t+YV2UoGgDJCwE/4gxD0uLVARNyWjGAABpq8ArQBEA\nTsDkmBNji5tX5SF4707F6OBrb8Kj+fCDYnjkBCz+rpKe9/wViusUEDMUDRq3WaATqWnvdYjDGYCH\nVkNsiM+wYHAIhf+B166DF5bA8Q+UaMSLy2DnM6AfuQlddVsvEQFe+Hur6KQ1DikR/pannBVvVUxM\nUpZZN6kkKYYdZXvMrqMpa+6hb9DA9Fj7CJqUCH8SwnzZdfoiQaPrVYqW1WqoeTHhk5UeYqa0Nneh\nvgA0HuescO3NpBmAdIGgOVTaQnO3jrVZsQwYBvjx7h8TGxDL00ufNqteUZIkfr3k14T6hPLjPT/G\nYDQgSRJLJkewr6R59FRmczAalWvkMMF3zhigoKYDrUYiIzqQk80nOdpwlLsz78ZTY13R/ZrkNQR5\nBfHB6ZH7R3l7aEmLDLDOGKDxlPL7HxRn1dosZVNXKVF6Pau8vewS6XU0QtCcR0FzATqjTnVBE+Eb\nQax/LPnN+XT1DzKgt8CtywnkNebhIXkwI8L68PmWUw0EeHuwcJSC1VlRsyjrKLugCJHCz5WdpxFS\nGSRJYlVGFPtKmi1zO4tfoOx+Fm2w9K8wLp26Th7f+ThhPmH8btnvRgxfn6zpQNObzf/M+i6byjfx\ncv7Llk3SWgYNBUpfnXEI8/cizN9rdOtmAA8vSFkBxVuc4nZWZxI01qZW1Z2Ad78GgdGw7jMlAheS\nqKQhqSEAACAASURBVDwUBkTC6l8pAidtFWz8AVQeImYoGlSnpv2oyig9aBy3Q5YY5uc4QXPkFSUi\n01kD1zwNj52Ch3Mg8ybY+Vt4cfmI0ZrK1l6H1c+YSInwp7K1l0FLCnqLt0LSYvCyIaqfsgx6GqHp\ntFmHn6xV7pvTY20wGhkDSZJYMTWS/SXN6PTnXYv6fOVBUW2HMxMajfLQWz9OnzJXoz4fIjOUHmiO\nwDsAIqZcIGg2n2rA20PDyoxIPjz9IbU9tfx80c8J9DK/xirUJ5Qfzf8RZR1lbKtUWh4snRxBe+8g\np2yxIm4rU6KY0Q5KyTvPGCC/poMpUQH4eGp58+SbBHgGcOuUW60e2sfDh69M/grbK7fT1DtynVlm\nTKCVEZpTSnTGAYY5Xbou9jTlcnVPP7O9VUgpdAGEoDmPnAZlV8jWhprns+tMEw++eZS2tmi+LD5E\n1v9uZv7TW/nVf06NbrHrZHIbc8kMz7ygyZQlGI0yWwsbWZEeOewqcjHZkUrIfDjtrKNGcbfJvGnU\ncVdmRNE/aBzujm0WGg1MvgpKdyh2oyohyzI/3/tz6nvqeXbFs4T6jJx/ml/TQUZMIA/NfJC1qWv5\na95f2VZhQW8ckxBLv96sw9Mi/SlpHGeHefJVSlO2lmLz16ES9Z1KlMSqWpGmM/D2LeAdCPf8GwIn\njXycfwTc+qoidD68hzgP5Yulrt01BY3eYKS+o98hls0mEsP8HFNDU7oLNv4QpqyB7+UpETS/MEV8\n3vYq3PUh9DTBp9+65PNZ1dpHggPNIwBSIwPQG2Xzr017lZLaYm26mYnkoehO+R7qe+o5VHeIz4o/\n4x/H/8G7he9e4qp0qrYTL62GKZPUaag5EiumRtGrM3C0ovXcD039ctR2ODuf6Cwl9cao3sbfjtON\nPPXvAl7aXcIXBfUU1XeqW1PniP4qFxOTPSxoZFlmW1EDSyZHYKSfl0+8zKKYRVa1Xbgq8SoSAxN5\nveB1ZFlm8WTFFnxvsQ1pZw6uDTEZA8i1ucOGALXdtWyu2MytU24lwMu2z83t6bejl/WjmgNkxgRR\n19FPe+/I0ecRkWXlOk1yzDXaXrmdQeMg07v8SaXGIXPaGyFoziO3MZfJIZMJ8QkZ/+BxOFXbybpX\nD3Hva4c5WdtBpNdU8Gjnu6snsSI9ircPlnP1n3bx9ZcOcNoWz3KV0Rl0FDQXMCvq0uaN5pJX1U5z\n9wDXTBvlgROYHj4draQ9J2hMD+5jCJpFqeH4eGosTzubvFrp4K1iXvZHZz5ie9V2Hp376KjXyuSu\nMj02GEmS+OXiX5IVkcVP9v5kZIe3kSjaoKQXhKWYdXhaZMDYERo4Z/1cvNW8NaiIKUoSHWShoNH1\nwntfV2qJ7v1cEStj4RsCd7wD/R1M+vLbeEl66l005ayhawC9USbegQ/vCWF+NHfr6BmwY11RSwl8\neI+yk3zrK5fUxQGKZfHaZ5UahKPnzDH1BsXcwlGGACZMTTwrzHWAM32GptgoaEKTkYMTePHsh6z+\neDUPbn6Qn+/7Oc8fe57fH/491396Pe8VvTfcAPFkbSdTowPw1NrvK3xRWjieWulCt7OaHOVhMfDS\nVGLViM5SCuwtdH0biY7eQR7/8Dj3v36E945U8duNRXznnRyu/cseHv5nnm1pVCa6m6C73nGGACZi\nspWoZ3cTJU3dVLX2sSojijdOvkHbQBuPzH3EqmG1Gi33Tr+XgpYCjjYcJSrQh/RJgeyzRdA0DUVg\nI6daP4YlDBkD6KvzaOnRkRUfzDuF7yAhcfe0u8c/fxySgpJYGLOQj89+jGEE4Z0xVNtmkTFAR7XS\nDNwRls3ApvJNhHtHI/XHEtlf7pA57Y0QNEPIsszJ5pNkRdi2y2I0yjz17wLW/nUPJ6o7+PkN09j5\ngyt5+jplh332lE7+eudsDvzkKn54bTrFjd189fl9bD6pkte7jZxqOcWAYcCmKNWWUw14aCSuTI8a\n9Rg/Tz+mhk7leOOQoCn8XAnZj3HD8/HUsnRyBNuLGi3bXUu9UmlEptIDvMFo4PWC18mOzOaeafeM\nelxVax+d/frhYkRvrTd/WfkXPCQPfnPwN+P/HbqboOqg0pPHTCZHBdDSo6OtZ4ydodAkiJh6rneG\nA2no6CfIx8Pyuogdv4HWEmVX31xr3EnT4aa/IlUe4Fd+H1Lroilnph45jqqhAYYjH3YzBuhrh3/e\noQjQO98HnzFqPaZ9RUkR3P40dCn3wbqOfgxGmYQwxxaqmpp4VphruVq8FYITlM+TDfQZ+vnRpCj+\npq/nuuTrePWaV9l4y0Zy7s7hreveIjk4md8e+i03fnYjeQ15nKztYHqMfdLNTAR4ezAvKezCOpqa\nXPvYNZ+PKdJRb17NaXt/OzurdvLnnD/z5N4n+b8j/8dLJ17i6d2vsfr/beCzYzV8d9Vk8v/3Go7/\n4ho+f3gJ/31lGhvy63jmi7GNKcyiwUF2xBdjMgaoP862QmWTb3aylrdOvcWa5DVMD7d+p/+mtJsI\n8wnj9YLXAVgyOYLDZa2WpXufT1OR8jnxVtdifExiZqJtOYsXg6RN8uSTM59wTfI1RPurI8bvSL+D\n+p56dldf6k54zunMgrSzRsWIwRERmrb+Ng7WHiTVdwnFxnh8uquUxqdujhA0Q9T11NE20GbTTUCW\nZX694RRvHqhg3cIkdv9gJQ8sTcHbQ0tmWCYekgf5zcrNLyLAm/++cjLrv7uMyVEBPPR2Dn/bftbp\n1rJ5jYp3uy0Rmj1nm5ibFEqw79hFd7OiZnGi+QT6rgao2DdmdMbEyowoqtv6LEvX8w2BhAWqPcDv\nqdlDdXc166atG7PYsmAoz31G3LmHuSi/KB6d+yiH6g+xvnT92BOd2aSYJIxj13w+w8YA40ZpVivX\n3ME3sbqO/uGaFrOpPAQH/g7zHjhncWsuM78GCx7i64b1eDSdtOxcB1HTrogKR6ecgSK67cJ/HlHy\n5u94e/zooiTB9c8q5h2bnxxal2N70JiICPDCz0tLhTkpZ3qd4rZnrV3zEA09Ddz3xX18MdjEI63t\nPDP1bhbELCAhKAEvrRezo2bz+prXeeHqF9BIGv5n28O062uZHmcfQ4DzWT41kqL6Lpq6BhSnyNYS\npeDankRmgMZzzDqa5r5mXsl/ha989hWWfbCM727/Lm+deosDdQf46MxH/DXvr3xQ9mcGJj3Dj2/r\n57HVU/H20BLs58nM+BB+sCaddQuT+P/snWdgVGX+tq8zmUnvvSekkZBA6BCagoCoYEUUsawuKsIq\n9kXXtfeyYteVXRUL2BXEAojSQq8phJBKeu9tkpnzfngyqZPMmUlhff/eX9CZOSVTznl+7brf25XF\nJ/tzB3a+w+Wv0lO+AjZE0Ql+TSsl2teJ73PXo9VpuXPcnQPata3alqXRS9ldsJszVWeYEelBS5ue\no7lVlu2wLE18rsMpn1hUchtRVoUUtx6isa2Ra0ZeM2i7Pz/ofLztvPk8vTccwMvRBg8Ha9KKzQho\nDIQz75hBOsO+tSt/FzpZh03LOIqsg5GQz0kL+mDrz4CmXSkV4ssU62l5QPPuziw+2JvDLdNH8MSl\nsbjYdy7obdW2RLlHkVTW/SLt62LL57cncMW4AF7ems59X544p0HNsdJjhDiH4GnXP1GrL1U1aEkt\nqmV6hOnt473iaWprIuPEerFwj1lkcpvZ7VWfHWa3nV0gnIPr+zCLM0OfnvoUb3tv5gT376ybVFCD\nWiUx0rd7Vmpx1GLGeI3h5cMvd4ci9FTGr6K9w4wbpfKA5gKxgMzZo3jfg6Hi2mbz5mdam+D7VSK7\nN+8Jyw46+2GaVPbMr/zUsu2HWPmVw1+h6TDXHIo5muzdkPodnPd34QWlRB7hMOMegd7O3tVRORru\nGRpJkgjxcFDWcpZ3ALT1nS2cFqiprYlbt91KTk0Or095jOU1tUhGfpOSJDE9YDrvzXsPWVZhH/QB\nQZ5Dbz6ZEC7mJw5kV3QuuPzGDO1B1dZi8WskoDleepz7d97PvC/n8drR13C1dWX1+NV8cOEH7Fu6\nj1+v/pVfLt+DXcFLuFc/yEjPYF5Peoy7f7u72wC3JEk8tmgUs0d68ej3yfx22sz7SVcVJ7fPbBgH\n4AyZ7FzBJQhtQRJHcquYHCnzZfqXXBl5JSHOA/d6uXbktdip7fgw5UMmj/BArZIsm6PR66D8zPAR\n4AxqbwE8z7mUn3O3EOAYMCArip5Sq9QsCl/E/sL9ve7jkiQR4+dsXstZaaq4z9kObeUVRFLWy86L\nonIP9J7tn4tCIMn/sv4MaNqVUp6CWlIT6RZp0fZfHs7jhZ/TuDTen0cuiTGauR/tOZqk8qRePZe2\nGiv+tSSeO+dE8M3RAr4+em4GtGRZ5ljpsQH96A9kVyDLMK39RtifDFWg41k/C5dtBQt3f1c7on2d\nLAho2hcdmWYM5BtRZnUm+4v2c+3Ia01iH5MLaojyceoFRlBJKh6d+ig1LTWsPbrW+MayLCoooTPM\nyv4GuAlzQJMVrJDpoLYb9jkaUaExI6D57VmoOAOXvm55u4KdG0e9r+L81r3IRow3z7UKqpvwdLTB\nVmO5ia25crXX4GSjHnwwgF4HvzwEzoECAGCOZtwjTPe23EdeRS1qlWQ5DW8ACnG3V9ZylrFdVBLC\nzrP4WK8cfoXsmmzWzl7L+dGLwW1Ev340QU5BzHH7O5K6lvdP/3PIzZrj/J1xtFGzL7NieCsRPUhn\nJQ0l/H3X37nhpxvYV7iPpTFL+f7y7/lwwYcsH72cib4TsVXbIssyD3+bRFWDnrcWX8pnl3zKvRPu\nZW/hXhZvXkxhfWHHPtVWKt68bjzRvs787dOjlJhj2txV5wIIYJD3KJoLk9HpZaqtt6FCxYr4FYOy\na1dbV66MvJIfs36kvq2cccGuls3RVOWI5NkwVB66SnYPoxlrouyzOVB0gIVhCxXhq83RBcEXoJN1\nfbadnS6pQ6d0TqskdVjmZ1r1rSQWJDIjYAZniutx9h8pWoP/DGj+/1FqRSqRbpHYWJmPXfztdClr\nvkliZqQnL18d3yfPe4zXGBrbGsmq6T3sKEkS98yNYlKoG09sTunw6xhOZddmU91SPaD5mcTMCuyt\nrRgTaBqs4O/gj6etOyfrckR1RuHFZk60N4dzq6hpMsPt3jceHLwGvIDfkLYBa5U1V0X1j300AAEM\n8zM9NdJ9JMtilvFV+lccLz3e+wXl6YL+pDTD3S6rdnPATFNeGhpbgYodxjkabZue8voW5RWawuOw\n702Y8BcInz2gY2dH/oUWNGh3vjKg/QyFhhrZLMsyWTVZlDSUdCRTJEkiaCjQzcc/Ewu8eU+Axsy/\nSWMnsM7l6bid3Y6/qx3qIRx670shHvbkVTaZXohk7xTO9hYG2jvzdvL56c+5cdSNJPgniAdHzIKc\nvf0SvsrKfXGpu4nkiiQe2fvIkFb01VYqJoW6sT+rQsy02HsIDP5Qy3c01JfQWlPAf5P/y6LvFrE9\ndzu3jbmNbYu38eCkBwlz6Y33/+pIPj8lF3Pf/JHEBbigVqm5Oe5mNlwigAp3/3Y3TW2dbZYONmre\nuX48zW163ttpAYSgtVlcq89VQOMzCofaLLwcG9lX8gsLwxfibd/37Kq5umHUDejRszFtI9MjPDlZ\nUENNoxn3XegCBBjelrOSeh3p+gByNGeQkVkYprx1W6liPWPxtvNmx9neRtVRPk5o2/TKrrG6VvE9\nGgZDzROlJ6hrrWOU6xQatDrC/T1EIqVsEObJzrH+DGhoBwJUpDDKw/wvU3pJHXd+doxoXyfeuX5C\nv07fBuCAYY6mQ21aqCtGVZrCq/NcadXpeeibk8PeenasZODzM4mZFUwKdVfkeC5JEnHWniRbayDm\nMsXHmBPtjU4vs/uMGe1jKhWEXyDauCzEgdZqa9mUuYmLRlyEu23/7QWFNc1UNbZ2m5/pqVVjV+Fj\n78PT+5/uTUoxZGnNDGgAwr0VkM5AVK0qMweFJqREpXXNyLIZhLOdL4KNs/CW6SGtTsv23O28c/wd\nHtz1IEs2L+Hiby5m6Q9LWbFtBWt2r+GL019Q2SyQs+7eAWzQzcE65UuoGmDP/CCroLppSOZndHod\nW3O2cs0P13DZd5cx96u5TPhkAhd8eQH3/X4f3m71gxvQtNTBjqfEIj/OQp+H6EvAJYhJZd8MO+HM\noBAPB7Q6PcX9ZeybqgUy19yZrnaVN5XzaOKjRLlFsXp8FxrViFmCdNTFX6SnUgprGec5i7vG38Uv\nOb+wLXdokxJTwzzILGugteCkaOMZBo8MfEdTo5K447c7efXIq0zxm8J3l3/HnePu7NNOILeigcc3\npTA1zJ1bZ3YPdiLdInl+1vOkVabx2N7Hut1bQzwcuHJcAJ8eyKW0zsxEYtkp4csz3ISzduk8Y7BC\nR0zQXpp1zVwfM3CCV1cFOAYwM2AmmzI3MTXcFVmGfVlmVmk6AprhbTlLKqjhlD6EXepqRnvGEeoS\nOujHUEkqZgfPZm/h3l7V0kgfkehIL1HQdlZ+BvStw4K13l2wG7WkxkkWFbNoXycRbJb/73UvmKs/\nAxogvz6fWm2t2fMzFfUt/PWjQ9hZW7Hupok4miA3hTiH4GztzMmyk+KGteV+eCkCnvaCV0bCu9MJ\n/DiBvS6PEpPxPj/v3DuQP8tsnSw/iYuNC6HOoRZtX1rbTEZpPdMjTLebGTS6oYZsaw11ZuAcxwW7\n4WqvMb/tLHIeNFWKzL8F+vbMtzS1NXFdzHUmX5uUbwAC9N0Pa6+x5/6J93O66jSbMjd1fzJnLzj5\ni8yJmYrwciSvstE0kaYD3zywNjylMlQdFVVoSlLh9BaYsqJbT3GLroWNaRu55NtLuOf3e3jnxDuc\nLDuJm60bcZ5xuNi6UKut5XDxYZ7a/xSzv5jNrVtvJaPxN95ruwhZUsHePtr8zoH0epmC6iYCB3l+\nZnvudi7//nLu23kfTW1NPDT5If459Z/cEncLU3ynsLtgN8fkf1DId708TizWnlehvgQWPG/5oldl\nBRNvZkzrCcbbnxuzt5AOdHM/Vc7cRDH3N2Km2fuXZZlH9z5KvbaeF2a+gLWVdZeDTxP/5h00um11\no5aC6iZi/V24OfZmot2jeenwS4P3GRpRQrgHVuhQlZ0atkrEWQdXrvfz5UhNJs/MeIY35rxBkFNQ\nv9s88l0yKpXEK0vGYmWkS2JWoAgCf8r5if8m/7fbc6tmR9Cq07Nut0KcvkHnCgjQrlNyEK1Atmo/\nCX4JFrfM96crIq+grKmMelUyDtZW5s/RlKaJFtThJJwhWr4PWruRrrHikgDL20JNaU7QHJramjhQ\ndKDb45HeYp71jJKApoNwNvQVmt0FuxnvM57ccjGDF+njBJ4RwsR7EL2fzoXMZKf+/6kOIIAZhLOW\nNh0rPjlCaW0Ln9+eoIjcpEIizsaL5NPfwdZXwcpGOMB7xYiBQnsPqC3EPeU7Hqz/An7/gsbSa7C/\nfC1YD322Mqk8iTjPOIv7TBMzheHltHCFQAFtA3FFaeDtRkrVKcUmYFYqiVmRXuxKL0eWZeXnGzYb\nkETbWaB5Ttc6vY6NaRsZ7z1eUSUvpbAGK5UYDOxPF4ZeyMenPub1Y69zYeiFIvsoy2JYP+x8ixaG\n4d6O6GXIqWgg2ref43uEi4ApYztMvtXs45grgweNIsrZnldB4wBTbgfEIvDbjG9569hblDaVMtZr\nLI9OfZRJvpOwVfcOkGRZJr0qnV9yfuGXnF/YX/QcutBAtmrmsuDYJzDrQXAehtYZEyqvb0Hbph/U\nlrNPUj/hhUMvEOUWxcvnvczc4LlY9fCAWd2wmjt/eZJTbOfS71J4bc6rAyI8Up0HiW/C6CUQOHFA\n598Qtwz19meZ2/ADYJp8ONgK6eJFM60vQnj2LlDbimqUmfoh6wd2F+xmzeQ1RLhFdH/S2R8cfTsN\nLHsotVBQk2L9nbFSWfHwlIe58acbWZe0jrvG32X2uSjRKD9n4mzKsNK3dJK1hlCHiw9z9+93I6k1\nrLONYkK46e/AoZxKdp8p5+GLo/uFa/w17q+crjzNa0dfI9o9mukB0wEI9XTgsrEBfLwvl9tnheHh\nqLD1vDgZrB0tSjwNhn4sdCLTwZFqfcOg+KsY06zAWXjYerAp8zumhN3A3gwzjK1BVGi8h5lwhgho\nSj3bUMsyF9kM3bV+ku8kHDWO7MjbwXlBnYGTg42aAFc7zighspakgEoNHoMfkHZVcUMxZ6rOcN+E\n+zieXIe/iy3OthrwiABdC9TkiXnmP6j+rNAAqeWpaFQaIl2VfZlkWebhb5I5lFPFy1fHMzZIgRFn\nXTFsWMqovKNkSjq0Fz4P95+Gxf+F8x6ASX+F2MshYSXS8q3k3XSIf+svxTb1C1h3gXBJH0I1tjaS\nWZ05IB+exMxyXOw0JhfxHTqzjdgm8WNPLk8261jTwj0or28xPSvSVQ4ewuE6w/wWjaOlR8mvz2fJ\nyCWKXp9UUEOkt6PJQW9Jknhw0oOUN5V3Zg3Lz0BDKYRON/s8AUa0e2nklCvI2kbOE4uz1qGf2VJc\noanMhuSvYeLNYO9OVXMVq39bzWOJjxHgFMD7899n/UXrmRk402gwA+J9Hek+krvG38UPV/zA8zNe\nQKWp5kF1Ks+7OtKQ+L9RpcmvbiecDUJAI8sy7xx/hxcOvcC8kHlsuGQDF4Ze2CuYAfBx8GFl7GM0\n5t5Gm07Pqu2rug1Mm609/wJkuOBRy/fRrrwWe7bopxJT8oNoYxtm+bnYobGS+iedZe+CoCmgNm/m\nsrG1kbVH1xLnEcfS6KXGXxQwQRhYGlFKl4AGYJz3OBaGLeTDlA85W3vWrHNRKrWViku82tt7h7gS\nsbdgL7dvux13W3c+s4liQlmOou1e3ZaOp6M110/tn+5lMDgOcwnjscTHqNd2LjZXzY6guU3Huj1m\nVGmKk4RviOrcLKW2p1fykas7oVgzI8D89mQl0qg0XBpxKbvydxEfoiK7vIEipSbFep1oZRpuZDNw\nsqCKYodcpjc1416ZM2TH0VhpmBkwk9/zfu/VOh7p40h6iYKApjRVeFmprU2/dgDaXSBa2WcGziSt\nuK6TwOrRnlj5g6Ob/wxoEBWaKLcoNFb9U6tALBoe25TC10fzuXtuJIvi/U1tACe/gLemQNZvxMQs\npk2CM1GzwM6tz82CRkSRPfYBluvWoK8rgfdnQ9JX5v5pinWq8hR6WT/AgKaCqWHuRsv9xg+6GRdb\nD0KdQ3rhrE3JgBPdl2VmtihiHuQfhsZKszbbmrMVGysbZgeZHk43AAFi/ZXhF+O94rko9CI+SvmI\n4oZiyG3Htoaa384CEOxhQPIqCPYi5gpX7rP7LDqWOSqqacbe2gpnWxOF4cTXRetRwioSCxO5ctOV\n7CnYwwMTH+DDBR8y1W+qWVVESZK4JPxinMoeJsBqDp85O3JL/mbqGgbgfD1Iym831QwcIJ5YL+t5\n8dCLvH3ibS6PuJwXZ73YvZXJiILd7dE1hrE0+Em0Oi2rfl1FndaCAKK2EI59AmOXgWv/bUFKlFfZ\nxMdt89C0NYhr5zDLSiUR5NYP6ayhHEpTLJqf+Sj1I0obS3lg0gOopD5uvwHjxMKiqbrXUymFNfg6\n23arINw74V40Kg0vHHrB7PNRqin2hbTIGkqsB/759qV9hftY/dtqwlzDWL9gPUF+E0VyR9v/dWx/\nVgWJmRWsOC8ce2vTTSf2GnuemP4EpY2lvH7s9Y7HI7wdWTjGn/WJOf0bExsky1CSfM7azQqqm8is\nTeaMNdzQoO37+zQIuiLiCnSyjgZr0VZ1MFvh/dNAOBvmgKa0tplK3SmaqWahzqYTOT5EmhM8h8rm\nSk6UdZ99i/JxIrOs3jRgpDR1WChwu/N34+/gT5BjKFllDUT1Cmgyh/wchlL/5wMavaznVMUpRe0W\nsizz+KYU1u/L5daZI1h9gYmKTpsWNt8F39wqou8Ve4hJuAeAUxWnTB7vrzNGsKN1NB+OXi+GDr/+\nKxxdr+jvMleGComlbSd5lY3kVzUpbzdra4H0XyD6YmI948yu0AS72+PvYsv+TDMDmrDzAdks/xW9\nrGf72e3MDJjZ50BqV5XUtlBer2W0GcZ3qyesRi/ref3o6+LcHH3BvTfFR4lc7DS42GmUDXyHzhCt\nj8OAby6ubcLXxbb/YKSuGPnYJxyOvYg7Dz/H7dtux9namc8u+YwbY28c0E3b38UDt6ZreT3mVtLV\nKlb9dOOQzh4oUUHV4HjQrEtaxyenPuH6mOt5YtoTqFWmF3YBbnZIEjQ1evLq7FfJqcnh3t/vpVVv\nJsVo72tinmTGPRaefXedrWzkmBxBm88YOLROLByHWSEe9n1XaAzAjhHm9eWXNJTwQfIHzAuZx3if\nfkiSAe3tsIXHej2VWlTbUZ0xyMvei5VjV7Irfxc783aadU5KFa7LIl0OYH+uGUaBZuhA0QHu3HEn\nIc4hvD/vfVxtXdsDBRlK+79XvrotHS8nG5PVma6K94rn2uhr2Zi2sRtl8s45ETRodfx3r4IqTXUu\ntNSeMyDA76dL0bjvxkmyZlFZHjQPzWcDMMJlBOO9x5NY8iMO1ioO5yg02DSggIc5oEkqqEHtchxb\nK3vOd40WrYFDqBkBM1Cr1L1oZ5HejqZJZy31UH1WjB4MobQ6LfuL9jMzcCZnKxvR6vSMbAcX4OAl\nADx/Vmj+2Mqry6Outc4kEECWZZ7YnMpH+3JZPmMED19s3GumQw3lsP4yEYDMvA9u+Rk8Iwl0DMRJ\n46QooInwdmL2SC/ePtpE83Xfimz6pruGpFKTVJ6Ev4M/HnbKB/q7KjFTZLuV+M8AkPkbaOsg5jJG\ne46mtKmUkgblQ8CSJDE1zIP9WRXm0eACJoDGvl+vh546VnqM8qZy5ofOV/T65ALTQIBep+UYwA2j\nbmBz1mZS8hPN9p/pqX4XZF1l7SAGkYchoDHlQVOnrWPzr3/nOh93bq47xvHS46yIX8HGhRuJZsJE\nQQAAIABJREFUdh/4DdHXxZaimmbOn/g3Xmi04kR9HnftuGvIvTz6U0F1I672GhxMAEX6U0p5Cu8c\nf4eLQi/iwUkPKg76bNRW+DnbcraykSl+U3h82uPsL9rPM/ufUX7wuhI48iGMuRbcBm7mByI54mij\nwWrycpG5zE0clP2aoxAPB85WNhq/tmTvFnMT/ubRIN849gZt+jbumWAi8PNv9wHrMUfT3Kojs6yB\nUf69EyXXxVxHqHMoa4+uRS8PsuGmLONQdYozqhEC3zzIOlJyhL/9+jeCnIJ4f357MAOdlY/ik31u\nm5hZzoHsSlaeH262j9Pq8avxtvfmiX1P0KoTQXyUjxNzY3zYcPAs2jYT72OJYZB76MlUxrQ1LR2N\nUypX+07DTjYd+A1UV0ReQW5dLlEh5RzKUVihKWs/p2EmnJ3Mr0TjlML5gbOx9R0D5adFgnmI5Gjt\nyBS/KezI29HtmqGIdFbeHvQN8ZzRkZIjNLU1MTNgZkcbXJQhoJEkMVP7Z0Dzx1ZKuWkggCzLPLPl\nFB8m5vDXGSP4Rx/GmR0qSYF/zxY3pKv+I/rK2/vYJUkixiOGU5XKLj7LZ4ZRXq9lU3IFLPlYGCJ+\ncxukbVH+RypQcnkycZ6WZ5oSMyvwdLQhop3sYVKnNoONC4yY1XHc5ArzsihTwz2oaNAqG7ozSG0N\nwVPFokShtuZsxVplzaxAZS0mSQU1SBJGFx79afno5bhqnHjDps3i+RmDgtztlZsmRs4Tg5vVeQM6\npikV1zTj69y9ElHRVMFX6V9xx/Y7mPX5LB6uOUqdrROPTHmErYu3smrsKuzUgzMw7+9iS2F1E7Ik\nMX/MzTxdXs7B4oOWVSUGSQP1oGlqa2LN7jV42Hnwj6n/MBvoEehuT36lqBJdFnEZy0cv5+szXxs1\nijOqxNdBp4WZ95p76n0qr7KRQDc7pNFXg60rHPlg0PatVCEe9tS3tFFhrPUoe5dIAihoUTYotSKV\nTZmbuD7mepO0LuzcwD0cCroHNIbWlY6+9y7SqDSsHLuSjOoMtuZsVXxeilRfgtRYTrP7KGGwOYjK\nrsnmrh134evgy7r567rj8F2DxT2i2Hg7sizLvLotHR9nG5ZODjb72A4aBx6Z+ggZ1Rl8kNL5HVs2\nJZjyei3bUk0k2AxkqnMwH9LSpuNwxTaQZK4yUDdLh7atan7IfBw0DkjOhzhdUqfMj6bsNDgHgK15\n98KBam/hfiSrJi4Ou1AEnPq2zsBhiDQnaA55dXlkVHcGBYpIZ6UGrPXQVmh2F+zGWmXNJN9JHcbb\nYV4OnS/wiPgzoPmjK6UiBWuVNWGufbf3vPVbBuv2ZPOXaaE8YiqYyfwN/nOhYIrf/COMXtzrJTHu\nMZyuPK1oETUt3IMYP2fW7clC1tjBdRtFBu/Lv0DW7wr+QtOqbK6koL7A4vkZWZZJzKxgWriHsgWV\nrlUgeUcuALU10e7RqCW12W1nCWHtczTm3mRDZ4rMUb1p7LNe1rM9dzszAmbgoHEw+XoQfe7hXo6K\n+rm7ytHakVvcx7HX3o5jzgpb9/pQiLs9+VVNtOkUZGs78M1DV6Vp0+kprWvBz8WWwvpCPk79mJt+\nuok5X87hiX1PkFOTwzKPCawvLGbTzFe5JvqaQQtkDPJzsaOlTU91YyuMXcaixlYecYpjd8FuXjr0\n0qAeS6kKqpoG1G72yuFXyKnN4ekZT+Nio7wiaFBwD3PNlfErCXMJ49kDz3YzIDSqhnI4/F8YfbXI\n7g2S8qoahQeNtb0ApaT9CNrhbQ3sSjrrptoiqDhj1nybLMu8cvgVXG1cuXWMQppgwPheAY1hEdKR\nVe2h+SHziXCN4O0Tb/f2tRqI2gMKp9Dx5FQ0Kh8IN6Gq5ipW/boKtUrN23Pf7t0dIEmiStNHQHMw\nu5JDOVWsmh1hdnXGoPODzmd+yHzeO/Ee+XX5AMyK8iLA1Y4NB01AFkpPgUvwsC/WAQ5lV4LjIcIc\nRxMcOBWsnTorRkMke409C0IXkNu8D1lq5shZBVWa0lPnJODLbEjEClumBUzrrPQN8RyNYb52Z35n\n26eBdNYvGKDslGj7dh9aUt6egj1M9J2IvcaezLJ6Alztuq9RPCJEUnMYAEFDpT8DmooUot2j0aiM\nZ9s+3pfDy1vTuXJcAI8uHNX/gv3kl/Dp1SKzdOuOzl7oHorxiEGr15JdY7pPV5Ikls8YQXpJPbvO\nlAuW+/VfiS/fV7eIgdwByhBIWFqhySyrp6yuRbn/TM4eaKqCGIHjtLGyIco9qrfhqAkFudsT6GZn\nfkBj6H1X0HZ2ouwEpU2litvNQFRoRpvRbtZV19Y34qGTeTP7O4u2NyjEw542vdyBSu5XnlHixjxE\nAY0syxwpTMPK7Vd+rvo7F359IS8eepG61jpuH3M7Xy36ih+v/JH7S4oY5xCIygIzUSUytLsV1jSB\noxfELGJJ+l5uil7GhrQNfHPmmyE5bl+SZbm9QmMZEGB3/m4+P/05N4y6QTHyvKeC3e0prm3u8CzS\nWGn459R/UlBfwHsn3ut/431vQmsTzLzfomMbkyzL5FU2EWQw1Yy7Clob4MwvgEgwnK09y7bcbbx1\n/C3WJa1TdB01V8HuInnRCwzQMT+jHAhwsPggB4sPcnv87ThZK/TiCJgAdYUigGrXmZJ6rFQSoR7G\nEytWKivuiL+D7Jpsfsr5SfH5mVR7y1f46CkAg9J2ptVpufu3uylpKOG12a/1XbXyHS0WokYCtE8O\nnMXZVs3VEwYGKvj75L+jklRifhEBhbhmUhB7Msr79yIqTR0W3xBj+iplNyqbcq4btVgEft4xnRWj\nIdTlEZej1Tdj65LMwWwTczQGwtkwDLt3VVFNA602J4lwnIyNlY2odlrZ9BkYD5a87L2IcotiX2F3\nwE6kj2P/XSSlaeIebIRGOVgqqi8iuyab6f6i8yOjtJ7wnt00HhGAPGxG20Oh/9MBjU6v41TFqT59\nRb4/XsCjm1KYG+PNC4vHoOqP3pX4BnyzXKA8b/5R+An0oRgP8QNXMkcDsCjeH28nG9btbv+i2bnB\nkvUikv7mtgGbISWXJ6OSVIr8VYzJbP+ZU5vFHEv4nI6HRnuOJqU8xez+76lhHuzPrkBviiLSVX7x\nIqOloO3M0G52XqCyAeDSumZKalt6De4qkixjl7ufW22DOVh8qJdRlzkyLAgVgQEkCSIugKydg95n\nfKDoADf+dCPLd1yDjfdWbNXW3DvhXrZcsYVvLv2GlWNXMtJ9JFJllqC7jbt+yJzI/dorIQZ8NBNv\nhuZq7rYJJsEvgaf2P9VtQHioVdXYSlOrzqIKTa22lkcTHyXCNaK707yZCm7/nhhoawATfSdyecTl\nfJTyEWeqzhjfsKEcDr4vKihmmOKaUnm9lqZWXcd5ETIdHH0g+Wu2ZG1hxsYZXPLtJdz7+738++S/\nee3oa1z63aVc8f0VvHP8HWpaagblPILcBTChV4Ume6cwelVItpJlmbeOv4W3vTeLo3pX6/uUfzs0\noMscTXpJHaEe9lir+75tzw2ZS5RbFO+eeJc2fZvy4/Wn4iRwDSE6JBAXO82A285kWeaxxMc4WnqU\nZ2Y8w1jvfmaRfEcLCmMP+lJZXQs/JxexeEIQdtYDWwh623tzY+yN/JTzU0dyb8nEIKxUEhsO9tGG\n26Y9J4t1gxJLfkYl27AoYoF4wBDQDDFAI94rXhiEe500PUdTndtOOBve+Znv0nYiqRuZGzRPPGCl\nFu/PEFdoABL8EjhWeqxbddsk6WwYfHr2FYkgK8E/Ab1eJqusgQgvYwENf+i2s//TAU1ubS6NbY1G\ngQCbTxRy3xcnmBzqzpvXjUdj1cdbJcvw61Ow9REYdRlc/zXY9e9LE+IUgp3aTvEcjbVaxU3TQtl9\nppyc8vaMkWckXPKyyBjuelnRfvpSUnkSYS5highexrQ3o5xAN7vOrGp/0ush7Qcxt9HFLDTOM476\n1npyanPMOnZCmAfVja2cVuLGa5CVWsyomKjQ6GU923K3MS1gGo7WymaDUgoEacaiCk1VNtQVsjj8\nUnzsfXjj2BvmAQ+6KMTDkGFW2KoTMVdAGvKNO5Sbq2Olx7jll1tYvnU5hQ2FXBp4B/VnHuKFae9z\nc9zNBDv36Hk//ilIKojvw5tjENRZoWkPaEJngkcE6iMf8dJ5L+Fr78s9v99jFpxiIOognPU1QyPL\noi3SCLZ27ZG1VDZX8vSMp0UW0kIZfrM9563unXAvjtaOPLX/KeNJhr1rxULz/IcsPrYxGQLwIPf2\n90RlhT7mMl4vTWTN7jVEukbyeMLjbLhkA/uv28+2xdtYM3kNztbOvHPiHa794VpOVw68V95GbYW/\ni13vhED2bvG9UZhN3Ve0j2Olx7h19K3mfU5+Y0Cy6uZHk1FaT6R3/xUelaRi5diV5NbmsiVrkOYs\niwWaWKWSmBrmzt4MM0EsPbQ+dT0/ZP3AqrGrWDBiQf8vNgzc95gP+fJIHq06meummD87Y0w3x96M\nu607rxx+BVmW8XWxZU60N18dyTMOB6jIEHMZ3sNfocksr6RRc4Ropxmd92yfWNH1UFc8pMeWJIlF\nYYtoskonqTiro7JrVB2Es+EN+nbkbUfWWbM4dm7ngz5xArE9xErwT6BV38qRks7frYF0ZrTa11In\nzCyHuC0vsTARLzsvIlwjKKxpoqlVR7h3j0qvoW34z4Dmj6nc2lysJKteQICNB89y18ZjjA92Y91N\nE/vuz5Vl2PE07H4Zxt8Eiz8AjQnTQERrQLR7tOIKDcCV4wOQJPjueEHng/FLYcw1sPN5yNmreF9d\nJcsyyeXJFs/P6PQy+7MqldPN8g9CfUlHu5lBcR7tYABz52jCBzBHU5HRb8teUnkSJY0lzA9R3m5m\nIJyZCwQA4KyoyNiEzuS2MbdxouwEewqU46W7ytfZFmsrFblKvGgAws4TTsVnzDcd7ap6bT2PJz7O\njT/dSFZ1Fmsmr+HHK38k3OYi5DYX/FyMLN71Ojj+mfAI6qeyOVB5OtqgVkkUtZtZIkkw4S+Qtx+X\n6nxen/M6Da0N3P3b3bToWobsPAzKrxKL5W5QgJp8gUH+/Hr4Vwy8HAnP+sMLofDuDPh2BcfTN/Nl\n+pcsi1lmMWbdIEPg0HPh7mbrxn0T7+NY6TG+y+jR/lhbJKozY64Z9Oyr4T0xVGgaWxu5lxLed3bg\nKvexrJu/jquiriLOMw47tR2+Dr4si1nGRxd9xPqL1qPVabn+x+vZnLl5wOcS4mFPTtdFSFWuyDor\nnJ+RZZm3j7+Nr4MvV0Zead7BNXainal9jqalTUdORQNRPqYTK3OC5hDjHsO7J94dOOxC2yCuk75j\nAJge4UlBdRN5lZbN0RwqPsSrR15lbvBcbh9zu+kNvKJFYNclu67Xy3x24CxTw9yVQ2hMyNHakTvi\n7+BwyeGOGYjrJgs4wPZTRhIchvaucxDQvH/0OyQrLctir+p80HAeQwwGAFgUvkj8h+NRTuT19krq\nkIG6NogVXFNq07eR0bAP29Y4PB26fDd846ChTNHc7EA03mc81irrbm1nBtKZ0bazYcBa6/Q69hft\nJ8E/AUmSOmbxelVobJyEXcQf2ItmUAIaSZIWSJJ0WpKkDEmS1gzGPodDs4Nns++6fYS7dg60rtud\nxZpvkpgV6cVHt0zGybYPkk3PYGbhWrN6IGPcYzrMLJXIz8WOhDAPvjtW0JkdkyS45BVwGwFfLzfb\nLBIgvz6f6pZqi+dnThXVUtPUqrzdLOU7sLKGyO5BwgiXEdir7c022PR3tSPEw958g80R7YuSftrO\ntuZsRaPScH7Q+Yp3m1RQQ5inQ9/fm/6Ud0Cw4L2iuSLiCgIcA3jz+JsWZUOtVBKBbnbKSWc2ThCc\nABm/mn0sg/YV7uPKTVfybca33Bx3Mz9e+SPLYpZhY2VDcW0z1moVbvZG3peMX6GuSLSbDaGsVBI+\nzradLWcgzCDVtnBoHZFukTw34zmSK5J5ct+TA8pCK1FBe2AV6NqeZS1NE3TEbY+KrHjoTLjwObjg\nMYi9Epz8aT21mSd2PoCvyoa/RSwZ8Dl4Odpgq1EZ/Z5cFn4Z473Hs/bI2u6tXLt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5acikbGBFpAdMk/KP5VGNC427qzcuxK9hXt47c80wu6YHeRjTlbaWZGKmIePzk583LmV8wPmc8D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\nIglLCY2IiIiIiCSs/w/YVcKt/u+TawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f088868ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first evaluate a covariance function into a matrix\n",
    "period = 0.2\n",
    "cov_cos = pm.gp.cov.Cosine(1, period)\n",
    "K_cos = theano.function([], cov_cos(X))()\n",
    "\n",
    "# now multiply it with a covariance *function* \n",
    "cov = pm.gp.cov.Matern32(1, 0.5) * K_cos\n",
    "    \n",
    "X = np.linspace(0, 2, 200)[:,None]\n",
    "K = cov(X).eval()\n",
    "\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying an arbitary warping function on the inputs\n",
    "\n",
    "If $k(x, x')$ is a valid covariance function, then so is $k(w(x), w(x'))$.\n",
    "\n",
    "The first argument of the warping function must be the input ```X```.  The remaining arguments can be anything else, including random variables.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:58.178027Z",
     "start_time": "2017-09-18T00:02:57.402447Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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k5R8FLgdy3H1cNeunAy8BO8JFL7j7fbWJSSRWnl2+h4zMfH57wyQ6tKnVn4pI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\nEank/wODuIen0kbwQAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08885fcc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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si2Dm9gv8sCeCQW39GNTOD3sr09d5P2ZaM6a2m0qf9X34YPcH/PDED5hp5cfY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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08881421d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def warp_func(x, a, b, c):\n",
    "    return 1.0 + x + (a * tt.tanh(b * (x - c)))\n",
    "\n",
    "a = 1.0\n",
    "b = 5.0\n",
    "c = 1.0\n",
    "\n",
