Dispersion_relation_chi_2_voxels_approach.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving phase and frequency matching conditions for $\\chi^{(2)}$  with voxels of increasing resolution.\n",
    "\n",
    "# Applying voxels of increasing resolution to $\\chi^{(3)}$.\n",
    "Refractive index from:\n",
    "\n",
    "http://refractiveindex.info/?shelf=main&book=LiNbO3&page=Zelmon-o"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "see also the notebook Dispersion_relation_chi_2_and_interpolations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "import numpy as np\n",
    "import scipy.constants\n",
    "from sympy.utilities.autowrap import ufuncify\n",
    "import time\n",
    "import itertools\n",
    "#from scipy import interpolate\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sympy import init_printing\n",
    "init_printing() \n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_arr(arr):\n",
    "    fig = plt.figure(figsize=(15,15))\n",
    "    ax = fig.add_subplot(111)\n",
    "    cax = ax.matshow(np.asmatrix(arr), interpolation='nearest')\n",
    "    fig.colorbar(cax)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## from https://www.andreas-jung.com/contents/a-python-decorator-for-measuring-the-execution-time-of-methods\n",
    "\n",
    "def timeit(method):\n",
    "    def timed(*args, **kw):\n",
    "        ts = time.time()\n",
    "        result = method(*args, **kw)\n",
    "        te = time.time()\n",
    "        print '%r %2.2f sec' % \\\n",
    "              (method.__name__, te-ts)\n",
    "        return result\n",
    "    return timed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lambd,nu,nu1,nu2,nu3,nu4 = sp.symbols('lambda nu nu_1 nu_2 nu_3 nu_4')\n",
    "l2 = lambd **2\n",
    "\n",
    "def n_symb(pol='o'):\n",
    "    s = 1.\n",
    "    if pol == 'o':\n",
    "        s += 2.6734 * l2 / (l2 - 0.01764)\n",
    "        s += 1.2290 * l2 / (l2 - 0.05914)\n",
    "        s += 12.614 * l2 / (l2 - 474.6)\n",
    "    else:\n",
    "        s += 2.9804 * l2 / (l2 - 0.02047)\n",
    "        s += 0.5981 * l2 / (l2 - 0.0666)\n",
    "        s += 8.9543 * l2 / (l2 - 416.08)\n",
    "    return sp.sqrt(s)\n",
    "\n",
    "def k_symb(symbol=nu,pol='o'):\n",
    "    '''k is accurate for nu inputs between 6-60.'''\n",
    "    return ((n_symb(pol=pol) * symbol )\n",
    "                .subs(lambd,scipy.constants.c / (symbol*1e7))) ## / scipy.constants.c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "expressions = [k_symb(nu1,pol='o'), k_symb(nu2,pol='o'), k_symb(nu3,pol='e')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dispersion_difference_function = sum(expressions)\n",
    "dispersion_difference_function = dispersion_difference_function.subs(nu3,-nu1-nu2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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zqaZFU1Kh3toHuPKdQ1hUWLZxnuDy5hxzEcF1+ZmHDwOnMXqfV2NWKO7vxuXR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\n6JTSd2t4AgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\nu_{1} \\sqrt{1.0 + \\frac{2402.73209483501}{\\nu_{1}^{2} \\left(-0.01764 + \\frac{898.755178736817}{\\nu_{1}^{2}}\\right)} + \\frac{1104.57011466755}{\\nu_{1}^{2} \\left(-0.05914 + \\frac{898.755178736817}{\\nu_{1}^{2}}\\right)} + \\frac{11336.8978245862}{\\nu_{1}^{2} \\left(-474.6 + \\frac{898.755178736817}{\\nu_{1}^{2}}\\right)}} + \\nu_{2} \\sqrt{1.0 + \\frac{2402.73209483501}{\\nu_{2}^{2} \\left(-0.01764 + \\frac{898.755178736817}{\\nu_{2}^{2}}\\right)} + \\frac{1104.57011466755}{\\nu_{2}^{2} \\left(-0.05914 + \\frac{898.755178736817}{\\nu_{2}^{2}}\\right)} + \\frac{11336.8978245862}{\\nu_{2}^{2} \\left(-474.6 + \\frac{898.755178736817}{\\nu_{2}^{2}}\\right)}} + \\left(- \\nu_{1} - \\nu_{2}\\right) \\sqrt{1.0 + \\frac{2678.64993470721}{\\left(-0.02047 + \\frac{898.755178736817}{\\left(- \\nu_{1} - \\nu_{2}\\right)^{2}}\\right) \\left(- \\nu_{1} - \\nu_{2}\\right)^{2}} + \\frac{537.545472402491}{\\left(-0.0666 + \\frac{898.755178736817}{\\left(- \\nu_{1} - \\nu_{2}\\right)^{2}}\\right) \\left(- \\nu_{1} - \\nu_{2}\\right)^{2}} + \\frac{8047.72349696308}{\\left(-416.08 + \\frac{898.755178736817}{\\left(- \\nu_{1} - \\nu_{2}\\right)^{2}}\\right) \\left(- \\nu_{1} - \\nu_{2}\\right)^{2}}}$$"
      ],
      "text/plain": [
       "          ____________________________________________________________________\n",
       "         ╱                2402.73209483501                    1104.57011466755\n",
       "ν₁⋅     ╱  1.0 + ───────────────────────────────── + ─────────────────────────\n",
       "       ╱           2 ⎛           898.755178736817⎞     2 ⎛           898.75517\n",
       "      ╱          ν₁ ⋅⎜-0.01764 + ────────────────⎟   ν₁ ⋅⎜-0.05914 + ─────────\n",
       "     ╱               ⎜                   2       ⎟       ⎜                   2\n",
       "   ╲╱                ⎝                 ν₁        ⎠       ⎝                 ν₁ \n",
       "\n",
       "___________________________________________             ______________________\n",
       "                   11336.8978245862                    ╱                2402.7\n",
       "──────── + ───────────────────────────────  + ν₂⋅     ╱  1.0 + ───────────────\n",
       "8736817⎞     2 ⎛         898.755178736817⎞           ╱           2 ⎛          \n",
       "───────⎟   ν₁ ⋅⎜-474.6 + ────────────────⎟          ╱          ν₂ ⋅⎜-0.01764 +\n",
       "       ⎟       ⎜                 2       ⎟         ╱               ⎜          \n",
       "       ⎠       ⎝               ν₁        ⎠       ╲╱                ⎝          \n",
       "\n",
       "______________________________________________________________________________\n",
       "3209483501                    1104.57011466755                   11336.8978245\n",
       "────────────────── + ───────────────────────────────── + ─────────────────────\n",
       " 898.755178736817⎞     2 ⎛           898.755178736817⎞     2 ⎛         898.755\n",
       " ────────────────⎟   ν₂ ⋅⎜-0.05914 + ────────────────⎟   ν₂ ⋅⎜-474.6 + ───────\n",
       "         2       ⎟       ⎜                   2       ⎟       ⎜                \n",
       "       ν₂        ⎠       ⎝                 ν₂        ⎠       ⎝               ν\n",
       "\n",
       "___________                     ______________________________________________\n",
       "862                            ╱                    2678.64993470721          \n",
       "──────────  + (-ν₁ - ν₂)⋅     ╱  1.0 + ───────────────────────────────────────\n",
       "178736817⎞                   ╱         ⎛           898.755178736817⎞          \n",
       "─────────⎟                  ╱          ⎜-0.02047 + ────────────────⎟⋅(-ν₁ - ν₂\n",
       " 2       ⎟                 ╱           ⎜                       2   ⎟          \n",
       "₂        ⎠               ╲╱            ⎝             (-ν₁ - ν₂)    ⎠          \n",
       "\n",
       "______________________________________________________________________________\n",
       "                 537.545472402491                           8047.72349696308  \n",
       "── + ──────────────────────────────────────── + ──────────────────────────────\n",
       " 2   ⎛          898.755178736817⎞           2   ⎛          898.755178736817⎞  \n",
       ")    ⎜-0.0666 + ────────────────⎟⋅(-ν₁ - ν₂)    ⎜-416.08 + ────────────────⎟⋅(\n",
       "     ⎜                      2   ⎟               ⎜                      2   ⎟  \n",
       "     ⎝            (-ν₁ - ν₂)    ⎠               ⎝            (-ν₁ - ν₂)    ⎠  \n",
       "\n",
       "___________\n",
       "           \n",
       "────────── \n",
       "         2 \n",
       "-ν₁ - ν₂)  \n",
       "           \n",
       "           "
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dispersion_difference_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k_of_nu1_nu2 = ufuncify([nu1,nu2],dispersion_difference_function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find maximum derivative of dispersion_difference_function over a range. This could be used as a bound for $\\epsilon$ to guarantee results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_max_der(expression,symbol,input_range):\n",
    "    expr_der = sp.diff(expression,symbol)\n",
    "    expr_def_func = ufuncify([symbol],expr_der)\n",
    "    return max(abs(expr_def_func(input_range)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## Apply the triangle inequality over a range of nus\n",
    "\n",
    "nus = np.asarray([6.+ i*5e-2 for i in range(1+int(1e3))])\n",
