amn41/coupledGPs.ipynb

## coupledGPs.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "To start with, we just show how to sample functions from a GP prior. We define a Kernel function, and sample a set of points from a GP by multiplying a random vector with the Cholesky decomposition of the Gram matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108416a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "cs = sns.color_palette(\"deep\",8)\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(665) \n",
    "\n",
    "def kernel(x1,x2,alpha):\n",
    "\treturn np.exp(-np.square(x1-x2)/alpha**2)\n",
    "\n",
    "\n",
    "num_samples = 100\n",
    "X = np.linspace(0,1,num_samples)\n",
    "\n",
    "# K is going to be the Gram matrix\n",
    "K=np.zeros((num_samples,num_samples))\n",
    "\n",
    "for idx in range(num_samples):\n",
    "\tfor jdx in range(idx+1,num_samples):\n",
    "\t\tK[idx,jdx] = kernel(X[idx],X[jdx],alpha=0.2)\n",
    "\n",
    "# add a little noise for stability\n",
    "epsilon = 3e-3 \n",
    "K = K + K.T + np.eye(num_samples)*(1. + epsilon) \n",
    "\n",
    "L = np.linalg.cholesky(K)\n",
    "\n",
    "# here we sample two functions from the GP prior\n",
    "rand_vec1, rand_vec2 = np.random.randn(num_samples) , np.random.randn(num_samples)\n",
    "y = L.dot(rand_vec1)\n",
    "y2 = L.dot(rand_vec2)\n",
    "\n",
    "#np.outer(m,K)\n",
    "\n",
    "plt.plot(X,y,'*')\n",
    "plt.plot(X,y2,'o')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll create 2 new functions which are a linear combination of these"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6CdSaoDvQcu+z9tVdsfFJV2exgYSBupPWk4FUDRWCIkqgn47N3ZEW2XKK3Q+6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\nCIIgCIIgCIIgCIJg4f8DyOBoLKeDdJsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107224310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mx = 0.45\n",
    "m=np.array([[1-mx,mx],[mx,1-mx]])\n",
    "\n",
    "a=np.vstack((y,y2))\n",
    "q=np.dot(m,a)\n",
    "\n",
    "\n",
    "plt.plot(X,q[0,:],'*')\n",
    "plt.plot(X,q[1,:],'o')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now instead we create a mega gram matrix first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YJozhJlVXE7ir++v37KJm+3uk/dfP7ffU79mF59Jl9mtG6vXjjIkq2jLZmZSG\n4V4cCzoPZEa0D1+eLiWruNGlEWs0zA9KQq3w4NX0d3gtfRsbp95AmDaE6vYaqjvriPfVO3Wpk5CY\nbBQ0F/N50ddsmHIDEbpQmyqoLh0fN2+iPSPs1/Xl2OlLgdzLSFU6Q2UAHXjOsV6us/uGy5M/sBJX\nb84hpftU+/HAe7bSenpwLd7RGK4H5jQq/d1z/XIaXWlMaiEwFLHh3sgEgezikWcaHI4ZftP58dzv\n81Lqa+zO39fvXGpNOrP8ZwxZc1VC4lIjiiIf5HxMWVsF+U2FPJR4LxarhU5zF0tCFti/v45J1gbm\n/h+NUddxYnd1rvd/x0nV0tGBXK0edJ+zYuoDJ+Xe1X7va13sNNziE/ruceJVtGHL7BEbrie6aMtk\nZ1ILgaFWIx5uCmJCdRRWtNLZbR61u6grInSh/GT+kxwoO4qH3IMgTQBnqlNIqU2nuKWUmAFGNQmJ\nyURaXSZlbRVEaEOpbK/m76mvE6wOBMByMpCXdh4Y8n5BYMQ7AFer5eEmbavRaC+nOHCV7WwCdzYp\nO672TQ21+D9wl/0eVzl8XLm3OsOZMLpSmbRCYCSrkfgoX/LLW8gpbSJpmv+EPdvX3Ydbp91sf60Q\n5KTUpnO+LlMSAhKTFlEU+azoKwQE7pt5F23GNl5Oe5uK9ipiDUupH0EeLrVWNSKj7lCr5eEm7YH+\n+o6rbFcT+KBJ2UFYCIY0u11jqMRtjvEDwzGRRVsmO5NSt6Hzch/RaiQ+yhbwleWg6xNFkZySRkzm\n8XsN9RLnG4tSpuB8XeaEtSkhMdFk1GdT2lrOnMBEQjRBxPpM5d/mPk6MZxRuTd7D3j9a186hMoAO\nPOeYKM7S2uLyPlcMTDTnONn7L5v4eITLNSPoWJiUO4Ef/3ztiAJhpoV5olTIyHKwCxxMqeDtL3JY\nPiuEB26cGEOOSq4izjeWtLosajrqCFRP3K7jSsZitSATZAjC2GIScxryOFxxgjURKwYlOpPojyiK\nfFb4FQDro6+zHw/VBvOT+U/w0lcHhrx/LMFdQ62WB57rN6kuWDjqVfbVNClfbCalEID+his3d4U9\nT7hjpSClQs60MC+yihtp6TBiNFr44Ns8AI6cr2T13HCixuGv7Eii/wzS6rJIr8tk9Qjyr1/tVLfX\n8Nvkv6AQFER5RhDlGUGCfxzRnsNP5tXtNXyc/ylpdTYPkvymQn624EcEMDGf5ZVIZoOB4tZSkgIS\nCdUOLpiloixEAAAgAElEQVTizDsGhYCHSoFMLowpuGuoiXms5yQuPpNSHfTOP473+8I6FooYGD/Q\nqxLKLm7kjX3ZdBstLJ8Vggi8/3Uu4nA16UZIov8MBARJJTRC9hR8TrfFiFKuJLMhh31FX/GH5L/x\nacGXWEWry/sOlR3j16f+j7S6LKZ5x7Aq4hpajK28kfEuFqtrFV+7qWPIdq9krKKVTwq+AGB99Bqn\n1wzMwW8E7n58Cfc/tWzUwV1XSxDV1cKYdwJ6vd4X+ACIAoqAOw0GQ5OT64qAFsACmAwGw7Civ3CY\nlNGO8QPx0T5wCP71bR4NLd3MmurH/evjaO0wkZJXx5mcWubHBY7+DQ7AU6Uj2jOC/OYi2k0daJTq\ncbd5uWOxWtiWvQOtUsOt0262q30Km4tJqU0nxjOKf5/3fdpNHeQ3F/Jh7l4+K/qKwpYS7p9xF1qV\npl97hc0l7Mjdg0apZot+M7N74jIauppIrU3ng/S9rA0ZPMnVdtTz3Ok/EakL5/uzHxyUHO1K5+uS\nQ5S0ljE/KIlzn9ayt8gAMKgQ+vrbEvnovRS6jGbC5oTgpRnbOA3lFipx+TGencDPgP0Gg0EPfN3z\n2hkisNJgMMwZiQAYKe2tRl56/gAZBwtxV8lpaOnGw03BfTfEIQgC31k9DblM4F/f5k2YkTjRfwZW\n0UpG/fhzFl0J7C85yKmqs3xTepjPi74BbLrpXfmfAXDLtBsRBAGtSsPsgAR+tuCHzPCbTlaDgedP\n/5nC5hJ7W53mLt7IeA9RFHlw5t0kBSYiCAKCIHBv/B34e/ixK+sL0pzsxA6VH6PbYiS3qYB/pr2D\nyTq4xOCVSkVbFZ8UfIGnSod3apzL+roAfkFaslUCee5yNqyKHfWzhovolbg8GY8Q2Ai81fP/W8BQ\nybhHZRmMGYW7Z3lxEwkWUGOrH+qjs1X5CfJVc938cOqau/jydOloHu+SRP8ZAHaVULupg6KWkqtq\n0umltLWCzwr346XS4ePmzSeFX5BSm05GfTZ5TYUk+MUPylSpUap5fNYD3BxzPU3dzfzp7EscKDtq\nD3Cq72pgXdQq9D7T+t3nofDgoYR7UcqVbMvaQae5y36uy9zNsYrTeKp0zPSLI7Mhhzcz3h9SdXSl\nYLFaeDtzO2bRwt1xt1FV0jLoGsf8OHllzTS3GZmjD8BNNfqigiMpxCKpii4/xiMEggwGQ3XP/9VA\nkIvrROArvV6frNfrHx5Jw/c+tqSf/nI45xLBIpLkrmJZYn+D2IalMWg9lHx+sgSTefz64hBNEP7u\nvqTXZfLM8d/yH4ef4ffJL/J/Z/5Om7F93O1fLpisZt7O3I5FtPDd+Dt5bNb9qOQq3sp4nx25exAQ\n2DR1vdN7ZYKM9TFreDLpITwU7uww7OaPZ/7G6epzRHtGclOM8/S+EbpQbo2/gTZTO18Wf2s/fqrq\nLF2WLq4JXcRDCfcS6z2FlNo0Xs94l5KWsgmzCU1GPi/+htK2ChaHzLcvUIbidHYNAAvHoB7tndyH\ncguFqyffzpXEkDYBvV6/HxjsagD/5fjCYDCIer3e1a9tmcFgqNTr9QHAfr1en20wGA4P17G7H1rE\n9tdtX7Lrbornq09tq4veCkIDcXdTEBjoOej4dQsj2XUwn9L6DhYlhAz32GG5dspidmZ+Roe5g1lB\n8chlMs5VZvDX86/w39c+ha96eH/s0RIQMLm8YralfkxFexVrpy5nZdx8AJ5SPcAfjr5MXWc910Yv\nZnbM0OqGgIC5zIiI4U/HXsVQX4CHwp1/X/4QQVrX43ezz3Xszz/Mt6WHuSXxOvzUPhxNPoFckLFp\n1nX4eHjx334/4NcH/0JKbToptemE6oJYEb2IDdOvQylXTug4XEpKmsr5ouhr/NQ+PLb4btQqD2Ji\n/SnM7W9P03m5s+XBBfj6aTmXW4tOrWT5/MhR1+tOe+ETAEJuvMHul1939Bj+Pd/N5rR0Srb/yx4V\nXPXC74nccideiRcn39Zk+41cToy5qIxer8/Gpuuv0uv1IcC3BoMhbph7fgG0GQyGPw51nauiMtDf\ndbSX3iAXZx4ORVUtPPtmMgvjA3ls0/i/kFbRSouxFS+VJ4IgIIoiH+V9wjelh/Fz9+HJpIcnNI5g\nshVSOVeTxmvp2/Bz9+HphT/GXdFXZPub0sOcrDzDo7Pus1duGw6L1cLB8mNE6sIHqY8GEhCg45Pz\nB3g76wMWBM1hcch8/pryT+YHJfHAzLvt15mtZjLrczhdfY60ukxMVjPXR61m49QbxvamLyG9OxnH\nWAtRFHk583XSqnP4/uwHmenX97NzlR8np6SR3753btTxMwNTQHjop7tMptZdXm6PEo569n8vWr6d\nyfYbuZRc7KIye4D7ev6/Dxi0B9Tr9Wq9Xq/r+V8DrAPGlad5oKtb7xfdlYtbVJCOIF81Kbl1dHaP\nX3cvE2R4u3nZf5SCIHDrtJu5OWYd9V2N/D31tSvWVfFQ2TFeS9+GUq7k/pl39RMAAKsjlvP0wh+N\nWAAAyGVyVkcsH1YA9LIgeA4RujBOV59jZ+5eAFaGL+t3jUKmYFbATL6XcA+/WfY/eKp0HCg7Qpvp\n8lLZWawWfn3yj7yavq2fjSOtLpO06hxm+sX1EwDgurBLcnYtAAviR6cKGk1B9uFURRKTk/EIgeeB\ntXq93gCs7nmNXq8P1ev1n/ZcEwwc1uv1KcBJ4BODwfDleDoMo6tgJAgCi2cEYTRbOZdbO95Hu3zG\n+pjrmB+URG1nPSWtZRfkORcSURRp6HKekVUURfbkf84Hhl1olRp+POexS5ZDSSbI7HmdKtqriNSF\nDxmAplZ6sDZqJd0WI9+UDKuFnFQYmvKp6qghpTaNj/Js6hiz1cxHeZ/0jMNNg+5xVtjFahVJzqlB\n464gLnLkArqXkU7uA1M7SFwejDlOwGAwNADXOTleAdzU838BMPpipcMwmkRQAItnBLH7SCEnMqtZ\n2mMXMJmt7D5SSOIUX6aP4YfhjLmBs0iuTiG1NmNEkbGTiS+Kv2FvwResjljO5mk32VMOmywm3svZ\nyamqs/h7+PHk7IcIUPtd0r7qfab2RHBnsjJ82bBpKa4JXcz+4gMcKDvC6sjlaJWaIa+fLKTUpgOg\nVWo4UHaUQHUAFquZ2s56bohdSbDGlS9Gf3LLmmhuN7JidsiobQEw8mRqUiTw5cmkjBieaIJ81cSE\n6MgsbKSl3YhVFHnt00w+O1HMO18aJsyDJN5Xj1Km5HxtxqjuM18kF9NOcxe78j6jvK2y3/E2Uzv7\niw8ANr3+W5nbMVvNNHY18aez/+BU1VmiPCP4ybwnLrkA6OWeuDu4J/5OFgTPGfZalVx52e0GrKKV\n1Np0tEoNP5n3JDqllh2G3XxS+CVqhQd3zBy8C+glObuGf3vxCG/uy6awssXuFTRc0KQr905pcr+y\nmbS5gyaaRTOCKazM5XR2DfUtXZzKqkEmCFTUtWMobZqQ3YBKriLeV8/5ugyq22sI0th+dKIosr/k\nAJG6cOJ8+3vNGBrzeDHlNe6Jv4OFwXPH3Yeh2JO/j0PlxzlXc57/XPRvuPVE1n5VfJAuSzfro68j\nuyGX5OoUmrqbqe6opdXYxqLgedw1/dZJ5V2jVWlYEjJ/xNdfbruBwuYSWo1tLA1ZSIDaj0dn3cef\nz71Mt8XI7bEb0blp6cJmDHV0lgiL8uZIUwdNbUYOpVZQlVqJJzAfGQUnSkmIcS3Eh6v8JXFlclXs\nBAAWxgciCLDrcAGfnywh2FfNE5tt3kLfniufsOfMCpgJ0C/H0Pm6THbn7+PV9G20GPu8GCxWCx8Y\ndmMRLRyvuLCGtKKWEg6Xn0AuyKnramB3T1Rvi7GVg2VH8Xbz4vqoVTw152ES/OLJayqk3dTB7bEb\nuTf+zkklAMaC427AMc5gMpBZn8Ph8hP9jqXU2vwnkgJt39EYrygenXU/66JWsTxssf26gd5y5cVN\nhDV3c21cIGuDPPFC6PmznXNWt9tZJHDN9vckf/+rhCtOCOzdnspLzx/gpecPsHd7qv24t9aN+Cgf\n2rvMeGpU/PjO2STF+hMWoOFMTi3Nbd0T8vxEv3gEBFJ7VEJW0cqegs8B6DR38qFhj/3aQ+XHqWq3\nxdvlNhXQamwb83OHUmlZrBbez/4IEZHHZt1PkDqQg2XHMDTm82XxtxitJq6PWo1SrkQlV/FI4lZu\nj93ID+c8yqqIa8acCnqycU3oYnzcvPm65BCHyo5f6u4Ats/t3ewP2Z7zkT0lhiiKpNSm4y537xc9\nHe+rZ9PU9ShkfRv4QZlBARUCYmkLTdWDv0+OEcS9DPQA6q38JaWGuDq4ooTAwFXRwNwp1y+MJDxA\ny4/vmE2AtweCILB6ThgWq8ih1IoJ6YNWpWGadwxFLSU0d7dwsuosVe3VLA6eT4xnFGdqUkmvy6LV\n2ManhV/ioXBnXdQqRERSewyBo+V01Tl+duRZvi094vT8wbKjlLVVsDh4PjP8prN1xp0ICLyd+QGH\ny0/g6+7D0tAF9uvlMjmrIq4Zsdvm5YJKruTJpO+hU2r5wPAxxyoufcWoivYqmrqbAXg/eycdpg5K\n28pp6GokwT8OpWxsGlvZKH/Zjh5A7tF9n/tQLqESVwZXlBBwtipyXPkkTvHj2e8t7FdjYPHMYNxU\ncg6mVmCxTox//+yABEREztac59OCL1HIFNw8ZR13x92GTJCxPedjduZ+Qqe5i5ti1nFNqG17f65m\n9CEUOQ15