Fly_Bloom_simple.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from nearest_neighbor_search import *\n",
    "from read_data import *\n",
    "from hashfunctions import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create input data to be hashed\n",
    "# should be uniform of size arbitrily larger than 350\n",
    "dIn = 500\n",
    "nIn = 5000\n",
    "m = 350 # nKC to a'3\n",
    "k = 17\n",
    "datIn = np.random.uniform(-1,1,(nIn,dIn)) # was [-1, 1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create projection matrix (dense Gaussian)\n",
    "M = np.random.randn(dIn,m)\n",
    "\n",
    "# create projection matrix (sparse binary)\n",
    "num_sample = 6\n",
    "MSB6 = np.zeros((dIn,m))\n",
    "for row in range(dIn):\n",
    "    idx = random.sample(range(m), num_sample) \n",
    "    MSB6[row,idx] = 1\n",
    "\n",
    "datHash = np.dot(datIn,M)\n",
    "datHashSB = np.dot(datIn,MSB6)\n",
    "# sparsify output    \n",
    "def sparsify_rows(space,n_keep):\n",
    "    nrow = np.shape(space)[0]\n",
    "    outHash = np.zeros(np.shape(space))\n",
    "    inds = np.arange(nrow)\n",
    "    for i in range(nrow):\n",
    "        this_line = space[i]\n",
    "        val_tuple = list(zip(this_line,inds))\n",
    "        this_hash = sorted(val_tuple)[-n_keep:]\n",
    "        this_hash = [ind[1] for ind in this_hash]\n",
    "        outHash[i,this_hash] = 1\n",
    "    return outHash\n",
    "\n",
    "outHash = sparsify_rows(datHash,k)\n",
    "outHashSB = sparsify_rows(datHashSB,k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bloomFP(n=20,n_chk = 1):\n",
    "    val_use = np.random.choice(nIn,size=n+n_chk,replace=False)\n",
    "    bloom = np.any(outHash[val_use[:n]],axis=0) # to go along columns\n",
    "\n",
    "    checker = outHash[val_use[-n_chk:]] # n_chk x m\n",
    "    mtchs = [np.all(bloom[check==1]) for check in checker]\n",
    "    return np.mean(mtchs)\n",
    "\n",
    "def bloomFP_tol(n=20,n_chk = 1,tol=10):\n",
    "    val_use = np.random.choice(nIn,size=n+n_chk,replace=False)\n",
    "    bloom = np.any(outHash[val_use[:n]],axis=0) # to go along columns\n",
    "\n",
    "    checker = outHash[val_use[-n_chk:]] # n_chk x m\n",
    "    mtchs = [np.sum(bloom[check==1])>=tol for check in checker]\n",
    "    return np.mean(mtchs)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sorted(val_tuple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-4798ce722cc6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m     \u001b[0mboot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnboot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnboot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m         \u001b[0mboot\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbloomFP_tol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m     \u001b[0mrFP\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mboot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0msFP\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstd\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mboot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-fc245f97d6f7>\u001b[0m in \u001b[0;36mbloomFP_tol\u001b[0;34m(n, n_chk, tol)\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0mchecker\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moutHash\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mval_use\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mn_chk\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# n_chk x m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m     \u001b[0mmtchs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbloom\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcheck\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m>=\u001b[0m\u001b[0mtol\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcheck\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchecker\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmtchs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-4-fc245f97d6f7>\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0mchecker\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moutHash\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mval_use\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mn_chk\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m# n_chk