mathematics/mcmc_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright (C) 2016 - 2019 Pinard Liu(liujianping-ok@163.com)\n",
    "\n",
    "https://www.cnblogs.com/pinard\n",
    "\n",
    "Permission given to modify the code as long as you keep this declaration at the top\n",
    "\n",
    "MCMC(二)马尔科夫链 https://www.cnblogs.com/pinard/p/6632399.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix = np.matrix([[0.9,0.075,0.025],[0.15,0.8,0.05],[0.25,0.25,0.5]], dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.9    0.075  0.025]\n",
      " [ 0.15   0.8    0.05 ]\n",
      " [ 0.25   0.25   0.5  ]]\n"
     ]
    }
   ],
   "source": [
    "print matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current round: 1\n",
      "[[ 0.8275   0.13375  0.03875]\n",
      " [ 0.2675   0.66375  0.06875]\n",
      " [ 0.3875   0.34375  0.26875]]\n",
      "Current round: 2\n",
      "[[ 0.73555   0.212775  0.051675]\n",
      " [ 0.42555   0.499975  0.074475]\n",
      " [ 0.51675   0.372375  0.110875]]\n",
      "Current round: 3\n",
      "[[ 0.65828326  0.28213131  0.05958543]\n",
      " [ 0.56426262  0.36825403  0.06748335]\n",
      " [ 0.5958543   0.33741675  0.06672895]]\n",
      "Current round: 4\n",
      "[[ 0.62803724  0.30972343  0.06223933]\n",
      " [ 0.61944687  0.3175772   0.06297594]\n",
      " [ 0.6223933   0.3148797   0.062727  ]]\n",
      "Current round: 5\n",
      "[[ 0.62502532  0.31247685  0.06249783]\n",
      " [ 0.6249537   0.31254233  0.06250397]\n",
      " [ 0.62497828  0.31251986  0.06250186]]\n",
      "Current round: 6\n",
      "[[ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]]\n",
      "Current round: 7\n",
      "[[ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]]\n",
      "Current round: 8\n",
      "[[ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]]\n",
      "Current round: 9\n",
      "[[ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]]\n",
      "Current round: 10\n",
      "[[ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]\n",
      " [ 0.625   0.3125  0.0625]]\n"
     ]
    }
   ],
   "source": [
    "matrix = np.matrix([[0.9,0.075,0.025],[0.15,0.8,0.05],[0.25,0.25,0.5]], dtype=float)\n",
    "for i in range(10):\n",
    "    matrix = matrix*matrix\n",
    "    print \"Current round:\" , i+1\n",
    "    print matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current round: 1\n",
      "[[ 0.405   0.4175  0.1775]]\n",
      "Current round: 2\n",
      "[[ 0.4715   0.40875  0.11975]]\n",
      "Current round: 3\n",
      "[[ 0.5156  0.3923  0.0921]]\n",
      "Current round: 4\n",
      "[[ 0.54591   0.375535  0.078555]]\n",
      "Current round: 5\n",
      "[[ 0.567288  0.36101   0.071702]]\n",
      "Current round: 6\n",
      "[[ 0.5826362  0.3492801  0.0680837]]\n",
      "Current round: 7\n",
      "[[ 0.59378552  0.34014272  0.06607176]]\n",
      "Current round: 8\n",
      "[[ 0.60194632  0.33316603  0.06488765]]\n",
      "Current round: 9\n",
      "[[ 0.6079485   0.32790071  0.06415079]]\n",
      "Current round: 10\n",
      "[[ 0.61237646  0.3239544   0.06366914]]\n",
      "Current round: 11\n",
      "[[ 0.61564926  0.32100904  0.0633417 ]]\n",
      "Current round: 12\n",
      "[[ 0.61807111  0.31881635  0.06311253]]\n",
      "Current round: 13\n",
      "[[ 0.61986459  0.31718655  0.06294886]]\n",
      "Current round: 14\n",
      "[[ 0.62119333  0.3159763   0.06283037]]\n",
      "Current round: 15\n",
      "[[ 0.62217803  0.31507813  0.06274383]]\n",
      "Current round: 16\n",
      "[[ 0.62290791  0.31441182  0.06268027]]\n",
      "Current round: 17\n",
      "[[ 0.62344896  0.31391762  0.06263343]]\n",
      "Current round: 18\n",
      "[[ 0.62385006  0.31355112  0.06259882]]\n",
      "Current round: 19\n",
      "[[ 0.62414743  0.31327936  0.06257322]]\n",
      "Current round: 20\n",
      "[[ 0.62436789  0.31307785  0.06255426]]\n",
      "Current round: 21\n",
      "[[ 0.62453135  0.31292843  0.06254022]]\n",
      "Current round: 22\n",
      "[[ 0.62465253  0.31281765  0.06252982]]\n",
      "Current round: 23\n",
      "[[ 0.62474238  0.31273552  0.0625221 ]]\n",
      "Current round: 24\n",