vJP1L9pM7XyYu4eduXv7xSk0dDWyt/BLNAo1m3tcCqM9I1kbtZLG7ibMVjPro9f0W11e\nyQRrgnhqziNolGrey97JsYpTlzTPUG8ywijPCJqNrezM+4TUGttiIClg+Bz/4dGDbVkeGpvrtLNz\nrtyqx1v5S+Ly5YoSAmPBw03B0pnBNLR0cz6vfkLanNWTx2V3/j4au5u4NnwpPu7ehGqDWRdpm3xP\nV58lWBPEirAl+Hn4EKWLwNCUP2RAU25jAdXtNfbXFW1VvJL2NgKwNf47BKsD+ab0MK+lb+NszXn+\nmfYOz574PUaLkVum3dQvdfONMWuJ0IURqglmUfC8CXnflwuh2mB+kPQw7gp33s3+kH8/9D/8Lvmv\nvJ/zEbmNBRc131B6XTYCAo8m3k+ENpQTlckcKj+OUqZght/0Ye8fGDwpKGXc/wNbjMBoAisHVv6S\n/P2vHkafSvAi8MwzzzzT0WEc9X1VZc20NPXPLdS78tFo3VzcBX6e7nx7rpyWdiML4wORj3YvPQC1\n0oPztRk0dTfjoXDnoYR7UfUYVqd4RXG25jzt5g4emHm3PcVEh7mTrAYDQepAInR94fYajRsdHUYy\n6rP5a8o/OVh+jPS6TDrNXezI3U2bqZ37ZmxhYchcFgQlUdRSQmZDDudqzlPVUUOAhz/X9xgTHXX7\nckHGkpAFXBO2GLlsUn4NBtE7FhOBl5snM/3isFgtWEUr5W1VFLeUcqIqmezGXHQqLYEe/hfUHtJh\n6mBH7h6iPSNYHbmcaM9IjlWewmg1kegXz6IQ18LZcSx8g7VkpldjRmT97Yn4+vTVugiN9KY4vx6V\nm3zY30EvjukeLlbqh/Ewkd+Ly53f//65X472nitKB7Bhy2yXuVOGIjxQS1ykN9klTfy/vx9jzbxw\nVs0NB6CmsZPapk6ig23pJ0ZKUkACZW0VrI1c2a8AjVKu5PHZD1LVXt3PXTQpIJFd+Z+RUpvWTz8P\ntqydHxr2IBNkTPeZRk5jHiWtNo+mTVPXM7/HV16tVPNE0kN8VrgfgPlBSYRqgl1OZJfL5H+hCNOG\n8N34OwDbGBc2F/N1ySHS67P4x/k3ifOJ5Ymk79kD5yaarIZcrKKVmX42nXu4LpQbotfwWeF+5gXN\nHuZuG6Io8snZcs6JVjYui2bqlP4uoKMNrJS4+riihADYUkr02gBGUzf18VsS+PxUCQfOVfDx4UJ2\nHS7EUSkQ6q/h1w8tGnF7ayJX4O/hx9zAWYPOBar9ByWZC1D7Ea4NJbshlw5TJ2qlh/3ctyWHqems\n49rwZdyp30SrsY2zNeeRCYLdntCLUqZwmcb5UiCKIl1GCx1dZrQeymHz2IuiSFVDBzklTWSXNFJc\n1crmFVNYGD+y6NixopQp0PtMRe8zlfK2SnYYdpPdmMvJqrNDxiPUdtRT01k7KIfPSOi1B8z071P7\n3Bh9HUkBCYRqnCXvHczRtCpOZ9cwLcyLDcuiR90HCYkrTgiMdeWjU6u4Y+U0bl4SzeHUCk7n1KDz\nUBHo44GhtImiqlYq69sJ8RtZkJFKrhpRNKsjcwITKSuoIK0u064KqO9oZF/x12iVGm6OWWfrq0rL\nteGTe3XX0NLFXz48T3ldOxarTZx6uCm493o9i2e4nuC2f53H/uT+RYBe/SQLPy/3i5YuOEwbwn0z\ntvDLE79nT/4+5gQkDkqWBzaB9XrGu5S0lvGjOY8R6zPFfs4qWnkj4z08FB5smb550G6it0Kdl0pH\nhLZP5SIIAmHa4VOev/OP4xTm1iEC8YKMBzbMGLcaU+Lq5LIXAo5uoQNrqo4FDzcF6xZGsm5hX+6f\no2mVvPZpFudy60YsBMbCnIBE9hZ8wdelh3BTuDHDdzo7Uj/GaDFyR+zGfruDycK3Z8vQeCgHrdTf\n/yqXkpo2ooJ0eGlVuKvkpObV88qeTM7n1XPPOj1q9/4BaNnFjexPLiXIV831CyKIi/KhtqmTF3ak\n8uJHacRGX7yUFT7u3qyNWslnhfv5svhbp2moi1pK7ckCP8zdw08XPGWf7A+WHeNszXkAAjz8WBu1\nst+9Ja1ltJnaWRKywKW6ztV32/G4AGhF+Ozdcy7TqUtIDMVlvXQYLi5gopg9zR+ZIHDWcGGykPYS\npAlklv9Mytsq+Wfa2/z0yC85VpJMlC6CxaNIkXCxyClp5J0vDby8O4MUh2ImKXl1nDHUEhvuxf/c\nP58f3TGbxzYl8MyDC5gS6smJzGp+/vopih0+J6PJwlufZyMI8MiGGaycE0awr5rEKX58Z9U0mtuM\n/PqNUxhNg905zRYrOw7kkZJXN+jceFgbeS3ebl58XXqI+s6GQecPl9sCzkI1wZS1Vdijvus7G9lT\n8DkapRovlY49BZ+T31TU796Muh5VkAs10lDf7eFcoUeDVA5S4rIWAhP5YxgKrYcSfYQXBRUtNLZO\nTGSxKx5J3MpP5z/F2siVeCq1KOVKvjP9lgtmnBwrVlFk+zd5AMjlMv75SQaV9e10myy8+6WB6Qh4\nl7Xy8m8P2iO3g3zUPH3PXDYui6axpZvn3ztLeqHNLXfvsSKqGztZOz+CmJD+FeLWLojgmsQQ8kqb\nePuLnEF9OZ1dw74TJfx153mOplUOOj9WVHIVm6aux2w1s6snzUYvbcZ2ztSkEujhzxNJ38NNrmJP\nwed0mDr5l8G2e7tt2gYemHm3XW3kWII0oz4HmSAblEuql4v13ZbKQUpMSveQkbqIJh8pcnpc5SZn\n9sKICe1TR7eZ9IIGgnw8Bk1SE4kgCHi5eRLnG8vK8GVsmXsT7tbJl+zsWHoV354rZ/GMIK5fFMnJ\nzBoyixqpberEXNSEl0PRupamLrJSKwiN9EarcycuyofwAA2ns2s5kVGN1Sqy70QJvjp3vr85YVC6\nY0EQSJjiR1ZJI+fz6pkT649Xj6ujKIq88Vk2zW1GPNwUnMqqwVOjmrDPKEQTRFaDgawGA2HaEIJ7\nkgIeKDtKVoOBG2LWEO+rByCtPgtDYz65TQVM95nGrdNuxs/DF5kg53xdBvlNReQ2FfBF0TeUtJYR\n6z2Fa8IWO32uy++2Sk6XTEA2oGb2SFyhHenIzqLq9VfpNORgrq+nIzsLpZ8/Sv+AEY7M5EFyEe1j\nLC6ik2t5OUpGExE5XubG2n4cZ3MnVuUwFIIg2OMLJhPdRgs7D+ajVMi47dqpLJkZzLoFEVQ1dPDN\n2XI8nVQtHbiKnTc9kJ9sScJNKWfP0SIsVpGtN0zHXeXcTKVUyNi63haEt+dokf14blkzRVWtJMX6\n8x93z0GnVvLOFzns+DaPMzm1FFS00NI+9glCJsjYMv1WVHIVb2S8h6ExH6to5Uj5CVQyJYuDbWq6\n1RHL8XP3pbi1FKVMwZbpt9p1/euiVhLvq6ewpZhTVWepaKskVBPMdQPsBI64+m6HzwnlbJcRUSHr\nd3yo6nrOGE3FMIkrm8vaMDzWuICx4OflTlSQjuziRjq6TIOMmlcT+04W09Rm5OalUfh5uQNwx6qp\nlNa0kVXcOOLC1foIb56+dx7/2JVOfJQPiQN83AcaRh94chlTQj05a6ilpLqVyCCd3ZNo3YIIIoN0\n/PTuufxh+zn2nSzp19YTmxOYN310pRV7idCF8kjiVl5KfYOXz7/JdZErqe9qZFnoQruxXilXcnvs\nBl5Je5ubp1zfzwVYJsh4OHEr+U2F+Hv44ufuO2yMxoYts3n9L0fp7jABYEREM82PPWdKUSlk3LZ1\nHl/ssKnZxrro6c0XBNCWfBq3jZM/MExi4pmU6SGHKjQ/kNqq1n5xASNdDY3Fq2jPUVv8wCMbZrB4\n5sj8uMfLZCuiXVbbxq/fSsbDTcFzjy7ut3I3W6zUNnWSvD9vkE67d4c2ls+nF52XO1MWhPPqVwbm\n6QO4c/U0fvbycSIDdfz8/vn2lXdLh5GsokYaW7tpbO3mqzOlRARo+cUDrj1xRsKZ6lTeyHgPsSeC\n5OkFPyJc1z+tQpuxvV96jvHw7t4M6jJqcFPKqXCXU9Zjj7p95VTu25Aw7u9Fa/KpfhXDLteCMZPt\nN3IpGUuh+ct6JwBDxwWMxMUO+jwvhpuk5uoD2HW4kLO5dRdNCEwWRFHkQEoF27/OxWS2svWGqez/\nKGPQ+Ib4aSZkh+bMMNra3EXeiRJiQjw5Y6jFaLYiirB2QXi/yd1TrWLRjD6X1eb2bk5l2WwWM2N8\nx/L2AZgXNJt2UwcfGD5mqlfMIAEATJgAEEWR1LJm2lQy/vzUNQiCzVW5prGTdQsmxt4lVQyTgCtg\nJ+AKZyvJ3tXoh2+ecXrPcJOVKIo8/fIJmtq6mRrmRXO7kS6jmfWLolgzL3xc/XXFZFjltHWaeOMz\nW5yExl3BAzfGU362YsjVvuMOTaN1o6bS9h5Guut66fkDTo9rdCqSbtDzwg6bD76XRsUqfy3lxU0u\n2y+qauHZN5OZEe3DT7aMLoDPGQXNRQR4+KNTacfdlquFSnFVK7988zSLZgTx6MaZg+6bDN+LyYI0\nFn2MZSdwWRuGh2IsLnbtrcZ+hWgGIggCSxOCMZqtZBU30tzWTXuXmXf3GziWPnGuiZeCqoYO3v48\nm4yiBnsWTVEUOZZeyX/98wTncuuIi/Tmlw8uZK4+YNjx7d2h+fhp7AIARh7L4cwwqvNyZ/1tiSRO\n8SMmxLZjS1Qq7ALAVfvRwZ7ER/mQWdTYLzZhrEzxip5wAQD9+36mJyZlnv7y89aRuLy47NVBo6W9\n1Yibu4LuLufF3YdTDW1YFs3KOWGo3RUo5DLKa9t4bttZ3vgsG51aNci4eTkgiiJvf55NdkkTB1Iq\niAjUsmpOGKeza8gqbkSllHHnqmmsWxCBTDa6hcZQwmLgrmvgqlijU/VTKf3452vtK76t18exP7mU\n7vQaBuKs/fWLIskqbuTzUyVOV9aXgqHGJkclQ6mQkTBl7OorCYmRcMXuBJytJHvp7jIzlH1wqB2D\nIAh4alR2X/awAC0/vGMWMpnA3z5Oo6CiZVz9vpA0txt5aVc6mUX9o18zixrJLmlCH+7FwvhAymvb\nefuLHLKKG5k91Y9fP7SIGxZFIpMJ9vKdzhiPe66zVbHFYsVDrXTablSwjodunjHi9mfG+BIeoOV0\nVg21TZ1j6uPFwmIRqazvICHG16XLrITERHHFCoGBBTUGIooMKQhGQ2y4N49tmonJbOVvH6dhtkxM\nhbKJ5sMDeZzOruHvH6dT12ybCEVRZOfBfADuuk7PY5sSeP7Rxdy6YgpP3TaLp26fhb+XzQ3SmZ2l\nF1e+6iON5XDWbleHGZlcGNIHfqTtC4LA+sWRWEWRT48XO23rYuOs7wp3BZ7Tbe6l86b3qYJc1c6W\nkBgvV6wQAJvL6FCCQK1VTVjA2ZzYAFbNCaOxtZv0wsF5ZoaioaXrglezKqxs4WhaFRp3BR3dZl7e\nnYHZYuWsoZaiqlYWxAXay276e3tw89JokmL7F1VxJQAEwbWv+kBhLJMLtLca+fDNMxMymY2metaC\nuECCfdUcSq3g6zNl4372eNmwZTYyh9TaJuCMxczJgnrkMoGkaTZh4GyX9Kdn948pR5aUK0hiIFe0\nEOg1Tg410Q83iYxmBXbNLFsK4GOjyF9zLreWn/z9GN+cLR/xPaPFKoq8t98AwBObE1k8I4j8ihZ2\nHszno0MFyASBzSumDNOKa9RaFScOFLgcp15hLJMLWC19ws7REDqcMN67PZVnf7J3yPaHE94KuYwf\n3TELT7WS9/YbOJ092J5wsanXKTEiotaqmHVtNEaTlbrmLuKjfOwBia7cZceSR0jKFSQxkCtaCPQy\n3ETvahIZbZbSqCAdYf4aUvLqaOs09TtnNFkGrfYtVis7vrWpYo6cH593UWe3c0M3wMmMavIrWpg/\nPYC4KB/uvX46gT4efHGqlMr6Dq6ZFUzwCKqmuZqoNVq3IcepVxg7CoBeencFZUWNyOVCv3Z7PyP7\n5yAO3f5IUicE+qj58Z1JuKnk/HNvBlnFznc3F4O2ThP59R10RXhx35NLWbkkmhWzbQuJBXFji252\nRUd2FqW/e45OQw6dhhxKf/ectCOQAK4SIQBDrxZdTSKjdTMVBIGlicGYLSKnsqrtx+uaO/mPl47x\nwo7zWKx99oIj5yupauhAAIqrW6lq6BjTe/vmbBlPvnCIT48XDTrXZTSz40AeSoXNwwdsNRMe35SA\nQi6gkMvYuCxmRM9xJUwdXUB7GUvGS4tFRBDAQ63s9xmN5nMYyc4tKljHD25NRBThzx+m8v5XudRc\nAvK3rxMAAB1qSURBVGNxZlEDIvQLYLtn3XR+fOdsliX2FZYZyl12pEi5giRcMWbXA71efwfwDBAH\nLDAYDGddXHcD8AK2jKWvGgyG3471meNhNBXHhjKADseSmcF8eCCfo2lVrJ4bjrUny2VLh4m0gnp2\nfJvPljWxdJss7D5SiEohY9PyGHZ8m8/JzGo2XTOyCbmXwsoW3v8qF1GEnQcL0HoouTbJlgOm22jh\nzX3ZNLUZ2bA0Gn/vvqI0UcE6fvrduVgsIkc/yxlxCo2xlu/sbXu4cRVFm91gLMVRRhMJHh/ty+O3\nJPDOlznsTy7lq+RSZk/zJyxAg1IuQ6GQERfpw5TQsWcjPZ9fj5tSxvRI555qvV5avULAsf9FDp+D\nswhsR3fZkSLlCpJwxnh2AmnAZuCQqwv0er0ceBG4AZgB3KXX6yf18mM4ATCc3tlb60ZCjB+FlS1U\n1LVz4Fw5WcWNJMT4EuKn5svTpRzPqOLrM2U0tRlZuyCClUlhKBUyTmZWj8pA3NFl5h+707FaRe5Z\np0froeTtL3I4k1NLeW0bv3o7mVNZNcSE6LhxcdSg+6eGepFztHhIVc7AlbWzXdNIjevDeWy5Yjwe\nRkPtSObqA/j940t5ZMMMooJ1pOTV8enxYnYdKeTDA/k8t+0MZTVtQ/ZNFEWs1sGfWUNLF3/deZ6/\n7Dw/SDXYe19GYQMadwVRQbphVY8jtXsMhVtYGP6bNuO/aTOq0MEpLySuTsa8EzAYDNkAer1+qMsW\nAnkGg6Go59rtwCZg0iojhxMAI9lNLEsMJq2gnj1HC0nJs6VaePCmeDq7zfz67WTe3JeNQi6gcVew\nflEUHm4KZk/zJzm7hpLqNruXzkByy5pQKmSEB2iRywTe3JdFbVMXNy2JYvXccGJCPPnde+d4eU8G\nMgGMZivXzQvnjlXTUCqcy/uhJk4fP82IVtajyRXkuJNwTCfRiyvhcaGyxSrkMhbPDGbRjCAq6jto\n7zRhtlipqGvnva9yefXTTP576/xBNQ562bbfwFlDLc88sBAvTZ+A23eyBItVpLPbwr6Txdyxclq/\n+6obO6lv6WZ+XCAymTBsUN1Ya2c7IuUKknDGhbYJhAGOVcPLeo5ddgzlBjmQObH+9gInRpOV767V\n4611I8RPw8MbZmI2W+nstnDz0mjU7jY5vKinRu9JB1uCI+kF9Ty37SzPvpnME386xC9eP01yTi36\ncC9uWW5TIcWEePLErQmIoohcLuOJzYncvVbvUgAMx2hW1iNdqTruJG67b96I3TvX35aIzst9yPad\n7Rh6XVKH8+4SBIEwfw36CG9mRPty3XxbNbOS6jY+cxFX0NDSxaGUCprbjOz4Ns9+vLndyKHU/9/e\n2YdHUZ0L/LdJICQhfCVBAQFFOYT6iV+t0ha0+FUrlNoWqR+19Fq11adPn7a26tPW6328tHptvWrr\n7dVq+1gptR8qVK1S671XhaJURLTg0UoEQgQSNYSEkBBy/9js7mQyMzszOzu7s/P+/kp2z86cfc/s\n+57zvue87w7qRlUytraSZ9Ztp33v4Ip0rw9sIz7a4VCjIISB40pAKbUKsEqXeYPWeqWL6/ve/N7Q\nUJiC2UdMr2eLqXBM7egRXLTkFCYcNsb1deaceBh/XtPEacdO4FNzjkrvtz+roZaDiQSvvtXK589u\nZPiw5D7xM8dU88CTm1j3xm6u/uwJg9IzjB5TzW/+upayBJx58hTebm6nqaWdMSMruf5LHx7k6z+j\noZbph9dRUzWMsbUjBvXpwf9aw5aBOrxHHFXPpVed5vh9773jOcsRLCsrGzI+DQ21fOhY7y6GL/zL\nh1l+f7I270VLTrEdd+P1rb4HwJJrP8pPbl5FR3s3AOUVZfQZKnBtb3qfX9/zN9dj+bVFs9i89X1W\nrm7ijFOnMm3S6EHvr1jzDn0H+6mqrGD1a+8yf85RHD2tjsfXvk7vgYN8bt4MysoS/Oz3G3jmlR1c\nufC49GffGjhZ/rGTptAwrtpxHJxkIiQRWfjH0Qhorc/K8frNgDHv7WSSq4GsFCor4LkXHjPE9XDJ\n1R/x3Kd5sybS39fH+acdTmvrYL/yiUfWceKRdbR/MHg30Kzp9byw8V3WvLIdNTmppBoaannw8ddp\nae3krJMns/gTSbfC/p4++umnv/fAkH5VJuBAdy+7uzO+aLPPecubrdx+01Ocd+Gx7Hp3j+X3PWzq\n0EBuTe1wzll4dGDjU1FZnr4fOMu4oaGW++963vZ7NBxayzkLj06vVFLfyUhHezfL7lvr2rVy2Tkz\n+PHDG7jtwXV874snp1dVXd29PLmmibG1lVw5/2h++NDL3PXwer69eBaPv7CF0TXDmTVtLIlEgvrR\nI/jzmibmHDuButEj2NPZw4Y3dzN+bBVlfX3s3t3h+bmTzJkZRBa5EZQ7yC4BwzpgulLqcKXUcGAR\nsCKge+aNIIJw40aNYNGZ0xlZ5b4CWSoH/vOvtqQDxO+2dfL4mncYPXJ42u0DUDm83FNeGSfXjt33\n9XIaNyzcZi8NKmZwzLQ6Pn78RLbv3ssDT27i4MC4PLu+mf09fcw7+TDU5DF8/PgJNO/u5NZl6+nu\n6eOcU6cwrKKcivIyFnz0CA709bP8mTd54IlNfOtnq+nu6RuSITSI584KOSUsOJHLFtGFwJ1APfC4\nUmq91vo8pdRE4F6t9fla6wNKqWuAp0huEf2F1rron8YggnB+mDl1LGNrK3l+Ywtbd3WwYPYRrNm0\ni94DB1l05lFUVeYnmZjT981lS2ihsdqS6kfBLp43nebWvfzt9Z2Mqh7OhXOO5C/rtjMzUUbTs1u4\n59ktHDp5NDUjKtjR2knNiArmzsq4xtpe28nJlIFuZSfQWFFGFWW0rt3Oyp2d6a2g+XruUieE5VyA\nYEXJFpWJKjvf6+KR597mpU270u74mVPH8q2LTsipNKJTkZ1Czuy9YOUOAufvEdSuor37eln667/T\n0tZF45QxHNzazmjTz6eisoIN+3s452NHcMHAATw3Z078jIMbF0jX5k20rXiUffoNAKrUDOrmf7rk\njIG4gzL4KSojRiAH/NQpdktzayd/Wt3E1p17ueYzxzChLveyhW4VYj6/Vy6kfuxeFLvfGtRWvLen\nm1se/Dvvd+znZBIkLH4+I6qH8cVrTufxh1/1dODQq4Fyq/j2Nzfzzg9uBGDqzbdQOTGSm/McESOQ\nQYxAiDjN8IJUnEE+4G4UYjGvGFKyCFKxp3Br+Jp37+WO321g2p6hB8AgKSvz+Qo3BGkEUv7/6saZ\ntD72SPr1RCJB3fxPe+pXFBAjkEGMQIjYFVZJEZTizPaABz1rdyoYU4g4iZFcf+x2svJq+A729/On\n5RsGlbU0fsauhrUdQbuDtt26FIDJ111Px7oX0wfDjH+XEmIEMvgxAlK2KE/YlVAMEqtUAz+/7X/T\n2TqdjEKxunzyhVNeIS8lMAHKEgnmLz7BV7whtdsqH6efzTGAbbcuHTTzL0UDIOSOGAEPGBWJU51i\np88FqXCtlJc5X39qZu808zUqxKB21BQbdore66zdiN3OKSsZJhIwoiqTHTUfO66qG2dSXjsqHQMY\nf8llJRkDEIJF3EEusXIZJBLJrJdWpBTn3/7nbUdXQzYDkVrqWrXL5pKy65Od4kvNSvOVpydXcln2\n+5WVFxeNcYzKyxP0DRjkfMjQThZxiAGYEXdQBj/uoNjUE8gVq5lkqk5xTe1wqqozh8KMh6qcXA1u\ni9bYtRs/wVu8wW2O/3wdWiokVnmF7PBTAtM8Rna1EfJF6kCYZAoVvCJGIEeqRyYV/vmfP86z4nSb\noM2u3a6WjkHVuMrK3U0CsqVm9lKpKyq4SWOdSOBYAtMJu0mC39oIbjCeBE6VjZRMoYJXxAi4xK/i\nDKqQvR3GGednLj3RUdG5ratcqhhrHZupqR3OhV88ybYEpp96vkFjTv/QtuJRdi1fJmUjhZwQI+AS\nv4rT6XNuDUQ2V4Zxxml05di5qKA0XT7ZSBnqK789J3AjmG9jD5nZftfmTWy88fvs02/Qs30bB/dn\n0lRL2UjBKxIY9oDfQ0pOn8sWhLU6JWuF1WfzcaiqkIRxcC6Xw3L5CqhbpX+YdM483rrrpwCMnnsm\n5bXJvsUlGGxEAsMZ5LBYBMmmqM2nZPd19Q5xWRTLid58E9aP3a8yz6fRNad/OPiPDXR2JlcAPS07\nmHjV14DSPRDmhBiBDGIEShCrB7xYt3Dmm7B+7MW4gjJv/axvPJJ+lXQ1xVHxGxEjkEFODMeEKKd3\njgKFSiXuROWkSYPSP9TPPj2t+OJsAITcESMQMkGcHi5GJSXkh9ROH9n6KeQLMQIh4pSuoRhcDsJQ\nCp1jSQrCCPlGYgIh4iVDZ1r5JJK1fks9wZsbwvb9Wu0UMh4my6dRyFYQRvzgGUQWGSRtRIkwSPn0\nuz+1KgSLmwR9+RqX6saZjL/4svT/sv9fyBdiBELE7YEit+kkhMKTz3HpWPci4y5YwLgLFrB33Ut5\nuYcgiBEIkbima4gqXpLO5QNJBieEgRiBkHFK17By+QbHuIFsBw0Xs9G2yzmU67iYcwKlkB1BQhgU\n9e4gY63UKOG0o8Rue6dTzeI4HQgrNsxnMp78w8bAD+rJDiChkBS1EYjij8PvNlA7A5BIyIGwQmI2\n2kEe1LMrBxml512IPkXpDmrf+Fpk0+MGHdQdOWqExAyKiCBrLcgOIKEYKEojMPrYY2L347DbOXTR\nklMK0JvCYecfL1VkB5BQaIrSCEB0fxx+88rb7RyacNiYwPtYzKRy5scF8w6guBlBofAUrRGI6va4\nXLaBRrHQS1BKq2vzpsi6AO1wIxvzDqC4GUGh8BRtYNj844jSTiG/wcMoJoZzG7zPNn7VjTMprx2V\nzpk//pLLqJw4KcCeho+XjQ0SJBYKhW8joJT6HHAT0AicorV+2aZdE7AH6AN6tda+NjxHaadQFJW5\nV7wqLTfjl3IBAuxd9xKV86NpBPwo9FI0gkI0yGUlsBFYCPw8S7t+YK7W+j23F27f+BocOhWQGVKx\n4lZpWY1fzQknMmLKlCFjaM6Zn/p86n5+CXsV6Vehl4oRFKKF75iA1nqz1lq7bO4ps93W5Q+n/5Zt\ndMWLm+C91fh1vvKypd/b6oRsED7yQvjZ/WxsiGocTIg25bleoK6u7nLg6ba2thab978OLKqrq7ui\nrq6uv62tzdJtZOTisfU3dW3exLC6eobVN/DBs89QNaORqhmN9LbsoHpGY67djgw1NZV0ddkXmC8k\nfXs7GHvmPKobZ9LXscd2tpsav4q6et57YiU927dxoK0N4xib6dq8iXfvv499+o102+oJh9A30v1u\nKatr2N0vaNzKxoixTbb2xfxchI3IIsNtty39V6+fcZyhK6VWAYdavHWD1nrlQJtngW86xAQmaK1b\nlFINwCrgWq31c073fX7+Z/pn3XUH1VMmA9D6wmrqZ58+6O/2ja8ByTMFQnGSGqPePXvS49f82Aqa\n7v8VAMYxtqJr61bWX/uNdNve9nbA25ibr+F0P0GIOolEIvxC89mMgKntD4C9Wuvbndq9s2x5f1dX\nD3XzP23bZtutSwGYfN313jocMaJUMMPse7caI3PBdKcxNrftfftNensOWI65nd/fy/2iRJSei3wj\nsshQyELzljdWSlUD5VrrDqVUDXA2kHW5MmXxIt5+8hnL97wGiqO0tTTqGP3udmNkFfy1I9W2a/Mm\ndj30ID0tO4Zcz3zv6saZg8bcy/0EIY74XgkopRYCdwL1QDuwXmt9nlJqInCv1vp8pdQ04I8DH6kA\nHtJaL8127WzlJfc3N6d3Xky9+RZH/2nUVwyFmuV4MZ5WpRBHnT6bnb+8H8g+Rm7uZTfmVvfu6+qi\nvLo6smPuBpn9ZhBZZPCzEohkjeFsS/yuzZvo3rqVzldetq3RGhUK9YB7NZ5mJd3xUmbWnc0N4+Ze\nrY89Qk1NJZ2d+4dcz3jvysOPYH/TFiC6Y+4GUXwZRBYZCukOCpVsS/yUa2D8xZfJ4RuP+D2XMWSP\nuws3jJd7VU6axJTzPsHu3R1Drme8d19HR9oIyJgLQnYiuRKww6xUKsbVUTWjkWH19ZENChZilmOe\n1fft2QNkP+1rVPpuK2F5ce3ZycJ4vx333M3wgWuEMeaFijnJ7DeDyCJDbFYCdphPao6Zdxbjzj4X\nkKCgF8yzerOis1J8fkshBnFKdtC9Tzk11ECw33QmsmFBKBZKygjAYKXS392dfl1qtDpjtaPGbldO\nkHmcgt69E1RdXqM8rBR2rulMopQLSyhtijaVtF/k6L0/jKkVUsqzunEmE676WrrNqNkfTSu+oNI9\nh11M3W3qa6M8rNJO+E1nUoops4VoU1IxgVIkaH+nlWvHvMXSOKM178QaedIprn34QROELLLtRDLL\no6yqioP79gHZZeM2/uAlDmKH+MEziCwyxD4mIGTH7IbIlvHS7K4plkyXXn3qbt03Znkc8uUraLn7\nTiC7bNxSLDIUBIi5EYhTcM5JCToppaHumheL4gSuV5+6l/TORnl88PRTQ2STem6sXFlunik5xSwU\nE7E2AnEKzjkpQS9KKWwfvplcArJmY9enrLe+GuWx67fLqF+wMP15cH5u3DxThZahIBgpiZhArq6B\nYj5ZGqS/0+zDrlIzgOgYwZQs/PrUzWcZPvhrMj+V21PRTs9Ntmcq6FWn+MEziCwyxDYmkE/XQClh\nnvFHdSXk16dudNl88NdnPK8mnJ6bbM9UVGUtlD6RXgnkMqOPSorhfMxyorQSMpKShd/TyUb8riac\nnhur9/Ila5n9ZhBZZIjdSiCXGX2cg3NRXwkF4VO3Wk3kGtS1ei/qshZKn0ivBCA6M3q/5DrLKaVi\nK0HO+KxWE/lKO54PWcvsN4PIIkPsVgIQ7xl9CqcZrJ0vOu5yM64gykfWpk/xgvcUENmIu6yF4iby\nK4FSx80sx2oGG1W/vxP5nPEFcYo3TGT2m0FkkcHPSqDkcgfFCac8NH5z28SVVIxg3AUL2LvupUJ3\nRxBCI/LuoDAo1pPF2YKOkp7APeKyEeJKrIyA17q5qbbFvMfbSdGLYnOPnOIV4kqsjIAXZd624tF0\nwfJ8BQxT5LLScFL0otgEQchGLIyAl3wz5raVUw9Pv5evPd65rDRE0QuCkAuxCAx7CZKa2444Ylre\nAoZSYEQQhEITi5UAeAuSGtv2tOzgkEsuS78eJHKaVBCEQhMbI+AlSGrXNh/uFr87eIp1x5IgCNEi\nNkbAi+88TD+73x08TnEEMRCCILglNkYgG4VSnF4MTtfmTXRv3UrnKy87BrmLeUurIAjFRSwCw25o\nW/FoWnkWK20rHqXzlZdtg9wSaBYEwSuxXwnkUq4wLMx9bP7PH1N72myG1dcPiiNIoFkQBK/4NgJK\nqduATwE9wD+BL2mt2y3anQvcAZQD92mtf+T3nvnAq+I0u42CdiNZXc/cxzHzzmLc2ecCQ+MIkipC\nEAQv5LISeBr4jtb6oFLqh8D1wHeNDZRS5cDdwDygGXhJKbVCa11UPgovitPsbw/a/253PWMf+7u7\n06+b4wiSKkIQBC/4NgJa61WGf9cCF1o0OxV4S2vdBKCUWg4sAIrKCLhRnGaXTNNN3wOgZ/s2wJsb\nyWq2b+eWouFU130EOUEsCII3ggoMLwGesHh9ErDN8P/2gdeKCjeK03ySeMJXrmLCFVel//eSqtkq\nCJ3tVLMod0EQ8oHjSkAptQo41OKtG7TWKwfa3Aj0aK2XWbTrz72LxYPZbdTf3+/J/54tCG2+fp/a\nQ/u71XDo1Hx9JUEQYo6jEdBan+X0vlLqcuCTwCdsmjQDkw3/Tya5GshKQ0Otm2ahkph5FPWzTweg\n9YXVAIP+r3foc/vG1xg+ppqGa69i/bXfAKDx2qupnpIRj/n6LU/8iT3AsbfcnI+vE0mK8bkoFCKL\nDCIL//guLzmw6+d2YI7WutWmTQXwBkkjsQN4EVicLTAc1fKSRl+/2e+fKgFZNaMx3d6u6HgploYM\nAikjmEFkkUFkkSHsQvN3AcOBVUopgDVa668qpSYC92qtz9daH1BKXQM8RXKL6C+KbWdQkBh39hh9\n/kaF3tfRwfiLL6W6caZtgFf2+wuCEBZSaD4AzDP3sqoqDu7bByRn8aNOn83OX94PuC9i3vrYIwDU\n1FTS1dVjuWKIGzLjyyCyyCCyyCCF5guEeWfPIV++Iv33+Esuo7etzXNNgspJk6hfsJApixcxfOLE\nwPssCIIAkjYiMIw7ez54+qnBu4Z8HOCSLaGCIISBGIGAMCr6Xb9dRv2ChUBS6YtCFwShWBF3UEAY\nlfv4RV+wfF0QBKHYECMgCIIQY8QICIIgxBgxAoIgCDFGjIAgCEKMESMgCIIQY8QICIIgxBgxAoIg\nCDFGjIAgCEKMESMgCIIQY8QICIIgxBgxAoIgCDFGjIAgCEKMESMgCIIQY8QICIIgxBgxAoIgCDFG\njIAgCEKMESMgCIIQY8QICIIgxBgxAoIgCDFGjIAgCEKMESMgCIIQY8QICIIgxBgxAoIgCDFGjIAg\nCEKMqfD7QaXUbcCngB7gn8CXtNbtFu2agD1AH9CrtT7V7z0FQRCEYMllJfA0cLTW+nhAA9fbtOsH\n5mqtZ4kBEARBKC58rwS01qsM/64FLnRonvB7H0EQBCF/BBUTWAI8YfNeP/AXpdQ6pdQVAd1PEARB\nCADHlYBSahVwqMVbN2itVw60uRHo0Vovs7nMbK11i1KqAVillNqstX4up14LgiAIhUcpdblS6gWl\n1AiX7X+glPpmvvslCIIguMO3O0gpdS7wbWCB1rrbpk21Uqp24O8a4Gxgo997CoIgCMHiO2CrlHoT\nGA68N/DSGq31V5VSE4F7tdbnK6WmAX8ceL8CeEhrvTSnHguCIAiCIAiCIAiCIAiCIAiCIAiCIAie\nKNhJ3oHdRXcA5cB9WusfWbS5EzgP6AIu11qvD7eX4ZBNFkqpi4HrSI5XB3C11vrV0DsaAm6ei4F2\npwBrgM9rrf9o1SbquPyNzAV+AgwDWrXWc8PsY1i4+I3UA78mea6pAvgPrfUvw+5nvlFK3Q+cD+zS\nWh9r08aT3ixIFlGlVDlwN3Au8CFgsVJqpqnNJ4GjtNbTga8A94Te0RBwIwvgbeDjWuvjgH8D/jvc\nXoaDS1mk2v0I+DMlmpLE5W9kDPBT4AKt9THAZ0PvaAi4fC6uAdZrrU8A5gK3K6V8p8UpYh4gKQdL\n/OjNQqWSPhV4S2vdpLXuBZYDC0xt5gO/AtBarwXGKKUOCbeboZBVFlrrNYYMrWuBw0LuY1i4eS4A\nrgV+D+wOs3Mh40YWXwD+oLXeDqC1bg25j2HhRhYtwKiBv0cBbVrrAyH2MRQGsi2879DEs94slBGY\nBGwz/L994LVsbUpR+bmRhZEvY5+nKepklYVSahJJBZCa4fSH07XQcfNcTAfGKaWeHcjNdWlovQsX\nN7K4FzhaKbUD2AB8PaS+FRue9WahjIDbH655qV+KP3jX30kpdQbJZH3fyV93CoobWdwBfFdr3U/y\n+ShJdxDuZDEMOBH4JHAO8D2l1PS89qowuJHFDcArWuuJwAnAT1PZCmKIJ71ZKCPQDEw2/D+ZpMVy\nanPYwGulhhtZoJQ6juRsZ77W2mk5GGXcyOIkYLlSagvJ9OU/U0rND6l/YeJGFtuAp7XW+7TWbcD/\nAceH1L8wcSOL04HfAWit/wlsAWaE0rviwrPeLFTgZB0wXSl1OLADWAQsNrVZQTLYs1wp9RHgA631\nzlB7GQ5ZZaGUmkIy/cYlWuu3Qu9heGSVhdZ6WupvpdQDwEqt9YowOxkSbn4jjwF3DwROK4EPAz8O\ns5Mh4UYWm4F5wAsDPvAZJDdUxA3PerMgK4GBgM01wFPAP4Dfaq03KaWuVEpdOdDmCeBtpdRbwM+B\nrxair/nGjSyA7wNjgXuUUuuVUi8WqLt5xaUsYoHL38hmkjukXiW5YeBerfU/CtXnfOHyufh34GSl\n1AbgL8B1Wuv3rK8YXZRSvwFWAzOUUtuUUkviqDcFQRAEQRAEQRAEQRAEQRAEQRAEQRAEQRAEQRAE\nQRAEQRAEQRAEQRAEE/8PI2GzUJj4gekAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107205b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "full_K=np.kron(m,K) + epsilon * np.eye(2*num_samples)\n",