x m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m     \u001b[0mmtchs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbloom\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcheck\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m>=\u001b[0m\u001b[0mtol\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mcheck\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mchecker\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmtchs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/dist-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36msum\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m   1880\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1881\u001b[0m     return _methods._sum(a, axis=axis, dtype=dtype,\n\u001b[0;32m-> 1882\u001b[0;31m                          out=out, **kwargs)\n\u001b[0m\u001b[1;32m   1883\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1884\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.4/dist-packages/numpy/core/_methods.py\u001b[0m in \u001b[0;36m_sum\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mumr_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_prod\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "n_try = 50\n",
    "nboot = 50\n",
    "rFP = np.zeros(n_try)\n",
    "sFP = np.zeros(n_try)\n",
    "\n",
    "for i in range(n_try):\n",
    "    boot = np.zeros(nboot)\n",
    "    for j in range(nboot):\n",
    "        boot[j] = bloomFP_tol(i,1000,k-2)\n",
    "    rFP[i] = np.mean(boot)\n",
    "    sFP[i] = np.std(boot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(n_try)\n",
    "err = sFP/np.sqrt(nboot)\n",
    "plt.plot(x,rFP)\n",
    "plt.fill_between(x,rFP-err, rFP+err)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7fd93fe5af98>"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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W1u1m1bZ9NDQfOfBXaYGfU2r688VzxulMXURiEsuZ+6nABudcHYCZPQzMATqG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\n7iIiWUjhLiKShRTuIiJZSOEuIpKF/j//fguQ/VMbvgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd93fe5a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(n_try)\n",
    "err = sFP#/np.sqrt(nboot)\n",
    "plt.plot(x,rFP)\n",
    "plt.fill_between(x,rFP-err, rFP+err)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_try = 50\n",
    "nboot = 50\n",
    "#tol_use = np.arange(k-6,k+1)\n",
    "tol_use = np.arange(6)\n",
    "ntol = len(tol_use)\n",
    "rFP = np.zeros((n_try,ntol))\n",
    "sFP = np.zeros((n_try,ntol))\n",
    "\n",
    "for tol_i in range(ntol):\n",
    "    tol = k-tol_use[tol_i]\n",
    "    for i in range(n_try):\n",
    "        boot = np.zeros(nboot)\n",
    "        for j in range(nboot):\n",
    "            boot[j] = bloomFP_tol(i,1000,tol)\n",
    "        rFP[i,tol_i] = np.mean(boot)\n",
    "        sFP[i,tol_i] = np.std(boot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Empirical m=350, k=17')"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wBUqllEYhRGOgKbBaSqmzenSKUkPt+2M5p3Ztp+d9/yKmeSub9Jl8NJu1c4/g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\n6aCgaZqm1dJBQdM0Taulg4KmaZpW6/8BspQ+JZw4G/IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd93faf50f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(n_try)\n",
    "err = sFP/np.sqrt(nboot)\n",
    "plt.plot(x,rFP)\n",
    "#plt.fill_between(x,rFP-err, rFP+err)\n",
    "plt.xlabel('Items in Bloom')\n",
    "plt.ylabel('% False Positives')\n",
    "plt.title('Empirical m=%i, k=%i' %(m,k))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute probabilities of true match\n",
    "from functools import reduce\n",
    "import operator as op\n",
    "def ncr(n, r):\n",
    "    r = min(r, n-r)\n",
    "    if r == 0: return 1\n",
    "    numer = reduce(op.mul, np.arange(n, n-r, -1))\n",
    "    denom = reduce(op.mul, np.arange(1, r+1))\n",
    "    return numer//denom\n",