    "max_derivative = sum([find_max_der(exp,om,nus) for om,exp in zip([nu1,nu2,nu3],expressions)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nekrwf89foMHcwN4H6GAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$7.60876091113$$"
      ],
      "text/plain": [
       "7.60876091113"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Methods for systematic search over ranges\n",
    "\n",
    "### Definitions:\n",
    "`base` -- The number base to use, i.e. the factor to increase the grid resolution at each step.\n",
    "`starting_i` -- index of starting step. `0` means we use a grid of size `base` by `base`.\n",
    "`max_i` -- final index.\n",
    "`eps` -- desired resolution at step max_i\n",
    "\n",
    "### Description \n",
    "\n",
    "To look for solutions more efficiently, we can recursively enhance the resolution of the grid in which we are looking. At each step, decrease the cutoff `eps_current` by some factor (for now let's make it `base`). For the set of voxels in each step that are close enough to a solution of the equation, increase the resolution by a factor of `base` and examine the resulting smaller voxels. Continue until the last step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eps = 0.00002\n",
    "starting_i = 0\n",
    "max_i = 4\n",
    "base = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "min_value = 6.\n",
    "max_value = 20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def setup_ranges(max_i,base):\n",
    "    ranges= {}\n",
    "    for i in range(max_i+1):\n",
    "        ranges[i] = np.linspace(min_value,max_value,1+pow(base,i+1))\n",
    "    return ranges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note: How to obtain the index of $\\nu_3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAAPBAMAAAB6sKBjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJMt0i\nu0SCRuA9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmUlEQVQYGWNgAAHmyM4FEALMZWBUZmBgF2De\nAyHAXJOQzwwMTQwM0yEEmMvABhS7wsAgbwAmwFww8YWB4b0AmICLMX8FiiWDiAS4GM9PBob1c0DE\nBIQYUMn6OSACIYZNLwPQeHmQHfICcL0MdxkY+g3ABEIM6OZwkJvDGRBi3ALMWgxgAizG6vTdg4F5\nWgowDEAEmAsJCBQSABtTQ/E9ZhpaAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1001$$"
      ],
      "text/plain": [
       "1001"
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1+pow(base,i+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.   ,   6.014,   6.028, ...,  19.972,  19.986,  20.   ])"
      ]
     },
     "execution_count": 279,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(min_value,max_value,1+pow(base,i+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAAPBAMAAABpZ+CXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVQYGW2PMQ4BQRSG/2Vli80iNKJgD6DY\ngkrjCBsn2E7BCUSvoNhCT78FR9gI3YabEJGQkOB/M6PiJS/fn28m780AlXYHUl9K7rMHqMWSNcdl\nyTPAXiEfMSpa26P4YgK4KZwLs+FZ/GIIlFJ4d2ZD5QP6pg/vRW8o3o7plwEKV3pD8Q2I943XFB+I\n/53jhOK5zzF7hbxfhXh3A1u9U5N+kmWPg/wnF3GvocwHEvYU9dC6aao5dE929bQH5oat9agHdN87\nHvytD92KRCb2v6JUAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0.014$$"
      ],
      "text/plain": [
       "0.014"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spacing = (max_value-min_value)/ pow(base,i+1)\n",
    "spacing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAPBAMAAAA/sQ3hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\niScAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$428.571428571$$"
      ],
      "text/plain": [
       "428.571428571"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_indices_from_zero = min_value / spacing\n",
    "num_indices_from_zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  6.   ,   6.005,   6.01 , ...,  10.99 ,  10.995,  11.   ])"
      ]
     },
     "execution_count": 282,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranges[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "list index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-283-c5d70f052923>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msample_index\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolution_containing_voxels\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m: list index out of range"
     ]
    }
   ],
   "source": [
    "sample_index = solution_containing_voxels[2].keys()[1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGcAAAAUBAMAAABi2T6lAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 150, \\quad 146\\right )$$"
      ],
      "text/plain": [
       "(150, 146)"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAAOBAMAAAC1GaP7AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJqyLvZs27djJE\nVN3lLQH2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVQYGR2OsUrDUBSGv6S3SVq1KR3EraF0\nERyk2bpYEKcupaDzdRBfI04FXUrXboqLk9gHMG/Qgi8QaB/ADKJQS3pOLtz/P+fjnP9eaMVXlCd+\neWd8OgfnnpuRopPUTZwBFynGYiJFM2pT08SzhAmVbyGHPyJehtnSnlLfSlezIkGuyJOpf+nCp/6Z\nGI1ct4JfKdsTvJX48hwe+dopynFvxTdy/beFZoUZvgS4kdRgcpFGgi8BzyUhGCi3OnUUcY1/x6f+\n/kCyLB/wSv3BmeD8wSXHq+o67mbQ66TlO5XOkKAoimwPfxQ3syOagzEAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$9.62$$"
      ],
      "text/plain": [
       "9.62"
      ]
     },
     "execution_count": 285,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranges[2][(sum(sample_index)+int(num_indices_from_zero))]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Main methods used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def initial_voxels(max_i,base,starting_i,eps):\n",
    "    solution_containing_voxels = {}\n",
    "    eps_current = eps * pow(base,max_i-starting_i)\n",
    "    solution_containing_voxels[starting_i] = {}\n",
    "    \n",
    "    for i1,om1 in enumerate(ranges[starting_i]):\n",
    "        for i2,om2 in enumerate(ranges[starting_i]):\n",
    "            err = k_of_nu1_nu2(om1,om2)\n",
    "            if abs(err) < eps_current:\n",
    "                solution_containing_voxels[starting_i][i1,i2] = err\n",
    "    return solution_containing_voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def add_high_res_voxels(max_i,base,starting_i,eps,solution_containing_voxels):\n",
    "    for i in range(starting_i+1,max_i+1):\n",
    "        eps_current = eps * pow(base,max_i-i)\n",
    "        solution_containing_voxels[i] = {}\n",
    "        for (i1,i2) in solution_containing_voxels[i-1]:\n",
    "            step_size = int(base/2)\n",
    "            max_length = pow(base,i+1)\n",
    "            for i1_new in range(max(0,i1*base-step_size),min(max_length,i1*base+step_size+1)):\n",
    "                for i2_new in range(max(0,i2*base-step_size),min(max_length,i2*base+step_size+1)):\n",
    "                    err = k_of_nu1_nu2(ranges[i][i1_new],ranges[i][i2_new])\n",
    "                    if abs(err) < eps_current:\n",
    "                        solution_containing_voxels[i][i1_new,i2_new] = err "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def plot_voxels(solution_containing_voxels,i):\n",
    "    voxels = np.zeros((1+pow(base,i+1),1+pow(base,i+1)))\n",
    "    for (i1,i2) in solution_containing_voxels[i]:\n",
    "        voxels[i1,i2] = 1\n",
    "    plot_arr(voxels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def voxel_solutions(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps):\n",
    "    solution_containing_voxels = initial_voxels(ranges,k_of_nu1_nu2,max_i,\n",
    "                                                base,starting_i,eps)\n",
    "    add_high_res_voxels(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps,\n",
    "                        solution_containing_voxels)\n",
    "    return solution_containing_voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'setup_ranges' 0.00 sec\n"
     ]
    }
   ],
   "source": [
    "ranges = setup_ranges(max_i,base)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'initial_voxels' 0.00 sec\n"
     ]
    }
   ],
   "source": [
    "solution_containing_voxels = initial_voxels(max_i,base,starting_i,eps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'add_high_res_voxels' 2.06 sec\n"
     ]
    }
   ],
   "source": [
    "add_high_res_voxels(max_i,base,starting_i,eps,solution_containing_voxels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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AAGCMQAIAAIzRMAIAgDVdPl3A4aJDAgAAjHnKgaSqrqqqd1bVh6rqg1X1/QdZGAAAcPzt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\nGyEBAAA2QgIAAGwCFnbWU6nBqZEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114a20850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'plot_voxels' 0.54 sec\n"
     ]
    }
   ],
   "source": [