    "\n",
    "#print(K)                                                                                                                                                                                                   \n",
    "L = np.linalg.cholesky(full_K)\n",
    "\n",
    "_y = L.dot(np.hstack((rand_vec1,rand_vec2)))\n",
    "\n",
    "func_1=_y[0:100]\n",
    "func_2=_y[100:]\n",
    "\n",
    "plt.plot(X,q[0,:])\n",
    "plt.plot(X,q[1,:])\n",
    "\n",
    "plt.plot(X,func_1,'*')\n",
    "plt.plot(X,func_2,'o')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Now we can try to fit one of the combined functions, with a gap in the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-17.7542697438\n"
     ]
    }
   ],
   "source": [
    "import george\n",
    "from george import kernels\n",
    "import scipy.optimize as scpo\n",
    "\n",
    "kernel = kernels.ExpSquaredKernel(0.01)+ kernels.WhiteKernel(1e-3)\n",
    "gp=george.GP(kernel)\n",
    "\n",
    "ins_uncoup=X[:50]\n",
    "outs_uncoup=func_2[:50]\n",
    "\n",
    "\n",
    "def nll(p):\n",
    "    gp.kernel[:]=p\n",
    "    ll=gp.lnlikelihood(outs_uncoup)\n",
    "\n",
    "    return -ll if np.isfinite(ll) else 1e10\n",
    "\n",
    "def grad_nll(p):\n",
    "    gp.kernel[:]=p\n",
    "    return -gp.grad_lnlikelihood(outs_uncoup)\n",
    "\n",
    "gp.compute(ins_uncoup)\n",
    "\n",
    "print gp.lnlikelihood(outs_uncoup)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.36073349 -5.25152202]\n",
      "45.0561874795\n",
      "[ 0.03470979  0.00523954]\n"
     ]
    }
   ],
   "source": [
    "p0=gp.kernel.vector\n",
    "print(p0)\n",
    "results=scpo.minimize(nll,p0,jac=grad_nll)\n",
    "\n",
    "\n",
    "gp.kernel[:]=results.x\n",
    "\n",
    "print gp.lnlikelihood(outs_uncoup)\n",
    "\n",
    "print np.exp(gp.kernel[:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PtPGm5zU6ndeQJIljt5Vhsxj48NogI04fer2BEbfKhNOZ6su+ZSjjrWKexjot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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc7b6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = np.linspace(0, 1, 500)\n",
    "\n",
    "mu_uncoup, cov = gp.predict(outs_uncoup, x_test)\n",
    "std_uncoup = np.sqrt(np.diag(np.clip(cov,0.,10.)))\n",
    "\n",
    "plt.plot(x_test,mu_uncoup)\n",
    "plt.fill_between(x_test,mu_uncoup-std_uncoup,mu_uncoup+std_uncoup,alpha=0.3)\n",
    "plt.plot(ins_uncoup,outs_uncoup,'*')\n",
    "plt.plot(X[50:],func_2[50:],'o')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now let's see if we can do better on the portion with no training data, by using the training points from the correlated task. We expand the input dimension from 1 to 2 to include a 1-hot encoding of which task the data came from.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.30258509 -6.90775528  0.         -6.90775528]\n"
     ]
    },
    {
     "data": {
      "image/png": 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qCTwGvLxA51xSiYHx9Fr6aB/scHVW5kzXdc43Xpo0iVthu/0pMSdiIwDv1+cC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b029d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def ourkernel(x1,x2,p):\n",
    "    return p[0] * np.abs(x1[1]-x2[1]) * np.exp(-(x1[0]-x2[0])**2/p[1]) \\\n",
    "         + p[2] * (1. - np.abs(x1[1]-x2[1])) * np.exp(-(x1[0]-x2[0])**2/p[1]) \n",
    "        \n",
    "    \n",
    "# p0 = [amplitude_cross, lengthscale, amplitude_self]     \n",
    "p1 = np.array([0.1,0.001,1.])\n",
    "kernel2=kernels.PythonKernel(ourkernel,pars=p1,ndim=2)\n",
    "\n",
    "comb_kernel = kernel2 + kernels.WhiteKernel(1e-3,ndim=2)\n",
    "gp2=george.GP(comb_kernel)\n",
    "print(gp2.kernel.vector)\n",
    "\n",
    "data_1=np.vstack((X,np.ones_like(X)))\n",
    "data_2=np.vstack((X[:50],np.zeros_like(X[:50])))\n",
    "\n",
    "# only provide half the data for func 2\n",
    "ins_coup=np.hstack((data_1,data_2)).transpose()\n",
    "outs_coup=np.hstack((func_1,func_2[:50]))\n",
    "\n",
    "# visualise the gram matrix\n",
    "gram = kernel2.value(ins_coup)\n",
    "#plt.matshow(gram[:10,:10])\n",
    "#plt.matshow(gram)\n",
    "\n",
    "gp2.compute(ins_coup)\n",
    "\n",
    "plt.plot(ins_coup[:100,0],outs_coup[:100])\n",
    "plt.plot(ins_coup[100:,0],outs_coup[100:])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try to fit a GP without optimising the hypers at all. I.E. just taking a guess at the coupling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000,)\n",
      "[-0.16390098 -0.10251806 -0.1287617  -0.12250335 -0.11770595  0.05333684\n",
      " -0.0933465  -0.05316287 -0.12554781]\n",
      "[-0.9425591  -1.03378595 -0.86454048 -0.96734902 -1.02975278 -1.12974338\n",
      " -1.16455428 -1.11799278 -1.1919264 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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9R/EzHtvPWMhgb0ucrzzVj9vum9dO2BH6zv5k0fOxVPqiA6iKSoW3\ncN0Y3/ltB90IAvVFtJwZmv78TFM7iitP/vexCO5Hv4s6Pkrqlk+SueZAfsaxgVmyTcCyrNMApmme\nr9l1QJNlWW2TbR8BPgOcWmq/K4Xb7Wb31mpOtQ7i8haR/vhnUWIR3OVhzudCqhnBdVWuMre/f9aP\n3yaEISYD6xQlq+v/XIhw4B5sfUbtEfbeQ3H0IdRJvbyj+HBVfZkry8swjNkJB/7oHGO9ELk3EYau\ncf1lOwhHIgwMjTKRvp1i+5doZCOQw47gpHYNZ4Mn6LkzxJ2dVew41AwLOK7ajuD46WZ279iCpq18\n4XEhBH2xASq85ehq4ZrZ2kfj9CD4lwd3EemPAFm1XyRtYLjyoBlOxvH87HuoIwOkr72NzE0fX/0x\nSC65TaAWmJ2ys2vys4IgGAyyra6YZDICqkrq01/ifAJAnUxQt17iB8LhyMIulpk0+hxDLYCqpwkm\nX5h+L4QgHh0j7r4dND+aEWST+WVqa6rnCIAss9Vymne+/ny2kA0GAmzbUs/+PVspa/gcaH5SwkXY\ncbjO+Q1f9gzy1eJSNt38VeLf+PfYY/MDnzJCoBIjGH+YlqP/QCQSXdTcXAwTqQjxTLxgVUEA3YMR\njg9FMOuLqSrxsW1XJeMTE3QPxjDyYQeYLAqj9neTueJ60h/5lKwJkCfO+9himuZLQK4ojf/Nsqyn\nF3H9JftZVlSsjp9yRUUQf6CP9r44Lk8QYdejpM5NNe0IAaqPlPd2gkEDzyoH0azUXFiHvkt4pAkA\n1VNL2HsXPvdmSHac004kIP1kC677c8trRVHw+w2cVJjKUh+Nmy+bXPBvX8QogtQ2/Mfpd0df+wvS\nyazqyXCH2Hfb/57zrIqKfbBzH9ah7+IaOTv9eY2WRsQfxin/LGz6V4iuv0FRshXkhC3QtZmFxU0/\nQ01/j7rtczRsvXwRY10c/f1ZYbm1vG7Vfm/h4n4vHvl1MwCf/5hJRUWQVCrFmbYJKqpXX3CJTBr7\nx99HdLWiXH41nvu+gneZNQFCIe+FG61z9BxR9os673wHLcu6Y0lXnaEbqJ/1vp7sbuCCDA4u7N+/\n0nhcftzKOIODCQzXpylOPYRK9onRjjv8z0gUs3gnNzv1vPLmKcwtFRSHVkeHWlERXJG5mKv7dxJd\neJM/YcJzkKAyPK3KEZEMyYc6sBt3oooSDOXcxGI2PiaUWygjTm1DLYqiMDaWAJZWurNsy/3Thvay\nLfef914rKoKEZwmAKRQngjL0OGP+B9F8nyYYfxaSCRSXPa+tKqL0N/2CniGV7Y2blzTmuZzqaQOg\nSCletd/bi/m9sE4P8N57nVQUe9ha6WdgYILDJ5pQ3SXEx+cH811SHBvXk/+EfvYU9rbdJD95P4ST\nFz7vPIRCXsZX+z4KEN2JLem8lVIHLbSPOwTsME1zi2maLuAB4KkV6nNF2VK/iRKfQzqdJOw9iIMf\nJwGZp3q479dhWobfpz/Zg8tXzJmOETq75xshC5nz6f6jPVtxojYikiHxWozkvX9A4vN/xAt2MeFZ\n5ThtvLhrvsoV+66jblP1iuTMn22wX46aTUw+BdlaBWOBP2Cs7E9Y6NdSURTGkgZHTjVh2/MFxcUy\nVVd4k78wUxv8+uUmKh3BXdc3oKoKp6xWhF60+gMRDq7nf45uHcPevI3kZ34fLoGNRnJxLNmKZZrm\nvcC3gXLgWdM0D1uWdZdpmpuA71mWdbdlWRnTNL8F/ArQgO9blpV3o/BCbG/czOmmNsLpEHbgQfDa\nuCofpfLkB3zu5Qy/+vhj3Nn4R3g9QfrHk6SGvovhFHZNgnQ6TVNbNz5yL4kiFsb45ZPEVIXjl5XS\ncmAzbncbw/3vMpoZIuUq5jN+HV3V2LT9i7jz7Aefq1aBZgQp3/x5Yr0TRNM6Lnc2Ejajz48mdoSH\nsPcgumbgiBAfHG9mz/Y6/P750bOLpTfSh6qoVPkqlnyNS0F3+yhv/6YFJ5KiCIWxkwMcSkcRAT+G\nscqLrxAYrzyFfvwQdk09yd/7Q8hhM5KsPgVpiRFCiNVUB83l9Nk2IrYbXTNAOBivPIXx/ptM+FRe\n/1gjV27/PA32O/MWmCmj5koajpeqDnIch7aObgbGk3h8xQTjT81fECMZ0s/20eyC966rZiygkHDi\nPBDw0KBrgEJGr2LL3q9fEq+ai2VqLmZ7GE1Vk5tieGSUlq4hdE8xiqKc47UkIhkSP+kjdfcXsHfu\nmz4nGR9ne10JZaWlFz0mIQT/7o3/TJErwH+84d8t8w4Xz2J+L4QQ/M9/+gBPd7bdRz67jYmMmBaS\nq4nx+vMY77yCU15N4kv/bEVrAkh1UBbdifDRA/suek2XQmABTlmtRB3PpCAQ6O+8guuNF0jpCi/e\nWMTnLi9b0JlhJXcFF/pjn5vWomLbV2jv6mFgJIbuCU0HewHzFsSBx7rpOXA9VXvvwqNlDWuB2JPz\n0jdcCuG2FKbmIhXrPaea3NxxOY6D1dLJRELBq0fxxZ8m4cQQSY2gZ1JtFPYxUfMgTCZ780cfxy2y\nQWUX8/2NJcf5s7f+T66suJxvXL56O8Hz/V5MRQJ3RpI88/QpKos97GsMMRZNseXy1U/Gpr/zCq7X\nn8cpKSfxpX8OgZVVRW1kISCEIJGIojppyoo93HTdXikEVpLTZ9sIZ1wYetb1ULOOYTzzMGo6g/uf\nN55XJ75SC+f5/tjnGnsBBCpT6RmmEq2lnCR9bW9T8+GbVN6UzbzZ1KLhu/pL+NwzycJsO0N5/Ls5\nfynmPnHng4vdFQ0MDtPWM4rhDREf/w51+rneE04CwoF78IkPlryrOzl8hr858n0Obvk4d2/9xOJv\nZpmcby6efPgwaVvw2kgEX8rhm1/cw/BolPCwQ1nd6gaF6YfewPXKkzhFxSS//C8QRSufnG4jCQEh\nBIlYGENz8HkM/B6D8tIQfn92Z1VZWXTRa3rhRrYUALt2bMFqbmc8ITBcbmzzcpyv/Cvcj/0ApyuO\nVr/wtnp2TvtLlYQul7FXmZWfx7C7KAn/LSCoSMZJnx2nKaOhffQ+GvefQk//FNJZYTEobqWqxIuy\njv6WKivKCBUFONXUQa2eI2+RB4ITT6B41XmPQ4utSdATzdqEagL5Nwp3t49y6M02ejqzLrd1CLbv\nq2BoNIzbG6JslTcB2pHfZQVAoIjkF/7kkgiAjUAyEUURKQJeFwGfQVVDLW63e8WuL4XABTC3NdDS\n1slgJE658xK6rwu+WoozpCAiaZTAwlOYSmdoO/YPqJmZcpZzi9YsVkDMbucONDLhuQUXF97KTRXR\n0ep98Ce7qAx8Bl/qXHuGYXdRpz