jason-neal/eniric

View on GitHub
docs/Notebooks/Convolution_speeds.ipynb

Summary

Maintainability
Test Coverage
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolution speed tests\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This Notebook compares the convolution speeds of Eniric to PyAstronomy. \n",
    "\n",
    "Enirics rotational convolution is faster than PyAstronomy's \"slow\" convolution but it is significantly slower than PyAstronomy's \"fast\" convoluions that use a fixed kernel (valid only for a small wavelength range) and require a uniform wavelength step.\n",
    "\n",
    "Eneric allows for a variable step wavelength array, with a unique kernel for each pixel (hence the longer time).\n",
    "\n",
    "Recalling a cached result is faster than PyAstronomy's convolutions.\n",
    "\n",
    "Requires PyAstronomy\n",
    "`pip install PyAstronomy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import PyAstronomy.pyasl as pyasl\n",
    "\n",
    "import eniric\n",
    "from eniric import config\n",
    "from eniric.broaden import rotational_convolution, resolution_convolution\n",
    "from eniric.utilities import band_limits, load_aces_spectrum, wav_selector\n",
    "from scripts.phoenix_precision import convolve_and_resample\n",
    "\n",
    "# config.cache[\"location\"] = None  # Disable caching for these tests\n",
    "config.cache[\"location\"] = \".joblib\"  # Enable caching"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data\n",
    "Select test spectra, flux1 is a M0 spectra, flux2 is a M9 spectra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "wav1, flux1 = load_aces_spectrum([3900, 4.5, 0.0, 0])\n",
    "# wav2, flux2 = load_aces_spectrum([2600, 4.5, 0.0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "wav1, flux1 = wav_selector(wav1, flux1, *band_limits(\"K\"))\n",
    "# wav2, flux2 = wav_selector(wav2, flux2, *band_limits(\"K\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# PyAstronomy requires even spaced waelength (eniric does not)\n",
    "wav = np.linspace(wav1[0], wav1[-1], len(wav1))\n",
    "\n",
    "flux1 = np.interp(wav, wav1, flux1)\n",
    "#flux2 = np.interp(wav, wav2, flux2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convolution settings\n",
    "epsilon = 0.6\n",
    "vsini = 10.0\n",
    "R = 40000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Timing Convolutions\n",
    "Times vary due to system hardware performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rotational convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 62.5 ms\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "rot_fast = pyasl.fastRotBroad(wav, flux1, epsilon, vsini)\n",
    "## Wall time: 15.2 ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 6min 7s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "rot_slow = pyasl.rotBroad(wav, flux1, epsilon, vsini)\n",
    "## Wall time: 36 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convolution settings\n",
    "epsilon = 0.6\n",
    "vsini = 10.0\n",
    "R = 40000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 62.5 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# After caching\n",
    "eniric_rot = rotational_convolution(wav, wav, flux1, vsini, epsilon=epsilon)\n",
    "## Wall time: 4.2 ms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rotational convolution in eniric is ~10x faster than\n",
    "the precise version in Pyastronomy and does not require equal wavelength steps.\n",
    "It is ~1000x slower then the fast rotational convolution that uses a fixed kernel and only valid for short regions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resolution convolution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 234 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "res_fast = pyasl.instrBroadGaussFast(wav, flux1, R, maxsig=5)\n",
    "## Wall time: 19.2 ms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 70000/70000 [01:17<00:00, 905.14it/s] \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1min 19s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Before caching\n",
    "eniric_res = resolution_convolution(\n",
    "    wavelength=wav,\n",
    "    extended_wav=wav,\n",
    "    extended_flux=flux1,\n",
    "    R=R,\n",
    "    fwhm_lim=5,\n",
    "    num_procs=4,\n",
    "    normalize=True,\n",
    ")\n",
    "## Wall time: 3.07 s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 46.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Same calculation with cached result.\n",
    "eniric_res = resolution_convolution(\n",
    "    wavelength=wav,\n",
