{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112934748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from copy import copy\n",
    "import math, random\n",
    "import matplotlib.pyplot as plt                   #   for plotting data\n",
    "from matplotlib.patches import Ellipse      #  for drawing\n",
    "\n",
    "actual_landmarks = [np.array([-0.5,0.0]),np.array([0.5,0.0]),np.array([0.0,0.5])]\n",
    "\n",
    "def draw_landmarks(landmarks):\n",
    "    xs = [ e[0] for e in actual_landmarks ]\n",
    "    ys = [ e[1] for e in actual_landmarks ]\n",
    "    \n",
    "    plt.scatter(xs,ys,s=300,marker=\"*\",label=\"landmarks\",color=\"orange\")\n",
    "    \n",
    "draw_landmarks(actual_landmarks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_x = np.array([0.2,0.3,math.pi*200.0/180])   #ロボットの実際の姿勢\n",
    "\n",
    "def draw_robot(pose):\n",
    "    plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color=\"red\",label=\"actual robot motion\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fv706L7XoUrjoUTj93Gr89HOr9UWXVH/a7L79+M8jSZ3Wxfya2eE+eghGX4ALNsPyO6pX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112aac860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_robot(actual_x)\n",
    "draw_landmarks(actual_landmarks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relative_landmark_pos(pose,landmark):\n",
    "    x,y,theta = pose\n",
    "    lx,ly = landmark\n",
    "    \n",
    "    distance = math.sqrt((lx - x)**2 + (ly - y)**2)\n",
    "    direction = math.atan2(ly - y, lx - x) - theta\n",
    "    \n",
    "    return distance, direction, lx, ly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "measurements = [ relative_landmark_pos(actual_x, ln) for ln in actual_landmarks ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0.7615773105863908, -6.2273593712933693, -0.5, 0.0), (0.4242640687119285, -4.2760566673861078, 0.5, 0.0), (0.28284271247461906, -1.1344640137963142, 0.0, 0.5)]\n"
     ]
    }
   ],
   "source": [
    "print(measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def draw_observation(pose, measurement):\n",
    "    x,y,theta = pose\n",
    "    mdistance, mdirection,tmp_x,tmp_y = measurement\n",
    "    \n",
    "    lx = x + mdistance * math.cos(theta + mdirection)\n",
    "    ly = y + mdistance * math.sin(theta + mdirection)\n",
    "    \n",
    "    plt.plot([pose[0],  lx],[pose[1],  ly],color=\"pink\")\n",
    "    \n",
    "def draw_observations(pose, measurements):\n",
    "    for m in measurements:\n",
    "        draw_observation(pose,m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xYqkSu4isU3Gxbyo2O+cTMSJe4JR9yT22AG/+pn9dq8kpeKMXXn8L5hb8N+17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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a3d668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_robot(actual_x)\n",
    "draw_landmarks(actual_landmarks)\n",
    "draw_observations(actual_x, measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def observation(pose, landmark):    \n",
    "    adistance, adirection, alx, aly = relative_landmark_pos(pose,landmark)\n",
    "    \n",
    "    mdistance = random.gauss(adistance,adistance*0.1) \n",
    "    mdirection = random.gauss(adirection, 5.0/180.0 * math.pi)\n",
    "    \n",
    "    if math.cos(mdirection) < 0.0:\n",
    "        return None\n",
    "    \n",
    "    return mdistance, mdirection, alx, aly\n",
    "\n",
    "def observations(pose,landmarks):\n",
    "    return filter(lambda x: x != None, [ observation(pose, e) for e in landmarks ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "measurements = observations(actual_x, actual_landmarks) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yZ8D/yUpVmXUtxzwO/Bt3vwW4D/hvZrY0izWmzcxKgKeA+4F24GEza79ks88D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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11305c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_robot(actual_x)\n",
