{ "metadata": { "name": "gp_derivative_constrained" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import pymc as mc\n", "import pymc.gp as gp" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Start with a simple GP example:\n", "==================================" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.arange(0., 10., 1.)\n", "xx=arange(0,10,.01)\n", "\n", "M = gp.Mean(lambda x: 0.*x)\n", "C = gp.Covariance(eval_fun=gp.cov_funs.matern.euclidean,\n", " diff_degree=2., amp=1., scale=5.)\n", "\n", "f = gp.GPSubmodel('f', M, C, x)\n", "\n", "m = mc.MCMC([f])\n", "%time m.sample(iter=10000, burn=5000, thin=1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " CPU times: user 4.89 s, sys: 0.07 s, total: 4.96 s\n", "Wall time: 4.94 s\n" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "for k in [0, 1000, 2000, 3000, 4000]:\n", " plot(x, f.f_eval.trace()[k,:], 'ks:')\n", " plot(xx,f.f.trace()[k](xx), 'k-')\n", "ylabel('f(x)',rotation='horizontal')\n", "title('5 MCMC draws')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "acorr(f.f_eval.trace()[:,5], detrend=mlab.detrend_mean, maxlags=300)\n", "title('acorr for f(5)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "output_type": "display_data", "png": 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7Mj2+rq6uaJW6DRs2ICwsDMePH5fpMQrVhLui2hpjRkYGNm/eDE9PT6nrqgnn\nsCpkZmYCAOzt7WFsbIy+ffsiNjZWrMzVq1dhZWUlSrp0dXWrPU5CyP/hXFJQlri4OLRu3Vq03bBh\nQyQnJ8usficnJ5ibmwMAhEIhtLS0MHz4cHTu3BkODg6iH29vb5kdk3DP5s2bYWlpiZcvX8o7lBor\nPj4eLVu2FG23bt0aV65cESsTHh4OHo+H7t27w9nZGeHh4dUdJiGkiBo3JZExVmxkJY/HK7H8uHHj\nRIMKGzRoAGtra9GdW2Ffb0nbZ86cwdu3byEQCIp9mZXn/WVtr1+/vkLxyGP75s2bosV6uBCPpO3C\n12RVn42NDTZs2IA1a9bA0NBQdAyuxCeL7YiICAQHBwOAxFk41eXLly+4efMmzp07h+zsbPTp0wd3\n7tyBqqpqsbJLliwR/V6YnBNS20VERMh23BLjoCdPnrA2bdpI3LdhwwYWGBgo2jY1NS2xHll8PD6f\nzwAU++Hz+VLXfeHCBanrqGq1JcaJEycyPp/P+Hw+MzU1Zbq6uozP57OJEydyIr6qVhVfBRkZGcza\n2lq07evry06ePClW5uTJk8zf31+0PWLECBYWFlYt8RHpuLq6sn379sk7DPINaa+VGtd9YGtriyNH\njuD9+/fYt28fWrVqJe+QKq0m3OnUlhgfPnyIyMhIREZG4vHjx0hLS0NkZCQePnzIifhqIk1NTQBf\nZyA8ffoUZ8+eha2trVgZOzs7REZGIjs7G+np6bhx4wa6du0qj3AJIeBg94GbmxsiIyORlpaGpk2b\nIiAgAAKBAMDXtedtbGzQrVs3dOzYEdra2tizZ4+cIyaElGT9+vXw8fGBQCDA9OnToauri6CgIABf\nr2cdHR14enqiY8eOaNiwIX755RdoaGjIOWpCai/OJQX79+8vs8yqVauwatWqaohG9ry9vUV3nxkZ\nGaKZDubm5ti+fbs8Q5MoIiKC83e6XI+R6/FVJT6fX2yGkI+Pj9j25MmTMXny5OoMixBSAs4lBVxT\nOBOhUG5uLmJjY0V/zCuqsJn6Wy9fvkRkZCS6dOkCZWXlStVNCCGESIOSgjJIunufOXMmrl+/DsZY\nqTMfKuLz58/w9/fHixcvMG3aNPj5+XHiwTs14Q5XFjGyKlxXvyacQ0IIAWrgOgVc8Ntvv+HDhw+V\nWtSopD8+5ubmiI+Px/nz53Hz5k20bNkSZ86ckTZUUk6qqqpQV1eHvb296HHbfD6/WEsRIYR8zygp\nqARFRUVQzkSPAAAgAElEQVSsXr0a06dPR25ubrnf9+rVK8TExEjcV1BQAMYYWrVqhUOHDiE4OBiT\nJk2Cn58f8vPzZRV6hdWEdfuljTEvLw+fP3/Gjh07EBkZKZr3GxERIZNxHjXhHBJCCEBJQaU5Ojoi\nPz8fgYGB5Sqfn5+PBQsWoG7duhL3P3nyRGyQZc+ePXHr1i3cvXsXQ4YMET3FkcjetGnTcO/ePQwf\nPlzeoRBCiFzxWFV2pspZVT+DPT4+Hj/++COSkpIkrsAGAFu3bkV2djYuXryI7OxsGBoa4smTJ8XK\nmZmZYfv27VBUVBR7XSAQYOzYsUhPT8fx48ehoqJSJZ+lNuvXrx8GDhwIX19feYciN1V9rUiL6/HV\nRm5ubhg0aBDc3NzkHQopQtprhZICKbm4uKBz586YPXu2xP2JiYmYOHEiTExMEBwcjDp16pRZZ2Rk\nJIRCoehxvfn5+XB1dUV+fj5CQkKgpETjQ2Xl+vXrGDRoEJKTk2t1wsX1P7pcj682oqSAm6S9Vqj7\nQErLli3DwoULRdMM8/PzMXz4cKSnp+PVq1dwc3NDp06dsGfPnmIJQUl9zeyb5zsoKSlh3759+PLl\nCyZPnlytX441oT+8sjG+e/cO06dPx//+978qTQhqwjkkhBCApiRKrXXr1hg0aBDOnz8PPp8PJSUl\n+Pr64t69exg5ciR8fX0xd+7cCk1dLDqFTSgUQiAQQEVFBSEhIXBwcEBAQIDYw2FqI1ksAhUTE4Ob\nN28iLCysyuIkhJCahJICGRg9ejRGjx4NX19f6Ojo4MaNG1ixYgX++usvDBw4sMT3lWf++sGDBxET\nE4MNGzZAQ0MDp06dQpcuXWBoaFgtj2/m6hz7khaBYoxBKBRCQaHsRrBjx45hzpw50NDQEEsyipLF\nSpNcPYeEEPKt7z4pKPxCrsplhG1sbNCnTx8MHz4c2dnZUFFRQUxMDMzMzKSu29XVVSyx0NfXR1hY\nGLp3744WLVqAz+dLfYzvSVRUFJSUlFCnTh2oq6tDQ0ND9N+ivzPGcOzYMbi7u2PatGk4ffo0Xr58\nKe/wCSFErr77pEDS3WRFlHQHmZubi8OHD6NJkybQ19dHp06dsHDhQkyaNAmbNm0qNotAkvKsic/j\n8VCvXj0AwOvXr3Hu3Dm4u7sjODgYo0aNwrVr12BgYFCpz1Ye8lq3Pz8/H2FhYThz5gxu3bqF58+f\nIzs7G3l5eRAIBPjy5YvE99nb2yMiIgIDBgzAmDFj0LVrV3z69Al+fn7o27cvWrRogdTUVEydOhWW\nlpZo164dhEIhPn/+XGWfpTY/+4AQUrN890lBIaFQiFOnTmHAgAEAvi4WlJmZCW1t7VLfV1IzdcuW\nLXH16lX88ccfOHToEBo2bAhvb2/k5+eXKyGojM+fP4v+ePXr1w9eXl4YO3YswsLCZLbcMhccO3YM\ns2fPRsOGDTF06FAMGzYMTZs2RU5ODoyMjKCsrAwbGxskJiYWey+PxwOPx8Pp06fFXj9y5AhUVFSg\noqKCZ8+eoU6dOjh48KCoNWfXrl24evVqtXw+QgjhqlqTFBQUFOCff/4RJQVv3ryBk5MTEhISAHxd\nbdDd3R3//fcfAOD9+/dYu3ZtifU9fPgQixcvhqOjI7Zs2QI+n4+MjAyYm5vD19cX5ubmJa5dUKii\nd4/NmzdH8+bNRdtz584Fn8/Hjh07ZDq+oCr710vz/v17+Pr64vr169ixY4doSiYAHD16FBcuXMDG\njRsBALq6uhWqu379+qLfV6xYgalTp4p176irq0t83+PHj5GdnS3VcyiolYAQUlPUmqQgOTkZO3fu\nFG03btxYlBAAX//IbNu2TbRdUFAAoVCIR48eSayvS5cuiI6OFntNS0sLM2fOxPDhwxEQEFCl83eT\nkpLg4eGBv//+Gz179oSjoyOMjY1lUndJrSMpKSkIDAyEsbExevbsCS0tLZkcDwBOnz6NiRMnYsSI\nEbhx4wY+ffqE4cOH49ChQ+DxeBgyZAhcXFxE5Ut6JkFZzyo4ffo0QkJCJCY9knz58gWWlpbYvn07\nevXqVf4PRAghNVCtSQrq1q0LOzs72Nvbw8HBAS1atICZmRkMDAzw5csXpKWlITU1Ff/++y/Onj2L\nCxcuwMLCosTFhkrqIpgxYwY2btyIVq1alRmTNH3NzZs3x6lTp6ClpQUTExO0b98ebdq0EetGkPWd\nfW5uLp4/f47z58/Dy8sL48ePx8KFC8vsginNp0+f8L///Q/h4eHw8fHBvHnzUKdOHaiqqoqtMPht\n90jRz1Xe88gYw6RJk+Dh4QEdHR2xfSUlE8bGxoiMjMS4cePg7e2NhQsXVrirhsYUEEJqCk4mBVFR\nUfDx8UF+fj6mT5+OadOmie2PiIjA4MGDYWpqCgAYOnQoFi5cKLGuwtH55ubmWLNmDY4fP46YmBiE\nhoYiOTkZb9++Rd26daGrqwt9fX388MMPGDFiBLZv3w49PT04ODjg6dOn5Y5dXV0dCxYswE8//YRT\np05V7gSUU+Gdet26dZGeno6oqCiZ1FtQUCDxdQMDAyQnJ+PkyZN48+YN5s2bBzMzM/zxxx8YOnRo\nifWV1B1Rp04dPHr0CHw+H7du3cIvv/yCt2/fomnTpuDxeDKfWfHgwQPk5ORIXOOhtOQpMzMT2dnZ\ncHZ2xuPHjxEUFFSulSkJIaTGYRxkbW3NIiMj2dOnT1mLFi3Yu3fvxPZfuHCBOTs7l1mPLD7exIkT\nGZ/PL/YzceLEEt/z5csXZmxszBYvXswOHz4sdQxl6datGwNQ7IfP51e4ruTkZKampiaxPnt7e/b6\n9WtR2du3b7MJEyYwMzMzNn78eHbmzBk2Y8YM0f7U1FSWmJjI+Hy+xPqUlJTY7NmzZXEKymXkyJFs\nxYoVlX5/VlYWs7a2Zj169GAfPnyQYWTyx9GvAhGux1cbubq6sn379sk7DPINaa8VzrUUZGZmAvg6\ntQwA+vbti9jYWNEAwUKsmpb6rUzzu4qKCpYsWYKNGzfC1dW1CqISJ6vZDjdu3EDfvn1LbB7n8Xhi\n0x/btGmDHTt2ICsrC/7+/pgwYQKmTZuGL1++oG7dukhMTMTZs2dLPJ6NjQ1Wr14tk9jLMn/+fJw9\nexZ//PFHpetQUlJCjx49kJubi65du+LUqVMwMTGRXZCEECJnnHv2QXx8PFq2bCnabt26Na5cuSJW\nhsfj4fLly7C2tsasWbOQnJxc3WGWyd3dHTk5OaV2PXBpTfxz587B0dER27Ztw8iRI8Hn88Hn89G2\nbVvR7yX1u9erVw9BQUHYt28f/vvvP+jo6MDa2hqLFy/GqVOncPnyZYnvU1ZWlslUyvKcx8uXL2PK\nlCnQ0NCo9HHq1q2LwMBAbN68Gd7e3ujSpQvi4+NlEh8hhHAB51oKyqN9+/ZISUmBsrIydu7ciRkz\nZuDkyZMSy44bN050N9egQQNYW1uLBn0VfllXxbaioiJcXV0xbdo0XLlyBRkZGUhJSRErf/PmTZkc\nryQZGRlig9xKen9CQgJ+/vlnBAQEQEdHB3/++ado/82bN+Hn5yfaLq0+oVCIBQsWoFOnTnjw4AGi\noqKgpqaGv//+u1hiV5H4yvv5S9qvoaGBpKQkLFiwQCbHc3BwgK+vLwIDA9GrVy8cOHAA/fv3r3R8\n8tiOiIhAcHAwAFBrByHk/8imF0N2MjIymLW1tWjb19eXnTx5ssTyQqGQ6enpsS9fvhTbJ++PJxQK\nWYcOHZivry9bu3ZtlR2n6LiH7t27MzU1NWZhYVHquIdCf/75JzMwMGA//fRTlcVX0piCyox5qKjP\nnz8zR0dHtnnzZpnX/fTpUxYTE8MaNmzIwsLCZF5/dZL3tVIWrsdXG9GYAm6S9lrhXEuBpqYmgK8z\nEIyMjHD27FksXrxYrMzbt2+hp6cHHo+HEydOwMrKqsoefSvNQj48Hg8rVqzA9OnTcefOnSqJDyg+\n7iE8PBy+vr6YNWtWqe87deoUfvrpJ5w7dw4WFhZVFl9l1xSQhdWrV+Py5cs4fvy4zOs2NjaGsbEx\njh07hgEDBuDAgQPo16+fzI9DCCHVRkbJiUxFRESwli1bMjMzM/b7778zxhjbtm0b27ZtG2OMsU2b\nNjELCwvWtm1b5u7uzm7duiWxHll8PGnvcoVCIevRo4eopUAoFIr2XbhwQer4SsLn81nLli0lxhMd\nHc06d+7MADAej8fq1KnDWrduzf73v/+xhIQEsfJVGaOslBZjz549WVBQUJUeXygUsoEDBzJtbW12\n+fLlYvtrwjnk6FeBCNfjq42opYCbpL1WONdSAHxdW+DevXtir/n4+Ih+nzp1KqZOnVplx//w4QO2\nb9+O+Ph43Lp1S2KZz58/o6CgoMyR/zweD3/88QdsbW2hqqqKe/fuYcOGDVURtpigoCB069YNqamp\n0NPTA2MMISEh+PnnnyEQCJCamooVK1Zg3rx5yMvLw+3btxEaGoo+ffpAQ0MDDRs2hIqKCjIyMtCg\nQQMAVb/MsaydP38ez58/h6enZ5Uep7DFKiwsDD/++CPOnDmD9u3bV+kxCSGkSsgmN+Gmyny8w4cP\nM319fTZ27Fh24MABZmlpKbGlQFVVlamrq7NRo0axqKgosRYASXbu3MlatmzJHj16VNmPU2F+fn7M\n29ub3bx5k9nZ2TErKyu2bt061rx5c7Z161aJ7/n48SMzNjaW2xgAWUlPT2empqZs9+7d1Xrco0eP\nsrp167Jly5ZV63GlxfWvAq7HVxtRSwE3SXutcLKlQB7y8/Mxf/58hISEIDQ0FDY2Nrh//z5evHgh\nsbyNjQ3U1NRgaWkJLy8vaGpqYtKkSRg7diyUlIqfVnd3d4SHh+OXX37Bzp07q+WphvPmzYOpqSn+\n/PNP/Pbbb9DX18ecOXPg7u6OSZMmSXyPhoYGTExM8OzZsyqPryqdOnUK2dnZVfr8CUmGDBmCXbt2\nwcvLC0FBQWjWrFmVLj1NCCEyVVbWsHv3btapUyc2ZswY9t9//7E5c+aUWn7y5MksLi5OqkxFVsrx\n8RhjjOXk5DBnZ2fWu3dvlpaWJnpdKBQyOzu7Mu+a8/PzWXBwMFNVVWXGxsZs6dKlLDExsdhxPn36\nxHR0dJixsTFr06YNa9u2bblWSKyMd+/eMXt7e2Zpack6dOjA8vLymLOzM3N3dxe1auTn54t93p07\nd7IZM2bIdbZAZXzbZ18466M6VpMsSZcuXWrUOSzvtSIvXI+vNqKWAm6S9lops6Vg3bp1OHr0KIyN\njTFkyBCsWbOm1PKenp7YtGmT2BMJuSwrKwuDBw+Gnp4eQkJCsHHjRjRt2hQjRowAj8eDpaWlxJkN\nRUfOKyoqYuzYsXB3d8fVq1exZ88e8Pl8CAQCzJgxA0OHDoWlpSXU1dWhoKAg8S78wYMHlf4M386Q\n+Pz5M+7cuQNzc3MEBATA19cXvXv3hoKCAubPny+6cz1x4gROnTqFHTt2AABcXFwwcuRIODo6SjxO\nampqpWOsTseOHUN+fr7YUxWrm7KystyOzSVlPcekUHx8PDp37oxDhw7J9d+NkFqvtIzBx8eH1alT\nh1laWrLly5czW1tb0b7BgwezXbt2Mca+zgwYPXq0aF+bNm3Yx48fpcpWZKGMj8fev3/PbG1t2YQJ\nE1h+fj5jjLH79++z9+/fS33svLw8FhoaymbNmsWMjY1Zo0aN2IABA5i6urrEO0hNTc1KH6ukO/uu\nXbuy1atXMzs7O6asrMy8vb2Zh4dHpetTUFBghw4dqnSc1SE7O5upqKiwgwcPyjWOmtbaUta1Ulll\nPceEsa8tVj169GADBgxgISEh1RofqTxqKeAmaa+VUlsKtm3bhvDwcERERCA+Ph73798X7du+fTu6\ndu0KExMTBAYGIjY2VrSvWbNmSExMhJ2dnfRZSxVJSUlB//790atXL3z+/BkCgQCKiopo0aKFTOpX\nVlaGs7MznJ2d8dtvvyE0NBQnTpxATk6OTOovqqRWhgcPHmDTpk3o1KmTaB59eebrl7R+gLa2Nvz9\n/XHz5k38/PPPVbY2hDRCQ0PRunVrDB8+XN6hSJSbmyvvEKpNeZ9jsnHjRgwbNqxcS0YTQqpWuZ59\nwBjDw4cPxZZD1dPTwy+//IKePXsiMDBQNG0NAMzMzKRqDq9qcXFxsLOzw9ixY7Fu3To4OTnJ7KFC\nkvB4PAwePBh//PEH6tWrJ7FMZmYmHB0dsXPnTqSlpWHXrl1iSVhaWhoEAkGx9+Xm5iI7O1tine/f\nv8ekSZNw+PBhzJ8/Hw0aNEBoaGiZ8W7fvl20pPGSJUtEvx89ehRxcXGIioqCgYGBxKWL5aFw+d78\n/HwsXrwYq1atqpaBnJVx8+bNCj2KuyYrz3NMXr58iePHj2Py5MkAwNl/N0Jqi3LPPuDxeMWeTJiQ\nkABdXV28fPlS7HXGGBQUOPesJQBASEgIvL294eXlBX9/fwDgRB+msrIyEhIS8O+//0JJSQkKCgpo\n3LgxLC0tYWtri+joaMyZMwc9evQAACxatAj29vaYOnUqPn78KLFONTU1LFiwQLS9a9cu2Nraws7O\nDo0aNarUmvf6+vq4cOECfv/9d7i4uMDZ2RkrV66EtrZ2pT63LC1ZsgTa2tro06ePvEMRa20putaD\nQCCAvb09/v33X7E/mLWVn5+fKIljjJX69NMlS5aIfndwcBA904GQ2qzwpk1myupfMDExYe/fv2dh\nYWFszJgxotdjY2OZtbU1e/XqFfvhhx/YkydPRPucnZ3ZlStXpOrXkIWiH08oFLLVq1ezJk2asCNH\njrB//vlHLjE1atRIYl9zo0aNGGOMvXjxgm3ZsoVNnDiR2djYsHr16jFlZWWmoKDAlJSUmL6+PjM3\nN2d6enqsTp06zNzcnCkqKpZ7nMKOHTuYkZGRTJ7F8OHDBzZ58mSmpaXFgoODy1yroSrl5eUxTU1N\n0TgXLvvrr7+YgYEBu3btmrxDESnHV0GFlec5Js2aNWMmJibMxMSEaWhoMD09PXb8+PFqiY9Ih8YU\ncJO010qZ727WrBl7//49e/HiBbOxsWGMMfblyxfWtm1bduPGDcYYY6GhoaxHjx6i91hYWHBmoCGf\nz2ddu3Zl+vr6zMrKiqWkpMg1pqIPLyr6I2lKYlpaGjty5AgrKChgERERzNnZmdWpU4fxeDxmaGjI\nFi5cyP766y+mra1daqJRlFAoZM7Ozmz+/Pky+TwvXrxgTk5OrEOHDsze3p7duXNHJvVW1Pbt21nv\n3r3lcuyKGjZsGFu+fDlr2LAhi4mJkXc4jLGqH2j45MmTEgcaFho3bhw7cuRItcZHKo+SAm6q8qSg\nqMGDB7MHDx6UWiY2NrZcI9yrQ9E/kPXq1Su2rr+8lbUm/osXL9jy5cuZvr4+MzIyYg4ODszPz48J\nBAK2atUqpquryw4cOFDhke5v3rxhBgYG7NKlS0wgEEgVY6H8/Hy2adMmpqury+bOncs+ffpUrvfJ\nwr///suMjIwkPneAC749h6mpqUwoFLKTJ08yfX199vDhQ/kEVkRV/dEt6zkmRVFSULNQUsBN1ZoU\nlHfxovj4eKmCkpXy/IGUp5L+4D558oSNGDGCaWlpMW9vbzZp0iT29u1bJhQKWW5urqjckiVLmJGR\nEdPS0mKamprFflq0aFHisY8dO8aaNm0q1sJTkRglycrKYp07d2YjRoxgxsbG7N9//y33eyuqaIuL\npqYm09DQqJJFoGShtHMYFBTEmjdvXuoddHXg+h9drsdXG1FSwE3SXisVWua4Z8+e6NmzZ6lltmzZ\nUpEqa7VvB0rl5OTg119/xa+//opevXrh+fPn0NDQECtTp04d0e/Kysq4cOECOnXqJJr+VZS1tXWJ\nx/7xxx8RGhoqcUZDaTGWRkNDAzt27ICFhQXOnj0Ld3d3rF69GmPHji13HeX18OFDREZGir327TZX\nlHQOY2JicPfuXQwZMgTu7u44ffo0jb4nhMgVPfugmn27+iDwdbZGnTp1kJycjPbt2+PkyZNo2rRp\nsYTgW4UzC9q0aYOoqKgKx7J+/Xq0bdsWoaGhGDRoUIXfL4mFhQUAoE+fPlizZg0WLlwIAFWSGNR0\nVlZWUFNTQ+vWrdG1a1ds3boVU6ZMkXdYhJBajJKCaibpDhf4OuXzzJkzJS4xXJrK3l3Wr18fe/bs\ngYuLC44dO4atW7eibt26YmUiIiIqNfVLKBQiPDwce/fuxYgRI1CvXj1OTP2Uh5LOobq6Otq2bQsA\n2L17N7p27Yq+ffuiefPm1RwhIYR89d0nBXw+H0DJq/RxhZ2dXaUSgtKU1TUAAF27dsXcuXOxefNm\n5OXlFUsKKktBQQF79+4FAHTu3Bmurq5o27Yt1NXVRWXoiYFfCYVC7NmzB35+fvDx8cG5c+eoG4EQ\nIhecXGEoKioKrVq1wg8//ICNGzdKLDN//nyYmpqiQ4cOYiv/fatwYQd5//GJj49HUlJSiYuzFB0r\nICvXr1/HjRs3yiw3c+ZMtG3bVmyho0KyWCAmPT0dAoEAV69eRWRkpOjn226UisjPz5c6rupS1jlU\nUFCAqakppkyZgszMTAQHB1dLXIQQ8i1OthTMmDEDQUFBMDY2hqOjI9zc3KCrqyvaHxcXh+joaFy9\nehXh4eHw9/fHyZMn5RhxcXfu3EFeXh7at28P4Ovytunp6bh27ZrMj1VSK4iioiL69u2LzZs3Y8SI\nESW+n8fj4a+//kLHjh0REBAAf39/sTt6rklJSUFubi709PTQqlUrsX1cbxEqiaenJwBgx44dcHR0\nRP/+/aGvr18tx5Y0SJUQUjtxLikoz0NUYmNjMWzYMGhra8PNzU00mK0qSBoYCBRv+k5OTsazZ89E\nszOePHmCnJwcaGhoIDIyEocOHcLTp09hbGyMu3fvyjTG0lpBoqOj0adPH/B4vFIfEtSgQQMcPXoU\ndnZ2aNGiBVxdXQFUfkxBVcnJycHAgQPx8uVLXL58Gebm5pyL8VsViU9DQwP9+vWDn58f9u/fX7WB\nAXj27Bk6d+5c5cchhNQMnEsKSnqIStGkIC4uDu7u7qLthg0bIjk5GWZmZsXqK/wyrmz/dUkDA/Py\n8nD06FHR4Ln379/j0aNH0NfXFzWPR0VFQUlJCXw+H2PGjMGoUaMwdepUNGzYEID4mvhVdYfbrVs3\nbNmyBVOmTIGZmZmo5UISKysr7NixA4sWLUK/fv3EHnLFFaqqqhg0aBBevHhRY1sFSvPw4UPY29tj\n5cqVOH36NPr3719lx8rOzsbw4cMxa9YszJ49u8qOQwipOTiXFJQHk/DglJIGZhX+QU9KSsLs2bPR\nsWNHuLi4QEFBAaGhodDS0oKDgwPy8vKwe/dumJmZwcHBATk5Odi8eTMyMjIk1nvz5k14enpi2rRp\nUFVVRW5uLt6+fQsdHR3069cPTk5O+PHHH2FgYCB6iFFERARGjRolSlQKH2JR1dvjx49HvXr10L9/\nf6xatQrjxo0rsXzjxo2hoqKC5s2bw9DQEAoKCqLkQENDA/7+/hU+fkkyMjLE7qJLqy8vLw9RUVH4\n+PEjtm7divj4+Go7f9W5ra6ujgkTJsDY2BhjxoxBcHAwnJycZH688+fPw9PTE0pKSvj06RMIIQQA\neKykkW9ykpmZCQcHB9EAuWnTpqFfv35iLQUbN25Efn4+Zs6cCeDro5qTk5OL1VU0UahTpw6EQiH0\n9fXx7t076OvrIz09HV27doWysjIYY7h27Rp69eoFVVVV1KlTB1FRUXjz5g3ev39frO4OHTpg//79\nomMoKytDT08PqqqqMj0fsuTn54c///wTb9++hZqaWonl7O3tER0dXex1Pp9fqadxfdsFU1BQgGvX\nrqFbt274999/y1XH5s2bkZqaihcvXkBHRwdr1qypcBw1zY8//ggTExOsX79epvUWFBRgypQpSE5O\nxunTp1GnTh2JT0HlEq7HVxu5ublh0KBBcHNzk3copAhprxXOtRRoamoC+DoDwcjICGfPnsXixYvF\nytja2mLWrFnw8PBAeHh4scFmknTu3Bnnz5+HgoICBAIBnj9/LhqwlpeXB4FAAA8PDwgEAuTk5ODj\nx48wNDTE/v37JSYFGhoa+OGHH6T6rNXdF7527Vrcu3cPP//8M3777bcSy8n6sdeSum0iIiIwePBg\nhISEYNiwYWXWMWnSJFy5cgXDhg3DgwcPitX1vYwpKPTx40ekpqbiypUrcHNzg62trUxi+fLlC9zd\n3fHu3TscP368Sma9EEJqLs4lBcDXlfZ8fHwgEAgwffp06OrqIigoCADg4+MDGxsbdOvWDR07doS2\ntjb27NlTrnoL/9gpKyvDzMxM4hiEb507d67yH4RjFBUVsW/fPnTs2BEdOnRAVlYWJkyYIPMkoDwc\nHBzQq1cvhIeHl5oUMMbA4/HA4/Ewb948LF26FPXr16/GSOWjfv36uHTpEvbt2wdvb29cvXoVysrK\nUtWZkZGBwYMHw8DAAOHh4VBRUZFRtISQ7wUnkwI+n4979+6Jvebj4yO2vWrVKqxatarKYylpMJss\nBrnJ4+5WR0cHR44cQd++fTF8+HAIhUK5JAUA8Mcff8DCwgIxMTESR8ALBALY29vjxIkTOHDgAPLz\n80VT94qSxXks7yyTyqhsfDweD6NGjcLff/+NtWvXYt68eZWO4cWLF+jXrx969+6NwMBAuf2bE0K4\njZNJgSxJu6KhvBc9qgrt27fHb7/9hlWrViE7O7vcd94FBQUyjUNbWxvr1q3DuHHj4Ofnh8mTJ4vt\nV1ZWxt69e5GRkYGAgABcunQJioqKMo2hUEmzTOSNx+OhSZMmWL58OVxdXWFiYlLhOhITE+Hk5IRp\n06bB39+fVkskhJTou79d4MqKhpJUZtCerIwbNw69evXCwIED8eTJE/Tq1Qt5eXkAviZQfD4ffD4f\nbdu2hb29PfT19ZGcnIwtW7bgyZMnMotj5MiRaNq0KcLCwiTuNzY2xrhx47Bw4cISE7uKnsebN29i\n3ngECSwAACAASURBVLx56NatGywtLdGlSxckJCRUNPRyk/bfecuWLZg3bx6mTp1a4QFE0dHR6Nmz\nJ1auXInZs2dTQkAIKdV331JASrZx40ZMmzYNLi4uWLNmjWjQWdEEqnCQnFAoxKRJkxAYGChqfZEF\nHo+HP//8Ex06dMCDBw/QokULnDhxAklJSZg5cybWr18PJSUlTJs2TepjxcfHIyAgADdv3sS4ceOw\nbNkyaGlp4ePHj5g8eTI+fPhQ7D3p6emicQ3yoqamhtmzZ8PAwABt2rQRrXNRqKQujpCQEEyePBn7\n9u1Dnz59qitcQkhNxr5j3/nHkwmhUMjWrFnDDAwMWEREBGOMscePH5dYdtq0aax9+/YsLS2N5ebm\nyiyOdevWMT6fz/777z/2+vVrlpCQwG7evMl0dXVZcnKyVHW/ffuWjRgxgjVp0oRt2rSJ5eTkiO1f\nsmQJa968OQNQ7EdNTY3Z29uzBw8eSBWDLLRq1UpijHw+v1jZjRs3MkNDQ3b9+vVy1c31a4Xr8dVG\nrq6ubN++ffIOg3xD2mvlu+8+cHBwgIODA7y9veUdCifxeDzMnj0bO3fuxMiRI+Hl5QUbGxvw+XzR\nuSv88fHxwe+//47evXujR48eGDdunMyeOTFt2jR8/vwZP/30EwoKCmBmZgY3NzcEBgbC1NS00vUe\nOnQIVlZWMDY2xsOHDzF16lTweDzExMSIysyZMweNGzeW+P4mTZpg0KBB6NKlCzZs2AChUFjpWKSl\np6dXZhmBQICZM2di48aNuHjxItq1a1cNkRFCvhffffcBFwePFeLS/Pq+ffvi7t27WLBgATIyMhAV\nFSWxHI/Hw6pVq6Cmpoa9e/fKbAaIgoICOnTogKNHj0JNTQ2zZs1Cu3btMGbMmDLfK+k8ZmVlwcvL\nCwkJCfjnn39gZ2cn2peeno7169fDzs4OPB4PqqqqEscrMMaQmZkJb29vODs7w8PDAxEREdi9e3eF\nHhhVXf/OL1++xMiRI1G/fn3ExMRAW1u7yo9JCPm+fPdJASk/bW1tbNu2DTdu3EBcXFyx/enp6bh7\n9y6MjIywePFi1K1bFz179sR///2HN2/ewMDAAMbGxpU6NmMMHTt2REFBAYYOHYpXr17h7NmzlerL\nf/HiBQYOHIhOnTrhxo0bUFVVxfr16zF06FA0bdoUjRo1wsGDB8XeU9ZA1Hr16uH8+fOYMmUK7O3t\nERYWVqxvX57Onz+P0aNHY+rUqViwYAFNOSSEVAp9c8gRV1oJvlXSUs0pKSno3Lkz9PT00KhRI5w9\nexZNmjRB+/btceTIETx69KjSx1RQUMCECRMwYMAAREZGws7ODocOHSrXe4uex+vXr8POzg6jR4/G\n9u3bRZ+lUaNGUi39yRhD//79MX/+fDg5OYHP5+P169cVjq8qPH/+HKNHj8bu3buxcOHCCicE5f0c\nhJDvHyUFpNwsLS1x4MABfP78GXFxcRg9ejSUlJRgamqK3377DXPnzsWpU6cqtJ7Bs2fPRNMR79+/\nDx8fHyxYsABXrlwptmBVWUJDQ+Ho6IgNGzbA0tJS9GwM4OvURyMjowrVVxSPx8P+/fvRokULLFu2\nDKNHj4a9vT3evn1b6Tor6s2bN9DU1ISmpibq168PZWVl8Hg8vHr1CvHx8ejdu3eF6zx27Bjatm1b\nBdESQmqiWtN9cPv2bbFHFXMBl8YUlIeCgoLoiX1NmzbFwIEDYWhoCEdHR4SGhmLUqFEYM2YMVFRU\nMGjQIGzduhWKioqlrhY4ceJEPHv2DE+fPkXfvn3x66+/wsPDA8+fP8fMmTOxY8cOiVMCi9b54cMH\nfP78GSkpKejfvz9cXFyQkZEBKysrmX7+Ro0aiX63tbVFVlYWBgwYgIiICGhoaJT4Pln9OxsYGBR7\n7gPwtWtDV1e3QnXl5ORg/vz5OHLkCE6fPo1OnTpJHR8hpOb77pOCLl264Pbt29DQ0EC9evXkHU6N\nUHTQXdFE6tvBeA0bNoSjoyMAYNCgQTh58iSmTp0KAIiNjYWJiQmcnJyQkJCA2NhYicfq1KkTGjVq\nBAcHB8yZMwceHh4AgE2bNqFdu3bYsGEDDh06hKioKLFm8ZJWIExLSwMANGjQoEoTwKioKIwZMwbv\n37/H8OHDceLECSgpyedy4vF46NOnD/755x/o6OiUWrbwEeFLlixBt27dcOvWLRqQSAj5P9LPiuSu\nwo+XlZXF+vTpwxwdHdm7d+/YmTNn2Lt37+Qc3fcpPz+frV69muno6LDRo0ez3r17MyUlJYnz6y0s\nLNju3btZ48aNWWBgIDtw4AC7ceOGqK6lS5eyBg0a/L/27jsqiqthA/izS68WEEGKIChNYAEBjQU0\nqGDDiL42rAki9miMxprYEiUa8qqJYo09auS1IUZQhCBFsGCoNiRSVpBeFli43x+E+VhZirKwo97f\nOZzjzszOPjvuzN69bciFCxcIIYTs3buXREZGEkIIcXZ2bvWY/fZUXV1NRo4cSebPn09qa2vb5TVq\nampITEwMcXJyEvuehwwZQlatWkV0dXXJlStXxO4jNTWVbNiwgejo6JBhw4aRqKgokfVsvxSwPd/H\niM5TwE5tPVc+ij4FqqqqCAoKgo2NDezt7fHHH3+IvR0y1XYyMjL4+uuvERYWhqSkJOTl5TXZwS8x\nMRELFy7E3r178eWXX0JRUVHk17ajoyO2b9+OhQsX4sWLF7CysmKq8IuKijrk/bREVlYWhoaGCA4O\nxq5du9rlNWprazF79mzEx8eLXV8/TPT48eNYsmQJHBwc8PXXX2PHjh3w9fWFpaUlXFxckJ+fjz//\n/BOhoaEiQzQpiqLqffDNB/VkZWWxfft2DBw4EN7e3ujbty/69OmDiooKyMvLS6Xq933oU/CuGfv2\n7Yvo6Ghs374dDx48aHI7PT09bNiwAUKhEJ999plIE8GIESMAAOXl5XB3d8fIkSMxevRo/Pjjj0hK\nSnrrTO1l3bp1WLFiBYYOHQojIyNMmDBBZP27HEMfHx+MGTMGAoEAfn5+UFVVBY/HQ1xcXJPPGTp0\nKNLS0nDr1i3ExMTg1atXMDMzw+zZs+Hg4ECHKVIU1aKPplBQb9y4cbCyssLEiRMREREBU1NTqKur\nY9WqVdKO9sGRl5fH+vXr8d1334kdkSAjI4O///4bQUFB2LhxIzZs2IAZM2Zg2rRpzEiB4uJi8Hg8\ndOrUCb/++iuOHj0Kb29v9OvXD3fu3OnotySWnp4eAODixYsYPnw4FBQUMHr06LfaR3x8PMrKykTu\n/TB9+nR88sknWL58Of7zn/9g/vz5YidNatjXQ0ZGBq6uru80EoGiKIpDmqrblYKSkhJ4eXnh/v37\nsLOzw4kTJ8T26jY0NIS6ujpkZGQgJycndqIdoK5atam3JxAI8O233yIgIACfffYZ1q9f/063paWa\nV15ejs6dO6O6urrROllZWVRVVTH/TxERETh58iTOnz8PLpeL2tpaCAQCWFtbY9iwYXjw4AGEQiHT\nobGpEQ3SvCOmr68vzpw5g/DwcFhZWTW7bVFRETp16oTi4mKsXbsWoaGhyMrKgpubG8aPHw93d3d0\n6tSpQ3I3d660VXh4OHx8fCAUCrFkyZJGN7c6efIkduzYAQCwtLTEt99+26hTa3vmo97N1KlTMW7c\nOEydOlXaUagG2nyutLFPg0Rt376dLFq0iAgEArJw4ULi5+cndjtDQ0Py+vXrFvfXmreXl5dH1q5d\nS7p27UomTJhAvL293zo3Jd79+/fJJ598QhQVFcV2kANA5s+fT0pKSkSeV1NTQ7Kzs0lubi4RCoXM\n8urqajJ27Fji4eFBgoODO/rttNqpU6eIkpISsbe3J87OziJ/9Z+vBw8eECcnJ7JixQrStWtXMnny\nZHLt2jUiEAikkrk9LwU8Ho/cvn2bpKenE1NT00adfO/cuUMKCwsJIYQcPXqUeHl5dWg+6t3Qjobs\n1