{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simple Multinomial MCMC example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "from __future__ import division\n", "rcParams['figure.figsize'] = (10.0, 8.0)\n", "rcParams['font.size'] = 14\n", "from scipy.misc import factorial\n", "from scipy.special import gammaln" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "k=3; n=6; alpha=array([0.5,0.25,0.25]); lnpvec = log(alpha)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8.0,8.0))\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " text(x1+0.5*x2,sqrt(0.75)*x2,('(%d,%d,%d)'%(x1,x2,x3)),\n", " ha='center',va='center')\n", "\n", "title(r'Possible $(x_1,x_2,x_3)$ values for $k=3,n=4$ multinomial')\n", "\n", "def make_grid(ax):\n", " nmax = n // 3 * 2\n", " for x1 in xrange(nmax+1):\n", " x2 = array([max(0,nmax-x1),min(n-x1,nmax)])\n", " ax.plot(x1+0.5*x2,sqrt(0.75)*x2,'k:')\n", " for x2 in xrange(nmax+1):\n", " x1 = array([max(0,nmax-x2),min(n-x2,nmax)])\n", " ax.plot(x1+0.5*x2,sqrt(0.75)*ones_like(x1)*x2,'k:')\n", " for x3 in xrange(nmax+1):\n", " x2 = array([max(0,nmax-x3),min(n-x3,nmax)])\n", " x1 = n - x2 - x3\n", " ax.plot(x1+0.5*x2,sqrt(0.75)*x2,'k:')\n", " ax.set_yticks(arange(n+1)*sqrt(0.75))\n", " ax.set_yticklabels(arange(n+1))\n", " ax.set_xlabel(r'$x_1$');\n", " ax.set_ylabel(r'$x_2$');\n", " ax.set_xlim(-0.5,n+0.5);\n", " ax.set_ylim(-0.5,n+0.5);\n", "\n", "make_grid(gca())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", 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iTUREJHEs1kRERBLHYk1ERCRxLNZEREQSx2JNREQkcSzWREREEsdiTUREJHEs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\n9OLhw4eQSqWd4guNmH7wMWvGGGPMxPExa9aprFmzBkVFRaLLYKxdNmz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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "def multipmf(xvec,lnpvec):\n", " if any(xvec<0):\n", " return 0\n", " # Should check that n == sum(xvec) but we will assume this\n", " # pmf leaves out n! factor\n", " return (exp(sum(-gammaln(xvec+1)+xvec*lnpvec)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8.0,8.0))\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " xvec = array([x1,x2,x3])\n", " pmf = factorial(n)*multipmf(xvec,lnpvec)\n", " text(x1+0.5*x2,sqrt(0.75)*x2,(r'$%.4f$'%pmf),\n", " ha='center',va='center')\n", "\n", "title(r'PMF values for $k=3,n=4$ multinomial')\n", "make_grid(gca())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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w0BbJ7du3Y8mSJQgODoaDgwOAx1PgvXr1KnFcOSgoCEuXLsVff/2Fnj17GiS+shQUFACo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\nQmCC\n", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "inds = arange(k)\n", "\n", "def nextpoint(xvec):\n", " random.shuffle(inds)\n", " xvecnew = xvec.copy()\n", " xvecnew[inds[0]] += 1\n", " xvecnew[inds[1]] -= 1\n", " ratio = multipmf(xvecnew,lnpvec)/multipmf(xvec,lnpvec)\n", " if ratio >= rand():\n", " return xvecnew\n", " else:\n", " return xvec\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "Nsteps = 12100\n", "x1trace = zeros(Nsteps)\n", "x2trace = zeros(Nsteps)\n", "x3trace = zeros(Nsteps)\n", "\n", "xstart = array([0,0,n])\n", "xvec = xstart\n", "seed(20140423)\n", "for step in xrange(Nsteps):\n", " x1trace[step] = xvec[0]\n", " x2trace[step] = xvec[1]\n", " x3trace[step] = xvec[2]\n", " xvec = nextpoint(xvec)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize=(8.0,8.0))\n", "x1 = x1trace[:10]\n", "x2 = x2trace[:10]\n", "plot(x1+0.5*x2,sqrt(0.75)*x2,'b-')\n", "make_grid(gca())" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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piMQyVBvcYrEgNTUVeXl5WLduHX744Qfs27cPnTt3vjYUi7Vb+vsWgu64naC7\nH//776to3NgDU6e63/Fff7zudvxksHXW3t7eaN26NTp16oRJkybh8ccfx7x580RGIAPr3bs3Tp48\nCYvFgq5duyInJ0d2JGEURcETTzyBgoICxMfH44UXXnCrJ6wrV0Zi9erXMHo0sGHDBowcOVJ2JKGW\nLFmCqVOnAgC++uorbNiwQXIiMhqpbzB79tln0bJlS/z222/XfJ6vrN1TUlISWrVqBS8vL8THx+Oe\ne+6RHUmov45ZVVUkJibibjfpBasq8MQTdvTsmYyvvroLubm5sFgsaNiwoexowhQWFiI3NxfNmzfH\nuXPn0LhxY5dfskjXMkwbfOTIkXj55ZfRokULXLlyBStXrsS0adOwc+dO/OMf/7g2FIs1kdtYsQKY\nNQsICQHc7A3wRFcZpg2emZmJt99+G23atMHzzz+PEydOlFqoyf3s2rULly9fvuHzNpsNa9eudfkn\nbuvXry91V7H8/Hxs3bpVQiJxsrIK8dlnmzBnzo2FOjk5GUeOHJETTJCYmBicPHmy1K8FBwfj3Llz\nghORUQkr1r/88gtSUlJgMpmQmZmJ3bt3s1ATAODAgQPIzc0t9Wv79++/6ddcgaIo+OOPP0r9WlFR\nEfbs2ePST1a++y4DTZqEomvXG7+WlJSE6Oho8aEESk5OvukWoOHh4SzWdBV33SIiKVJSgIcfBsLD\ngZYtZachksswbXCi69lsNl1u6yzc/fi/+MKGzz4rX6F2teO32WzlfkGiqirsdrvOicjoWKxJmh49\neiA0NLTM21ksFjz00EMutZRLURR07NixXLtqxcXFoVu3bi7VbVq6NBxbt76EESPKvu3q1asxojw3\ndCKLFy/G+PHjy3XboUOHYv369TonIqNjG5ykycrKQoMGDcp1DewLFy643GUYy3tMqqoiMzPTZY7f\nZgMefljFgAGZ+Pjjso/pryc0rnSteIvFgvz8fNSvX7/M22ZlZaF+/fqoUqWKgGQki2GWblUEizWR\n61qyBFi2DDhwAOBFuohK8Jw1Gc66deuQkZFR4ftZLBYsXLjQqc9fqqqKxYsXw2QyVfi+ly5dwooV\nK3RIJc7Zs7kYMeJXzJlT8UJ96tQp7NmzR59ggoSHh2P//v2Vuu+OHTsQFxencSJyFizWJFxycnKl\n3jDj5eWFjIyMcp3nNSqTyYSUlBR4eVV8wzsPDw/Ex8c7dddp/PgctG2bjYceqvh98/PzcfHiRe1D\nCZSbm1sRjjC3AAAgAElEQVTqNQXK4+LFi8jLy9M4ETkLtsGJSIjYWKBrV+DUKaBxY9lpiIyFbXAy\njMq0fkWMJYq7H//QoSaMHKlNoXa24zebzZotv7JarbBarZqMRc6DxZqEefXVV3H8+HGHx3HGpVwV\nWapVFmdcyvXjj+HYv/8lDBni+FgBAQFOtyvX0qVL8e2332oy1uDBg/H7779rMhY5D7bBSZgrV66g\nZs2amuzTe+XKFdSqVUuDVOJomdmZjt9iAe6/Hxg37gp693Y8s8lkgqenJ6pWrapBOjHsdjuKioo0\nWX6m5c8RGQeXbhGRVLNnAzt3Ajt2cKkW0c3wnDVJt2TJEqSkpGg+rsViwcSJE2GxWDQfWyt2ux2T\nJ09GUVGR5mOfP38eP/74o+bjaunMmYsYM2Y2Zs3SvlCHhoYiMDBQ20E1duTIEWzbtk2XsdesWXPT\nTUDI9bBYk+5sNhuqV6+u+bheXl6oUaOGod9sZDab4e3tDR8fH83HrlGjBqxWq6G7UJMnm/HEE7XR\ntq32Y3t5eZXr6ncyeXp6wtvbW5exq1Wrpsu4ZExsgxORLiIigH/+E4iJAW67TXYaImNjG5ykEbkP\ntRH3vHbn47fbVXz6aS78/fUv1Ha73XAXCyksLITZbBYyl6IoKC4uFjIXycNiTbrp06cPQkJCdJ/H\nYrGgS5cuhlrKpSgKnnjiCSFXW4uLi8OLL75oqG7UrFmRCAvrhQ8/1H+ugIAAjBs3Tv+JKmDFihXw\n9/cXMtfQoUOxdetWIXORPGyDk27+Ol8rYomJ2Ww23FIekZmMdPwmE9C2LbBwoRn/+pf+maxWKzw9\nPQ13/lrUY2Kkx54qj0u3iEioSZOAEyeADRtkJyFyHjxnTcLNmDFDyu5AFosFw4cPl/rucJvNhi++\n+AKFhYXC505NTcX48eOFz/t3oaHpmDDhO0yfLn7u4OBgLF++XPzEf7Nnzx6sXbtWytxLly4VctqJ\n5Kj41j9EZWjRogUaNmwofF5vb288+OCDml2DuTJsNhvatWuny1K1stSvXx+tWrWCqqrSrm41bZo3\n/v3vDmjdWvzcDRs2lL7mvnHjxvD19ZUy9+23347b+LZ7l8U2OBFp4uhRoFevkqVaTnIlVCLDYBuc\nhElPTzfMk6z09HS3mLM0qqoKz2K12jFwYAYmT5ZfqC0WCzIzM4XOmZuba5h91nNycqSchiF9sViT\nZj799FOEhobKjgGLxYJXXnlF6FIuRVHw0ksvGeIXdnx8PN5++22hT5ymTo1GUlJ/vP22sClvavXq\n1ZgzZ47QOQMDAzFlyhShc97MmDFjsGfPHtkxSGNsg5Nm7Ha7YZbPyMjirsdfUADcdx+wbp0dXbrI\nP3673Q4PDw/h5+2N8vgbJQdVDJduEZGuRo8Gzp0DJL8Rm8ip8Zw16W7MmDE4ffq07Bg3sFgs6Nev\nn67n78xmMz744ANDtL+vl5KSgmHDhuk6x4EDyfj++2EwSAf4Gnv27MH8+fN1nWPz5s349ddfdZ2j\nsubMmYP9+/fLjkEa4dItcthTTz2FVq1ayY5xA29vb/Ts2VO3XY+Akl2Vunfvjpo1a+o2R2U1a9YM\n3bp103Up18yZ9fDmmy+ieXNdhnfI3XffrftSpg4dOhjuuuR/eeyxx9CyZUvZMUgjbIMTUaXs2wf0\n6wecPg1IWlpM5DLYBifdxMbGwmq1yo5RLnq06Y3Y+i+N3W7HmTNnNB3TZLLik09iMX268Qt1YWEh\nUlJSNB0zKysLFy9e1HRMvaSnpxtuVzaqOBZrqrRx48YhIiJCdowyWSwWDBgwQNOlXIqi4OOPPzbk\nuerrJSUl4csvv9S0WzVx4hlkZ49Br16aDambzZs3Y9myZZqOuWfPHixcuFDTMfXy/fff49ChQ7Jj\nkIPYBieiCsnJKdlVa+dOoGNH2WmIXAOXbhGRpj7/HFAUwEleWBI5BZ6zJs0NHDgQkZGRsmNUmMVi\nQc+ePR16967JZMKrr77qFO3v6yUmJuK9995z6Inwtm0xWLCgPyRv7lUp27Ztw+TJkx0aY9WqVbov\nB9PLpEmTsH37dtkxqJL4ypoqLCQkBA888AB8fHxkR6mw4OBgdOnSpdJXeFJVFcHBwXjqqac0TqY/\nq9WKY8eOoWvXrpW6v6oC//ynCR06RGLWrEc1Tqe/8+fPo6CgAPfcc0+lx8jMzERubi7uu+8+DZOJ\nERUVhRYtWnBnLoNiG5yINLFtGzB8OBAZCVStKjsNkWthG5w0c+LECSiKIjuGw1RVrdS7Yw8fPuwS\nTyLNZjNCQkIqdJ+CAjMGDAjBrFnOX6izs7MrvJQtLS0NZ8+e1SmRWLGxsU6z7Iz+h8Waym3x4sWI\nj4+XHcNhVqsV06dPr9BSLkVRMGXKFBQVFemYTIz09HTMnj27Qk88xo1LgKouwgsv6BhMkP3792Pr\n1q0Vus/Ro0exYcMGnRKJtXLlSoSFhcmOQRXENjgR3VJWFtC+PRAcXLK7FhFpj+esicghH30E1KoF\nzJwpOwmR6+I5a3LY22+/7ZJtM4vFgm7dut2yHa4oCvz8/JxyqVZZ4uPj0aNHj1v+gli3LhrLlr2B\nsWMFBhNk48aNGDNmzC1v8/PPP2Omiz5LGTNmDDZu3Cg7BpUTX1lTmWJiYnDXXXfpunuVLNHR0Wjf\nvv0td6WKiorC/fffLzCVGH9dM7x9+/alfl1VgWeeseHZZ2Ph799OcDr9Xb58GcXFxWjWrNlNb5Of\nn4+cnBzcfvvtApOJkZiYiKZNm6J69eqyoxDYBieiSlq3Dpg4EThxAqhSRXYaItfGNjhVWlBQkFvs\n1mO327Fly5YbflC2bdvmNLuKOaKwsBB79uy55nPZ2Qo+/XQX5sxx/UKdlpaGEydOXPO5hIQEREdH\nS0okVmhoKNLT02XHoDIILdaTJ0/GI488gjp16qBRo0bo3r07Tp06JTICVcC2bduQmZkpO4buVFVF\nYGDgNU9MFEXBunXr3KJY5+bmYsOGDdc8Wfnuu3OoW3cPnnlGYjBBTp06hWPHjl3zuZiYGBw5ckRS\nIrEOHDiAhIQE2TGoDELb4P/+97/Rp08fPPLII7Db7fjmm29w5MgRnD59+ppL4LENTiRPWhrw4IMl\n7e877pCdhsg9GPqcdWFhIerUqYNNmzbhpZde+l8oFmupVFW95RuuXNlf33fufPxvvw20bu3hlJt1\nOMput1f6uvHOzt2/92Urq+55Ccxyg/z8fNjt9lIvLO/v73/1735+fvDz8xMXzI35+/tj9erVCAgI\nQOfOna8+Du7w0WKxoGXLVlBVOxITE1GzZk1D5BL1MS4uDl27dkNOTnXk5cVLzyP649q1azFy5Ejc\neeed2Lt3r/Q8oj8OHz4cjz/+OHr37g3SX1BQEIKCgsp9e6mvrHv37o3ExESEhoZe82yOr6zlSk9P\nR5MmTVDF1d9ZVIqPPkpFXh6wZk1L2VGEs9lUdOqUig8+8MBnn7nf8efn50NRFHh4eKBRo0ay4wh3\n/vx5NGzYEF5eUl/DuS3DtsGHDRuGtWvXIjg4GHdcd2KMxZpkOHUK8PMr2ahiwwbg8cdlJxLr11+B\nxYuBQ4cAdkKJxDLk0q3PP/8ca9aswZ9//nlDoSZ5Nm3adPXd34GBgcjKypKcSBy7XcUbbyzDqFHF\nmDjRir59f4XVapcdS5iMjCsYNmw15swBcnKysX79etmRhIqOjr767u/Y2Fjs379fciKxdu3adXVX\nsb179yIpKUlyIrqe8GL92WefXS3U9957r+jp6RYiIiJgMpkAAMnJyW5VrH//3YTz58PxySeeePtt\nTyjKKSxZki87ljDjxmXhjjuS8MgjgM1mQ2hoqFt1ty5cuHC1WGVlZSElJUVuIMFiY2OvLl1MTk52\niyWbzkZoG3zQoEEICAhAYGAg2rZte/XztWrVQo0aNf4Xim1wEqi4GOjQAfjxR+Bf/yr53NGjQK9e\nQExMySYWriwxEXjsMSAqCmjaVHYaIvdkqHPWnp6epQby9/fHN998879QLNZCWSyWm17322KxwMvL\ny6WXc0yZYsGhQ97YsuXaz7/7LtC0qQVTp7reNdH/rkcPC554whsjR974tVt9b7iCsr6/3eH4b3Z8\ndrsdqqq65RtNZTDUOWu73Q6bzQa73X7Nn78XahKve/fuOH78eKlf69u3b4WWFziblBQFY8Y8gHHj\nbtxVa9w4C2bO