    "draw_landmarks(actual_landmarks)\n",
    "draw_observations(actual_x, measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### クラスや関数のコピペ ###\n",
    "\n",
    "class Particle:\n",
    "    def __init__(self,w):\n",
    "        self.pose = np.array([0.0,0.0,0.0])\n",
    "        self.weight = w\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return \"pose: \" + str(self.pose) + \" weight: \" + str(self.weight)\n",
    "        \n",
    "\n",
    "def f(x_old,u):\n",
    "    pos_x, pos_y, pos_theta = x_old\n",
    "    act_fw, act_rot = u\n",
    "    \n",
    "    act_fw = random.gauss(act_fw,act_fw/10)\n",
    "    dir_error = random.gauss(0.0, math.pi / 180.0 * 3.0)\n",
    "    act_rot = random.gauss(act_rot,act_rot/10)\n",
    "    \n",
    "    pos_x += act_fw * math.cos(pos_theta + dir_error)\n",
    "    pos_y += act_fw * math.sin(pos_theta + dir_error)\n",
    "    pos_theta += act_rot\n",
    "    \n",
    "    return np.array([pos_x,pos_y,pos_theta])\n",
    "\n",
    "### 描画関数は少し変更を ###\n",
    "def draw(pose,particles):    \n",
    "    fig = plt.figure(i,figsize=(8, 8))\n",
    "    sp = fig.add_subplot(111, aspect='equal')\n",
    "    sp.set_xlim(-1.0,1.0)\n",
    "    sp.set_ylim(-0.5,1.5)\n",
    "    \n",
    "    xs = [e.pose[0] for e in particles]\n",
    "    ys = [e.pose[1] for e in particles]\n",
    "    vxs = [math.cos(e.pose[2])*e.weight for e in particles]  #重みで長さを変えるようにしましょう\n",
    "    vys = [math.sin(e.pose[2])*e.weight for e in particles]  #重みで長さを変えるようにしましょう\n",
    "    plt.quiver(xs,ys,vxs,vys,color=\"blue\",label=\"particles\")\n",
    "    \n",
    "    plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color=\"red\",label=\"actual robot motion\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rd9X755aIOKltWcfPZVNMom/vjIg9bX14d9uyS+rP7vaIuGT0urNpEv26sq1P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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131544e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11333d9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xvoa6KyJibkTcXT8m9aU/kiQNJX3dEz8duCUz9wBuqefX9hLwwczcBzgC+FpE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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1132460b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCGuCRJhTLE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\nEJckqVD/H+kq4sczC+v6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b0a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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88pTSFuChiOgsj3drA+ql0TJpN2ibBmuuHnzbHX+CR6/rX77f22HScxpfN2ki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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112a39f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jFsO02UPTPil3fsbUQzNCfAWwT9X83mVZzWUiog14GbB6gOsCkFK6KKXUnlJq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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113095940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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P/aoZsOP2MGLEwNZPGqQMcUkDZ9363OJetjxPb1MP03fJt4eNttUtdccQl9S/\nUso9y59uyj3NIY9d/qpp+Vq3rW6pxwxxSf2jy1b3JBg9aqBrJxXJEJe09bS2uluvdaeUW927T8tj\nmdvqlvrEEJdUe+s3tLW6166D+nrYdad8rXuMrW6pVgxxSbWRUn5i2LKm/ASxlGD7cfkBJJMn2OqW\ntgJDXFLfrN+Qn9W9rAnWrIP6Opi6E0ydBGNGD3TtpCHNEJfUeynBqpfg6eWwfEWeHz8uP4DEVrfU\nbwxxST23YWPlWnd1q3tyvtY91la31N8McUk98+iTOcBTgvFj81CokydAXd1A10watgxxST1TNyLf\n0z1lMowbM9C1kYQhLqmnXjV9oGsgqQN7n0iSVChDXFJ7Lc2w4KL8KmlQM8Qltdf0G3jgH2H5bwe6\nJpK6YYhLau/Jq4GAJ64e6JpI6oYhLqlNaoE/XQ+k/JpaBrpGkjbDEJfU5vl7oWVDnm5ZD8/PG9j6\nSNosQ1xSmyeugeY1ebp5DTx5zcDWR9Jm1eQ+8Yg4Cvg6UAdcnlK6uMPyM4AvA0srRf+RUrq8sux0\n4DOV8otSSlfWok6SurDuBbjnTNi4etNly++BVOmVnpph8eWwcsGm69WPg7dcASMnbt26StqsPod4\nRNQB3wAOB5YA8yJibkrp4Q6r/jil9JEO204EPgc0AAmYX9l2RV/rJakL22wH9WNg6Y3dr9v8Mjx7\n+6blu50K24yvfd0k9UotTqcfACxOKT2WUloPXAuc0MNtjwRuTSm9UAnuW4GjalAnSV0ZsQ0cfDUc\ndDXUj4Xo4djnUZdb4AddAwf/CEY44KM00GoR4rsCT1XNL6mUdfSeiHggIm6IiNbxG3u6LRFxTkQ0\nRkRjU1NTDaotDXMzT4FjHoTxe0FdN2Oh143J6x3zAMyc0z/1k9St/urY9p/AzJTS3uTWdq+ve6eU\nLkspNaSUGiZPnlzzCkrD0rhZcPR8mHlabmV3pn5sXn70/Ly+pEGjFiG+FKh+MsI02jqwAZBSej6l\ntK4yeznwxp5uK2krG7ENjJ6SbynrTMsGGD01rydpUKlFiM8DZkfErIjYFpgDzK1eISKmVM0eDyys\nTN8CHBEREyJiAnBEpUxSf3r8B+1DPKoCu2V9Xi5p0OlziKeUNgIfIYfvQuC6lNJDEfGFiDi+stpH\nI+KhiLgf+ChwRmXbF4ALyX8IzAO+UCmT1F9eXARrn2mbrxsNM0/Nr63WLoOXFvd/3SRtVqSUBroO\nvdbQ0JBH2eSrAAASAElEQVQaGxsHuhrS0LDgn2HBPwEjYNRkOOQ/YcI+sOJ++NVxsLYJSPCGz8Hr\nPjXQtZWGjIiYn1Jq6Ms+HLFNGu4evzJf955xMhy7MAc45NdjF8KMk/Ip9ccch0kabAxxaThr2Qgt\n6+Dga+Ggq3JP9Gr1Y+GgH+TlLWvz+pIGDUdrkIazEfVwwhPdr7fbe/OPpEHFlrgkSYUyxCVJKpQh\nLklSoQxxSZIKZYhLklQoQ1ySpEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JU\nKENckqRCGeKSJBXKEJckqVCGuCRJhTLEJUkqlCEuSVKhDHFJkgpliEuSVChDXJKkQhnikiQVyhCX\nJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIKZYhLklQoQ1ySpEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqU\nIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCGuCRJhTLEJUkqVE1CPCKOiohHImJxRFzQ\nyfKPRcTDEfFARNweEbtVLWuOiPsqP3NrUR9JkoaD+r7uICLqgG8AhwNLgHkRMTel9HDVav8LNKSU\nXomI84F/Bd5XWbYmpbRvX+shSdJwU4uW+AHA4pTSYyml9cC1wAnVK6SU7kwpvVKZvQeYVoP3lSRp\nWKtFiO8KPFU1v6RS1pWzgJur5kdFRGNE3BMRJ9agPpIkDQt9Pp3eGxHxfqABOKSqeLeU0tKI2B24\nIyIeTCn9sZNtzwHOAZgxY0a/1FeSpMGsFi3xpcD0qvlplbJ2IuIw4NPA8Smlda3lKaWlldfHgLuA\n/Tp7k5TSZSmlhpRSw+TJk2tQbUmSylaLEJ8HzI6IWRGxLTAHaNfLPCL2Ay4lB/hzVeUTImJkZXoS\ncDBQ3SFOkiR1oc+n01NKGyPiI8AtQB1wRUrpoYj4AtCYUpoLfBkYB1wfEQB/SikdD7wWuDQiWsh/\nUFzcoVe7JEnqQqSUBroOvdbQ0JAaGxsHuhqSJG2xiJifUmroyz4csU2SpEIZ4pIkFcoQlySpUIa4\nJEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCGuCRJhTLEJUkqlCEuSVKh\nDHFJkgpliEuSVChDXJKkQhnikiQVyhCXJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIKZYhLklQoQ1yS\npEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCG\nuCRJhTLEJUkqlCEuSVKhDHFJkgpliEuSVChDXFtfSzMsuCi/Sqo9v2PDliGura/pN/DAP8Ly3w50\nTaShye/YsGWIa+t78mog4ImrB7om0tDkd2zYMsS1daUW+NP1QMqvqWWgayQNLX7HhjVDXFvX8/dC\ny4Y83bIenp83sPWRhhq/Y8NaTUI8Io6KiEciYnFEXNDJ8pER8ePK8v+JiJlVyz5VKX8kIo6sRX00\niDxxDTSvydPNa+DJawa2PtJQ43dsWKvv6w4iog74BnA4sASYFxFzU0oPV612FrAipfTqiJgDfAl4\nX0TsBcwBXgdMBW6LiD1SSnaxLMm6F+CeM2Hj6k2XLb8HWj/O1AyLL4eVCzZdr34cvOUKGDlx69ZV\nKpHfMXWhzyEOHAAsTik9BhAR1wInANUhfgLw+cr0DcB/RERUyq9NKa0DHo+IxZX93V2Deqm/bLMd\n1I+BpTd2v27zy/Ds7ZuW73YqbDO+9nWThgK/Y+pCLU6n7wo8VTW/pFLW6ToppY3AKmDHHm6rwW7E\nNnDw1XDQ1VA/FqKuZ9tFXW4dHHQNHPwjGFGLvymlIcjvmLpQTMe2iDgnIhojorGpqWmgq6POzDwF\njnkQxu8FdWM2v27dmLzeMQ/AzDn9Uz+pdH7H1EEtQnwpML1qflqlrNN1IqIe2B54vofbApBSuiyl\n1JBSapg8eXINqq2tYtwsOHo+zDwttwA6Uz82Lz96fl5fUs/5HVOVWoT4PGB2RMyKiG3JHdXmdlhn\nLnB6Zfok4I6UUqqUz6n0Xp8FzAburUGdNJBGbAOjp+TbXTrTsgFGT83rSeo9v2Oq6HOIV65xfwS4\nBVgIXJdSeigivhARx1dW+y6wY6Xj2seACyrbPgRcR+4E91/Ah+2ZPkQ8/oP2/8FE1X8mLevzcklb\nzu+YqE3vdFJKNwE3dSj7bNX0WuDkLrb9IvDFWtRDg8SLi2DtM23zdaNhxnvhT9e13c+6dhm8tBi2\ne/XA1FEqmd8xVRTTsU0F+dP1+X7VEaNgzHQ44m448Pv5dcz0XP7noSIl9ZrfMVUY4qq9x6/M1+Rm\nnAzHLoQJ++TyCfvk+Rkn5dN9j105sPWUSuV3TBWGuGqrZSO0rIODr4WDrsq9ZKvVj4WDfpCXt6zN\n60vqOb9jqhK5k3hZGhoaUmNj40BXQ5KkLRYR81NKDX3Zhy1xSZIKZYhLklQoQ1ySpEIZ4pIkFcoQ\nlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCGuCRJhTLEJUkq\nlCEuSVKhDHFJkgpliEuSVChDXJKkQhnikiQVyhCXJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIKZYhL\nklQoQ1ySpEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXK\nEJckqVCGuCRJhTLEJUkqlCEuSVKhDHFJkgpliEuSVKg+hXhETIyIWyNiUeV1Qifr7BsRd0fEQxHx\nQES8r2rZ9yPi8Yi4r/Kzb1/qI0nScNLXlvgFwO0ppdnA7ZX5jl4BPphSeh1wFPBvEbFD1fJPpJT2\nrfzc18f6SJI0bPQ1xE8ArqxMXwmc2HGFlNKjKaVFlemngeeAyX18X0mShr2+hvjOKaVllelngJ03\nt3JEHABsC/yxqviLldPsX4uIkZvZ9pyIaIyIxqampj5WW5Kk8nUb4hFxW0Qs6OTnhOr1UkoJSJvZ\nzxTgB8CHUkotleJPAXsCbwImAp/savuU0mUppYaUUsPkyTbkJUmq726FlNJhXS2LiGcjYkpKaVkl\npJ/rYr3xwC+AT6eU7qnad2srfl1EfA/4+17VXpKkYayvp9PnAqdXpk8Hbuy4QkRsC/wUuCqldEOH\nZVMqr0G+nr6gj/WRJGnY6GuIXwwcHhGLgMMq80REQ0RcXlnnvcDbgTM6uZXsRxHxIPAgMAm4qI/1\nkSRp2Ih8KbssDQ0NqbGxcaCrIUnSFouI+Smlhr7swxHbJEkqlCEuSVKhDHFJkgpliEuSVChDXJKk\nQhnikiQVyhCXJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIKZYhLklQoQ1ySpEIZ4pIkFcoQlySpUIa4\nJEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRCGeKSJBXKEJckqVCGuCRJhTLEJUkqlCEuSVKh\nDHFJkgpliEuSVChDXJKkQhnikiQVyhCXJKlQhrgkSYUyxCVJKpQhLklSoQxxSZIKZYhLklQoQ1yS\npEIZ4pIkFcoQlySpUIa4JEmFMsQlSSqUIS5JUqEMcUmSCmWIS5JUKENckqRC9SnEI2JiRNwaEYsq\nrxO6WK85Iu6r/MytKp8VEf8TEYsj4scRsW1f6iNJ0nDS15b4BcDtKaXZwO2V+c6sSSntW/k5vqr8\nS8DXUkqvBlYAZ/WxPpIkDRt9DfETgCsr01cCJ/Z0w4gI4FDghi3ZXpKk4a6vIb5zSmlZZfoZYOcu\n1hsVEY0RcU9EtAb1jsDKlNLGyvwSYNc+1keSpGGjvrsVIuI2YJdOFn26eiallCIidbGb3VJKSyNi\nd+COiHgQWNWbikbEOcA5ldl1EbGgN9sXYhKwfKArsZUM1WPzuMozVI/N4yrPa/q6g25DPKV0WFfL\nIuLZiJiSUloWEVOA57rYx9LK62MRcRewH/ATYIeIqK+0xqcBSzdTj8uAyyrv25hSauiu7qUZqscF\nQ/fYPK7yDNVj87jKExGNfd1HX0+nzwVOr0yfDtzYcYWImBARIyvTk4CDgYdTSgm4Ezhpc9tLkqTO\n9TXELwYOj4hFwGGVeSKiISIur6zzWqAxIu4nh/bFKaWHK8s+CXwsIhaTr5F/t4/1kSRp2Oj2dPrm\npJSeB97VSXkjcHZl+nfAG7rY/jHggC1468u2YJsSDNXjgqF7bB5XeYbqsXlc5enzsUU+qy1Jkkrj\nsKuSJBVq0IZ4RJwcEQ9FREtEdNkzMSKOiohHKkO3XlBVPiiHdO3JULUR8c6qYWrvi4i1rffXR8T3\nI+LxqmX79v9RbGooD8Hbw89s34i4u/I7+0BEvK9q2aD6zLr6zlQtH1n5DBZXPpOZVcs+VSl/JCKO\n7M96d6cHx/WxiHi48vncHhG7VS3r9PdysOjBsZ0REU1Vx3B21bLTK7+7iyLi9I7bDqQeHNfXqo7p\n0YhYWbVs0H5mEXFFRDwXXdwKHdklleN+ICL2r1rWu88rpTQof8gd4l4D3AU0dLFOHfBHYHdgW+B+\nYK/KsuuAOZXpbwPnD/QxVeryr8AFlekLgC91s/5E4AVgTGX++8BJA30cW3pcwOouygfl59XTYwP2\nAGZXpqcCy4AdBttntrnvTNU6fw18uzI9B/hxZXqvyvojgVmV/dQN9DH14rjeWfU9Or/1uDb3ezkY\nfnp4bGcA/9HJthOBxyqvEyrTEwb6mHp6XB3W/xvgikI+s7cD+wMLulh+DHAzEMBbgP/Z0s9r0LbE\nU0oLU0qPdLPaAcDilNJjKaX1wLXACRGDekjX3g5VexJwc0rpla1aq74bykPwdntsKaVHU0qLKtNP\nk8dMmNxvNey5Tr8zHdapPt4bgHdVPqMTgGtTSutSSo8Di9myjqlbQ7fHlVK6s+p7dA95bIoS9OQz\n68qRwK0ppRdSSiuAW4GjtlI9e6u3x3UKcE2/1KyPUkq/Jje+unICcFXK7iGPmTKFLfi8Bm2I99Cu\nwFNV861Dtw7mIV17OlRtqzls+ov7xcopmK9F5R78QWAoD8Hbq88sIg4gtyz+WFU8WD6zrr4zna5T\n+UxWkT+jnmw7UHpbt7PILaFWnf1eDhY9Pbb3VH7HboiI6b3cdiD0uG6VSx+zgDuqigfzZ9adro69\n159Xn24x66vYzJCuKaViB37Z3HFVz6S02aFqqfxl9gbglqriT5GDZFvy7QmfBL7Q1zr3RI2Oa7fU\nxyF4t4Yaf2Y/AE5PKbVUigfsM9OmIuL9QANwSFXxJr+XKaU/dr6HQek/gWtSSusi4lzymZRDB7hO\ntTQHuCGl1FxVVvpnVhMDGuJpM0O69tBSYHrVfOvQrc/TiyFda21zxxU9HKq24r3AT1NKG6r23doi\nXBcR3wP+viaV7oFaHFeqwRC8W0Mtji0ixgO/IP8Rek/VvgfsM+tEV9+ZztZZEhH1wPbk71RPth0o\nPapbRBxG/sPskJTSutbyLn4vB0sgdHtsKY/Z0epycj+O1m3f0WHbu2pewy3Tm9+nOcCHqwsG+WfW\nna6OvdefV+mn0+cBsyP3bN6W/EHPTbmHwGAd0rXboWqrbHINqBIirdeRTwQGy4NghvIQvD05tm2B\nn5Kvc93QYdlg+sw6/c50WKf6eE8C7qh8RnOBOZF7r88CZgP39lO9u9PtcUXEfsClwPEppeeqyjv9\nvey3mnevJ8c2pWr2eGBhZfoW4IjKMU4AjqD9mb2B1JPfRSJiT3Inr7urygb7Z9aducAHK73U3wKs\nqvyx3/vPq7977fX0B/gL8vWAdcCzwC2V8qnATVXrHQM8Sv4L7NNV5buT/4NZDFwPjBzoY6rUa0fg\ndmARcBswsVLeAFxetd5M8l9lIzpsfwfwIDkIfgiMG+hj6ulxAQdV6n5/5fWswf559eLY3g9sAO6r\n+tl3MH5mnX1nyKf3j69Mj6p8Bosrn8nuVdt+urLdI8DRA/3Z9PK4bqv8X9L6+czt7vdysPz04Nj+\nBXiocgx3AntWbXtm5bNcDHxooI+lN8dVmf88ebju6u0G9WdGbnwtq/yfsITcB+M84LzK8gC+UTnu\nB6m6A6u3n5cjtkmSVKjST6dLkjRsGeKSJBXKEJckqVCGuCRJhTLEJUkqlCEuSVKhDHFJkgpliEuS\nVKj/H7Px+9U3bs58AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d097b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QziurRJJCXESkIxSXeO27tNxblU+bCL2b+S/3aJkHeE0MFsyAoYM7ragSXQpx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\nPUayIX4x8ED88QPAJQ03CCFsDCFsij/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112e3f710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+3/kppzRuu2uXVxk7+WTv9PbNb/pQOZHmdDpdRPq0Z5+F//kfWLoU3nraQR78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\nA4aqkDO/xclqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c1ffd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bLlhS7aO5JAK8vr7xmOj9+8P06X6