    "#def factorial(n):return reduce(lambda x,y:x*y,[1]+range(1,n+1))\n",
    "def pTP(m,k,tol): # probability True Positive\n",
    "    if tol == 0:\n",
    "        mf = 1 # mult factor\n",
    "    else:\n",
    "        mf = reduce(op.mul,np.arange(k, k-tol, -1))\n",
    "    prob = mf/ncr(m,k)\n",
    "    return prob\n",
    "def hamming_distance(x1,x2):\n",
    "    assert(len(x1)==len(x2))\n",
    "    try:\n",
    "        return sum(x1^x2) # ^ is xor\n",
    "    except:\n",
    "        return sum((x1>0)^(x2>0)) # ^ is xor\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# outHash (5k x 350) (nIn x m) vs. datIn (nIn x dIn)\n",
    "import numpy.linalg\n",
    "np.linalg.norm(datIn[0]-datIn[1])\n",
    "np.linalg.norm(outHash[0]-outHash[1])\n",
    "hamming_distance(outHash[0],outHash[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "if np.any(None): print(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# check relative distances in Hash space. \n",
    "# Only rho = .05\n",
    "# Even less when taking abs of input\n",
    "# w/o threshold rho = .24\n",
    "# w/o threhold rho (SB) = .25\n",
    "## inversely correlated w/ size of input mat\n",
    "# when input is [0,1], correlation increases, more diverse hamming distances\n",
    "n_check = 40000\n",
    "dOG = np.zeros(n_check)\n",
    "dProj = np.zeros(n_check)\n",
    "for i in range(n_check):\n",
    "    ind1,ind2 = np.random.randint(0,nIn,2)\n",
    "    dOG[i] = np.linalg.norm(datIn[ind1]-datIn[ind2])\n",
    "    dProj[i] = hamming_distance(outHash[ind1],outHash[ind2])\n",
    "#     dProj[i] = hamming_distance(outHashSB[ind1],outHashSB[ind2])\n",
    "#     dProj[i] = np.linalg.norm(datHashSB[ind1]-datHashSB[ind2])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8343059286825631"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NDg4iacqvfVmnC8elVGOYLwa2A5+Yrg1LWiGpKak5PDw8XZuNiP3Uli1bsD3l176so4XD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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded0231d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(dOG,dProj,'ko',alpha=.1)\n",
    "# plt.xlabel('OG Dist')\n",
    "# plt.ylabel('Proj Hamming Dist')\n",
    "plt.hist(dProj,20,color='w',edgecolor='k')\n",
    "plt.xlabel('Avg Hamming Distance')\n",
    "plt.ylabel('# Pairs')\n",
    "# plt.hist2d(dOG,dProj)\n",
    "from scipy.stats import spearmanr\n",
    "from scipy.stats import pearsonr\n",
    "spearmanr(dOG,dProj)\n",
    "# pearsonr(dOG,dProj)\n",
    "# ?plt.plot\n",
    "np.mean(dProj)\n",
    "np.std(dProj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# make clones of a value, perterb\n",
    "clone = outHash[-1]\n",
    "hamming_distance(clone,outHash[0]) # hamming distance = 0\n",
    "# now lets perterb\n",
    "def perterb_hash(brown,n_perterb):\n",
    "    hashbrown = brown.copy()\n",
    "    keys = np.where(hashbrown==1)[0]\n",
    "    assert(len(keys)>=n_perterb)\n",
    "    key_perterb = np.random.choice(keys,n_perterb,replace=False)\n",
    "    noMove = keys.copy()\n",
    "    for i in range(n_perterb):\n",
    "        randInt = np.random.randint(0,len(hashbrown))\n",
    "        while any(noMove == randInt):\n",
    "            randInt = np.random.randint(0,len(hashbrown))\n",
    "        hashbrown[key_perterb[i]], hashbrown[randInt] = (0,1)\n",
    "        noMove= np.append(noMove,randInt)\n",
    "    return hashbrown,noMove\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9AGCwQiAB0BnDUvFL2gX4IrAs8BXbx4xbvyJVnfjnwB+BfW3f3s0y9uKMYDHw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\niBhxCYKIiBGXIIiIGHH/H/281110dp2RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37585d1400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_match_bits = np.mean(match_bits,axis=2)\n",
    "# avg_match_bits\n",
    "# plt.imshow(avg_match_bits)\n",
    "plt.contourf(avg_match_bits)\n",
    "plt.yticks(np.arange(0,len(n_use),6),n_use[np.arange(0,len(n_use),6)])\n",
    "plt.xlabel('Hamming Distance Probe')\n",
    "plt.ylabel('# Items in Filter')\n",
    "plt.yticks()\n",
    "cb = plt.colorbar()\n",
    "cb.set_label('Avg. Hamming Distance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EtgdeBXwB2EHS7hFxV9p25xBjNsp/dNRVRGbdQdJ+9fZHxK319kOdRBAR7xhOUDk7A+em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\nBGZmfc6JwMyszzkRmJn1uf8PDaMh+ekCysYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f37595c05f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tol = 5\n",
    "avg_match_bits = np.mean(match_bits<tol,axis=2)\n",
    "# avg_match_bits\n",
    "# plt.imshow(avg_match_bits)\n",
    "plt.contourf(avg_match_bits)\n",
    "plt.yticks(np.arange(0,len(n_use),6),n_use[np.arange(0,len(n_use),6)])\n",
    "plt.xlabel('Hamming Distance Probe')\n",
    "plt.ylabel('# Items in Filter')\n",
    "plt.title('tolerance: ' + str(tol))\n",
    "plt.yticks()\n",
    "cb = plt.colorbar()\n",
    "cb.set_label('% w/in tol')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# dataset #1 take [clone, n_buffer, clone_1]\n",
    "# n = 20\n",
    "# timing bloom filter\n",
    "timer = 14\n",
    "n_use = np.arange(2,61,2)\n",
    "pert_use = np.arange(0,18,1)\n",
    "laps = 30\n",
    "# tol = 3\n",
    "Sop = outHash[-1]\n",
    "So = np.expand_dims(Sop,1)\n",
    "match_bits = np.zeros((len(n_use),len(pert_use),laps))\n",
    "for i_n in range(len(n_use)):\n",
    "    n = n_use[i_n] \n",
    "    for i in range(laps):\n",
    "        S = outHash[np.random.choice(nIn-1,n-1,replace=False)]\n",
    "        F = np.append(So,np.transpose(S),axis=1) # timer here, only look at first _elements\n",
    "        if n>(timer):\n",
    "            F = F[:,-timer:]\n",
    "        for i_n_pert in range(len(pert_use)):\n",
    "            n_pert = pert_use[i_n_pert]\n",
    "            probe,_ = perterb_hash(Sop,n_pert)\n",
    "            bloom = np.any(F,axis=1)\n",
    "            match_bits[i_n,i_n_pert,i] = sum(bloom[probe==1]==0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(350, 5)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "foo = np.transpose(F)\n",
    "np.shape(foo) # 14,16\n",
    "bar = F[:,5:10]\n",
    "np.shape(bar)\n",
    "# bloom = np.any(foo,axis=0)\n",
    "# bloom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GmG3Z53YA5wE4Te3fb4yZzL5/D0CLiNYOs02AG0ztbmIHN5HjeRsRFdIgu6dS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded2e2f6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(outHash,axis=0)*100)\n",
    "plt.xlabel('Bit #')\n",
    "plt.ylabel('% activated')\n",
    "plt.title('[0,1]')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Implement FLY bloom filter\n",
    "\n",
    "def present_odor(odor,wts):\n",
    "    response = np.dot(wts,odor)/k\n",
    "    wt_n = wts\n",
    "    wt_n[odor==1] = wt_n[odor==1]*.5\n",
    "    wt_n[odor==0] = wt_n[odor==0] + (1- wt_n[odor==0])*.2\n",
    "    return response, wt_n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = 20\n",
    "n_pert = 4\n",
    "rep = 100\n",
    "converge_weight = .887\n",
    "# n_odor = np.shape(F)[1]\n",
    "\n",
    "my_resp = np.zeros((n+1,rep))\n",
    "for j in range(rep):\n",
    "    S = outHash[np.random.choice(nIn-1,n-1,replace=False)]\n",
    "    F = np.append(So,np.transpose(S),axis=1)\n",
    "    _S,_ = perterb_hash(Sop,n_pert)\n",
    "    _S = np.expand_dims(_S,1)\n",
    "    F = np.append(F,_S,axis=1)\n",
    "\n",
    "    w = np.ones(np.shape(F)[0])*converge_weight\n",
    "    for i in range(n+1):\n",
    "        my_resp[i,j],w = present_odor(F[:,i],w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9BfgpcAfZ33pDnVJE0lXAWuBFkrZIOhv4CPBaSb8gW9v6SJE1lhqj3k8D+wA3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded2dfd668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(my_resp,axis=1),'ko')\n",
    "plt.xlabel('Odor #')\n",
    "plt.ylabel('$\\Delta$F/F')\n",
    "plt.title('Fly Model (Hamming Dist: ' + str(n_pert) + ')')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def timing_bloom(S,O=10,q=None,bloom=None):\n",
    "    # S, input set\n",
    "    # O, timing max\n",
    "    # q, query\n",
    "    T_ = 0\n",
    "    if np.any(S):\n",
    "        n_item,n_dim = np.shape(S)\n",
    "        bloom = np.ones(n_dim)*np.nan\n",
    "        for item in range(n_item):\n",
