Dispersion_relation_interpolation (newton's method, tracing).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary of solving phase and frequency matching for $\\chi^{(2)}$ nonlinearity, plus interpolation\n",
    "\n",
    "# Solving phase and frequency matching conditions for $\\chi^{(3)}$ with Newton's method\n",
    "\n",
    "# 2D interpolation for $\\chi^{(3)}$.\n",
    "\n",
    "Here, we use Newton's method to find a set of solutions for a set of equations representing the restrictions on the frequencies for which nonlinear interaction occurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "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",
    "from scipy import interpolate\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sympy import init_printing\n",
    "init_printing() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_arr(arr,bounds = None):\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,boundaries = bounds)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lambd,omega,omega1,omega2,omega3,omega4 = sp.symbols('lambda omega omega_1 omega_2 omega_3 omega_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=omega,pol='o'):\n",
    "    '''k is accurate for omega inputs between 6-60.'''\n",
    "    return ((n_symb(pol=pol) * symbol )\n",
    "                .subs(lambd,scipy.constants.c / (symbol*1e7))) ## / scipy.constants.c\n",
    "\n",
    "def make_newton_update_expression(dispersion_difference_function,symbols):\n",
    "    expression_diff = [sp.diff(dispersion_difference_function,sym) for sym in symbols]\n",
    "    return [- dispersion_difference_function / der for der in expression_diff]\n",
    "\n",
    "dispersion_difference_function = k_symb()\n",
    "update_expression = make_newton_update_expression(dispersion_difference_function.expand(),symbols=[omega])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calling 1e6 trivial functions: \n",
      "'trivial_func' 0.57 sec\n",
      "calling 1e6 newton's functions: \n",
      "'newton_update_func' 1.25 sec\n"
     ]
    }
   ],
   "source": [
    "## Let's get an estimate for how long it takes to call the Newton's function, in comparison to calling\n",
    "## a trivial function\n",
    "\n",
    "@timeit\n",
    "def trivial_func():\n",
    "    f = ufuncify( [omega] , 0.)\n",
    "    for i in xrange(int(1e6)):\n",
    "        f(10.)\n",
    "        return\n",
    "\n",
    "@timeit\n",
    "def newton_update_func():\n",
    "    f = ufuncify( [omega] , update_expression)\n",
    "    for i in xrange(int(1e6)):\n",
    "        f(10.)\n",
    "    return\n",
    "\n",
    "print \"calling 1e6 trivial functions: \"\n",
    "trivial_func()\n",
    "\n",
    "print \"calling 1e6 newton's functions: \"\n",
    "newton_update_func()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\omega \\sqrt{1.0 + \\frac{2402.73209483501}{- 0.01764 \\omega^{2} + 898.755178736817} + \\frac{1104.57011466755}{- 0.05914 \\omega^{2} + 898.755178736817} + \\frac{11336.8978245862}{- 474.6 \\omega^{2} + 898.755178736817}}$$"
      ],
      "text/plain": [
       "       _______________________________________________________________________\n",
       "      ╱                2402.73209483501                     1104.57011466755  \n",
       "ω⋅   ╱  1.0 + ────────────────────────────────── + ───────────────────────────\n",
       "    ╱                       2                                    2            \n",
       "  ╲╱          - - -0.01764⋅ω  + 898.755178736817   - - -0.05914⋅ω  + 898.75517\n",
       "\n",
       "______________________________________________\n",
       "                    11336.8978245862          \n",
       "─────── + ─────────────────────────────────── \n",
       "                         2                    \n",
       "8736817   - -474.6⋅(-1)⋅ω  + 898.755178736817 "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dispersion_difference_function.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "k_o_vs_omega = ufuncify([omega],k_symb())\n",
    "k_e_vs_omega = ufuncify([omega],k_symb(pol='e'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\chi^{(2)}$ example, see also the notebook Dispersion_relation_chi_2_and_interpolations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "dispersion_difference_function = k_symb(omega1,pol='o')+k_symb(omega2,pol='o')+k_symb(omega3,pol='e')\n",
    "\n",
    "symbols=[omega1,omega2]\n",
    "update_expression = make_newton_update_expression(dispersion_difference_function.expand(),\n",
    "                                                    symbols=[omega1,omega2,omega3])\n",
    "\n",
    "update_expression = [ex.subs(omega3,-omega1-omega2) for ex in update_expression]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "newton_update_func_0 = ufuncify( symbols , update_expression[0])\n",
    "newton_update_func_1 = ufuncify( symbols , update_expression[1])\n",
    "newton_update_func_2 = ufuncify( symbols , update_expression[2])\n",
    "\n",
    "omegas_dict = {}\n",
    "\n",
    "ind_range = range(2,5)\n",
    "for i in ind_range:\n",
    "    omegas_dict[i] = np.asarray([6.+ j*5*pow(10,-i) for j in range(1+pow(10,i))])\n",
    "\n",
    "def trace_omegas(omegas,arg2 = 24.):\n",
    "    '''\n",
    "    Trace through triples of frequencies constrained by \n",
    "    :math:`omega1+omega2+omega3 = 0`.\n",
    "    \n",
    "    At each step of incrementing omega1, find the new omega2 \n",
    "    and omega3 by applying Newton's method to omega2 \n",
    "    and the constraint to obtain omega3.\n",
    "    \n",
    "    \n",
    "    Trace through the omegas, when finding the next\n",
    "    step with Newton's method occasionally check the error \n",
    "    and allow terminating early.\n",
    "    \n",
    "    Args:\n",
    "        omegas (list of floats):\n",
    "            The frequencies in the range desired\n",
    "        fixed_omega_3 (optional [float]): initial value of omega3.\n",
    "        \n",
    "    Returns:\n",
    "        oms (list of floats): A history of the Newton's steps\n",
    "        converged_points (list of tuples): \n",
    "    '''\n",
    "    fixed_omega1=omegas[0]\n",
    "    omegas_delta = omegas[1]-omegas[0]\n",
    "    oms = [(fixed_omega1, arg2)]  ## k is accurate for omega inputs between 6-60.\n",
    "    converged_points = []\n",
    "    for i in range(int(1e5)):\n",
    "        arg2 += newton_update_func_1(*(oms[-1]))\n",
    "        oms.append((omegas[0],arg2))\n",
    "        if sum([ (oms[-1][i] - oms[-2][i])**2 for i in range(2)]) < omegas_delta * 1e-10 :\n",
    "            break\n",
    "    for arg1 in omegas:\n",
    "        for i in range(50):\n",
    "            for j in range(10):\n",
    "                arg2 += newton_update_func_1(*(oms[-1]))\n",
    "                oms.append((arg1,arg2))\n",
    "            if sum([ (oms[-1][k] - oms[-2][k])**2 for k in range(2)]) < omegas_delta * 1e-10:\n",
    "                break\n",
    "        converged_points.append((arg1,arg2))\n",
    "    return oms,converged_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i = 2\n",
      "'timed_trace_omegas' 0.14 sec\n",
      "i = 3\n",