NZzhVVnmqenJ9P7PD4+nkycOFHsdoaGhiQvL6/F/b3NwXn9+jVZuXIlUVdXJ59//jl5/vx5q5/7\nrm7dutXur9FWb5OxvLycuLi4kKKiIhIYGEimT59OunTp0uToA1VVVTJp0iSipaVFNm/eTHx8fFr8\nUiwrKyM8Ho/06NGDDBkyhDg7OxMbG5tGX7rSZmFhIfY9Dx48mMTExJApU6aQrl27khUrVpD09HRp\nx223L93CwkLC4/GYx4sXL25yhAQhhOTm5hJ9ff0Oy0e9O1ooYKe2nius6lNw9+5dmJmZAQDMzMya\nbRYYNmwYjIyMMHfuXIwbN67Nr921a1fs2LEDq1evxk8//YR+/fphxIgRCAgIaHZimo/dunXrwOPx\nkJubi7S0NFRVVcHAwAD29vbw9PSEn58fhg4dipycnEbP1dbWxtmzZ5GUlITNmzfj6tWr0NbWxtKl\nS6GoqAiBQIAuXbqIPEdZWRk3b96Evr5+kzdtYoOm7otw7949TJ06FQsXLsT+/fuhrq7ewck6VsNz\nGgAsLCwQHR3dZJ+LgIAAjB07tqPiURT1hg4vFAwfPlzsF8TWrVtb3Q4SGRkJHR0dJCcnY+zYsXB0\ndIS2trbYbWfPns30FejcuTN4PB7TEzwsLAwAGj3evHkzpk6dimHDhkFLSwsWFhZQVVVFYWEhs58+\nffpg2rRpYp/f2sf1y971+e31+NSpU0hLSxN5v0Dd0E5XV1eUlZUhKSkJoaGhKCoqgp2dHSwtLSEj\nI4NRo0bhf//7H7p164awsDCkpqYiJSWlyderf/+nT5/GyZMncfLkSZiZmcHb2xtRUVFYv3692LxW\nVlaIjo7Gm+ozs+F4iqOtrY20tDRwuVyp5gsLC8PRo0cBgDV9aUJCQnDixIkmO5B+++23zL/rb+dN\nUR+7+uuoxEimwkIyJkyYQO7du0cIISQuLo54enq2+Jwvv/ySBAQEiF0nibdnbm7OiklyOlJTEwNp\namoSJSUl8umnn5JDhw6RlJSUdpmwJzY2llhYWBBPT0/C5/MJIYQcPnyYhIaGMttoa2uLzaitrS3x\nPO+CLZMrtVZ7XQrebD5YtGiR2OaDhw8fEmNjY/L48eMOzUe9O9p8wE5tPVdYNXDZyckJhw8fRkVF\nBQ4fPix2gpXy8nKUlJQAAHJzc3H9+nW4ubm1WyYtLa1227dES3dtUFVVhZSUFFy/fh0HDhzA8+fP\nxW7XuXNnZGdnIyQkBHPnzoWpqek73dq4JQ4ODoiPj4eJiQmsra1x+vRp9OnThxn6BwBlZWVin1tW\nVoaHDx8iPT39rW7MRLWP+tET4eHhSE9Px40bN+Dk5CSyTUZGBjw9PXHy5EmYmJhIIyZFUf9iVZ8C\nX19feHl5wdTUFHZ2dti+fTsAICsrC97e3rh69SpycnKYyWE0NDSwYsUK6OvrSzP2eykrKwvHjh3D\nn3/+ibt370JbWxs9e/aElpYWiouLxT5HV1e3w4bIKSoq4ocffsD48eOxZMkSFBYWYtasWejfvz90\ndHSaLBSUlpZi+vTpKCoqQnl5OVxdXTF58mR4eHhARkamQ7IDrb9/xMfA398fPj4+qK6uxpIlS6Cp\nqYn9+/cDqJukadOmTcjPz8f8+fMBoNlhxhRFtS9WzVMgaZIY2+zi4iL2xjv6+vrIyMho076lIT09\nHevWrcPVq1cxadIkjB8/HnZ2dujevTs4HA6qqqpgZWUldg4AZ2dnqdRuEEIQGRmJCxcu4N69e8jO\nzsbTp0/F1gRoaWnhn3/+QUxMDHr16oXr168jICAABQUF2LRpEyZNmkRn9hOD7fMAsD3fx4jOU8BO\nbT1X6NXxHZWXl6OqqkraMVqttrYW33//Pezt7WFiYoIXL14gICAAo0aNwsSJE5GYmAigbhbChrcI\nZgMOh4NBgwZh165dTOfFQYMGid22oqICL168wP79+6Grq4u5c+fiwoULGDp0KH788Uf069cPQUFB\nqK2tFXnevHnzmM5rDf/mzZvXEW+RoiiKFVjVfMBG4qp7a2trkZGRgVGjRuH48eOYPHkyrly58tbD\nyzrq3gd5eXmYMWMGiouL8eDBA+Tk5CAxMREDBgwAANy4cQNKSkrM9u9z1beysjLmz58Pe3t7keWf\nfPIJfv31VwQGBmLJkiXIycmBj48PXFxcYGRkhOTkZPz111/tkonN97iIiYnB6tWrpR2DoiiWoIWC\nFjQ1ZW5NTQ2+/vprDBkyBLt27WLtePOrV6/Cx8cH06ZNw9atWyEnJ4ekpCSRaYcbFggA0ffM1i+0\npgouxsbGePnyJSIiIlBRUQElJSX06NEDM2fOBABMmDABI0aMwO3btxEbG4tffvkF8fHxyM3Nlcr7\nkBY+n481a9bg2rVr+OGHH1jT6ZWiKOmifQra6MiRI1i1ahV+++03uLu7w9/fH1paWswcBh1h3rx5\njfoAVFdXIzc3F0KhEN999x0OHz6MW7dudVgmaaqqqsKcOXPw/PlzXLx4ERoaGi32Ixg0aBAiIyMb\nLbewsEBCQkKHdlJsT3w+H35+fjh8+DDmzJmDjRs3Ql1dnfVt9mzP9zGifQrYqa3nCq0paKM5c+ag\nT58+mDRpElasWIHJkyd3+MUrLS1NbGfIHj16IDU1FSoqKnB2du7QTNIkLy+P48ePY/369bC2tsbQ\noUNx6tSpZp/T1K2z//nnH9jZ2WHHjh0YOXJke8RtNXGFP6Dlm0CVl5cjPDwcFy5cwPnz5zF9+nQk\nJCSIDPGkKIoCaKFAIgYOHIioqCh4eHjg/v37+OWXXwDUteUvWbIEx48fF/tLs72r5vX19Zkpmutv\nRfy22Np80JC4jFwuF1u3boWhoSHWrl2L8PBwDBky5K33bWlpiZycHCxevBiGhobw8/ODjY1Nm/M1\np6KiAikpKUhPT0dWVhYIIVBWVkZMTAwSEhKafS6fz0doaCiio6Px9OlTpKWlITMzE7a2thg/fjwe\nPXoEXV3dt8pPUdTHgxYKJKRnz56IjIzE8uXLwePxcPz4cTg6OsLb27tdqp6zsrJQW1sLPT29Jmsm\nFBUVJf667xtvb28YGRlh4sSJ2L59OyZMmCB2roWmOlH26dMHly9fRqdOnRAQEIARI0bA19cX69ev\nl9j/66tXr3Dt2jVERUUhNjYWKSkpMDY2Rq9evaCrqwsOh4PS0lK8ePFC7POfPXuGWbNmIT4+HpmZ\nmXBxccGgQYPg6uoKExMT9O7dG3JychLJSlHUh432KWgHFy9ehI+PD+bNm4f169czF2Q/Pz9ERkaK\nzM9fr6Uq4L/++gslJSVwd3cHAOzevRu5ublQVVXFt99+i4qKikbPkda8Amz06NEjuLi4oF+/fggO\nDn7nmRinTJmC5ORk9OjRA+fOnWvTzbJevHiBVatWITg4GMOHD8fgwYPh6OgIGxubRp0/g4KCMGfO\nHLx69arRfoyMjLB+/Xr07dsXdnZ271RYYXubPdvzfYxonwJ2ovMUsFB9M0JsbCxsbGywc+dOREVF\nwdLSErm5ubh9+3ajv9TUVPD5fGYfgYGB2LBhA4C6NuHExEQEBQXB29sbDg4OWLVqFS5cuID09HSY\nmppK662+N6ysrPDw4UPw+XwsWLDgnadA3rt3LyIjI9GjRw8MHz4cr1+/fqf9/P333/jkk09gZmaG\nzMxMnDt3DkuWLEH//v2hpKSEsrIybNu2jTm5hw8fLnK3wYYMDAwwZ84cODg4fDAdIimKkg7afNBO\ndHR0cO3aNYSFheHMmTPMnQcFAoHY7dPS0jBp0iR88cUXUFVVBZ/PB5/PR//+/fHo0SNYWFjA1tYW\ntra2mDNnDqysrKCmpgagrgPa21SJv433tU+BOHp6eoiIiMDYsWMxYcIE7N69+637WmhoaAAADh48\niFmzZqFXr15ITU1t8i6d4vLdv38fo0aNwq5du0R+ZZWXl0NeXh6ysrJQUlKCnJwchEIh5OTkICcn\n1y73maAoimqIFgraEYfDwdChQzF06FAAddP11ndKfJOsrCwsLS1x48YNlJWVQV5eHtbW1pg2bRoc\nHBygrKzc5Os01+xAiVJTU8PVq1fB4/Ewb948BAUFvdO0xxwOB0eOHMHKlSsxZMgQhISEtKqAER0d\nDQ8PD/z666/MPTzqTZw4EevXr8eAAQPA5XKxcuVKkfXN9XugKIqSBNqnoIM1dS8F2v7fsUpLS+Hu\n7g5zc3Ps27evTfdD8Pf3x48//ggTExPs2bMHffv2FbtdeHg4Jk6ciCNHjmD06NG4efMmysrKMHbs\nWAB1c0tIq0MgG8+Vhtie72NE+xSwE+1TQFHvQFVVFUFBQUhJSYG9vT3i4+PfeV/Lli3DwYMHkZiY\niN9//x0CgQBmZmbo3Lkz86eqqgoXFxfIy8tj9OjRAOpqLRo2+9ARAhRFSRttPuhg79t9BT6kPgVv\nUlNTw59//omRI0di5MiR6NOnD+Tl5UW2aWlUSD03Nzc8evQICxYsgLGxMXJzc0Wmkq6Xk5PD/NvB\nweGtM1MURbUnWijoYO/DfQU+JoqKiggLC4ORkZHYvh5vKi0thbKyMtPcEBwcjE8//RRycnLQ1taG\nhYUF1q5di4EDB4p9fluGMFIURbU32nwgRe9DgeBjyMjhcGBoaCh2XUJCgsiww759+4o8PnbsGMrK\nypjHOjo6MDc3pxNHURT1XmJVoeDcuXOwtLSEjIwM7t271+R24eHhMDc3R+/evbF79+4OTEh9bIyN\njZmhnwCQnp6Obt26MY9PnTrFNAEBwMKFCyEvL9/k0NPy8nKxk1dRFEWxAasKBVZWVggMDGxxjvql\nS5di//79CAkJwd69e5GXl9dBCSXrfRht8LFnTE9PR2hoKIRCYYvbVlVV4Y8//oCNjU2TkyNxOBxY\nWVkhODhY0lEpiqLajFV9Cpqasa2hoqIiAGAKDiNGjEBMTAzTo5uiJKlz587YtGkTZs2aBVtbWxgY\nGKBLly7o3LkzlJWVUVZWhn/++Qf37t1DYmIi7OzssG3bNqxatYrpVCgUCpm7MGppaUEoFGLevHlw\nc3PDzp07RWoiKIqipIlVhYLWuHv3rkjhwcLCAtHR0e9loeBjaK/vCJLI2NzEQAEBAcjIyMCjR4+Q\nmZmJgoICFBYWgs/nQ1lZGRYWFpgxYwZsbGyYjoQeHh5Nvhafz4eSkhKWL18Oa2trHDp0CMOGDWvz\ne6AoimqrDi8UDB8+XGRYVr1t27Yxk7hI0uzZs5lOZJ07dwaPx2O+ROqrnelj+jggIKDJ9UDd/QWe\nPXuGPn36SOz1vby8UFNTg5kzZ2L8+PEYM2YMFBUVO+T9hoWF4ejRowDQZCdLiqI+QoSFXFxcSHx8\nvNh1hYWFhMfjMY8XLVpErly5InZblr49xq1bt6QdoUU0Y9s1lU8gEJAZM2aQ9PR04uXlRYyNjUls\nbGzHhvsX288Vtuf7GE2ZMoWcOnVK2jGoN7T1XGFVR8OGSBPTNNbPABceHo709HTcuHEDTk5OHRmN\noiRCQUEBx44dQ8+ePXH8+HFs374do0ePxo0bN6QdjaKojxSrCgWBgYHQ19dn+gi4u7sDALKyskT6\nDPj7+8PHxweurq5YsGABNDU1pRW5TT6W9vr2xvaMrcknFApx4sQJHDx4EF5eXrh+/Xr7B6MoinoD\nvSESRbFEdHQ0nJycEBUVhfHjx+PSpUvo379/h7w2288Vtuf7GNEbIrETvSHSe+xjnwNAUtiesbX5\n+vfvDw6Hg08++QQ//PADPDw8kJyc3L7hPhA7duxAbW2ttGNQVLtKS0vDhQsX2vU1aKGAoliGEIIT\nJ05g1apVcHd3R1ZWlrQjsd4333zT7jUJZ86cadUkVh+iK1eu4IcffmhxuzFjxny0M3a+ePECERER\n7foaSUlJOHbsWLu+Bi0USBHb28IBmlES3jYfh8NBaGgoli9fDh8fH7i7uzOTdlGSl5aW1uy06vXm\nzJkj9s6X7zM+n489e/agoKCgxe0eP36M7Oxs/P33343W37p1C0KhEDExMS0eo5SUFPz8889tys1G\n0dHR2LNnT4vbXblyBaWlpR2Q6N3QQgFFsRCHwwEArFq1CkpKShg1ahQqKyulnEr6ioqKYGlpiaio\nKPz2228i63bs2IGamhrU1ta2qtYgIiIChYWFuHbtWqN9FRcXIzs7m3n88OHDVuXbtGkTsrKyUF1d\njfT09Ebrq6qqsHTpUpFl2dnZ2Llzp9gv24YKCgpw7ty5Rstfv34NAwODRss3b96MXbt2wdfXt8l9\nZmVlYePGjTA3N29ym4qKCly+fBkAcPPmTXz//feNtvHw8EB5eTlqampw/PjxJveVnp4Oa2trbN26\ntcltAMDU1BTff/89QkJCRJZHRUXB1dW10fZFRUX4/fffm90nAFy8eBG7d+8W+Xw0VUiprKxERkYG\nAOD69esIDAxscf8FBQUin5snT540mvJ88eLFyM3NRWpqKtLS0lrcZ/3nOSUlpdGdXFesWIGwsDB4\nenq2uJ/WooUCKWJ7WzhAM0pCW/JxuVz4+vpCU1MTlpaWcHZ2houLi8jfvHnzJBdWwlpz87JvvvkG\nvXr1gr29PVJSUprdHyEEz58/x5o1a3Dz5k2RdRs3bkRNTQ3mzZuH6dOnIygoSOw+Xrx4galTp2LZ\nsmV4+vQpszwnJwcVFRUAgEuXLmHlypXMOj8/P+bi3r9/fxw5cgTh4eF48uQJfHx8mALbmTNnkJeX\nh5cvX2Lo0KEA6i7qxcXFAOpGmRw4cIDZL5/Px9mzZ+Hv74+vvvoKoaGhIlkzMjKwY8cOJt+GDRuY\ndbm5uRgwYAAWL16MoqIinDx5EtXV1VixYgWAukJSdnY2srKyUFxcjGfPnuH69euoqqpq9hi/qbKy\nEtevX2e+wF6+fIktW7aAEILa2lqMGzcOhBBkZWWhsrJSbMGlJfVThSckJAAAHj9+jJCQEHz//fdI\nSUnBL7/8gpycHNy5cwdPnz7FihUr8Nlnn4kci7Vr1wKoKyDU/7uh7777Dtu2bcOSJUsQEhLCaVlR\noQAAHndJREFU9EHJzMzEpUuXANT9/9T/ik9LS2NGvcXHxyMmJobJ5uXlBQDYu3cv9uzZg9WrVwMA\nkpOTRZoQ7O3tmf3l5+eL1PidOnUK+/btw5QpU5o8Lhs3boSLiwsuX76Mv//+u1HzxJEjRzBx4kSJ\nNjG+d9McU9THZtasWfjPf/4DHR0dkS+x90H9zct69uyJkSNHYurUqSJDiGNjYxEREYG4uDhcv34d\nX331Fa5cuSJ2X19++SW0tLQA1P16FQqFuHHjBg4dOgRCCPPrLzExEXw+n7k/yrlz5zBq1CioqKgA\nAAQCAe7duwdZWVkEBgbixIkTGDBgAKZNm4YePXpg+fLljV67vkBw4MABJCQkYM+ePbCxsYGtrS2O\nHDmC6dOno7q6GtnZ2Zg9ezaGDx8OoK5AqK2tjSFDhuDVq1ci+zxw4ADy8vKYL6QbN27Azc0NpaWl\n0NXVxdatW1FQUICSkhKR2oXk5GT07NkT1dXViIuLQ0FBAQghmDt3Lnr27Im9e/di586dKC0txZMn\nT1BSUgJDQ0PY29sjPj4ekZGRePLkSbMzyP7111+wtLREly5dmGXR0dGws7PDw4cPkZiYiNraWty9\nexfp6emQkZHBjRs3GtVmpaSkQEZGBr179xb7OpWVlfj9999RW1uL0NBQnD59GrNmzQIhBCUlJRAK\nhcjIyMD//vc/pKSk4MqVKxAIBAgNDWVuhJednQ0+nw+grtCYn5+PgwcP4urVq9DQ0MCxY8eQkpKC\ny5cvM7U3o0aNwp49e8Dj8UTyxMXFYdmyZTh48CCzraurKx48eIA+ffogMzMTu3btwh9//AE7Ozuc\nP38excXFUFBQgLq6epM3Qtu3bx+uXbsGFxcXFBUVwdvbG506dUK3bt0aNV2lpKSgsLAQ/fv3R0xM\nDBITE5GWlgZDQ0O8evUKRUVF+PLLL+Hr64va2loIhUJUVlZi586dEmneojUFUsT2tnCAZpQESeRT\nUlJC37592x6mAzW8eVnPnj2Zm5c1FBMTg4kTJ6Jr166YOnVqs6MtDh06BD8/PwB1v+L4fD5++eUX\n/P7778yv1sePH+Pu3bvIz8/HnTt3EBwcjOXLlyM/Px+vX78WqQIuLCxEcHAwCgoKkJubi5cvX+Ls\n2bON7rqalZWFly9fMm3mtbW1yM7ORlpaGk6cOIHq6mpcuXIFt2/fRlVVFVJSUpCYmAhCCNasWYOj\nR4+ivLyc2R8hBGlpafD398e+ffsA1DUr1NeCTJw4EXw+HzExMXj69Cny8vKYoamVlZXg8XhITU1l\n9vfkyRMAQHV1NXbu3CmSPSUlBUVFRSgtLUVFRQUIIdi7dy/Wr18PAHj+/LnIqI2kpCTcvn0bnp6e\nOHLkSKP/g4iICOaLr/4eIEBdbcibVeEFBQVYvXo1vvjiC1y7dk3kV3J1dTXy8/NRXl6O+fPnIz4+\nntlP/fF/s9392LFjEAgEqK6uxuPHj5nl27ZtY37Rv3z5EgMHDkR5eTmePXuG2NhYXL58GSNHjgQh\nhNknIQQLFizAkSNHUFRUJHIM0tLSmLvwCoVCJCQkoKKiAmlpacjMzERQUBCqqqpw4MABCAQCpKam\ngs/nIzc3F9nZ2cjPz2dqhuqFhobi5s2buH37NmpqahAfH4+bN28yeUpLS3HmzBkAdU00v/32G7Zt\n24bi4mLk5+fj8uXLePjwIfLz85GUlISzZ88iMjISFRUVqK6uRlVVFY4ePdqqPg0tofMUUNR7wsXF\nBbdv32603NnZuc1NKO1xroSEhODQoUM4ffo0gLpfS5mZmdi8eTOzzYwZMzBjxgyMGDECQF3V/MmT\nJ2FsbNwon5mZGRQUFFBVVYXq6mqoqKiguLgY1dXVqKmpgZycHHR0dJhf5GpqaqisrISsrCwMDAxQ\nU1MDPp8PNTU15nkyMjIQCARQU1Njvqj09fVBCEH37t0B1H3RVFVVQSAQgMut+x3F5XKhpaWFrKws\nlJWVQUtLC2ZmZkhMTGTa1lVVVaGgoAAul4uamhoYGxsjKysLOTk50NHRQXl5OfLy8tC1a1cIBAKU\nlJRAV1cX+fn50NHRQWZmJgghUFFRgZ6eHoqLi/Hq1SsIhUI4ODiAz+cjKysLhBDmjp3KysoghMDc\n3BxpaWkghEBfXx/Pnj2Drq4uysvLUV5ejh49esDAwABPnjzBixcvoKKiAm1tbRQXF6OmpgZFRUVQ\nUVGBUChEly5dwOfzweVyYWNjg9jYWMjKyqKiogKKiorMcXR3d0dQUBDU1dWhqqqKkpISyMrKQiAQ\nQFZWFmpqaujcuTNSUlJQU1MDe3t7aGho4M6dO5CTk4OGhgZevHgBPT098Pl8cDgcGBkZobS0FIWF\nhSgsLISysjK4XC4qKiogLy8PHR0dyMvLIzExEXJycjAxMUFxcTFTcyAjIwNNTU28evUKKioqyMvL\ng6qqKrhcLsrKyqChoQFZWVlUVlZCTU0Nenp6SEhIgJqaGjgcDkpKSlBWVgZ5eXl06tQJtra2CAkJ\nQXV1NZSUlKChoYHXr1+Dw+FATU0Nubm50NDQgJKSEkxNTZGamoqamhoIhUK8evUK3bp1g0AgQG1t\nLTgcDlRUVFBdXY3OnTujoKAApqamTG1AdXU1uFwuCgoKmNq10tJSlJaWQlVVFSoqKkxzV6dOnVBT\nU4OKigqkpqa26VymzQdSFBYWxvpfuTRj27E9nzQ1rPavV9/J8k0pKZMbPHL590/Uv/3CGklMbH2m\n1jbPNvixjpwc4N/m8CY9ePD//37+/P///fLl//+7vo/as2eiz01KEn3c1Pus17DCpf69N/wh/+hR\n4+eIW/am5rp87N3b8vMbEtMPEwDQoBKgxf+3NyuW3jxuAPBvRYpYDY99a7w5SEVca179PqOjG6/L\nzGx+/031NX3zMynaEhX271+975p/kRbQ5gOKes+9bcexjuLg4CDScTAxMbHRDI1OTk5IavCNl5ub\ni169eond3969Wpg+/Qk+/fQvBAdXwtbWDkOGOIMQIDDwf3By6g8NDU34+MzHzZu34OIyFJGRd6Cl\n1R329v3A5cqgS5euWL9+A37++b8gBODxbKGp2Q35+QUgBDhw4CA+//wLEALU1NQC4MDa2gaysnKI\ni4uHt/c82NnZQ1VVDQMGfAIezxaZmVno1csYRka98OjR38jKysYPP2yHnp4+lJVVYGVljbi4eNTU\n1MLFZShsbHjw8poBQoC4uHhwuTIYPnwELl++AllZORQUFIIQIDMzC69e5WL16m+wbdv3MDe3QGJi\nEggBli37EoMGDYaLy1AsWrQYhACEAKWlZeDxbAFwcP78H5gwwZNZ9+ZfSkoq9PT0YWhohDlz5iI8\nPAIKCorQ1dXD2rXrYGTUC8rKKgA4GD16DNzdR+HixUuQlZXDuXPn4ek5EXJy8rh48RLc3Nzh4zMf\nv/66DwoKiuBwuJCXV8CqVathYWGJHj10oanZDRcvXsK0adPh4jIU//nPZOa4i/uTlZXDxYuXwOFw\nsWvXTxAIKpl1PXsawsCgJ/T09BEaehOEAD/8sB1ff70KAwZ8gsjIO3jy5ClKSkpBCHDo0GFwuTL4\n669IDB48BI6OTvjnn5cgBOjUqTMUFZWwZ89eEAKsWbMWI0aMhKysHLS1dfDgwUNkZWXDz+9HuLgM\nxbJlX+LIkaNYunQZFBWVMGSIM+Tk5DF79hycP/8HRo50A5crg08/dWXyduumBT7/FaqrhQgPj0D3\n7trYvHkLCAHGj/8MX321EioqqpCXV0CPHrro1KkzSkpKoaKiCqGwBn36mALggMuVgVBYA0IAOTl5\n/Pe/u7Fw4Xls2SKHHj0OICPj8zaft7RQIEXvw69HmrHtJJWvT58+cHZ2Zv7q2+oTEhJw584dibyG\nJLXm5mVOTk74448/8Pr1a5w6darZoXEAoK6uDhkZGQB1w7H09PSYdSoqKswwPAMDA0ydOhW9evVC\n//794erqiq5du8LW1haLFy/GkiVLANQNpZOVlRXpUFePw+EgMjISFy9exMiRI2FjY4PNmzfD398f\nx44dg5ycHO7fv48ePXrA2dkZFhYWUFNTg46ODoC62213794dCQkJsLe3B5fLxcyZM6Gurs68Rv3y\nq1evQlFRUeT1e/TogW7dujGPt2zZwuxbV1cXsrKNK3pVVFSYmpZBgwaJjFZ4k6mpKbOPb775Bubm\n5tixYwczuqBLly5MNbW2tjYCAgIwePDgJvf37bffYsqUKVBRUWE6F6qqqiIxMREPHz7E+vXrMW7c\nONjZ2QEAtLW1xR73eteuXWOaa+Tl5aGgoNBoGzk5Oejq6gIA3N3dMXHiRGadsbExVFVVmceysrIY\nOHAgli1bBl1dXZHPjpKSEjMKYOvWrfjvf/8LJSUlqKioMM1S2tra6NWrF8zNzTF79mx89913kJOT\nw4ULF/D777/jyJEj6N69OwYNGoSIiAiRUSYNM9Qf0/pzITAwEOPGjYOqqipMTExgZGQEX19fyMnJ\nYfny5ZCRkUFUVJTIaBgAUFRUxKxZswDUnWv1x6qtaPMBRb0nAgICxC6/cuUKxo8fj3Xr1mHx4sVN\nVr9LQ/3Ny6qrq7FkyRJoampi//79AAAfHx84Ojpi0KBB6NevH7p27YoTJ06882upqakxY/KNjY2Z\nfgkmJibo1q0b5s2bB2VlZZEv2i+++AIHDx5kHhsaGjI9uOunnAbAjIjo3r07unfv3qhvx+HDh0Ue\nf/rpp8jIyMCAAQNand/V1RXh4eEiX2QA4ObmBgUFBZFalnnz5qGysrLROH4AmD9/PubPn89kbU5Q\nUBCSk5PRvXt3qKurM4UloO5Lx8vLC4mJiTAxMYGenh5zbFRVVaGtrQ0TExNme21tbQB1/UIePHiA\nIUOGQE5ODgCgqanJ7HvUqFHg8XgwMzNr8XgEBQWBw+Fg8uTJYrc5ceIEU7NkbW0NAFiwYAF69uwp\nst2YMWMwcODAZl+vIVNTU2hra8Pb25s5hl5eXsxQxHocDgcaGhrM8MhBgwZh0KBBjfY3ZswYkUKN\nuro6M0IFAAYPHgxDQ0P4+/tj1apVzP/5pk2bAABdu3bFjh07GnUkbRdtuvEyy7H97d26dUvaEVpE\nM7ZdR+R7+vQp4fF4ZOrUqaSkpOStn8/2cwUA2bt3L/H19SWlpaWkqqqKVFVVkYqKCkIIIYGBgcTD\nw0Psc+Pj40lSUhJZs2YN2bJli8g6gUBA7ty589Z5Hjx4QJYtW9bsNv7+/mTNmjUiy44dO0aGDRtG\nvLy8mGWpqamktrb2rTPs2rWLzJ8/n2RlZYksv3//PuFyuW+9vzfV1taSS5cukd27dzPLqqqqiKys\nrMh2QUFBxM3NTWSZl5cX4fP57/S+Grp69SoxNTUlAoFAZHlaWhrp1asXefLkyVvvs7i4mGRmZjKP\nO3XqRPT09EheXp7Idjwej6SlpTW5n5KSEjJ27Nh3ev24uLhGy52cnEhUVBS5ceMGycnJEftcLpdL\nhEIh8/q1tbWkvLycCAQCoqenRzIyMtp8LtOaAor6APTq1Qt37tzBggUL0L9/f/zxxx8wNTWVdqx2\nUT/fAADml2hz6qurxVFQUHirX/P1bGxs8NNPPzW7zZszFwJ1oy1Gjx4tMtyuT58+b/369RQVFZkm\nhXrW1tbYvn37O++zHofDaTSXAYfDgYeHh8iy7t27NzqGzc1q+DbMzMywZcuWRk0HTc170BpqampQ\nU1NjHkdERMDCwoJplqp3//79ZvejqqrKzDHxtq9vb2/f5HpxMzY29fpAXdOHJNFCgRSxvS0coBkl\noaPyKSkp4fDhwzhw4AAGDRqEgIAAkVnfPmRcLhfy8vLNbqOpqSnxC+i76Nq1K7p27drm/cybN0/s\nZDlcLhdfffVVm/cvjqysLM6fPy+yzM7OrtmCV1v06tWryY6n0dHRzfZJaC0rK6s270MSevbs2ahf\nyZtaWi8JdJ4CivoAxcbGYtKkSZg2bRq2bNnS6FfQm9h+rnA4HCQkJOD169esLwRSlDQcPXoUnp6e\nUFdXb9O5zKrRB+fOnYOlpSVkZGSavWuZoaEhrK2tYWtrC0dHxw5MKFlsn7MfoBk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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Now add a bound on the (approximate) derivative at a point\n", "=============================================================" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.arange(0., 10., 1.)