9FZfkXGUvlNryu1Shpt9vNlXt30H4493HFq7BQpLHjXDjMpTdS\nOJ5BtQ0leH0uHv3+ewC4NgWorfXkJSeQdvKDyapg/mxVsJLcBWwk85l62ve4IOgz2FpVQlHRpfPm\nWtdZRFeKrVvqqeFFDLsrm+wM0MoFwu1GxGxEZv5TpqP4iXg/hZJZuJ7xYksjzm2XjLTiGvxRNu/C\nRaBpKYKJ59Dt+aEaTibCYMsjVG7/6jkZV7V1EiXtXaDIkDJZ/3guQoBjR+g48f3zXrcz0o2h6nnP\nGdTdPkpX+yjPvmjRjWDco1LvUfH4ild9LJp1DNczj4DbTeIBWRVsMQghiEXHUDNhSr0prt5Tx/49\nW9m+pf6SCgCQO4HFk86RQsGwcTQ/8SfC+D7hTO8KHPyTqZPPc7m0TSbdOu/5006H6Tv7MHbxF0hl\nHDr63Ijw/Ha5Fi7HgWUGXgIzdRimXq8HFlNkaDbT05vqpu3Dv6Rmx5dw+zed0yZpp+iJ9NEYakBT\nL7331JTBdyr7Z3f7KAIoqw7y+itNjIaTNMdTEDC4/epKlMTq/3mrzSdxPflPoOsk7/s6oqpgssQU\nJPHYBD4DSoJuNjU25Ey1cqmRQmC5aBrJr/xLksefpZjsYp18vQ/tssPYu67IWfnKVvx0aNeyJfOb\nnJd0hMJ4KpuawqV6F7VdE44g/fNuXHdXL6iisvERc91KqXaSdKz93NuYpfKZCuBab0wXGVpAECxU\naU4VMXqsh6nc+S/w+2bsQJ3hbgSCLUX1cy91STj0ZhsAxVUBnn3mBGffaMXOCDIIilBQgM2Gxnaz\nhPLy1d+ZaE0ncD3+I1BVkp//Gk7tllUfw1oglUqgOglKgm52mjV4vflNeSGFwCLJFaRk4yPiOZh9\n/N73aV7ufpaid3/LvvYk7taHcV5/jvhVt6DtGUGdzIBpKz4ejrroTT7DAwEPW4xzvwJH8c/LpZ9L\nkMwj7pDceTuJol0Exa+znwkHlfjkWL0EN3+NxrJS4Nrz+tqvV6aEWy6vKkfxE1ZvpUg8l/NcRVE5\n3tTL5qogNVXZfDttE9mcS5daCMw1+H7v229hOwLf5P7QcemQykY+X3HjJoorVt8Aq509geuJH4Gm\nkvz8H+Fs3r7qYyhkhBAk4hMUeTXqa4ooKy2cusnSJrBIcunKtYovEUvOWOl3V9/Km9eW8It76kld\neQNKNILr10+T+kUzTgKcjMEr4yq9yU7qPI28kjw3LYOjZNVItnZu5GnWzXN+hszp8zIGE6HfI3PL\nJ7B9mxnzP8iY/0EmPHdj40WoPjaZX6a8bCYYanY2z/Wi8lksc79LG1923gONZNT56ospwez2huga\nSnHsdDOZTIa28SkhsDI5iBaitqGEA5+YSdluOQ47bpjp87I9FdTvLKJmZynhwfQlHUsuNOv4LAHw\ndSkAZpHOpMgkxihyJbhmz2b2mluWFJR4KZFxAhdBriClSCSK1dqDMIJoms47o69yPHKIm0vuYI+2\nE/3o79BPfIA6OGPsDYc8eOovI1NSygnvMfZvcePWPMSSN+GkA5CMo8SiqCODuMLD2J0daPoErrsn\nDWyamnVrZEZwzCURG6c0qLOtoa4gon1XgpVKpgfnfpdG2V20DhrTXjTn1EaIZhiIfwzXlr3nnJ+M\njfLExCMIBP/XLf/HiuRROh/vvdHKh01DtPdH2FEX4po91cSiSRLJJN1dY+y8aRuKojDcNb6qsQCa\ndQzXkz8GTSd53x/h1G9btb6nKMQ4gWQyjktNUV0apGYVM7UuJU5ACoEVorWjm/7ROI7b4JHe7+BR\nPdxf8010JavuCfefoeXwI9QNpKkdclDTqUVf23a56CiH+KZNNF52L2qZQTD5fPa6noPn7BwS0XFC\nfo2tm2tW1Je4EFhJITCXcDjMqZY+XL4SNHswW1QnFSfzeAdiOE36zvuxL792un0kM8FPe/+eBncD\n37rqa/gusV739Tda+eFbrdRV+PnKjVsoDnkJp8cZithEBu1VDwID0E68j+vZR8EwSN73dZy63B5Y\nl5pCEgKJRJiAAbXVJZQUr75nlgwWyyONm2vZVJWkub2HXZ7LOBH/kA8n3uGa0AEyTpoXxduM7PVy\n9S078TICAjKpEmKtdVgDb5PKRNnp2oXbHUR4fODx4pSUE2jYzM8Gfklvqot7q+5DuKqwgTF95ulf\nCEEyNkZJ0MXu3XXrbvFfDYLBIPt2Ghw70wG+Csb8D5LxpvnNFf+DT7w+hOe5R0kP95O+7SAoKl2J\nrE1hk3c7R8/0UFaks/US7Lq620fJ2A7Pn+xDAf7grt2EPDYj4QkmEi7cbg13HtTL+vtv4nr5CYTb\nm90BbHAjcCIWpsirsL2xkkBg5fIirQZSCKwgbrebPWYjVeMh/tuHTRyeeAcFhYFULyPpQb4WqqCI\nkWxjBQz3KMHdKYr2fIInhl+i2+vn4+WfPuea3foAvaku6jyNlLvOzeCZTiXBjlEe8rJ529Z1o/bJ\nFx6Ph/17t3LkVAuKqxhdNfiYWU3IzP5RG12niT8+SOpTX6Iz0QJAnacRjxEikhEcOt5KechNQ10N\nur4yf1qH3mxjcDxB/0ScW/dVEhkfYnDEoLKyFC2Vh6dfIdDffgnXmy8i/EES938DUbnpwuetU5Lx\nMAE37NhRdY7n2FpCCoFLQFmolG9d9XW+ffg7fDDxNgCbXJspV0fmtVVFlO0cpdyopjV+hpH0EKVG\nOcH4U+h2FyUCHgh4iPtuArKGJicVJehzUV8TpKxU+mGvJLqus3/vdo6dbsafeB2XEmFKa6rV+/CX\nhFGf+WtG99gUh0oJ6VlPHEVRcPuKmUgJDp1oI+QzqF1GpOdcj6C9qkqNW8PRi3Dn669WOBivPI3x\n/hs4oRKSD/zxho0ETiYi+F2CHdvX7uI/hbQJXELCqQgfDh6nyBWkRqki3vm3OSfcUfwcUW/mxaFf\n0uDdzuf8+vzYAryk/R+juKSBivLSS26ILEQupU1gLkIIOj78r7lrMEQyjDzaRfPB29m+42COFlmS\niRi6kiboMygNBSgtKT4nq+tC2LbN0PAIrW0jHH4161BQvr+GHVtnfP9XXQ+eTuF65ifo1nGcsqps\nKojg6tshcrGac5FMxvFoKRrrKigK5qEwzwWQNoECI+gKcKD2hun3A2PzYw2E4iPh/QjbKKXGVUN7\nvAndE5h3LY04rtRrVFasf3/+QkBRlAWfkJIuFW/S4fInXyd1Rxn2FdfnbOf2ZJ8QYzaM9cc52zGM\n26XhNjR0TUFTsykrhBDYjiCdcUikM6TTAs3t551DwwwjqCrx4kksvwLakolM4H7sB2h9XdmKYPc+\nCJ61/fR7saQzKTQ7xraaUsrLVic4cLWQQmAVmZu6YG6QVoginOhENnHNBnzSLzRyBQiGHYfHEgmu\nuPtWdr38Hu4Xfk6mu53UHfeet1KWy3CDkTXYp4G0w1TGb8YHIwCEKgLoblAMhxff62RoIoGr1MeN\nt25lvDc/O2NlsBf3L76POjFG5vJrSX3yc6BtnGXDcRwyiXE2VQSp27Q+4x8K+tucmytlrXC+zKAL\n5eUZaPoxIta9oJpnIwZ15Zu5QjslXLyYrmFnUT2bay4nUXsz7id+hH7sXdSBbpKf/X1E8cWna+g6\nOQBA6LYA6YzDs++00TEQYVO5n0/ftAVdU/PjAnrmKK7nHkVJJUndeheZGz66oR5OkrEJSot0tm5f\n304XBfmNTtkEnnw4m//3M1/en+cRLZ5cKQkWU6Ck4/CfL3hso6R1uBCraROYYnZQmR34OP2REMbs\n8oyZNK6XHkc/+i7C482Wrty+d4Grncv4YISukwNMDGVTigTLfbTbNs2jcbZUBzl4QwO6ltuGcEn1\n4I6N8drzGO/+BmEYpO56AHv3lZemrxVgpecilUrgUZNsa6hZc0bfdRMs1np2ULz8zMlpzwjVb3DV\nzf9/e+cdHdd1Hvjfm4JBmwFRBpUg+gUIgp0UJZEUaVWqS7EVWXZcU5z1JvbuSbVzdu2c3bPZrFMd\n24FNIRQAACAASURBVLGjxHYcS5YjybKqZZISJZEUxSKCIEQSvACI3nsbTH/7x6DXAQgMBsD9ncNz\nMPPuvPfxvve+7977lZvF3l3hU29jNmZT5vMp8tmNgEZq4e+s+lLOS8FKGIGpNLW00dg5jGWK38ZY\ndpaIYy+h+bx4dtyK52MPQ8T8+RqOfidlx6oAcGfaKGvoJTvVyoO3ZWM0zP56LpsRGOzH8uozGOur\n8SfYcT32OXR7eJeCXqq+8Pv9+Fx9ZKUlkGxf2dLgi2UxRiAsawdl5ydx4J6Csc9lQy6efquS6qa+\nFZRqeYmcod690Wxl861fWVcGoKmuZ2wZMBzJSEshKzkGl3Nw0ve+7ftwfvYr+O1pmC99QOSP/x5D\nc/285+tq7GPjZju2TXF0NPSSHm1mf27inAZguTBeLyfqh3+Dsb4aryjB+dmvhr0BWCpcwwNYI5zs\nLslbtQZgsYSlEQB4+90bNKHjtEVwZ74dn0/nx29WBLXb00oymzKfbz1/ts1com3hPftZaqV94VTt\nWMnkcCU1xU52ihWXa7Ih0JPTcX72K3j2HsLQ04njhecZOv42eGYv6hZtiySzOIVrDjfDQK7ZTKvs\nXOb/wRRcTiJefw7LL/8dPG7cdz+G+7HPgSUytHKsAB6vG93dy5bcZApyNgUVwrvWCMv/scPpoayh\nl64IA5//zG52lqRwa3YC/R1DlFaG+AVZIDezM9dqrOwZrNKez1g01fXw8jOlNDf00dzQx8vPlIb1\njCAlOZHcVBuu4SnLUyYznjsfxvnJL1Fj3019q5/IH/4NhprrM54ncWMcbT0OBjqH2GQ24epz0t/p\n4Mq7N8aihpYNXcdYUUbkv34L00cX8Kdk4Pzcf8e7+8C6cAA7Hb2kWDV2bslfdaUelpJFRwcJIZ4A\nvgkUAXullBdnaVcL9AM+wCOlvGW+c794oopmt5fHDuYQb7UQX5TMhx/Uk47GqcvN7C60z3eKFWWx\nO3Otps1cpma0vvxMKXsOZM8ayTVqKDKy4meM+pq6P26Hxcj3jl6nOCuBTxzOwxIRftEZ9qRASeAb\nTb1YoscTh/o6BmmsNdIfEcimLWUvua++ijXrPJ5D90+LICqt7GQA2FiSQntpIDksZ2c60bblG4lr\nPZ1EHHsJY811dKMRz+334Ln9rnUR/ulxO7EYXewsylR1tri5ENFy4HHgB/O004HDUsrpNRNm4diJ\nKjbERnDf3k1jyqardRAbGgPV3ciKdkRR6MqzLpTVpMwXy1SlffA+QULS9NHUVGPxy2dKcbu8WCym\naQajuqKdLXsyOFXegqOqkzZNY7CrkbamPv7b5/YsWtblDDW2JyVgMEB1Yx8RUYEZYJw9FvNO05jD\nN3u/wHbyCsaKSxhlOd4dt+K5/W6IsTLs8lLV2EuCzYJ52MvGzYEBTldjP9HFy2AEBvsxn3kL06UP\n0Pw+fNkC9z2PoyeE98BqqXA5etiUGkdaSngvs4aSRRsBKWUFgBBivqawwCikZJ/OrQdysEQYpymb\nWnRu9DkJ6qqKZaW6op09+7NG/u4g4cB0I5CRFU+3wz1mBKob+hgNups6e4iNj+K1c/U0uLzcU5jM\nNx4u5l++8z6DbYOcKG3ik0cWl6Y/cRayHCQmJKBpBirru8dmBKMOX4DOYY2oz/whxmtlmE++ifni\naUzl5/Fu34dMKcGvw+ZN8cTEWMbyAboalzYIQuvrxvThaUyl76N5Pfg3JOI+9AC+wm3rYunH43YR\nZXSxpTh7RfbxDWdCMffTgeNCCB/wAynl0/P9wIZGz5V2muKjyciKH1M2bq+f5nP1nL3WxtbUwKhr\ntSWSrSUS7DHkjczIqivapx1vqO3m3LU2yspa8QMbYiLweXzgDqTKJoqksfvn9fn59bU2GtoHObwz\ng4NFybzx8zIMTi82NC69VUVGhAmrzRLUPff7da5ea6OytIXWxuCWrG6GhPgNFBo0rtd1YomKI9oW\nOVmhawZ8xTvxFW7FdPkcpvePY75wkm2cIjImk5Siw1jSxvMLliQ5zO/HUFeF6fJZjNfL0XQ//lgb\nnv2P4N16C6zhBKiJuB29bErdQKra9H5G5jQCQohjwEwxYl+XUr4a5DX2SylbhBB24JgQokJKeXK+\nHz32yZ3YRxR9dl4SxdsD5WpL63u42NLP+dN1RJiN7NizvFv7hQN2u3X+RiuA3W5F1vfw8nvVNHUM\nknipmbSkGLZtS2fI6eHtX1xh2O1FizLz+5/Zzc7CZP7zx+fpcXspk500vVVJbZ+TB/fn8Nyx61yu\n7mJXUTJffWoXJqOBjI3xfP9b7wBQ7fdz9kwd9vjoGe95bVUgYCA7P4ny6k7+4blS2rsdxJkMY7PG\nRyc8U8vVH3a7jXLZQu6W8dcmLm7KhjOH70I/cAjHh+fo+dUbFA3Vw2s/gROxGLbsQBPFaLkCLXLu\njWqmnRfQXU702ip0eRV/+UUYHHFcp2Vg3H8npm27sZjW3kh4pr5wu53EmD2U7C1Ro/85uOl5oBDi\nBPBHszmGp7T9BjAopfzbudqdeLNCdzjc7D2QPe3YG29VUn6+EduI6OmZcXOO7lZr6YlRwiFBajaO\nXWjgueOV6IDZZCDXGwjfbUYnHW3sHqVk2Nh3R87YrC6vKJnmziF+8vxlZN8wo2o5Mzuer3x8GxHm\nwAj1/MlA5nV3t4OKax2M7rI80z0fzS7fciiX7z1biq7r5Iskuqq7cXv9bM9LJDvNNuMztdQMDAxw\nraaNiKi5d5a6VNnJe2VNPJBlYHNfNaarpWjDgW0tdYMBPSkVf3I6fnsaujUOPdaGbokETcMaa2Gw\nsxfNMYg20IehowWtowVDWzOaP1BsTo+Kxlu0HV/xrsCmL2t02WemZDGXo5dNqTbSUsLXd7gcrGQV\n0RkvLISIBoxSygEhRAxwL/CX853s8H2FfHCyesZjB27L4vXzDZSMXHI2h+Qoy70evFaZz3ieutzC\nz45XEhcbwRN7N9Fe1UXLyLq/PS4SW7qNjmsdABy+v3DsHo0uH6UnxfDHv7ePExebuPFBPVEWE5/+\nze0YJ8RpT1xuahm8yHBDPzD5nk91PFc9W0qGXyfVHsunH9/KxQuN/Ph0DcfruvlSTmg2+LZarRTn\nGrh6o2VOQyAbe9E0jfStRXgit+K582EMzfUYa65jqK3E0N6Mqb15xt96galuY91gxJ+chj9b4Msu\nCGz3uA6ifSbicbuIMAyzQ0X+BM3NhIg+DnwbSAJeF0KUSinvF0KkA09LKR8ksJT0ixHnsQl4Rkp5\nNJjz580S/WOLjqDAFklTv4t792bO6JBsquuhs22Q2srOoEMYFZOZy3heru7kx7+qICbSxJ98cifp\nSTF05yaOOe8fe2Ib1dfayZrHadzW2IdDduIf8jA05OG1n5VNukcTn4HcFCvHGvqwRpupvtZOwsGc\nMfkmBg74/TqxaPR3DI3d80/dU8C/vHKVc0297NqzvFEhvYMufvRGBbKxl82ZcWzP9hK3YfrGK72D\nLlq7HWQmxxIdObJUYTDi35gTUN4Hj4Dfj9bdgaGrHW2wD22wHzxu0HUsZiMugxk9OhY9xoo/KQU9\nIXndrPPPhNPRS2aylYy0tVntc7m4meigl4CXZvi+GXhw5O8bwJJXnsrOTuDy5WbccRYyYqdb+1EF\ndvBeMW8Io2IyM8X/ZxckkZQSS0ZWPNfqevjuSx9hMmp89YntpI/06bRIoXmcxhB8mClAxsY48nx+\n3ittYu+UrPHqinZytqZwqryVuEgTjNTeHz1fmq5z9FwD5661c2RfP9mpy7MZiF/X+e4vyqlu7icm\n0sSl6m76hmK5Z7tGZOzk3ICKkZnW5rkGJQYDelIKvqSUaYei46LwhMnm6iuNx+MGdw/bCzOJilz7\nWc5LTVhmDM/HoYM5aMDZq22TRovTsk5/domCLcns2Z9FdUXHygm8isjIiufgveMBuKlbkrl+rZ0P\n3qvhxMVG/vGFMmL8Op/en0N+xngES4I9hr0Hc9h7MIeEpOhJ92W2WR2MG4/57lFeUTKPHwqM8C40\nTw6ftMVHcbK5jxZ0cpNjp53PoGl84nAeAK8scUmKiZnQH1xppbq5n92Fdv7xqwe5ZXMyNa2DNPcb\n8Di6xn6j6zp1Nd3EGwzkpYfH7lyrFdfwAOnxRnZsKVAGYJGsSiMQb7VQnJNAdXM/zZ1DY99nZMVP\