      "'timed_trace_omegas' 0.21 sec\n",
      "i = 4\n",
      "'timed_trace_omegas' 1.72 sec\n"
     ]
    }
   ],
   "source": [
    "@timeit\n",
    "def timed_trace_omegas(*args,**kw):\n",
    "    return trace_omegas(*args, **kw)\n",
    "\n",
    "@timeit\n",
    "def interpolate_omegas(omegas_few,omegas_many,omegas_few_values):\n",
    "    f = interpolate.UnivariateSpline(omegas_few, omegas_few_values,k=2,s=1e-10)\n",
    "    return f(omegas_many)\n",
    "\n",
    "omegas_converged = {}\n",
    "for i in ind_range:\n",
    "    print \"i = \" + str(i)\n",
    "    omegas_converged[i] = timed_trace_omegas(omegas_dict[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "omegas_2_converged = {}\n",
    "for j in ind_range:\n",
    "    L = range(len(omegas_converged[j][1]))\n",
    "    omegas_2_converged[j] = [omegas_converged[j][1][i][1] for i in L]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'interpolate_omegas' 0.01 sec\n"
     ]
    }
   ],
   "source": [
    "omega_values_interpolated_3_to_4 = interpolate_omegas(omegas_dict[3], \n",
    "                                omegas_dict[4],omegas_2_converged[3] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11ce04fd0>]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rVzgXLVL+riQbYyqmZT9eLXR04REA1tod1to7U1YD3QWcA2Y7HMvnjDGFgOeB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\n7tcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ce04210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(omegas_dict[4],omega_values_interpolated_3_to_4)\n",
    "plt.plot(omegas_dict[4],omegas_2_converged[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANkAAAAVBAMAAAA5ulaKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E7xDN\nqzIhoty3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAADqUlEQVRIDcWUT4hbVRTGf/kzL39eMkkLFZmN\nIWVmRKRGRhcq6kNwI5Y8p2RR7UBw0UU3MxbqrMrEqjulARGKm4m0iHVAQ6G0FCWByogM2ii0ilIn\nFAQ3MqOdjqYZjd+97wUGdB3P4t3vnO+d89137rkPRmbFV0cmBZn6xAjVTnJphGrnRqgFW4svjU4v\ncoczUttbfCTQLB7vCvwM+w49ZSJCkeJ+j1+uF4sFd/ZlsReL34QJkcpMN2CITh8Ig5eOHzaJu+zi\nlDhr7ha5OhGfctX4n9bH2lpex+3wUN0i9hHfZn4wGHQynvsa7gdM5IOEz4j2Asb9kiNhFZ+sp8TQ\nnmvC51zOx2dkT9AjVyUhzZrhHyVWgsRZsk3SDYtY8viTFyDLMXiQbIOsHyT8CB8FTMxnJqgSrxJp\nm1LG3OvrTZwG0bZ1YdV8W+o8LRNI/Waj91wlXSP7NwjxXt3doQAHeBLKzVyb6GaQ8CGsdy2znDfZ\npkq0hFuTE9pSk1iHeD903+F5i2wnYw2LC1fJ9K2akEydVK0F/oJlr1UioX2Y1l9rSs0yjytgrFxN\n3W5Gqxbbh9RyHVJbYcSZtTPpnjJ+7utpHbGTtxrJ/hBdLoiL4d6R2kJa39ZTk2wCp3UuMdi5daKu\nd0xwfXtKaGhSa/mk/hj6do3cbzVbq6Q9XXertlwI0d43VZIpIr/DRiG6SWabMCGlkBh3p4ourg1G\nB2u7SkvtvgLj5rXd9oDZW6vP2IrOyKq9zRBFz2vbm+i2SI0veMY0xiYkO5ZxB01eNFtS8OCZu6YU\nxgWj5v9bLb0iToPp9OJdqzbmEyJNXpNEO+wkzuItc242oSIgRkPLvNFIrzgdlkwpTZax/+pkJE/M\n7DfZxtm+gFU7AQHaA097JEuYKSl7ei3bDxMSvkkS85bUqjaYzjNuZ0KtkUlNUxIfTomN5fqBmu6S\n0zt48+bd74j77AmQuiS1VgddKeabSsh0woRnkYJhfjDfZoMt8TdsUfuQmm6wM7wBNpYukTRXbVzn\n1tB61v6yXgmQnNN5NnzM7T6C8z4b+SBh3CcRMBs6N2xQ38bDSgxNak6DsfbQN6tTpbxgOv0tVzz5\nt4mcKs7VLOIocQ1wWWpJz/2YxJq7GiRwb3Hy+4DJFtxzQTC1hrOgxNCkxhtc6Q59u75beQzU6Wjl\nJ/n7Bzcy+i/WLCJVOVSHCU8nP32yC5MVuTbh2mCg8TAMk3NibPDX2cPyQ5v75KsqFxZN0f/J/gEI\nNkGYKCrzMgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$3.64243709327638 \\cdot 10^{-6}$$"
      ],
      "text/plain": [
       "3.64243709327638e-6"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "om1 = omegas_dict[2][45]\n",
    "om2 = omegas_2_converged[2][45]\n",
    "om3 = -sum([om1,om2])\n",
    "D = { omega1:om1, omega2:om2, omega3:om3 }\n",
    "dispersion_difference_function.subs(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAAUBAMAAABrOwuzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left ( 8.25, \\quad 7.89212602296, \\quad -16.142126023\\right )$$"
      ],
      "text/plain": [
       "(8.25, 7.89212602296, -16.142126023)"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "om1,om2,om3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Four wave mixing ($\\chi^{(3)}$) example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dispersion_difference_function_4wv = k_symb(omega1,pol='e')+k_symb(omega2,pol='e')+k_symb(omega3,pol='e')+k_symb(omega4,pol='e')\n",
    "\n",
    "symbols_4wv=[omega1,omega2,omega3]\n",
    "update_expression_4wv = make_newton_update_expression(dispersion_difference_function_4wv.expand(),\n",
    "                                                    symbols=[omega1,omega2,omega3,omega4])\n",
    "update_expression_4wv = [ex.subs(omega4,-omega1-omega2-omega3) for ex in update_expression_4wv]\n",
    "\n",
    "newton_update_func_2_4wv = ufuncify( symbols_4wv , update_expression_4wv[2])\n",
    "\n",
    "diff_disp_4wv = dispersion_difference_function_4wv.subs(omega4,-omega1-omega2-omega3)\n",
    "func_disp_4wv = ufuncify([omega1,omega2,omega3],diff_disp_4wv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def trace_omegas_four_waves(omegas,omegas_2,arg3_init = -6.):\n",
    "    '''\n",
    "    omegas and omegas_2 are the two 'free' axes;\n",
    "    Their initial values determine omega3 and the implicit omega4.\n",
    "\n",
    "    Returns:\n",
    "        converged_dict(dict): maps pairs of frequencies to a third frequency.\n",
    "        The fourth frequency is determined by minus the sum of the first three.\n",
    "    '''\n",
    "    omegas_delta = omegas[1]-omegas[0]\n",
    "    converged_dict = np.zeros((len(omegas),len(omegas_2)))\n",
    "    for i1,arg1 in enumerate(omegas): ## to parallelize in the future\n",
    "        arg3 = arg3_init\n",
    "        oms = [(arg1,omegas_2[0],arg3 )]\n",
    "        for i in range(int(1e2)):\n",
    "            arg3 += newton_update_func_2_4wv(*(oms[-1]))\n",
    "            oms.append((omegas[0],omegas_2[0],arg3))\n",
    "            if abs(func_disp_4wv(*oms[-1])) < omegas_delta *1e-5:\n",
    "                break\n",
    "        for i2,arg2 in enumerate(omegas_2):\n",
    "            for i in range(100):\n",
    "                for j in range(500):\n",
    "                    arg3 += newton_update_func_2_4wv(*(oms[-1]))\n",
    "                    oms.append((arg1,arg2,arg3))\n",
    "                if abs(func_disp_4wv(*oms[-1])) < omegas_delta *1e-3:\n",
    "                    break\n",
    "            converged_dict[i1,i2] = arg3\n",
    "    return converged_dict\n",
    "\n",
    "@timeit\n",
    "def interpolate_omegas_4wv(few1,few2,fewz,many1,many2):\n",
    "    '''\n",
    "    Interpolation in 3D. The quadratic interpolation wasn't available,\n",
    "    so I used a cubic interpolation (might be slower).\n",
    "    '''\n",
    "    f = interpolate.interp2d(few1,few2,fewz,kind='cubic')\n",
    "    return f(many1,many2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's fix the first axis and see what happens with the rest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "o1 = -15\n",
    "o2s = np.arange(12,16,0.5)\n",
    "o3 = np.arange(-23,-6,0.05)\n",
    "zs = [map( lambda z: func_disp_4wv(o1,o2,z), o3) for o2 in o2s]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x115d94450>]"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/ueYmNWly9fPjEcfVZX4Xzew4UxULV/S88OnTUqdO0oQJqQ9k8sGh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\nAABgEIESAAAAAIMIlAAAAAAY5P8bfxCEYx2P2gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1165bc0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (20,10))\n",
