MC_particles.ipynb 135 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distribution of sampled hadrons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def rapidity(p0, p3):\n",
    "    return 0.5 * np.log((p0 + p3)/(p0 - p3))\n",
    "\n",
    "def create_image(event_id=0):\n",
    "    mc_particle_list = np.loadtxt('event_ideal/mc_particle_list%s'%event_id)\n",
    "    mass = mc_particle_list[:, 4]\n",
    "    four_momentum = mc_particle_list[:, 5:9]\n",
    "    pid = mc_particle_list[:, 9]\n",
    "    pion_4mom = four_momentum[np.absolute(pid) == 211]\n",
    "    pion_rapidity = rapidity(pion_4mom[:, 0], pion_4mom[:, 3])\n",
    "    pion_mid_rapidity = pion_4mom[np.absolute(pion_rapidity) < 1.0]\n",
    "    a = plt.hist2d(pion_mid_rapidity[:, 1], pion_mid_rapidity[:, 2], bins=70)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jmDlzZkRELF++PPbu3dv6K/5HHnkkRowYEaNHj46PP/441qxZE5s3b46f/vSnlS4VAIDE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\nAIBkCasAACTr/wFFVsk9wnc6rAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117e65310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_image(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MGTMmOjo6Dms/cuRIs6rwe9rb2ytdQr898cQTedtcddVVR32M2tra+PrXvx7/8z//E7/9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\nKgAAyRJWAQBIlrAKAECy/h/4lYpDT4T+xQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116fae810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_image(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lFf9gsqyKP9LhYPz48TF//vx49tln46233hryvjZs2DDo8y0tLWW3ceedd5Ydk6VrQ17n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\nJawCAJAsYRUAgGT9P7hIWpS52L23AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116bbee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_image(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Qrao6ty5VVQpXVSEdEdFsvv5t8V3vete4JxlUca+qOgHhwQcfbNumTGV9nZX+7a69TGV9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\ndu4L1U8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11858c950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_image(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   6.,   22.,   38.,   59.,  123.,  193.,  236.,  254.,  284.,\n",
       "         362.,  350.,  341.,  321.,  309.,  242.,  244.,  173.,   83.,\n",
       "          64.,   22.,   12.]),\n",
       " array([-7.10273207, -6.44595922, -5.78918637, -5.13241352, -4.47564067,\n",
       "        -3.81886782, -3.16209497, -2.50532212, -1.84854927, -1.19177643,\n",
       "        -0.53500358,  0.12176927,  0.77854212,  1.43531497,  2.09208782,\n",
       "         2.74886067,  3.40563352,  4.06240637,  4.71917922,  5.37595207,\n",
       "         6.03272492,  6.68949777]),\n",
       " <a list of 21 Patch objects>)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mJmr06NGqrKwMXZU/b948nT9/XosXL1ZLS4smTpyoTZs2yeFwhMZYtGiR7Ha7SkpK5Pf7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\nQAUAAIBR/n/rb9o8tj0o3gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115804450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pion_rapidity, bins=21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1042"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pion_mid_rapidity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x115f82e10>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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r58CPsSu2f43wPhoCf96O++h5e07TurrzKCp6KKZm+vaueaLmyQyd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\nREREXKEgKiIiIiKu+P8BZTNL1Gg4XCoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115eb5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pion_mid_rapidity[:, 1], pion_mid_rapidity[:, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4pQ0bNsRtt932X691Op1otVrx2muv9agqmmTVqlXx9NNPf+r13//+93HhhRf2\noCLqbHh4OB5++OHYvXt3zJ8/P1avXh0LFizodVk0wJYtW2LFihWfeobn0qVLY926dT2qiqYYGho6\n4vNf161bF0uXLu1BRdVoXPAEAKCZGv84JQAAmkHwBAAgheAJAEAKwRMAgBSCJwAAKQRPAABSCJ4A\nAKQQPAEASCF4AgCQQvAEACCF4AkAQIr/D7IsKID4TyIBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ff5150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}