    "plot_voxels(solution_containing_voxels,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V9aokX1//Egfm3u+ZvgAAYBEHpy92si0HlWkQeaKqXjPGeCzJFUm+NH29M8kH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117fabcd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'plot_voxels' 0.60 sec\n"
     ]
    }
   ],
   "source": [
    "plot_voxels(solution_containing_voxels,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BsyaGXXu6AgMAAAdJJYY9UYUBADgAh5Y9gGkRYjhr1sAAALBM2snYFQEGAIBlUYlhx1Rg\nAACWxKx9gUoMZ0WAAQBg2WQ6tqUCAwDAlAgx7IgAAwCwRGbtC3wcnJYKDAAAU2RNDGckwAAAMDUq\nMTyDCgwAwMT4scsFKjGckgADAMBUqcTwRSowAACMQCWGBQIMAABTpxKDCgwAwNSZtS9QiSGJAAMA\nwDhkujWmAgMAwIiEmDUnwAAADMCsfYF2sjV1S44IMAAADEmIWUNPt5EBAMCIFKbWjAoMAMCAzNoX\nqMSsERUYAABWgUy3JlRgAABYFULMGlCBAQAY3KFlD2BahJgVpwIDAMCqsSYGAAAYihCzwlRhAABY\nRdrJVpQAAwCwQszaF6jErCABBgCAVSbErBgBBgCAVacwtUJspQwAsKLM2heoxKwYVRgAAFadTLcC\nnq7ACDAAAKwDIWZFCDAAACvs0LIHMC3ayQZnIT8AAOtGiBmYhfwAAKwj7WSDUoEBAGBdCTEDUoEB\nAFgzZu0LtJMNShUGAIB1JcQMRhsZAADrbtchpqoOV9W9VfXRqvpIVf347Phzq+qeqvpYVb2nqi6Y\ne83NVfVoVT1UVd9zLv4B1okAAwCwps4f4HaA9lKJ2UjyE939kiTfkeS1VfWiJG9M8t7uvjzJvUlu\nTpKqenGSVya5IsnLk7y9qmovgwcAANbPrjNTd386yadn9z9fVQ8lOZzk+iR/e3ba7UmOZivYXJfk\nju7eSPJYVT2a5Kok/2bXo18TTy/kV4UBAIBzVPipqkuTfEuSDyS5sLuPJ1tBp6qeNzvtoiS/O/ey\nY7Nj7IAAAwCwxg4tewDTsueF/VX15UneleT13f35JH3SKSc/5ixYBwMAAIv2VImpqvOzFWB+pbvv\nmh0+XlUXdvfxqnp+ks/Mjh9L8oK5lx+eHTuNo3P3L53d1ovfgwEAOJcem90YXXXvvlBSVb+c5LPd\n/RNzx96S5HPd/ZaqekOS53b3G2cL+9+Z5Nuy1Ub2z5P8jT7FAKqqo/oAAMC+OpLunvxGU1XV/SvL\nHsX26gdzYJ/nXrZY/s4kP5Dku6vqgar6UFVdm+QtSf6zqvpYkmuSvDlJuvvBJHcmeTDJbyV5zakC\nDFtUYQAA4NT2sjvZv8rplxi99DSveVOSN+32PdeFdTAAAHB6e17Yz7knwAAAwOkd8G9rciZ+DwYA\ngFMya1+gEjMxAgwAAJyZEDMR1sEAAMDOKExNgJ3IAAA4I7P2BT6OCVCBAQCAndNOtmSqMAAAcHZU\nYpbIOhgAAHbkdL/OuKZUYgAAgKEIMUuiCgMAALujnWwJrIMBAOCsmLUv8HEcMBUYAADYG+1kAADA\nUISYA6SNDAAA9k472QHSRgYAwK6YtS9QiTkgqjAAAHBuCDEHwGJ+AAA4dxSmAABg6g4tewDTohKz\nz1RhAADg3BJi9pF1MAAAcO5pJ9tHKjAAAJwTZu0LVGL2iSoMAADsDyFmH1gHAwAA+0eIAQAAhqK7\n7hxThQEA4JwbeNZeVdcmeWu2Cii3dfdbTnr+v0vyA0k6ybOSXJHka7r7T093TZWYc8g6GAAA+GtV\ndV6StyV5WZKXJLmxql40f053/8Pu/o+6+8okNyc5eqYAkwgx55wqDAAAfNFVSR7t7se7+0SSO5Jc\nf4bzb0zyf2530YELU9OijQwAgH1zaNkD2LWLkjwx9/jJbAWbZ6iqL01ybZLXbndRlZhzQBsZAADs\n2X+e5P3btZIlKjHnjCoMAADr5OiHkqMPbHvasSQXzz0+PDt2KjdkB61kSVLdvZPzDlRVdQYJBdrI\nAABGdSTdXcsexXaqqvsDyx7F9urb84zPs6oOJflYkmuSfCrJB5Pc2N0PnXTeBUk+nuRwd//Fdu+l\nEgMAAOyL7t6sqtcluSd/vcXyQ1X16q2n+9bZqa9I8p6dBJhEJWbXnl4HowoDADAqlZhz6VSVmP2i\nErMHAgwAAAfCrH2B3cl2SYABAIDlEGJ2wZbKAACwPELMWbIbGQAALJfuOgAAmDqz9gUqMWdBFQYA\nAJZPiAEAAIaiMLVDqjAAACzNoWUPYFpUYnZIgAEAgGkQYnbAlsoAADAd2sm2IcAAALB0Zu0LVGJ2\nQCsZAABMhxBzBhbzAwDA9ChMnYY2MgAAJsOsfYFKzBmowgAAwPQIMachwAAAwDQJMaeglQwAAKZL\nd91JLOYHAGByDi17ANOiEgMAAAxFiJmjCgMAANOnnQwAAKbOrH2BSsyMKgwAAIxBiAEAAIaiMBVV\nGAAAJs6sfYFKDAAAMJS1DzGqMAAAMBaFKQAAmDqz9gVrXYlRhQEAgPGsdYgBAADGs7YhRhUGAADG\ntLbddQIMAACj6EPLHsG0rGUl5pYcWfYQAACAXVq7ECPAAADA2NaynUwrGQAAI9lcy1n76a1dJUaA\nAQCAsa1ViNFKBgAA41OYAgCAidNOtmhtKjF+FwYAAFbD2oQYAQYAAFbDWoQYa2EAAGB16K4DAICJ\n2zg0Qu3hCwf2TiN8GntiLQwAAKyWlQ8xAADAaln5djJVGAAARrd5/gjT9r86sHda6UqMBf0AALB6\nVjbECDAAALCaRqhL7ZpWMgAAVsHmoUPLHsKkrGwlRoABAIDVtJIhRisZAACsrpVrJxNgAABYNZvR\nTjZvJSsxWskAAGB1rVyIEWAAAGC1rVSI0UoGAACrb+XWxAAAwKrZsCZmwcpUYm7JEa1kAACwBlYm\nxAAAAOthJdrJVGEAAFhlm6sxbT9nVGIAAIChDB9iVGEAAGC9qEsBAMDEbdqdbMHwlRhVGAAAWC9D\nhxg/bgkAAOtHOxkAAEycdrJFw1ZiLOgHAID1NGyIAQAA1tOwIUYVBgAA1tOQIcaCfgAA1slmDk3+\ndpCGDDEAAMD6Gi7EWNAPAADrzRbLAAAwcRu2WF4wVCVGFQYAABgqxAAAAAzTTqYKAwDAutocZ9p+\nIFRiAACAoQwTYlRhAACAZKAQAwAAjKeqrq2qh6vqkap6w2nOubqqHqiqP6yqf7HdNYdorrMeBgCA\ndbY56BbLVXVekrcluSbJJ5PcV1V3dffDc+dckOTnknxPdx+rqq/Z7rqTr8TckiPLHgIAALA7VyV5\ntLsf7+4TSe5Icv1J53x/kt/o7mNJ0t2f3e6ikw8xifUwAAAwqIuSPDH3+MnZsXkvTPJVVfUvquq+\nqvrB7S46+XYyAQYAgHU3ajvZDp2f5Mok353ky5L8blX9bnf/2zO9YLKshQEAgGm6/+if5f6jf77d\naceSXDz3+PDs2Lwnk3y2u/8yyV9W1e8k+eYkY4YYAABgmr716i/Lt179ZV98fOuRUy5luS/JZVV1\nSZJPJbkhyY0nnXNXkv+1qg4l+feSfFuSf3ym955siFGFAQCALRuDtpN192ZVvS7JPdlaj39bdz9U\nVa/eerpv7e6Hq+o9ST6cZDPJrd394JmuO9kQAwAAjK+7353k8pOO/cJJj/9hkn+402tOdncyVRgA\nAOBUVGIAAGDiNk3bF0y2EgMAAHAqQgwAADAUIQYAABiK5joAAJi4zUG3WN4vKjEAAMBQhBgAAGAo\ne24nq6rzktyf5Mnuvq6qnpvk15JckuSxJK/s7qdm596c5KYkG0le39337PX9AQBg1WknW3QuKjGv\nT/Lg3OM3Jnlvd1+e5N4kNydJVb04ySuTXJHk5UneXlV1Dt4fAABYI3sKMVV1OMn3JvnFucPXJ7l9\ndv/2JK+Y3b8uyR3dvdHdjyV5NMlVe3l/AABg/ey1neynk/z9JBfMHbuwu48nSXd/uqqeNzt+UZLf\nnTvv2OwYAABwBtrJFu06xFTV30lyvLt/v6quPsOpvbt3ODp3/9LZDQAAduux2Y3R7aUS851Jrquq\n703ypUmeU1W/kuTTVXVhdx+vqucn+czs/GNJXjD3+sOzY6dx9R6GBgAAJ7s0i38x/r7lDIM92/Wa\nmO7+ye6+uLu/PskNSe7t7h9M8ptJXjU77YeT3DW7f3eSG6rq2VX1dUkuS/LBXY8cAADWxEYOTf52\nkPa8xfIpvDnJnVV1U5LHs7UjWbr7waq6M1s7mZ1I8pru3mWrGQAAsK7OSYjp7vdlVo/r7s8leelp\nzntTkjedi/cEAADW07n4nRgAAIADsx/tZAAAwDm0adq+QCUGAAAYihADAAAMRV0KAAAmbvOAtzCe\nOpUYAABgKEIMAAAwFO1kAAAwcdrJFqnEAAAAQxFiAACAoWgnAwCAidvQTrZAJQYAABiKEAMAAAxF\niAEAAIZiTQwAAEzcpmn7ApUYAABgKEIMAAAwFHUpAACYuE1bLC9QiQEAAIYixAAAAEPRTgYAABOn\nnWyRSgwAADAUIQYAABiKEAMAAAzFmhgAAJi4DWtiFqjEAAAAQxFiAACAoWgnAwCAids0bV+gEgMA\nAAxFiAEAAIaiLgUAABO3aXeyBSoxAADAUIQYAABgKNrJAABg4rSTLVKJAQAAhiLEAAAAQxFiAACA\noVgTAwAAE2dNzCKVGAAAYChCDAAAMBTtZAAAMHEb2skWqMQAAABDEWIAAIChaCcDAICJ2zRtX6AS\nAwAADEWIAQAAhqIuBQAAE+fHLhepxAAAAEMRYgAAgKEIMQAAwFCsiQEAgImzJmaRSgwAADAUIQYA\nABiKdjIAAJi4De1kC1RiAACAoQgxAADAULSTAQDAxG2ati9QiQEAAIYixAAAAPumqq6tqoer6pGq\nesMpnv/bVfWnVfWh2e1/3O6a6lIAAMC+qKrzkrwtyTVJPpnkvqq6q7sfPunU3+nu63Z6XSEGAAAm\nbnPcLZavSvJodz+eJFV1R5Lrk5wcYupsLqqdDAAA2C8XJXli7vGTs2Mn+46q+v2q+r+r6sXbXVQl\nBgAAOGuPHX08jx99/Fxc6veSXNzdf15VL0/yz5K88EwvEGIAAGDipthO9oKrvz4vuPrrv/j4d468\n/1SnHUty8dzjw7NjX9Tdn5+7/9tV9faq+qru/tzp3ls7GQAAsF/uS3JZVV1SVc9OckOSu+dPqKoL\n5+5flaTOFGASlRgAAGCfdPdmVb0uyT3ZKqDc1t0PVdWrt57uW5P8l1X13yQ5keQvknzfdtcVYgAA\nYOKm2E62U9397iSXn3TsF+bu/1ySnzuba2onAwAAhiLEAAAAQ9FOBgAAE7cxcDvZflCJAQAAhiLE\nAAAAQxFiAACAoVgTAwAAE7dp2r5AJQYAABiKEAMAAAxFXQoAACZu0xbLC1RiAACAoQgxAADAULST\nAQDAxGknW6QSAwAADEWIAQAAhqKdDAAAJm5DO9kClRgAAGAoQgwAADAUIQYAABiKNTEAADBxm6bt\nC1RiAACAoQgxAADAUNSlAABg4jZtsbxAJQYAABiKEAMAAAxFOxkAAEycdrJFKjEAAMBQhBgAAGAo\n2skAAGDitJMtUokBAACGIsQAAABDEWIAAIChWBMDAAATt2FNzAKVGAAAYChCDAAAMBTtZAAAMHGb\npu0LVGIAAIChCDEAAMBQ1KUAAGDiNu1OtkAlBgAAGIoQAwAADEWIAQAAhmJNDAAATJw1MYtUYgAA\ngKEIMQAAwFC0kwEAwMRtaCdboBIDAAAMRYgBAACGop0MAAAmbtO0fYFKDAAAMBQhBgAAGIq6FAAA\nTJwfu1ykEgMAAAxFiAEAAIYixAAAAEOxJgYAACbOmphFKjEAAMBQhBgAAGAoe2onq6oLkvxikv8w\nyReS3JTkkSS/luSSJI8leWV3PzU7/+bZORtJXt/d9+zl/QEAYB1saCdbsNdKzM8k+a3uviLJNyd5\nOMkbk7y3uy9Pcm+Sm5Okql6c5JVJrkjy8iRvr6ra4/sDAABrZtchpqq+Isl3dfc7kqS7N2YVl+uT\n3D477fYkr5jdvy7JHbPzHkvyaJKrdvv+AADAetpLO9nXJflsVb0jW1WY+5P8t0ku7O7jSdLdn66q\n583OvyjJ7869/tjsGAAAcAabNhVesJdP4/wkVyZ5bXffX1U/na1Wsj7pvJMf79DRufuXzm4AALBb\nj81ujG4vIebJJE909/2zx7+RrRBzvKou7O7jVfX8JJ+ZPX8syQvmXn94duw0rt7D0AAA4GSXZvEv\nxt+3nGGwZ7sOMbOQ8kRVvbC7H0lyTZKPzm6vSvKWJD+c5K7ZS+5O8s5ZxeaiJJcl+eAexg4AAGvB\nj10u2mvqoQS1AAASeUlEQVRz3Y9nK5g8K8nHk/xIkkNJ7qyqm5I8nq0dydLdD1bVnUkeTHIiyWu6\ne5etZgAAwLraU4jp7j9I8jdP8dRLT3P+m5K8aS/vCQAArLe9/k4MAADAgbJXGwAATJw1MYtUYgAA\ngKEIMQAAwFC0kwEAwMRpJ1ukEgMAAAxFiAEAAIainQwAACZuY+B2sqq6Nslbs1VAua2733Ka8/5m\nkn+d5Pu6+/860zVVYgAAgH1RVecleVuSlyV5SZIbq+pFpznvzUnes5PrCjEAAMB+uSrJo939eHef\nSHJHkutPcd6PJXlXks/s5KJCDAAAsF8uSvLE3OMnZ8e+qKq+Nskruvvnk9ROLmpNDAAATNzmak/b\n35rkDXOPtw0yK/1pAAAA++PPjt6fPz96/3anHUty8dzjw7Nj8741yR1VVUm+JsnLq+pEd999uotW\nd+9iyPurqjq5ZdnDAABgpR1Jd++ofWmZqqqv6A8texjbeqiufMbnWVWHknwsyTVJPpXkg0lu7O6H\nTnWNqnpHkt/cbncylRgAAJi4zUG3WO7uzap6XZJ78tdbLD9UVa/eerpvPfklO7muEAMAAOyb7n53\nkstPOvYLpzn3pp1c0+5kAADAUFRiAABg4kZtJ9svKjEAAMBQhBgAAGAo2skAAGDiNrSTLVCJAQAA\nhiLEAAAAQxFiAACAoVgTAwAAE7dp2r5AJQYAABiKEAMAAAxFXQoAACZu0xbLC1RiAACAoQgxAADA\nULSTAQDAxGknW6QSAwAADEWIAQAAhqKdDAAAJm7zC9rJ5qnEAAAAQxFiAACAoQgxAADAUKyJAQCA\nidvYsCZmnkoMAAAwFCEGAAAYinYyAACYuM0N0/Z5KjEAAMBQhBgAAGAo6lIAADBxm3YnW6ASAwAA\nDEWIAQAAhiLEAAAAQ7EmBgAAJs6amEUqMQAAwFCEGAAAYCjayQAAYOI2Tmgnm6cSAwAADEWIAQAA\nhqKdDAAAJu4Lm6bt81RiAACAoQgxAADAUNSlAABg6vzY5QKVGAAAYChCDAAAMBQhBgAAGIo1MQAA\nMHXWxCxQiQEAAIYixAAAAEPRTgYAAFO3UcsewaSoxAAAAEMRYgAAgKFoJwMAgKnbWPYApkUlBgAA\nGIoQAwAADEU7GQAATJ12sgUqMQAAwFCEGAAAYChCDAAAMBRrYgAAYOqsiVmgEgMAAAxFiAEAAIai\nnQwAAKbuxLIHMC0qMQAAwFCEGAAAYCjayQAAYOo2lz2AaVGJAQAAhiLEAAAAQ9FOBgAAU+fHLheo\nxAAAAEMRYgAAgKEIMQAAwFCsiQEAgKmzJmaBSgwAADAUIQYAABiKdjIAAJg67WQLVGIAAIChCDEA\nAMC+qaprq+rhqnqkqt5wiuevq6o/qKoHquqDVfWd211TOxkAAEzdoO1kVXVekrcluSbJJ5PcV1V3\ndffDc6e9t7vvnp3/jUnuTHLFma6rEgMAAOyXq5I82t2Pd/eJJHckuX7+hO7+87mHX57kC9tdVIgB\nAAD2y0VJnph7/OTs2IKqekVVPZTkN5PctN1FhRgAAGCpuvufdfcVSV6R5Ke2O9+aGAAAmLopron5\nyNHkD49ud9axJBfPPT48O3ZK3f3+qvr6qvqq7v7c6c4TYgAAgLP3jVdv3Z52x5FTnXVfksuq6pIk\nn0pyQ5Ib50+oqm/o7j+a3b8yybPPFGASIQYAANgn3b1ZVa9Lck+2lrLc1t0PVdWrt57uW5P83ar6\noSR/leQvkrxyu+tWd+/nuHelqjq5ZdnDAABgpR1Jd9eyR7Gdqur8xvTm7M/wd+vAPk8L+wEAgKEI\nMQAAwFCsiQEAgKk7sewBTItKDAAAMBQhBgAAGIp2MgAAmLrNZQ9gWlRiAACAoQgxAADAUIQYAABg\nKNbEAADA1G0sewDTohIDAAAMRYgBAACGop0MAACmTjvZApUYAABgKEIMAAAwFO1kAAAwddrJFqjE\nAAAAQxFiAACAoWgnAwCAqdNOtkAlBgAAGIoQAwAADEWIAQAAhmJNDAAATJ01MQtUYgAAgKHsKcRU\n1d+rqj+sqg9X1Tur6tlV9dyquqeqPlZV76mqC+bOv7mqHq2qh6rqe/Y+fAAAYN3sOsRU1dcm+bEk\nV3b3N2WrNe3GJG9M8t7uvjzJvUlunp3/4iSvTHJFkpcneXtV1d6GDwAAa2BjgNsB2ms72aEkX1ZV\n5yf50iTHklyf5PbZ87cnecXs/nVJ7ujuje5+LMmjSa7a4/sDAABrZtchprs/meQfJflEtsLLU939\n3iQXdvfx2TmfTvK82UsuSvLE3CWOzY4BAADs2K53J6uqr8xW1eWSJE8l+fWq+oEkfdKpJz8GAADO\nxollD2Ba9rLF8kuTfLy7P5ckVfVPk/ytJMer6sLuPl5Vz0/ymdn5x5K8YO71h2fHTuPo3P1LZzcA\nANitx2Y3RreXEPOJJN9eVV+S5P9Lck2S+5J8PsmrkrwlyQ8nuWt2/t1J3llVP52tNrLLknzw9Je/\neg9DAwCAk12axb8Yf99yhsGe7TrEdPcHq+pdSR7IVoHrgSS3JnlOkjur6qYkj2drR7J094NVdWeS\nB2fnv6a7tZoBAABnpaaYI6qqk1uWPQwAAFbakXT35H/yo6o6//P05uzP8D/UgX2ee91iGQAA4EAJ\nMQAAwFD2srAfAAA4CBvLHsC0qMQAAABDEWIAAIChaCcDAICp0062QCUGAAAYihADAAAMRTsZAABM\nnXayBSoxAADAUIQYAABgKEIMAAAwFGtiAABg6k4sewDTohIDAAAMRYgBAACGop0MAACmbnPZA5gW\nlRgAAGAoQgwAADAU7WQAADB1G8sewLSoxAAAAEMRYgAAgKFoJwMAgKnTTrZAJQYAABiKEAMAAAxF\niAEAAIZiTQwAAEzdiWUPYFpUYgAAgKEIMQAAwFC0kwEAwNRtLnsA06ISAwAADEWIAQAAhqKdDAAA\npm5j2QOYFpUYAABgKEIMAAAwFO1kAAAwddrJFqjEAAAAQxFiAACAoQgxAADAUKyJAQCAqTux7AFM\ni0oMAAAwFCEGAAAYinYyAACYus1lD2BaVGIAAIB9U1XXVtXDVfVIVb3hFM9/f1X9wez2/qr6xu2u\nKcQAAAD7oqrOS/K2JC9L8pIkN1bVi0467eNJ/pPu/uYkP5Xkf9/uutrJAABg6jaWPYBduyrJo939\neJJU1R1Jrk/y8NMndPcH5s7/QJKLtruoSgwAALBfLkryxNzjJ3PmkPJfJfnt7S6qEgMAAJy9zx5N\n/vjoObtcVf2nSX4kyX+83blCDAAAcPa+5uqt29MeOXKqs44luXju8eHZsQVV9U1Jbk1ybXf/yXZv\nLcQAAMDUjbsm5r4kl1XVJUk+leSGJDfOn1BVFyf5jSQ/2N1/tJOLCjEAAMC+6O7NqnpdknuytR7/\ntu5+qKpevfV035rkf0ryVUneXlWV5ER3X3Wm61Z37/fYz1pVdXLLsocBAMBKO5LurmWPYjtV1Xn5\n9Obsz/DbdWCfp0oMAABM3YllD2BabLEMAAAMRYgBAACGop0MAACmbnPZA5gWlRgAAGAoQgwAADAU\n7WQAADB14/7Y5b5QiQEAAIYixAAAAEMRYgAAgKFYEwMAAFNnTcwClRgAAGAoQgwAADAU7WQAADB1\nJ5Y9gGlRiQEAAIYixAAAAEPRTgYAAFO3uewBTItKDAAAMBQhBgAAGIp2MgAAmDo/drlAJQYAABiK\nEAMAAAxFiAEAAIZiTQwAAEydNTELVGIAAIChCDEAAMBQtJMBAMDUnVj2AKZFJQYAABiKEAMAAAxF\nOxkAAEzd5rIHMC0qMQAAwFCEGAAAYChCDAAAMBRrYgAAYOo2lj2AaVGJAQAAhiLEAAAAQ9FOBgAA\nU6edbIFKDAAAMBQhBgAAGIp2MgAAmLoTyx7AtKjEAAAAQxFiAACAoWgnAwCAqdtc9gCmRSUGAAAY\nihADAAAMRYgBAACGYk0MAABM3cayBzAtKjEAAMBQhBgAAGAo2skAAGDqtJMtUIkBAACGIsQAAABD\n0U4GAABTd2LZA5gWlRgAAGAoQgwAADAU7WQAADB1m8sewLSoxAAAAEMRYgAAgKEIMQAAwFCsiQEA\ngKnrZQ9gWlRiAACAoQgxAADAUIQYAABgKEIMAAAwFCEGAAAYihADAAAMRYgBAACGIsQAAABDEWIA\nAIChCDEAAMBQhBgAAGAoQgwAADCU85c9AAAAYDsnlj2ASVGJAQAAhrJtiKmq26rqeFV9eO7Yc6vq\nnqr6WFW9p6oumHvu5qp6tKoeqqrvmTt+ZVV9uKoeqaq3nvt/FAAAYB3spBLzjiQvO+nYG5O8t7sv\nT3JvkpuTpKpenOSVSa5I8vIkb6+qmr3m55P8aHe/MMkLq+rka8I2Hlv2AJikx5Y9ACbnsWUPgEl6\nbNkDgD3aGOB2alV1bVU9PCtmvOEUz19eVf+6qv6yqn5iJ5/GtiGmu9+f5E9OOnx9kttn929P8orZ\n/euS3NHdG939WJJHk1xVVc9P8pzuvm923i/PvQZ26LFlD4BJemzZA2ByHlv2AJikx5Y9AFhLVXVe\nkrdlqyjykiQ3VtWLTjrtj5P8WJL/ZafX3e2amOd19/Ek6e5PJ3ne7PhFSZ6YO+/Y7NhFSZ6cO/7k\n7BgAALC6rkryaHc/3t0nktyRrYLIF3X3Z7v793Kmcs5JztXuZH2OrgMAADzDsLuTnVzkeDJbwWZP\ndhtijlfVhd19fNYq9pnZ8WNJXjB33uHZsdMdP4Mjuxwaq+19yx4Ak+R7wcl8JzgV3ws4t/5lkvcv\n5Z13GmJqdnva3UleleQtSX44yV1zx99ZVT+drdR1WZIPdndX1VNVdVWS+5L8UJKfPd2bdXed7jkA\nAGAKvmt2e9qbT3XSsSQXzz3eQTFje9uGmKr61SRXJ/nqqvpEkltmI/z1qropyePZ2pEs3f1gVd2Z\n5MFs1bxe091Pt5q9NskvJfmSJL/V3e/e6+ABAIBJuy/JZVV1SZJPJbkhyY1nOH9HxYz664wBAABM\nTVX11gZeU/fVp+yoqqprk/xMtjYVu62731xVr07S3X1rVV2Y5P4kz0n+/3buWMfKKooC8Nq8gCWF\nCCZgQrShIr6BSEMLpdUU0tv6DMbCkNhYQUtB4RsQGjoI0BCYGDuLsRs9FjPFYcJwCXJzz06+r7v3\nnvz3b1fWPjv/JjlI8uUY4+C0fxJiAABgYd1DzDZ86IplAACAnfhYK5YBAICtabtieSs0MQAAQCtC\nDAAA0IpxMgAAWJ5xspkmBgAAaEWIAQAAWjFOBgAAyzvc9QssRRMDAAC0IsQAAACtCDEAAEAr7sQA\nAMDyrFieaWIAAIBWhBgAAKAV42QAALA8K5ZnmhgAAKAVIQYAAGjFOBkAACzPdrKZJgYAAGhFiAEA\nAFoxTgYAAMuznWymiQEAAFoRYgAAgFaEGAAAoBV3YgAAYHlWLM80MQAAQCtCDAAA0IpxMgAAWJ4V\nyzNNDAAA0IoQAwAAtGKcDAAAlmc72UwTAwAAtCLEAAAArQgxAABAK+7EAADA8qxYnmliAACAVoQY\nAACgFeNkAACwPCuWZ5oYAACgFSEGAABoxTgZAAAsz3aymSYGAABoRYgBAABaMU4GAADLs51spokB\nAABaEWIAAIBWhBgAAKAVd2IAAGB57sTMNDEAAEArQgwAANCKcTIAAFje4a5fYCmaGAAAoBUhBgAA\naMU4GQAALM92spkmBgAAaEWIAQAAWjFOBgAAy7OdbKaJAQAAWhFiAACAVoQYAACgFXdiAABgeVYs\nzzQxAABAK0IMAADQinEyAABYnhXLM00MAADQihADAAC0YpwMAACWZzvZTBMDAAC0IsQAAACtGCcD\nAIDl2U4208QAAACtCDEAAEArQgwAANCKOzEAALA8K5ZnmhgAAGBrqupaVT2tqmdV9cMpZ36qqudV\n9biqrmx6phADAABsRVWdSfJzkm+SfJXkVlVdPnHm2yQXxxhfJNlL8sum5xonAwCA5bVdsXw1yfMx\nxsskqaq7SW4keTqduZHktyQZYzysqk+q6uwY48/THqqJAQAAtuXTJK+mz6+Pv3vXmf23nHmDEAMA\nALRinAwAANb2Mvnxwq5f4j28bfxrP8n56fO54+9Onvlsw5k3CDEAALCwMcbnu36H/+FRkktVdSHJ\nH0luJrl14sz9JN8nuVdVXyf56133YRIhBgAA2JIxxj9VdTvJ7zm6yvLrGONJVe0d/TzujDEeVNX1\nqnqR5O8k3216bo0xtvvmAAAAH5GL/QAAQCtCDAAA0IoQAwAAtCLEAAAArQgxAABAK0IMAADQihAD\nAAC0IsQAAACt/Afz2lsIuTgLvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1138e6910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'plot_voxels' 0.63 sec\n"
     ]
    }
   ],
   "source": [
    "plot_voxels(solution_containing_voxels,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n",
      "79\n",
      "749\n",
      "7609\n",
      "75791\n"
     ]
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "\n",
    "for i in range(0,5):\n",
    "    print len(solution_containing_voxels[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x114a20b50>]"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZOm9ERLIl1oT/1luh82btWrjrLp2MFRHJplinR27d2rn9drjoIp2MFRFJR32m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\nSIFQwhcRKRBK+CIiBeJ/AehqpsBt+pNgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114a20090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "plt.title('Number of voxels per step')\n",
    "plt.semilogy([(len(solution_containing_voxels[i])) for i in range(0,max_i)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different bases comparison"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Base 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 298,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eps = 0.006\n",
    "starting_i = 0\n",
    "max_i = 2\n",
    "base = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACYAAAAPBAMAAAB6sKBjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJMt0i\nu0SCRuA9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmUlEQVQYGWNgAAHmyM4FEALMZWBUZmBgF2De\nAyHAXJOQzwwMTQwM0yEEmMvABhS7wsAgbwAmwFww8YWB4b0AmICLMX8FiiWDiAS4GM9PBob1c0DE\nBIQYUMn6OSACIYZNLwPQeHmQHfICcL0MdxkY+g3ABEIM6OZwkJvDGRBi3ALMWgxgAizG6vTdg4F5\nWgowDEAEmAsJCBQSABtTQ/E9ZhpaAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1001$$"
      ],
      "text/plain": [
       "1001"
      ]
     },
     "execution_count": 299,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## maximum grid length:\n",
    "1+pow(base,max_i+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'setup_ranges' 0.00 sec\n",
      "'initial_voxels' 0.00 sec\n",
      "'add_high_res_voxels' 0.07 sec\n"
     ]
    }
   ],
   "source": [
    "ranges = setup_ranges(max_i,base)\n",
    "solution_containing_voxels = initial_voxels(max_i,base,starting_i,eps)\n",
    "add_high_res_voxels(max_i,base,starting_i,eps,solution_containing_voxels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "37\n",
      "239\n",
      "2265\n"
     ]
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "\n",
    "for i in range(0,max_i+1):\n",
    "    print len(solution_containing_voxels[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 302,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11064d4d0>]"
      ]
     },
     "execution_count": 302,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9XCN3afHns9QJP5+pm+OBywHMrA/whbsvKXFclarZ9zO7hmdmvQnd1MvbNsyK\nkjvdOJs+my3X5Pupz2aLPQjMcPchTdze4s9nSUs67l5vZjcSpm62A4a7+0wzuy7c7Pe5+zNm1s/M\nPgL+DlxZypgqWT7vJ3CBmf0MWA+sBS6KL+LyFk03TgE7m9kCYDDQCX02W6W59xN9NvNmZscClwJ/\nMbN3AQf+jTBDr9Wfz7zX0hERkcqmUxyKiCSEEr6ISEIo4YuIJIQSvohIQijhi4gkhBK+iEhCKOGL\niCSEEr6ISEL8f0DTqXxer6IIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114403f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "plt.title('Number of voxels per step')\n",
    "plt.semilogy([(len(solution_containing_voxels[i])) for i in range(0,max_i+1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 303,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TohLDORFgAABYNiGGXRNgAACYAu1k7IoAAwCwRGbtC1Ri2JEAAwDAlAgxnJUAAwDA1ChM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\nAFoRYgAAgFaEGAAAoBUhBgAAaOU7JYEAFztJFIEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11440d190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'plot_voxels' 0.63 sec\n"
     ]
    }
   ],
   "source": [