    "cov_m52 = pm.gp.cov.ExpQuad(1, 0.2)\n",
    "cov = pm.gp.cov.WarpedInput(1, warp_func=warp_func, args=(a,b,c), cov_func=cov_m52)\n",
    "\n",
    "X = np.linspace(0, 2, 400)[:,None]\n",
    "wf = theano.function([], warp_func(X.flatten(), a,b,c))()\n",
    "plt.plot(X, wf); plt.xlabel(\"X\"); plt.ylabel(\"warp_func(X)\"); \n",
    "plt.title(\"The warping function used\");\n",
    "\n",
    "K = cov(X).eval()\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing `Periodic` using `WarpedInput`\n",
    "\n",
    "The `WarpedInput` kernel can be used to create the `Periodic` covariance.  This covariance models functions that are periodic, but are not an exact sine wave (like the `Cosine` kernel is).\n",
    "\n",
    "The periodic kernel is given by\n",
    "\n",
    "$$\n",
    "k(x, x') = \\exp\\left( -\\frac{2 \\sin^{2}(\\pi |x - x'|\\frac{1}{T})}{\\ell^2}     \\right)\n",
    "$$\n",
    "\n",
    "Where T is the period, and $\\ell$ is the lengthscale.  It can be derived by warping the input of an `ExpQuad` kernel with the function $\\mathbf{u}(x) = (\\sin(2\\pi x \\frac{1}{T})\\,, \\cos(2 \\pi x \\frac{1}{T}))$.  Here we use the `WarpedInput` kernel to construct it.\n",
    "\n",
    "The input `X`, which is defined at the top of this page, is 2 \"seconds\" long.  We use a period of $0.5$, which means that functions\n",
    "drawn from this GP prior will repeat 4 times over 2 seconds.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:02:59.214842Z",
     "start_time": "2017-09-18T00:02:58.553184Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eU8vDl3O65TT9hn6r2i2YOeb0Wmc4oQGcqo7mxcOVRPm7szYxxN6mWBXh0FgJ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\nyQjNEO931u0ioZlUZ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+EA9Kf/5/b95mC3iVZ+zMpT3yNC/Ig1+SufYu+ie2Bt9ygOGdZq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\n0QB9md28fAWkZOg4T6U6G7XAJsqo2Rv+tvtet9E9MThJbV9pgyYSRi+Ej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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08880742b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mapping(x, T):\n",
    "    c = 2.0 * np.pi * (1.0 / T)\n",
    "    u = tt.concatenate((tt.sin(c*x), tt.cos(c*x)), 1)\n",
    "    return u\n",
    "\n",
    "T = 0.6\n",
    "ls = 0.4\n",
    "# note that the input of the covariance function taking \n",
    "#    the inputs is 2 dimensional \n",
    "cov_exp = pm.gp.cov.ExpQuad(2, ls)  \n",
    "cov = pm.gp.cov.WarpedInput(1, cov_func=cov_exp, \n",
    "                               warp_func=mapping, args=(T, ))\n",
    "\n",
    "K = cov(X).eval()\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Periodic\n",
    "\n",
    "There is no need to construct the periodic covariance this way every time.  A more efficient implementation of this covariance function is built in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:03:00.122133Z",
     "start_time": "2017-09-18T00:02:59.707804Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cXowPCz60UYTCVd7Sg8rWPkGNax4qIViBuo5+NHTSmhqpmu4avJX7Fub7zcfd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\n2gt6I3vDUk5g8KXCc3Oeg8FkwKvnXrV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Y02wOsWmx7HyyM59Gpz5Xgq+QkJFQZAU23sWy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h5eSmZeJv4+/oRVCaNhcEOC/IPw9fElPSedhIwEjiQf4XTmaQCCA4LpXKczg8IG0b9h/8KHrh1a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\nhLCt/wdBwWYSAVsYngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f088861b470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "period = 0.6\n",