      "[[ 0.624809    0.31267462  0.06251639]]\n",
      "Current round: 25\n",
      "[[ 0.62485839  0.31262947  0.06251215]]\n",
      "Current round: 26\n",
      "[[ 0.624895    0.31259599  0.06250901]]\n",
      "Current round: 27\n",
      "[[ 0.62492215  0.31257117  0.06250668]]\n",
      "Current round: 28\n",
      "[[ 0.62494228  0.31255277  0.06250495]]\n",
      "Current round: 29\n",
      "[[ 0.62495721  0.31253912  0.06250367]]\n",
      "Current round: 30\n",
      "[[ 0.62496827  0.31252901  0.06250272]]\n",
      "Current round: 31\n",
      "[[ 0.62497648  0.31252151  0.06250202]]\n",
      "Current round: 32\n",
      "[[ 0.62498256  0.31251594  0.0625015 ]]\n",
      "Current round: 33\n",
      "[[ 0.62498707  0.31251182  0.06250111]]\n",
      "Current round: 34\n",
      "[[ 0.62499041  0.31250876  0.06250082]]\n",
      "Current round: 35\n",
      "[[ 0.62499289  0.3125065   0.06250061]]\n",
      "Current round: 36\n",
      "[[ 0.62499473  0.31250482  0.06250045]]\n",
      "Current round: 37\n",
      "[[ 0.62499609  0.31250357  0.06250034]]\n",
      "Current round: 38\n",
      "[[ 0.6249971   0.31250265  0.06250025]]\n",
      "Current round: 39\n",
      "[[ 0.62499785  0.31250196  0.06250018]]\n",
      "Current round: 40\n",
      "[[ 0.62499841  0.31250146  0.06250014]]\n",
      "Current round: 41\n",
      "[[ 0.62499882  0.31250108  0.0625001 ]]\n",
      "Current round: 42\n",
      "[[ 0.62499912  0.3125008   0.06250008]]\n",
      "Current round: 43\n",
      "[[ 0.62499935  0.31250059  0.06250006]]\n",
      "Current round: 44\n",
      "[[ 0.62499952  0.31250044  0.06250004]]\n",
      "Current round: 45\n",
      "[[ 0.62499964  0.31250033  0.06250003]]\n",
      "Current round: 46\n",
      "[[ 0.62499974  0.31250024  0.06250002]]\n",
      "Current round: 47\n",
      "[[ 0.6249998   0.31250018  0.06250002]]\n",
      "Current round: 48\n",
      "[[ 0.62499985  0.31250013  0.06250001]]\n",
      "Current round: 49\n",
      "[[ 0.62499989  0.3125001   0.06250001]]\n",
      "Current round: 50\n",
      "[[ 0.62499992  0.31250007  0.06250001]]\n",
      "Current round: 51\n",
      "[[ 0.62499994  0.31250005  0.06250001]]\n",
      "Current round: 52\n",
      "[[ 0.62499996  0.31250004  0.0625    ]]\n",
      "Current round: 53\n",
      "[[ 0.62499997  0.31250003  0.0625    ]]\n",
      "Current round: 54\n",
      "[[ 0.62499998  0.31250002  0.0625    ]]\n",
      "Current round: 55\n",
      "[[ 0.62499998  0.31250002  0.0625    ]]\n",
      "Current round: 56\n",
      "[[ 0.62499999  0.31250001  0.0625    ]]\n",
      "Current round: 57\n",
      "[[ 0.62499999  0.31250001  0.0625    ]]\n",
      "Current round: 58\n",
      "[[ 0.62499999  0.31250001  0.0625    ]]\n",
      "Current round: 59\n",
      "[[ 0.62499999  0.3125      0.0625    ]]\n",
      "Current round: 60\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 61\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 62\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 63\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 64\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 65\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 66\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 67\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 68\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 69\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 70\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 71\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 72\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 73\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 74\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 75\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 76\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 77\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 78\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 79\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 80\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 81\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 82\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 