nKjx33eHieFMfG4uTSUhaXSVhQ82oMuvqc/KT58toQqcDnTNvSrpaBmhv6ufc0UqsOuxOiKH7xuTc\nv2CV/lSmGo+5yM/cQElOAtfqeii/Ma5UP2zpp6XLwV27N7JjV8aM59ucFU9eho1LVZ00TXhmZmOi\ncp+r5MVo2Qyn28vz71RjNhl48s58DJrGZ+8rJMFm4Y0PGklISsY33IWu6zR2DLLB5SPHbMRsWpWv\n4Irj83nxO7spyUshJ0uFft4MYbmA+M1vfvObDod7zjYRJgPnK9rx+XV25AfWXHVd52cvlFM/6EKP\nNJEWH43sdlB+o4uHP5a/Kl+4mBgL8/XFUnDi9Qrqarr5+YeN9PU7SclJYNeuwMvl6nUCYM9PJCvC\nTE/bIAP9LprrerDGRWLbMHco41xMXP6Zb7kuJsZCfLSZk5dbuFbXwy5h51JlJy++e4O0xGi+/FgJ\n9pTxENCJ59M0DWuUmWvX2unrGWZ3ydzVMU+8XkFTfS+DEUbe+dV1aqu7KNqWNvYMNdX1cOL1Cpob\n+hjod3HlShttAy7uuS2LXSJgBM0mIxvtsZz+qJWalkGeuHsL1VdruXqujRg/GHw6/R2DWGLMRMZE\nzCXONCIjzbhc3gX9Zq3gGh4gKVajWOQQEWEO2TuyGvjWt/5q3sCbqaza0IFdwk5yfBSnLrdw955M\n0hOjefZYJVdb+4mxx/Bfn9pJe30vSW0DvH6mjldP1/KbdyqH0dSon6k+gCR0crem8YkHitA0jfMu\nH4wuWWgaeYX2FfWzbEqx8ht35PLmO9X87++fYQCItpj40iNbxkJLZ2N7QRI5JiM9NT109ztJmKE2\nz9T+aGjoxYSGC/j+t09z/0NFFG1OmebPuDzowmy1cP++rEnnK85O4I7tabxX1sJPj1aSHG9FejvY\nOjIJX+4aQWsJn88Hnn6Kc1KxWsMzd2Y1smqNgMGg8eSd+fzTi+X83c8vkRIfRUV9Lxn2GP74qZ1Y\noyOwFiWzKT+RM1daeetiI3fv2Tjji7+emBr1k5EVz7DPT3NDOQC5O9N54r7CsfZTHbzBlIpYbu6/\nNYv2y630Dbox5WzgsYO5Yw7q2RhV7havjgWNF//jIg88tHla9NNU5d5vs5DQHxhlVvp8tJ+s4Wub\n4rHFRIz1xfmKdmxdQzx0OI/Olv6x84zy5J0F1LYMcKo8UBwuy2ggLdcGmmn5agStMVzOAZKsJnIL\n82fdglWxOFatEQDYWWDn8YM5/PJkDT0DLoo2beD3Hy3BFj0+tTabjDy6P4cf/aqCV9+v5XNHisaO\nrfZEsoUwW9XPAeCFlz7CiY7YGEd29ORlielr/e3zRv0sJ6P/D0f3MGYg3eFFH3LDPEZgqnK/4nRz\np9tHU13PtPtfXtZMqwGMBo3iWAtZW9PQgajaHt5r6uW7P73IJ+/OJ8EeQ79R48LpGooSotlXnMIr\nz14au94oURYTf/qpXRw9X8/QsJeihGh279lIQ1MLV64EXVdxXeLz+dDdfWzOScVmXZ6orvXOqjYC\nAA/vz+HAtnScbi+pCdEzjhJu35rK6x/Ucbq8hUcP5LBhJKx0PSWSTVWCWpqVZ49JGjuHMAP33VXA\nPXsz51Xsi3UALxULCSudyujIvbKpj9jabt49XkmiLXLa/b/c2EeD389v378Z2ofYO5KTkJAUgy8h\nks7yNl59+SpFB7L55akaTEaN+27dxCvPXpo1L6WnbYC9m+InXSszIw1LRAQ1zX2TSlErAriGB0iy\nmcgtLFCj/2Vk1RsBAEd3YKNuLXFmZWA0GDhyyyZ+8uvrHL/QyG05CQuqhb9WqPioFRKjaOpy0HSu\nHisaBRYzDzy5ndz0gBJaCcW+UBa7JDW6tJVY1UlbbS+uPhfNfa5J9//D6+2UtvZTmLmB20tSJymf\nqGgzib0u3Gjg9lP6djUWDT7/SDHbN6eQmRY3q3GabcCRbE8kKjKCqzdasESHJqM53PH6PBi8gxTn\npGG1xs7/A8VNsfrCZWYgmN2tbi9JxRZt5kRpEwmp1kmx8AfvE2veALg9Pt6taON81xCxCVHkxERi\nQ8Po8lF+ojqsd/GaykLCSicyauBy85NI2zYeHTR6/x1ODz89KjEZDXz2SOG00WdGVjx3THhuduzP\n4mu/t49bNgeSuWbKeQhmxzSr1cqu4hz8zu6A83Md43T0kRTjZ1dJgTIAIWJVzwQWsrtVhNnIXXsy\neem9G7x7qZlEt2/FHZyh5GdvVVLZ52T/1lS+cP9merscqzabeimWpDIsJioMgZpqZaXN3HFXHj98\noRz/kJtH7sglbZZZ5cRZCJpGcvy4EZopSzrY5Suz2czOkgKuV9fT7zISEbG+nMWju33tKMwgUiV9\nhZRVbQQWuj78sZ0ZvHGmjmMXGvjSx/IRxeMjuLVKU10PNS39vHupmczkWD57XyEGgxYWUT4rSXqG\njXtTCvnX165xrKyZ47Vd2LqGybeYObJv9vLkc5XDmM04BdvXmqZRlJ9FS1s79a3968JP4Pf78Tr7\n2JQWT2qy2u1rJVjVRgAWtj4cG2Xmju3pHLvQQIfPP1ZnfjWsg8/FXFFO50/VUtc6gAb8zkPFmE2B\nWPpgavusZfKKkskDPF4/r79VRVLXMFY0cPl4/bmyWWeUi5mFLLSv01KSscXGUnGjCcw2jGu0KJzL\n0U+CzUReQR4Gw5pYmV6VrHojsNAX7N69mbz1YSNvnq3ntpJUDGsg6mAmp+PoUllLQx8RwN5oC4Zh\nz9jxlY7yCRcO7cjg4LZ02tsGeOnfA1tiLPXy2GL6OiYmml0l+VTV1NM9pGOJXDvr4y7XMNEmDyUF\nqcREq3IuK82qN78LfcES4yK5dUsKTZ1DnLrcEtQ15qods5LM5XTMyIrntrvHM6TvfahozTu/F4vB\noNFQ1RVUIbtQomkaBblZiMwNeIa78fv9Ky3STeHxuNBdveSnx7K1KFcZgDBh1RuBhTCqzD9+KA9L\nhJHnT1TRP0vNkYmKP5joo5VgasXPqVFOb79zgyZ0LGmxdDWH5+5k4cJiI45CQfyGDewuycca4cQ1\nvPruo9fnwefsZWOCmZ0l+SQmqMFIOLGujMCoMo+3Wnj8QA5DTi/f/+VHeLzTR1gXTtVy+njVvOF9\nS8HNzDRmK8U8OOzhckMvPRYjTzyxLewUW7gR7stjBoOBgpxNbMlNBk8vbrdzpUWaF6/Pg9fZQ6pN\nY/fWfNJSw69fFWvAJxAMM4WS7t6fzW5h50PZwfdeKucLD27GFh1BU10P507W0NoYqAETGz9eIXO5\nQikXm7k8OOyhfdiDPTOOrbmJNNeMlyB44Z0qWr0+nrwjf6yOkmL1Exsbw47ifPy6i9KP6vGbYjCb\nFlaBdLnxuJ0YdSfpSVbSUwvm/4FiRVkXRmC2UNLfzbDheOEyZdVd/PF33yc1IRqvz09ft4OSkUlS\ndY8Do8nAtrzEJQ+lXEiew1Sqmvr4x+fLGHJ64WIjMZEm7r1lE/H9Ts5caeW9shY22mO5a7cKu1uL\npCQnsXurhda2Dpo7evFqkSueWzDs6CfWorExNY6kRPXcrRbCMjRG13W9o2Np1z7Pn6wZ/6Bp7D2Q\nDYDP7+ed0mbeK2ums8+JBuRbTNhiIoiONDPUN8z5ASduj58n92Ry391LO7Lp7hgaM05P/s7eaTMN\nu93K1L7oG3LzjX87y5DTy0O3Z+P367x9sTFgEEaIi43gzz+1i5SEtbMMNFNfrFem9kVnVzctHX0M\nunSiQphf4HYPY9BdbIi1sDHVviKJXuq5GCc52bZgnb4uZgIweyip0WDgrt0bJ42YqysmV8q8Jz6K\n//vMRV4sbSK/OHlJtwSsrmincFc6RoMW9Ezj9TO16A4PD+zI4NEDgeJmR/Zt4p3SJqqb+9lg0Nhb\nlLymDIBibpISE0hKTMDlctHY0k7fkBuXRyMy2rrkxdeGhwcwG3zYoiPI3mhjQ1zmkp5fEVrWjRGY\nz/E3MbRyprZffqyEv//PMv7ttWv85Rf3jiVd3Qxuj4+z1V1cbA34Hw7nJbFH12d9aZvqenA4vbx3\nqRlhNKJ1OcaORVlM3H9rIGnu5WdKqfiwiULlB1h3WCwW8rIDSnl4eJi2zm6GHB6GXB68PgOWyBiM\npuBfe7fbhdczTIQx8IzFRJkRGSlEq/DONcO6MQLzMZ9ztiQ3kTt3b+StDxt59f1afuOOvJu+5n/8\n+joXW/vJSbPhcHp4p7qT5HMNs5YtuHCqlrYuBzlenSigZSRiadSPcDM+BsXaIyoqiuzM8f133W43\nPb39OJwuPF4fXp+O3x/4B4CmYTRoGAxgNhowmwzEJkYRZ0vBtADDoVhdrPs7uxDF+fFDuVRca+fk\nmXr2FaeScRORQhV1PZz+qJXsVCtf+61dDDm9fOOH5zj27g2ybRaKRipTziSjWdNg5L2dGLF0M7X2\nFWufiIgIUpKTVloMRZix6DwBIcS3hBDXhBBlQohfCCFmXCgXQhwRQlQIISqFEH+2eFGXh/kSriYS\nGWGiKDqCVB1++uvr6Lq+qBh/Xdd58b1qAD5zXyEmo4G4mAg+cSiPZL/OiaOVc8poT7POmt06W96A\nQqFQzMTNJIsdBbZIKbcDEvja1AZCCCPwHeAIUAw8JYTYfBPXXBaCUZyjJRr6Ox3Y0KChj6Pv3lhU\nNnFZVRfVTf3sEnZy0mxj5+8sbw2ce9jLcz+6MMm4XL/SSodJo8MISTGWWbNbwznzVaFQhB+LNgJS\nymNSytFU27PATIHBtwBVUspaKaUHeA54dLHXXC6CUZxTR+O9Bo3ysw0Lzib26zqvHZfYgMfvyJ10\n/okbltTiJ33ThrHPzYMuar0+tt+Whdgyu5M73DNfFQpFeLFUZSO+CLwxw/cZQMOEz40j34UVwSrO\niTOG3bkJ3NDHy00EuzvZuattmPtcFEVbpvkURs/vT4hksG2Q4ydvUFvVyZDTw7vVXURGGLlr90al\n3BUKxZIxp2NYCHEMSJ3h0NellK+OtPkLwC2lfHaGdvpiBbPbrYv96bKRnZdE8fZ0AK5caqJ3yE1t\nywDJG6Koq+6mcPNMXRWgtqqThroezhy9jg0N3eHhjefLOXSvIDs/adL5d3YO8Rf/723KPmigp6aX\n7vgoBoc9fOGhYnI2re99aMPxuVgpVF+Mo/pi8cxpBKSU98x1XAjxeeAB4K5ZmjQBEzNJMgnMBuYl\nHDMA7enjmYnJGTYO7snEXdnBhYp22k7XUN/rYEtuIvkFSdM2ejn+2lXae4ep9PrYOjIBu/VjucTE\nWcbOOXr+troetsRFMdQ9TFfLAP0t/WxJjuX24uSw7JdQoTJDx1F9MY7qi5tj0SGiQogjwJ8Ah6SU\ns5U0vAAUCCGygWbgSeCpxV4z3CjckkLB5mTeTLXy6vu1VJQ2c720hQ3FdmI7HERHBrp3YnhnkWYg\nf3MyG+KjZs0QzsiK56HHS8ZCPXN3pvPInfkY1e5LCoViibmZPIF/AiKAY0IIgDNSyi8LIdKBp6WU\nD0opvUKIPwB+DRiBf5NSXrtpqcMIg0Fje5qNYbuV9qZA5q/rajs+NPqA1165iilhvBLp5p3p3DPi\nAJ5rJ7RR/0B0jAWHw43FvDa3GFQoFCvLuikgt9xMLAS37VAOl98NFKwrx08CGpFmAzuFneT46LHi\ndXMxWr/Ibrfywclq5QxGTfsnovpiHNUX46gCcivIxA3vm250s2d/Fj6/TsGwhyibhX37NmEyGoLe\n1F2FeioUilCgjMASMbFKqfutKvYeDFT3nFiRFJRCVygU4YXyNC4RE5X7/rvyZ/xeoVAowg1lBBQK\nhWIdo4yAQqFQrGOUEVAoFIp1jDICCoVCsY5RRkChUCjWMcoIKBQKxTpGGQGFQqFYxygjoFAoFOsY\nZQQUCoViHaOMgEKhUKxjlBFQKBSKdYwyAgqFQrGOUUZAoVAo1jHKCCgUCsU6RhkBhUKhWMcoI6BQ\nKBTrGGUEFAqFYh2jjIBCoVCsY5QRUCgUinXMojeaF0J8C3gIcAPVwBeklH0ztKsF+gEf4JFS3rLY\nayoUCoViabmZmcBRYIuUcjsgga/N0k4HDkspdyoDoFAoFOHFomcCUspjEz6eBT4+R3NtsddRKBQK\nxfKxVD6BLwJvzHJMB44LIS4IIX53ia6nUCgUiiVgzpmAEOIYkDrDoa9LKV8dafMXgFtK+ewsp9kv\npWwRQtiBY0KICinlyZuSWqFQKBQrjxDi80KI00KIyCDbf0MI8UfLLZdCoVAogmPRy0FCiCPAnwCP\nSimds7SJFkJYR/6OAe4Fyhd7TYVCoVAsLYt22AohKoEIoHvkqzNSyi8LIdKBp6WUDwohcoFfjBw3\nAc9IKf/qpiRWKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKxYJYsUzekeiifwCMwL9KKf96hjbfBu4H\nHMDnpZSloZUyNMzXF0KITwN/SuB+DQD/RUp5OeSChoBgnouRdnuBM8BvSil/MVOb1U6Q78hh4O8B\nM9AppTwcShlDRRDvSBLwUwJ5TSbgb6SUPw61nMuNEOKHwINAu5Ry6yxtFqQ3V6SKqBDCCHwHOAIU\nA08JITZPafMAkC+lLAB+D/jnkAsaAoLpC+AGcIeUchvwv4B/Ca2UoSHIvhht99fAm6zRkiRBviMb\ngO8CD0spS4BPhFzQEBDkc/EHQKmUcgdwGPhbIcSiy+KEMT8i0A8zshi9uVKlpG8BqqSUtVJKD/Ac\n8OiUNo8A/w4gpTwLbBBCpIRWzJAwb19IKc9MqNB6FtgYYhlDRTDPBcAfAi8AHaEULsQE0xefkFXB\nQgAAAk5JREFUAl6UUjYCSCk7QyxjqAimL1oA28jfNqBLSukNoYwhYaTaQs8cTRasN1fKCGQADRM+\nN458N1+btaj8gumLifw2s9dpWu3M2xdCiAwCCmB0hKOHRrSQE8xzUQAkCCFOjNTm+kzIpAstwfTF\n08AWIUQzUAZ8NUSyhRsL1psrZQSCfXGnTvXX4gsf9P9JCPExAsX6/mz5xFlRgumLfwD+XEqpE3g+\n1uRyEMH1hRnYBTwA3Af8DyFEwbJKtTIE0xdfBy5JKdOBHcB3R6sVrEMWpDdXygg0AZkTPmcSsFhz\ntdk48t1aI5i+QAixjcBo5xEp5VzTwdVMMH2xG3hOCFFDoHz594QQj4RIvlASTF80AEellMNSyi7g\nPWB7iOQLJcH0xe3A8wBSymqgBigMiXThxYL15ko5Ti4ABUKIbKAZeBJ4akqbVwg4e54TQtwK9Eop\n20IqZWiYty+EEJsIlN/4LSllVcglDB3z9oWUMnf0byHEj4BXpZSvhFLIEBHMO/Iy8J0Rx6kF2Af8\nXSiFDBHB9EUFcDdwemQNvJBAQMV6Y8F6c0VmAiMOmz8Afg1cBX4upbwmhPiSEOJLI23eAG4IIaqA\nHwBfXglZl5tg+gL4n0A88M9CiFIhxLkVEndZCbIv1gVBviMVBCKkLhMIGHhaSnl1pWReLoJ8Lv4P\nsEcIUQYcB/5UStk98xlXL0KInwHvA4VCiAYhxBfXo95UKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQK\nhUKhUCgUCoVCoVAoFAqFQqFQKBQKxRT+PwUpqj9YvY2hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bc7b990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test_2 = np.hstack(\n",
    "             ( np.vstack((x_test,np.ones_like(x_test))),\n",
    "               np.vstack((x_test,np.zeros_like(x_test))) )).transpose()\n",
    "\n",
    "mu_coup, cov_coup = gp2.predict(outs_coup, x_test_2)\n",
    "print(mu_coup.shape)\n",
    "std_coup = np.sqrt(np.diag(np.clip(cov_coup,0.,10.)))\n",
    "plt.clf()\n",
    "plt.plot(x_test,mu_coup[:500])\n",
    "plt.plot(x_test,mu_coup[500:])\n",