7IiwsJvvyuXsFi0Kx+7dL2Do0Bu/FhcXh2eeecalnzj/9NNPV5cvXW/lypUYMWKE\n2ECC9evXDzt27Cj1a4MHD3a79y4YGTfyIOTk5KBu3bqlvrrIzs7Gbbfd5rKvrPv3B3x8svHjj/VK\n/fqYMdk4c6YeNmwQHEwAqxXo1An44otsvPtu6cefnZ2NevVK/5orsNlsKCgoQJ06dW74mqIoAABf\nX1/RsYS5cuUKfHx8Sn11favfC6Q9Q7XBy4vFmkQ4cQJ4+eWS89Kl/K4GAJhMQNu2wNKlwLPPis2n\nt/nzS5ao7dnDpVpEshmqDU7Gsnz5cqSmppbrtr/99hvS0tJ0TiSO3a7i9ddnY+xY5aaFGgB8fErO\nab/11vcwmVxnU4/ExGx89dUCzJ5ddqHOzMzETz/9JCaYIMePH8cff/xRrtuGh4dj+/btOicSa/36\n9YiNjS3XbTdu3IjTp0/rnIjKwmLtxrKzs8t9tSKbzYaioiKdE4kTEFAMk+kK+vevWuZtX3/dC76+\nxZg/33WOf8KEAjz0kIr77y/7ttWqVcOlS5dcqttlNptRXFxcrttarVaX+t4HStrf5VWR/yvSD9vg\n5HaKioA2bYAVK4CnnirffSIigH/+s6RlXsql7J3KqVNAt27A6dNAgway0xARwDY4laKg4MZ3PpdX\nUVER7HbnvrLXxIkF6NKl/IUaKNky8rXXgNGjK/9/ZwR2u4rBgwswZkzlCrUj3ztGYDKZKr1Huaqq\nTn/8juQ3m80wm80apqGKYLF2Q6+//jpCQkIqdd933nkHBw8e1DiROHFxCqZM6Yxvv634L62xYy1Y\nvPhRHDnivEu5fvwxEseO9cCAARW/b1xcHP7xj384ddfrt99+w7ffflup+wYEBGDs2LEaJxJr4MCB\n2LZtW6XuO2TIEGzevFnjRFRebIO7IUVR4OPjU6klGYqiOPVSlj59gDvvVDBpUuWOYdo0BXv3+mLn\nTud7B/VfV2qbOVNB9+6VO35nf/xVVYXJZKrUMZjNZnh6ejr1rlRmsxlVqlSp1IVOnP2xNzou3SL6\nfwcPAn37lpx3/tvVbSvEYgEeeACYPr1k2ZczmT695P+AL46IjIfnrOmqH374AYmJiZqMNXfuXM3G\nEsFqtaN377EYN66w0oUaALy9genTLXj33dEoKHCe83dRURfg7z8ZM2c6PlZ6ejqmT5/u+EAC7d+/\nHxs3btRkrCNHjmDNmjWajCXKzz//jIiICE3GWrZsGU6ePKnJWFR+LNZupHbt2qhbt64mYzVv3typ\n2oFLl1rg69sU771X3eGxXn7ZG82b3465cy0aJBNj8mSgW7c7cM89jo9Vt25d1K5d26m6X7Vr18Zt\nGr2NX8ufI1Hq1q1b6lXaKqNBgwaoXt3xnyOqGLbByeXl5wP33Qds2QJ07qzNmLGxQNeuJcugGjfW\nZky9lOdKbUQkF9vghKysLN2e/Fy+fLnSS2FEGTUqCy+8oF2hBkqK/3vvAcOHG3vPb7tdxcCBFzFh\ngj6F2uh7nl+5cuXqNb61ZrPZcPnyZV3G1srFixd1+9nX8/+WbsRi7QY++OCDm+6q5ahPPvkEhw8f\n1mVsLURFKVi06Fld1kePHGnBmjXPIyjIuEu5pk+PxJkzb+H997UfOy4uDr169TJ0F2zt2rUYP368\nLmOvWLECU6dO1WVsrYwcObLSS7XK8sUXX2Dnzp26jE03YhvcDdhsNt32pNVzbC107w506WLDyJH6\nZFy0yIaAgCo4cMB4S7n+ulLbsmU2+Pm55+MP6JfRZrPB09PT0LtS2e12eHh46JLRGR57Z8I2OOn6\nA2XkH9bdu0suqfn55/pl7N+/Cq5cAdat022KSps+HejSBboVasDYj/9f9MpYpUoVQxdqALo+mXCG\nx96VsFi7sPHjxyMmJkbIXBMnTjTUzjyKYsWbbw7ChAkFqFZNv3mqVAFmzrTggw8G4PJl45y/O3Lk\nHKZMGYVp0/Sf6+zZs/j666/1n6gCduzYgYCAACFz7du3z3C7ks2ePVu3U1/Xmz9/Pg4dOiRkLnfG\nYu3CHnjgATRr1kzIXI888gjq1asnZK7yWLRIRfPmT6F3bwcWVZfTc895o0OHZzF7tnFeZU2fXhM9\nez6JVq30n6tx48bo1KmToU5dtW7dGvfee6+QuVq1aoV27doJmau8OnTogObNm7vcXO6M56zJ5Vy6\nBLRrB/z5Z8nlNUVISQEefhgIDwdathQz580cPAi89VbJUi0uhyVyDjxn7YaSk5Ol7YyVmpoqfe/b\noUMT8cYb4go1ANxxBzBoEDBwoNyrulksNgwYkIypU8UXalVVkZSUJHbS61y+fBm5ublS5jaZTEhL\nS5My91/Onj0Li0XOxXqysrKQn58vZW53wGLtgr788ktplwMcNWoUQkNDpcwNAMePK1iz5k2MGCF+\nK8NhwyzYvbsvduyQt5Rr0qRTyMj4DG++KX7u+Ph4fPLJJ1K7Ytu2bcOsWbOkzL1+/XosXrxYytx/\nmTp1Kv744w8pc0+YMAH79++XMrc7YBvcBamqKu1dqnLnBp5/Hnj1VRWDB8vJEBCgYvZsD4SEAJ6C\nnwr/70ptKjp3dr/HX3YGoxw7ALc9fmfGNrgbkvkDI3PuTZuAzExgwAB5Gd56ywNVqwK//SZ+7gkT\n8P9XanPPx192BqMcuzsfvytjsXYhw4YNQ3R0tOwYAEqunHTixAlh8+XlFePtt/tg8uQCyNxfxMOj\nZCnXwIF9kJYm7vzdH3/EY+7cQZg0SdiUN5WUlISPP/5YaHds/fr1WLJkibD5bmXXrl34/vvvhc7p\n7+9vmOVT06dPl9aKd2Vsg7uQAwcOoHPnzobYEefo0aNo27atZjv9lGXSJDu2bt2Lw4f/IWS+svzr\nX3vxwAPPYPp0Mc8cXnyxELffHoYFC54UMt+tWCwWHDhwAM8995ywOdPT05GTk4MOIt9VeBNpaWnI\ny8tD+/bthc0ZGhqKO+64Aw0aNBA2582cPHkSLVu2RMOGDWVHcSpl1T0Wa3J6588D998PHD0K3H23\n7DQlRGbavRsYOLBkBzA9LwBDRPrhOWs3EBUVBbPZLDtGqc6cOYOioiJd5/j445Po1081TKEGgKZN\ngREjgP799X1XflGRBQMGROL7741XqK1WKyIiInSd4/z588jIyNB1jsrKz89HfHy8rnOI+PmqrOTk\nZGRnZ8uO4TJYrF3ArFmzcOrUKdkxSjV37lxERkbqNv7Bgwp27RqJoUMLdZujsgYNsiAk5Gv8/rt+\nS7kmTIhDUdF0vPKKblNU2tmzZzF+/Hhdu2QHDhzA8uXLdRvfEbt27cL69et1neOXX34x7K53S5Ys\nQUhIiOwYLoNtcHJaqlqyUcVHHwH//a/sNKULDARGjwYiIqD5G99kXKmNiPTBNji5rJUrAYsFeO89\n2UlurkePkpb4woXaj/3ttxB+pTYikoPF2on169cP4eHhsmOUy6effqppu+7SJQUffPAvTJ5cIPzi\nIxXh4QFMm2bBsGH/RmKidu3wjRtPYenSd/Ddd5oNqZuEhAT07t1b027ZsmXLMGfOHM3G09PmzZvh\n7++v6ZjDhg1DUFCQpmPqxd/fH5s3b5Ydw+mxDe7EIiMj0aZNG1StWlV2lDJFR0fj7rvvho+Pjybj\njR2rIiTkBHbt6qzJeHp7/fUTaNz4Ifz4o+MXjlBV4NlnLXj88dOYPPlBDdLpy2azISIiAg899JBm\nY2ZnZyM3NxetW7fWbEy9ZGVlwWQyoZWGW6DFxcWhSZMmqF27tmZj6iUmJgbNmzdHrVq1ZEcxNC7d\nIpdjpB2uyuvyZaBtW23OLwcGAmPGlBy/zAvAEJF2eM7aBR0+fBgFBeI3qtDC0aNHHd6Z57339mDw\nYJvTFGoAqF8fGDNGxTvv/AG7vfJPRHNzTRg4cD9mz3a+Qq0oCg4cOODQGCkpKYiLi9MokVgXLlxw\neCnb8ePHnXY5VGRkJC5cuCA7htNisXZCq1evxrlz52THqJTAwECHftnu3q0gNHQJPv1U7jaclfHh\nhzYkJf2CVasqv4XjuHEp8PFZj+ef1zCYIBcvXsSvv/7qUNcsPDwcu3fv1jCVOKGhoQ6fZ962bZth\nl2mWZdu2bTh9+rTsGE6LbXByGjYb0LkzMHJkybugnZEjVxsz4pXaiEgbbIO7EFd6AlOZY1m6VEXN\nmkDv3joEEuSf/yxZGz17dsWPf9QoFR984BqFuqKPvyt97wM8flc7HhFYrJ1I7969he5kpad+/fpV\n6Pzl+fMKBg16HJMnF8DZd+KbMsWCMWO6ICam/Eu5Vq6MxOrVr2H0aB2DCRIfH48XXnihQr+wlyxZ\ngqlTp+qYSpwNGzZg5MiRFbrPxx9/jD179uiUSKwvv/wSGzZskB3D6bAN7kSSk5PRsmVLeDnbO4tK\nUdFjGT4cSE1NwNq1LvCyEsCHHybAZrsbP/9c9m1VFXjiCTt69kzGV1/dpX84namqisTERNxdgRZB\nUVERcnNz0axZMx2TiZGbmwur1VqhHbIyMjJQt25dQ+yo56hz586hcePGqGa0i9lLxqVb5PRiY4Gu\nXUvO8zZuLDuNNvLzgfvuA7ZsKTkPfysrVgCzZgEhITD0BWCIqPJ4ztoF7Ny5E5cuXZIdQxc7d+7E\n5cuXb3mbvn3XYcQIs8sUagCoXRsYN86Gt95ac8ulXFlZhfjss0DMmeN6hTovLw9btmy55W1iYmJc\n5tTP9ZKSknDkyJFb3mbfvn1IT08XlEis4OBgnD17VnYMp+FiP/6uKTg42OG1yUYVHh6OtLS0m349\nMFBBYuKf+PRTgaEEef99D+TkBOPnn/NuepvvvstA06Zh6NpVYDBBFEXBvn37bvlqIiUlxWmXKpXl\n7NmzZR7byZMnXXZtcmRkJFJTU2XHcBpsg5NhWSwlS5VmzABefll2Gn0EBwN9+gAxMUCNGtd+zRmv\n1EZElcM2uBOz2WyyIwhjs9lu+Eb94Qcb7rgDeOklOZlEePLJkj9Tptz4WH/xhQ2ffeYehfr67/XS\nvh9cWWnH7y5UVYXdbpcdw/CEFusDBw6ge/fuaNGiBTw9PfHbb7+JnN7p9OjRA6GhobJjCPHWW29d\nc3Wnc+cUfPllR0yY4PxLtcoyYYIFkyd3QmTk/5ZyLV0ajq1bX8SIERKDCRIXF4du3bpdU5wXL16M\n8ePHS0wlzurVqzHiuge6X79+2LVrl6REYn322WdYt26d7BiGJ7QNvmPHDhw6dAidOnXCu+++iwUL\nFuDdd9+9MRTb4ABKLs9Yv359eLraO4tKkZWVhYYNG8Lj/yvzgAGA1ZqJJUtc6F1ltzBiRCbS0hpj\n9eqSK7U9/LCKAQOy8PHHrn/8qqoiKysLjf/2DkKr1Yr8/HzUq1dPYjIxCgsLoaoqatasefVzubm5\n8PX1dYvlTe70e+5WDLt0q1atWpg3bx6LNd0gIqLkSl8xMcBtt8lOI0ZREdCmTckyrZgYYNky4MAB\nuHxXgYhK8Jy1E1q7dq3LLtcoy6pVq/Daa1MxerTJbQo1AFSvDkyaZMEbb8zE8OFLMWeO+xXqS5cu\nYcKECQ5vduGsoqOjMW7cOCQkJMiOIsW2bducdkc1EQx7KSx/f/+rf/fz84Ofn5+0LCINHeqPX389\njObNu8LbG7hwwR8A0KRJyUdX/3dCwnLYbFn46KPhAP73feAOH/v29cKAAetQq1YNPPTQB9LziP7o\n6emJDRs2ICoq6urPuxFyifpYUFCAwMBAZGZmYt68edLziP6Yk5ODvLybL2N0NUFBQRV6Yso2uMH8\n5z9A69ZA376yk8hz551AnTqyU8hRUFCyG5e3t+wkRCRSWXXPsK+s3dHu3SaEhvpg+XLAx0dFcXEx\nfHx8ZMcSxmQyXT1ek8mEatWqXX3DmTswmUyoWfN/x+9Oj31xcTG8vb2vvsnI3Y7/78erqipMJhN8\nfX0lpxLn78dvtVqhqiq8+Yz1GjxnbRA2G9Cr16v4+OPj8PUFZs2ahe+//152LGEURUHHjh1RUFAA\noGQp1/79+yWnEic8PBwv/f+CcovFgk6dOiEnp/y7cjm7n3/+Gd988w2A0pdyuboPP/wQ27dvBwCs\nWLECo0aNkpxIHJvNhkceeeTqldoGDx6MjRs3Sk5lPELb4IWFhYiPjwcAdO3aFSNHjsQrr7yC+vXr\no+Xfrvzgjm3wRYuA5csLcOBADXh6eqCoqAjVqlVDlSpVZEcT5sqVK6hVq9YNf3cX7nz8qqqisLDw\n6vIldzt+RVHg7e0NLy8vFBcXw8PDA1WrVpUdS5i/P94FBQWoUaOGW3XVAIMt3QoKCsKzzz57Q7D3\n338fP/9tr0B3K9Y5OSXLdnbtAjp2lJ2GiIhEM9TSLT8/P9jtdtjtdthstqt//7k8m/q6sNdfX4xn\nn00utVDv27cPf/zxh/hQgtjtdkyaNAlFRUWlfn3RokUuvTPPxYsXMWvWrFK/ZrFYMGHCBFgsFsGp\nxDl8+DC2bt1a6tfOnz+PH374QXAisVasWHHTzTyOHz/u8u3gGTNmIDs7u9SvrV69GpGRkYITGRff\nYCZZTAxw9KiKY8dqlPp1b29vl24Hmc1m+Pj43PTNRLVq1YLVahWcShyz2Yy6deuW+jUvLy/UqlUL\nJpPJZd9s4+XlddN2b82aNWG326Gqqsv+DHh6et70e79q1arw8nLdX9E2mw0eHh7XXLnt73x8fFz2\nca8M7rol2YsvAs8/DwwbJjsJERHJYqg2OF1rzZocJCaiXHs1W61WXLlyRf9QAlXk3c75+fkutROR\nqq0oBvQAABi9SURBVKoVOn5Xe2d4YWEhzGZzuW/vasefk5NT7hckdrsdubm5OicSqyKPZ1FREUwm\nk45pnAOLtSRmM9Cv31v45JMQlOdNn7Nnz8b8+fP1DyaIoijo0qXL1aVaZfnvf/+L4OBgnVOJExkZ\nif/85z/luq3FYsGTTz7pUgVr5cqVV69eVZa4uDi89NJLLtVt+/zzz7Ft27Zy3TYgIMCldiCz2Wzw\n8/O7ulSrLBX5v3JlbINL8v33wO7dZuzcWb7lGRaLBV5eXi51DsdsNpd7eUpFbussePzue/xWqxWe\nnp7l2mmqIrd1Fu782N+MoZZulZerF+usLKBdOyA4uGTJFhERuTeeszag7t2n4+WX4ypVqLdt24bA\nwEDtQwlitVoxYsQIFBYWVur+06dPR2xsrMapxElPTy93+/d6FosFw4YNc+rzd3v27MGaNWsqdd/U\n1FSMGzdO40RizZ8/HydPnqzUfQ8ePIhly5ZpnEgcVVXx9ddf49KlS5W6/08//YRjx45pnMp5uO66\nAIMKDwfOnLkdq1Y1rNT9mzZtCrvdrnEqcex2Ozp06IDq1atX6v5t27a96VIPZ1C1alU8+OCDlbqv\nt7c3OnXq5NSPf5MmTSp9zesGDRrgzjvvdOqlXHfccQcaNWpUqfs2atTIqd9kqaoq7rnnnpsuVSzL\nnXfeifr162ucynmwDS6QqgJ+fiU7an38sew0RERkFGyDG8iiRWnIyVHRv7/jYymKUul2kiypqama\njXXhwgWnurKX3W5Henq6ZuNp+X8pQm5urmZLD1VVdbrjz8jI0OxVscViKfc7qY1Cy8crOzu73KtI\nXAmLtSCKAgwbNhgDB4ZCi7055s+fj4CAAMcHEkRRFHTv3l2zH7KhQ4fi6NGjmowlQnR0ND788ENN\nxrJYLHj11VedailXYGAgpk2bpslY8fHxeO+995yq++bv74+dO3dqMtbq1asxd+5cTcYSwWazoVev\nXpo9wRg7diz27t2ryVjOhG1wQSZMAMLC7NiwQZvnR8543k7LzHa73emWsmiZmY+/cz3+f/0+0+L4\ntRxLFHd+7MuLS7cMIC0NePBBIDQUuPNO2WmIiMhoeM7aAP7976/xn/+c0qVQr1+/3tDtcLPZjP/+\n97+6nWP65ptvDL0zT1JSEj7//HNdxrZYLHj//fcNff5u06ZN+OWXX3QZOzk5GUOHDtVlbK1MnjxZ\nt9M1e/bswY8//qjL2Fqw2+34+OOPkZWVpcv4s2fPRlBQkC5jGxGXbuns8GHgwgU/fPfd7bqM3759\ne0O3w6pUqYKePXvqttzqueeeQ/PmzXUZWwsNGjTAyy+/rMvY3t7e+M9//mPoqzs98MADyMvL02Xs\n5s2b4/nnnzf0KYGnn34arVu31mXse+65B/Xq1dNlbC14eHjgpZdeQoMGDXQZ/4knnkDLli11GduI\n2AbXkd0OPPYY8NlnwNtvy05DRERGxTa4RNOmxcDT04q+ffWfKzc3V9OlQVo4deqUsLkSExMNdWUv\nq9WKmJgYYfOJ/L8uj6ysLFy8eFHIXHa7HWfOnBEyV3klJCSguLhYyFyFhYVISUkRMld5nTp1StgL\nrvT0dJfblaw0LNY6uXIFGDduAgYOjICINy4uX74cmzdv1n+iclIUBQMGDBB2PnXSpEkICwsTMld5\nxMTE4JtvvhEyl8ViwaBBgwy1lGvPnj1YtGiRkLmSkpLw1VdfGaob9+OPPwo7n7p582YsX75cyFzl\nYbPZMGTIEN3OVV9v1qxZOHz4sJC5ZGIbXCejRgEZGcBvv8lOQkRERselWxIkJpacq46MBJo1k52G\niIiMjuesJfjHPwaib99IKYU6ICAACxcuFD/x/zOZTOjRo4e05UTDhg2TujNPTEwMPvjgAylz/3Vl\nM73efV0eK1euxLx586TMnZiYiHfffVfqE/1Ro0bh4MGDUubetm0bJk2aJGVuoKT9/frrryMzM1PK\n/BMnTsT27dulzC0CX1lrbO9e4N13Q3Dq1AOoW9dH+PzJycnw9vZGixYthM8NlFyp6NChQ3jyySel\nzH/y5Ence++90nbmMplMiIyMxKOPPipl/kOHDuGJJ56QdoWnrKws5OTk4L777hM+t81mw7Fjx9Cl\nSxfhc/8lKioKLVq0wG233SZ87vPnz6OgoAD33HOP8Ln/EhwcjK5du0pZSifz/14LbIMLZLUCnToB\n330HvPaa7DREROQs2AYXaPToUNSrp6BnT9lJSnb5SUxMFDrnoUOHDPMkKywsTGgr3mw2S22//52q\nqggODhY6Z2pqqmGWD8l4LCIiIpCfny90zpu5fPkyTp8+LXTOI0eOGGav7djYWGHLBkVisdZIdjYw\nd+5SDBmSACNcTGnHjh04cOCAsPkURcG0adNQVFQ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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "tally = zeros((n+1,n+1),dtype=int)\n", "for step in xrange(100):\n", " tally[x1trace[step],x2trace[step]] += 1\n", " xvec = nextpoint(xvec)\n", "\n", "fig, (ax1,ax2) = subplots(1,2)\n", "fig.set_size_inches(16.0,8.0)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " ax1.text(x1+0.5*x2,sqrt(0.75)*x2,(r'%d'%tally[x1,x2]),\n", " ha='center',va='center')\n", "\n", "ax1.set_title(r'Number of visits in first 100 steps')\n", "make_grid(ax1)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " xvec = array([x1,x2,x3])\n", " pmf = factorial(n)*multipmf(xvec,lnpvec)\n", " ax2.text(x1+0.5*x2,sqrt(0.75)*x2,(r'$%.4f$'%pmf),\n", " ha='center',va='center')\n", "\n", "ax2.set_title(r'PMF values for $k=3,n=4$ multinomial')\n", "make_grid(ax2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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LE0qlUgQHB4svvvhC1K1bV9ja2oq+ffuKy5cv6zw+MTFRfPjhh6JevXrCyspK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mXLloL03bZtW7rtPSEGytzcXLBlowypZllYWAhWs1q1amVQNcvDw0OQvj08PGBlZSVI39qysbGB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\nlQrx8fEA/v1qPzU1FREREWjVqhUeffRRiaPjZ+bMm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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "tally = zeros((n+1,n+1),dtype=int)\n", "startstep=100; stopstep=1100\n", "for step in xrange(startstep,stopstep):\n", " tally[x1trace[step],x2trace[step]] += 1\n", " xvec = nextpoint(xvec)\n", "\n", "fig, (ax1,ax2) = subplots(1,2)\n", "fig.set_size_inches(16.0,8.0)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " ax1.text(x1+0.5*x2,sqrt(0.75)*x2,(r'%d'%tally[x1,x2]),\n", " ha='center',va='center')\n", "\n", "ax1.set_title(r'Number of visits in steps %d-%d'\n", " % (startstep+1,stopstep))\n", "make_grid(ax1)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " xvec = array([x1,x2,x3])\n", " pmf = factorial(n)*multipmf(xvec,lnpvec)\n", " ax2.text(x1+0.5*x2,sqrt(0.75)*x2,(r'$%.4f$'%pmf),\n", " ha='center',va='center')\n", "\n", "ax2.set_title(r'PMF values for $k=3,n=4$ multinomial')\n", "make_grid(ax2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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bYWdnBw8PD1y4cAG7du1CixYtyoxF9Ui2//u//8PMmTORmZmJDRs2oE2bNhpJ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\npLb+VL0+ZTIZlZaWKvazX1LFhY/YbGdnR+PGjVPa1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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "tally = zeros((n+1,n+1),dtype=int)\n", "startstep=1100; stopstep=2100\n", "for step in xrange(startstep,stopstep):\n", " tally[x1trace[step],x2trace[step]] += 1\n", " xvec = nextpoint(xvec)\n", "\n", "fig, (ax1,ax2) = subplots(1,2)\n", "fig.set_size_inches(16.0,8.0)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " ax1.text(x1+0.5*x2,sqrt(0.75)*x2,(r'%d'%tally[x1,x2]),\n", " ha='center',va='center')\n", "\n", "ax1.set_title(r'Number