rrEzvWLhIdxTVKWaz8L3qYjPbgPc4LwQI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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b9a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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C6eWNfPjDPkjv1FPbFowRkfwaqHPi04CVaY8rk8s6Wy4SSUVFXkClJ5Ys8R57\nfb3XGJ85s/Pb+PF+vvzww/1wdm+UlvprTZnigZu6ff7oKjZuT7D/+8bxdtpr19bCj37U9jXGjvXR\n9Pu9J8H0kdv484W9a4uI9K/YDGwzs3nAPICZM2fmuTUi2WtogMceg2nTMgweaycEn6f7+efbLp85\ns7Xn/+abXddab2ry0q/nn+9HDMrLYVvtNoa9spFvXDeVt9/NfFHK9Olwxhne4z7qKC/VyvJiqMpc\ndlVE8m+gQnwVkD5Gd3py2Sr8kHr68kczvUAIYT4wH6CioiKPsy+L9Mx73pP9tlde6VN8lpX57Gin\nnOJlU4cP9+u3H3yw43PKyrznPGZMa6/7wQd9qtQf/AA+9jE4amIVZx5VxG8WTMz4e6dO9apzkya1\nW1GSgOYWP49QpCtSRaJmoEJ8AXCJmd2GD2yrDyGsMbP7gO+bWeos24nA1weoTSKR8tRTPovYggXw\nvvd5cIP3uu+6y+ut/9d/dQzs9pOorFzpA9Yuu8wf3/OnBq7+4zrm/3UC6zZm/sivXu0Tsjz8cLsa\n6iXJ7RuboEwznYhETa4uMbsV71FPMLNKfMR5CUAI4TfAvfjlZcvxS8w+lVy3zsy+CzyXfKkrUoPc\nRAabI47wW3tmPlq9vdWr2wZ4CHD99fDFL7YdPX7Jh2tIFAduf2oS8+f7YfniYh9pnrqlHq9f3y7E\nE8k/EU3N0M2pABEZeLkanX5ON+sD8PlO1l0PXJ+LdogMBi0t8Ne/+iQqjzziy955x4P+X/9qu+2w\nIc3855lrqW4Zw2PPDOkwdWq30nviIhI5OsklEjNnnumDzxoafBDbpz/tM6W1D/CTToIX76tj1LBm\nplRM7nmAg0JcJOJiMzpdRHzk+t13+/033vDiMO1nT/vgB32A3AH7B3i2GkqHw+gRvfuF/z6crhAX\niSKFuEgMtLTAf/yHF4JJWbu27TZHHunnxHfbLbXBBti+A3buwxRkJZknQRGRaFCIi0RcQ4PPQ37X\nXZnXz5wJt98Ohx7aumzhQphZV8XUCWUwYUzvf3lxMRSZQlwkonROXCTCNm3ya8U7C3CAww6Dvff2\n+zU1PqHJly/azNQRW6hkEj09Gd6hkEwiocPpIhGlEBeJqJoan2zkoYe63u6+++C//9tHq++2G9xw\nA3z17CrWbSzmj4+N7/rJaRoa4He/8y8EbeY6L0lAY45mYRGRnFKIi0TQm2/6NePtR5y3t+++cPrp\nfqnZl7+vb7/uAAAgAElEQVTs9dl3mbadM967gc2jJ/KV/y7u9ndt3Qq//CXssgtcdJHPZPbjH6dt\nkEjocLpIRCnERSJm2zY/x33ssR3XFRV5ZbWrr4ZnnvEQv/FGeO01Xz9mDNz1y2qs2Jh5WGuJ1Uxf\nBjZsgO9/H2bN8gIxlZW+fNgwf51/K9HhdJGoUoiLRMzQofCBD/gc3wDjxvl58aFDfSrQe+7x3vP7\n39+6DcCFF8IbrzSxb3kdNmk8lJYQAlx+OXz3u63b1dT4BCk77eQ/U6Pcx4zxbd95x8P930qK1RMX\niSiNTheJmDVr4NJL4XOfg9NO81nIjjnGe+hLlsB++8GyZa3bV1TANdckp0h9p8avR5s+iaYmf41r\nr/W5yVeuhJ/8xB+nX1s+cSJ85Svw2c/6decdJBJedjWEHg+SE5H+pRAXiZgxY1oHs61e7dd/p3rL\nK1a0bjd+PPzwhz4avagID+9VNTBuFNuLh3LOR1sLwzz8sJ/zbmxsff7MmT4g7oILvJffqZKEB3hz\nc2vxFxGJBH0iRSImFajr1vlh9bff7rjNpz7lvepx49IWVtdBYxObx0zmlBPhiSdaV9XVtd7ffXef\n4ezcc5Nzhnfn36VXFeIiUaNz4iIRtGWLn/9esiTz+sceazdYLQSorKaxbChHfHBkmwBPKSuDW2+F\npUvh/POzDHBoDW6dFxeJHIW4SMQ0Nvo57Kef7nybTZtg/vy0w+vr6mHrdi795WRefjnzeesdO+C3\nv4Xa2h42qET100WiSsfGRCKkpcV7yX//e9vl5eV+yVnqtueebceYbXylms11JVxz+9iMr2sGs2f7\n5WP/939+TXnWY9Q0k5lIZCnERSIiBPjSl/yyse5CO93TD2zh8NJNfPf26QwZWsQee/h57z32aL3t\nuisMGdLLhiWSBWPUExeJHIW4SES88IKH79KlXYd2uvp6KN9eTVNJEV+6agJX3doPV4GpJy4SWQpx\nkYg48EC/9cTosgZGj1oH0yYxdWY/fZzNvDeu+ukikaOBbSJxtqraf06f2PV2faWZzEQiSSEuEldN\nTbBmLUwcB0PK+vd3lWgSFJEoUoiLxNWaWmj2Eqv9TvXTRSJJIS4SR6kSq6NHwsjh/f/7dDhdJJIU\n4iJxtHY97GiAGQPQCwcdTheJKIW4SNwkS6wybAiMGz0wv7Mk4YfuW1oG5veJSFYU4iJxs2ETbN7q\n58IHamrQVP30Jl1mJhIlCnGRuKms9p7xpPED9ztV8EUkkhTiInGyZZtPdjJ1YnIS8QGSKr2qEBeJ\nFIW4SJxUVkORwbTygf29mslMJJIU4iJx0dAI1XUwaUIPJgPPER1OF4kkhbhIXKyq8ZHpA1HcpT2F\nuEgkKcRF4qC5GVbXwPgxfmnZQCsq8pHwGp0uEikKcZE4qKrzAB2o4i7tmangi0gEKcRFoi4En61s\n5HAYNSJ/7VCIi0SOQlwk6uo2wLYd3gsfqOIumSSKNTpdJGIU4iJRt7IahpTChLH5bYd64iKRoxAX\nibKNm/02Lc+9cEjOZKaBbSJRohAXibKV1X4Ye8qEfLektSceQr5bIiJJCnGRqNq2A2rXw5RyKC7O\nd2s8xEPw2cxEJBIU4iJRtaraD6FPm5jvlriESq+KRI1CXCSKGptgTS1MHAdlpflujSvRJCgiUaMQ\nF4miNWuhpSU/JVY7o9KrIpGjEBeJmpYWr5M+dhSMGJbv1rTS4XSRyFGIi0RNzTqfsSxKvXBI64nr\nMjORqFCIi0RJCD5n+PCh3hOPEh1OF4kchbhIlKzfCFu2eS8838Vd2jPzS910OF0kMnIS4mZ2kpkt\nM7PlZnZZhvU/M7MXkrfXzWxD2rrmtHULctEekdhaWQWlJT4qPYpUelUkUhJ9fQEzKwauAU4AKoHn\nzGxBCOGV1DYhhC+lbf+fwIFpL7EthHBAX9shEnubt8KGTTB7ms/fHUUlxQpxkQjJxV+KQ4DlIYQV\nIYQG4Dbg9C62Pwe4NQe/V6SwVFZ7eE8pz3dLOpdI6HC6SITkIsSnASvTHlcml3VgZjsBs4GH0xYP\nMbNFZrbQzM7IQXtE4mdHg49KnzKhdQBZFJUkNDpdJEIG+q/FXODOEEL6X4GdQgirzGxn4GEzezmE\n8Gb7J5rZPGAewMyZMwemtSIDZVWNj0yfFrHLytrTOXGRSMlFT3wVMCPt8fTkskzm0u5QeghhVfLn\nCuBR2p4vT99ufgihIoRQUV4e4cONIj3V1Ayr10L5