83\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 84\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 85\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 86\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 87\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 88\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 89\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 90\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 91\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 92\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 93\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 94\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 95\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 96\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 97\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 98\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 99\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 100\n",
      "[[ 0.625   0.3125  0.0625]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "matrix = np.matrix([[0.9,0.075,0.025],[0.15,0.8,0.05],[0.25,0.25,0.5]], dtype=float)\n",
    "vector1 = np.matrix([[0.3,0.4,0.3]], dtype=float)\n",
    "for i in range(100):\n",
    "    vector1 = vector1*matrix\n",
    "    print \"Current round:\" , i+1\n",
    "    print vector1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current round: 1\n",
      "[[ 0.695   0.1825  0.1225]]\n",
      "Current round: 2\n",
      "[[ 0.6835   0.22875  0.08775]]\n",
      "Current round: 3\n",
      "[[ 0.6714  0.2562  0.0724]]\n",
      "Current round: 4\n",
      "[[ 0.66079   0.273415  0.065795]]\n",
      "Current round: 5\n",
      "[[ 0.652172  0.28474   0.063088]]\n",
      "Current round: 6\n",
      "[[ 0.6454378  0.2924769  0.0620853]]\n",
      "Current round: 7\n",
      "[[ 0.64028688  0.29791068  0.06180244]]\n",
      "Current round: 8\n",
      "[[ 0.6363954   0.30180067  0.06180393]]\n",
      "Current round: 9\n",
      "[[ 0.63347695  0.30462117  0.06190188]]\n",
      "Current round: 10\n",
      "[[ 0.6312979   0.30668318  0.06201892]]\n",
      "Current round: 11\n",
      "[[ 0.62967532  0.30819862  0.06212607]]\n",
      "Current round: 12\n",
      "[[ 0.62846909  0.30931606  0.06221485]]\n",
      "Current round: 13\n",
      "[[ 0.6275733   0.31014174  0.06228495]]\n",
      "Current round: 14\n",
      "[[ 0.62690847  0.31075263  0.0623389 ]]\n",
      "Current round: 15\n",
      "[[ 0.62641525  0.31120496  0.06237979]]\n",
      "Current round: 16\n",
      "[[ 0.62604941  0.31154006  0.06241053]]\n",
      "Current round: 17\n",
      "[[ 0.62577811  0.31178839  0.0624335 ]]\n",
      "Current round: 18\n",
      "[[ 0.62557693  0.31197244  0.06245062]]\n",
      "Current round: 19\n",
      "[[ 0.62542776  0.31210888  0.06246336]]\n",
      "Current round: 20\n",
      "[[ 0.62531716  0.31221003  0.06247282]]\n",
      "Current round: 21\n",
      "[[ 0.62523515  0.31228501  0.06247984]]\n",
      "Current round: 22\n",
      "[[ 0.62517435  0.31234061  0.06248505]]\n",
      "Current round: 23\n",
      "[[ 0.62512926  0.31238182  0.06248891]]\n",
      "Current round: 24\n",
      "[[ 0.62509584  0.31241238  0.06249178]]\n",
      "Current round: 25\n",
      "[[ 0.62507106  0.31243504  0.0624939 ]]\n",
      "Current round: 26\n",
      "[[ 0.62505268  0.31245184  0.06249548]]\n",
      "Current round: 27\n",
      "[[ 0.62503906  0.31246429  0.06249665]]\n",
      "Current round: 28\n",
      "[[ 0.62502896  0.31247352  0.06249752]]\n",
      "Current round: 29\n",
      "[[ 0.62502147  0.31248037  0.06249816]]\n",
      "Current round: 30\n",
      "[[ 0.62501592  0.31248545  0.06249863]]\n",
      "Current round: 31\n",
      "[[ 0.6250118   0.31248921  0.06249899]]\n",
      "Current round: 32\n",
      "[[ 0.62500875  0.312492    0.06249925]]\n",
      "Current round: 33\n",
      "[[ 0.62500649  0.31249407  0.06249944]]\n",
      "Current round: 34\n",
      "[[ 0.62500481  0.3124956   0.06249959]]\n",
      "Current round: 35\n",
      "[[ 0.62500357  0.31249674  0.06249969]]\n",
      "Current round: 36\n",
      "[[ 0.62500264  0.31249758  0.06249977]]\n",