    "for z in zs:\n",
    "    plt.plot(o3,z)\n",
    "plt.plot(o3,map(lambda z: 0., o3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAAAPBAMAAACPYumWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ntgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$7.1054273576e-15$$"
      ],
      "text/plain": [
       "7.1054273576e-15"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Testing error. All the $k$ functions are the same, so the root should be at (x,y,-y,-x).\n",
    "func_disp_4wv(15,18,-18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## Testing the time using other root-finding routines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import brentq\n",
    "from scipy.optimize import ridder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def brent_test(F = lambda z: func_disp_4wv(15,18,z),N = 10000,A=-26,B=-20):\n",
    "    for i in range(N):\n",
    "        brentq(F, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@timeit\n",
    "def ridder_test(F = lambda z: func_disp_4wv(15,18,z),N = 10000,A=-26,B=-20):\n",
    "    for i in range(N):\n",
    "        ridder(F, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'brent_test' 0.32 sec\n"
     ]
    }
   ],
   "source": [
    "brent_test()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'brent_test' 0.04 sec\n"
     ]
    }
   ],
   "source": [
    "brent_test(F = lambda z: z, A = -5,B = 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'brent_test' 0.32 sec\n"
     ]
    }
   ],
   "source": [
    "brent_test()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Next, let's use the tracing method to find solutions for the matching conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## introduce some displacements to the ranges of omega so we can find solutions\n",
    "\n",
    "dis1 = 10.\n",
    "dis2 = 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'trace_omegas_four_waves' 21.95 sec\n"
     ]
    }
   ],
   "source": [
    "## Trace to find solutions for resolution 2 (101 x 101 grid)\n",
    "\n",
    "omegas_4wave_converged = {}\n",
    "omegas_4wave_converged[2] = trace_omegas_four_waves(omegas_dict[2]+dis1,omegas_dict[2]+dis2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## retrieve the values for all omegas\n",
    "\n",
    "om1s = omegas_dict[2]+dis1\n",
    "om2s = omegas_dict[2]+dis2\n",
    "om3s = omegas_4wave_converged[2]\n",
    "\n",
    "om4s = np.zeros_like(om3s)\n",
    "for i in range(len(om1s)):\n",
    "    for j in range(len(om2s)):\n",
    "        om4s[i,j] = -om1s[i] - om2s[j] - om3s[i,j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(18.149999999999999, 16.75, -7.4333349004664537, -27.466665099533543)\n"
     ]
    }
   ],
   "source": [
    "## sample omegas\n",
    "\n",
    "i = 43\n",
    "j = 55\n",
    "\n",
    "om_ls = om1, om2, om3, om4 = om1s[i], om2s[j], om3s[i,j], om4s[i,j]\n",
    "\n",
    "print om_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAAVBAMAAAC+i7+MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$-7.62463756132092 \\cdot 10^{-7}$$"
      ],
      "text/plain": [
       "-7.62463756132092e-7"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Error at sample omegas\n",
    "\n",
    "D = { omega1:om1, omega2:om2, omega3:om3, omega4:om4 }\n",
    "dispersion_difference_function_4wv.subs(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIsAAAAPBAMAAAAmFiECAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
      "text/latex": [
       "$$0.107215731961$$"
      ],
      "text/plain": [
       "0.107215731961"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Find total error\n",
    "\n",
    "er = 0\n",
    "for i in range(len(om1s)):\n",
    "    for j in range(len(om2s)):\n",
    "        om_ls = om1, om2, om3, = om1s[i], om2s[j], om3s[i,j]\n",
    "        er += abs(func_disp_4wv(*om_ls))\n",
    "er"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'interpolate_omegas_4wv' 0.03 sec\n"
     ]
    }
   ],
   "source": [
    "## interpolate to a grid of higher resolution, 101 x 101 -> 1001 x 1001.\n",
    "\n",
    "interpolated_from_i_to_j = {}\n",
    "for i,j in [(2,3)]:  ## other combinations could be[(2,3),(3,4),(2,4)]\n",
    "    interpolated_from_i_to_j[i,j] = interpolate_omegas_4wv(omegas_dict[i]+dis1,omegas_dict[i]+dis2,omegas_3wave_converged[i],\n",
    "                                          omegas_dict[j]+dis1,omegas_dict[j]+dis2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bK2mtXyhb9zn1imJJ/z1RXt+t88dVimKH+c5/vFsUS/rlsEphK+lXrCpFsep8a69vq+O3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\nBQAAWILmBQAAWML/AhAzdMVVfJEvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1165c4850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2,3):\n",
    "    plot_arr(omegas_3wave_converged[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2+jHu+Z4cn57hq/XKb9oxQ0b/PoVziH0OvvVZg89qetbXly+HcsYnZU5885M6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\nK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7Mjo0Tc+bV5z5/jz+P6aLxGEx+OZ01e9/IJT3xqWo34SD2kPqj1tB7vPSedo73AsKxP\n+rWw1kziY3ueUyeJz2mCTxKf1JkU9swPilxou5n1fDXtmuV1+aGsN781TjLP4oO4b463UA0O7uYo\n7+WjliW8WEkOd9yIT65vpb24tvqM+KTSciEulcYPcbEu9U3i41sjiQ/OK3jwiSC3s0M+tqngCk1+\niOpndlpERnuept8F7vi3To1GHa1Juq79+L00DQ60gaVPWXj1eV6+xEfjWV2Xgvg8PLZbS+VLx6I+\nXGpTk/WN1EKRjiSZb12XxnuWj6YGuo6Hn9bTUjOJj+15Tp0kPqcJPmcmPisGn9z2hlFY8kNUJxDY\nbmg6f04w4Zzz4TYakK6Pu8ZeXQnN4pyJ4c4dIQ2FkrymV+Z4t7TmjkG/EUsCxqj5Ut+ZpEYqZPDR\n1PHw03r2fD2/f7NokrU2ssYo4jPSZ5ZX8OATQUl8Uh4KS340REbWrY3nz5nHGc+vdRxaOOvj1qz9\n/VYW4mPd7mY9bzSisxvqXj5Q4nMk7tz9OC/i4zG/9TjCI4mPfE5PrZ9h7TpnUhnt6/GujarBqZPE\n5zTBJ4lP6swKG372kpzB6d+fR0clLA0Ojsbr1mEnPqh5LZ+alzQ4Wet7BJ9q3dE3Ma0JPZc7biTx\nkfgeeaMCywitSnwsnh7Bx6rIwYejJD6xvIIHnwhK4lPXi9z2BlHY8NPbTiYhPs/nt6mIN8GxEhvN\nfL95NuITobPbXgjiU/VFER8i3gW9NQwg1yKdL6nfetwz+CADFIJk9eqMJj7aIOkVbjzDyezgg6Ax\nI2ok8ZGNS+LT903ik1Iq9JmfJ1lJh6YLnPTMztGauLKSF0lnN8S8nk+04FOTZBvgoQezwUFP1eBT\nk+SCXjsX/eZ85InYSoWgNTOJjyb4INc7mvh4zOvNtXwfLcHH6j0q+Hi+Rsk6RvrM8goefCIoiU9q\nhMKSnyf1iMyT+meD5CTGMm8/vjVHd/+f+nzJOrWd3VYjPghPIr97+VRloSzoudYw4jUfQWu8iQ/a\nC7Xe3nNamjGD+Hi8Ds7zsygWoj53TBKfsTUd6ibxyeCTulfo8NMjMshucNYucq01tfxHtrRuSdsY\noeXDmTvijBDi/kLaltb3PvePsagPOvjUJHmjshAoxHyJr9QbSXxGBB+NRgYfy37H42kAACAASURB\nVFosc2cSH+v3KkIoSeKD8woefDzkFXykOlvweRn7sn0Zhf0qcs/gaM/fSDq7Hc3jjJf692vIiY9k\n3l4WH+/mBjVJGxxoiE+1rpL43AWfFYiPxRMxfwStQfgggpi2hraOR/DxClMrEp8I9UfV4CiJj1vd\nJD7nCz4pnJY480OkJz6yLnAyImNtcMCRhvi0PHrzJA0O0JrR4KC7JmVL63uf+8fUxKcmC/GR6CzE\nxztAaYIPKqRp63j4ocOZtaZVVwg+KCHqjKY0Fws+Hkrik1pB4cnP/eOSMIMjPl7juXP20t0PiE9q\nJMEDfcZH42ElPtV1jbyXj+XN1EJ8ao/PJj4IX6n3TB9kDW2dJD5JfDg1VqsjGXex4JPERz42gl5S\ntrpGaAnyo+vW1ic39Vp6gqMhDdwzOj3yVR8ned18cuSxXa1dTxZ8dDXlwafqg/zSoC4QEPM9iM+R\nPD8xPkPwaSmJj4+uEHw4ilQH6YX+2QkefDy0IvFZLfikcApLfp7E7damJTFIglMbY63Bnd/30JEa\nVIe43lyth5T4cDxr0t7EdE991Pfy8QgpaIqECARnJD4tJfHhPWepaa17heATifhwlMTnTkl8Mvik\n+AodfpBnTNBEhNs0QBOWpPP7HvzfTBIfxJmaVm2PM0aaBgda4gNtac2dy5UkZHhodP2ZwQdJdqQ1\ntHW0a/OiL17Bp6fowYejlYjPaJ8kPmYl8Rmr3PaGUdjwoz+78+LZuPbY9ryj9exlORfUqqOpKanb\npyzHwSvavXwQFImoH3yGE5+jcfvHPOiK1dM6H+Hbehzl05LU64rEx1KzpyQ+thoj63B8kvjcKYnP\