WBhalu/WdC2RgOZmzWQmEhG5CPHngDlmNtvM\nSvGg7jDK3Mz2AMYCT6ctG2tmZcn7E4AjgVfaP1ekoFXVejBGrbhLJrpWXCRS+nw4PYTQZGaXAPcB\nxcD1IYSlZnYFsCiEkAr0ucBtIbT5Cr8n8Fsza8G/UPwwfVS7SMFLFXcZPQJGjch3a7qXPglKaUl+\n2yIiuTknHkK4F7i33bJvtXv8nQzPewrYNxdtEImltet9UNuuM7rfNgpUP10kUiJ6MarIIBACVFb5\nefDxY/LdmuzocLpIpCjERfKlfjNs2hrNEqud0SQoIpGiEBfJl8oqD8VJ4/PdkuzpcLpIpCjERfJh\n63aoq4ep5T6pSFwUF/lRAx1OF4kEhbhIPlRWeRhOnZjvlvSMGSQ0k5lIVCjERQZaQyNU18Hk8fG8\nTEtV20QiQyEuMtBW10BLiEdxl0wU4iKRoRAXGUjNLV5idfxoGDY0363pnUTCS8WKSN4pxEUGUnWd\n92KnT853S3pPPXGRyFCIiwyUVHGXkcO8zGpcpUJck6CI5J1CXGSg1NXDth3eC49LcZdMEsUe4C0t\n+W6JyKCnEBcZKJVVUFbqU47GmUqvikSGQlxkIGzc7GVWp0+Mdy8cVHpVJEIU4iIDobLaK7NNLs93\nS/pOpVdFIkMhLtLftu/wKUenTPDzyXGnw+kikaEQF+lvldV+CD2uxV3aU4iLRIZCXKQ/NTbBmlof\nzFZWmu/W5EbqaIIOp4vknUJcpD+tWeuXYs2IcXGX9oqKfDYz9cRF8k4hLtJfWlpgVQ2MGQkjhuW7\nNbmlqm0ikaAQF+kvNet8xrJC6oWnJBI6nC4SAQpxkf4Qgg9oGzYExo7Kd2tyrySh68RFIkAhLtIf\n1m+ELdu8Fx734i6Z6HC6SCQoxEX6Q2U1lJbAxHH5bkn/SBTrcLpIBCjERXJt81bviU+d6CO5C1FJ\nck5xzWQmklcF+hdGJI8qqz28pxZAidXOqPSqSCQoxEVyaUeDj0qfPKG1slkh0iQoIpGgEBfJpVU1\nfoh5+sR8t6R/qfSqSCQoxEVypbnZK7RNGAtDh+S7Nf0roRAXiQKFuEiuVNX6YK8ZBTLRSVdKdE5c\nJAoU4iK5kCruMmo4jBqR79b0v5LkJCjqiYvklUJcJBdq18P2hsIssZpJcbEXsVGIi+SVQlykr0KA\nldUwpAzGj8l3awaGmQq+iESAQlykrzZuhk1bYPqkwiyx2hnVTxfJO4W4SF+trPZe6eTx+W7JwNJM\nZiJ5pxAX6Yut26Fug5dYLS7Od2sGliZBEck7hbhIX6yq9kPo0wq8uEsmJcUKcZE8U4iL9FZjo18b\nPmm8z1g22OhwukjeKcRFemv1WmgJPqBtMCpJ+P43a3CbSL4oxEV6o6XF66SPGw3Dh+a7NfmhSVBE\n8k4hLtIb1XV+Pniw9sJB05GKRIBCXKSnUiVWRwyDMSPz3Zrca2mGJVf6z65oJjORvFOIi/TUunq/\ntKxQi7us/Se8dDnUPtn1dgpxkbxTiIv01MpqKCuB8rH5bkn/eOcWwODtW7reLpG8Ll6H00XyRiEu\n0hObtkD9Jpg2CYoK8OMTWuDdO4DgP0NL59uqJy6SdwX4V0ikH1VWQ3ERTJmQ75b0j7pnoaXR77c0\nQN1znW9bVOQ3jU4XyRuFuEi2tu+AmnUwpbx1ZHaheftWaN7m95u3wTu3dr19iQq+iORTTv4SmdlJ\nwC+AYuC6EMIP260/H/gxsCq56OoQwnXJdecB30wuvzKE8IdctEkk51bV+M+4l1jdsQ4WXgBNmzuu\nq10IIdmzDs2w/DrYsKTjdokRcNj1qp8ukmd9DnEzKwauAU4AKoHnzGxBCOGVdpv+MYRwSbvnjgO+\nDVQAAVicfO76vrZLJKeammDNWpg4zucNj7OSkZAYBqv+0v22zVug+qGOy3f6OJSMgsRahbhIHuXi\ncPohwPIQwooQQgNwG3B6ls/9APBACGFdMrgfAE7KQZtEcmtNLTS3FEZxl6ISOPIWOOIWSAwHy3L2\nNSv2HvgRt8KRN0NRQofTRfIsFyE+DViZ9rgyuay9M83sJTO708xm9PC5mNk8M1tkZovWrl2bg2aL\nZKmlxWcrGzMSRg7Pd2tyZ9Y5cMrLMGovKB7W9bbFw3y7U16CWXNbl+twukheDdTAtnuAWSGE/fDe\ndo/Pe4cQ5ocQKkIIFeXl5TlvoEin1q6HHY2F0Qtvb8RsOHkxzDrXe9mZJIb7+pMX+/Zt1iWgqdmr\n2InIgMtFiK8CZqQ9nk7rADYAQgh1IYQdyYfXAQdl+1yRvEqVWB02xCc7KURFJTB0il9SlklLIwyd\n6tu1N2IYTBjrRytEZMDlIsSfA+aY2WwzKwXmAgvSNzCzKWkPTwNeTd6/DzjRzMaa2VjgxOQykWjY\nsAk2by3cEqspb93UNsQtLbBbGnx9JuVjYe9doDjL8+oiklN9DvEQQhNwCR6+rwK3hxCWmtkVZnZa\ncrMvmNlSM3sR+AJwfvK564Dv4l8EngOuSC4TiYbKaj/vO2l8vlvSfza+AdurWh8XD4VZH/efKdvX\nwKblA982EemShRiey6qoqAiLFi3KdzOk0G3ZBouWwqypsNPUfLem/yz5Piz5H6AIhpTDMffA2P1h\n/Yvw2Idg+1ogwL7fhr2/nu/WihQMM1scQqjoy2uoYptIZyqrvazo1AIfSPnWH/y898yPwqmveoCD\n/zz1VZh5lh9SX6E6TCJRoxAXyaShEarrYPJ4KMkwoKtQtDRByw448jY44kYfiZ4uMRyOuMnXt2z3\n7UUkMgq0ALRIH62q8ZHp0wrwsrJ0RQk4/e3ut9vpY34TkUhRT1ykveZmWF0D48f4pWUiIhGlEBdp\nr6rOC5jMKPBeuIjEnkJcJF2quMvI4TCqkwpmIiIRoRAXSVe7wecNn1HgxV1EpCAoxEXSVVbBkFIv\nJSoiEnEKcZGU+s2wcUvhl1gVkYKhEBdJqayGRDFMnpDvloiIZEUhLgKwbTvUrocp5ZrMQ0RiQyEu\nAlBZ44fQp03Md0tERLKmEBdpbIKqWpg4DspK890aEZGsKcRFVq+FlhaYMTnfLRER6RGFuAxuLS1e\nYnXsKBg+tPvtRUQiRCEug1vNOp+xTL1wEYkhhbgMXiHAyirvgY8Zme/WiIj0mEJcBq/1G2Hrdu+F\nq7iLiMSQQlwGr5VVUFoC5SqxKiLxpBCXwWnzVtiwya8LL9LHQETiSX+9ZHBaWQXFRTC1PN8tERHp\nNYW4DD47GmDteq+RnkjkuzUiIr2mEJfBp7LaR6ZPn5TvloiI9IlCXAaXpmZYU+uD2YaU5bs1IiJ9\nohCXwaVqLTQ3w3QVdxGR+FOIy+ARgs9WNnoEjBqe79aIiPSZQlwGj7XrfVCbeuEiUiAU4jI4pEqs\nDi2D8aPz3RoRkZxQiMvgUL/ZC7xMV4lVESkcCnEZHFZWQUkCJo3Pd0tERHJGIS6Fb+s2WFfv1dmK\n9V9eRAqH/qJJ4aushiKDqRPz3RIRkZxSiEtha2iEqjqYNMFnLBMRKSAKcSlsq2tUYlVECpZCXApX\nczOsXgvjx8CwIflujYhIzinEpXBV10Fjk3rhIlKwFOJSmELwAW0jh3mZVRGRAqQQl8JUtwG27VBx\nFxEpaApxKUyV1VBW6lOOiogUKIW4FJ6Nm73M6vRJ6oWLSEFTiEvhqayG4mKYPCHfLRER6VcKcSks\n23b4lKNTyyFRnO/WiIj0K4W4FJZV1X4IfZpKrIpI4VOIS+FobII1tTBxnA9qExEpcApxKRxr1kJL\ni4