      "Current round: 37\n",
      "[[ 0.62500196  0.31249821  0.06249983]]\n",
      "Current round: 38\n",
      "[[ 0.62500145  0.31249867  0.06249988]]\n",
      "Current round: 39\n",
      "[[ 0.62500108  0.31249901  0.06249991]]\n",
      "Current round: 40\n",
      "[[ 0.6250008   0.31249927  0.06249993]]\n",
      "Current round: 41\n",
      "[[ 0.62500059  0.31249946  0.06249995]]\n",
      "Current round: 42\n",
      "[[ 0.62500044  0.3124996   0.06249996]]\n",
      "Current round: 43\n",
      "[[ 0.62500033  0.3124997   0.06249997]]\n",
      "Current round: 44\n",
      "[[ 0.62500024  0.31249978  0.06249998]]\n",
      "Current round: 45\n",
      "[[ 0.62500018  0.31249984  0.06249998]]\n",
      "Current round: 46\n",
      "[[ 0.62500013  0.31249988  0.06249999]]\n",
      "Current round: 47\n",
      "[[ 0.6250001   0.31249991  0.06249999]]\n",
      "Current round: 48\n",
      "[[ 0.62500007  0.31249993  0.06249999]]\n",
      "Current round: 49\n",
      "[[ 0.62500005  0.31249995  0.0625    ]]\n",
      "Current round: 50\n",
      "[[ 0.62500004  0.31249996  0.0625    ]]\n",
      "Current round: 51\n",
      "[[ 0.62500003  0.31249997  0.0625    ]]\n",
      "Current round: 52\n",
      "[[ 0.62500002  0.31249998  0.0625    ]]\n",
      "Current round: 53\n",
      "[[ 0.62500002  0.31249999  0.0625    ]]\n",
      "Current round: 54\n",
      "[[ 0.62500001  0.31249999  0.0625    ]]\n",
      "Current round: 55\n",
      "[[ 0.62500001  0.31249999  0.0625    ]]\n",
      "Current round: 56\n",
      "[[ 0.62500001  0.31249999  0.0625    ]]\n",
      "Current round: 57\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 58\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 59\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 60\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 61\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 62\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 63\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 64\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 65\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 66\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 67\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 68\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 69\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 70\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 71\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 72\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 73\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 74\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 75\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 76\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 77\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 78\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 79\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 80\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 81\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 82\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 83\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 84\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 85\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 86\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 87\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 88\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 89\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 90\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 91\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 92\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 93\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 94\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 95\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 96\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 97\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 98\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 99\n",
      "[[ 0.625   0.3125  0.0625]]\n",
      "Current round: 100\n",
      "[[ 0.625   0.3125  0.0625]]\n"
     ]
    }
   ],
   "source": [