    "            expire_val = O-T_  # 10,\n",
    "            bloom[bloom==expire_val] = np.nan\n",
    "            bloom[S[item]==1] = T_\n",
    "            T_ +=1\n",
    "            if T_>O: \n",
    "                T_=0\n",
    "    if np.any(q):\n",
    "        this_query = bloom[q==1] # might want to loop for multiple queries\n",
    "        return ~np.isnan(this_query)\n",
    "    else:\n",
    "        return bloom\n",
    "    \n",
    "def stable_bloom(S,O=10,Om = 20,q=None):\n",
    "    # S, input set\n",
    "    # O, timing value\n",
    "    # Om, max value\n",
    "    # q, query\n",
    "    if np.any(S):\n",
    "        n_item,n_dim = np.shape(S)\n",
    "        bloom = np.ones(n_dim)*0\n",
    "        for item in range(n_item):\n",
    "            bloom[bloom>0] -=1 #decay factor\n",
    "            bloom[S[item]==1] += O # adding factor\n",
    "            bloom[bloom>Om] = Om # top out\n",
    "    if np.any(q):\n",
    "        this_query = bloom[q==1] # might want to loop for multiple queries\n",
    "        return this_query>0\n",
    "    else:\n",
    "        return bloom\n",
    "def exact_cylinder(S,q,time=14,space=5):\n",
    "    S = S[-time:]\n",
    "    n_item,n_dim = np.shape(S)\n",
    "    for item in range(n_item):\n",
    "        this_ham = hamming_distance(S[item],q)\n",
    "        if this_ham<=space:\n",
    "            if this_ham==0:\n",
    "                print('Exact Match')\n",
    "            return True\n",
    "    else:\n",
    "        return False\n",
    "    \n",
    "def exact_cone(S,q,space=10):\n",
    "    n_item,n_dim = np.shape(S)\n",
    "    for item in range(n_item):\n",
    "        this_ham = hamming_distance(S[-item-1],q) # minus sign is key here\n",
    "        if this_ham<=space:\n",
    "            if this_ham==0:\n",
    "                print('Exact Match')\n",
    "            return True\n",
    "        space -=1\n",
    "        if space==-1:\n",
    "            return False\n",
    "    else:\n",
    "        return False\n",
    "def get_distances(S,q):\n",
    "    n_item,n_dim = np.shape(S)\n",
    "    d = np.zeros(n_item)\n",
    "    for i in range(n_item):\n",
    "        d[i] = hamming_distance(S[i],q)\n",
    "    return d\n",
    "def d_wt(d,degree=-1):\n",
    "    wts = (np.arange(len(d))+1.0)**degree\n",
    "    return np.dot(wts,d[-1:None:-1]) # convolution order\n",
    "hnorm = lambda x: (x-32.32)/32.32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = np.transpose\n",
    "tst = F[:,-1]\n",
    "stable_bloom(T(F[:,:15]),q=tst)\n",
    "exact_cylinder(T(F[:,:12]),q=tst,time = 14,space=8)\n",
    "exact_cone(T(F[:,:5]),q=tst,space=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15, 350)"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(T(F))\n",
    "# np.shape(F[:,-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ndim([0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# foo = F[:,0]\n",
    "foo = F[:,-0-1]\n",
    "bar = F[:,-1]\n",
    "hamming_distance(foo,tst)\n",
    "norm = lambda x: (x-np.min(x))/np.max(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded22e7ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "d1 = np.array([30, 34, 34, 32,30,32,32,34,34,32,32,30,34])\n",
    "d2 = np.array([32, 30, 32, 34,32,30,32,32,34,34,10,32,30])\n",
    "d3 = np.array([30, 26, 32,30,34, 32,32,34, 34,32,32,30,32])\n",
    "d1 = (d1-32)/32\n",
    "d2 = (d2-32)/32\n",
    "d3 = hnorm(d3)\n",
    "\n",
    "plt.plot(d1,'o')\n",
    "plt.plot(d2,'o')\n",
    "plt.plot(d3,'o')\n",
    "\n",
    "# step 1, normalize\n",
    "from functools import reduce\n",
    "import operator as op\n",
    "# reduce(op.mul,d2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.008560363247863249 -0.08015491452991452 -0.1798294321190361\n"
     ]
    }
   ],
   "source": [
    "wt = np.arange(len(d1))+1\n",
    "wt = 1/wt\n",
    "s1 = np.dot(wt,d1)\n",
    "s2 = np.dot(wt,d2)\n",
    "s3 = np.dot(wt,d3)\n",
    "print(s1,s2,s3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9bZl7fwfyi8yMmrWJqb/sJvV8nr1DU5QqoVJJQQgxGNgFLC1+31oIcfE/8OVI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded03f2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting some simple functions\n",