    "    extended_wav=wav,\n",
    "    extended_flux=flux1,\n",
    "    R=R,\n",
    "    fwhm_lim=5,\n",
    "    normalize=True,\n",
    ")\n",
    "## Wall time: 8.9 ms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resolution convolution is around 500x slower \n",
    "although it can handle uneven wavelenght spacing and has variable kernal. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare the results of convolution\n",
    "Eniric gives a comparible rotational convolution to PyAstronomy's slow version. The PyAstronomy Fast convolution gives different results, which are maximum at the edges.\n",
    "PyAstronomy also has edge effects which are ignored using [10:-10] slicing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEWCAYAAAB8LwAVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4VFX6wPHvOy2990IIhEDovSgoiLgq1RVU7N21K7rr6urPta51LWvvvWNHREWagAKh94SS3nsvM3N+f8yAISRkAiGN83meeRjuPffcdyYz895T7r2ilELTNE3TGjN0dACapmla56QThKZpmtYknSA0TdO0JukEoWmapjVJJwhN0zStSTpBaJqmaU3SCUJDRN4VkUeOYfvtIjKpDUPqlEREiUifo9z2FBHZ3dYxadrxpBNEJyMiKSJSLSIVIpLj/PH27ui4DmgqmSilBiqllnVQSJ1S42SilPpNKdXvOOwn1rmvCucjRUTuPsY640WkRkQ+bLT8IhFJFZFKEflGRAIbrAsUka+d61JF5KK22lbrODpBdE4zlFLewDBgOHBPB8ejdX7+zs/MHOD/ROSMY6jrJWBdwwUiMhB4DbgUCAOqgJcbbVPnXHcx8Ipzm2PaVutYOkF0YkqpHOAnHIkCABFxE5GnRSRNRHJF5FUR8XCuCxaRBSJSIiJFIvKbiBic6/qLyDLnuu0iMrOpfYrIFSKystEyJSJ9ROQ6HF/gu5xHq98716eIyJQG8T0nIlnOx3Mi4uZcN0lEMkTkThHJE5FsEbmyudfvPLJ8x1lPsYh802DdtSKyx/k6vxORyEbxXi8iyc7tXhIHN+frH9SgbIizxRbaUr2NYlsmItc09b6JyArn4s3O9+mCA6+9Qflm/x7OVtpLIvKDiJSLyBoRiWvufWpIKZUIbKfBZ6Y1RGQuUAL82mjVxcD3SqkVSqkK4P+Ac0XER0S8gNnA/ymlKpRSK4HvcCSEY91W60A6QXRiIhINnA3sabD4CaAvjh+APkAUcL9z3Z1ABhCC42jsX4ASETPwPfAzEArcAnwkIq3q8lBKvQ58BDyplPJWSs1ooti9wDhnfEOBMcB9DdaHA37OuK8GXhKRgGZ2+QHgCQx0xv0sgIhMBh4DzgcigFTg00bbTgdGO2M4HzhTKVULfAVc2KDc+cBypVSei/W2SCl1qvPpUOf79FnD9S7+PS4EHgQCcPz9H3Vl3yIyDhhEg89Mg4OGph4LGpTzBR7C8TlqbCCwucFr3IvjqL+v82FTSiU1KL/Zuc2xbqt1oA5NECLytvNIcpsLZXuKyK8issV55BXdHjF2kG9EpBxIB/KAfwOIiADXAvOUUkVKqXLgP8Bc53b1OH7Yeiql6p393grHD7Y38LhSqk4ptQRYwKE/lG3lYuAhpVSeUiofx49cw6PBeuf6eqXUQqACOCxRiUgEjuR4vVKq2Fl+eYN9vK2U2uD80b8HOElEYhtU8bhSqkQplQYs5c8j6o859HVf5Fzmar1twZW/x1dKqbVKKSuOpNxSi6BARKqB33F03xxsbSmlpiul/Jt5TG9Qx8PAW0qp9Cbq9wZKGy0rBXxaWHes22odqKNbEO8CZ7lY9mngfaXUEBxHOY8dr6A6gXOUUj7AJCABCHYuD8FxRL3+wBEgsMi5HOApHEeOP4vIPvlzsDISSFdK2RvsIxXHUXxbi3TW3XA/DbtpCp0/egdU4fiRaKwHUKSUKm5pH85ui0IOfT05zexjCeAhImNFpCeOH96vW1FvW3Dl79Fc/M0Jdpb5O47Pjbk1AYnIMGAKzlZaEyoA30bLfIHyFtYd67ZaB+rQBKGUWgEUNVwmInEiskhE1jv70BOcqwbwZ7/oUmBWO4baIZxHzO/iSI4ABUA1MLDBEaCfc3ASpVS5UupOpVRvYAZwh4icDmQBPQ6MRzjFAJlN7LYSRxICQETCG4fVQthZQM9G+8lqYZumpAOBIuLf0j6c/dhBNP16DuH8Uf4cx9H6RcACZ0ustfUe8j7h6DpzVWv+Hi5TStmUUv8FaoAbDywXkR/lz1lOjR8/OotNAmKBNBHJwZFoZovIBuf67Ti66w7U2RtwA5KcD5OIxDcIZ6hzm2PdVutAHd2CaMrrwC1KqZE4PqQHZjtsxjGYBfBXwEdEgjogvvb2HHCGiAxz/ri9ATzbYFA1SkTOdD6fLo7BZAHKAJvzsQbHD9pdImIWxzkLM2i6f30zMFBEhomIO/BAo/W5QO8jxPsJcJ9z8DcYx/jIh0co3ySlVDbwI/CyiAQ44z7Qt/8xcKUzRjcc3WxrlFIpLlb/MXABji6ljxstd7XeTTgGWj3FMZ316kbrj/Q+tebvcTQed9btDqCUOts5FtLU42znNq8DcThaVMOAV4EfgDOd6z8CZojjfA4vHK34r5wHJZU4xnYeEhEvERmP4wDugzbYVutAnSpBiGO+/8nAFyKyCcfUuAjn6r8DE0VkIzARx9GWtcmKuhFnP/77OGZ+APwTRzfSHyJSBizmzz78eOf/K3D2RSulliml6oCZOPr0C3Ak3cuUUrua2F8Sji/wYiAZWNmoyFvAAGcX1zeNtwceARKBLcBWYINz2dG4FMeYxS4cYzG3O2P8Fcf78SWQjeOHbW4zdRxGKXXgBzoSRxI6sLw19T6LY6A1F3gPx49gQw8A7znfp/Mb7d/lv8dR+gEoxjFe5RKlVJVSKufAA8dnqMb5+UMptR24HsfrzMMxRnBjgypuBDyc6z4BbnBuc0zbah1LOvqGQc4BwAVKqUHOWRS7lVIRLWzjDexSSnXngWpN07QO1alaEEqpMmC/iJwHjlk7IjLU+Ty4QZ/tPcDbHRSmpmnaCaGjp7l+gqMrpJ84TqC6Gke/8NUishnHQNWBwehJwG4RScIxx9+leeGapmna0enwLiZN0zStc+pUXUyapmla52HqqB0HBwer2NjYjtq9pmlal7R+/foCpVRIyyWPXYcliNjYWBITEztq95qmaV2SiKS2XKpt6C4mTdM0rUk6QWiapmlNcqmLSURScFw8ywZYlVKjGq2fBHwL7Hcu+kop9VDbhalpmqa1t9aMQZymlCo4wvrfGl06WNM0TevCdBeTpmma1iRXE4TCcY+B9eK47WRTThKRzc5LCzd5NygRuU5EEkUkMT8//6gC1jRN09qHq11M45VSWc5LTP8iIruc93I4YAOOu5hViMhUHHezim9cifOWla8DjBo1Sp/CrWma1om51IJQSmU5/83DcfetMY3WlznvvoXzNpJm570ANE3TtC6qxQThvImHz4HnwF+AbY3KhDtvUoOIjHHWW9j24WqapmntxZUupjDga+fvvwn4WCm1SESuB1BKvQrMAW4QESuOW2LOVfoqgJqmaV1aiwlCKbWPBveTbbD81QbPXwRebNvQNE3TtI6kp7lqmqZpTdIJQtM0TWuSThCapmlak3SC0DRN05qkE4SmaZrWJJ0gNE3TtCbpBKFpmqY1SScITdM0rUk6QWiapmlN0glC0zRNa5JOEJqmaVqTdILQNE3TmtRpE8S6lCK+3phBZa21o0PRNE07Ibl6R7l29diPO3lt+T4AEsL38fWN4/GwGFtdT2WtFQ+zEYNB2jpETdO0bq/TJYhlu/N4bfk+LhwTw5heAcz7bDOvLt/LvDP6HlJufWoR+/Ir+cuAcPw8zYes25NXzr++3sb61DR6WgrwD+hBhd2P3LJafNxNXDOhF1eM79Xq2Kw2O2+u3E9qYSVXnNyLfuE+x/RaNU07/pRSOO9no7VSp0sQzy5OpkegBw/OHIjFZODHrTl88EcqN0yKw93saEV8kZjOP+ZvAey86FPGk38JZqx3Pfn52/lPys+sroYqcwWe/arIB2JrTyPU43KmB21nZ+UH/LqiD6a667jktFNaFduLS/fw3OJkzFLPls2LOSOhknprLYUZvih3f6ZPiGNEwgA8vML4aXsua1OKOGdYFEN7+B+sIym