redux.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Lets see what happens if the velocity array fills up at every cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x34b19d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nvelocities = 200\n",
    "fhi = np.arange(nvelocities/2)                 #first half of array\n",
    "shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
    "esi = 2*fhi + 1                                #every second index\n",
    "ids = np.zeros(nvelocities,dtype=np.int)       #position id of where velocity was generated\n",
    "\n",
    "#Assume worst case senario that it reduces at every grid cell\n",
    "for i in range(100):\n",
    "    ids[fhi] = ids[esi]\n",
    "    ids[shi] = i+1\n",
    "\n",
    "plt.hist(ids);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##The first calculated cells are missing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#How many unique cells are represented after each iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
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       "lwR8W8z1EPsAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x34b7e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nvelocities = 10000\n",
    "fhi = np.arange(nvelocities/2)                 #first half of array\n",
    "shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
    "esi = 2*fhi + 1                                #every second index\n",
    "ids = np.zeros(nvelocities,dtype=np.int)       #position id of where velocity was generated\n",
    "\n",
    "uniques = np.zeros(100)\n",
    "#Assume worst case senario that it reduces at every grid cell\n",
    "for i in range(100):\n",
    "    ids[fhi] = ids[esi]\n",
    "    ids[shi] = i+1\n",
    "    uniques[i] = np.unique(ids).size\n",
    "    \n",
    "fig,ax = plt.subplots()\n",
    "fig.set_size_inches(8,5)\n",
    "ax.plot(uniques);\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('# unique')\n",
    "ax.set_ylim(0,20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##The number of unique cells represented saturates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Lets see how the that number changes with number of stored velocities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_velocities = 10000\n",
    "unique = np.zeros(num_velocities)\n",
    "for num in range(num_velocities):\n",
    "    nvelocities=num+2\n",
    "    fhi = np.arange(nvelocities/2)                 #first half of array\n",
    "    shi = nvelocities/2 + np.arange(nvelocities/2) #second half of array\n",
    "    esi = 2*fhi + 1                                #every second index\n",
    "    ids = np.zeros(nvelocities,dtype=np.int)       #position id of where velocity was generated\n",
    "    nunique = 0\n",
    "    i=0\n",
    "    while True:\n",
    "        nunique_old=nunique\n",
    "        ids[fhi] = ids[esi]\n",
    "        ids[shi] = i+1\n",
    "        nunique = np.unique(ids).size\n",
    "        if nunique == nunique_old:\n",
    "            break\n",
    "        i=i+1\n",
    "    unique[num] = nunique\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x36307d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "fig.set_size_inches((8,5))\n",
    "ax.plot(unique,'-')\n",
    "ax.set_xlabel('# of velocities saved')\n",
    "ax.set_ylabel('Max number of unique cells')\n",
    "ax.set_xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#This might be a problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.5+"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}