Lab_Lec4_unsolved.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Domain: Exploring light SDSS light curves\n",
    "In this notebook we explore several things studied in classs for the analysis of astronomical light curves. We first demonstrate how the light curve of a RR Lyrae star can be decomposed into a series of harmonic signals, using Fast Fourier Transform. We then show some examples of bootstrapping using the same Chandra date we used in Lecture 2. We then go back to the light curves and compute single-band and multi-band periodograms in order to find their periods, and apply bootstraping to find the significance of the periodic signal found. This notebook is heavily based on work by Jake Vanderplas.\n",
    "\n",
    "## Fast Fourier Transform of an RR Lyrae Light Curve\n",
    "Here we take a template for the light curve of an RR Lyrae and perform a Fast Fourier Transform (FFT) fit to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd95278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from astroML.datasets import fetch_rrlyrae_templates\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "#from astroML.plotting import setup_text_plots\n",
    "#setup_text_plots(fontsize=8, usetex=True)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Load the RR Lyrae template\n",
    "templates = fetch_rrlyrae_templates()\n",
    "x, y = templates['115r'].T\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Plot the results\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "fig.subplots_adjust(hspace=0)\n",
    "\n",
    "kvals = [1, 3, 8]\n",
    "subplots = [311, 312, 313]\n",
    "\n",
    "for (k, subplot) in zip(kvals, subplots):\n",
    "    ax = fig.add_subplot(subplot)\n",
    "\n",
    "    # Use FFT to fit a truncated Fourier series\n",
    "    y_fft = np.fft.fft(y)\n",
    "    y_fft[k + 1:-k] = 0\n",
    "    y_fit = np.fft.ifft(y_fft).real\n",
    "\n",
    "    # plot the true value and the k-term reconstruction\n",
    "    ax.plot(np.concatenate([x, 1 + x]),\n",
    "            np.concatenate([y, y]), '--k', lw=2)\n",
    "    ax.plot(np.concatenate([x, 1 + x]),\n",
    "            np.concatenate([y_fit, y_fit]), color='gray')\n",
    "\n",
    "    label = \"%i mode\" % k\n",
    "    if k > 1:\n",
    "        label += 's'\n",
    "\n",
    "    ax.text(0.02, 0.1, label, ha='left', va='bottom',\n",
    "            transform=ax.transAxes)\n",
    "\n",
    "    if subplot == subplots[-1]:\n",
    "        ax.set_xlabel('phase')\n",
    "    else:\n",
    "        ax.xaxis.set_major_formatter(plt.NullFormatter())\n",
    "\n",
    "    if subplot == subplots[1]:\n",
    "        ax.set_ylabel('amplitude')\n",
    "    ax.yaxis.set_major_formatter(plt.NullFormatter())\n",
    "\n",
    "    ax.set_xlim(0, 2)\n",
    "    ax.set_ylim(1.1, -0.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrapping\n",
    "We have discussed in the lecture the concept of bootstrapping, which consists on estimating the parameters of a population by using a single sample of that population. Here we demonstrate it using the distribution of detected photons in the Chandra ACIS data that we have seen in previous lectures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'N')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b92e780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the data first\n",
    "from astropy.io import fits\n",
    "hdul = fits.open('Data_Lecture4/acisf18344N001_evt2.fits')\n",
    "\n",
    "# Create a mask to select the desired pixel\n",
    "mask = ((hdul[1].data['ccd_id']==7) \n",
    "        & (hdul[1].data['dety']>=3961.)\n",
    "        & (hdul[1].data['dety']<3962.)\n",
    "        & (hdul[1].data['detx']>=4519.)\n",
    "        & (hdul[1].data['detx']<4920.))\n",
    "\n",
    "# Get the times of arrival of the photos for that pixel\n",
    "times = np.array(hdul[1].data['time'][mask])\n",
    "\n",
    "# Split the time into equal intervals\n",
    "t_intvls = np.linspace(np.min(times),np.max(times),300)\n",
    "\n",
    "# Count how many photos were detected in each equal time interval\n",
    "n_events = []\n",
    "for i in range(len(t_intvls[0:-1])):\n",
    "    n_events.append(len(times[(times>t_intvls[i]) & (times<t_intvls[i+1])]))\n",
    "\n",
    "#Plot the histogram\n",
    "plt.hist(n_events,alpha=0.4)\n",
    "plt.title('No. of photons detected on pixel (3961,4919) per unit time')\n",
    "plt.xlabel('No. of photons')\n",
    "plt.ylabel('N')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a sample of events, we will use bootstrapping to try to estimate parameters of the entire population, and to estimate the error in the determination of those parameters due to sampling. We do it here for the mean of the distribution, both parametric and non-parametric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a36ad4978>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAF8VJREFUeJzt3X90VPWd//HnmwCmrIF6JD1LCdmkNKEgWLBB+ILrhrXQ6FHSrd0qW/1iq6Zylq5SsdVakeNy2tq64vaAWr6tjfhtoWjFUstWpciX+oNCEIEEDsq6KLPsfsHYQhVRCe/9Y4Y0DJPMzeTm1yevxzlzmDv3M/e+82F48cln7nzG3B0REQlXv+4uQEREOpeCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCVz/7jrx0KFDvaSkpLtOL9Ixe/Yk/xw1qnvrkD5n69atb7p7YXue021BX1JSQl1dXXedXqRjKiuTf27Y0J1VSB9kZq+39zmauhERCZyCXkQkcAp6EZHAddscvYj0Dh988AGJRIJjx451dyl9Sn5+PkVFRQwYMKDDx1LQi0ibEokEBQUFlJSUYGbdXU6f4O40NjaSSCQoLS3t8PE0dSMibTp27Bhnn322Qr4LmRlnn312bL9FKehFJCuFfNeLs88V9CIigVPQi0iPl0gkqK6upqysjJEjR3LjjTfy/vvvd+iYmzZtYtKkSYwfP57Ro0ezcOHCeIptRW1tLXPnzu3Uc7RGb8aKZLD4mVfa3P/5P7wLwIiuKKaPc3c+97nPMWfOHH75y1/S1NRETU0Nt99+O9///vcjH6epqYm8vLzm7dmzZ7Nq1So++clP0tTUxJ6Ty1oESCN6EenR1q9fT35+Pl/60pcAyMvLY/HixTz00EMcPXr0tJHypZdeyobU0hRnnnkmCxYsYNKkSbz44ounHPfgwYMMGzas+ZhjxowBYPPmzUyZMoUJEyYwZcqU5v8Aamtr+exnP8tll11GaWkpS5Ys4d5772XChAlMnjyZt956C4DKykpuuukmpkyZwtixY9m8efNpP9OhQ4e4/PLLmThxIhMnTuT555+Pt9PSaEQvItHddBO8/HK8xxw/Hu67r9XdDQ0NfOpTnzrlscGDB1NcXMzevXvbPPQ777zD2LFjueuuu07bN2/ePEaNGkVlZSVVVVXMnj2b/Px8PvGJT7Bx40b69+/PunXr+OY3v8kvfvELAOrr69m2bRvHjh3j4x//OHfffTfbtm1j3rx5LF++nJtuuqn5vC+88AIbN27ky1/+MvX19aec+8Ybb2TevHlccMEFvPHGG3zmM59h9+7dkborFwp6EenR3D3jFSitPd5SXl4el19+ecZ9CxYs4Itf/CJPP/00P/vZz1ixYgUbNmzg8OHDzJ49m1dffRUz44MPPmh+zrRp0ygoKKCgoIAhQ4Zw2WWXATBu3Dh27NjR3G7WrFkAXHjhhRw5coQ//vGPp5x73bp17Nq1q3n7yJEj/OlPf6KgoCBLb+RGQS8i0bUx8u4s55xzTvOI+qQjR46wf/9+Ro4cyfbt2zlx4kTzvpbXnufn558yL59u5MiRzJkzh+uvv57CwkIaGxu54447mDZtGqtXr2bfvn1UnlypFDjjjDOa7/fr1695u1+/fhw/frx5X/p/QOnbJ06c4MUXX+RDH/pQhB7oOM3Ri0iPdtFFF3H06FGWL18OJN9Uvfnmm7nmmmsYNGgQJSUlvPzyy5w4cYL9+/dnnBPP5Ne//jXuDsCrr75KXl4eH/7whzl8+DDDhw8HkvPyufj5z38OwHPPPceQIUMYMmTIKftnzJjBkiVLmrdfjns6LI2CXkR6NDNj9erVPProo5SVlVFeXk5+fj7f/va3AZg6dSqlpaWMGzeO+fPnc95550U67iOPPMKoUaMYP348V199NT/96U/Jy8vj61//OrfddhtTp06lqakpp5rPOusspkyZwg033MCPf/zj0/b/4Ac/oK6ujnPPPZcxY8bw4IMP5nSeqOzk/2itNjB7CLgUOOjuY9toNxHYBFzh7o9lO3FFRYXri0ekp8p6eeX8qwEYsf33XVFOt9q9ezejR4/u7jJ6jcrKSu655x4qKio6fKxMfW9mW929XQePMqKvBaraamBmecDdwFPtObmIiHS+rG/GuvtGMyvJ0uyrwC+AiTHUJCLSa23ogV8v2eE5ejMbDvwd0LmTTCIikpM4Lq+8D/iGuzdlu6bVzGqAGoDi4uIYTi3SO2Sb8z9p3vTyTq5E+qI4gr4CWJkK+aHAJWZ23N2fSG/o7suAZZB8MzaGc4tEFjVsRULT4aB39+avPzGzWuDJTCEvIiLdI2vQm9kKoBIYamYJ4E5gAIC7a15epI+J+zejnjZdFeflkT1FlKtuZkU9mLtf06FqREQkdlrrRqQDNO/fNd555x2+8IUvkEgkaGpq4o477mDPnj386le/4t1332XKlCn88Ic/xMyorKxkwoQJbN26lUOHDrF8+XK+853vsHPnTq644goWLVrEvn37qKqqYtKkSWzbto3y8nKWL1/OoEGDTjnv008/zZ133sl7773HyJEj+clPfsKZZ57Jrbfeypo1a+jfvz8zZszgnnvu6aaeiUZLIIhIj/eb3/yGj370o2zfvp36+nqqqqqYO3cuW7Zsob6+nnfffZcnn3yyuf3AgQPZuHEjN9xwA9XV1SxdupT6+npqa2tpbGwEYM+ePdTU1LBjxw4GDx7M/ffff8o533zzTRYtWsS6det46aWXqKio4N577+Wtt95i9erVNDQ0sGPHDr71rW91aV/kQkEvIj3euHHjWLduHd/4xjf43e9+x5AhQ3j22WeZNGkS48aNY/369TQ0NDS3nzlzZvPzzjnnHIYNG8YZZ5zBxz72Mfbv3w/AiBEjmDp1KgBXXXUVzz333Cnn3LRpE7t27WLq1KmMHz+ehx9+mNdff53BgweTn5/Pddddx+OPP37abwE9kaZuRKTHKy8vZ+vWraxdu5bbbruNGTNmsHTpUurq6hgxYgQLFy48ZXnilssHpy8tfHI54WxLCbs706dPZ8WKFafVs3nzZn7729+ycuVKlixZwvr162P7WTuDRvQi0uMdOHCAQYMGcdVVVzF//nxeeuklAIYOHcrbb7/NY49lXUfxNG+88Ubz1wuuWLGCCy644JT9kydP5vnnn2/+FqujR4/yyiuv8Pbbb3P48GEuueQS7rvvvk5fYjgOGtGLSLt0x+WQO3fu5JZbbqFfv34MGDCABx54gCeeeIJx48ZRUlLCxIntX2Zr9OjRPPzww3zlK1+hrKyMOXPmnLK/sLCQ2tpaZs2axXvvvQfAokWLKCgooLq6mmPHjuHuLF68OJafsTNlXaa4s2iZYulqcV4hc3KZ4sfueSS2Y0LPu6YcwlymeN++fVx66aWnfZdrT9OVyxSLiEgvpqAXkT6npKSkx4/m46SgF5GsumuKty+Ls88V9CLSpvz8fBobGxX2XcjdaWxsJD8/P5bj6aobEWlTUVERiUSCQ4cOdXcpfUp+fj5FRUWxHEtBLyJtGjBgAKWlpdkbSo+lqRsRkcAp6EVEAqegFxEJnIJeRCRwCnoRkcAp6EVEApc16M3sITM7aGYZPy9sZl80sx2p2wtm9sn4yxQRkVxFGdHXAlVt7P8P4G/c/Vzgn4FlMdQlIiIxyfqBKXffaGYlbex/ocXmJiCej3KJiEgs4p6jvxb4t5iPKSIiHRDbEghmNo1k0F/QRpsaoAaguLg4rlOLiEgbYhnRm9m5wI+AandvbK2duy9z9wp3rygsLIzj1CIikkWHg97MioHHgavdPb7vahMRkVhknboxsxVAJTDUzBLAncAAAHd/EFgAnA3cb2YAx9v7fYYiItJ5olx1MyvL/uuA62KrSEREYqX16KXXW/xMODOGUX+WedPLO7kSCYmWQBARCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcFmD3sweMrODZlbfyn4zsx+Y2V4z22Fm58VfpoiI5CrKiL4WqGpj/8VAWepWAzzQ8bJERCQuWYPe3TcCb7XRpBpY7kmbgA+b2bC4ChQRkY6JY45+OLC/xXYi9ZiIiPQAcQS9ZXjMMzY0qzGzOjOrO3ToUAynFhGRbOII+gQwosV2EXAgU0N3X+buFe5eUVhYGMOpRUQkmziCfg3wv1NX30wGDrv7f8VwXBERiUH/bA3MbAVQCQw1swRwJzAAwN0fBNYClwB7gaPAlzqrWBERab+sQe/us7Lsd+AfY6tIRERipU/GiogETkEvIhK4rFM3It1l8TOvdHcJIkHQiF5EJHAKehGRwCnoRUQCp6AXEQmcgl5EJHAKehGRwCnoRUQCp6AXEQmcgl5EJHAKehGRwCnoRUQCp6AXEQmcgl5EJHAKehGRwCnoRUQCp6AXEQlcpKA3syoz22Nme83s1gz7i83sWTPbZmY7zOyS+EsVEZFcZA16M8sDlgIXA2OAWWY2Jq3Zt4BV7j4BuBK4P+5CRUQkN1FG9OcDe939NXd/H1gJVKe1cWBw6v4Q4EB8JYqISEdE+c7Y4cD+FtsJYFJam4XA02b2VeAvgE/HUp2IiHRYlKC3DI952vYsoNbd/8XM/hfwiJmNdfcTpxzIrAaoASguLs6lXhEh+henz5te3smVSG8QZeomAYxosV3E6VMz1wKrANz9RSAfGJp+IHdf5u4V7l5RWFiYW8UiItIuUYJ+C1BmZqVmNpDkm61r0tq8AVwEYGajSQb9oTgLFRGR3GQNenc/DswFngJ2k7y6psHM7jKzmalmNwPXm9l2YAVwjbunT++IiEg3iDJHj7uvBdamPbagxf1dwNR4SxMRkTjok7EiIoFT0IuIBE5BLyISOAW9iEjgFPQiIoFT0IuIBE5BLyISOAW9iEjgFPQiIoFT0IuIBE5BLyISuEhr3YhI76R16wU0ohcRCZ5G9NLloo4yRSQeGtGLiAROQS8iEjgFvYhI4BT0IiKBU9CLiAQuUtCbWZWZ7TGzvWZ2ayttvmBmu8yswcx+Fm+ZIiKSq6yXV5pZHrAUmA4kgC1mtib1heAn25QBtwFT3f0PZvaRzipYRETaJ8qI/nxgr7u/5u7vAyuB6rQ21wNL3f0PAO5+MN4yRUQkV1GCfjiwv8V2IvVYS+VAuZk9b2abzKwqrgJFRKRjonwy1jI85hmOUwZUAkXA78xsrLv/8ZQDmdUANQDFxcXtLlZERNovyog+AYxosV0EHMjQ5pfu/oG7/wewh2Twn8Ldl7l7hbtXFBYW5lqziIi0Q5Sg3wKUmVmpmQ0ErgTWpLV5ApgGYGZDSU7lvBZnoSIikpusQe/ux4G5wFPAbmCVuzeY2V1mNjPV7Cmg0cx2Ac8Ct7h7Y2cVLSIi0UVavdLd1wJr0x5b0OK+A19L3UREpAfRJ2NFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCZyCXkQkcAp6EZHAKehFRAKnoBcRCVykZYpFolj8zCvdXYKIZKARvYhI4BT0IiKBU9CLiAROQS8iErhIb8aaWRXwr0Ae8CN3/24r7T4PPApMdPe62KoUkU7VnjfS500v78RKpDNkHdGbWR6wFLgYGAPMMrMxGdoVAP8E/D7uIkVEJHdRpm7OB/a6+2vu/j6wEqjO0O6fge8Bx2KsT0REOihK0A8H9rfYTqQea2ZmE4AR7v5kjLWJiEgMogS9ZXjMm3ea9QMWAzdnPZBZjZnVmVndoUOHolcpIiI5ixL0CWBEi+0i4ECL7QJgLLDBzPYBk4E1ZlaRfiB3X+buFe5eUVhYmHvVIiISWZSg3wKUmVmpmQ0ErgTWnNzp7ofdfai7l7h7CbAJmKmrbkREeoasQe/ux4G5wFPAbmCVuzeY2V1mNrOzCxQRkY6JdB29u68F1qY9tqCVtpUdL0tEROKiT8aKiAROQS8iEjgFvYhI4BT0IiKBU9CLiAROQS8iEjgFvYhI4BT0IiKBU9CLiAROQS8iEjgFvYhI4BT0IiKBU9CLiAQu0uqV0rctfuaV7i5BRDpAI3oRkcBpRC8i7RL1N7x508s7uRKJSiN6EZHAKehFRAKnoBcRCVykoDezKjPbY2Z7zezWDPu/Zma7zGyHmf3WzP4q/lJFRCQXWYPezPKApcDFwBhglpmNSWu2Dahw93OBx4DvxV2oiIjkJsqI/nxgr7u/5u7vAyuB6pYN3P1Zdz+a2twEFMVbpoiI5CpK0A8H9rfYTqQea821wL91pCgREYlPlOvoLcNjnrGh2VVABfA3reyvAWoAiouLI5YoIiIdEWVEnwBGtNguAg6kNzKzTwO3AzPd/b1MB3L3Ze5e4e4VhYWFudQrIiLtFCXotwBlZlZqZgOBK4E1LRuY2QTghyRD/mD8ZYqISK6yBr27HwfmAk8Bu4FV7t5gZneZ2cxUs+8DZwKPmtnLZramlcOJiEgXi7TWjbuvBdamPbagxf1Px1yXdAGtSinSN+iTsSIigdPqlSLSKbTKZc+hEb2ISOAU9CIigVPQi4gETkEvIhI4Bb2ISOAU9CIigVPQi4gETtfRi0i30vX2nU8jehGRwCnoRUQCp6mbwGihMhFJpxG9iEjgFPQiIoFT0IuIBE5z9CLSK+gyzNwp6HsJvckqIrnS1I2ISOAijejNrAr4VyAP+JG7fzdt/xnAcuBTQCNwhbvvi7fUMGmkLhIvTfGcLuuI3szygKXAxcAYYJaZjUlrdi3wB3f/OLAYuDvuQkVEJDdRpm7OB/a6+2vu/j6wEqhOa1MNPJy6/xhwkZlZfGWKiEiuokzdDAf2t9hOAJNaa+Pux83sMHA28GYcRfYk+rVQJAzdOW3a1fkQJegzjcw9hzaYWQ1Qk9p828z2RDh/r/S1tncPJcD/BHPUK/ui+e93xqg4D9sr+6ITBN8PWfKhpUx98VftPV+UoE8AI1psFwEHWmmTMLP+wBDgrfQDufsyYFl7iwyNmdW5e0V319ETqC/+TH2RpH74s7j6Isoc/RagzMxKzWwgcCWwJq3NGmB26v7ngfXuftqIXkREul7WEX1qzn0u8BTJyysfcvcGM7sLqHP3NcCPgUfMbC/JkfyVnVm0iIhEF+k6endfC6xNe2xBi/vHgL+Pt7Sg9fnpqxbUF3+mvkhSP/xZLH1hmmEREQmblkAQEQmcgj5GZvaQmR00s/oM++abmZvZ0Fae22RmL6du6W929zqZ+sLMFprZf7b4OS9p5blVZrbHzPaa2a1dV3Xn6GBf7DOznak2dV1Xdfxa+/dhZl9N/X03mNn3Wnlu8K+J1ONR+qL9