    "#plt.fill_between(x_test,mu_coup-std_coup,mu_coup+std_coup,alpha=0.3)\n",
    "\n",
    "plt.plot(x_test,mu_uncoup)\n",
    "plt.fill_between(x_test,mu_uncoup-std_uncoup,mu_uncoup+std_uncoup,alpha=0.3)\n",
    "\n",
    "#plt.plot(ins_coup[100:,0],outs_coup[100:],'*')\n",
    "#plt.plot(X[50:],func_2[50:],'o')\n",
    "plt.plot(ins_coup[:100,0],outs_coup[:100],'*')\n",
    "plt.plot(ins_coup[100:,0],outs_coup[100:],'o')\n",
    "print(outs_coup[90:99])\n",
    "print(outs_coup[140:149])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.30258509 -6.90775528  0.         -6.90775528]\n",
      "150.445672147\n",
      "[ -4.05699700e-01  -4.85597013e-02   1.58457589e+00   6.97931500e+01]\n"
     ]
    },
    {
     "ename": "LinAlgError",
     "evalue": "102-th leading minor not positive definite",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-82-1735239c4ead>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     15\u001b[0m \u001b[0;32mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrad_nll2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0mresults\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscpo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mminimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnll2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mp0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mjac\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgrad_nll2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Powell'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     18\u001b[0m \u001b[0;31m#results=scpo.optimize.basinhopping(nll2,p0)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc\u001b[0m in \u001b[0;36mminimize\u001b[0;34m(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)\u001b[0m\n\u001b[1;32m    435\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_neldermead\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    436\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'powell'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 437\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_powell\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    438\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmeth\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'cg'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    439\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_minimize_cg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36m_minimize_powell\u001b[0;34m(func, x0, args, callback, xtol, ftol, maxiter, maxfev, disp, direc, return_all, **unknown_options)\u001b[0m\n\u001b[1;32m   2351\u001b[0m             \u001b[0mfx2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2352\u001b[0m             fval, x, direc1 = _linesearch_powell(func, x, direc1,\n\u001b[0;32m-> 2353\u001b[0;31m                                                  tol=xtol * 100)\n\u001b[0m\u001b[1;32m   2354\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mfx2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mdelta\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2355\u001b[0m                 \u001b[0mdelta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfx2\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36m_linesearch_powell\u001b[0;34m(func, p, xi, tol)\u001b[0m\n\u001b[1;32m   2173\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmyfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2174\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2175\u001b[0;31m     \u001b[0malpha_min\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfret\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbrent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmyfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtol\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2176\u001b[0m     \u001b[0mxi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0malpha_min\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2177\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0msqueeze\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfret\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36mbrent\u001b[0;34m(func, args, brack, tol, full_output, maxiter)\u001b[0m\n\u001b[1;32m   1912\u001b[0m     options = {'xtol': tol,\n\u001b[1;32m   1913\u001b[0m                'maxiter': maxiter}\n\u001b[0;32m-> 1914\u001b[0;31m     \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_minimize_scalar_brent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbrack\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0moptions\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1915\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1916\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'fun'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'nit'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'nfev'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36m_minimize_scalar_brent\u001b[0;34m(func, brack, args, xtol, maxiter, **unknown_options)\u001b[0m\n\u001b[1;32m   1944\u001b[0m                   full_output=True, maxiter=maxiter)\n\u001b[1;32m   1945\u001b[0m     \u001b[0mbrent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_bracket\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbrack\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1946\u001b[0;31m     \u001b[0mbrent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moptimize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1947\u001b[0m     \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnfev\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbrent\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_result\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfull_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1948\u001b[0m     return OptimizeResult(fun=fval, x=x, nit=nit, nfev=nfev,\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36moptimize\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1750\u001b[0m         \u001b[0;31m# set up for optimization\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1751\u001b[0m         \u001b[0mfunc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1752\u001b[0;31m         \u001b[0mxa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfuncalls\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_bracket_info\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1753\u001b[0m         \u001b[0m_mintol\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_mintol\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1754\u001b[0m         \u001b[0m_cg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_cg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36mget_bracket_info\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m   1724\u001b[0m         \u001b[0;31m### carefully DOCUMENT any CHANGES in core ##\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1725\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mbrack\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1726\u001b[0;31m             \u001b[0mxa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfuncalls\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbracket\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1727\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbrack\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1728\u001b[0m             xa, xb, xc, fa, fb, fc, funcalls = bracket(func, xa=brack[0],\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36mbracket\u001b[0;34m(func, xa, xb, args, grow_limit, maxiter)\u001b[0m\n\u001b[1;32m   2100\u001b[0m     \u001b[0m_verysmall_num\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1e-21\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2101\u001b[0m     \u001b[0mfa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxa\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2102\u001b[0;31m     \u001b[0mfb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2103\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mfa\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mfb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m                      \u001b[0;31m# Switch so fa > fb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2104\u001b[0m         \u001b[0mxa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mxb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxa\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36mmyfunc\u001b[0;34m(alpha)\u001b[0m\n\u001b[1;32m   