    "plot_voxels(solution_containing_voxels,max_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Base 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eps = 0.006\n",
    "starting_i = 0\n",
    "max_i = 9\n",
    "base = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAPBAMAAACVcstdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJMt0i\nu0SCRuA9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVQYGW3OMUtCURjG8X8dvdf0FHdxFmwI\nyuEMfoAwQsFBhUScDKqt7yA05aRDJU6db9DYEnQXp1a3EPwGDhUigdf3cEsIOtM5P57nPS+4o9o9\ni25OLf5FuiGwtQ9+oF4osrNiO4oGUDz7gBsYcgJ5/LtrV/UEJ5AzR1CzCUcxfsI86Jo/qL4EzyXw\nahK3V1YuUtdLeJL5e0t2jV79oCQdZo7lzXuMv/WmMzrh5qNcgFeHMjzOYpxC35BFhweSNDHK8i3S\ndbxQws8ywi2fCdQhb6P7KmNSBUiWFhXUw6WlG0Xf6PaptP87a0PWQWRfDKqfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1025$$"
      ],
      "text/plain": [
       "1025"
      ]
     },
     "execution_count": 305,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## maximum grid length:\n",
    "1+pow(base,max_i+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'setup_ranges' 0.00 sec\n",
      "'initial_voxels' 0.00 sec\n",
      "'add_high_res_voxels' 0.07 sec\n"
     ]
    }
   ],
   "source": [
    "ranges = setup_ranges(max_i,base)\n",
    "solution_containing_voxels = initial_voxels(max_i,base,starting_i,eps)\n",
    "add_high_res_voxels(max_i,base,starting_i,eps,solution_containing_voxels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 307,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "16\n",
      "32\n",
      "52\n",
      "85\n",
      "158\n",
      "307\n",
      "613\n",
      "1199\n",
      "2381\n"
     ]
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "\n",
    "for i in range(0,max_i+1):\n",
    "    print len(solution_containing_voxels[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 308,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x114d56f10>]"
      ]
     },
     "execution_count": 308,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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plslEJsGJiEj9NKRbZjXQLu1+22ibiIjErC7J3fjm5Ohc4DAza29mzYGLgaez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\nQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114d56f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Number of solutions found for each resolution:\n",
    "plt.title('Number of voxels per step')\n",
    "plt.semilogy([(len(solution_containing_voxels[i])) for i in range(0,max_i+1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmbv/6Wzui9kxIYZdU4EBAGAZ7IlhV1RgAABYFpUYzpvfgQEAOGCHlj2BaVGJ4bwIMAAA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\nAKAVIQYAAGhFiAEAAFoRYgAAgFa+AVXcVRvoihnFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1166acd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'plot_voxels' 0.69 sec\n"
     ]
    }
   ],
   "source": [
    "plot_voxels(solution_containing_voxels,max_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of solution voxels increases by a factor of `base` at each step. This happens because the function being optimize is close to linear near the solutions and because we decrease `eps_current` by a factor of `base` at each step. As a result, the total number of voxels increases by a factor of `base**2` at each step, but the thickness of the solution voxel surface decreases by a factor of `base`.\n",
    "\n",
    "The cost of the algorithm is dominated by the last step. This is because the number of voxels increases approximately by a factor of `base` at each step, and the computational cost at each step is the number of voxels from the previous step multiplied by `base**2`. As such, the algorithm runtime is essentially the number of solution points. Notice in the above experiments the runtime was similar for different bases used. \n",
    "\n",
    "A more careful analysis assuming a large number of points and the scaling described above gives a geometric series for the runtime, where the sum starts at the last step ($b$ stands for `base` and $p$ stands for number of points):\n",
    "\\begin{align}\n",
    "b^2(\\frac{p}{b} + \\frac{p}{b^2} + ...)\n",
    "=\n",
    "p\\left( b + 1 + \\frac{1}{b} + ...\\right)\n",
    "\\approx \\frac{pb^2}{b-1}.\n",
    "\\end{align}\n",
    "\n",
    "The other factor contributing to the runtime is breaking away from the scaling law in the above discussion. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using the same technique for $\\chi^{(3)}$.\n",
    "\n",
    "Let's extend the above search technique to using four-wave mixing.\n",
    "\n",
    "The problems here will be larger, so runtime may be more important. For this reason, I tested different values of epsilon at each stage. Using a smaller epsilon will improve the runtime, but may miss correct solutions. Compare the number of solutions and runtime to the methods used in the notebook Dispersion_relation_two_approaches. The complexity is essentially linear in the number of solutions, but here the constant factor may be large if epsilon is not chosen carefully at each step. For this reason one may prefer to use the other techniques for $\\chi^{(3)}$ problems. The number of solutions in the method below converges to the number of solutions using the other two methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eps = 2e-4\n",
    "starting_i = 0\n",
    "max_i = 1\n",
    "base = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "relative_scalings = [4,4,10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "401 401 1001\n"
     ]
    }
   ],
   "source": [
    "phi1_min = 30.\n",
    "phi1_max = 34.\n",
    "ranges1 = {}\n",
    "for i in range(0,2):\n",
    "    ranges1[i] = np.linspace(phi1_min,phi1_max,relative_scalings[0]*pow(base,i+1)+1)\n",
    "\n",
    "phi2_min = -13\n",
    "phi2_max = -9\n",
    "ranges2 = {}\n",
    "for i in range(0,2):\n",
    "    ranges2[i] = np.linspace(phi2_min,phi2_max,relative_scalings[1]*pow(base,i+1)+1)\n",
    "\n",
    "nu3_min = -26.\n",
    "nu3_max = -16.\n",
    "ranges3 = {}\n",
    "for i in range(0,2):\n",
    "    ranges3[i] = np.linspace(nu3_min,nu3_max,relative_scalings[2]*pow(base,i+1)+1)\n",
    "\n",
    "print len(ranges1[1]),len(ranges2[1]),len(ranges3[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phi1, phi2 = sp.symbols('phi_1 phi_2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ex1 = (k_symb(nu1,pol='e')+k_symb(nu2,pol='e')).expand().subs({nu1:(phi1 + phi2)/2, nu2: (phi1-phi2)/2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ex2 = -(k_symb(nu3,pol='e')+k_symb(nu4,pol='e')).expand().subs(nu4,-phi1-nu3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f_phi12_nu3 =ufuncify([phi1,phi2,nu3], ex1-ex2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def initial_voxels_4wv(max_i,base,starting_i,eps,eps_factor = None):\n",
    "\n",
    "    if eps_factor is None:\n",
    "        eps_factor = pow(base,max_i-starting_i)\n",
    "    eps_current = eps * eps_factor\n",
    "        \n",
    "    solution_containing_voxels = {}\n",
    "    solution_containing_voxels[starting_i] = {}\n",
    "    \n",
    "    for i1,om1 in enumerate(ranges1[starting_i]):\n",
    "        for i2,om2 in enumerate(ranges2[starting_i]):\n",
    "            for i3,om3 in enumerate(ranges3[starting_i]):\n",
    "                err = f_phi12_nu3(om1,om2,om3)\n",
    "                if abs(err) < eps_current:\n",
    "                    solution_containing_voxels[starting_i][i1,i2,i3] = err\n",
    "    return solution_containing_voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 318,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def add_high_res_voxels_4wv(max_i,base,starting_i,eps,solution_containing_voxels):\n",
    "    for i in range(starting_i+1,max_i+1):\n",
    "        eps_current = eps * pow(base,max_i-i)\n",
    "        solution_containing_voxels[i] = {}\n",
    "        for (i1,i2,i3) in solution_containing_voxels[i-1]:\n",
    "            step_size = int(base/2)\n",
    "            max_length = pow(base,i+1)\n",
    "            for i1_new in range(max(0,i1*base-step_size),min(relative_scalings[0]*max_length,i1*base+step_size+1)):\n",
    "                for i2_new in range(max(0,i2*base-step_size),min(relative_scalings[1]*max_length,i2*base+step_size+1)):\n",
    "                    for i3_new in range(max(0,i3*base-step_size),min(relative_scalings[2]*max_length,i3*base+step_size+1)):\n",
    "                        err = f_phi12_nu3(ranges1[i][i1_new],ranges2[i][i2_new],ranges3[i][i3_new])\n",
    "                        if abs(err) < eps_current:\n",