q7iMigkZMQN7OTzGyZmS03s8syrP+ymb1iZi+Z2UNmtlPaumYzeyF5W5CL9sgg1NICq2pgzEgY\nMSzfrRERGRCJvr6AmRUD1wAnAJXAc2a2IITwStpmzwMVIYStZnYxcBVwdnLdthDCAX1thwxyNet8\nxrLdZ+W7JSIiAyYXPfFDgOUhhBUhhAbgNuD09A1CCI+EELYmHy4Epufg94q4VInV4UNh7Kh8t0ZE\nZMDkIsSnASvTHlcml3XmQuDvaY+HmNkiM1toZmfkoD0y2KzfCFu2qbiLiAw6fT6c3hNm9gmgAjgm\nbfFOIYRVZrYz8LCZvRxCeDPDc+cB8wBmzpw5IO2VmKishtISH5UuIjKI5KInvgqYkfZ4enJZG2Z2\nPPAN4LQQwo7U8hDCquTPFcCjwIGZfkkIYX4IoSKEUFFeXp6DZktB2LzVe+LTJkKRLrYQkcElF3/1\nngPmmNlsMysF5gJtRpmb2YHAb/EAr0lbPtbMypL3JwBHAukD4kS6Vlnt4T1FX+xEZPDp8+H0EEKT\nmV0C3AcUA9eHEJaa2RXAohDCAuDHwAjgDvNzlu+GEE4D9gR+a2Yt+BeKH7Yb1S7SuR0NPip9ajmU\nDOiZIRGRSMjJX74Qwr3Ave2WfSvt/vGdPO8pYN9ctEEGoVU1PjJ9moq7iMjgpJOIEk/NzV6hbcJY\nGFqW79aIiOSFQlziaU0tNDXDDPXCRWTwUohL/ITgs5WNGuE3EZFBSiEu8VO7HrY3qBcuIoOeQlzi\nJQRYWe3nwcePyXdrRETySiEu8bJxM2zaohKrIiIoxCVuVlZDIgGTxue7JSIieacQl/jYuh3qNnhx\nl+LifLdGRCTvFOISH5XVfgh92sR8t0REJBIU4hIPDY1QXeuH0UtL8t0aEZFIUIhLPKxeCy3BB7SJ\niAigEJc4aG6B1TUwbjQMH5rv1oiIRIZCXKKvpg4am9QLFxFpRyEu0ZYq7jJiGIwZme/WiIhEikJc\nom1dPWzbruIuIiIZKMQl2lZWQVkplI/Nd0tERCJHIS7RtWkL1G/268KL9F9VRKQ9/WWU6FpZ7ZXZ\nppTnuyUiIpGkEJdo2r4D1q6DKRMgoRKrIiKZKMQlmiprkiVWdVmZiEhnFOISPU1NULXWB7MNKc13\na0REIkshLtGzptartE2fnO+WiIhEmkJcoqWlxWcrGzMSRg7Ld2tERCJNIS7Rsna9z1imEqsiIt1S\niEt0hACVVTBsiE92IiIiXVKIS3Rs2ASbt6nEqohIlhTiEh0rq6AkAZPG57slIiKxoBCXaGhu9nPh\nKrEqIpK1RL4bIAJ4edWD9vLz4iIikhWFuESHmc6Fi4j0gI5bioiIxJRCXEREJKYU4iIiIjGlEBcR\nEYkphbiIiEhMKcRFRERiSiEuIiISUwpxERGRmFKIi4iIxJRCXEREJKYU4tL/WpphyZX+U0RyT5+x\nQUshLv1v7T/hpcuh9sl8t0SkMOkzNmgpxKX/vXMLYPD2LfluiUhh0mds0FKIS/8KLfDuHUDwn6El\n3y0SKSz6jA1qCnHpX3XPQkuj329pgLrn8tsekUKjz9iglpMQN7OTzGyZmS03s8syrC8zsz8m1z9j\nZrPS1n09uXyZmX0gF+2RCHn7Vmje5vebt8E7t+a3PSKFRp+xQS3R1xcws2LgGuAEoBJ4zswWhBBe\nSdvsQmB9CGFXM5sL/Ag428z2AuYCewNTgQfNbLcQgoZYxsmOdbDwAmja3HFd7UJIvZ2hGZZfBxuW\ndNwuMQIOux7KxvVvW0XiSJ8x6USfQxw4BFgeQlgBYGa3AacD6SF+OvCd5P07gavNzJLLbwsh7ADe\nMrPlydd7OgftkoFSMhISw2DVX7rftnkLVD/UcflOH4eSUblvm0gh0GdMOpGLw+nTgJVpjyuTyzJu\nE0JoAuqB8Vk+V6KuqASOvAWOuAUSw8GKs3ueFXvv4Ihb4ciboSgX3ylFCpA+Y9KJ2AxsM7N5ZrbI\nzBatXbs2382RTGadA6e8DKP2guJhXW9bPMy3O+UlmDV3YNonEnf6jEk7uQjxVcCMtMfTk8sybmNm\nCWA0UJflcwEIIcwPIVSEECrKy8tz0GzpFyNmw8mLYda53gPIJDHc15+82LcXkezpMyZpchHizwFz\nzGy2mZXiA9UWtNtmAXBe8v5ZwMMhhJBcPjc5en02MAd4NgdtknwqKoGhU/xyl0xaGmHoVN9ORHpO\nnzFJ6nOIJ89xXwLcB7wK3B5CWGpmV5jZacnNfgeMTw5c+zJwWfK5S4Hb8UFw/wA+r5HpBeKtm9r+\ngbG0PyYtDb5eRHpPnzEhN6PTCSHcC9zbbtm30u5vBz7ayXO/B3wvF+2QiNj4Bmyvan1cPBRmfgze\nvb31etbta2DTchi5a37aKBJn+oxJUmwGtkmMvHuHX69aNASGzYATn4bDf+8/h83w5f8uFSkiPabP\nmCQpxCX33vqDn5Ob+VE49VUYu78vH7u/P555lh/uW/GH/LZTJK70GZMkhbjkVksTtOyAI2+DI270\nUbLpEsPhiJt8fct2315EsqfPmKQxHyQeLxUVFWHRokX5boaIiEivmdniEEJFX15DPXEREZGYUoiL\niIjElEJcREQkphTiIiIiMaUQFxERiSmFuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjElEJc\nREQkphTiIiIiMaUQFxERiSmFuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjElEJcREQkphTi\nIiIiMaUQFxERiSmFuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjElEJcREQkphTiIiIiMaUQ\nFxERiSmFuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjElEJcREQkphTiIiIiMaUQFxERiSmF\nuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjEVJ9C3MzGmdkDZvZG8ufYDNscYGZPm9lSM3vJ\nzM5OW/d7M3vLzF5I3g7oS3tEREQGk772xC8DHgohzAEeSj5ubyvwHyGEvYGTgJ+b2Zi09ZeGEA5I\n3l7oY3tEREQGjb6G+OnAH5L3/wCc0X6DEMLrIYQ3kvdXAzVAeR9/r4iIyKDX1xCfFEJYk7xfBUzq\namMzOwQoBd5MW/y95GH2n5lZWRfPnWdmi8xs0dq1a/vYbBERkfjrNsTN7EEzW5Lhdnr6diGEAIQu\nXmcKcBPwqRBCS3Lx14E9gIOBccDXOnt+CGF+CKEihFBRXq6OvIiISKK7DUIIx3e2zsyqzWxKCGFN\nMqRrOtluFPA34BshhIVpr53qxe8wsxuAr/ao9SIiIoNYXw+nLwDOS94/D/hL+w3MrBS4C7gxhHBn\nu3VTkj8NP5++pI/tERERGTT6GuI/BE4wszeA45OPMbMKM7suuc3HgKOB8zNcSnazmb0MvAxMAK7s\nY3tEREQGDfNT2fFSUVERFi1alO9miIiI9JqZLQ4hVPTlNVSxTUREJKYU4iIiIjGlEBcREYkphbiI\niEhMKcRFRERiSiEuIiISUwpxERGRmFKIi4iIxJRCXEREJKYU4iIiIjGlEBcREYkphbiIiEhMKcRF\nRERiSiEuIiISUwpxERGRmFKIi4iIxJRCXEREJKYU4iIiIjGlEBcREYkphbiIiEhMKcRFRERiSiEu\nIiISUwpxERGRmFKIi4iIxJRCXEREJKYU4iIiIjGlEBcREYkphbiIiEhMKcRFRERiSiEuIiISUwpx\nERGRmFKIi4iIxJRCXEREJKYU4iIiIjGlEBcREYkphbiIiEhMKcRFRERiSiEuIiISUwpxERGRmFKI\ni4iIxJRCXEREJKYU4iIiIjGlEBcREYkphbiIiEhMKcRFRERiqk8hbmbjzOwBM3sj+XNsJ9s1m9kL\nyduCtOWzzewZM1tuZn80s9K+tEdERGQw6WtP/DLgoRDCHOCh5ONMtoUQDkjeTktb/iPgZyGEXYH1\nwIV9bI+IiMig0dcQPx34Q/L+H4Azsn2imRnwPuDO3jxfRERksOtriE8KIaxJ3q8CJnWy3RAzW2Rm\nC80sFdTjgQ0hhKbk40pgWh/bIyIiMmgkutvAzB4EJmdY9Y30ByGEYGahk5fZKYSwysx2Bh42s5eB\n+p401MzmAfOSD3eY2ZKePD8mJgC1+W5EPynUfdN+xU+h7pv2K3527+sLdBviIYTjO1tnZtVmNiWE\nsMbMpgA1nbzGquTPFWb2KHAg8CdgjJklkr3x6cCqLtoxH5if/L2LQggV3bU9bgp1v6Bw9037FT+F\num/ar/gxs0V9fY2+Hk5fAJyXvH8e8Jf2G5jZWDMrS96fABwJvBJCCMAjwFldPV9EREQy62uI/xA4\nwczeAI5PPsbMKszsuuQ2ewKLzOxFPLR/GEJ4Jbnua8CXzWw5fo78d31sj4iIyKDR7eH0roQQ6oD3\nZ1i+CLgoef8pYN9Onr8COKQXv3p+L54TB4W6X1C4+6b9ip9C3TftV/z0ed/Mj2qLiIhI3KjsqoiI\nSExFNsTN7KNmttTMWsys05GJZnaSmS1Llm69LG15JEu6ZlOq1syOSytT+4KZbU9dX29mvzezt9LW\nHTDwe9FRIZfgzfI9O8DMnk7+n33JzM5OWxep96yzz0za+rLke7A8+Z7MSlv39eTyZWb2gYFsd3ey\n2K8vm9kryffnITPbKW1dxv+XUZHFvp1vZmvT9uGitHXnJf/vvmFm57V/bj5lsV8/S9un181sQ9q6\nyL5nZna9mdVYJ5dCm/tlcr9fMrP3pK3r2fsVQojkDR8QtzvwKFDRyTbFwJvAzkAp8CKwV3Ld7cDc\n5P3fABfne5+SbbkKuCx5/zLgR91sPw5YBwxLPv49cFa+96O3+wVs7mR5JN+vbPcN2A2Yk7w/FVgD\njInae9bVZyZtm88Bv0nenwv8MXl/r+T2ZcDs5OsU53uferBfx6V9ji5O7VdX/y+jcMty384Hrs7w\n3AtAfTQAAAQsSURBVHHAiuTPscn7Y/O9T9nuV7vt/xO4Pibv2dHAe4Alnaw/Bfg7YMBhwDO9fb8i\n2xMPIbwaQljWzWaHAMtDCCtCCA3AbcDpZpEu6drTUrVnAX8PIWzt11b1XSGX4O1230IIr4cQ3kje\nX43XTCgfsBZmL+Nnpt026ft7J/D+5Ht0OnBbCGFHCOEtYDm9G5jaH7rdrxDCI2mfo4V4bYo4yOY9\n68wHgAdCCOtCCOuBB4CT+qmdPdXT/ToHuHVAWtZHIYTH8c5XZ04HbgxuIV4zZQq9eL8iG+JZmgas\nTHucKt0a5ZKu2ZaqTZlLx/+430segvmZJa/Bj4BCLsHbo/fMzA7BexZvpi2OynvW2Wcm4zbJ96Qe\nf4+yeW6+9LRtF+I9oZRM/y+jItt9OzP5f+xOM5vRw+fmQ9ZtS576mA08nLY4yu9Zdzrb9x6/X326\nxKyvrIuSriGE2BZ+6Wq/0h+E0GWpWpLfzPYF7ktb/HU8SErxyxO+BlzR1zZnI0f7tVPoYwne/pDj\n9+wm4LwQQktycd7eM+nIzD4BVADHpC3u8P8yhPBm5leIpHuAW0MIO8zsM/iRlPfluU25NBe4M4TQ\nnLYs7u9ZTuQ1xEMXJV2ztAqYkfY4Vbq1jh6UdM21rvbLsixVm/Qx4K4QQmPaa6d6hDvM7Abgqzlp\ndBZysV8hByV4+0Mu9s3MRgF/w7+ELkx77by9Zxl09pnJtE2lmSWA0fhnKpvn5ktWbTOz4/EvZseE\nEHaklnfy/zIqgdDtvgWv2ZFyHT6OI/XcY9s999Gct7B3evL/aS7w+fQFEX/PutPZvvf4/Yr74fTn\ngDnmI5tL8Td6QfARAlEt6dptqdo0Hc4BJUMkdR75DCAqE8EUcgnebPatFLgLP891Z7t1UXrPMn5m\n2m2Tvr9nAQ8n36MFwFzz0euzgTnAswPU7u50u19mdiDwW+C0EEJN2vKM/y8HrOXdy2bfpqQ9PA14\nNXn/PuDE5D6OBU6k7ZG9fMrm/yJmtgc+yOvptGVRf8+6swD4j+Qo9cOA+uSX/Z6/XwM9ai/bG/Bh\n/HzADqAauC+5fCpwb9p2pwCv49/AvpG2fGf8D8xy4A6gLN/7lGzXeOAh4A3gQWBccnkFcF3adrPw\nb2VF7Z7/MPAyHgT/B4zI9z5lu1/AEcm2v5j8eWHU368e7NsngEbghbTbAVF8zzJ9ZvDD+6cl7w9J\nvgfLk+/JzmnP/UbyecuAk/P93vRwvx5M/i1JvT8Luvt/GZVbFvv2A2Bpch8eAfZIe+4FyfdyOfCp\nfO9LT/Yr+fg7eLnu9OdF+j3DO19rkn8TKvExGJ8FPptcb8A1yf1+mbQrsHr6fqlim4iISEzF/XC6\niIjIoKUQFxERiSmFuIiISEwpxEVERGJKIS4iIhJTCnEREZGYUoiLiIjElEJcREQkpv5/vUs1/FIm\nc7wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113405240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### 行動もコピペベースで。ランドマークの観測と描画を入れる ###\n",
    "\n",
    "actual_x = np.array([0.0,0.0,0.0])   #ロボットの実際の姿勢\n",
    "particles = [Particle(1.0/100) for i in range(100)]\n",
    "u = np.array([0.2,math.pi / 180.0 * 20]) #ロボットの移動\n",
    "\n",
    "import copy\n",
    "\n",
    "path = [actual_x]\n",
    "particle_path = [copy.deepcopy(particles)]\n",
    "measurementss = [observations(actual_x, actual_landmarks)]\n",
    "for i in range(10):\n",
    "    actual_x = f(actual_x,u)\n",
    "    path.append(actual_x)\n",
    "    measurementss.append(observations(actual_x,actual_landmarks))\n",
    "\n",
    "    for p in particles:\n",
    "        p.pose = f(p.pose,u)\n",
    "    particle_path.append(copy.deepcopy(particles))\n",
    "\n",
    "for i,p in enumerate(path):\n",
    "    draw(path[i],particle_path[i])\n",
    "    draw_landmarks(actual_landmarks)\n",
    "    draw_observations(path[i],measurementss[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}