    "ls = 0.4\n",
    "cov = pm.gp.cov.Periodic(1, period=period, ls=ls) \n",
    "\n",
    "K = cov(X).eval()\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gibbs\n",
    "\n",
    "The Gibbs covariance function applies a positive definite warping function to the lengthscale.  Similarly to ```WarpedInput```, the lengthscale warping function can be specified with parameters that are either fixed or random variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-09-18T00:03:01.759179Z",
     "start_time": "2017-09-18T00:03:00.967786Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f088861ba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Yenn3knk6QghxDpL4tHO9gtxIym194mNSTaSUpDCpa9smFm52bgQ6B55d4CD9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08823d5940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def tanh_func(x, ls1, ls2, w, x0):\n",
    "    \"\"\"\n",
    "    ls1: left saturation value\n",
    "    ls2: right saturation value\n",
    "    w:   transition width\n",
    "    x0:  transition location.\n",
    "    \"\"\"\n",
    "    return (ls1 + ls2) / 2.0 - (ls1 - ls2) / 2.0 * tt.tanh((x - x0) / w)\n",
    "\n",
    "ls1 = 0.05\n",
    "ls2 = 0.6\n",
    "w = 0.3\n",
    "x0 = 1.0\n",
    "cov = pm.gp.cov.Gibbs(1, tanh_func, args=(ls1, ls2, w, x0))\n",
    "    \n",
    "wf = theano.function([], tanh_func(X, ls1, ls2, w, x0))()\n",
    "plt.plot(X, wf); plt.ylabel(\"tanh_func(X)\"); plt.xlabel(\"X\"); plt.title(\"Lengthscale as a function of X\");\n",
    "\n",
    "K = cov(X).eval()\n",
    "plt.figure(figsize=(14,4))\n",
    "plt.plot(X, pm.MvNormal.dist(mu=np.zeros(K.shape[0]), cov=K).random(size=3).T);\n",
    "plt.xlabel(\"X\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining a custom covariance function\n",
    "\n",
    "Covariance function objects in PyMC3 need to implement the `__init__`, `diag`, and `full` methods, and subclass `gp.cov.Covariance`.  `diag` returns only the diagonal of the covariance matrix, and `full` returns the full covariance matrix.  The `full` method has two inputs `X` and `Xs`.  `full(X)` returns the square covariance matrix, and `full(X, Xs)` returns the cross-covariances between the two sets of inputs.\n",
    "\n",
    "For example, here is the implementation of the `WhiteNoise` covariance function:\n",
    "\n",
    "```python\n",
    "class WhiteNoise(pm.gp.cov.Covariance):\n",
    "    def __init__(self, sigma):\n",
    "        super(WhiteNoise, self).__init__(1, None)\n",
    "        self.sigma = sigma\n",
    "\n",
    "    def diag(self, X):\n",
    "        return tt.alloc(tt.square(self.sigma), X.shape[0])\n",
    "\n",
    "    def full(self, X, Xs=None):\n",
    "        if Xs is None:\n",
    "            return tt.diag(self.diag(X))\n",
    "        else:\n",
    "            return tt.alloc(0.0, X.shape[0], Xs.shape[0])\n",
    "```\n",
    "\n",
    "If we have forgotten an important covariance or mean function, please feel free to submit a pull request!"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
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 },
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