    "x=np.arange(1,21)\n",
    "\n",
    "# plt.subplot(2,2,1)\n",
    "\n",
    "plt.plot(x,1-(x-1)/20,label='1-t/20')\n",
    "plt.plot(x,1/np.sqrt(x),label='$t^{0.5}$')\n",
    "plt.plot(x,1/x,label='$t^{-1}$')\n",
    "\n",
    "plt.plot(x,1/x**2,label='$t^{-0.5}$')\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Multiplier')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yjyRdZNtVFBcRhyPi2WL5bUn7Jc23uX0vl/TP0fC0pMW2VySo4yJJL0VEt18064uIeFLS\nGzNWN59jWyWtb7HrOkk7IuKNiPgfSTskXVpFfRHxk4h4v3j6tKQz+t1vWW3Gr4wyr/WezVZfkRtf\nlXRPv/tNpW6Bfrqk/2p6/qo+HpgftilO6jcl/XIl1TUpLvWskbSzxebP2n7e9mO2f63SwqSQ9BPb\nu2xvbLG9zBhX4Uq1fyGlHD9JWh4Rh4vl1yUtb9GmLuP4dTX+xdVKp3NhkK4tLgnd2eaSVR3G77cl\nHYmIg222pxy/rtQt0OcF26dIekDS9RHx1ozNz6pxGeE3JP29pAcrLu/zEXGepC9J+qbtL1Tcf0e2\nT5L0ZUn/2mJz6vH7iGj827uWt4LZ/o6k9yXd3aZJqnPhNklnS1ot6bAalzXq6CrN/u689q+lmeoW\n6JOSzmx6fkaxrmUb2wslfUrSf1dSXaPPETXC/O6I2DZze0S8FRHvFMuPShqxvayq+iJisvh5VNKP\n1finbbMyYzxoX5L0bEQcmbkh9fgVjkxfhip+Hm3RJuk42v5DSb8j6feLPzofU+JcGIiIOBIRJyLi\nA0m3t+k39fgtlPS7ku5r1ybV+PWiboH+H5LOsf3p4l3clZIentHmYUnTdxR8RdJP253Q/VZcc7tD\n0v6IuKVNm1+ZvqZve60aY1zJHxzbn7R96vSyGh+e7Z3R7GFJf1Dc7XK+pDebLi9Upe07o5Tj16T5\nHNsg6aEWbbZLusT2kuKSwiXFuoGzfamkP5P05Yj43zZtypwLg6qv+TOZK9r0W+a1PkhflPRiRLza\namPK8etJ6k9lZz7UuAvjZ2p8Av6dYt1fqnHyStLJavxT/ZCkZySdVWFtn1fjn9+7JU0Uj8skXSPp\nmqLNtZL2qfGp/dOSfqvC+s4q+n2+qGF6/Jrrs6R/KMZ3j6Sxio/vJ9UI6E81rUs2fmr8YTks6T01\nruNercZnMo9LOijp3yQtLdqOSfrHpn2/XpyHhyT9UYX1HVLj+vP0OTh919dpkh6d7VyoqL5/Kc6t\n3WqE9IqZ9RXPP/Zar6K+Yv1d0+dcU9vKx6/fD74pCgCZqNslFwBAlwh0AMgEgQ4AmSDQASATBDoA\nZIJAB4BMEOgAkAkCHQAy8f/+p0w38xAi/gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fded0308d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d  = get_distances(T(F[:,:-1]),T(F[:,-1]))\n",
    "plt.plot(d,'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.10098028172412045"
      ]
     },
     "execution_count": 398,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_wt(hnorm(d))\n",
    "# output in above case = -0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_ex = len(dProj)\n",
    "l_ex = 20\n",
    "n_try = 20000\n",
    "dd = np.zeros(n_try)\n",
    "st_val = np.random.choice(n_ex-l_ex,n_try,replace=False)\n",
    "for i in range(n_try):\n",
    "    st_ind = st_val[i]\n",
    "    this_v = hnorm(dProj[st_ind:st_ind+l_ex-1])\n",
    "    #this_d = get_distances(this_v,dProj[st_ind+l_ex])\n",
    "    dd[i] = d_wt(this_v)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HOcz/4gIwzFgeBy6tqtcCq4G/S3LyGGuc1pDv5cuAn1fVq4DPAOM9s2JIQ47lh8Cqqnod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\nogVqjKvjAx0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdecbf169e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(dd,50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# d_wt(hnorm(np.array([34,34,34,34,34,34,34,34,34,34,34])))\n",
    "this_d = list()\n",
    "for i in range(50):\n",
    "    this_a = np.ones(i)*34\n",
    "    this_d.append(d_wt(hnorm(this_a)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fdecbc52c18>]"
      ]
     },
     "execution_count": 454,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U1cyuXbv6732P2b072b5tC1sDV23bwuzenZv6HEmaZv2Ud44DNyW5gZXAvhP4mVVtjgB3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\nU5/JCzcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdecbc86a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(this_d,'.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for %: 'builtin_function_or_method' and 'list'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-459-eda60ea5fe79>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'%.2f'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m \u001b[0;34m%\u001b[0m\u001b[0mthis_d\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for %: 'builtin_function_or_method' and 'list'"
     ]
    }
   ],
   "source": [
    "print('%.2f'.format %this_d)"
   ]
  },
  {
   "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": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}