rwl31y2mG3AhcB5Qn/b4CJJvZr8ODG3luW93d/2d3RfAQmB+luflAf8OfAwYCGwHxnT3z9MdfZFqt6+110xvu7XSD9OAdcAZqe2P9OHXRNa+yPU1oRF9jNx9Ixk+P0By/Z+vk+FDZKFqoy+yibLkRq/Sgb4ISiv9MAf4rru/l2pzMMNT+8prIkpf5ERB38nMbCbwn+6+PUvTfDOrM7NNZvbZrqitm8w1sx2pX13PyrA/05Ibw7umtC6XrS8gOTh42sy2pj5ZHppy4K/N7Pdm9v/MbGKGNn3lNRGlLyCH14SCvhOZ2SDgdmBBtrZAsSc/AfcPwH1mNrJTi+seDwAjgfHAfwH/kqFNpOU0AhClLwCmuvt5JFeP/Uczu7CL6usq/YGzgMnALcCqDAsi9pXXRJS+gBxeEwr6zjUSKAW2m9k+kstHvGRmf5ne0N0PpP58DdgATOi6MruGu/9/d29y9xPA/yH5K3m6KEtu9HoR+6Ll6+IgsLq1dr1YAnjckzYDJ0iu75LeJvjXBNH6IqfXhIK+E7n7Tnf/iLuXuHsJyb/I89z9v1u2M7OzUl/eQuqqnKnAri4vuJOZ2bAWm38HnHZ1EtGW3Oj1ovSFmf2FmRWcvA/MyNSul3sC+FsAMysn+WZr+iJefeI1QYS+yPk10d3vPod0A1aQ/DX8A5Khfm3a/n2k3i0HKkh+WxfAFGAnyasJdqY/rzfeMvUF8Ejq59tB8h/qsFTbjwJrWzz3EuAVklda3N7dP0t39QXJq0y2p24Nvb0vWumHgcD/TYXVS8Df9uHXRNa+yPU1oU/GiogETlM3IiKBU9CLiAROQS8iEjgFvYhI4BT0IiKBU9CLiAROQS8iEjgFvYhI4P4Hosl6ZvzAHcQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd8fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bootstrapping\n",
    "n_events = np.array(n_events) # The total number of events in our sample\n",
    "M_samples=10000  # The number of bootstrap samples we want\n",
    "N_points = n_events.shape[0]  # The number of points we want to samples from the dist.\n",
    "\n",
    "# Let's sample with replacement.\n",
    "bs_np = np.random.choice(n_events, size=(M_samples, N_points), replace=True)\n",
    "\n",
    "# Calculate the mean\n",
    "sd_mean=np.mean(bs_np, axis=1)\n",
    "\n",
    "# And the standard deviation\n",
    "sd_std=np.std(bs_np, axis=1)\n",
    "\n",
    "# Plot results\n",
    "plt.hist(sd_mean, bins=30, normed=True, alpha=0.5,label=\"samples\");\n",
    "plt.axvline(n_events.mean(), 0, 1, color='r', label='Our Sample')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can do it even more explicit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a36baf908>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd8f908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M_samples=10000\n",
    "N_points = n_events.shape[0]\n",
    "bs_np = np.ones(shape=(M_samples, N_points))\n",
    "for i in range(M_samples):    \n",
    "    bs_np[i,:] = np.random.choice(n_events, size=N_points, replace=True)\n",
    "sd_mean=np.mean(bs_np, axis=1)\n",
    "sd_std=np.std(bs_np, axis=1)\n",
    "plt.hist(sd_mean, bins=30, normed=True, alpha=0.5,label=\"samples\");\n",
    "plt.axvline(n_events.mean(), 0, 1, color='r', label='Our Sample')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we do it with a parametric Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a36cc0f60>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd8f240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now parametric\n",
    "\n",
    "from scipy.stats import poisson\n",
    "M_samples=10000\n",
    "N_points = n_events.shape[0]\n",
    "bs_p = poisson.rvs(n_events.mean(),size=(M_samples, N_points))\n",
    "sd_mean_p=np.mean(bs_p, axis=1)\n",
    "sd_std_p=np.std(bs_p, axis=1)\n",
    "plt.hist(sd_mean_p, bins=30, normed=True, alpha=0.5, label=\"samples\");\n",
    "plt.axvline(n_events.mean(), 0, 1, color='r', label='Our Sample')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lomb-Scargle Periodogram\n",
    "We have seen that we can find the period of a variable light curve by constructing the Lomb-Scargle periodogram and looking for the highest peak. The periodogram is a representation of the power of the different frequencies that compose the signal. Below we create 30 noisy measurements taken at irregular times, with a period of 0.3 days, and compute the Lomb-Scargle periodogram using the python package astroML. We also compute the significance by using bootstrap. It is pretty straightforward with astroML."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jmartine/anaconda/lib/python3.6/site-packages/astroML/time_series/periodogram.py:8: UserWarning: Using slow version of lomb_scargle. Install astroML_addons to use an optimized version\n",
      "  warnings.warn(\"Using slow version of lomb_scargle. Install astroML_addons \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a36accba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from astroML.time_series import\\\n",
    "    lomb_scargle, lomb_scargle_BIC, lomb_scargle_bootstrap\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate Data\n",
    "np.random.seed(0)\n",
    "N = 30\n",
    "P = 0.3\n",
    "\n",
    "t = np.random.randint(100, size=N) + 0.4 * np.random.random(N) # Times\n",
    "y = 10 + np.sin(2 * np.pi * t / P)  # True magnitudes\n",
    "dy = 0.5 + 0.5 * np.random.random(N)  # Magnitude errors\n",
    "y_obs = np.random.normal(y, dy)       # Observed magnitudes\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Compute periodogram\n",
    "period = 10 ** np.linspace(-1, 0, 10000) # Periods where periodogram is evaluated\n",
    "omega = 2 * np.pi / period  # Angular frequency\n",
    "PS = lomb_scargle(t, y_obs, dy, omega, generalized=True) # Periodogram\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Get significance via bootstrap\n",
    "D = lomb_scargle_bootstrap(t, y_obs, dy, omega, generalized=True,\n",
    "                           N_bootstraps=1000, random_state=0)\n",
    "sig1, sig5 = np.percentile(D, [99, 95])\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Plot the results\n",
    "fig = plt.figure(figsize=(5, 3.75))\n",
    "fig.subplots_adjust(left=0.1, right=0.9, hspace=0.25)\n",
    "\n",
    "# First panel: the data\n",
    "ax = fig.add_subplot(211)\n",
    "ax.errorbar(t, y_obs, dy, fmt='.k', lw=1, ecolor='gray')\n",
    "ax.set_xlabel('time (days)')\n",
    "ax.set_ylabel('flux')\n",
    "ax.set_xlim(-5, 105)\n",
    "\n",
    "# Second panel: the periodogram & significance levels\n",
    "ax1 = fig.add_subplot(212, xscale='log')\n",
    "ax1.plot(period, PS, '-', c='black', lw=1, zorder=1)\n",
    "ax1.plot([period[0], period[-1]], [sig1, sig1], ':', c='black')\n",
    "ax1.plot([period[0], period[-1]], [sig5, sig5], ':', c='black')\n",
    "\n",