ndYJPCqfwZ360DQ5qz0vmtefW1yTdHteaw63Z9tMTH22HuPrfZcEHIQ1F4rS0vqvjTXwshMQSfKye\niPmen2Yig8+IEHWkMxAfLzIzgySink/i4+uTxMesJD6plRWW/BDxQkZvbG3OyM5ut+J3ZTsOD9qb\nkcrO5vDqS+ci5veaX3A8q+tyuompO/Gxzp1NfI60CvFBeSFrtJ7TXvRFJD4e9Krny5mfxEdWh+OT\nxOdOSXyuGXxy2xtGYcmPNmT0Q1I/mFiCz329PlVCEx/JPIlPf+x44qPx1HSr4253gwkdfKzyID4I\n35lChDxtjZa09TXzkvhgn0/i4+uTxMesJD6pMyg0+SHidGtrBxKPrWvcc0HyGjrigpsnCy9ozejs\npiU+qnv5EN2/uc0iPh6eCAoiIRZXJT5R/FpK4jO+PqLGyDqoWtwxSXyq8iI+It8kPqnBCkt+iLDE\nhzOvN7Y2XhquENKSIlmXOxm1md3gANXS+s5DSXzY2900Y4jsn2B6hClrffRWLS/NJj5oQqNdt8cW\nOkvNmcQQtW3Lcw0oj5GkZuR6JF7Bg4+HpMTHSxl8UgiFJT/aRgI9qiLdhqY5b6Obc/y6+PcD0m1R\n8w4uIzq77SUlPkR16nM/5vnfocSnpmjE50gIMsP1PfJYifi0nluB+GgD4Azi03s+ic/YOqha3DFE\n2BtGBw8+SXzkY1fSizzzA1Fo8kOkJyuaBgRaafwRLa1b0jZGaPlwvEY0ONjL8vpemcPY7uZKfLjj\nrG+o3OAj8bXOl/rO+gQSSaCQwaelJD5zidAIXZX4cHWh4OOhJD6pMyos+SGS0RjOOZrevNu/a+gL\nt2W2lfhI5snWEov41ITw1JzzGd7SGv1mbFmL53yJ7wwPD6/IxGeGZxIf3XxEDVSd0bWS+NzbCT6U\nYHdfOznxCZLrUhMUNvwgiI9kXmuutKU1t4ZmvnSepMGBpzS1Ned8evJqaU10QH32smwvs7ypziY+\nCF/ENjqNRhAf9JxVgk9Plq/92a9sIhGfkcGHqwsFH4k8go+nkvg818u4l+1LaYltb9zObpZ50jM7\n+/GW+/+0amrr9mr3fPavYe8lnX9Uuza/NoZDfFprIuLdxLRGfFTnfF7Q/RscN/hwAkHN3+In9ZQE\nFInvkaTBBxWgWj4IwsWpI62/SvBpvYZeTUvdlx3v3rqsz1vrE+P5pzpWj2jBh/O1IbpU8Hnxkk9S\nvIiP5D4+IkLFHyomPkGyXYqISilfX0r5YCnlZSnlC3fPvb2U8pFSyi+VUr7yYP6fLKX8SinlZx//\n+4O9mstESO39crhb0bTj9+Lf/+d4u9nxOP5vDW7tiNI0OOiJ0+AgBPGxEBaP3+YIMiMZi9hG5x18\nWkIGH420Xh7Bx1NepGkFjQo+HJ2d+CBrCurOJD5RlMTnUvpFIvo6IvqLtw+WUt5CRN9ARG8hojcS\n0ftKKb9327at4vHObdveyS0YNvxot6BZtq5p6I1uTr9mbR6nbr/e8fr3XjPO+GiIz71Hn/j0gg/3\njE+V+OyFDj4W4mP1PJJkPiJszCQ+RxpBfHrPaeaMJj6Wmta6liBnfR5xUY6iHtZ1cOsgiQ9HFyM+\nXHl0dsszPnP0ks7X7W3btg8TEZVSyu6pryWiH9627QURfbSU8hEi+iIi+j8qNvu5TYXf9kbUv0iW\nUhzrWNscHvHxmHf/XDu8rChUS+u91MSHK0vw4fpZPRHzJb5H3lcmPiP9POZ5zkWEj5kaFXw8/71K\n6yTxeabZxCfCOZ8kPqkbfRYRfezm7x9/fKymby+l/Hwp5QdLKa/rGYclP096upiVNhDoERlue2qp\nf3vO8W9KRGe3Pmnh+fC8sPM1zQ003eI4W92gLa33y16Z+FjnIymL1UMTfDQB50ho4jPKz+JpqWmt\nm8QnVh3kGKIkPgdK4vO4DtkyUg4qpfwkEb3+9iEi2ojou7Zt+zGj/fcT0Z/atm0rpfxpInonEf2R\n1oTQ4Udy/ka6fU1aB31Gh9N9rlf3LC2tNWeQUC2t73wr31poS2vOPMu4I52B+Bw9jgo+LWm8RpAl\nDz+PeZ5zk/gk8UHVmxR8PDSb+EQJPil//fr7P0T/+P0fao7Ztu0rFNYfJ6LPvvn7Gx8f23v/+s1f\nf4CIumEqbPjRkpsRnd1q49tzji/UtTcj1RKflg/Payzx4XjW1As+XOKzDz5Q4lOT9U0VTZGO5h8J\n4YsMLRIh14OkXGji05I2KMwiPj150iREKIkSfJL4JPFBegYJPmckPhHP/Pzut34+/e63fv4rf//w\nd/+Ixe727M57iOiHSinfRw/b3d5ERB+4m1DKG7Zt+8TjX/8wEX2wVyT8mR8eubl/nLdNrk9fuFQC\nTXxw8/hbw2YHH82aqutitLS+8xhNfI7mRhpHhDmLI5E0aHhvd0MGH43QxKfnGWkeZ+6sUMXRKsGH\nIxQ9W534cJXEh60kPqlSyttKKR8joi8moh8vpfwEEdG2bR8ioncT0YeI6G8S0bc9dXorpfzATVvs\nP1tK+bullJ8noi8loj/WqxmW/BBxScwTCdJvXdNsjRvZ0hpxL59afUuDA0RnN6lnTb3gg7qJqZr4\nHI3bP8a9+EZsB7PO534tVgksSHoym/hoPbUX6jPDySxvzvOrBJ8kPkl8kJ5Bgs8Zic+ZtW3b3yCi\nv3Hw3PcQ0fdUHv+Pb/78H0prhg0/0gYHvbmSsag52m1rz/34pKYlj7bUFo1qcHDnoWxwoJaFkFjG\neREbL+IjqUe0XktrqUYGH8taPOZZvVcPPhwl8cHUO9FVchKfa+hFwG1vKyps+HkS5xxNjYxYmhtw\n/PtzjomP5h5C2to9n56Xx3zOOZ+9umtSEp998GG3tOaQG29aJPEbOR/h23p8peCjDSpHikJ8LM/1\n6l6Z+CBqcDyS+CTxQXoGCT7SX6kZqq6r8Gd+niRtcMCZKz0X1PJEEx/JPK0Pxytig4ORxIe93Y0z\nBh18ahpJfBBjpfIOPi0hiQ+a0IwmPpbvsYUmZPCxe3C0KvHhKokPTFGCTyolUVjyoyU+I8a31vr8\n8XZwOPK4SktrRPDR3sT0lMTnSB7ER+J75L0K8UETlQh+Xp6ziE9PGXz461iV+ESuSUl8iJL4IPQy\n7mX7UlqG/Ow1usHBUQ3Jc5x17mVpcIDUiDNCiNfD2e7mSny4Ar+xHnp6vQ5r8LmqohAfj+DTkxfx\n6Xln8FlbM4LPAkrik0rpFT5CvtrNrb91DUV8jvx7c7jUSHM2qLXG+lp49XtzEfO9mhtozvm4t7Te\njxtFfCRkxTo/iY8uWCTx0c3N4ONfA1mLMy6Jz71dEh/x2CsRnxRWocOPhspwx2o6rGmCj8SjJUuD\ngzPKq6U10QH12csaNpCyBgzJG5k1UJ1dyODTkvZnTfs9SeIjq81VpF/VqH+vqNcUOfhMVBKfayvi\nTU5XVNjwo6U4luYGHP/+WvnEhVO3vkZ+8JE0Soh4xqe6LsZNTLXE5y74IIlPbS43pHiRFQSZkQQq\nxHY5b+KjqdGq0xJ6q2ASH55G1I5QgztmFPHhjokcfJL48Hz5Q8Xjk/ikrAp/5sfj3I6lc1xrvkRc\nUiSpjbyJ6Qhxvo6oBgd7TSE+4DfXocTnSNbgE1GadVou8qVCrw9dy1oT4W0JbBGCD0ejgwaiFvLf\nQhKfQ0UgPhJlOEmNVljyQ2Q7t+MxvjVf72EhNTwfntdY6qM558MJPrB7+VgoCXquB7FBkBnJG6zX\n2lqPawKJ5qIZXSeCX0/WgOBFkzjzveZyPZL4HCuJT1VJfB7X4eidupbChh/UvXmkDQ64a5I0GDjy\n2EtCarQd4up/jx98anJtaa3ViOAjkReZkQQBRHhCanbwaWmkX0/a749nOLF6W3/mZtfneiTx4SmJ\nT98ziU8o5ZkfjMJveyPSNS3Q+mvCkr4tNn/emRsccL6PqAYHamm3u6G3ulnWopEkkC1wIaGS5mtr\nIRsj/Lw8LTV7z3sHD2/iNDKQIOqMDjWoNXloIvXhShJ8JIFKIs8wk9QnhVRY8vMkaYODp/Ga9tKa\nBgd7aba7SUnL8+cs2+bGEh+OZ3VdKzc46M2TjrNQJMn81uNevt7b3SIQn1F+Xp6WgHDl4MMRogYq\nYKFqIQnMLOIzKfh4ER+ub6Subhl8UmiZwk8p5XVE9INE9HlE9DtE9K1E9PeJ6K8S0ecQ0UeJ6Bu2\nbfuNx/Fvfxzzgoi+Y9u297b8PRoccAMIZ77eg/9P2XLOJ5pQwYdzzmevyzU44M4/kiQoxP6x0ysC\noYkUfHryCj49rRB8rDVQGrnVjaskPiYl8Xku72A1Wy9y2xtE1m1v/y0R/c1t295CRF9ARP8nEX0n\nEb1v27Y3E9FPEdHbiYhKKZ9LRN9ARG8hoq8iou8vpZQj45kNDo7nPJ+v8dhLMu9s53z2QgSf17ww\nNDjYP2ahLJa5Vj/JfAk1kgQf6dqk60P4kOLxpzrSOS3ig/R78tTM6z3nUZPzvKf3CsGn97XnjuGG\nDERQ5fgQYYMPtx74QykP4sOmM07Ex6vBwW8Lx2fwSXlJHX5KKf8sEf0727b9JSKibdtePBKeryWi\ndz0OexcRve3xz19DRD/8OO6jRPQRIvqiXh3u/Xm041vSBJheXS4psvisEHy8GhzsBSU+NY0IPty6\nR0J82mgNPhGFDD6aOug5RPFaWmfwsdXgCPn7DFGLq9HBRyJw8PFQEp/nyuCTksiy7e1fIaJ/XEr5\nS/RAfX6GiP5zInr9tm2fJCLatu0TpZTPfBz/WUT0d27mf/zxscbiMMTnVtwzMohGBdrAIg0f7bFz\ngw9vjfevp9fggNPSuqZq8NFexMwiPkeS/Da3Eh/pGlrkw8ND64WmGyODlBfxaSmDT+wanDrIWtzf\nFTOID8rrUWc740PkS3wkyuBzrJfxj+ovIctX8bVE9IVE9Ee3bfuZUsr30cOWt203bv93lv7Xd/zt\nV/78e976L9Ob3trMSU1xKBG3wYGkwcBzDz6paemMDQ724jQ4uKtT+W1Woz530gYO9CeSXsFFEi64\ntaS+mtCCECLMPclyIT7bz0vo18D17sk7+CDWgFASn2lXsWckPp738pFoRPD5aXr4tD51XVnCz68Q\n0ce2bXv6GfoRegg/nyylvH7btk+WUt5ARL/2+PzHieizb+a/8fGxqv7AO76EiI4vno8u5DUd1rjU\nRU9utKRIFl4sstAmpKempTUn+LCJz76c5ZNMD+Izan7rcc/gM8tHU0NbB+3XkjYIRCU+vfkjgs8K\nVImrJD6ympTE5wzE5/c9/vekvyD0Sa0vdfh5DDcfK6X8a9u2/X0i+jIi+nuP/30LEX0vEX0zEf3o\n45T3ENEPPRKizyKiNxHRByQ1UTc+5Xhy5/c89uKSIolPzcs7OCEaHOzl2dL6TlriczRXM0YqSXDh\nzpcKsQ3v7MGnJQ9aov2nPLoepyYiGHjV5nhEIT5E8bowJvExKYPPWP+oypucYmTdPPif0UOg+VQi\n+gdE9B8R0WuI6N2llG8lol+mhw5vtG3bh0op7yaiD9HDz+23bdt2uCUOSXCsLa0lTQq0ragl5Gi1\nBgdexKcmGPE5Grd/zBqYkGtprUdSHxE2ogWfllYmPtqvg5aeeFIZa/DxvrqJQJW4QoVI1NccGcRm\nUCZK4pPBJ3UmmcLPtm2/QM/p4ZO+/GD89xDR90jrWAiOdsuZbm3HHpJtctr69b+PDT4aaYjPw2Pm\n0seyUBbLOEvwkdSReiDCxszgg9xOdmbi40VWZgef2fU5QhFlVNAYFcQk9ValXgZl8Bnrn7qGwreN\nsJ7ZqY1vzeF2aLPcfFRzxqjn01s7Yr6V+FTXpLyJqepePkQ8cuNNi6x+R7JuSRuxvczqobmoQdYY\nRXxmeJ6V+MyujyIQiOCD/AAHGcRGB58kPnxf/tAMPqllFD78PEl34L5PibQd2o78+mvC+Fjl0eCg\nX1MefKo+jKVdrqU1YkuaRIhAMYLGIGto5EFnRgefnrx8OfOjBx+OViQ+yH8/SXyqyuAz1n8V5Zkf\njMKGHzvB4RGbo8e1ram1Nx/Nm5jyzvlcnvh4zJf4arxRFySo9SCJT+85tF8SH9zzZyE+SNJxduIj\n8EMTHyJ+SMngM9Y/dT19yuwFcCQlOB7E5mgOtyNcy2cEdRmpkQ0O9lITH67Ab7BuxIc7v/W4RNJA\ngQomI8iOV3BA+mlfrxfxsSp68EFoNGFB1Fqd+Ex8a83g87gO4fho/qlzKCz5eRKqsxuXunBvIiqh\nLZIbfSKpDZr4aDxr8rqXT1VaUjKC+NTkRXwk9aIFFm/io6kRxc/i6UV8Znpznr8S8UHV4o5J4lNV\nBp/HdQjHR/OPoNz2hlFo8sMhOFZ6w+3Qpr2Xj2wtuODjIa8GB3dzFC2tiQ6oz16IwNCSxMvypi39\nsfcmYnvNCj4ajQwqGj+PeZ5Cf2243pznr0Z8RgYfrk4QfCTyCD4SZfDB+KfOpbDkR35mR0dsOPPv\nx/JoSz+s8IIXzwsbnBA3Me0FHyTxuQs+SOJTm2slORaKJK0l8ZWEwzMTn5bQxKclD+LTe96yve7K\nxAdRgzMmiQ++Js0lPhIl8RnvnzqfwoafJ2nO7HCJDZfmaBsTcD17PisEn1EUagrxAb/JmumTNaBI\nwwZCmmDiLc1FvgfV0HwNLF83LzLjSXwstUfU59RI4oOrdyLiQ+RDfTL4YPyj6UVue4MofPh5ErfR\nAP+MTn9+y6N3cc+tzfGSaMZNTLthTNncQNXS2kJktLRolB9i/pEkxGIV4qOp0fM7EprQeAWpGcSn\npysQH45QdVYlPlydjPhwg08Sn/H+qfMq9JkfzjkfTic4zfz7ce3fJtrzQdEbHNyvV779revJDD6s\nBgc1aS8Y0MGHW/dIVmJ0NB69VSuK0MEHTWi0X1+PeV7Ex+q9ghCBZMXgwxXyd2ESn76n07+3aMEk\ng0/KorDkx9LZbS/NfG1HNu29fDhriN7gQHMTU23wYbe03i8hEvGpCUECJIQEQVlmER9kDY2X1q/1\nnJZSRCU+nt6rEJ8odZBj0MQncPBJ4hMvmGTwSVkVNvw8ybObm86vHViO5llq1v+ODU6IBgc91ba7\n3Y+5fwza0pozb8Q46VjufO3FMdpjhJDrRL+2JD5JfIgwP1ej6iB9JF6Bg49ESXwelMHHVy/jX7Yv\nodBfRU2jgWPKI59/78EPHCif3toR86XBZ+RNTF2JT00W4sP1k3ha57cel2yjG+2h9dJc6EcgPl6e\nEYlPb/5s4oOowfFI4hM6+CTxiRdMrh58UjiFPfPD3XYmbWndmi9Zgzb4oDWjwUF3TY4NDu7kscVM\nK8sbvpXMSF+Ld2hBaETwQStS8GnJ8+uBCB8zNSL4cLQq8UHWTOLT90ziA/FPXUuhyc+TpJ3dNPPv\nx/FIkaS21Cc68amuSXETU/W9fGrSkhsuFZBceFso0mjicySpB2otyC1t0hqt585AfHqy+CbxWY/4\ncDSD+HDlEHy4geKsxEeqDD7j9JKy1TVCYcnPk5ANDrh17p/j1e3V9m5QMFqaBgdasbe7ccag36BH\n0SfEWESoihh8kHRq5D9T7T8Pyxot2920vlbvEboi8UF7IesBvw6rBB+JvIgPkSw8rB58ov9aSvko\nNPnRtLTm3peHfz+g438aku1t2g5xvbma+aNuYqrp7MYmPhxyY6Es3LkWvyNZt6ShwgbCI2LwGUlo\nohEfr+111uAzm/ogroBWJD4j1yQZd8HgE4X4ZPBJXUFhw4/kvE1tDne+5DyOLLDwgtcKQjU4uPNl\n/OaBEp+aRgSfI3nMl/42l1y0zwo+LY36BBxNS85EfHo6Q/AZQbVGvy2ggg+yHrfmyYKPREl85vhH\nUW57wyhs+HmSlthw5t+PlZMizt9b9S3UR9OFDXHOZ69e8IHexFQbGKIRH4/5IyiL1QO5DW1V4tOS\n17wkPrrno9Tg+lyB+DgoiU8Gn9S1FP7Mz600DQ5a0pAiiefD31/9Z4ZucCDVrAYHdx7M4ANtcMCZ\nV5PHb0kP4oNYQ+tx7/VJ17Mq8el5tuRRL4mPrcaKWpn4CPzQLa2T+DwoWjDJ4JPSKDT50bS0tnZ2\nQ93Lp+bVHisLPjNuYtoLPpyW1urgoyUl6E8mJeFgFDGS+Gq8UdvUUOvRBDRNiPKgJdqvpQe16sni\ne4XggyIxo+pwx0UmPicKPmcnPpqOaxl8+nqR294gCkt+NJ3ROA0S7sfpqE5v3koNDmpCdKrT3MSU\nyJn4HM2tyeI38reslSQdebR8vAPUKLJzpJHBpyfLtrQZvpa6nOcRYaEnxKfsowjL6ODDVQYfiFYl\nPlJl8EmNVGjyQyQhNrxta9qW1tp7+dS8LLIGH4Qnp6U1rLObhZRw5kouvtFrQcyX/EafFVgiEp+R\nfl6eXmTmzMQnSg1UHa6S+Dy3cwgUSXx065D6a2pk8EntFZb81MQNO7r7AfH/eWg7xNXmjgxOmvVw\npG1w4CoLDUEHnyNZ52su3rmKtmVOo5FkI1Lw6enKxMdag6ORhGVUEPPQAsGHG1Q8iI+nkvikrq6w\n5EdLfDjnhO49LFvUeD48r7Hb3TyIT02we/kQ8cgNmtCsRHwkgWp14qOp0XouiU9b2teCeH5EKFmN\n+IwMPhckPujgIyE+RIJteTLbJD6L62Xcy/altAT58SQ+e0nmac8L1f8+N/hopG1wsJc6+NSEfpNG\njyPyOyM049PbmUIGn5Y8SMnoeb25I8KHp1YIV6g63FpJfJ7bLUR8vM75JPFJpR4UPkJyz9poGxxo\nSJHERzoXMR9NfIj8OrtBiU9NI4jPkTzmIyjLKsRHU6OlJD7y53re1tBhrY9YQxKfMfXQNWmN5gZJ\nfGz+mhoZfFI9hQ8/txrZ4IC7jr3PGcW5l4+2s9udLIEB+SYt+ZZKAobH/JnnajyFDiuo+tE8PWt6\nk4HZwQehaMQHKWS94MEngpL43CuDz3O9zFbXEIUNP+2zNfLzOtp78FioTXTiw1qTorPblJuY7h8D\nv9GayYp1vidlmUV8kDU0Xj2/lkZSpN7zXmTGkyZxxswmPogaqDrIMURj18StJ/BbgfiIfZP4mGt4\n+6fOo1Od+eESH9Q8785s3tIQLE6Dg71MDQ44Y9A0xzJuJPGR+KK8kUKuUzPHK6ig5RHerL7Wr8Hs\n4MPRKKqEDBkcIc9OInUy4uPV0lq0BsHYJD6pKyks+XmSd0trfkc4X2pjIUa1r9GIcz7L3MtHMnfE\nWo7GHikKrdFcLEvXM6JGy6s3T0N8WvOuRnwQpCQC8eEoiU8SH45vEh9zjSsRn9z2htES5OdJiAYH\nt9J2hOv5nOFePpxzPnupO7txZHmzRQcfL40mQaizQhGDT0ujiY/HvFWJT0+z63NrjCBLyDFElyE+\ns5XEx+afxCc1QmHJD/d+Ovz7AfFJjeRePpJ1S9fBmW/t7FZdE4D4PPg8/7t7S+tZxMdrviS0zAos\nSBpzpNnEx0IStGFqBvHpyeJ9JuITpQ53DFESn52S+DyuIZC31F9TY2Xik8IqbPi5FZr4SOb1fFZr\ncLAXp8FB14MRfKqyBobePG5Ni9+Rp3W+dnsVxydi8EG93pYsoQHt6RF8evIKcZznexpJWI8Uifgg\nfaISn5Pp7MTHOzgk8eHp5e/ktjeEwocf75bW3PsI9XysQgcfXg0Z8Xl4TN7S2kR89uO4v/EsxIfr\nd/S4lfgcyctX44Pchoasgazfey5S8PGkIlZvKylBBC/EdrokPph6Ar8rEx8iWSCIEnyS+KRW0GJn\nfnjhQ7JN7XheOyi05nLmS84bae4jpGlw0PVUNji4E5L4HM21yPIGbiU+CN+WEAEKGUqQH9+hicno\n4DNLM4PPCI0IPhwl8TmlMvjYlMQnNUNhyQ+XukjO50i2qB3V3vtwvKTze7Ke80Hcy+fhsed/H34v\nn9pc7kW25MLeQoyk863b1Ly2TFk0M1yN9LN4epEZBK3QeifxkQl5VYcMPoivs7BmEh+fsUl8UqkH\nhQ0/t0JsN5PMkzRKaM3lzJ9xzqcnbYODvdT38qnJQkMsn5R6bUuryRp8Wop2zueMxEfr2ZPHWaWe\nb887iY9MI31GB58TKYOPzlujJD46vXiRZ34QCh9+tA0ONB3han+/lTfx9TK+5gAAIABJREFU8e7s\nprmXT01q4rN/DEl8JHPRfoj51pDUenyV4KO5yB9JfFrymjeL+HgGn1VoDKoGKigiCczoepOIDxE/\npGTwGeMt9dfUSOKT6mmpMz+RGhwgCAu3tkc9IlyDg73ciQ93nGUds4mP1HeV4KORxgtNfLSeHF9N\nPc+PQS3eq4SSUR8jRyNHXK+TfMx+1uDjqWjEJ5XyUFjywz2vIznILyE+XB/O3NnEp7omRkvrffCB\ntbS2bOUaQXxq8gooGgpi9TgD8fHwO5LFT0tQIhIf79rW+qNqjKzDHYckMEl8zJ5EMYgPkexX3hWJ\nz2o5/+WLsJftS2kJ8oM45yO77087vKwmVIODvdQNDmrSUhoPkuPx29BKko48EOEJ6YMUenuax3Y3\nj3pRiY/3VUKE4MPRSLIUMfgsoLMGH6m8go9GEYnPSX7cUwqFj5Dc8zraVtLe1MZyE1TOvXwQLa17\nwYdLfO6CD5e0cC7qwZ80mgOGdT6CsqxOfDQ1Ws+NJEhaz95zlrBp8bUGj5nEieOPqIGqgxwzI/gA\nw18SH5+xRL7Bx5vIJPFJeSt8+LlVK7TcStLgoCV0gwO0RjU4uPe4f8y9pXVNI8ZZiRHiNyyCGkWU\nx7kc6RwkqfSs5+lrqct53jv4cBSJ+Jw9+EyUJKTM9CRal/iMCCbeWjn4vMxubxCFDT+yDm2v/ihr\nO7uNvpfPiHM+e/WCD6ylNZL4WOeOWItkPsLX0wPpo6mhqeNxPsbD04vMXJn4RKnB9blC8GH4cYkP\nEZ+keNzLJ4nPOG+p/6gaqXNqiTM/LUkaE3Cf69eMFXzqa9ytidHg4M6j8qVlNThAakTwqclKfDzH\nrvLbGx1WUPV7z3msL4kP3h9Rg6MMPj6/Nzl2E4OPl65CfCLqDK8hhVFY8vMkLq2RBA5LS2vpmRqP\ncz79Gu3gw2lpzQk+7JbW+3LRic+RJPM9SFLrcc+zQpr1aN5lNF7orXNnIT497+jEh6MI4YrrEzH4\ncAWuiT7n4xV82GeHkviE99fUSJ1b4cPPrVrb1Ljz7p/D/pPgNlqo1eYRHVsYq3oqO7vdSUtaRhAa\nyUWyZT1H8xE/Zojgg6yLDCuataIJzSgixZVX8LFqRPCZ+frQNVA/O+jfiRPC1tmCj0RXIT55xsdX\neeYHo7DhR3KmRdZRjXfOR9VMQLE9rSXzuSNlS+s99XElPlwh39Bb46zEyEpaPInPCB9k8EETmtHE\nx6tmT6sTnwg1OBpJfLjK4FP3ZI7NMz5674j+mhqpa2jJMz+tbWrtebwApVGEcz49oRoc3AlNbmZR\nHw/icyTEp8rRgk9LyE/qRxIfi9Db9bx9I2gE8UFe+FvrcIX8vmbwGaokPvOUwSd1pLDk51aI7W6W\n7WERGxxoqE9PwxscWCiLlj5J1iIZiwgKnh4jJA1XrTmoEG7xs3h6UU5Pejqb+iCCD+Lnf1Qdrg/y\nd9jFrgYj3MtHIkmAWP1beYZwNUMvfju3vSEUPvygtqk9fw673U0izTmfew9Z8MkGB51xR7LOl4Qx\nFK1BeGguvkcEH4+taR6eFjIzwxfxvHd9jhA1EMFn9Naz3OpW95wcfKQX617BJyLxibadLnU9hd72\npt2mZrmfj1SI++94+tUUssEBV+itbkee1vmeF3Oa0ILQKEozSh5nbiISH0tdzvMjgg/inI+1BqoO\n12f0VrcTaXbwkSqJz7GS+KQ8FJb8cNtRSxoc7KW9kWptLm8ttu1usxocEClvZGoJKshPM1vjrMRI\nEnysvkceM300NALpNdKv91xLXsSn530G4hOhBtcHNWY08QHXRBMfIkHr6QDBx6vBQRIfrL+mxmz9\nzsuwl+1LKTT5eRKqwYHkfj5SnbnBQXW7m1aRqI8H8TkS4hPDMwefltCExuscmwctsoYPi7yDD0ee\nr09SI1rw4cqDlE9QBp8kPh5aLfikcAofIVtnbNqkhn9WR0xYBjc4YLXZZpzz2UtFfIjuf4tpz+pI\nLpC5j1nODR1JMt+DJB15zPRp6YrEx6NmTysTnxE1kvjwlMSn7btg8IniParGFYhPCqvw4edWre1u\nLSEbHFjPCHlI0+CAI3aDA84Yyxs2OvgcyTrfSpKk8g4+mtrI1+sVGqTyCj6WujN/DSFqzyRa6Bqo\nn8UkPnfK4BOTmEgUkVhF+xqJlDc5hShs+JGEDutZHe3cVVpau3V2s1AWy1wP4mOd70WSRpCaI40I\nV8jg1XsOGf4s9Tg1LcHHi2BZa3OeR9TgjkF4RCQ+XFm2B1c0s7MbVxl8xnhr/KPWSJ1TS5z5kTQm\n0PpIhTiTI62BanCwl+u9fGqyEBb0OCIf4oPwRWrEOR+p0GTDg5Sgg5a15ohzNjM1giqNrDNDyNe/\nQPDhUh+PMEXkdzG9OvGJqPwapZ4Ulvw8SdaR7fY5LLXpbXebcc7nbg2d4MO9iamqs1tt3CzicyQP\nYoQIPpLXpQkl3sEHTXwi+HnUs9ZM4tNXpDrIrWfID30y+LQ9AxAfqZL4pFIyhQ8/t2rfuFRyBsgW\nfEY3OKhJ0+Dg3uP+MVZnNy3RGEWYJOHFQ9bgg9TMbXNHWp34tORFfDznnkUrEp8MPs/kdRNTtqdT\n8JFK8tKSZvB0mq9TnvmBKGz4kQQES0vraMGnpt52N7eW1kjiU5OVsKDPHEnmSykIt1bLA7UOb+Kj\n8Wr5jSYwFoLSksXXiyYl8ZF5cDSa+CDrCfxWCD4rEh+v4HNl4nOa4JOCaYkzP3u1CZDfR6CrNDi4\n82Rud+vKcoYF/Ym4dbsatw7ixwkRWlb6ZF+zVjTx0c6zfJ0tAcXLd6WfG61GUmfU1xNJfFD1BDVX\nCD4SJfE5r/LrlKopLPl5Uj9w8M75eBMfhKTBh9PSGtbZrSYtZZFQgWjEB+F7JNQWNe8zPpoarefQ\noWEG8fGoafFFPO9NfRABABV8EIQlKvHh6kTBJ4mPzlfqrfHX1BhZJ7xelNkrOIWWJD9PagWQ0ffj\nGXHOp7sGVGc3ycU9Yt7R3Jo8vq3W4CPxPXrcO/gghd6eppmD9rPMm0F8eooefDhCeEQLGqOJD7im\nx01MuUri86BTXtB3lMEnhVZo8sPt7Pbw91f/eSDP+XBCindnN21L6z31URMfDrlBExqLH2K+xbPl\n6xWe0GtBhis08Rnlx9EM4mP1nh18RgWSkcEnEoHyqEk+wQd9E9MkPjG9tTVG1kldS2HDj6x72/E/\nD3RL617tXvBBCNXg4E4WcqP195D1dUhIkESIQDGC+CDDRQTiY5Fm619vnlUrBx+ORpGYFYOPRBcL\nPhJdgfiM/lXpoQw+FZ3hGxtAYcPPrbid3YjGnvMZcS8fTUvrHvEhAre03j+GJj5WTysxsq5J6tEa\nL5V0PSOCz0ji05pnuZD3OotjDR+WuSOCD+L1nZH4cMX9/gNrcoOPRKsQH4lWpTIjaExU4pM54roK\nf+ZHQoBalMU7+HhI0+CAI/cGB2ihg8+R0NtJtB7eAWoUpUF6aeuMnufpawkfVwk+HI0MPlwh66HP\nWXLtwA0OZhMfIj+KECX4aDTiLT+JT8pbocmPtrNbbS6qbq32rJbWbp3dvCmL5OLbspYjSeZ7kKQj\nj5k+GhqB9GrJg8Bon/M6izNzu5knbeLW4OisxCdw8JnV2S0C8eFeTEeiMt5EJolPAC29+DgKS34s\n3dCQ53w8iI9Xg4O91J3dNGOIbA0F0OOIxjY4QGhW8GkJuS0PfUZmdPDpycvXUte7Nscf8XtoFPEZ\n6cP1uljw8VASn/j+mhraOqlUaPLzpFGd3WrjpWvz2D7XCz7cm5jeUR/txT2a0HgQH+t8L5I0i/i0\nNCJcoZslJPHBPO9df0TwQX0gsSrxcdjaeybiI9EVurpF9NfU0NRJaJJ6Uljy8yQkeYnW4KAmTYOD\ne4/7x6ANDjjzapKEBIs8iA/CFyXk1jFp8NFoJPFpSfu98go+Vl0h+KAUiRxxvdBfm+DBx0teDQ5E\nawjkfdXgk0rdagny86SVO7vV1NvuhmpprSY+nHk1oYkPYr7F88hXEihmEp+ZNVpCUDfuPK+AYplr\nCYVXCD6oD14QdTjKMz538mhu4HHOR3ohLRnvGR4y+PjVCKtTvZh5Ck1+JA0OfNchCz51D4ezQxUL\n1jmfvSxEY8Snu1ZiZJ2PaHAwSyPWadnWJRW6YYJHPU7dGWfHuLVHhAWEx0iyNNLnYsFHotVaWmfw\nwdbQ1kml9gpLflrkpEVZRhOfmsQUStHSGtbZrSYtZbGQoZqfZS3S+YjtX17UqLUOTbgZRXwi+LVk\nCQmWgHBl4oO6+B9JfEatR6KTBJ8kPvG8R/hramjqRPssMhVHYcPPrSQNDkYLcc6nJ9fObp7zjubW\nhPY7Guv1qTUiPK0mNNnwICXa7/eKxKcnRDCJoGjEB/k9HV2P8MHHQ6sRH0/vDD4XV34hIAofflrb\nw5DnfKxnfFTrUba03lMfNfHhkBtu8LEQFo9td5KAYiVJR5p1zgfl35rT0ijiY/GcQWY8GydEJz6I\nGqg6yDHIIIYMPkl82p58S/H4JD7YGpo6q3yOk5qn0Gd+9vJscBBBnM5unAYHd7KQG62/dbsat45V\nVpJ09Hi04KMRcuuctk6k4NOTV/A5gxCvb8Xgw9UE4rOCkvi8qgw+qRROYckP8kakEVpae5zzcW9p\nvX9sJvHxmO8ZWhAe3sRHU6P13CiC1PPzCj4WMqP1tdZdgfhwx4yqk8TnVbskPvw1LOqt8ddoVPA5\n++dIV/wQxENLkZ8ntajN6ODDEWe7290cxjmfvdwbHGjGSMZJ5luJkefFVrQGB0dCb0/TzEH7ecyz\nzvVscBBdkShLpLXMqreIkvi8qojBJ2KNkXVS6yss+XnSiIYCr3rJg8+Icz6wzm4WcoP8pNN6TgcR\nLmryDC0SIc4b9eYgt6ehCc2ZiI9X8JlNfBA1otWJSHy4Ck58iPjUxyv4SC5yI4UTT+8MPqmrKnz4\naQm93c1ev72eqofiYyt1ZzfNGCJbQ4IZFwKaWjNCC+o1IwMacq1JfPS+0YlPlODDEeprOZr4cGtG\n/1mh8wYfqTyDQ8RQksHHQQv8e19BocOPZ4ODEed89uqd89F0diOqUB8kuZl1zse6pUxyEW8lUVKP\nET7IcBGB+LSkfTOYRXx6sgajCOd8elqN+HCE/qAHGHxWID4SRQg+kbajRQwlGXxSkRX2zI/mbM3R\nXO/gU5PmnM+dhyb41KQlNzMbHFjWcyRr8JEqYvDxfL0cr9H0ZgYt8gxVKwSfEVvqOEL+TI8+d3Mx\n4kMkC1RsT6exUmXwwdcYWSd1PoUmP0TxiQ9rTQDiU5Oa+HDm1TQq+HgQI2tIOgPxQW7LQ54Z6vlp\nw4JHPYtvb24GH16d0aQmwjZjpTxuYDqzs1sSH5u3Rhl8UmdU+PATXZpzPl3PigXrnM9eFlIyosGB\nxRNxAWQlSSiNoDHIT64twQHp5xF8erJ8TzznrhB8OEL9nKL+7YwmMNzXP4n6zG5pzfbEW6oUreW0\nd3DTKIOPUAsQ3xUUOvxYqM+q9/KpSdXZrSYtpUEHEivxkfhKSAtiXWcgPq3n0M0SIgWfWcSn9/zs\n4MPRqK1uCMKyOvFh+p3pXj5JfM7nr6kxsk7q3Ap75se63W0FaRsc3EkbGixhY9Ib+uFYyXwPEnUm\nIYNPS9EaHHjU5My1eI8IPqO2ofWEDBo9LU58zhR8JFr1IjdaMIn6dbzi23HKR6HJz5OinfPhbHXj\nUJ+93Dq7aYmPZC7aT0IrrMQnukfrcWSN3nPSOdp3qiQ+/Oe9FSFccX1QY5L4PNPViQ+R7J9htGAS\nzV9TY2Sd8Jr9nnAShSU/T4oefGrSbHdTNTioCQnARgQfiazER+J7pBHncyTSUBqpl9avJfT6vORZ\n0xocIpzzGaEVgw9aFww+Enle5M78FbBXtOAzSnm9n0IrfPixKGpL617wee1L5TkfLWl5WZk7ivh4\nBKcjz6uc8xl1Lufo++fh11Jvnse5Io6vxTt68OG8Pk4NxJa6aMGH+3PMef3cmjT3Xj5cSYiP4v7f\n/frkd87H0/vJX6IR/poao8hS1CCXulcp5etLKR8spbwspXzhzeNfXkr5mVLKL5RSfrqU8gcO5n9G\nKeW9pZQPl1L+Vinldb2aocOPlfq05vaCj2o9leDDaWvdk3uDA80Yj3FEfg0OJLIGrdbjZwk+LXkQ\nJO33FX1OieNrVfTgM0qoi+9oPg41V7iJqUeYIvK7yE3iM19JfCp6scB/cv0iEX0dEf3t3eO/TkRf\nvW3bFxDRtxDRXzmY/51E9L5t295MRD9FRG/vFQx75ge93c1ev3/O586jE3zULa338zzO1vTm1WTd\nu24lM16+nh4aHy0dkQp9ZsiDwIyuZ/FFPD87+CA+PEGFq5HEhytkvQsGHynt4V605xmfef6aGiPr\npOZr27YPExGVUsru8V+4+fPfK6V8WinlU7dt23+rv5aIvvTxz+8iovfTQyA6VGjyc6RVz/n0Pe4f\nY53z2csSVmZRHy/iY/X19kAGnFENDtBekYJPTzOpyIjmA1ZFoiyjf7YnfEy9QvDxUhKf8f6jNPJH\nK+rXIPVcpZSvJ6KfrQQfIqLP3Lbtk0RE27Z9gog+s+cXlvw8KVqDA01nN21La1Vnt5q487ihAu0n\nuWiX/FacQWskQgZb5PY0dHC4AvGxel+B+HDqcHxGE5+I9QgffCTy2Orm0dktic88f02NkXUs81Jy\nlVJ+kohef/sQEW1E9F3btv1YZ+6/TkTfQ0RfwSy39QaEDz/RxWlwsJdrZzfkvBHB50jWsYg3fO8G\nB0dC+o/aOjdqK55lnqcirmmkRgWf0QpKfLgSBQpumHJ4vV4trUVrcPLVKFrw0WhU8NFq2eAT6Qf1\nSb/4fqIPvr85ZNs2bnB5plLKG4norxHRN23b9tGDYZ8spbx+27ZPllLeQES/1vMNHX5uKcuKxOfh\nMfk5HzXx4cyraWXi4+XrHXykPkgyhSY+o/x6z3mRGU/qEp34IGqMrMMZdxHiIxE6+MwmPtKxSXxw\n/poaI+tY5qUO9PlvffjvST/83Ra3V879PHZt+3Ei+i+3bfvfG3PeQw8NEb6XiL6ZiH60VyTsmR9O\nQ4GZQrS0fvBBrYipGQ0OJBpJh1CaFXxGCU18tLLU8noNqAv2qIoSfLga6RP8ezvzXj5crRZ8vDUi\nmHgriU9KqlLK20opHyOiLyaiHy+l/MTjU99ORP8qEf3XpZSfK6X8bCnln3+c8wM3bbG/l4i+opTy\nYSL6MiL6M92a29bdGjdcpZTt57ff+8rfJZRG09JaSn20La1753zYLa335ZHzao9zL+5H0hlJ4PBa\nl3QdGp8RxKfl15o30q/1fBIfvD/HI1Id7piR60HWIxnxmRV8zkx8InlH9NfUGFmnNe/riWjbtnLw\ndBiVUjb6kXjX7Hf690r4r2dY8vOkM7S0fnhMsTjJxTli3tHcmix+kRscXFFRGhy05DFvBg1cRaOC\nD0ejt5+hNKkz4MybmHIVIfhIFYkYRPz1ksQntZJCn/mZfc6nuiZFS2tVZ7eaUMRHMhftZw0o2k//\ntR6rEB+NVxQ/y3NX6+w2IpQk8QlVL4kPfmwSH5y/poZWecYnhVLo8NMSOvjUa7S3u3EaHHDE3u6G\n0ojgUxMioEjkFZ4iKgKhiRR8LIoafDiKEHxQikh8IhKmR52N+Eh0FeITUdqvz6gfw9N9/073guYo\nbPjRhBWLpOd83Dq7Ed3/VtCSlkjE50jWsZqzLxYPb+KDrNF7TjrnDMTH4svxtsyNcM6npyQ+9npM\nL4/7+Hg0N2B7JvFRe0f019TQ1krik0Ir/JkfohhtrRFSNzjgjEEuGXkx8CSv7W7c+UePI8ITUqOC\nT4TXra1luYj3DD6zttkh/BE1OBpJlqISn4nkBa2ZFIkoic9MJfFJrayw5OdJs4OPF/GpinNxjqQ0\n6O1qkgt3a/BBkharx8xzPkdCB5+RfisSH8s7+hmCTxIfnBfhqc9M4kMkWCffMgyViUZkIjceSOID\n0Opb9INoCfJzJI9zPh6CNTjgynIuBz1uJPE5klcoO/LQ+GiCD3p7mrSOh5+XZgafqKEL6RGhhocm\nEHWP7W5oeTU4YNfHWw7xjqhR292S+KQiKSz5mU18iPrUR9vS+i74IMlNpHM+Xg0OPEMLwgMVfFpC\nBp8oW+csdMGy5awlz+Bjrc3RiHCFurhFfS1HUihkPUrigx6bxAdbY1SdJD4pby1NfjyFaGn94KMo\nriU3lq0X6OBjrX30OOJCa3STBKm3tgZaaOLT82zJst3Ny3fEVjFP/xHhilsH9TON3O42uF4Sn7m6\n2oVz1OCjVfQzSKlYCkt+nuTR0lp6zqe6LkZL6+kNDqIRH6/gI/EdEVokGrFOdHBYpbObF0lCPD/7\nnM8o4oMIPkl8XrUDEx8iPvWZTXwk4yNRmasSH+1bp+b1XCr4LLnoeLoc+dEEH812N1iDA+95NXl8\nYmcNPhJfqVBb5lDb3UZ9YoreKhYp+PTk5cuZPzv4IJTEB6aZxGf2TUwl8iIzoy7qo2gU8dEog09q\nlC4XfqRyO+dTE3K7G/dftmUcukZLXmd0Vgo+aOojrePh5yWPLXsc7xWCD4q0WD1GBh+uUMSL6+Wg\nVW5i6nXOJ5IiUh+pIm910yr6+lL+CrvtzbvBQc3T65xPNjhgzpf4etKUWcGnpREhqvdcNjjwo03e\ntVE1RhKfkVvvkPWYXivcxNSL+GSDg/j+mhoj62jnLR98ln8BMXRZ8jP1fj57WcgNR+jtbtZtadbg\nI1U2OODJg5Zo1x5xu5tnOEF4j2hw0NOqb8wnID4ztdpWN29vqSL+yEQPFtHXl4qtsOTnVqNvZFpd\ngyL4uDc42C/b8gmnJYBZGxFIfyNJPLLBAX8e2g9NmCyeFl/E897ncKI0OOgJuR0OFfYmfNB0tpbW\nbE+nsUl8cP6aGiPraOdl8EndKnz4GXE/n7uaXh9jacmGhYig/8VbLiika/EiYqgtZKjtbsgft5Fb\nxSIFn54iB5/Z/hyNbijQ06imIJJ6wYOPRLMbHFyF+ERU9GARfX3uOtWLmafQ4QfR1ron6Y1MuVvd\nVA0OtMSHO1dy8Y1ey5Gsazp6HBVYZgUfTXhAB58rEJ+eZgeT2f6cGqg6KOITtR6dj/jkTUx13hH9\nNTVG1tHOy6yQqinsmR9p8Kl72Le7aaTe7qaVpd7MBgdewQelaFvmWjWiEJ9I84hs4cD6/ZwdfBBa\nkfgg13OC4CNREp/rKnqwiL6+1FoKTX4ksp7z0ba0Vp3z0QaO6J3dJKEAsQXMMzzN3OqGDFdo4oOu\nZaln9bUEn9lEBrHVDRGuEMSHOy4i8WEqb2KKVRKf9Wpo62jnnTb4nPaFjVVY8nMrRFtr8xoYwacq\n7Zsx8k0cPU4ihKdXeIooTfAZ+ZpH/+L1IjOexMdSe5RGBB+uRgYfroBnKq8afKSKcBPTCP80rRoR\nfEYqg0/KQ+HJz4jObhzqsxfrnA+HmCC3mKE/0bSSFcmFvObsi8VjFvFB1tB4af1a87Sf/nuRGc8G\nAFcgPhyh6qxMfIBXWGcLPtILVu74SBf2SXx862jnZfBJcbQE+fGUZrsbrMEBV5amAuhxHg0OEGEA\nEZ5GCLlO9CewHp3WPOZ5hpdoPy9oef6ektYZSY7QYtbkUB8PkpLEZ0yDgEhaff17ZfBJeSos+fFo\nac25kendOjTBh3txjponeWzEOR8tIZjtcYbObiOJT7R63tRlZu1R529GkaVRIcyjHjD4SOTR2Y0r\nSfCJ0NnNM/icgfho6pyV+ETf9nenTHgQXYb8cIIPp621SlpaYnkz9ggvHsoGB8ca9X1YqcGBl1Yn\nQiOCD2Id3DEr16PztbRmezqN9fznF/2fdk8jQ8mIGhl8UiNkCj+llD9WSvlgKeXvllJ+qJTyT5VS\nPqOU8t5SyodLKX+rlPK6m/FvL6V8pJTyS6WUr+TW8Tjns1cv+Lz2Zb2zG4v67KUNHC8q40YRHyuB\nkqxJ8vXxCk+t8QgqpfU6+l706mvXpnmtFuITzZfzvLW2lfogrt44NRABixvCRp7zQdajcwWfFy8F\n6+SXdyU+UTq7cf7J7L0j0hjp69DUsMzL4JPSSB1+Sin/EhH9p0T0hdu2/Rv0sIXuG4noO4nofdu2\nvZmIfoqI3v44/nOJ6BuI6C1E9FVE9P2llNKrg9jutpemwcFe7Hv5aN9UIzU44I6VzEd8yjy6SYLm\ncU0NjUZSGO26Ld/zWSTJGkysGrENbRTxQWo08WHqTMFHogjBR6pRF/ReSuKjV7TvpUgvFvhvAVm3\nvb2GiP6ZUspriejTiejjRPS1RPSux+ffRURve/zz1xDRD2/b9mLbto8S0UeI6Ita5oiW1tL7+bzm\nBe+cz504Aab2g6Gdd7QG5LjaWp7mcx+TBDsvj9bj3tKs8+j1jjrno/0F5jVPG3ys1MUaGqykJErw\nQfzb4f5sRCU+DL8zBZ8kPvf+EkXz19YY9bapDSNRA2AqvtThZ9u2f0REf46I/iE9hJ7f2LbtfUT0\n+m3bPvk45hNE9JmPUz6LiD52Y/Hxx8eq6gWfmjTb3Xpy7ewmuajnzNWuw7oWhFAXWJLHI57zkcoj\nNGjrteRRLzLx8Q4+HHn+m0LXIRrf0hqomffy4SqJj877isFHK02dDD6pGVJ3eyul/HP0QHk+h4h+\ng4j+p1LKf0BE227o/u8QSc/5uLa03j+GbHAgoSxIP2sTAS9agwos0Tq7oS/yLbRE+pzlQt5CXlqy\n+K4QfCLUQKzjSaODT57xqXtmV7dT+Y+qoamjnUN08eBzmhcyV5ZW119ORP9g27b/i4iolPLXiej3\nE9EnSymv37btk6WUNxDRrz2O/zgRffbN/Dc+PlbVn3vH//PKn7/kra+h3//WV5eqOefTE6ezG/uc\nD2cMcp41vHDmHkn72npjPT/6m9ngQCptcNDII4h4rX/k14Vbl1OppjaCAAAgAElEQVR7BI05I/FB\nKmK3QUfNJj4SJfHB+WtqaDXyehzxdfilx/9S15Ul