    "matrix = np.matrix([[0.9,0.075,0.025],[0.15,0.8,0.05],[0.25,0.25,0.5]], dtype=float)\n",
    "vector1 = np.matrix([[0.7,0.1,0.2]], dtype=float)\n",
    "for i in range(100):\n",
    "    vector1 = vector1*matrix\n",
    "    print \"Current round:\" , i+1\n",
    "    print vector1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MZcoQdOrswv9daJQn4D7qUNR/Uq0+sO1/71KtlL57/ofnm9MlkMjDnElQUaAd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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12016b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12037b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "import math\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def bivexp(theta1, theta2):\n",
    "    lam1 = 0.5\n",
    "    lam2 = 0.1\n",
    "    lam = 0.01\n",
    "    maxval = 8\n",
    "    y = math.exp(-(lam1 + lam) * theta1 - (lam2 + lam) * theta2 - lam * maxval)\n",
    "    return y\n",
    "\n",
    "T = 5000\n",
    "sigma = 1\n",
    "thetamin = 0\n",
    "thetamax = 8\n",
    "theta_1 = [0.0] * (T + 1)\n",
    "theta_2 = [0.0] * (T + 1)\n",
    "theta_1[0] = random.uniform(thetamin, thetamax)\n",
    "theta_2[0] = random.uniform(thetamin, thetamax)\n",
    "\n",
    "t = 0\n",
    "while t < T:\n",
    "    t = t + 1\n",
    "    theta_star_0 = random.uniform(thetamin, thetamax)\n",
    "    theta_star_1 = random.uniform(thetamin, thetamax)\n",
    "    # print theta_star\n",
    "    alpha = min(1, (bivexp(theta_star_0, theta_star_1) / bivexp(theta_1[t - 1], theta_2[t - 1])))\n",
    "\n",
    "    u = random.uniform(0, 1)\n",
    "    if u <= alpha:\n",
    "        theta_1[t] = theta_star_0\n",
    "        theta_2[t] = theta_star_1\n",
    "    else:\n",
    "        theta_1[t] = theta_1[t - 1]\n",
    "        theta_2[t] = theta_2[t - 1]\n",
    "plt.figure(1)\n",
    "ax1 = plt.subplot(211)\n",
    "ax2 = plt.subplot(212)        \n",
    "plt.ylim(thetamin, thetamax)\n",
    "plt.sca(ax1)\n",
    "plt.plot(range(T + 1), theta_1, 'g-', label=\"0\")\n",
    "plt.sca(ax2)\n",
    "plt.plot(range(T + 1), theta_2, 'r-', label=\"1\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(2)\n",
    "ax1 = plt.subplot(211)\n",
    "ax2 = plt.subplot(212)        \n",
    "num_bins = 50\n",
    "plt.sca(ax1)\n",
    "plt.hist(theta_1, num_bins, normed=1, facecolor='green', alpha=0.5)\n",
    "plt.title('Histogram')\n",
    "plt.sca(ax2)\n",
    "plt.hist(theta_2, num_bins, normed=1, facecolor='red', alpha=0.5)\n",
    "plt.title('Histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Arde8BrjnHrfO177mfOPBwOdxM1KVsyCFcLaira3D0TivxbFj/nM5Az3glsun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\ndf9JFAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1183bd10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.linalg import cholesky  \n",
    "mu = np.array([[3, 5]])  \n",
    "Sigma = np.array([[3, 0.5], [1.5, 3]])  \n",
    "R = cholesky(Sigma)  \n",
    "s = np.dot(np.random.randn(1000, 2), R) + mu  \n",
    "# 注意绘制的是散点图，而不是直方图  \n",
    "plt.plot(s[:,0],s[:,1],'+')  \n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1NU8llLFINYNRaO7cuZTEjTKOAncB3wn2vEuYuGoFY0InqeHBXcH9MuAonZ2O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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a45770>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def norm_dist_prob(theta):\n",
    "    y = norm.pdf(theta, loc=3, scale=2)\n",
    "    return y\n",
    "\n",
    "T = 5000\n",
    "\n",
    "t = 0\n",
    "while t < T:\n",
    "    t = t + 1\n",
    "    theta_star = norm.rvs(loc=theta[t - 1], scale=sigma, size=1, random_state=None)\n",
    "    #print theta_star\n",
    "    alpha = min(1, (norm_dist_prob(theta_star[0]) / norm_dist_prob(theta[t - 1])))\n",
    "\n",
    "    u = random.uniform(0, 1)\n",
    "    if u < alpha:\n",
    "        theta[t] = theta_star[0]\n",
    "    else:\n",
    "        theta[t] = theta[t - 1]\n",
    "\n",
    "\n",
    "plt.scatter(theta, norm.pdf(theta, loc=3, scale=2))\n",
    "num_bins = 50\n",
    "plt.hist(theta, num_bins, normed=1, facecolor='red', alpha=0.7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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