    "                            solution_containing_voxels[i][i1_new,i2_new,i3_new] = err "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eps_factors = [1.5,2.,2.5,3.,3.5,4.]\n",
    "num_found = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'initial_voxels_4wv' 0.41 sec\n",
      "big voxels:  6184\n",
      "'add_high_res_voxels_4wv' 26.67 sec\n",
      "little voxels:  3766866\n",
      "'initial_voxels_4wv' 0.41 sec\n",
      "big voxels:  7776\n",
      "'add_high_res_voxels_4wv' 34.65 sec\n",
      "little voxels:  3979085\n",
      "'initial_voxels_4wv' 0.40 sec\n",
      "big voxels:  9295\n",
      "'add_high_res_voxels_4wv' 38.42 sec\n",
      "little voxels:  4094222\n",
      "'initial_voxels_4wv' 0.39 sec\n",
      "big voxels:  10772\n",
      "'add_high_res_voxels_4wv' 45.57 sec\n",
      "little voxels:  4158570\n",
      "'initial_voxels_4wv' 0.38 sec\n",
      "big voxels:  12168\n",
      "'add_high_res_voxels_4wv' 50.95 sec\n",
      "little voxels:  4193377\n",
      "'initial_voxels_4wv' 0.38 sec\n",
      "big voxels:  13556\n",
      "'add_high_res_voxels_4wv' 56.38 sec\n",
      "little voxels:  4208929\n"
     ]
    }
   ],
   "source": [
    "for eps_factor in eps_factors:\n",
    "    solution_containing_voxels_4wv = initial_voxels_4wv(max_i,base,starting_i,eps,eps_factor = eps_factor)\n",
    "    print 'big voxels: ', len(solution_containing_voxels_4wv[0].keys())\n",
    "    add_high_res_voxels_4wv(max_i,base,starting_i,eps,solution_containing_voxels_4wv)\n",
    "    num_found[eps_factor] = len(solution_containing_voxels_4wv[1].keys())\n",
    "    print 'little voxels: ', num_found[eps_factor]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1138c4750>]"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7Z2bVU/pla9SoUdXLjC1SV30oIuInETEgIjYGhgF3tBBMFGsLbgCG5ZEbGwEf\nA+6LiFeBuZIG506aw4HrC/uMyMv7A3fk5VuBXXPwsBqwa04DuDNvS9636VhmLZo7F444IvWL2Gwz\neOIJ+Ne/YMQIBxNmVpvqKqAoR9K+kqYAOwD/lHQzQERMAq4CJgE3AUcWJoI4CrgQeAaYHBG35PQL\ngTUlTQa+DxyXjzUbOBF4AJgAjMqdM8nbHCPpGWD1fAyzFl1/fQoiFixIgcSxx6bhn2ZmtcwTW9UQ\nT2zVs73yCvzv/8Kjj8J554G7z5i1jye2qg09oobCrJZFpFEan/pU+i2NRx5xMGFm3U+9dco061ae\neQa+8x2YNw9uvz0FFWZm3ZFrKMyq4IMP4De/gR13hH33hXHjHEyYWffmGgqzLnb//fCtb6VZLB94\nADbcsNo5MjOrnGsozLrI22+nERt77w0//CHcfLODCTOrHw4ozLrArbfC5pvDjBnw2GNpgipPk21m\n9cRNHmad6PXX4Zhj4D//gXPOSVNlm5nVI9dQmHWCCLj88lQrseaaqVbCwYSZ1TPXUJh1sBdfhMMP\nh2nT4IYbYPDgaufIzKzzuYbCrIMsWABnngmf/jT8z//Agw86mDCznsM1FGYd4NFH4dvfhpVXhnvv\nhU02qXaOzMy6lmsozCrw7rvws5/BF76Q5pa44w4HE2bWM7mGwmwZ3XVXmjZ7iy1SDcW661Y7R2Zm\n1eOAwmwpzZkDP/4x3Hgj/PGPsN9+1c6RmVn1ucnDbClcd10aCtqrFzzxhIMJM7MmrqEwa4eXX4bv\nfhcmTYIrr4TPfa7aOTIzqy2uoTBrxcKFcN55sOWWsNlm8PDDDibMzFriGgqzMp5+OnW6fO+9NHpj\niy2qnSMzs9rlGgqzEu+/DyedBDvtBF/5Ctxzj4MJM7O2uIbCrOC++9J8Ev37p5kuBw6sdo7MzLoH\nBxRmwFtvpQmqRo+G00+HYcP88+JmZkvDTR7W4918cxoKOns2PP44fO1rDibMzJaWayisx3rtNfjB\nD9Jvb5x/Puy6a7VzZGbWfbmGwnqcCLj00lQrsc468NhjDibMzCrlGgrrUZ5/Hg4/HKZPT1Nnb7tt\ntXNkZlYfXENhPcKCBamz5XbbwS67wP33O5gwM+tIrqGwuvfII2koaJ8+MG4cDBpU7RyZmdUf11BY\n3XrnHfjJT1L/iCOOgNtvdzBhZtZZ6jKgkNRL0kOSbsiPV5M0VtLTkm6V1K+w7fGSJkt6UtJuhfRt\nJD0q6RmSj/OpAAAVDElEQVRJZxTSe0sanfcZJ2lAYd2IvP3TkoYX0jeUND6vu1KSa4Y6WWNj+v2N\nZ5+FRx+FQw/1UFAzs85UlwEFcDQwqfD4OOC2iPg4cAdwPICkTwIHAJsCQ4CzpEUfO2cDh0XEJsAm\nknbP6YcBsyJiEHAGcGo+1mrAL4DtgO2BkYXA5RTgtHysOfkY1glmz4ZvfxsOPhh++1u46qo0ksPM\nzDpX3QUUkvoDewIXFJL3AS7OyxcD++blocDoiJgfES8Ak4HBktYB+kTE/Xm7Swr7FI91DbBLXt4d\nGBsRcyNiDjAW2COv2wW4tvD8+1V6nra4CLj22jQUtHdveOIJ2GefaufKzKznqMeq99OBHwL9Cmlr\nR8R0gIh4VdJaOX19YFxhu2k5bT4wtZA+Nac37TMlH2uBpLmSVi+mF48laQ1gdkQsLBxrvcpO0Yqm\nTYOjjoJnnkk1EjvtVO0cmZn1PHUVUEjaC5geEQ9Lamhl0+jIp+2gbQA44YQTFi03NDTQ0NCw9Dnq\nIRYuhPPOg5//PAUUY8bAiitWO1dm1tkaGxtpbGysdjasRF0FFMBOwFBJewIrA30kXQq8KmntiJie\nmzNm5O2nARsU9u+f08qlF/d5WdJyQN+ImCVpGtBQss+dETFTUj9JvXItRfFYSygGFFbeU0+lvhLz\n56cOmJttVu0cmVlXKf2yNWrUqOplxhapqz4UEfGTiBgQERsDw4A7IuJg4B/AN/NmI4Dr8/INwLA8\ncmMj4GPAfRHxKjBX0uDcSXN4yT4j8vL+pE6eALcCu+bgYTVg15wGcGfetvT5bSm9/z6ceCJ87nNw\n4IFw990OJszMakG91VCUczJwlaRDgRdJIzuIiEmSriKNCPkAODIimppDjgIuAlYCboqIW3L6hcCl\nkiYDM0mBCxExW9KJwAOkJpVRuXMmpFEmo/P6ifkYtpTGj08TVG20ETz0EGywQdv7mJlZ11Dz56dV\nm6Tw67GkN9+En/4Urr4azjgDDjjAc0qYWTNJRITvClVWV00eVn9uvDENBX3rrTQU9MADHUyYmdWi\nntLkYd3MjBnw/e/DhAlw4YXwxS9WO0dmZtYa11BYzfn732GLLaB/f3jsMQcTZmbdgftQ1BD3oYB/\n/xu++tXU1LHddtXOjZl1B+5DURscUNSQnh5QPPssfPazcNllrpUws/ZzQFEb3ORhNWH2bPjSl2DU\nKAcTZmbdkWsoakhPraF4/33YYw/Yaiv4/e+rnRsz625cQ1EbHFDUkJ4YUESkKbRnzIDrroPllqt2\njsysu3FAURs8bNSq6ne/gwceSFNoO5gwM+u+HFBY1fz973DmmTBuHHz4w9XOjZmZVcIBhVXFQw+l\npo6bb/ZvcpiZ1QOP8rAuN20a7LMPnHsubLtttXNjZmYdwQGFdam33oK994bvfhe+/OVq58bMzDqK\nR3nUkHof5bFgQQoi1lwTLrjAP/JlZh3Dozxqg/tQWJf58Y/hjTfSz5A7mDAzqy8OKKxLnH8+3HAD\njB8PvXtXOzdmZtbR3ORRQ+q1yeP22+HrX09zTQwaVO3cmFm9cZNHbXCnTOtUTz2VgomrrnIwYWZW\nzxxQWKd5/fX0g1+nnAKf/3y1c2NmZp3JTR41pJ6aPN57L/1q6Gc/C7/5TbVzY2b1zE0etcEBRQ2p\nl4AiAkaMgHnzUlNHL9eDmVknckBRGzzKwzrcSSfBk0/CXXc5mDAz6ykcUFiHuuoqOO88mDABPvSh\naufGzMy6ips8akh3b/KYMCF1wrztNthyy2rnxsx6Cjd51AZXSFuHePFF2G8/+MtfHEyYmfVEDiis\nYm+8kWomfvSj9MNfZmbW87jJo4Z0xyaP+fNh6FAYOBDOOsu/0WFmXc9NHrXBNRRWkWOOSUHFH/7g\nYMLMrCerq4BC0oqSJkiaKOkxSSNz+paS7pX0iKTrJX24sM/xkiZLelLSboX0bSQ9KukZSWcU0ntL\nGp33GSdpQGHdiLz905KGF9I3lDQ+r7tSUl2MrvnTn1IHzKuughVWqHZuzMysmuoqoIiI94CdI2Jr\nYCtgiKTtgfOBH0XElsB1wI8AJH0SOADYFBgCnCUt+p59NnBYRGwCbCJp95x+GDArIgYBZwCn5mOt\nBvwC2A7YHhgpqV/e5xTgtHysOfkY3drNN6f5Jv75T1h11WrnxszMqq2uAgqAiJiXF1ckzbOxEBgU\nEXfn9NuAr+TlocDoiJgfES8Ak4HBktYB+kTE/Xm7S4B98/I+wMV5+Rpgl7y8OzA2IuZGxBxgLLBH\nXrcLcG1evhjYryPOtVoefzzNhHnNNbDxxtXOjZmZ1YK6Cygk9ZI0EXgV+FcOCp6QNDRvcgDQPy+v\nD0wp7D4tp60PTC2kT81pi+0TEQuAuZJWL3csSWsAsyNiYeFY61V8olUyfXoa0XH66bDTTtXOjZmZ\n1Yq6aMsvyh/cW0vqC/w9N2scCvxR0s+BG4D3O/Ap29MVsd3dFU844YRFyw0NDTQ0NCx9jjrJO+/A\nPvvAN78JBx1U7dyYWU/V2NhIY2NjtbNhJeouoGgSEW9IuhPYIyJ+T2qSQNIgYK+82TRgg8Ju/XNa\nufTiPi9LWg7oGxGzJE0DGkr2uTMiZkrqJ6lXDnaKx1pCMaCoJQsXwiGHpCaOkSOrnRsz68lKv2yN\nGjWqepmxReqqyUPSmk0dISWtDOwKPCXpIzmtF/Az4Jy8yw3AsDxyYyPgY8B9EfEqqSljcO6kORy4\nvrDPiLy8P3BHXr4V2DUHD6vl5741r7szb0vet+lY3cYJJ8BLL6WZMD081MzMStVbDcW6wMU5cOgF\njImImyR9T9JRQAB/i4iLACJikqSrgEnAB8CRhZmljgIuAlYCboqIW3L6hcClkiYDM4Fh+VizJZ0I\nPJCfZ1TunAlwHDA6r5+Yj9FtXHpp+pswAVZaqdq5MTOzWuSZMmtILc6Ueffd8OUvw513wmabVTs3\nZmZL8kyZtaGumjysY/33v/DVr6baCQcTZmbWGgcU1qI5c9Lw0F/8Anbfve3tzcysZ3OTRw2plSaP\nDz6AIUNSrcSZZ1Y7N2ZmrXOTR21wQFFDaiGgiIDDD4dp0+D662G55aqaHTOzNjmgqA31NsrDKnT6\n6TB+fOqM6WDCzMzaywGFLXL99XDaaTBuHPTpU+3cmJlZd+KAwgCYOBG+9S248UYYMKDt7c3MzIo8\nysOYNg2GDoWzz4bBg6udGzMz644cUPRwb7+dgokjjkhzTpiZmS0Lj/KoIV09ymPhQvjKV6BfP/jr\nX/0bHWbWPXmUR21wH4oe7PjjYdYsGD3awYSZmVXGAUUPdeGF8Le/pSGiK65Y7dyYmVl35yaPGtJV\nTR533AFf+xr8+9/w8Y93+tOZmXUqN3nUBnfK7GGefjoFE6NHO5gwM7OO44CiB5k5M/3g169/DTvv\nXO3cmJlZPXGTRw3pzCaP996D3XaD7beHU0/tlKcwM6sKN3nUBgcUNaSzAooIOOQQmDsXrr0Werle\nyszqiAOK2uBRHj3AySfDY4+lTpgOJszMrDM4oKhz11yTptQePx5WWaXauTEzs3rlgKKO3XdfmlJ7\n7FhYb71q58bMzOqZK8Dr1EsvwX77pQmstt662rkxM7N654CiDr35Zhoeeswx6Ye/zMzMOptHedSQ\njhjlsWAB7LNPauI491z/RoeZ1T+P8qgNrqGoM8ceC+++C3/+s4MJMzPrOu6UWUfOPhtuuQXGjYMV\nVqh2bszMrCdxk0cNqaTJ49ZbYcQIuOce+OhHOzhjZmY1zE0etcE1FHXgiSfg4IPTz5E7mDAzs2pw\nH4pubsaMNKLj97+Hz3622rkxM7Oeqq4CCkkrSpogaaKkxySNzOlbShqX0++TtG1hn+MlTZb0pKTd\nCunbSHpU0jOSziik95Y0Ou8zTtKAwroRefunJQ0vpG8oaXxed6WkDqkZevdd2Hdf+MY30p+ZmVm1\n1FVAERHvATtHxNbAVsAQSdsDpwIjc/pI4LcAkj4JHABsCgwBzpIWjY04GzgsIjYBNpG0e04/DJgV\nEYOAM/KxkbQa8AtgO2B7YKSkfnmfU4DT8rHm5GNUeK5w6KGwwQYwalSlRzMzM6tMXQUUABExLy+u\nSOojsjD/NX24rwpMy8tDgdERMT8iXgAmA4MlrQP0iYj783aXAPvm5X2Ai/PyNcAueXl3YGxEzI2I\nOcBYYI+8bhfg2rx8MbBfpec5ahQ89xxcdJF/8MvMzKqv7jplSuoFPAh8FPhzRNwv6QfArZJOAwTs\nmDdfHxhX2H1aTpsPTC2kT83pTftMAYiIBZLmSlq9mF48lqQ1gNkRsbBwrIp+WeOKK1IgMWECrLxy\nJUcyMzPrGHX33TYiFuamjf6k2obNgCOAoyNiAPAD4C8d+JTtGarUYcOZ7r0Xvv99+Mc/YO21O+qo\nZmZmlam7GoomEfGGpEZSs8PwiDg6p18j6YK82TRgg8Ju/XNaufTiPi9LWg7oGxGzJE0DGkr2uTMi\nZkrqJ6lXrqUoHmsJJ5xwwqLlhoYGGhqaD/ncc/CVr8All8AWW7TrMpiZ1Z3GxkYaGxurnQ0rUVcT\nW0laE/ggIuZKWhm4FTiZ1AnzyIi4S9IXgJMjYrvcKfNyUifK9YF/AYMiIiSNB74H3A/cCPwhIm6R\ndCSweUQcKWkYsG9EDMudMh8AtiHV/DwAfDoi5kgaA/wtIsZIOht4JCLOaSH/ZSe2mjMHdtwRjjwS\nvvvdDrtkZmbdnie2qg31VkOxLnBx7kfRCxgTETdJmgucmWsU3gW+AxARkyRdBUwCPiAFHU2f6EcB\nFwErATdFxC05/ULgUkmTgZnAsHys2ZJOJAUSAYzKnTMBjgNG5/UT8zHa7YMP4IAD4AtfcDBhZma1\nqa5qKLq7lmooIlKtxIsvwg03wPL1FgKamVXINRS1wR9PNe7MM+Huu9NvdDiYMDOzWuWPqBr2z3/C\nqaemXw/t27fauTEzMyvPAUWNeuQROOSQNDx04MBq58bMzKx1dTcPRT145RXYe2/4859hhx2qnRsz\nM7O2OaCoMfPmwdCh8J3vpJEdZmZm3YFHedQQSfHlLwerrAIXXwxyn2UzszZ5lEdtcB+KGjNjBtx2\nm4MJMzPrXlxDUUMkxWuvBWuuWe2cmJl1H66hqA0OKGpIa1Nvm5lZyxxQ1AZ3yjQzM7OKOaAwMzOz\nijmgMDMzs4o5oDAzM7OKOaAwMzOzijmgMDMzs4o5oDAzM7OKOaAwMzOzijmgMDMzs4o5oDAzM7OK\nOaAwMzOzijmgMDMzs4o5oDAzM7OKOaAwMzOzijmgMDMzs4o5oDAzM7OKOaAwMzOzijmgMDMzs4o5\noDAzM7OK1VVAIWlFSRMkTZT0mKSROX20pIfy3/OSHirsc7ykyZKelLRbIX0bSY9KekbSGYX03vl4\nkyWNkzSgsG5E3v5pScML6RtKGp/XXSlp+c6/GmZmZl2nrgKKiHgP2Dkitga2AoZIGhwRwyJim4jY\nBrgW+BuApE2BA4BNgSHAWZKUD3c2cFhEbAJsImn3nH4YMCsiBgFnAKfmY60G/ALYDtgeGCmpX97n\nFOC0fKw5+RjWisbGxmpnoWb4WjTztWjma2G1pq4CCoCImJcXVwSWB6JkkwOAK/LyPsDoiJgfES8A\nk4HBktYB+kTE/Xm7S4B9C/tcnJevAXbJy7sDYyNibkTMAcYCe+R1u5ACGfK++1V0kj2Ab5bNfC2a\n+Vo087WwWlN3AYWkXpImAq8C/yoEBUj6HPBqRDyXk9YHphR2n5bT1gemFtKn5rTF9omIBcBcSauX\nO5akNYDZEbGwcKz1Kj5RMzOzGlJ3AUVELMxNHv2B7SV9srD6a8CVHfyUanuTdm1jZmbWbSmitEWg\nfkj6OfB2RPxe0nKkWoNtIuLlvP44ICLilPz4FmAk8CJwZ0RsmtOHAZ+PiCOatomICfmYr0TEWnmb\nhog4PO9zTj7GGEkzgHUiYqGkHfL+Q1rIb/2+GGZmnSgi/MWtyupqtIGkNYEPImKupJWBXYGT8+pd\ngSebgonsBuBySaeTmiw+BtwXESFprqTBwP3AcOAPhX1GABOA/YE7cvqtwEm5I2av/HzH5XV35m3H\n5H2vbyn/fkOYmVl3VVcBBbAucLGkXqQP9TERcVNedyAlzR0RMUnSVcAk4APgyGiusjkKuAhYCbgp\nIm7J6RcCl0qaDMwEhuVjzZZ0IvAAqSPoqNw5E1JgMTqvn5iPYWZmVjfqusnDzMzMukbddcqsdZIu\nlDRd0qNl1n9e0pzCRFw/6+o8dhVJ/SXdIemJPBHZ98ps94c8kdjDkrbq6nx2hfZci55SNspNUNfC\ndnVdLtpzHXpKmWiSR/E9JOmGMuvrukzUunpr8ugO/gr8kTS3RTn/joihXZSfapoPHBMRD0v6MPCg\npLER8VTTBpKGAB+NiEGStgfOAXaoUn47U5vXIqv7shER70naOSLm5Y7P90i6OSLua9qmJ5SL9lyH\nrO7LRMHRpCbqvqUrekKZqHWuoehiEXE3MLuNzXpE58yIeDUiHs7LbwFP0jzfR5N9yMFXREwA+kla\nu0sz2gXaeS2g55SNtiao6ynloq3rAD2kTEjqD+wJXFBmkx5RJmqZA4ra9JlcZXdjyTwadUvShqTp\n0ieUrCo3+VjdauVaQA8pG61NUJf1iHLRjusAPaRMAKcDP6TloAp6SJmoZQ4oas+DwICI2Ar4E/D3\nKuen0+Uq/muAo/O38x6rjWvRY8pGGxPU9RjtuA49okxI2guYnmvxRA+pleluHFDUmIh4q6maMyJu\nBlbIU3vXJaVfXr0GuDQiWpqfYxqwQeFx/5xWd9q6Fj2tbABExBukeVz2KFnVY8oFlL8OPahM7AQM\nlfQcafj/zpJK+6H1qDJRixxQVEfZCLvY5pcn1lJEzOqqjFXBX4BJEXFmmfU3kCYWI88yOicipndV\n5rpYq9eip5QNSWvmCeIoTFBX2jm17stFe65DTykTEfGTiBgQERuT5v65IyKGl2xW92Wi1nmURxeT\ndAXQAKwh6SXSVN+9SVOAnwd8VdIRpIm23iFNyFWXJO0EHAQ8ltuJA/gJMJB8PSLiJkl7SnoWeBs4\npHo57jztuRb0nLLR4gR1kv4fPatctHkd6DllokU9sEzUNE9sZWZmZhVzk4eZmZlVzAGFmZmZVcwB\nhZmZmVXMAYWZmZlVzAGFmZmZVcwBhZmZmVXMAYWZmZlVzAGFmZmZVez/A58BNb3fEJycAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f85910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('number of solutions found as a function of the epsilon multiplier for the voxel method')\n",
    "plt.plot(eps_factors, [num_found[eps] for eps in eps_factors] )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding solutions in the voxels:\n",
    "\n",
    "In general the nus to be considered do not lie on a grid. For this reason it is necessary to find which nus lie in each voxel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup for the experiment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eps = 0.006\n",
    "starting_i = 0\n",
    "max_i = 2\n",
    "base = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'setup_ranges' 0.00 sec\n",
      "'initial_voxels' 0.00 sec\n",
      "'add_high_res_voxels' 0.08 sec\n"
     ]
    }
   ],
   "source": [
    "ranges = setup_ranges(max_i,base)\n",
    "solution_containing_voxels = initial_voxels(max_i,base,starting_i,eps)\n",
    "add_high_res_voxels(max_i,base,starting_i,eps,solution_containing_voxels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "i = 2  ## where to draw points from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "scale = 0.1  ## scale on random noise to add to points\n",
    "Delta = ranges[i][1] - ranges[i][0]  ## Delta here was made with ranges[0] spacing\n",
    "range_min = ranges[i][0]\n",
    "ranges_perturbed = [num+random.random()*scale for num in ranges[2]] ## make "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "values = [ int(round( (el - range_min) / Delta)) for el in ranges_perturbed]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_dict_values_to_lists_of_inputs(values,inputs):\n",
    "    D = {}\n",
    "    for k, v in zip(values,inputs):\n",
    "        D.setdefault(k, []).append(v)\n",
    "    return D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "D = make_dict_values_to_lists_of_inputs(values,ranges_perturbed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "solution_nus = []\n",
    "for indices in solution_containing_voxels[i].keys(): \n",
    "    if all([ind in D for ind in indices]): ## check all indices are in D,\n",
    "        for it in itertools.product(*[D[ind] for ind in indices]): ## get all nus in the voxel.\n",
    "            solution_nus.append(it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x114354990>"
      ]
     },
     "execution_count": 330,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4JztyDDCEjRs35hKnJElSV2airy5p+vTrmTnzRtKCWU2kEp4mUvLfemLu+nwC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e711850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13,13))\n",
    "plt.title('perturbed grid points still in the solution voxels')\n",
    "plt.scatter([el[0] for el in solution_nus],[el[1] for el in solution_nus])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Development for method to be used in the package"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def setup_ranges(max_i,base,min_value = 6.,max_value = 11.):\n",
    "    ranges= {}\n",
    "    for i in range(max_i+1):\n",
    "        ranges[i] = np.linspace(min_value,max_value,1+pow(base,i+1))\n",
    "    return ranges\n",
    "\n",
    "@timeit\n",
    "def initial_voxels(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps):\n",
    "    solution_containing_voxels = {}\n",
    "    eps_current = eps * pow(base,max_i-starting_i)\n",
    "    solution_containing_voxels[starting_i] = {}\n",
    "\n",
    "    for i1,om1 in enumerate(ranges[starting_i]):\n",
    "        for i2,om2 in enumerate(ranges[starting_i]):\n",
    "            err = k_of_nu1_nu2(om1,om2)\n",
    "            if abs(err) < eps_current:\n",
    "                solution_containing_voxels[starting_i][i1,i2] = err\n",
    "    return solution_containing_voxels\n",
    "\n",
    "@timeit\n",
    "def add_high_res_voxels(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps,solution_containing_voxels):\n",
    "    for i in range(starting_i+1,max_i+1):\n",
    "        eps_current = eps * pow(base,max_i-i)\n",
    "        solution_containing_voxels[i] = {}\n",
    "        for (i1,i2) in solution_containing_voxels[i-1]:\n",
    "            step_size = int(base/2)\n",
    "            max_length = pow(base,i+1)\n",
    "            for i1_new in range(max(0,i1*base-step_size),min(max_length,i1*base+step_size+1)):\n",
    "                for i2_new in range(max(0,i2*base-step_size),min(max_length,i2*base+step_size+1)):\n",
    "                    err = k_of_nu1_nu2(ranges[i][i1_new],ranges[i][i2_new])\n",
    "                    if abs(err) < eps_current:\n",
    "                        solution_containing_voxels[i][i1_new,i2_new] = err\n",
    "\n",
    "@timeit\n",
    "def plot_voxels(solution_containing_voxels,i):\n",
    "    voxels = np.zeros((1+pow(base,i+1),1+pow(base,i+1)))\n",
    "    for (i1,i2) in solution_containing_voxels[i]:\n",
    "        voxels[i1,i2] = 1\n",
    "    plot_arr(voxels)\n",
    "\n",
    "def voxel_solutions(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps):\n",
    "    solution_containing_voxels = initial_voxels(ranges,k_of_nu1_nu2,max_i,\n",
    "                                                base,starting_i,eps)\n",
    "    add_high_res_voxels(ranges,k_of_nu1_nu2,max_i,base,starting_i,eps,\n",
    "                        solution_containing_voxels)\n",
    "    return solution_containing_voxels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_k_func(pols=(1,1,-1),n_symb = None):\n",
    "\n",
    "    lambd,nu,nu1,nu2,nu3,nu4 = sp.symbols(\n",
    "        'lambda nu nu_1 nu_2 nu_3 nu_4')\n",
    "    l2 = lambd **2\n",
    "\n",
    "    if n_symb is None:\n",
    "        def n_symb(pol=1):\n",
    "            '''Valid for lambda between 0.5 and 5. (units are microns)'''\n",
    "            s = 1.\n",
    "            if pol == 1:\n",
    "                s += 2.6734 * l2 / (l2 - 0.01764)\n",
    "                s += 1.2290 * l2 / (l2 - 0.05914)\n",
    "                s += 12.614 * l2 / (l2 - 474.6)\n",
    "            else:\n",
    "                s += 2.9804 * l2 / (l2 - 0.02047)\n",
    "                s += 0.5981 * l2 / (l2 - 0.0666)\n",
    "                s += 8.9543 * l2 / (l2 - 416.08)\n",
    "            return sp.sqrt(s)\n",
    "\n",
    "    def k_symb(symbol=nu,pol=1):\n",
    "        '''k is accurate for nu inputs between 6-60 (units are 1e13 Hz).'''\n",
    "        return ((n_symb(pol=pol) * symbol )\n",
    "                    .subs(lambd,scipy.constants.c / (symbol*1e7)))\n",
    "\n",
    "    expressions = [k_symb(nu1,pols[0]),\n",