3nOTcCkbHBhDq697q96e8ph5vN5P+wGsnnJp6G9uzykgI98HLreWfrqo6K3d8tpklu/IY3yeIJ+cMJcTHrR0i7T46VYJIKahkc3oJ903rj8FgZ0nSd4Ta/ktPSyw/buvP9B6VzPr+PKrsiui+ilqBIoOwdlUpY0tKcTMIm6Ki8JEwJvU+iwF+YXgU7GXk4IuJCx/B2t+X8emucsojN7E19QZ+etvEKYEDOH/w1dgCRxDo74+I8Me+Ql5YkszIGF8uGmUhPLAPmSXV7N90Cyf1zibDZCPNaOCtOgizWllcmwW1cENiCDfu8MCIG3U1AfSzVrBjTzDXn/0Wp/YN4clFu3hthaPrzGIy8NqlIzmtX6hL702d1c4/5m/m201ZxId6886Vo4kO8Dyefw5N61Dbs0rZlF7C0Gh/auptzPt8E+lF1UT5e/D1TScT6nPkA6z7vt7GzztymDk0kkXbc5j2v9/434XDGdc7qJ1eQdOSc8u556uteLubeHLOkBZfR0eSjroz6KhRo1RiYuIhy15dvpfHf9zFCxdbeW3PG6SWpeKpoGfFQKyGW/jyohhunn8+1dVWonw88fXyJ8AtlP0pAWzJ7kGqCmXcgDieuWAY3s0cYdTb6li24QveXfUBlV7Z7LXY+Sk9k0irjVf8Qvjcz4N8uz9K6jEZK7ELrL9kPfM+24Y592YKAuro4xVBXGA/gjzjCfcJZkRALNVlRTy84ns2lhWxz+RFr/Ba3Go2I3W+bEv9J739jQwzPkBAyGz+MvFq7vtmG1kl1fx+z2Q8LUfO03VWO7d8soGftudy/qhoftyWQ2yQF1/feDImY/PzDJRSKIUeg9Fctjm9hI1pxQyK8mNYD/8jfr6Opy/XZ3DX/I3YpA7s7kRSQLCfFzMnjODJn3YzdVA4z80d3uz2WzNKmfHiSm6YFMc/R8CGHcu5Y4Mfafle3DApnnlT+nbIa7Pa7Mx4cRXJueXYlWJyQhhvXj6qVXWIyHqlVOs2OkqdqgWxZk8ecyJe4F8bMuntE8Ozk55lYo+JvL86g4cX7OCPwgRWZj7IiBh/Hr5izMHt6m12Vu8txMNsZHRswBG7X8xGC2eMvpi02pN5eMEOQtzyedS6j1kxNRSWbCaqopwq935MSYgmMykJW7GNhxds54ct2dw+5V2em9K3yXo9ouCRflNYn1aMr7v54PhESVUdj/6wk6rsRFb5lFNhfxfjqp/591mvMvednXy9MZOLx/Y8rL7iyjp+2JpNWlEVK5Ly2ZNTzON/iWDupEGc2jeEmz/eyNur9nPdqXFNxrO/oJJr308kq6Sa26fEN1tO0w5YujuPq95dx4FjRjeTgQg/d3oGeXFSXBAXjo45bLyvKR+vSSOtqIq/ndqbAC9Lq+P4ed1yFq18kP69c8lwM3N3wlckJL3JssKP+L1iEhOHn8z3G+r419T+TXbTKqV4dcGb+EZv55KTn4Y/nmHd7k8pDPLAP8ibn3cFUpo5nAcu+z9MpuPT5VReU88lb62loLyWRbefgo+74337YWs2O7PLePGi4aQWVvHUT7vZlF7CsAbd0E1ZtC0HN7PB5R6HttJpWhC2ymLWPDkTT/ddfNN7NHef8znubt4AlFbVM/axxdTU2wH44dYJDIz0O6b92+yKxxbuZGN6CbeeHs/EviGUVNWxI7uMUT0DsZgMFFXWce7Lq0gprGJItB+fXXfSUc2mOqC0Iof/Lbqezyv3MshmwFp8A54BI3jvqjGHlCuvqefcl1eTnFdBvPtuBgR/yl73cipEiLEppgQNZmPpZfy438jiOyYe1tWklOL8135nd045AyJ9+WNfEf+eMYArj2JgXjsxKKWY9PQyzEYDb142iu1ZZWxKLyartIaknHKS8yqI9HPn+1smEOTd/I/qyuQCLnlrDQAT+4bw7pWjDx6w1dTbSMotZ0CE7yFH7/sLKnl75X56eqazOf0pVhnzsAIjDd5M6H8BFw77G55l2Xy+8RXeLdtBenk6HjYDp0oPbjrzAXpFOg6mq2or+HX9i3yyaz5bjbVYMPH+9A8ZaPIno3Q/a2vzWJuzliV7fqDaAJFWxQ8x52LqN43ygBg8PUNIzncckBVV1uPtZiTcz4Mgbwtmg4GECB+Cj/DaG/p5ew7XfbAegHlT+nLblHiUUsx4cSXW2io+vSCAstpq5nyQz/gBfXj2gmEHty2tqsfX489xxi/XZ3DnF5sdz284mVGxge3WgnApQYhIClAO2ABr4+DE8UqeB6YCVcAVSqkNR6qzV8JgtX/XVuzKzo/r/sfe9W9xfU4mW4c/wMhzbj2s/Gfr0njkh53cdno815zS29XXd8zKaurZmlHK8Bj/FruCXPXrmme4b8fb+NgVUSmX8Nq//4nF9OcX5p1V+3nw+x28cdkohmU8z5yMbxniEUGQZzA7y1LYYa/k6eJqvim8EsvAqTzfqKm9Zl8hF7z+B4+cM4gLx8Rw/YfrWbY7j69uGM/g6NYl1oKKWgI9Lbqbqptbn1rM7FdW88z5Qzl3RDSlyT+xYsu7lNVXMDByLPaoq5j79mbOGR7Jk3OGNlvPNe+tY1tmGVdP6MWjC3fy0kUjmDYkgsKKWs5/7Xf25ldy6biePHzOIMCRmC57+n3OLv2GIR6ruSIyhDF1wdx0+iMM7DPhsPrtys66rN959ft5bHSv4qzKKh6XcIrcPDjNmItdhOh6GzGVffnPZS8QFNDjsDrKKor5+5v3EqU2cn/ZbkTZOCcqnL0WCxa7wkMplN2dgoqh1ObM5hLjL6xQCWRLDNOHRHLP2QktTjB5+qfdvLJ8L2NiA9mbX8HquyezfcNqcr+7n9Fu2zi1RxgAJqXoWacY1HcGsxJmo4qDufSDrQyOCeK9K8diEGHiU0vx9zSTWljF7JHRPHbukE6ZIEYppQqaWT8VuAVHghgLPK+UGnukOgNifNRlj09gV302WdgYWKeo3XcFz//9RmKCmh587U7T1dLTV7Hrm1uYXLCPtOG34THpSsL9YymvKeWmN28h262Yn6/5Dqmvpr6mFLNvxMFtt+5ZyKDFjyI527jfMoE5l77AkB5/Js17v97KlxsyWPX3MSTt/pic3G0s31VNISfx2m3XIggb0ooZ1sP/iLNB3vxtH/9ZuJPBUX58eM3Yg81krfMprqxjf2EltfV2MkuqsdntzBoWdXDmX0v+s3An765KYf19k6n/5U6mFS6lwvDnQcsQKwR63cvi7f4k3jelyc9NUWUdYx5dzNXjY7k0bh/P/PwK5YY8vPrOYO/uycTnLcIWupFF1kjOH9kLS/E2Egt3EF9dzhOFZVT0v4D8EVfTJ675sYUDvt2UyTNffs5/hmYyvjaNvKIinhOFMgxhftqpPHPhWGYMjWx2+9/3FnLhG39w9XBvBtt38X36jxgslQT5gLu7UO0TSP9e0zjdawyhH4zhtF7xhFgmsGvnyUT6hPLNjeMPdrfZ7Irymnr8Pf/sTrv0rTUUVtRx6+nxXP/heu4cuZD83B+5s6AWrzGX8qmbFaPBxJ68vSQWpZDlbeKOUbcS8OXneKgd3BTtiafRjwhbDZ7VNfTw9KVHRSw5pf34z333dbkxiFnA+8qRbf4QEX8RiVBKZTe3gc1gJakqhd6YuT3iFJaVXsSvXtX0CPRodifdJTkA9OgxHrcLf+HH5y+kbs8bPFjyJSFe4eRX5WP3sTPU6kFZXRl+bn6YLYcmzMF9pkLPyeQv+CdLin9h0dK5XD/iesaGj8VurWHxrkxm9fFg8bujecTfy7FRKBjVBm5/6zVqSy5ieelAEsJ9+O7mCYe0Xg7IKa3hyUW7ifT3YEtmKf/9OYkHZg5sj7dGa8Hniel8vi4dN7OBaH9PkvLK2Zxegr3Rsd6vO/N4/TLXfkcSU4oYEuWLz+J/woYP+MewmfQbN48wvxiWbHiVN1MX8pe+wXy/qZZlu3KZNjTqsDp+2JrNUMtvlGbdy4z8eqx+QoAV8pO2Qt4YXhpQzhOVGZikkB9SNuGu6oizKqqrBlJ/y2v4BUTgavv2zIHh3Pv1AL5Wkwk6vRdnPfcbFqMBheLS8bFMHxJxxO1PigvivJHRvLU+A4hm9ogHuX/6gCbHWCpuWsfU3R/z1b7vCOizktjM3rz1Wzh3nJmAUoq5r//OloxStj945sGus335lYztFcjpCSGcFvUKr1el0tfox/tjX+aWs0/iEmfdSikmPrWMvmYPYt1682ZVMheMGMEAVc2WrAzCzElUWRTrVTHTK5O4vm4B/3HxPWoLriYIBfwsIgp4TSn1eqP1UUB6g/9nOJcdkiBE5DrgOoCAyF7s2/80n9x7Bv6eFp54aikjYo48wNzdhAYH8bDHXZwTsI3rfVaREdaXkjJv1q+Df139N/zcjvB1MbsT8tfniXvhJbZ7/sqz6589uKqaOQyIv5wpFRcS7R9OZO/TKSxN5dPVb7PXuJ2P6v7Dlh5zuCJ9Kgu3ZnPO8MO/7J+uS6PebueTa8fxyvK9fLwmjRsnxR3VuRta2/llRy53zd9C3zBvBtStpLbyB+KMbpw6+TWG9fDHWLqJiJ7j+HZzNi8u3cOevHL6hB75hM5aq41tWWVc1/srErd/y6gJ8zh3ygMH158//j7OGXcXBkys/OZJUlfcS6L3Y4yKOxtw/MjZ83aQsOR2zvLbxRtmf+aGjOKScfdiMEWzak8hY2IDiQk6i5eA815dTVmZlUW3TeCkx5cyPMYf94Aj/6A35m42MmNoBF9tyCSloBIvi5FVd0/Gz8Ps8m/I47OHMG1IBIFeFoZENz9I7B3cl/uCH+CSQVfw7+8vJjFiJ5J0FZUTFrIt18a6lGIA9uRXkBDui1KK/IpagnzMPLbuURJ9Uxld5kkxj3Ll5NGH1C0i/HV4FM//mkxaURUllrG8MPN0JhkMPLc4icpaK3edlYCXm4ms/EKmPfMFcEOr3qtj4WqCGK+UyhKRUOAXEdmllFrRYH1Tf5HD+q6cieV1gIFDh6tKG3y3OYtpgyNIKaxi7piYVr+Arm5ItD+/5A1jydW3A3D7pxupNxSQEBng0vZjBp3J8p9iWTBvADmbnmdfhZnHKvsysmcAQVGPMt5ZrlfwAEbFnY2tugzj0kcYtu51JvT8g3fW/oNzhl9+WL2Ld+YyIiaAHoGe/O3U3nyyNo2P16ZxezOzuLT28eKSZIYE13JK6LN8VJ+DAv7qHce8M/pSWriHqb/PY/z+aG78y8e8snwv32zM4u9n9jtinbtzyokwbuZzWc32yF68Pfn+w77QFqOj+yQ21J2v3RWvrLyL/jveIaK2hn2VGVyTn8PkWjtV0Vfx07m3EeAddnDbOSOjD6lrxtBI7v92O5+syyCnrIYp/cM4Gtec0ptP1qaTmFrMnWf0PaSLxxVGgzCpFbOCYv1ieWvuUh75fC5lxs3UvzmNtT0fO7h+U1oJCeG+lNdasVqt7Kh8iS35v3HNwKu4ZuANmM2WJlvrl58cy1sr95NeVM1Np8UdHOu866yEQ8pFhgShQvq36jUeK5cmAiulspz/5gFfA2MaFckAGo4GRQNZR6rTw2ykf4Qv89dnsDGtBIARMa79KHYnQ6P92FdQSWl1PUopVu4pZHyfYJcHhcf1DgQgI9+DKWc+R5b5CtwlgIRmLgNi9PCFqU+SNed1dnt6sdftv8xb8g+27P8Vm90GQHZJFflZSUwL30XR/qX09BFOjgviqw2ZdNSsNw3SCqvIy96Cl9+/ed+ayzm+fVk8+ycemPMtAGbvMC6MOIWf63K4ZfkV9IuuYW1KUYv1bs/OpyDqZ9xNnjwx9T3E0PzPgme/qezd929uHHIrnmZP0kr3EWm1kex+KlNs/2Pw7AcOSQ5NOXtQBBajgX99vRVPi5GzBoW37o1wigvx5sOrx3Lb6fFce2r7TFwxmSzce8F87AVX4F6yh4nbr2BK7Gp8PUxszigFoKC8lodM73BN5gr+MfxWbhs1Dy8P9yaTA0Cgl4V3rhzNk7OHcNvpRz4Au+OM9j1Aa7EFISJegEEpVe58/hfgoUbFvgNuFpFPcQxSlx5p/OGA80ZG89CCHby9aj9mozCklTNsuoMDTdttmaUEeFooqKhlQnywy9sPjvLHzWRgzf5CzhoUzvrUYpdOcOo98Hye9z2FC794hBXyK4vTF2ExmFh14e9kL3ycqZHv82yZD8+ugFCrjUkSRmrZbLZnjWBQ1In3d+oMFidu5d+ez/GY0cx/B/yNv4w+dLafp5sPN5/1KuNyErlj2TysHg9hypyO1Tb24OehsKKWWz/dyLTBkVw0NgalFJ/teQKxFPDYaa8TGpzQ1K4PGh0biN3uxgCvc7jhrGvZn1vMrZ9v56fMUu6b1p9AF857CPFx4/qJvfnfkj3cdFofly6b0ZwJ8cGt+r60BbPRQPjo8zhnRTB9o/7HGo/v6B2xmKzCoTz2WyjlVj+SbON5Iu4kThtyrUt1jo4NZHRsYIvlzh7cuq64Y+VKCyIMWCkim4G1wA9KqUUicr2IXO8ssxDYB+wB3gBudGXns4Y5Zhms3lvItMERLs+46E4OJMXNGSUs2JKF0SCtOhnGYjIwIiaAtfuLqKqzsiO7jJE9XWuJDY8OJ9w2h7G19/BkyClcHD8HN6MbX5YmUFV3Bg/0Po+7ekxlgGcE8435BPd8kbxfX4IGrYhF27IZ959feXnZnta9cK1V6quLmbD2RibVl/DT6W8elhwaGhU+ig8mPouvspHg/ynp6xcdXPfc4mRW7Sk8+Pf6Zdn/sbduDeEVkxgfPa7FOIbF+GM0CIkpRdRZ7dzwyVbSi6v434XDuXqC6+fZzDujL2v+dTo3ndbH5W06kyvHx0LYQPbWPMk/vBKoNZSxwfI7X+z7nqyKHBJVP+pG/a2jwzxmLaZupdQ+4LCJz0qpVxs8V8BNrd15kLcbj587mK82ZHLL6fGt3bxb8Pe0kBDuw4LN2RRX1TG+T3CrLyg2tncgz/+azNJd+djsilGxriUIEeGsQeG89Vs1957/X8729yCntIZP0vy4cdLfmX2Ko+/6UmBPxu/8/uk/mFzxBOq7bNS0/1JeL/xj/hbKa6w890syF42JaXU/sHZkZTX1zH1lCZ4edzPTs4Csvs8wqedJLW7XM2IUT53yHurDy4hZdDk1Pm/r2p1pAAAgAElEQVTh3n8m65xdTrllNVTX2ZjS/wIu2ZhIcsCFLsXj7WZiUJQfy5Py6RHoya6ccl69ZGSru4lEhLAuPOEhzNedRbef6vzfDFI++4305NW8fM1UPtnvwzK2u3xSXWfW4TcMmjsmhs+vP4m4EO+ODqXDzBkZzY7sMrJLa/jbUfSljukViFKOuewWk4GxvVy/GNllJ8ViMAi3f7qRbzdl8tCC7dgVzG40sNgn+iSKhr7FS9ZZvLb/G/6x8DI+S9xPeY2VJ+cMoc5mZ+HWnCb3YbXZ2ZJRQllNfatf24nuhV+TSDW9xW4PK2tNkxk/9SKXtx0YN5wbeIBkj95cuPIubvpkCnnlKxjQI43eoS+xOHkrEjaI90pup0ewr8v1njUwnC0Zpdw1fwv9I3w5c+DRDTJ3J94BofxaOQhD6CAKymsxCC51t3V2HZ4gNDh/dA8uO6knd5+dwPg+re9PHRMbSLC3hcySasb1DmrV5UCi/D14/NzB7Mwu57ZPN7Fwaw43ToqjV7DXYWUn9w/nKesFZMZcwM/F23l15wOM6OnDeSOjCfA0szWz5LBtlFJc98F6Zr64ivGPL2HxjtxWv74TlbLb+T79eQy+O/n7yL/z7M3vYG7FBeYMBiEyIpJHPB9kmk88G6uzqY/5jHTvlynwTWXLzvcpqaqnqs5GlH/z5x81NmPon/3g/zet/wk1Nb05IT5u2BUUVtaSX1FHoJcFYze4+kCnuljficrX3cxDswYd9fYmo4H7pg3gndUp3D99QKu3P3dENNOHRLInrwKDAfqFNT0DalCUL7FBnuzOn83sfn35MvUFAuz/wlr3E33DfNiVU37YNot35rFkVx4Xj41ha2Ypf/twPS9fPIIzBx7dzJUTyX++nkulx05Gek/j8kGHT0V2xcBIP75ILOP9G77D/MP3rN/8MbOGhvDKH+F4TZpDZkk1ANEBrieI6ABPVv7zNNKKqjg5rn0HiDurA93CeWW1FFTUdovuJdAtiG7jnOFRfHvTePqEHl1XncVkYECkLwnhvs0eEYoIF4yOYe3+It5dFMWY4iGsNZTyz+V30i/Mm6SccuyNTudduDUbf08zD84cyMfXjmNwlB83f7yBpbvzjirO7qqgopYr31nLx2vSDi4zmXoyptiXm4bfedT1Doj0pbLORmpRFSsKI9jucT2nz3iBNM+xZJbUHEwQUf6tu7dIdICnTg4NhDjv6ZBfUUthRS1B3l2/ewl0gtBa6crxsYzt5ejSunrG89w9Yh6T4qaSEO5LZZ2VrNLqg2VtdsWSXXlMTgjFZDTg7WbivavG0DfMh+s/WH9wwFSDeZ9tYunuPD5e+jCffXMLADbzVfxWcB9DYlqe/ticARGOsYWtmaVsSCtmuPNco6gADzKKq8ksdvy9Iv277oBxZxDqbEHkl9VSUFHXbVoQuotJaxV3s5FPr3NMhxQRTuYqsNvJXnML13pmsT9/1MHLj6cXVVFaXc8pUQZ++v0pfqrNprimmIEBe+lVP4g7v3Dj59snnnDTm/fmV7Aru/zgbWfX7i9if8ofTOzzERvM1fyaCxdY61iXUsTQaD/cTEf//vQN88FsFD5dm0ZxVT3j+zgmMEQHeLI5vYSM4mrczYZuMaDakQ50MeVXdK8uJp0gtFY7rAtKhGJLPV/1SGbjqpmE+L5Cv7ARrN2znpuM3zBz2Y/8X2gQW/1DifSO4HdbCSXBv1FfWsbCrX05d0R00zvqhlbvKeDSt9disyvcTAYuHBVF2f7HsPbewg6EqTX9WZJzGcW1jpMnj/XS9haTgZPiglmRlA/AKfEhAMQEerBwazbJeeXEBnnpgeZj5G424uNuIrWwkqo6m04QmnaQCH1mvcy4/57PxtDdnPfTFZgUWAW+8MpGxUzmnkl34RU1AoMYqLXW8Pnuz3nl1yJ2/fYVhI6H6JEd/SraxaMLd9IjwIMnZg/hi7X7Cdh+K19GFzLI7smTZ71GcmkUn72byP99u416m2JywrHfQezScT1ZkZTPtCERB3+44kK8sdkVvyUXMK2dz87trkJ93NiZ7ZioEdxNxiB0gtDahMVsYr39Jv5qSKWX+/