\n", "xx=arange(0,10,.01)\n", "\n", "M = gp.Mean(lambda x: 0.*x)\n", "C = gp.Covariance(eval_fun=gp.cov_funs.matern.euclidean,\n", " diff_degree=2., amp=1., scale=5.)\n", "\n", "f = gp.GPSubmodel('f', M, C, x)\n", "\n", "@mc.potential\n", "def deriv_bound(f=f, x_0=5., c=0., eps=.2):\n", " # use secant approximation of derivative\n", " Df = (f.f(x_0+eps) - f.f(x_0-eps)) / (2*eps)\n", " \n", " # \"soft\" constraint may help convergence\n", " return -1000. * (Df - c)**2.\n", "\n", "m = mc.MCMC([f, deriv_bound])\n", "%time m.sample(iter=10000, burn=5000, thin=1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " CPU times: user 38.69 s, sys: 0.06 s, total: 38.74 s\n", "Wall time: 38.73 s\n" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "for k in [0, 1000, 2000, 3000, 4000]:\n", " plot(x, f.f_eval.trace()[k,:], 'ks:')\n", " plot(xx,f.f.trace()[k](xx), 'k-')\n", "ylabel('f(x)',rotation='horizontal')\n", "title('5 MCMC draws')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "acorr(f.f_eval.trace()[:,5], detrend=mlab.detrend_mean, maxlags=300)\n", "title('acorr for f(5)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "output_type": "display_data", "png": 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f8vLy1BBoAzQ3LXJNTQ3YbDZPnxBK24AaBUImOTkZISEh9c6rqamJQE3TtIX1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\nk52dLZ5HITk5WWKvcQsLC/brhQEAFBcXY9WqVfj777/Rpk0bCAQC9O3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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that autocorrelation function shows nonzero correlation out to 200 or more lags, meaning convergence is 200 times slower when this constraint is included." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. This approach can also add a bound on the approx derivative for many points\n", "==============================================================================" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.arange(0., 10., 1.)\n", "xx=arange(0,10,.01)\n", "\n", "M = gp.Mean(lambda x: 0.*x)\n", "C = gp.Covariance(eval_fun=gp.cov_funs.matern.euclidean,\n", " diff_degree=2., amp=1., scale=5.)\n", "\n", "f = gp.GPSubmodel('f', M, C, x)\n", "Df = mc.Lambda('Df', lambda f=f, x=x: np.diff(f.f_eval) / np.diff(x)) # use secant approximation of derivative\n", "\n", "@mc.potential\n", "def deriv_bound(Df=Df, ub=0.):\n", " return -1000. * np.sum(np.maximum(0, Df-ub)**2)\n", "\n", "m = mc.MCMC([f, deriv_bound])\n", "%time m.sample(iter=10000, burn=5000, thin=1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " CPU times: user 9.62 s, sys: 0.04 s, total: 9.66 s\n", "Wall time: 9.64 s\n" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that MCMC is much faster if you don't evaluate GP off of f_eval mesh." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "for k in [0, 1000, 2000, 3000, 4000]:\n", " plot(x, f.f_eval.trace()[k,:], 'ks:')\n", " plot(xx,f.f.trace()[k](xx), 'k-')\n", "ylabel('f(x)',rotation='horizontal')\n", "title('5 MCMC draws')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "acorr(f.f_eval.trace()[:,5], detrend=mlab.detrend_mean, maxlags=300)\n", "title('acorr for f(5)')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "output_type": "display_data", "png": 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Fn58fhg0bJjAVcFth+v3imZ6PoiiqWrus7BsjIyPDH+tem7GxMQ4ePCjwWvUN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\n04qpQ11Rh4wMwwfsND7DMAzDMDKxxl5J+H49l+/5AP5n5Hs+hmGYaqy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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Extensions you may consider\n", "===========================\n", "\n", "1. Speed up example 2, by choosing the mesh for f_eval to respect the $\\epsilon$ value in the derivative approximation.\n", "2. Fix example 3, so that it is decreasing for $x>9$.\n", "3. Experiment with different scale parameters in the Matern covariance function. I think this can break the derivative constraint approximations. Can you fix it?\n", "4. (Advanced) Experiment with alternative step methods for the MCMC. Can a custom step method achieve convergence speeds more like those of the GPStepMethod has for the unconstrained case?" ] } ], "metadata": {} } ] }