    "                   k_symb(nu2,pols[1]),\n",
    "                   k_symb(nu3,pols[2])]\n",
    "    dispersion_difference_function = sum(expressions)\n",
    "    dispersion_difference_function = dispersion_difference_function.subs(\n",
    "                                     nu3,-nu1-nu2)\n",
    "    k_of_nu1_nu2 = ufuncify([nu1,nu2],\n",
    "                                   dispersion_difference_function)\n",
    "    return k_of_nu1_nu2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pols = (1,1,-1)\n",
    "k_of_nu1_nu2 = generate_k_func(pols)\n",
    "\n",
    "eps = 0.006\n",
    "starting_i = 0\n",
    "max_i = 2\n",
    "base = 10\n",
    "\n",
    "min_value = 6.\n",
    "max_value = 20.\n",
    "ranges = setup_ranges(max_i,base,min_value,max_value)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 384,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'initial_voxels' 0.00 sec\n",
      "'add_high_res_voxels' 0.06 sec\n"
     ]
    }
   ],
   "source": [
    "pos_nus_lst = np.random.uniform(min_value,max_value,1000) ## 100 random values\n",
    "\n",
    "Delta = ranges[max_i][1] - ranges[max_i][0] ## spacing in grid used\n",
    "\n",
    "## get index values\n",
    "values = [ int(round( (freq - min_value) / Delta)) for freq in pos_nus_lst]\n",
    "\n",
    "## make a dict to remember which frequencies belong in which grid voxel.\n",
    "grid_indices_to_unrounded = make_dict_values_to_lists_of_inputs(values,pos_nus_lst)\n",
    "grid_indices_to_ham_index = make_dict_values_to_lists_of_inputs(values,range(len(pos_nus_lst)))\n",
    "\n",
    "solution_containing_voxels = voxel_solutions(ranges,k_of_nu1_nu2,\n",
    "    max_i,base,starting_i,eps)\n",
    "\n",
    "## Let's figure out which indices we can expect for nu3\n",
    "spacing = (max_value-min_value)/ pow(base,max_i+1)\n",
    "num_indices_from_zero = min_value / spacing  ## float, round up or down\n",
    "\n",
    "solutions_nu1_and_nu2 = solution_containing_voxels[max_i].keys()\n",
    "\n",
    "solution_indices = []\n",
    "for indices in solutions_nu1_and_nu2:\n",
    "    for how_to_round_last_index in range(2):\n",
    "        last_index = (sum(indices)\n",
    "                      + int(num_indices_from_zero)\n",
    "                      + how_to_round_last_index)\n",
    "        if last_index < 0 or last_index >= len(ranges[max_i]):\n",
    "            print \"breaking!\"\n",
    "            break\n",
    "        current_grid_indices = (indices[0],indices[1],last_index)\n",
    "        if all([ind in grid_indices_to_ham_index for ind in current_grid_indices]):\n",
    "            for it in itertools.product(*[grid_indices_to_ham_index[ind] for ind in current_grid_indices]):\n",
    "                solution_indices.append(it)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 385,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAOBAMAAABeLhj4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVQYGS3QsWoCQRCA4f/w7jQqcqS0Oiwi\nIQQLq6S6ztKtUgfBwlgoIrEJ5N4gpDTBJ0iR1k4UfAGfwCdIyogW6+xsivmYGWZ2lyVotDMUii9T\nKtvwFh4oHjzRkhsurB1DH+aeQkqbyvMa+IBRprwlUsYSsDLSVO5c6ZuSfBvl1NnkxD+bTCpKf0p0\n2rOgYIKDa5Yflcgart3OvQSNf47wm0vekgurqSSOL2nuh/Caw44gUQZu8lMmDWFKNVG6ciZ+oz6b\nPKHE42jBJbV3eby1Rw+TK/maZs9wBvTWPoSf/MGfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$2265$$"
      ],
      "text/plain": [
       "2265"
      ]
     },
     "execution_count": 385,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(solutions_nu1_and_nu2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACcAAAAOBAMAAABeLhj4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAzXYQMplU74mrIma7\nRN0SDTw+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVQYGS2OsUoDQRCGv3ODmjUGW6ucqIU2\nrpWl+wRGC+UQJPsGQbBKdYpFgsXF4rA0IGJ7pIlgEVtBxDcQWystBBVlnY1OMzMf///PEM2XdlDJ\ntWUjb7dTlXR6MOF9SuTUC0PvfXet0C2IOsswgEN2ocwZ5KFL3UHTpHDMG2T/8BOeHEzH6htWLOWb\nRaveBcZQgX1RPlIx+kd/QF3cJyNvrUDqQYtSoHqVu/F45gJsXPzZx2Zk6S9kltMQIoeajuptkHBu\nQnLD3MPQsN4dwVnYhOfw/JbEyjzolb7gkqkWVacOJEHgnFktQCe5QR0tWbhyMLm9B7/AY0Plhb57\nZgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$5079$$"
      ],
      "text/plain": [
       "5079"
      ]
     },
     "execution_count": 386,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(solution_indices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sample_indices = solution_indices[random.randint(0,len(solution_indices)-1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKQAAAAUBAMAAADxUYsHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nru2pDh1fhh0z+VH8A/VYtassZJm9AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 213, \\quad 523, \\quad 423\\right )$$"
      ],
      "text/plain": [
       "(213, 523, 423)"
      ]
     },
     "execution_count": 375,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAc4AAAAUBAMAAAD2GsB+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/FgAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left ( 8.01874256402, \\quad 8.15636006023, \\quad 16.1780985831\\right )$$"
      ],
      "text/plain": [
       "(8.01874256402, 8.15636006023, 16.1780985831)"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_nus_lst[sample_indices[0]], pos_nus_lst[sample_indices[1]], pos_nus_lst[sample_indices[2]] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAAPBAMAAABgoIKoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nWtcquiqzR+7KMzAuuDd/5qTq/4zfdVck5LBQioIAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$-0.00299595885004$$"
      ],
      "text/plain": [
       "-0.00299595885004"
      ]
     },
     "execution_count": 377,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pos_nus_lst[sample_indices[0]]+pos_nus_lst[sample_indices[1]] - pos_nus_lst[sample_indices[2]] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([], shape=(0, 0), dtype=float64)"
      ]
     },
     "execution_count": 395,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHcAAAAUBAMAAABFd79NAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVQ4EWNgYFRgIAsognQJk6WVgYFXAKjR\nEYg7D2CagE0MpopjDgMDjwMDA1MAA8/V+xiasYnBtDKcjf0DZG9nYGAD2V6PoRm7GEw7O0jzSQYG\nMZAAWZpZFjCUkq2ZNYDBiGzNTA4MGWRr5khgmEWC5iNpIODHwAAOML4PJGkG2QMGMM3kO5srgbIA\n2wpyBzCeeb5AXAQnsYnBJMHOZt3AsAwoEDvfV4Eh7QBMCkxjE4MpYL355RIDA8sDSPIEiXKA0ika\nwCYGVwJMm8CMAQHccFEEA5sYXBaYMRgMobzjcFEEA5sYTBaUJeGFgQJMFInGJgaTZgZ5k1EBSJAB\ngMUQAK6rS4CB2esmAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left ( 1, \\quad 1, \\quad -1\\right )$$"
      ],
      "text/plain": [
       "(1, 1, -1)"
      ]
     },
     "execution_count": 401,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tuple(map(lambda z: int(np.sign(z)),(4.5,5.5,-3.4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAAPBAMAAACcmWsnAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77ur\nRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAl0lEQVQYGWNgEDIxZQABGA1kpjNITAAJQegq\nAQYGlgUMzAlAETDNeOg8UIj7AAP7R6AQlH4PFOI/wMD7HSgEpUFC8goMvP+AQlAaJDTfgIH1M1AI\nSoOFFKBCEBqHRqCx7FDjQTRIFfcGBhawIyA0SAjoRKYEoPFQGiTE0M4gFcD4DUJDNDIIvzvKwNDD\nAKF11uc4AJWhAwCcHDYT04/v5wAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$0.01$$"
      ],
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def make_dict_values_to_lists_of_inputs(values,inputs):\n",
    "    '''\n",
    "    Make a dictionary mapping value to lists of corresponding inputs.\n",
    "\n",
    "    Args:\n",
    "        values (list of floats):\n",
    "            Values in a list, corresponding to the inputs.\n",
    "        inputs (list of floats):\n",
    "            Inputs in a list.\n",
    "\n",
    "    Returns:\n",
    "        D (dict):\n",
    "            dictionary mapping value to lists of corresponding inputs.\n",
    "    '''\n",
    "    D = {}\n",
    "    for k, v in zip(values,inputs):\n",
    "        if not math.isnan(k):\n",
    "            D.setdefault(k, []).append(v)\n",
    "    return D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOoAAAAVBAMAAAC6fm+xAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left \\{ 3 : \\left [ 1\\right ], \\quad 4 : \\left [ 2\\right ], \\quad 5 : \\left [ 3\\right ]\\right \\}$$"
      ],
      "text/plain": [
       "{3: [1], 4: [2], 5: [3]}"
      ]
     },
     "execution_count": 441,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_dict_values_to_lists_of_inputs([float('NaN'),3,4,5],[1,1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 432,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.isnan(float('NaN'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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