    "ax1.annotate(\"\", (0.3, 0.65), (0.3, 0.85), ha='center',\n",
    "             arrowprops=dict(arrowstyle='->'))\n",
    "\n",
    "ax1.set_xlim(period[0], period[-1])\n",
    "ax1.set_ylim(-0.05, 0.85)\n",
    "\n",
    "ax1.set_xlabel(r'period (days)')\n",
    "ax1.set_ylabel('power')\n",
    "\n",
    "# Twin axis: label BIC on the right side\n",
    "ax2 = ax1.twinx()\n",
    "ax2.set_ylim(tuple(lomb_scargle_BIC(ax1.get_ylim(), y_obs, dy)))\n",
    "ax2.set_ylabel(r'$\\Delta BIC$')\n",
    "\n",
    "ax1.xaxis.set_major_formatter(plt.FormatStrFormatter('%.1f'))\n",
    "ax1.xaxis.set_minor_formatter(plt.FormatStrFormatter('%.1f'))\n",
    "ax1.xaxis.set_major_locator(plt.LogLocator(10))\n",
    "ax1.xaxis.set_major_formatter(plt.FormatStrFormatter('%.3g'))\n",
    "\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SDSS Stripe 82 Light Curves\n",
    "We will now look at some SDSS Stripe 82 light curves. We will find their periods, fold them, and see what they have to tell us about the variable source they represent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>filter</th>\n",
       "      <th>mag</th>\n",
       "      <th>mag_err</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>51081.358382</td>\n",
       "      <td>r</td>\n",
       "      <td>17.969</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>51081.359215</td>\n",
       "      <td>i</td>\n",
       "      <td>17.845</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>51081.360049</td>\n",
       "      <td>u</td>\n",
       "      <td>19.406</td>\n",
       "      <td>0.030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>51081.360882</td>\n",
       "      <td>z</td>\n",
       "      <td>17.809</td>\n",
       "      <td>0.022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>51081.361715</td>\n",
       "      <td>g</td>\n",
       "      <td>18.251</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>51819.429492</td>\n",
       "      <td>r</td>\n",
       "      <td>17.927</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>51819.430325</td>\n",
       "      <td>i</td>\n",
       "      <td>17.860</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>51819.431159</td>\n",
       "      <td>u</td>\n",
       "      <td>19.439</td>\n",
       "      <td>0.037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>51819.431992</td>\n",
       "      <td>z</td>\n",
       "      <td>17.835</td>\n",
       "      <td>0.026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>51819.432825</td>\n",
       "      <td>g</td>\n",
       "      <td>18.209</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>52225.254160</td>\n",
       "      <td>r</td>\n",
       "      <td>18.051</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>52225.254993</td>\n",
       "      <td>i</td>\n",
       "      <td>17.940</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>52225.255827</td>\n",
       "      <td>u</td>\n",
       "      <td>19.511</td>\n",
       "      <td>0.033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>52225.256660</td>\n",
       "      <td>z</td>\n",
       "      <td>17.877</td>\n",
       "      <td>0.023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>52225.257493</td>\n",
       "      <td>g</td>\n",
       "      <td>18.348</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>52288.088581</td>\n",
       "      <td>r</td>\n",
       "      <td>17.653</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>52288.089414</td>\n",
       "      <td>i</td>\n",
       "      <td>17.630</td>\n",
       "      <td>0.009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>52288.090248</td>\n",
       "      <td>u</td>\n",
       "      <td>19.006</td>\n",
       "      <td>0.024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>52288.091081</td>\n",
       "      <td>z</td>\n",
       "      <td>17.654</td>\n",
       "      <td>0.019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>52288.091914</td>\n",
       "      <td>g</td>\n",
       "      <td>17.760</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>52551.361873</td>\n",
       "      <td>r</td>\n",
       "      <td>17.663</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>52551.362706</td>\n",
       "      <td>i</td>\n",
       "      <td>17.648</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>52551.363540</td>\n",
       "      <td>u</td>\n",
       "      <td>19.014</td>\n",
       "      <td>0.026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>52551.364373</td>\n",
       "      <td>z</td>\n",
       "      <td>17.631</td>\n",
       "      <td>0.019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>52551.365206</td>\n",
       "      <td>g</td>\n",
       "      <td>17.760</td>\n",
       "      <td>0.005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>52558.394748</td>\n",
       "      <td>r</td>\n",
       "      <td>18.188</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>52558.395581</td>\n",
       "      <td>i</td>\n",
       "      <td>18.079</td>\n",
       "      <td>0.009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>52558.396415</td>\n",
       "      <td>u</td>\n",
       "      <td>19.626</td>\n",
       "      <td>0.033</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>52558.397248</td>\n",
       "      <td>z</td>\n",
       "      <td>18.058</td>\n",
       "      <td>0.022</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>52558.398081</td>\n",
       "      <td>g</td>\n",
       "      <td>18.470</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>287</th>\n",
       "      <td>54362.403012</td>\n",
       "      <td>z</td>\n",
       "      <td>17.700</td>\n",
       "      <td>0.027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>288</th>\n",
       "      <td>54362.403846</td>\n",
       "      <td>g</td>\n",
       "      <td>17.963</td>\n",
       "      <td>0.019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>289</th>\n",
       "      <td>54376.395597</td>\n",