/PxDIvriUsqnEdE/IaIvI6KfJqLfJKJvIaLv\nJaJvJqIffRz/HiL6oVLK99HDdrc3EdEHjsz/+Dv+aSKyd3bTtrSudXZ7JiRpsWxNQxMfbl2pp5Uk\neXpofFD+Gq/WnJHEZ0Y9i6+17gitQJWQY5BnjgbXuyrxkSiJzxz/UTU0dbRziHBfh7c8/vekv65b\nTmphqcPPtm0fKKX8z0T0c/Tw8/VzRPTfEdHvIqJ3l1K+lYh+mR46vNG2bR8qpbybiD70OP7btm1z\n2RLXEqezG6vBAUcegcPL60keb4JWkiT1WEma3+YjiU+keUR+wcdaG1Ef0eDAqmjBh6vR9S6ss++6\nuWLw0Wo14pNKPalMyB9dlVK2X91e9+wxzlY3BPXpEh8iPW1Bzqs9zqUOVrIioQ7S7Xdcj6Ox0YiP\nxqvlhyY+Ws/R9Sy+luc4dTke3sFnFPU4M/Fhep2J+BDJqA/3YtLzAv9KXd1G1Dgr8ZHU+yYi2rat\ne+uV2SqlbPTfxLtmv9N3lfBfT2ur6zBCbXfrCnGBb53nMc6ylqOx0k9arcEnojzCClKjyZPX923m\ndrYRW9GsGtnSeqQGB5+zyavBgWgNgrGen+RfMfhoFZ34ECX1SbVlOfMzTNJzPlUPIfEhMrS0RhEf\nyWPozm41aT+x742V/nZDUBkk7UAGNOSZoZZfa5723caLzHj5cp6PvtUtiQ9GgYkPEZ/6JPGR+0q9\nR/hHraGtE5X4pK6r8OFH09mN09a6J3VnN6RGBB9JbYmsJEnqodmOJhEy+CDXig4+lnraebNIUoRg\n4q2zEh+uRr1+R0m2u7E9k/ioFTWUjKiRxCeAgv++WkWhww/nxqbS+/moOrsR3f/AIUmL5ZNOD+Jj\nIVCSNUk9joQKJiOClcYLvXVOG0RG1/MMH7ODD6K5AWI73agAh9x6xl3ThTq7zSY+0rFXIT4aRQ1X\nSXxSZ9JSZ340ba17YnV2Q37ajbwI8DgrYCVGo0NLxOCD3E428lMer5Ci8bTKM/hEUCRaE82HKIPP\nkeeJg09EnSFcEZ07+CRIuabCkh/r/XxqW91U53wstEU7j7OGmiQX3aM6u0l9PRscIEMJqgaamKxC\nfHqa1dJ6NvFB1ODUQREWVJBM4vPcz+GK7MzBJyItOcM5Im2dDD6OWnLR8bQE+eGc8+l6MCxgDQ6O\nHkPNO1oHt4b1k23Jt8NKklrjkdvREP4jQhS6jsXP8nX2IEk9X8+6KI0IPoh1cMeganEF/B6uEHwk\n1MdDEYLPCEULPhpl8MHUS51DYcnPkzRb3SDnfJC0JHpnN0m4sBKfI6G2qc3a7qahSqOaJWh/y3vN\n8yJJnkQoAo1Zifhw1oKsxa3H9Dtb8GGvk28ZJvh4h6powSeJz7x6qfMofPiRitPZjXXOZy+Pjmo9\ncb3QFwdHnl5bz1Cf1kZscHAkdGc3rUZTn1nkBbU9SytEKLHW4Ghk8JmhDD4QRSEz3hex0YKPRqMu\n9DP4DNLyLyCGwoaf2lY3j3M+6pbWSNIy4ZPN5lgrsdFQEKtHNOKj8WrN8aAl2uc86vVk8bUGn9n+\nUWpwx4w+5+Pxe7FnBQ4+Ep2V+Hh6J/HxrZPBJ7WaljjzQ6Tr7MY553MnJJnQNkbwGGdZy9FYz85u\nq2vU9rRVgk9PXr6WupzaUUKJVagaMxocoOoRj/p4kJTZnd248iQ+nqFKqhHBxFvRic/oehl8UrcK\nS35utQ8+NfXO+bA6u9W0n4ckPqP8RnV286Qp0YiPxqulKxMfL9/oxIcjRA3Euz6KwCA/1AETH+52\nN65WaGkd4QamRHGIzwhScibio1USn9RshQ8/teDD2e7Wk3q7G1Kjwot23NFYxEXdiI5pnkKHFalW\nanDQ0izi09OI4GOtwVEUsiRRUOJDhN/uNrultUReF8eRiI9UVyY+RGNffwafR0X8oVtQ4cPPXr3g\no+rsRnT/LwRJWiIRnyNZw+AMWoM6b4RaZ0vIM0MtjSY+2rVYfHveI7aiWRUhXCHW8STU1zQw8TnT\nTUyl10/c8VGIj7e31H9UDY20NUYRKW0tS73U+RX6zI/mnM+9B2OQ9iLBi4pIvbxCSk3Ws0NHQm5H\nQ9Qd1eBA6qX185LXuws6FCJ1hnDFHcOR979FR0UPPhG0IvE5w4fjI8OFVEl8UqsrLPnx6OxGpLyf\njzelQW9Xs56lQVzES4IhKvhIfUaEFTTx8SBI2q+DF0nyeC3Wutwx3ueIEDWQY0adOXKoFz34eDU3\niNDZLUrjBCL/YDWK+IwKiEl8JivSh58LKzT5kYjT2U3V4MAiC2VBUx8P4oPwleosDQ6kNYh8fulp\n1+5FZryCD0Ke2/i4GvXGNzr4jP7dzNTMltZcnT34RPEepSQ+NkX8nqbiKSz5eVJtqxvknI+W3CCJ\nj4ffyJbWVmqEuoCeGUqQIaqlM3R289wOZgkmEWjMqLARkfgMrpfEBzs2SjhJ4uNXQzsviU8qqsKH\nn704nd1Y53z2Qp5lsbzpW9Yxu8HBkaTfD+R2NIT/KLKjqTM6+GjXYpXl63aGbQKRWlojfYISnxW0\nWvCRKlLwGaGzEZ+IX+NTKL+wEIUOP5obmao6u9VkIS1IL0tIkdAKK/Hx9ED6ePtrvFrPrUJ8evIm\nL5q6iNoRzhFxPM5MfJhe0YmPyHOx4JPEB1tDUyeJD65ean2FPfOj3e7WFTLAeHU+03hZLhK8PjFG\nkZSIDQ6OFKGltVZerae9fK11PUMXVyOCD2IdaA0OPitodvCRKIkPTpGpSuS1pVIWhSY/t+oFH1Zn\nt5pGd3arPWZ9k0cTI4mn1Hd14qPxagkdGtAhizPPiyR5hhNv4oOowRGK6PSEDCKDPyA6E/Hx0orE\nR6oRpCRiDW2dJD5BlekSorDk51accz57qbe7ceaMoCzccSMbHEhkPX8UVejtaUfy2n6mqdeSF/Gx\n1O3VjhBKkOTDWgf184SsNbqF9kRFaHDAru/gqfWOcjZJWyODTyo1T+HJD6SzGxGPtmgvSLTEx+pn\n/TTWulUNQVOiER+NV0saL4+1edAZL/IygspYFKGzGypooL6WQYMPh/p4tLNepbNbhBuYEsUKPkl8\nximJT2qWliA/LbE6u2nfmL22CT3JY0+7x8cvo7bnRBAyrEQhPl7b0lry8rVerHsHq5FbzFpK4sPe\n7obWKsFHqii/wqNdwEb5uuw18usU9WuQSh0pLPmpbXVTnfPh0A0tKTqaqxkjGWclKxIaMoPWRDvn\ngw4+6K1z2ue8iI+X7xmCT4Qa3DGeHyxp6zEV/ZzP7OATpfuaNzGJ5h+1hnYO0bj1aWtZ6oXUqV7M\nPC1Dfjid3VQNDiyy0CI09bGSK+/OdVzvaMGnJXRDAo08tqVFJD6WupzaUUKJVaga3vfU0tZj+GXw\nwcor+Eh1xeCjURKfVKqvsOTnVqpzPhziUxunnSd5DH3Ox0qWrM0JVic+LSFD1CiCpK3F0Qzf6MSH\nI0QNxJXGSOLD1YWCj0TsNQp9I3R2ixZMIgafJD62WpZ6qfNrifCzF+ucz17eDQ5qGhF8JLUlspIk\nqc7S4EBagygGQeL4Wmp6+UaQNVwhaqDqeJPxAF4rtLSWEB+JIgQfqa4YfDRK4nMReTf0uYjCh5/e\nOR91S2vveTOJjzVMeW2XQxIZlEaEqJbQfhbC4EWSLMHHqy7n+RH38hl1rgZ1tWKlzLcCb/2d1dmN\nq9k3MY0QfKIFk4jBJ4mPrZa1ZuoaCn3mh3PO505aYmIlLT0vyzhrbUkdSRjwDi3e1GfUJ9PoEKNd\n99laWs/WiPWNIj5E48/5AL2Qnd1mt7TmarXg460zBB+NkvjcK9LPZSqmwpIfVWe3mjSd3bjzWo+3\nvI4kuXi3hhwEsZGMlYanWcFHQxo0F/hn6Ozm2fbZi2BZvVE1OHVQwQf1O2pkLa4X4c/5cIUOPkl8\ndN4j/DUaEa40WuHcTRKfhlZJoMEVmvy0pN7uxpljeXNGUx9rFzYrsbEGstbj0pozt9OhGxJo5niF\nlBmyfN0ivh6pMvhAFL3BwUrEx2sN3hoRfCKGq5F1RgYfiyL9XKZiKyz5uZXqnI93gwMtQRo11+rZ\netwrPGnWMpP4tLQ68Znlaw0+3tRnBPHhaMXgw9Uk4jMr+KxGfKTy3EZ3huAzKlisQHxWqpdaW+HD\nD6uzm/bN2XMeEf5ePhJZic+RJKFiBJHx1qz71nDltQYvkmRZ7+zgg1C2tIYoevDxUATiI/WO8CvS\noqjrPyvxWaXeVC256HgKHX5Y53w4F/laUlTTLOIjmW/dFoeiKQgPJJVCbcvTeqHXZgko0UiSpS6i\n9ohtaKPOEkUkPsCgFT34eNzENMINTIlinB+Semv8o9bQ1hl57maV4JO6tpY686NqcGBRpIRtDTnW\ns0NHQgSKEV9nZFjRrDcSQfIKVBZZvgZXCT4coX6WghIfrma2tOYqwr18vHwjvXVqNPMtqaWRLa01\nWin4rP4zmrIpLPnpnvPR0hbkPIufx1zENjMriUKtA+mPDCujiI/2Oc977nj5em5Hi3oVI/VAvY7R\n7ayBW3+vSHyIfLa7JfHB+GtqjKyTxAdbM3UehQ0/Ynk3OKhp1HY3D1lJksSXKF6DA43XSHmEFMv3\n14tcjaAynv6jaXRL0ajPzDOPgTU7+Eh1JeIzQpGDj1YZfAYq9/lBtMS2N9Z2t728Lu5bXh5v9qtt\nd+OuAbUOrTTBJ8J2N6+vmdd2N6/AxfGeHaw4NVB1UCEs6JXBmagPV6sFH2+dhfpErPGkqF8DlIL+\nektNUHjyo97uthdyu5uFDB1p1HY36/Y9qceRUMSHyHedFq9RzRd6tXq+Hlv2rM+vEHwQ2/UQZGlk\n8EFud2N6nSX4RCA+XlvSogWTiMEnOvEZGXyS+KRmK3z46WrGdjeuX03orXJHQtzPR6JZW8hm389H\n4zV625pXoLLIc6vcWYIPR9G2uhGdosFBtrSOI+/go9FZajwpic9CirAt/wQKG35YNzKtSUuKLJRl\nRIODI1m230nnSwNFxHM+R0KeGWpJ6+dBZ7wCiHc4meXNrYHwQL1bJ/F5RSs0OIhAfDy9k/j4KYkP\ntmbq3FrizA8R2S/yEfXQ292sIcUakjx/K8y8n8+RRnh5+HltS2tpVmvuEedwLP6oLWYIRXtXD/yJ\n5BlbWnspGxwcaxTtiH4T01V09teX0iss+XkmTvDRkpZZxKcmSQBAEJuaENvlvINPSyPokSaMrER8\nvHy9t6PN9kfUQI1BNl9BBj6G1xWJDxH/gjeJz3j/UTU0dVagMJYQMvr1hddpX9hYrUN+boVscOC5\nBsR8L2IzmqQhNaLBwZFGEp+WvL5XqxIf7+DD0agtdajvw8haaK8F5NXgwEtJfOYrOvEZ/XOawSfl\npfjkZ/9T7N3gYP+Yx9aylRocSDyQocSbKq3c0tqrA5vXWZvZROZKxIezltG1uF7Eoz4zmxvM7Ozm\nSR5WpElSb42/psbIOnkTU1y91LUUm/xo36A95xGdr8HBkccIkiLxH0GmLBfxI/wsstSL9DoktVeh\nmSsGH66AwWemZre0lmjF4HMWRQ4+WmXwSZ1NcckP5yKfEziid3aryYu2IEKFN5Hx9td4tZ7zOB/j\nQX0sxMcSfLzqcp6PQHy4PgiPJD5ElMTHK/hIFSlUJfFZJ4hk8OnoMi/UV7HJz61Gf4LrEV6sYz08\nPcPTLHLU0qhzOasEn55mzT2LRlEW1O/HCd+zsxAfkSfekoh8v31RQlVURQ4+Wl0h+FzxZzUVmfzc\nikNbtJRmxHY1a8CwblVDhRaEhzfx0Xi15ljIhdTPI/j05HV+yEJlZhMfRA1UnUj0yaHeFTu7RbiX\nTySaFI36JPHR15pRz6IMPtdV/PDj3eBAKyvVkISUmrxeH4LWoIKPRujtaUca2eDAMg8d3ji+iOAw\nU6O2qUUjHsjtbgxdMfhIFKX7WgYfbA1tnSQ+2JrLKhMbRPHDz17a0KClLNbzMBEbHIzomIbQiO10\naOKDDnjar/FM8qKti6gd4ZzPKOKDWgt33GjCROcKPkl89N4R/TU1tHWS+MSpmTqHYp/58byfj4W8\noC5Mep7WkOT5CXbE7W5HGnV/Jy96g57nRXx6z18h+HCECggjz/mAP+iI3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bo+rQqQkcXJ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\nAAAAS/g//e7eQuSItR0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116742c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i,j in [(2,3)]:  ## other combinations could be[(2,3),(3,4),(2,4)]\n",
    "    plot_arr(interpolated_from_i_to_j[i,j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Let's check the error before and after doing the interpolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def check_disp_at_freq(om1,om2,i1,i2,arr,printing = False):\n",
    "    '''\n",
    "    Function for measuring error\n",
    "    \n",
    "    Args:\n",
    "        om1,om2 (floats):\n",
    "            values of omega1 and omega2\n",
    "        i1,i2 (integers): \n",
    "            indices of omega1 and omega2\n",
    "        arr (2D array):\n",
    "            grid to take two integers and obtain omega3.\n",