of visits in steps %d-%d'\n", " % (startstep+1,stopstep))\n", "make_grid(ax1)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " xvec = array([x1,x2,x3])\n", " pmf = factorial(n)*multipmf(xvec,lnpvec)\n", " ax2.text(x1+0.5*x2,sqrt(0.75)*x2,(r'$%.4f$'%pmf),\n", " ha='center',va='center')\n", "\n", "ax2.set_title(r'PMF values for $k=3,n=4$ multinomial')\n", "make_grid(ax2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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HDx8iLCwMAAo92+/hw4fw8fFBv379cOnSJaxZswa9e/dG9+7dAbx8XlhZ901q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QsX0KVLF5iZmZVZptFoEBYWZhA31KnK+fPn0a1bNzRoUPZycrVajQsXLuD111+XITJxhYaGokeP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\nOnWqWpkpU6bQ6NGjRVLIDS/6eevWLZJIJJSSkqJW5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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "tally = zeros((n+1,n+1),dtype=int)\n", "startstep=2100; stopstep=12100\n", "for step in xrange(startstep,stopstep):\n", " tally[x1trace[step],x2trace[step]] += 1\n", " xvec = nextpoint(xvec)\n", "\n", "fig, (ax1,ax2) = subplots(1,2)\n", "fig.set_size_inches(16.0,8.0)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " ax1.text(x1+0.5*x2,sqrt(0.75)*x2,(r'%d'%tally[x1,x2]),\n", " ha='center',va='center')\n", "\n", "ax1.set_title(r'Number of visits in steps %d-%d'\n", " % (startstep+1,stopstep))\n", "make_grid(ax1)\n", "\n", "for x1 in xrange(n+1):\n", " for x2 in xrange(n-x1+1):\n", " x3 = n - x1 - x2\n", " xvec = array([x1,x2,x3])\n", " pmf = factorial(n)*multipmf(xvec,lnpvec)\n", " ax2.text(x1+0.5*x2,sqrt(0.75)*x2,(r'$%.4f$'%pmf),\n", " ha='center',va='center')\n", "\n", "ax2.set_title(r'PMF values for $k=3,n=4$ multinomial')\n", "make_grid(ax2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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NGgTg6bPBqrtthg0bhhs3biAgIED5PDSFpk2b4pVXXlH+Hh4ervIcwZycHOWz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\nGzdi2bJl6N+/P5555hnMnDkT3bp1w+LFi7UM3+5ZozY3bNjwo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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "x1mean = x1trace.cumsum()/(1+arange(len(x1trace)))\n", "x2mean = x2trace.cumsum()/(1+arange(len(x2trace)))\n", "x3mean = x3trace.cumsum()/(1+arange(len(x3trace)))\n", "\n", "fig, (ax1,ax2) = subplots(1,2)\n", "fig.set_size_inches(20.0,8.0)\n", " \n", "ax1.semilogx(x1trace,'kx',label=r'$x_1$')\n", "ax1.semilogx(x2trace,'r+',label=r'$x_2$')\n", "ax1.semilogx(x3trace,'bo',mfc='None',mec='b',label=r'$x_3$')\n", "ax1.legend()\n", "ax2.semilogx(x1mean,'k-',label=r'$\\overline{x}_1$')\n", "ax2.semilogx(x2mean,'r-',label=r'$\\overline{x}_2$')\n", "ax2.semilogx(x3mean,'b-',label=r'$\\overline{x}_3$')\n", "ax2.legend();\n", "ax2.grid(True);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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MbrfUtesv+uc/k3zHWrp0qVasWKGioiIlJSX5jpmamqqEhAStXLlSXbp0keS5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\nxxbcLfUS1p2rjcQ0O2iePG1rq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