       "      <td>r</td>\n",
       "      <td>18.025</td>\n",
       "      <td>0.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>290</th>\n",
       "      <td>54376.396431</td>\n",
       "      <td>i</td>\n",
       "      <td>17.911</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>291</th>\n",
       "      <td>54376.397264</td>\n",
       "      <td>u</td>\n",
       "      <td>19.525</td>\n",
       "      <td>0.037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>292</th>\n",
       "      <td>54376.398097</td>\n",
       "      <td>z</td>\n",
       "      <td>17.807</td>\n",
       "      <td>0.024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>293</th>\n",
       "      <td>54376.398931</td>\n",
       "      <td>g</td>\n",
       "      <td>18.340</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>294</th>\n",
       "      <td>54382.380777</td>\n",
       "      <td>r</td>\n",
       "      <td>18.005</td>\n",
       "      <td>0.019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>54382.381611</td>\n",
       "      <td>i</td>\n",
       "      <td>17.890</td>\n",
       "      <td>0.016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>54382.382444</td>\n",
       "      <td>u</td>\n",
       "      <td>19.478</td>\n",
       "      <td>0.043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>54382.383277</td>\n",
       "      <td>z</td>\n",
       "      <td>17.807</td>\n",
       "      <td>0.028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>54382.384111</td>\n",
       "      <td>g</td>\n",
       "      <td>18.312</td>\n",
       "      <td>0.012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299</th>\n",
       "      <td>54385.398492</td>\n",
       "      <td>r</td>\n",
       "      <td>18.016</td>\n",
       "      <td>0.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>300</th>\n",
       "      <td>54385.399325</td>\n",
       "      <td>i</td>\n",
       "      <td>17.888</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>301</th>\n",
       "      <td>54385.400158</td>\n",
       "      <td>u</td>\n",
       "      <td>19.483</td>\n",
       "      <td>0.032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>302</th>\n",
       "      <td>54385.400992</td>\n",
       "      <td>z</td>\n",
       "      <td>17.848</td>\n",
       "      <td>0.020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>303</th>\n",
       "      <td>54385.401825</td>\n",
       "      <td>g</td>\n",
       "      <td>18.341</td>\n",
       "      <td>0.015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>304</th>\n",
       "      <td>54390.391492</td>\n",
       "      <td>r</td>\n",
       "      <td>18.103</td>\n",
       "      <td>0.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>305</th>\n",
       "      <td>54390.392325</td>\n",
       "      <td>i</td>\n",
       "      <td>18.003</td>\n",
       "      <td>0.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>306</th>\n",
       "      <td>54390.393159</td>\n",
       "      <td>u</td>\n",
       "      <td>19.514</td>\n",
       "      <td>0.044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>307</th>\n",
       "      <td>54391.399829</td>\n",
       "      <td>r</td>\n",
       "      <td>17.992</td>\n",
       "      <td>0.017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>308</th>\n",
       "      <td>54391.400662</td>\n",
       "      <td>i</td>\n",
       "      <td>17.891</td>\n",
       "      <td>0.016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>309</th>\n",
       "      <td>54391.401495</td>\n",
       "      <td>u</td>\n",
       "      <td>19.534</td>\n",
       "      <td>0.061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>310</th>\n",
       "      <td>54391.402329</td>\n",
       "      <td>z</td>\n",
       "      <td>17.807</td>\n",
       "      <td>0.040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>311</th>\n",
       "      <td>54391.403162</td>\n",
       "      <td>g</td>\n",
       "      <td>18.313</td>\n",
       "      <td>0.012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>312</th>\n",
       "      <td>54402.392171</td>\n",
       "      <td>r</td>\n",
       "      <td>18.033</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>313</th>\n",
       "      <td>54402.393004</td>\n",
       "      <td>i</td>\n",
       "      <td>17.947</td>\n",
       "      <td>0.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>314</th>\n",
       "      <td>54402.393838</td>\n",
       "      <td>u</td>\n",
       "      <td>19.439</td>\n",
       "      <td>0.076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>315</th>\n",
       "      <td>54402.394671</td>\n",
       "      <td>z</td>\n",
       "      <td>17.919</td>\n",
       "      <td>0.034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>316</th>\n",
       "      <td>54402.395504</td>\n",
       "      <td>g</td>\n",
       "      <td>18.284</td>\n",
       "      <td>0.024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>317 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             time filter     mag  mag_err\n",
       "0    51081.358382      r  17.969    0.007\n",
       "1    51081.359215      i  17.845    0.007\n",
       "2    51081.360049      u  19.406    0.030\n",
       "3    51081.360882      z  17.809    0.022\n",
       "4    51081.361715      g  18.251    0.007\n",
       "5    51819.429492      r  17.927    0.007\n",
       "6    51819.430325      i  17.860    0.008\n",
       "7    51819.431159      u  19.439    0.037\n",
       "8    51819.431992      z  17.835    0.026\n",
       "9    51819.432825      g  18.209    0.007\n",
       "10   52225.254160      r  18.051    0.007\n",
       "11   52225.254993      i  17.940    0.008\n",
       "12   52225.255827      u  19.511    0.033\n",
       "13   52225.256660      z  17.877    0.023\n",
       "14   52225.257493      g  18.348    0.007\n",
       "15   52288.088581      r  17.653    0.007\n",