    "    '''\n",
    "    om4 = - (om1 + om2 + arr[i1,i2])\n",
    "    if printing:\n",
    "        print 'omegas are ', om1,om2, arr[i1,i2], om4\n",
    "    D = {omega1:om1,omega2:om2,omega3:arr[i1,i2],omega4:om4}\n",
    "    return dispersion_difference_function_4wv.subs(D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omegas are  19.65 16.25 -6.74098429597 -29.159015704\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAAVBAMAAAC+i7+MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\npj1JQUWvrQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$-2.07817976161095 \\cdot 10^{-8}$$"
      ],
      "text/plain": [
       "-2.07817976161095e-8"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## first set up the grid to the original to see what the error is like at one point\n",
    "\n",
    "i1 = 73\n",
    "i2 = 45\n",
    "om1 = omegas_dict[2][i1] + dis1\n",
    "om2 = omegas_dict[2][i2] + dis2\n",
    "\n",
    "arr = omegas_4wave_converged[2]\n",
    "\n",
    "check_disp_at_freq(om1,om2,i1,i2,arr,printing=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## original grid, evaluate all error values.\n",
    "\n",
    "err_array = np.zeros((101,101))\n",
    "\n",
    "for i1 in range(101):\n",
    "    for i2 in range(101):\n",
    "        om1 = omegas_dict[2][i1] + dis1\n",
    "        om2 = omegas_dict[2][i2] + dis2\n",
    "\n",
    "        arr = omegas_4wave_converged[2]\n",
    "\n",
    "        err_array[i1,i2] = check_disp_at_freq(om1,om2,i1,i2,arr,printing=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAAAPBAMAAACPYumWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$1.0510315847e-05$$"
      ],
      "text/plain": [
       "1.0510315847e-05"
      ]
     },
     "execution_count": 283,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Average error in absolute value for the original grid:\n",
    "sum(sum(abs(err_array)))/101**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mF6V+yIy72K1UlxyvyYrvqNwHlwg/IllzQjJ3oks7X+DX/P0lvpP7fl3VOH7X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\nefJaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ea6950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plot_arrot the error values for the original grid\n",
    "plot_arr(err_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "omegas are  19.65 16.25 -6.74098429597 -29.159015704\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAAVBAMAAAC+i7+MAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\npj1JQUWvrQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$-2.07817976161095 \\cdot 10^{-8}$$"
      ],
      "text/plain": [
       "-2.07817976161095e-8"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## multiply indices by 10, the dilation factor for the interpolation\n",
    "\n",
    "i1 = 730\n",
    "i2 = 450\n",
    "\n",
    "## higher resolution omegas\n",
    "om1 = omegas_dict[3][i1] + dis1\n",
    "om2 = omegas_dict[3][i2] + dis2\n",
    "\n",
    "## retrieve the interpolated omegas\n",
    "arr = interpolated_from_i_to_j[2,3]\n",
    "\n",
    "check_disp_at_freq(om1,om2,i1,i2,arr,printing=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "## interpolated grid grid, evaluate error values at the original locations.\n",
    "\n",
    "err_array_inter_original = np.zeros((101,101))\n",
    "\n",
    "for i1 in range(101):\n",
    "    for i2 in range(101):\n",
    "        i1_inter = 10*i1\n",
    "        i2_inter = 10*i2\n",
    "        om1 = omegas_dict[3][i1_inter] + dis1\n",
    "        om2 = omegas_dict[3][i2_inter] + dis2\n",
    "        arr = interpolated_from_i_to_j[2,3]\n",
    "\n",
    "        err_array_inter_original[i1,i2] = check_disp_at_freq(om1,om2,i1_inter,i2_inter,arr,printing=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAAAPBAMAAACPYumWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$1.0510315847e-05$$"
      ],
      "text/plain": [
       "1.0510315847e-05"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Average error in absolute value for the interpolated grid at the original points:\n",
    "sum(sum(abs(err_array_inter_original)))/101**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Lk1BWdj3cXPaXbGUuLfb5/1eeN2quoSn2SbXrnpXvXLUvX+MfR65wVyn2ZecxW8U+qVbt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\nKsV85PKhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cd36250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plot_arrot the error values for the interpolated grid at the original points:\n",
    "plot_arr(err_array_inter_original,bounds = np.arange(-5e-5,5e-5,1e-6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## interpolated grid grid, evaluate error values at the original locations.\n",
    "\n",
    "err_array_inter_between = np.zeros((100,100))\n",
    "\n",
    "for i1 in range(100):\n",
    "    for i2 in range(100):\n",
    "        i1_inter = 10*i1+5\n",
    "        i2_inter = 10*i2+5\n",
    "        om1 = omegas_dict[3][i1_inter] + dis1\n",
    "        om2 = omegas_dict[3][i2_inter] + dis2\n",
    "        arr = interpolated_from_i_to_j[2,3]\n",
    "\n",
    "        err_array_inter_between[i1,i2] = check_disp_at_freq(om1,om2,i1_inter,i2_inter,arr,printing=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAAPBAMAAACl0hg5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nzPA6/+0AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1.03989044985e-05$$"
      ],
      "text/plain": [
       "1.03989044985e-05"
      ]
     },
     "execution_count": 285,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Average error in absolute value for the interpolated grid at the new points:\n",
    "sum(sum(abs(err_array_inter_between)))/100**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FPlr4izqrcfyxSbvanknrnrG1jUebyPFTbIuP85akxUmtx4zfl/RkNReZ7NOt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1194953d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## plot_arrot the error values for the interpolated grid between the original points:\n",
    "plot_arr(err_array_inter_between,bounds = np.arange(-5e-5,5e-5,1e-6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vv55VM1u569trZiuXg5qKmS3yWsDeiTtcAAAANWPCBQAAUDMmXAAAADVjwgUA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d03390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Let's display both error charts on the same diagram:\n",
    "\n",
    "big_arr = np.zeros((200,101))\n",
    "\n",
    "for i in range(101):\n",
    "    for j in range(101):\n",
    "        big_arr[i,j] = err_array_inter_original[i,j]\n",
    "        \n",
    "for i in range(100):\n",
    "    for j in range(100):\n",
    "        big_arr[i+100,j] = err_array_inter_between[i,j]\n",
    "        \n",
    "        \n",
    "plot_arr(big_arr,bounds = np.arange(-5e-5,5e-5,1e-6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "We see that the error after the intepolation is similar to before, both at the points of interpolation as well as between. "
   ]
  }
 ],
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    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
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  "widgets": {
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