2172\u001b[0m     \"\"\"\n\u001b[1;32m   2173\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmyfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2174\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2175\u001b[0m     \u001b[0malpha_min\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfret\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbrent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmyfunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfull_output\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtol\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2176\u001b[0m     \u001b[0mxi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0malpha_min\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/optimize/optimize.pyc\u001b[0m in \u001b[0;36mfunction_wrapper\u001b[0;34m(*wrapper_args)\u001b[0m\n\u001b[1;32m    287\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mwrapper_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    288\u001b[0m         \u001b[0mncalls\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 289\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwrapper_args\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    290\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    291\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mncalls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfunction_wrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-82-1735239c4ead>\u001b[0m in \u001b[0;36mnll2\u001b[0;34m(p)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mnll2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m     \u001b[0mgp2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m     \u001b[0mll\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgp2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlnlikelihood\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mouts_coup\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mll\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mll\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;36m1e10\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/george/gp.pyc\u001b[0m in \u001b[0;36mlnlikelihood\u001b[0;34m(self, y, quiet)\u001b[0m\n\u001b[1;32m    229\u001b[0m         r = np.ascontiguousarray(self._check_dimensions(y)[self.inds]\n\u001b[1;32m    230\u001b[0m                                  - self.mean(self._x), dtype=np.float64)\n\u001b[0;32m--> 231\u001b[0;31m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecompute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mquiet\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mquiet\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    232\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minf\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    233\u001b[0m         \u001b[0mll\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_const\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m0.5\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply_inverse\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/george/gp.pyc\u001b[0m in \u001b[0;36mrecompute\u001b[0;34m(self, quiet, **kwargs)\u001b[0m\n\u001b[1;32m    204\u001b[0m                 \u001b[0;31m# ordering of the points.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    205\u001b[0m                 \u001b[0minitial_order\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 206\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_x\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_yerr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msort\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    207\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minds\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minitial_order\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    208\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mValueError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/george/gp.pyc\u001b[0m in \u001b[0;36mcompute\u001b[0;34m(self, x, yerr, sort, **kwargs)\u001b[0m\n\u001b[1;32m    183\u001b[0m         \u001b[0;31m# Set up and pre-compute the solver.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    184\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 185\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_x\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_yerr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    186\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    187\u001b[0m         self._const = -0.5 * (len(self._x) * np.log(2 * np.pi)\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/george/basic.pyc\u001b[0m in \u001b[0;36mcompute\u001b[0;34m(self, x, yerr)\u001b[0m\n\u001b[1;32m     67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     68\u001b[0m         \u001b[0;31m# Factor the matrix and compute the log-determinant.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_factor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mcholesky\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverwrite_a\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlower\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     70\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog_determinant\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_factor\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     71\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcomputed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/linalg/decomp_cholesky.pyc\u001b[0m in \u001b[0;36mcholesky\u001b[0;34m(a, lower, overwrite_a, check_finite)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \"\"\"\n\u001b[1;32m     80\u001b[0m     c, lower = _cholesky(a, lower=lower, overwrite_a=overwrite_a, clean=True,\n\u001b[0;32m---> 81\u001b[0;31m                             check_finite=check_finite)\n\u001b[0m\u001b[1;32m     82\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/alan/Developer/reinforcement/virtualenv/reinforce/lib/python2.7/site-packages/scipy/linalg/decomp_cholesky.pyc\u001b[0m in \u001b[0;36m_cholesky\u001b[0;34m(a, lower, overwrite_a, clean, check_finite)\u001b[0m\n\u001b[1;32m     28\u001b[0m     \u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpotrf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlower\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlower\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moverwrite_a\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moverwrite_a\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mclean\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mclean\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     29\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 30\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"%d-th leading minor not positive definite\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0minfo\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     31\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     32\u001b[0m         raise ValueError('illegal value in %d-th argument of internal potrf'\n",
      "\u001b[0;31mLinAlgError\u001b[0m: 102-th leading minor not positive definite"
     ]
    }
   ],
   "source": [
    "def nll2(p):\n",
    "    gp2.kernel[:]=p\n",
    "    ll=gp2.lnlikelihood(outs_coup)\n",
    "\n",
    "    return -ll if np.isfinite(ll) else 1e10\n",
    "\n",
    "def grad_nll2(p):\n",
    "    gp2.kernel[:]=p\n",
    "    return -gp2.grad_lnlikelihood(outs_coup)\n",
    "\n",
    "print(gp2.kernel.vector)\n",
    "p0 = np.hstack((p1,np.array([2e-3])))\n",
    "gp2.kernel.vector[:]=p0\n",
    "print(nll2(p0))\n",
    "print(grad_nll2(p0))\n",
    "\n",
    "results=scpo.minimize(nll2,p0,jac=grad_nll2,method='Powell')\n",
    "#results=scpo.optimize.basinhopping(nll2,p0)\n",
    "\n",
    "gp2.kernel[:]=results.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_test = np.vstack((np.linspace(0, 1, 500),np.ones(500)))\n",
    "mu, cov = gp2.predict(outs, x_test)\n",
    "\n",
    "std = np.sqrt(np.diag(np.clip(cov,0.,10.)))\n",
    "print(std.shape)\n",
    "plt.plot(x_test,mu)\n",
    "plt.fill_between(x_test,mu-std,mu+std,alpha=0.3)\n",
    "plt.plot(ins,outs,'*')\n",
    "plt.plot(X,func_2,'o')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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