dkVOdRX+nHQ3INH19yGw3nRbmZ3Ll04GVU5+1m0tK/8t3nz7Er8t94hJzMdRN7H1OXSmeWXlTF9qwy/jU1gbG9Ahm75X6o38jQkCsZf+aTmI0WIkLt9Aj0YMGWbAK9LG1yfbIzBoSx+I6JxIX8OXW54XlHTU1p1lovxMeNP/Y5xtXC/brHmI4epNbaTHSABxtq+3P+BV9zxxWrWFZ/D+aw5s/6PXd0LFfb7+Bxf09Wlj3JO4tXce3767E1vrFBN7Ei2dHNM6V/GOtXPsbOHZ/BqXcxaepzmJ1XSzUZDTx+7hB6h3jx9HlD2mwufZ9Q70O6keJCdYJoa6E+fyaF3t3kxF+dILQ2Ex3gcXDapM2u2JtfQd+w5r8owd5uPHTpTIbZzifVIkyKe4UVSXm8tLR7XtcpKaccL4uRAK8a7trzKfdHxqAm3n1YufF9glly5yQmJxy/M5S93UwkhPvg72nmlHa+2F13dWAmk9EgRHThy4g0pBOE1maiAzzJLq3BarOTWlhJndVOfDMn3R1wWr9QXr72fq4JHsMv5iqu7r2A5xYnsS2ztJ2ibj/JeRX0CfPhhc0vU2Q08NDp/0OMHded9t3NE1h/3xn6JlBt5GTnDDGbXXWbe7jrBKG1megAD2x2RU5ZDUm5FUDzZ2U3dv2Zr9AXM8tMvxHjUcKTP+0+nqF2iKTcCvr47+PL5C+5IGEu/XtM6NB4LCZDt7gcRGdxYIaYq5/5rkAPUmtt5sD5DxnF1STnOmZzuHpmt9nsxgMnP0TmN38jOmIZ05P8Wb23oNucrVtaXU9BRTX51c/ibVLcMOT6ljfSuhSz0cCKf5yGl1v3mWShE4TWZqKc1/PJKK4mKa+C6ACPVt0MZnD8dAYPmItKfIeR3qfw2vJ93SZB5JTWAIoeAeOYHuiHn3vz90DWuq6YoNZdsqSz0wlCazOR/u4YDcL+ggqSc8vpexRNbXXqXbyV/RvRXhv4dnMQ6UVV9Ajs+l+67NJqwMhfRz7CKBfuHKZpnYEeg9DajJvJSJ8Qbzanl7Ivv5L4I8xgao74hLE7fiK/238HQzULt7Z459ouIXHjA5zn9yrh3vorp3Ud+tOqtamBkb6s3FNAnc3OyKM8yevqwVdTba1iRPQvLNre9E2IOhulFN9uymTWS6u47O21zhaDQ05RMp9XryDXL41Qv+4zgKl1fzpBaG1qQOSfdyYbF+f6ne0aSghMYKzBhwq3lexIz6O8k9+JrqbexlXvruO2TzdRXlPPiqR8nv0lCYB6ez3/XHgFCkVNycVYTrALE2pdm8sJQkSMIrJRRBY0se4KEckXkU3OxzVtG6bWVfx1eBQjewYwdXA4vu7mo67n/MFXkW0yYPXcy4a0w+9U15k8sWgXS3fn8+8ZA1g8byIXjY3h201ZlNfU89TCa9lgK2N6ZX+qfU7u6FA1rVVa04K4Ddh5hPWfKaWGOR9vHmNcWhcV5O3GlzeczMsXH9vF904bcjnTes1E7L4kduL7RqQVVvHe6hQuGRfDleN7YTAIfxkQhsFaxdIFd/JJ4XouUz6sqb+p21yfRztxuJQgRCQamAboH36tXZgNZh4fegMvmH6mMG1HR4fTrI/XpiEi3HxaPJX1lXz88zx2rpzJZrdrmbHtPV4wxfL3uT+RWVZPhE4QWhfj6jTX54C7gCONsM0WkVOBJGCeUiq9cQERuQ64DiAmJqaVoWonHIOJfmo564ptwF87OprD1FptfJGYzpR+QSSVreFfP95LaW0pIw1mfMwzyAs/jTsuupyqehul1fW6BaF1OS22IERkOpCnlFp/hGLfA7FKqSHAYuC9pgoppV5XSo1SSo0KCQk5qoC1E4hPOA9ExLI8IInSyqqOjuYwP23PpbCylpN5lJuW3EyEVwQfnf0h7165gRUxt7CwrBeIOE+Sg3B9zSOti3Gli2k8MFNEUoBPgcki8mHDAkqpQqVUrfO/bwAnxt1ftONufPBk8swGfv39tY4O5TAf/ZFKr8B6XiONsW5hfHD2BwwJHQpAfJg3KQWOCxbmlDkThG5BaF1MiwlCKXWPUipaKRULzAWWKKUuaVhGRBrekmomRx7M1jSXnT72Njztdpanfd3RoRxiT14Fa/YXcd6Ywbw5/WOemvU57qY/E0B8qA9WuyK1sFK3ILQu66gvtSEiDwGJSqnvgFtFZCZgBYqAK9omPO1EFxcWQb8Kf/7wLqSqMh9Pr87RNfnxmjTOcfuFC6OCCAgad9j6Axcp3JNXQXpRNSIQ6e/R3mFq2jFp1YlySqllSqnpzuf3O5PDgVbGQKXUUKXUaUqpXccjWO3EIyJ4yBlYEXZsfLujwwEcJ8b9smETm2J+5oPEh5osExfijYjjHhBpRVWE+7rjrk+S07oYfSa11ukFRpzDh+l1jNy3uqNDAeCHLdkM9viYQpORk4Zf3WQZD4uR6AAPZ4Ko7BYXHNROPDpBaJ3egEh/fqobD/uWYy85bPZ0u5u/bh/Z/vuIFzdG9Tu32XJ9QrxJzi0nraiKGJ0gtC5IJwit0+sX7st8+0mc13swb++Z36GxpBZWovK/YI+bkYtiZyDS/B3Z4sN82JVTTm5ZrU4QWpekE4TW6fUL8yHDHkWZJYLvMpailOqwWOavz8Db7w887YqpY+84YtlBUX4Hn4/W94DQuiCdILROz8/TTM8gT9yrR7G/dD+79i/ukDiUUizbuIsnS/bxYvAEPN2OfOnuMweGHXw+ppdOEFrXo+8op3UJk/qGsHBDGKZeild+eZrRQ/ty6bie7RpDUm4F/ct+I9BsJXDUDS2WdzMZmX/9SVjtCqOh+a4oTeusdAtC6xLOGBBOfm0wlsoYlhgr+b9vtrA9q7RdY/hlRw4StIKvQ3pA+BCXthkVG8i43kd3XwxN62g6QWhdwvg+Qdw+JZ4Ij/O5dvB1eLsZeW91SrvG8PPOLBYH1LE5sj8cYXBa07oL3cWkdQkiwu1T+nI7fWHV/4gPWsPDyeeilDriTKK2kldew/bCTXh625g48sbjvj9N6wx0C0Lrckpyt1Jm+5Gi0mL25le0yz7X7i8i2GcdZjEzNmJsu+xT0zqaThBal7MhagCPBnox2Gcxa/cXt8s+1+zJx99nA2MNXnia9TkN2olBJwity5kw/Dp87Aofv02sT22fBLE2NROrRDI5fla77E/TOgOdILQux2Lx4hT3cPZ4lrM1JfO476+4so7duYpze7/KeWP/ftz3p2mdhU4QWpd0Wq+zKTEaCKxdSEFFbcsbHIO1KUWca1zKRL/c47ofTetsdILQuqTxQ6/EpBSRHtvYcJy7mdbvyWRj74Ws3PfMcd2PpnU2OkFoXZKPRyCL3YdyT/k+ElMKj+u+MlIXUmAyEhU27LjuR9M6G50gtC4rqP9MQqSUnJ2/H7d9VNVZqa37A4DR/c87bvvRtM5IJwity6rtfSqXxwxmnW0T2aXVx2Ufm9JKqPfIIsImhAcnHJd9aFpnpROE1mW5+USQ5xtAiXc2P28/PgPI6/bmkuFeyxD3sJYLa1o3oxOE1qWdEj0Oi9c+Fm1KOi715+9dxyVlZczsOeW41K9pnZnLCUJEjCKyUUQWNLHOTUQ+E5E9IrJGRGLbMkhNa85Ykx92sWIr/J7MkrbtZrLa7HjkbOSq0nJOHXRxm9ataV1Ba1oQtwE7m1l3NVCslOoDPAs8cayBaZorRvW/AAF2eVhZsDmrTevekV1GsHkHWZ6h4BvVpnVrWlfgUoIQkWhgGvBmM0VmAe85n88HTpf2uMSmdsLz8wrhnD5/xd8rlhXJ+W1a99r9RfwYmsPdYYH68t7aCcnVFsRzwF2AvZn1UUA6gFLKCpQCh90lRUSuE5FEEUnMz2/bL7N24npo8A3cbakjOTWdWqutzepNTM1lr5uR4QnntlmdmtaVtJggRGQ6kKeUWn+kYk0sO+zO8kqp15VSo5RSo0JCQloRpqYdQdFeJmf8lwS1ja0ZbXOXOaUUiTlbQWwMjRjdJnVqWlfjSgtiPDBTRFKAT4HJIvJhozIZQA8AETEBfkBRG8apac0qC47npJ7RWAJ+Z1tm2ySIzJJq4lgEwJBg124vqmndTYsJQil1j1IqWikVC8wFliilLmlU7DvgcufzOc4yh7UgNO148PUOI0oZqfPIY0d2WZvUuT61mBq3IkKVkWDP4DapU9O6mqO+5aiIPAQkKqW+A94CPhCRPThaDnPbKD5Nc8lQz0h+U2mUZLXNdZk2pBaTXHIVb/w1vk3q07SuqFUJQim1DFjmfH5/g+U1gL5QjdZhhoeN4LvUDPyLV2O1TcJkPLZzQDemlzA0rC/jo8e1UYSa1vXoM6m1bmFI7zMBCHDbRlpR1THVZbMr3AoWc3b1tZSm/dEW4Wlal6QThNYt9I46iTvKahlXW0ZyXsUx1ZVaWImX5xae8ocyi0cbRahpXY9OEFq3YDKaudR3IJNs6STnlh9TXbtzyhH3bLztiqiwwW0UoaZ1PTpBaN1GecRAUrxL2JtzbAPVu3LKKXMrp6/BE4Por4h24tKffq3bWN5jEHeF+bO1MO2Y6tmblU+6RdHfW19/STux6QShdRsDw0cCkFGVjM1+9KfhlOX/QbXBQL9g3b2kndh0gtC6jV5+vbBgYLDb8qOeyVRTbyOiOIflqRmc0U/P3NZObDpBaN2GyWAiTlmodis+6oHqPXkV9JV0fMUN79CBbRyhpnUtOkFo3UqfuLPZbzGQdAwJIjVgL5+F9gCD/npoJzb9DdC6lb8NvRrvotuOugWRnFfOr76wLii8jSPTtK5HJwitW+lpU3xa9wwBmUuPavvdOcWUmWvpE3dmG0emaV2PThBat2L3CGSdezZVdX9Qb2vu/lbN21+4C0QR5x93HKLTtK5FJwitWzG4+/JKQAC5PinszmldN1Ot1UZY3RIAeovb8QhP07oUnSC0bifO6E2JWzWbM0patV1KQRXp4o07RnpF6qu4appOEFq3k+AdTYYZtuzPatV2yXnlpBdP550py7BYPI9TdJrWdegEoXU7fYMHUGcQcrJXtmq75NwKhhj20cdX3wxR00AnCK0bio86CQB79XYqaq0ub7cvO4+Ani+wasW/jldomtal6AShdTvxPU9jZVoOE6rq2JpR6vJ2JYVr2ODuRrV3yHGMTtO6Dp0gtG7HZHbHKzCevpLh8kB1vc2OtXY7AHERo49neJrWZbSYIETEXUTWishmEdkuIg82UeYKEckXkU3OxzXHJ1xNc83iXsN4K9zMpjTXEkRqYRUWSyaiFLE9TjnO0Wla12ByoUwtMFkpVSEiZmCliPyolGp8s97PlFI3t32ImtZ6+yMHszl/JV4ZeS6V35NXjtVSRKRd8PDwP87RaVrX0GILQjkcuMmv2fnQ0zy0Ts1xJrSiqDaF8pr6Fssn51YQZatmnCng+AenaV2ES2MQImIUkU1AHvCLUmpNE8Vmi8gWEZkvIj2aqec6EUkUkcT8/PxjCFvTjqyPyRuAUe6/sS+/ssXy+/JKeLQ4mwciJh3nyDSt63ApQSilbEqpYUA0MEZEBjUq8j0Qq5QaAiwG3mumnteVUqOUUqNCQvRMEe346RE+AjNCukXYV1DRYvmK7L2YsUJwv3aITtO6hlbNYlJKlQDLgLMaLS9UStU6//sGMLJNotO0o2Q2uTMgZCj54sfevCO3IJRSlNcv48zoSNK8dBeTph3gyiymEBHxdz73AKYAuxqViWjw35nAzrYMUtOOxod/eZMxtWNJKTxygiipqme30UC22URI9Nh2ik7TOj9XWhARwFIR2QKswzEGsUBEHhKRmc4ytzqnwG4GbgWuOD7halorrH6B92tupbi46IjF0ourqHYrJcASjodnUDsFp2mdX4vTXJVSW4DhTSy/v8Hze4B72jY0TTs2Ozx9eDgyDFXyO46Gb9PSiqrwdUshzqNXu8WmaV2BPpNa67a8Qgawzc0NAzux2ZufmZ1SUEq9pZQBtUd3m1JN6650gtC6reiosbjZFUZLNnnlNc2Wyyotw618OCePuKodo9O0zk8nCK3bMposxNiN1FhKyCqpbrZccaUJn/prODl+VjtGp2mdn04QWrfW2+xPgVsduWW1zZYJLFzKZfI92G3tGJmmdX46QWjd2gi/eIbX1lBc3PyZ+/ssX/KF90IwGNsxMk3r/HSC0Lq1C+LP4Zm8AqRgb5PrlVIUmSoJVe7tHJmmdX46QWjdmjGsPwCm4qbP3cwrryTXbCfSFNyeYWlal6AThNa9BcQyMXow7xqSmly9JXUNNhGivHq3c2Ca1vm5cj8ITeu6DEbqjNFUktvk6t1pywDoFaLvIqdpjekWhNbtRRnCqJNMaqyHnwvRt6KCW4pK6NGr+TOtNe1EpROE1u2dVF+KEsXurLWHrUsoSufMYncCAsM6IDJN69x0gtC6PQmbA8DW8vRDltfZ6kiq3kEiPfH3NHdEaJrWqekEoXV7QUEDqSs8lUjPPocs35mzgXlBRpZ7BeBu1udAaFpjOkFo3V6AlxvjC8IZnLz6kOXbyhznRmxUszsiLE3r9HSC0Lo9fw8zkwwbydv0LKXVf94bYm32WiwE4e0R1YHRaVrnpROE1u0FeFpYZQpnbpgfP23/AIB6Wz1rMpbTv9qdAD3+oGlN0glC6/b8Pc3sqB1JbF09P+9fBMCGvA1UKhvxVe4EeFo6OEJN65x0gtC6vQAvC+kqnIl1FtZVZZBSmsKY8DF8OPVDvq38m57BpGnN0AlC6/a8LEbMRmGgeQIWu515v94ElYUMCR5CabXSLQhNa0aLCUJE3EVkrYhsFpHtIvJgE2XcROQzEdkjImtEJPZ4BKtpR0NE8POwsMlvNg8XllJQmkbG8wnUrH4Nm13pFoSmNcOVFkQtMFkpNRQYBpwlIuMalbkaKFZK9QGeBZ5o2zA17dgEeJpJrfPnrJPv5rfUNHr4xpLfy3EHOX/dgtC0JrV4sT6llAIqnP81Ox+N7wA/C3jA+Xw+8KKIiHNbTetwAZ4Wiqvq4OSbYdhF4O5HUWa5c51uQWhaU1wagxARo4hsAvKAX5RSaxoViQLSAZRSVqAUCGrLQDXtWPh7mimpqnf8xzMQDEZKquqc63QLQtOa4lKCUErZlFLDgGhgjIgMalREmtqs8QIRuU5EEkUkMT+/+VtAalpbC/C0UFJdd8iyAwlDtyA0rWmtmsWklCoBlgFnNVqVAfQAEBET4AcUNSqDUup1pdQopdSokJCQowpY046Gv6eZ4qp6GvZ6FjtbEHoWk6Y1zZVZTCEi4u987gFMAXY1KvYdcLnz+RxgiR5/0DoTf08LdVY71fW2g8uKq+oRAV8P3YLQtKa4cke5COA9ETHiSCifK6UWiMhDQKJS6jvgLeADEdmDo+Uw97hFrGlH4UA3UnFVPZ4Wx8e+pKoOPw8zRkNTPaSaprkyi2kLMLyJ5fc3eF4DnNe2oWla2zkwEF1cWUeUv4fjeVU9/rr1oGnN0mdSayeEAy2I0ur6g8tKqur0DCZNOwKdILQTwsEWRNWfM5lKqur1DCZNOwKdILQTQsMxiAOKq+r0DCZNOwKdILQTwoEWREnloS0I3cWkac3TCUI7IVhMBrwsRkqcYxB1VjsVtVbdxaRpR6AThHbC8D9wPSY4eFa1vpKrpjVPJwjthNHwekwH/tVdTJrWPJ0gtBNGQIMWRH55LQAhPm4dGZKmdWo6QWgnDH9PM6XOlkNuWQ0AYb7uHRmSpnVqOkFoJ4yGLYjcMkcLIlS3IDStWa5ci6nd1NfXk5GRQU1NTUeHorUTd3d3oqOjMZuP/2BxkLeFkup6aq028spr8HYz4eXWqb4CmtapdKpvR0ZGBj4+PsTGxiKiL6DW3SmlKCwsJCMjg169eh33/UUHeKIUZJfUkFdWS6ivbj1o2pF0qi6mmpoagoKCdHI4QYgIQUFB7dZijA5wXKQvvbiK3LIa3b2kaS3oVAkC0MnhBNOef+8egZ4ApBdVk1FcTYSfR7vtW9O6ok6XIDTteAn3dcdkELZmlpJTVkO/cJ+ODknTOjWdIBrJyMhg1qxZxMfHExcXx2233UZdXV2TZbOyspgzZ06LdU6dOpWSkpKjiueBBx7g6aefbnJ5VFQUw4YNY9iwYdx9990ATJo0icTExKPaV3dnNAg9Aj35fnMWAP0jfDs4Ik3r3HSCaEApxbnnnss555xDcnIySUlJVFRUcO+99x5W1mq1EhkZyfz581usd+HChfj7+7d5vPPmzWPTpk1s2rSJxx9/vM3r747G9wmiotYKwACdIDTtiDrVLKaGHvx+Ozuyytq0zgGRvvx7xsBm1y9ZsgR3d3euvPJKAIxGI88++yy9evXiwQcf5PPPP+eHH36gpqaGyspK3n77baZPn862bduoqqriiiuuYNeuXfTv35+UlBReeuklRo0aRWxsLImJiVRUVHD22WczYcIEVq9eTVRUFN9++y0eHh688cYbvP7669TV1dGnTx8++OADPD09j+n1ent7U1FRAcD8+fNZsGAB7777LrNmzWL27NlcdtllvPbaa6xYsYKPPvromPbVVUzpH8aHf6QRH+qtz6LWtBboFsT/t3fv0VFV9wLHvz9iYryCEqBgBCkE4SIQVkh4qICAFFPUgsRL8bGAAOpC0gta9S5bRYtWiheRZYuG2srLVzAX44uiFxdygSqvvAmURzAsEIpIBSKhkpDf/eOcxMlwkkxgyEzo77NWVib77HP275zZmT37PPb2UVRURFJSUo20K664go4dO7Jnzx4AvvjiC5YuXcqaNWtq5HvllVeIiYmhoKCAmTNnkp2d7VnG7t27SUtLo6ioiJYtW7JixQoAUlJS2LJlC/n5+Vx33XW89tpr9cY7f/786lNMn7hR+IYAABRdSURBVHzyScD7+eqrr/LMM8+wfv165s2bxx/+8IeA123qhnT7Ea+OTyIrbWCoQzEm7IVtD6Kub/oXiqp63lXjmz5ixAhatWp1Vp4NGzYwY8YMAHr16kXv3r09y+jcuTMJCQkAJCUlUVJSAsC2bdt48sknOXbsGN999x3Jycn1xvvwww/z6KOPBrRvvtq1a8czzzzDsGHDyMrK8tyfi5WIcEvPq0IdhjFNQr09CBG5RkQ+E5EdIlIkIjM88gwVkeMikuf+PHVhwr2wevbsedYF3hMnTrB//366dOkCwOWXX+65rqoGVMall/5wWiMiIoKKCud8eGpqKgsWLKCwsJCnn346KM8G+DZ2/tsrLCykdevWHDx48LzLMcZcnAI5xVQBPKKq1wHXA2ki0sMj33pVTXB/nglqlI1k+PDhlJWVsWzZMgDOnDnDI488Qmpqar3XAwYNGsQ777wDwPbt2yksLGxQ2aWlpcTGxlJeXh606wHt2rVjx44dVFZWkpWVVZ2+efNmVq1aRW5uLi+88AJffvllUMozxlxc6m0gVPWQqua4r0uBHUD7Cx1YKIgIWVlZZGZm0rVrV7p160Z0dDSzZ8+ud91p06Zx5MgRevfuzfPPP0/v3r258sorAy772WefZcCAAYwYMYLu3bufz25UmzNnDrfffjs333wzsbGxAHz//ffcf//9LFq0iKuvvpp58+YxefLkgHtAxph/HdKQDwYR6QSsA3qp6gmf9KHACuAAcBB4VFWLPNZ/AHgAoGPHjkn79u2rsXzHjh1cd911Dd2HsHDmzBnKy8uJjo6muLiY4cOHs2vXLqKibEKa+jTl992YxiYi2aratzHKCvgitYg0x2kEHvJtHFw5wI9V9TsRuRV4D+jqvw1VfRV4FaBv374X1VfWsrIyhg0bRnl5OapKenq6NQ7GmCYtoAZCRCJxGoc3VfVd/+W+DYaq/kVEXhGRNqr6TfBCDW8tWrSwJ5iNMReVQO5iEuA1YIeqvlhLnqvcfIhIf3e7R4MZqDHGmMYVSA9iIDAeKBSRPDft10BHAFVdCPwH8KCIVACngLvUrnoaY0yTVm8DoaobgDrHZFbVBcCCYAVljDEm9GyoDWOMMZ6sgfATERFRPb5RQkJCvaOkfvDBB7XmqWuZMcaEuwY9BxFMffv2Vf+7fsLhfnjfEVDPR0VFBZdcErZDXYWVcHjfjWkqwvI5iJBYfFv9ebolw8DpP+RPuAf63Asnj8I7E2rmnbTynEPp1KkTEydO5MMPP6S8vJzMzEy6d+/OkiVL2Lp1KwsWLCA1NZVWrVqRm5tLYmIi8fHx1csOHz7M1KlT2bt3LwDp6enceOON5xyPMcZcaHaKyc+pU6dqnGJavnx59bI2bdqQk5PDgw8+6DnLG8CuXbv49NNPmTdvXo306dOnM2TIEPLz88nJyaFnz8YfrdYYYxoivHsQDf3G75v/8tbn1GO47LLLyMvL81yWkpICOMN0v/vuWc8LAjB27FgiIiLOSl+zZk31IIARERENGqfJGGNCwXoQDVA1VLfvMN3+ahsO3BhjmhprIBrJ8OHDSU9PB5yB/U6cCO50qsYYE2zWQPjxvwbx+OOPB2W7L730Ep999hnx8fEkJSVRVHTWYLfGGBNW7DZXE3L2vhsTuMa8zdV6EMYYYzxZA2GMMcaTNRDGGGM8WQNhjDHGkzUQxhhjPFkDYYwxxpM1EH6qhvvu1asXY8eOpaysrN515s+fT3R0NMePH68z37Fjx3jllVeCFWqj8R8CvaSkpMHbmD17dvADM8ZcUNZA+Kkai2nbtm1ERUWxcOHCetd5++236devH1lZWXXmq6uBOHPmzDnF2xiqjknVT6dOnRq8DWsgjGl6wnqwvkkfTzorLblTMnd1v4tTFaeY9um0s5aPvnY0d1x7B9/+81t+ufaXNZYt/uniBpU/ePBgCgoKmDlzJm3atGHGjBkAPPHEE7Rr147p06dTXFzMd999x9y5c5k9ezapqakAFBUVMWnSJE6fPk1lZSUrVqxg5syZFBcXk5CQwIgRI7jtttuYNWsWsbGx5OXlsX37dl588UUWLVoEwH333cdDDz1ESUkJI0eOZNCgQXz++ee0b9+e999/v/qDe+rUqZSVldGlSxcWLVpETEwMQ4cOpU+fPmRnZ3PkyBGWLVvG7373OwoLCxk3bhy//e1v69yv+pSUlDB+/HhOnjwJwIIFC7jxxhs5dOgQ48aN48SJE1RUVJCens7KlSurn1Dv2bMnb775ZoPeB2NMaNTbgxCRa0TkMxHZISJFIjLDI4+IyO9FZI+IFIhI4oUJt/FUVFSwatUq4uPjmTJlCkuXLgWgsrKSjIwM7r33XsDpPdx9990MHjyYnTt38vXXXwOwcOFCZsyYQV5eHlu3bqVDhw7MmTOHLl26kJeXx9y5cwHYvHkzzz33HNu3byc7O5vFixezadMmNm7cyJ/+9Cdyc3MB2L17N2lpaRQVFdGyZUtWrFgBwIQJE3j++ecpKCggPj6eWbNmVe9DVFQU69atY+rUqYwePZqXX36Zbdu2sWTJEo4ePVrnfvnyHX5kzJgxALRt25bVq1eTk5PD8uXLqxuVt956i+TkZPLy8sjPz6+ela+qMbPGwZimI5AeRAXwiKrmiEgLIFtEVqvqdp88I4Gu7s8AIN39fV7q+sZ/2SWX1bk8JjqmwT0G+OHDEJwexJQpU4iKiqJ169bk5uZy+PBh+vTpQ+vWrQHIyMggKyuLZs2akZKSQmZmJmlpadxwww0899xzHDhwgJSUFLp27epZXv/+/encuTMAGzZsYMyYMdUjwqakpLB+/XpGjRpF586dq+NKSkqipKSE48ePc+zYMYYMGQLAxIkTGTt2bPW2R40aBUB8fDw9e/YkNjYWgLi4OPbv309CQkKt++XLawj08vJyfvGLX5CXl0dERAS7du0CoF+/fkyePJny8nLuuOOO6piNMU1PvQ2Eqh4CDrmvS0VkB9Ae8G0gRgPL1BnYaaOItBSRWHfdJqW2+SDuu+8+lixZwt///ncmT54MQEFBAbt372bEiBEAnD59mri4ONLS0rjnnnsYMGAAK1euJDk5mT//+c/ExcWdtV3f4cHrGheraqhxcC4anzp1qt59qVqnWbNmNdZv1qxZ9XDlXvsViPnz59OuXTvy8/OprKwkOjoagJtuuol169axcuVKxo8fz2OPPcaECRPq2ZoxJhw16CK1iHQC+gCb/Ba1B/b7/H3ATbtojBkzho8//pgtW7aQnJwMOKeXfvOb31BSUkJJSQkHDx7kq6++Yt++fezdu5e4uDimT5/OqFGjKCgooEWLFpSWltZaxk033cR7771HWVkZJ0+eJCsri8GDB9ea/8orryQmJob169cD8Prrr1f3Js5nvwJx/PhxYmNjadasGa+//nr1RfZ9+/bRtm1b7r//fqZMmUJOTg4AkZGRlJeXNyg2Y0xoBXyRWkSaAyuAh1TVfzID8VjlrK/DIvIA8ABAx44dGxBm6EVFRTFs2DBatmxZPWNcRkYGq1atqpFvzJgxZGRkUFlZyRtvvEFkZCRXXXUVTz31FK1atWLgwIH06tWLkSNHctttNefcTkxMJDU1lf79+wPOt/s+ffrUeVvp0qVLqy9Sx8XFsXhxw06ree1XIKZNm8add95JZmYmw4YNq+4JrV27lrlz5xIZGUnz5s2rZ9F74IEH6N27N4mJiXYdwpgmIqDhvkUkEvgI+ERVX/RY/kdgraq+7f69Exha1ymmpjbcd2VlJYmJiWRmZtZ6PaEpCof9Cuf33ZhwE1bDfYuIAK8BO7waB9cHwAT3bqbrgeNN8fpDbbZv3861117L8OHDL6rG4WLdL2NMcARyimkgMB4oFJGqq7e/BjoCqOpC4C/ArcAeoAw4+wGGJqxHjx7s3bs31GEE3cW6X8aY4AjkLqYNeF9j8M2jQFowAlJVnE6L+VcQqhkNjTH1C6uhNqKjozl69Kh9aPyLUFWOHj1afYusMSa8hNVQGx06dODAgQMcOXIk1KGYRhIdHU2HDh1CHYYxxkNYNRCRkZHVTxUbY4wJrbA6xWSMMSZ8WANhjDHGkzUQxhhjPAX0JPUFKVikFNgZksIbpg3wTaiDCIDFGVxNIc6mECNYnMH276raojEKCuVF6p2N9bj4+RCRrRZn8FicwdMUYgSLM9hEZGv9uYLDTjEZY4zxZA2EMcYYT6FsIF4NYdkNYXEGl8UZPE0hRrA4g63R4gzZRWpjjDHhzU4xGWOM8WQNhDHGGG+qGtAPcA3wGbADKAJmeOTpDnwBfA886rdsEfA1sM1jvf/EeSaiCPhvn/Rf4cwxsRNI9kn/qZu2B3g8lHECI4BsoND9fbNP/rVu/jz3p20I4+wEnPKJZaFP/iQ3/j3A73FPPYYoznt9YswDKoGEUB1PYLlPeSVA3rnWz8aOkTCrm3XE2Ykwqpt1xBludTMB2OiWtxXo76aLe6z2AAVAos86E4Hd7s9E/zjOiqu+DD4bjq0qCGgB7AJ6+OVpC/QDnvPYyZuARI+dHAZ8ClxatQ33dw8gH7gU6AwUAxHuTzEQB0S5eXqEMM4+wNXu617AV37/hH3D5Hh28s/rs85m4Aa3Yq0CRoYqTr888cDeUB5PvzzzgKfOtX6GIMawqpt1xBlWdbO2OMOtbgL/W3U8cCZsW+vzepV7zK4HNrnprYC97u8Y93VMbfuuqoGfYlLVQ6qa474uxWkN2/vl+VpVtwDlHuuvA/7hsekHgTmq+n3VNtz00UCGqn6vql/itIb93Z89qrpXVU8DGW7ekMSpqrmqetDNUwREi8ilHuv7l9PYx9OTiMQCV6jqF+rUomXAHWES593A23XF3whxAtVT7/7cJ54G18/GjjEM66ZnnHXkC1XdDCTOcKibClzhvr4SqHqvRwPL1LERaOkey2Rgtar+Q1W/BVbj9HZrdU7XIESkE863k03nsr6fbsBgEdkkIv8nIv3c9PbAfp98B9y02tJDFaevO4Hcqg8912IRyRORmVLLVHmNGGdnEcl10we7ae1xjmGVcDqe4zj7n7Cxj2eVwcBhVd3t/n1e9bORYvQVDnWzrjjDqW7WFWeVcKibDwFzRWQ/8ALOKU8IwmdnlQYPtSEizYEVwEOqeqKh69cSQwxOV6gf8I6IxOE9zani3ahpqOJ0v9kgIj2B54FbfNa5V1W/EpEWbizjcb4FNXqcwCGgo6oeFZEk4D035tqOcw0hOJ4DgDJV3eazTiiOZxX/b4znXD8bMcaq8sKlbtYWZ7jVzdrirCovXOrmg8DDqrpCRH4OvAb8hNqPW0DH01eDehAiEomzg2+q6rsNWbcOB4B33e7QZpwLP23c9Gt88nXA6ULVlh6qOBGRDkAWMEFVi6tWUNWv3N+lwFs4px9CEqd7KuSoG082znnybm5+3yndQn48XXfh988ZouOJiFwCpOBcvPSNv8H1s5FjDLe66RlnGNbNWo+nK1zq5kSgaluZPmWe82env4AbCLfL9BqwQ1VfDHS9ALwH3OyW0Q3nwt43wAfAXSJyqYh0BrriXLDaAnQVkc4iEoXzZn0QqjhFpCWwEviVqv7VJ45LRKSqAYkEbge2+Sxv7Dh/JCIRbnoczvHcq6qHgFIRud6NaQLwfqjidP9uBozFOX9fFUeojic438r+pqq+pzsaXD8bO8YwrJu1xRluddMzTrfMcKqbB4Eh7uubce5MAqe+TRDH9cBx91h+AtwiIjEiEoPTo/ykzhK0jivYWvOK+SCc7kgBP9zKdSswFZjq5rkKp5U6ARxzX1/hLnsbpytZ7qZPcdOjgDdwDmgONW/FewLn28ROat69cCvOnQDFwBOhjBN4EjhJzdvf2gKX49xaWIBzgfAlICKEcd7pxpHvpv/MJ5a+bv5iYAE1byUMxfs+FNjo976G5Hi6y5ZUbcMvpgbVz8aOkTCrm3XEGVZ1s573fChhUjfd7Wa7x20TkOSmC/Cye8wK8bm7CpiMc0PFHmBSfZ/7NtSGMcYYT/YktTHGGE/WQBhjjPFkDYQxxhhP1kAYY4zxZA2EMcYYT9ZAGOMSkbUiEtRJ60WkpYhM8/l7qIh8FMwyjLlQrIEw5sJqCUyrN5cxYcgaCBP2ROS/RGS6+3q+iKxxXw8XkTdEJF1EtopIkYjMcpeNFJF3fLYxVEQ+dF/fIiJfiEiOiGS6Y+T4l+mZR0RKRGSWm14oIt3d9B+JyGo3/Y8iss99unYO0EWcQdzmuptvLiL/IyJ/E5E33SdtjQk71kCYpmAdzsia4DxZ29wd0mAQsB7naeW+QG9giIj0xhnK+HoRudxdbxyw3P3QfhL4iaom4ky08kvfwgLI842bng486qY9Daxx07OAjm7640Cxqiao6mNuWh+ckTh74MwbMfDcD40xF441EKYpyAaSxBkp83ucmbf64jQa64Gfi0gOkAv0xJmMpQL4GPiZO/DabTjj+FyP88H8VxHJwxnw7Md+5dWXp2qAtGycyW7AaawyAFT1Y+DbOvZns6oeUNVKnGEXOtWR15iQafBw38Y0NlUtF5ESYBLwOc6YNsOALjhTVT4K9FPVb0VkCRDtrrocSMOZbGWLqpa6p3NWq+rddRRZX56qORXO8MP/UENOE/nOyeC7DWPCivUgTFOxDqchWIfTa5iK8+37CpwB6Y6LSDtgpM86a3GmaryfH4Zt3ggMFJFrAUTk39zRZH0FksffBpzZxxCRW3DmugAoxZlm0pgmxxoI01Ssx5nb9wtVPQz8E1ivqvk4p5aKcCZ3rx7WWlXPAB/hNBofuWlHgFTgbREpwGkMuvsWFEgeD7NwhlLOccs7BJSqM8/BX0Vkm89FamOaBBvN1ZggEGeu5zOqWiEiNwDpqpoQ6riMOR927tOY4OiIM21qM+A0zmktY5o060EYY4zxZNcgjDHGeLIGwhhjjCdrIIwxxniyBsIYY4wnayCMMcZ4+n+EZybnirCVKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(wav, flux1, label=\"Original Flux\")\n",
    "plt.plot(wav[100:-100], eniric_res[100:-100], \"-.\", label=\"Eniric\")\n",
    "plt.plot(wav[100:-100], res_fast[100:-100], \"--\", label=\"PyAstronomy Fast\")\n",
    "plt.xlim([2.116, 2.118])\n",
    "plt.xlabel(\"wavelength\")\n",
    "plt.title(\"Resolution convolution R={}\".format(R))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(wav, flux1, label=\"Original\")\n",
    "plt.plot(wav, rot_fast, \":\", label=\"PyAstronomy Fast\")\n",
    "plt.plot(wav, rot_slow, \"--\", label=\"PyAstronomy Slow\")\n",
    "plt.plot(wav, eniric_rot, \"-.\", label=\"Eniric\")\n",
    "plt.xlabel(\"Wavelength\")\n",
    "plt.title(\"Rotational Convolution vsini={}\".format(vsini))\n",
    "plt.xlim((2.116, 2.118))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    wav[100:-100],\n",
    "    (eniric_rot[100:-100] - rot_fast[100:-100]) / eniric_rot[100:-100],\n",
    "    label=\"Eniric - PyA Fast\",\n",
    ")\n",
    "plt.plot(\n",
    "    wav[100:-100],\n",
    "    (eniric_rot[100:-100] - rot_slow[100:-100]) / eniric_rot[100:-100],\n",
    "    \"--\",\n",
    "    label=\"Eniric - PyA Slow\",\n",
    ")\n",
    "plt.xlabel(\"Wavelength\")\n",
    "plt.ylabel(\"Fractional difference\")\n",
    "plt.title(\"Rotational Convolution Differenes\")\n",
    "# plt.xlim((2.3, 2.31))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    wav[50:-50],\n",
    "    (eniric_rot[50:-50] - rot_slow[50:-50]) / eniric_rot[50:-50],\n",
    "    \"--\",\n",
    "    label=\"Eniric - PyA Slow\",\n",
    ")\n",
    "plt.xlabel(\"Wavelength\")\n",
    "plt.ylabel(\"Fractional difference\")\n",
    "plt.title(\"Rotational Convolution Differenes\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "assert np.allclose(eniric_rot[50:-50], rot_slow[50:-50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyAstronomy slow and eniric are identical (within 1e-13%) (except for edge effects). \n",
    "\n",
    "PyAstronomy Fast and eniric are different by up to 1.5%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    wav[100:-100],\n",
    "    (eniric_res[100:-100] - res_fast[100:-100]) / eniric_res[100:-100],\n",
    "    label=\"(Eniric-PyA Fast)/Eniric\",\n",
    ")\n",
    "plt.xlabel(\"Wavelength\")\n",
    "plt.ylabel(\"Fractional difference\")\n",
    "plt.title(\"Resolution Convolution Differenes, R={}\".format(R))\n",
    "# plt.xlim((2.3, 2.31))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resolution convolution is within 1.5% as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}