       "16   52288.089414      i  17.630    0.009\n",
       "17   52288.090248      u  19.006    0.024\n",
       "18   52288.091081      z  17.654    0.019\n",
       "19   52288.091914      g  17.760    0.007\n",
       "20   52551.361873      r  17.663    0.006\n",
       "21   52551.362706      i  17.648    0.007\n",
       "22   52551.363540      u  19.014    0.026\n",
       "23   52551.364373      z  17.631    0.019\n",
       "24   52551.365206      g  17.760    0.005\n",
       "25   52558.394748      r  18.188    0.008\n",
       "26   52558.395581      i  18.079    0.009\n",
       "27   52558.396415      u  19.626    0.033\n",
       "28   52558.397248      z  18.058    0.022\n",
       "29   52558.398081      g  18.470    0.007\n",
       "..            ...    ...     ...      ...\n",
       "287  54362.403012      z  17.700    0.027\n",
       "288  54362.403846      g  17.963    0.019\n",
       "289  54376.395597      r  18.025    0.014\n",
       "290  54376.396431      i  17.911    0.018\n",
       "291  54376.397264      u  19.525    0.037\n",
       "292  54376.398097      z  17.807    0.024\n",
       "293  54376.398931      g  18.340    0.018\n",
       "294  54382.380777      r  18.005    0.019\n",
       "295  54382.381611      i  17.890    0.016\n",
       "296  54382.382444      u  19.478    0.043\n",
       "297  54382.383277      z  17.807    0.028\n",
       "298  54382.384111      g  18.312    0.012\n",
       "299  54385.398492      r  18.016    0.017\n",
       "300  54385.399325      i  17.888    0.018\n",
       "301  54385.400158      u  19.483    0.032\n",
       "302  54385.400992      z  17.848    0.020\n",
       "303  54385.401825      g  18.341    0.015\n",
       "304  54390.391492      r  18.103    0.014\n",
       "305  54390.392325      i  18.003    0.017\n",
       "306  54390.393159      u  19.514    0.044\n",
       "307  54391.399829      r  17.992    0.017\n",
       "308  54391.400662      i  17.891    0.016\n",
       "309  54391.401495      u  19.534    0.061\n",
       "310  54391.402329      z  17.807    0.040\n",
       "311  54391.403162      g  18.313    0.012\n",
       "312  54402.392171      r  18.033    0.018\n",
       "313  54402.393004      i  17.947    0.014\n",
       "314  54402.393838      u  19.439    0.076\n",
       "315  54402.394671      z  17.919    0.034\n",
       "316  54402.395504      g  18.284    0.024\n",
       "\n",
       "[317 rows x 4 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the data\n",
    "import pandas as pd\n",
    "df = pd.read_csv('Data_Lecture4/LC_1301781.dat', comment='#', delimiter=\" \",names=[\"time\",\"filter\",\"mag\",\"mag_err\"])\n",
    "df = df[df['mag'] >= 0] #Cleaning the data\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here we just create arrays representing the different columns of the table.\n",
    "#times = np.array(map(float,df.iloc[:,0].values))\n",
    "times = df.iloc[:,0].values\n",
    "#mags = np.array(map(float,df.iloc[:,2].values))\n",
    "mags = df.iloc[:,2].values\n",
    "#dmags = np.array(map(float,df.iloc[:,3].values))\n",
    "dmags = df.iloc[:,3].values\n",
    "filters = df.iloc[:,1].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the unfolded light curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3abd2278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(times[filters == 'u'],mags[filters == 'u'],marker='o',color='b',label='u')\n",
    "plt.scatter(times[filters == 'g'],mags[filters == 'g'],marker='o',color='r',label='g')\n",
    "plt.scatter(times[filters == 'r'],mags[filters == 'r'],marker='o',color='g',label='r')\n",
    "plt.scatter(times[filters == 'i'],mags[filters == 'i'],marker='o',color='orange',label='i')\n",
    "plt.scatter(times[filters == 'z'],mags[filters == 'z'],marker='o',color='purple',label='z')\n",
    "#plt.ylim(18,20.5)\n",
    "#plt.xlim(0.,1.)\n",
    "plt.title('Light Curve',size=15)\n",
    "plt.xlabel('Time (d)',size=15)\n",
    "plt.ylabel('mag',size=15)\n",
    "plt.legend(loc=4)\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's look at the r filter data only\n",
    "mags_r = mags[filters == 'r']\n",
    "times_r = times[filters == 'r']\n",
    "dmags_r = dmags[filters == 'r']\n",
    "\n",
    "mags_u = mags[filters == 'u']\n",
    "times_u = times[filters == 'u']\n",
    "dmags_u = dmags[filters == 'u']\n",
    "\n",
    "mags_z = mags[filters == 'z']\n",
    "times_z = times[filters == 'z']\n",
    "dmags_z = dmags[filters == 'z']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first use the single band periodogram to find the periods in the different bands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Period (days)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3ab37898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Single band Lomb-Scargle for band r\n",
    "from gatspy import periodic\n",
    "periods = np.linspace(0.2, 0.9, 1000)\n",
    "P = periodic.LombScargleAstroML().fit(times_r,mags_r,dmags_r).periodogram(periods)\n",
    "plt.plot(periods, P, lw=0.5)\n",
    "plt.xlabel('Period (days)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Period (days)')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bqIQoDM7KJ1rD2rIb6T7J2HzBsD2memwM//j+MwOo2fmNKkJ/G4DriOgaIhoC8G4AW/0CRHQDgM9AC/xT3k/fBvBWIrrYGHDfao6dk9Caybk5IgduIDs3m2lZUeC0adIweP76WDtCXzFDKca/+PHL7LFMde86cQW5ePQU+sycArgFWlg/D+DLzLyTiG4loptNsT8DsAnA3UT0NBFtNeeOAfgo9MSxDcCt5tg5CW2MW+laLAyDFiYrOTl+7JsvYPvBVdbNClwxxYAbumyeox1sIWAtxP2o3F70zrmqdK0m1KsUYuZ7ANyTO/Zh7++3dDn3DgB3LLSCqwnncgbEgXP6K5h75+DpGZw6Rza74dxn/u/zGc1U4exsK9g9S6nuNo2o6S8eMSIXwImJ+Uo7YpX1t53HJjDfzpa2UkuOwa5SlksjY2aMz7a6lkmS1WdTKBJl1pDrZ9lcQ8FZB07P4MEXR4MALdWDhVwjTbOsiEIfwJ5TU9g/Ot2zHJcYmbYdGLPb3lXFf9i6s6/yS4FBCpPl0shamcIXHz3UtUxCtCqTdnV47wTCXuK91w6BIS6biSf1sx4um2tlQlxORKFvMOiu9LePHBxoBx40vbNcj1blOWoJrT5Nvywi199JpUu58xGKGZnqtGl05/QjFoso9FF9oJUVW4iR9OINDZydbfd30iIweK+Q5btZr+dIiFZdPn/NWuQMuQi9dmzZNSLZFAOZUoEhN+vC6bPx9olYHKLQRx8CscSHeiGunJduGq5kR1gqDNrddLnGZpXnSIiQLbPkXIpVmsuy6V8XWCv6rNb0uYPTL89TtFZaZnkRhT5QebeismjJhYzTei1BOkB1lDHYEbNc9EoVt9lagmXXCD/94P6+yhfRFvnsmsAa89NXIvTz3jvFWCPNsuyIQh/VhXZZtCQvIF9IQgP2mz+fOP0eF0+Ilt21b7aVLom2z8xG+LP9vpaEW8ZsxoJ+6m4Rub34/ohqiEIfQFUluKuBqc/OOGgPk8EHZwFfe3KkZ7mFXLfXYyTJIOid/tqzqKhE4hIBf3X/Xhwbn1tTAp+h4zmSxNk2unnvFNlFIvpHFPqoHmnbTXD22xmTAXuYDHrDbWbGwdMzy3LdnvQO0bLTOwtpzW71fu7oJMZmWqV2o/MRsmojuJ3DumULWUt5iZYTUeijupGzbOm9kM6Y0OADiAZNJy2H3K2i7Q2ibfsNourWx/wtA9dUlk2wScPg2jJTjL9+qD97SUR/iELfYDEyYiGDtDYA3tnHwDl9dOZKX5LrVphMkmT5qbMqNFO+fB6Us+vI97WkzSpj02Dv+8RcsSszgzHfzmKA1iIRhT6qC0RN7xR47yxAoCYDoCB8FO3ctKz3WyZNvwr9oSfU1cXpyzk+JLWyS7xGfU8m5zJk3PiTn3j0lJX/xrPHcejMbOHvEdUQhT7KhXlHuRLhXvV8H0RYdmOjj0Fr+kW7Ii0FqtAf2l6y5Lfuux7hCZ1lKbfHUJKsLS1fJk69baR473Sn5qKv/uIRhT76cZMr7nEL0fpqnsfCwDDA+yleHl/5boY+wUA8oxai6RcdYwSavj62dsSazTnkee900/R7bbIS0RtR6KO6LFzKvpYMgILwMeiIXCyrIbc7BhGc1bfnDjqFuY3INcLe30lrLYGCiNywBdJM4Us/PAzAednFTAyLQxT6qKY9AuWeIwvZXIUI57mf/nIZcnvnXxlEcFa/gUJFZQnhRCCplpmBidk2njkyvuh6rmbICjvIQZQbixkzTpt0JaLpR4Jncagk9InoJiLaTUR7iehDBb+/mYieJKKUiN6V+y0zu2nZHbVWHyqmYShZ0i9Eix40vTPoaEadQ2U5OP3eQ54GZMjt9x750uR4HfPdlTk728KeU73TfVfBak5SpiQi1zx5pkJlwefwRXGJ7M7i0FPoE1ENwG0A3g7gegDvIaLrc8UOA/hdAHcWXGKOmd9o/t1c8PuqQLXgrO6FZBlaBQOnd7AShtylv26VQU/df16aeqBfl83iSbfjEDsT8VJMmgdOz+BbO08s+jrLARHiRI6yydM7ALxVAC9bv1pLqKLp3whgLzPvZ+YWgLsAvMMvwMwHmXkHgFWW0LYa+tEeio1xekAfH5+rfM9kwPQOlknzLryVGZjLwU+Xec08d3Riye/VtR5L0J525yz/mt61l6L10kyhna3OYcmsx4Gmd/TTKhVOjv4qmiGTQpT6i0EVoX85gCPe9xFzrCrWEdF2InqMiN7ZV+0GhKpaW3d6pz8XzMXwzuOzLXzlif7y2gx6qDAzHnxxFMcnqk+ERXjx5FTuwsXv4NsroM32pekXdbLcksSnL3ptG1gVq10rTogCWiuvLORXSIO2TZ2PqCL0i1bL/TT7Vcy8BcBvAfgEEV3bcQOi95mJYfvo6Ggfl14aVNXaupXgPpedvegdZsbUfHFkYitTmOlze8ZBcqFyr7HpFmaai9s7+OvPHAuvjeJ3lQ5Yui3EeF92JeH2xR1R9NqloP+Wrp5LD/ae3XfZ7NT0vb+NLWXvEtk71iKqCP0RAFd6368AcKykbAeY+Zj53A/gAQA3FJS5nZm3MPOWzZs3V730kqGXFpxmCk8ePouypGWilPUzSHtt6ffc0Un89mcfL67vgo2IA6J34HP6i7tnXpYXcb6AfkeDRL9OJEXG/jJ6J//3Yuu5WukQS+94qn7e4YCloP2iv77lzx8cZFXPK1QR+tsAXEdE1xDREIB3A6jkhUNEFxPRsPn7UgA/C2DXQiu7XOilBc+1Mzy674wtW3Z+P3LYN14VoZVlqCfFJsmFaO2D9nqQyMrF3jNPmZU9RzsbvGDrR5gW0RI6EtUrY/sRF5ZfUB0H/N77RUJkcu/oSubtXL5tw66BVvHznAvoKfSZOQVwC4BvA3gewJeZeScR3UpENwMAEf00EY0A+A0AnyGineb0HwOwnYieAXA/gI8x8+oT+t7/i5CZfCBl2pcZon25xvXKvdNMFRq14tezEB/4QXL6bGiKpfC0yLdR2YpqoEZxdGqkC4FM6eK5Kc9luf0leGOSyXI1giGavhPkeVdf/307hX9pH+jI2NrK5VOvUoiZ7wFwT+7Yh72/t0HTPvnzHgHw+kXWcdmhO1m5o1874x4bNuvPfgy5veiddsYYqpcI/QVqbwPj9OHoncUO0HwblXm1DJ7T79eQW56WO39dLNEqSa6/WtMWaHdNCrNs5rZL9Pu6T30tJe7efgQffOtrl/aiqxgxItegW0eSgBEuWXNbzWwJ6Z12qjBUqukvgNMfMLebp3fuePjAgq6Tp+rL2jkr2G/43979zILuWQULsavkYbNsmu9+Xpml4vSBQVlyFgKdYVTvIKZr2THZBXYO/ddce3HOAXms1pXQciEKfYNu772dqa70DowW148Q6EXvtLJyeqfb5tFlWCqOuNK9PIEv9zw721rQtYrbtPNYXtNnAHf36dbaDxbiFdOReye3uvTpi6VKha2WcvZYBvTjsilHb7t/75LWYZDZblcDotBHby09U9yzY/Sr+fXK+d7OVCm9AyxAyyyhF5YD4UDVfyyUc++kd4rfVZoz5KaZKjWELwUWsnIqo3dCl82FOQYsZT0HBeu9A/es+Y1l/PrL8fkl1/RXZ/ssF6LQh9OsypAqZbXrQu8d9Gcwc0vZ8jKtbobcBQgE9u47CHSkzF2g0O/w5igxYufLtVKFTevqSy4gXD1QLMXLyheU7RBwCA3uS/G+BrnC6xcMrenDy6cv/L7tP/Z/Tvg306V1z13NuYmWA1Hoo7cQ1YZc55VSdn7VQfrk4bPYdnCs6+qhlSkM1UtcNhew9B/kwNernvDYQrWp/HVKNf0cp9/OFC67cB3OzCyMVuqFflmT8tw7HPrps0ePLUk9V6uer0GktX2pJBFhar6Nu7bpJABF9V9q99xByfxWqnB6ujmYm3VBFProPYCtIRclS3QzoKtqs+2MA6NdYZluhtwCodoLg8+ymdf0F3idAq6+6DE6NP2McdH6xrJp+lgIp5+reT7LZuCTvlT0DoqvM9fK8N3nTy7+BosAMxs/fZeShKDHh0ScBytU8+EH4jEzmuni3vGg3H0f3juKP1pG54KqiEIfvakPMeSWzQxyatW+o1iHn3frbO2MUS8z5PJC/PSrcbvjsy2cWQJtJM/pL1TT7wzOKha2ee2vlSpsGKot24Dulysve/wOeocdxbM0mn5xPZtphgOnZ5bgDv1BKbYJ4Bgw3jve6pXCvuJPfnLUN9qPTjVx9/bFGex7rZrnWllnDqgFIFMotDM9OzLYZIFR6KP3SxdDbrf0uP0ETJm+3XWSkDzjhecDmJpPcbSPrJ5VNcfdJ6aw6/hkpWvuG50uDGzxjdp+ytyFoMOQi+L3lRfuzTTDhqF6h4F3qbAgTTxX3gZnmb+Ucn2sjErMY8/JKcy1umm6xX12KefCfqjGZ49O4KE9Lr+Wjchl4DPf3283VAk9meQ++tPPGppVbKdu6NUWZ2aaePLQ2UXdA9B9NKHOQX3vrsEmC4xC36AXpy8pX8uK9SMEHPXR/QQq6CByr8Njs3j6cPWdlcqW+QstBwBHz87h+MR8aR31p/5joRp3vi5l7yCfPridKaxr1IJJYykNdv1GOBeVzb9e9j5Vxf70xKGzODNTvjIrW6BKxPRS4NMP7q9cNmOGmF+YTXAWiSLjEgwqJ/U7Vo3+RN4PrVqGXu2wEDq17D61Ak1u0HbkKPRRTn34Aivr4hvv6J3qmj565NPv0Q27RggX37Na6X4MlGVat7/qkV8XTO90tFGxZpcv184Y64cSSwVkivGpB/ctqA5FYO5/EikWvmEaBrazbrX322uS5pICvSaVibk2nq+44uuV8fXvHjsU1Mdp7hzk0xdnCSCcAPMum77RXibIxaBK31yKCTJVjKRA6A86TiAKfcD2sGaa4eSk01ztclIp+2LKhFw/Godi7knvAOWJIZS5V9+GxAon9KMBSqqFPL3ga0bOkLtAod/B6RcLz3xwltA7EqmbKrWkRt2+mZ0CW0THRuj+nxU1/V5lStM/9JhSzkw3Kwt9rb2XX+3EhD+mwklbu2zK83ZSOUWcvm+/UWrxK5ZefXOpPKmUYtQKVu+DdhldE0J/Yq7dVeCJ0H7q8Dj+7zuf8o7rgZl69E7JBfrm9IHu2kMv7S2/l6iPh/aMFqYarqTpVy1oyk03U3zh0YMFdfR1tYV77+TfW5lm26Hpp4x1jZq9b7f2Wli9gNE+DN5Fdxb+2qVhcIKPS87Jo5dRv6y9ek0qVeklQNuB7u3iCeRP3Azgm8+dwDNHxsFwwVlA+I56rbzDui7uvfaSuczAPTuO47/dt2dR98lUGb0Thf6S429/cLA7lWI6+LpGrcP9i6DzumRc3BEBN7AK0r8UQrx3es7wpYZc7vo8O0YmOtMSVJQi3OU5i+uhOkrrJXe4JF8qekevIjqvlX/etlJY36hZKiBVvOCJpwyff+RgX+U7XTbDT2fE7UPTR28FoTS2pMt77se/v5lmXQ3m/jtUivH1Hcdw8MwMwMLpk10d+ho+IG0S9iXffqOYcWRsDk8dXrihtWgcjpydtQZnBnBqah6nportV1WRcbEhN3L6SwyhK7q1q8jD4XoSRPtJZ0u9hGvFWlN/uXcs9dG1Tt0nqW6aa9GSt1fUsasbV568mHXb5Kvh7yI2NZ9i17HJRUTk5q5d8BRcQC8kRBiqJ/a+WbbEmn6PibfghFLPL/s3ixCXPlttlu7Vj4p+75XFUxLmVUEv+1JgeIWmZy5a3wBgXDbhVsp5J4ciOs+f4JmBsZlWQMv2i6LnnGlmODvbtnVR3Gl47/s+iguvMei04Oe10E8zhZs+8VAhn+pDtKFGLUErDY1E4k+fmA0vunXufvz0/c8y5BNy+fXNbyuXr0fVSFYA+NZzx105VGd3xLZQ9Bxy7PR0E88dm1gwJ9pB7xRUUHEn91/LCf1U9Smke1Zs8YNVuyqyc9n03mkVTf/x/Wew59R0d1tNl8mm23n9JGpLs14TCHf8va5RM/QO2XQUvnLm8/j5a/vtzjBpUhbxKooWKf4KQ/p5kZbeD1LFHXtbV3XNXUqc10JfsfYlr6K1GL0imImFb80Uo2acicv50U4tJY9mmmHbwbGE6QTbAAAgAElEQVSgMy0EirlQwxZkBTxvN2G+85gz2PXTCZk50OLm25n1cvJpHW0PWaCm77VpmqlCDbho4kkSvXJzQl8tsabfXw7/wvbPCRFRKuxnj/pOzLUxNZ/2iPcofu9dbVRAYTuXIS2Z+AXB5Cj9wvQJu4mKlLP9xhT36lF0C8W8aHtNodKi/Pvpeyw2fV/RffqYW5cM57XQZ3DPDcilHIx2XMa5JQmVvhwZ0HKf279f7Lc828zw9OHxUl66H3TzWiha2XTTHPPL5ao1k4Eq1Mp//KdduPPxQ3huZMIzuhkKqOI1wzo7mujA6Rnc89yJQttJEVWREGG47lw2xRi/EPzR3c/guaNh1GQRpbQQMDxO36cQK2j6iuXdlRfsNnl0uzxzdaWk14rH71/yZ2a0eiLSq2jO0TueoHdav7tOYttsYZ5sPoreo0+Hyngti5upCmkn/36+3BgUKgl9IrqJiHYT0V4i+lDB728moieJKCWid+V+ey8R7TH/3rtUFa8CZpiw7t6eMsIpBpq+0fyV0DslAlE6przLSS/IxIdiNlq4W0V0rXuX31LF2Ds6jf2j04X36fR6KdfcwuVyP5q+E+hnZ1pQinF2to2njowHg3uhOd1lBQUYbVKFAsEvl3+/tUQLfTmnSnrsIpyamsfOY5OYzvmiM4B2P5p+wTvxUwoDvnCrRrPJ6qdXXylCb06/uiBt96iDyvUvwPU5Ed6KQ+06aBd0HnPKGfdcafRCmQYuyoVMrv3QO0UTobUv5eiuAcv83kKfiGoAbgPwdgDXA3gPEV2fK3YYwO8CuDN37iUAPgLgTQBuBPARIrp48dWuBhGsPTl9OMHt8+jyPWPnX1tI78iC3NNui5B5S1FmxuGx2cCGkEdZH2NoAXh8fB6npjrdBvvl9AOhX0HDdGWN9w4DN3z0XrMbWLjcZu4/kMw9Rzg4yozpRW6LYsi1mn6B985sq3tQEQDsODKBg6dnOukyLt6tqwzSx3zo98tecJbj2qsIAxFGXTX2gvsCTtEpPa/H72E9ur9fEXLPH59Es63cOSycvjbl+rRkYMj1JkOBCGDh2xeDotN9PUWM9v0o+p8s2OhFns2v7+3f32/v00yzZUwQ6FBF078RwF5m3s/MLQB3AXiHX4CZDzLzDgD5UfA2APcy8xgznwVwL4CblqDelaDz11Dv4Ap23jcdL9ZEziaJ29Kt4PTA3axMGMhSVIKavv/iKMa77ChV1se0hq0KuXug3He7rA0Cl7ouSvm2g2O4d5fzx2aEfK6sivzldpb73g/knQBa61LsOO8XT07hgd2nTJ07PY60pu8SrmUFdoU3/MfvVKpDPu+9HK8ibLqtmij3F3sSrorQrcJn+5x4cBzd6Zt+NFBNnZX/Lu306L4zdsWUZmzpV1nxyLiQ+ulPt+bx25I8emfRmn5BQ/irZRm3/ezJM1+Q+VOUDp/uGp9t2XZ+7ugkHj8wVv0mC0QVoX85gCPe9xFzrAoWc+6iwdDLx570DvRL3T86E/B2/kqhlsiSu/g6kiwLKDfw+QLQuagV18l37/qfTx8NfzPnqRIJXUR3+AKlqF5+ubK2euHEFH7/C9uD+4TpKchMfq4tpO0XJPS9KoeaPmPbwTF8e+eJ4B4+Euo05PrPuW90ulJe9jJPK1nBdMPkfBt3/vCwfZayZ7R/wxd2xUL5kb2ng7p1M+jbaxb8rnos6eQ9VkEvpUrayZ8ofUVBK2YIDP5Wuy/Q9OUcfcxMfIuIwSii/fKeVELxVr5mQX1EGcy8ftfO/Gfub2JZKKoI/aJqVB3Clc4lovcR0XYi2j46OlpwysIgxpdelAWzTiXwrZ0nUJTNOFOMZlth76npLhypJ6BKhIEILtFMi4SV1ZThOvYLJ8K0rlrDVkbLK7hPgSDwl6sdz2cKf+bBfZhppaXPeMFwPVcPDjRoIlibhfLaIlMLM1Zp+4K5jtG8RIj50Y1FE1WHn36O098xUi1ZnfSdIk2/l/dOK1WYnncUUv4aZNyAiwy5ZZP0b332cfu31vS78+koee/d+oOtS5ffc7foOkFYoe9NlJnh74kI64cSzLWzYJXpDLrhBAAAQ7XE2QJUXvHoH4X0DuApLnpy7ceQW9TfZSJoezNU6r2/pXALrYIqQn8EwJXe9ysAHKt4/UrnMvPtzLyFmbds3ry54qV7QzT1IsNm7v56AGUccvqGb81Yb+z9w5Kll2i2lrMruZdSshQ19yxYlj51ZByP7DutJyxzrJ3j/bXmUc6l+hOQe5byiU80j7/5wUGMz7ZLB9DGnNC3nLI5gWCEPIdtURS1WwX+ikUmEhFGacaoJ0nwmw+hd3xO35+Mq0bn5hOAuR8qeK1kbO8v78nnbIsMuWz/661ZKeVoktIyJausXnauoj7U7z0ETui7sSHeOwkBG4fqmGmmQZpkuVxIT+nPoXrSqekvZCnp3aPomH+4X04/U4yJWefQ4Ssmfr/x35/iYu/BpUYVob8NwHVEdA0RDQF4N4CtFa//bQBvJaKLjQH3rebYQMDMho+tZhTLcssrZh1EMt/OQESle3OKQPVn7OJ7OJ91GdT5ZWnAgZsOkE8bDHB3Tb9A89XPU1wvGYiNOqGVqtJyG4ZqHddLsxynz6ERMrOTXOElu8LXRu114QaQaPqy2vCpD3HZzLyB5rdVVSEhr6Ez7oF75upPlbJlCHof2M88uN/mRcptnBW0U7U+29teIhNJ0XP1miyqtNGzIxOYaWaVDLlSXyLgD7+kc1wlRNg4XMd0MzVKkKu3rWfu0sP1xGarZKt4LFzoF41X9hQJmayKxPHnHj5Qes3PPexct//4qzvw2P4zAMIVYtsLbFs19A4zpwBugRbWzwP4MjPvJKJbiehmACCinyaiEQC/AeAzRLTTnDsG4KPQE8c2ALeaYwOBLB+7GScB4U+1+1vA6UNrIVPzKQjaul6Wx8TnNcuEfuYNUjEad9A73mCXmrSyTk0/U3oFUqalFHmblLWBaMASkVw2for6Y+Y9N4E0leMbhpUs6fsflOxxE+KzL8+RKra7EOnJnfBbn33cDsIkMfSOabt2pkJXuQpGWMCjGQras5dQ1BN4+O4yDmkm/7pWw7fP2f36zNpttKvQR/GE282eJL9XkaM7jo4HxsgiHBmbxYmJeTvO7O5RbDT9Ya3p+2OoKA2D3MOnd/RY6EFx9UCxM4Rrf1lN5LXwD9z5JEYLvOfkmvKenz4yju0Hz+KscdoIOX23Cs64OPXyUqOSnz4z38PMr2Hma5n5T82xDzPzVvP3Nma+gpk3MvNLmfl13rl3MPOrzb+/WZ7HKIYyM2cvrYVZC4G0YAm3YaiG6WYbRCgViJrage2dZVwvs/MpVuyop3yd84O9lebL6I6uSrjMYnqniOfnoL6NROceKjVWM/C/XPtS7/xwwDmXTXeOP9H1C7F5/MW9L+LFk5JugM3zO01fMaxL7Ue/vgsAUDOGXD+ffkDvVNX0c5qnf7wXp9/OOPDlZw55ba39+/n0nZDjgneYh+X0u0wO3TzOeq8QekOotW5NsW90GgeM22umHC2n6VPCxuGapncK8unD67dyLE/vCGW6UPjzstBvfmCgfOZlwzd2HC9YhWukylF7Z2dbmGtnmDPXTnOcvk9hrhZ655wFw3kG9NKGhIf2m5yZsWG4bo1xZfQOEArrckOu07CYtTaaL6onoPBYvmOJ4CizVRRNcvlBPNtKcfNf/QCAW5k06oRWpko9IcQFdmymZe/vL61lEgv968PVQD8QGuzRfWcwOtV0nk+sqRUn9DsnazHkSl3yuXeqCgl/QAZ1Q2/vncy7p6QakDbTB4uel+276lVHPfl1L8coFvy9fOvL+hYzBztcOSHdQ6kyK4dMMeo19+AJAZuG65hpZcEKNfTTd38DWujLilyu6d+/X6rHVwA++YDeaEfJzOtdr8iQW5TCHNAywMoB1qvoeROj4PebduYGpiipy43zWuiLMCiKhvQhRtU0C5dwDGDjUA3TzRQJGb47d24rVbjz8cOBZpAqxree69z3UoSADCgJP8/XOS+wO4S+d63ipXuRpg/c/8Ipmx62nbJObws3wC29U9hKjt/+xrPHcWpqXg+4zKN3THI6/5mk8y+EcxWBJXyqT9NlSgVCP68hNWoJGjVP089l2axK7zAXr8i0pt/dGhxy+u48f3mvrx8G/mnB310oA46S7N63ixUes2jCPz51tPNHlBtyp5sp7nz8sCvnGWm71VP6mDL9TM4hEOpJgtTQb3IdT156ZlyjnPjeOyx2JXe/z5SkQelWP4HdtN1TVOSzSCC3Suw6mafp62cmNK2m785JPXqnX7fQheK8Fvq6NSsEZ0G0ppzQZ2CDcPpUnEZYMvwpszQ9M93EfFth57EJ7Do2mbtH2PklhiBfj/yxTk3fj+4teOyCiQPMeHjvaTxl9tXNONSUldFGml0MueICm2XKusnlvWLy9bfGxsIrdkc7Vfa9+AZ5LXB9Tr9z6T1UT1BLyArYVqYsrQBUj+K0vK7XJqcm5/GdXScD4V0E7b0TpupW7AY9QSgOdy+XcRM9+RWu1LbFv8tqYu+pzjQe+v7lnmEvnJiyfdIZO7utGtwkkim49wadGK9mVrz+RON/5jV9LfTdNfKKhqxEvrPzBM7OlAc/+vWzVKcIfXROaEVZb8si6v3dxBQDQ/Watc0F3jte3RWjcJOVpcZ5LfQ1R9bb/cwK0QKaYONwDbOtzG3mnBsIfuAJA/juC6cwcnYWqWL8i798KKyPcbFzGmtnMjglKpiHvDbx/T2jFeid3DOaT4kA1plDnYBhZrOfQFYuREx7ClWSF+g2Iterk7Rrv4o+M2PLn95nKRF5Luteqxg167JZrOnXiGxdpptp4HJa1XvHz78iEJovK2j/yfm2Hew+rys++QGnr6W+98x+9G/viXJ8tt0zOKus7zO441352HNyqmSFwHhg9ynMNjNzfV3o5GSxQZO9d6cY+NIPD1tNH5CEa87m4vzz9ecXHzvYacit+4bczv4lbX5yqml59K7wzpeAvSKjcpE8LuP0/bYVTV8mCF/T91fWRTTlcuC8FvrTzTTI1V0G8bHP0zswmv5sK+1q3NSfLkpWcTHfq2wHZbOU69Q4fZpIkPfTf3TfGRNsVMzn+pqLu64WKGMzbVsX3+1NsdlEpq1wfLx4QwqxedilK+fSMJhJLO+9s5B9TE9NNfWk5K1aZLLMa/oyufsYMm59UpXZZoqNw87ltB+XTSAUnD4FkW//3/7rx7HL7C2bKXbumd5984LWd9n0aaByI6w+/l/vfbEwvURYttw7ZWKuHaTV9vG1J4+WOgn471wu/UVv8/P8/aXODJ1vyg+qqydkufJQ0OrPv3vscEB7Abqf5jl9/xllBVa44i2qI3za0D2Xu69GkWdNmdDPOAxKa9QS21d8jy5/tR7pnSXAbffvtby5vLhb7nyysKwIknyWzY1DNcy1MreczPUh5b3YZ46M45kRnWGyyIdblnwivCRzZ3i9zkGad9lsZ0Ipda4KgDJNn3HBcN1mAG1nCo1cROtQPcF8O8PfPV4+gBMiS+loY2bovZPPB6S4uqdM8MypMoZYF70pxkDrQteF03/1yzYF32daeqN0QdXgLLl2PjMigEJbxXpjAwI0VZBPW604x+l75zKzpddkcsujllCOHuge+FZmGWBmnJicx85cymhBMy3ef8Bx6KFG3i02BZB+rY+JIZfhYj9Gzs5hrp0FGrx7BjmmP4dqCYSpY6Aj06gfm1Gl6/l2tFQpm2AvP7H5XezrO3SMaanQ9+w5eaXElw3tSO8sLabmU9Rr4pGiG/brO453lGN2GqkvPO54+AA2GM8Cx7uGyHt3zLeVWcIXbEzOzmVTNO9ufvqCfMdqe9ygYtigD/958kOdGajXwrQEtZqnYTFQTxK0MlXukcBsjbVCK/hCLSHYSU2gDc7d6bXSe0E/Ry1x9hT/uayGrDqXxe/6qSuCMk0zifjXrwIJ8PPfZ0A35cpv8ry9Ao8hz69ch967dN2+1vq5hw+4Ca6gPrWEgjavEpxVVEAUk7xCIZhvZ4XX1d5Hbqcqf6VbBKvdeqpzw7Ot/MEvvhoAcN/zJ3FyYt5z5/SfIbz2cCNx1KRHNQpcfp+qSfFcE7UzvbuVf0t/JSsQe12ZIVcpN/kwh+cG3js5eid67ywSM80Um4YbVvP6h6dGCss9uv8MMtOZiWATeY1Ot7BxqNYRtOXD5+0ArZX7wvD0tOM6JQeNDOqiDV4UF2j6OXpHvsu1vv9imK9IUyxhPWVlIVpGO2M0kgS/+pcPmZWHi2koS0SmzETlOP1waU1EmnLKCSU/GV1VKCMMmbUPflsmbjOA/LZTXO7f7N/VL1HFe+cfnzqKT9y3B0lCgXbmC7z8u9o4XMeMSdms6Z1AfDk7CHcan0O3Q51J9OkjLkeQvPfPPOi8U3pFozLK7MFsvYuKzi9zT1YqTBLmT4BFaYF9Q3iHps+OMlFKT0B1TxHxn8HHtZs34e2vf7n9rYzTF1rxyNgsjo3PFT6P1EPqKUF8flxLkaYvileeehWIo4X/LKLFS+wGG5kD258Wv1FLFZy3Ql8pxmwrxYahGmabGRQz9pws9lT4/oujlhskIjvQ0kxhuJ4EwSB59Sdv6GubZbG86FOegUsGfKjph3XJh98zc4emL4NfrpX/vUgYMcMKdTm3XiO8cGLKam4i3Mq0P0DsEOK905nlsdNP35WZa+ntIqtANH2pl03nYH6vJaHAqbIs9lukCuV0ZqaFs7OtjsnZCrwCLXuTSSkAaMEg3jsEx9NLDny973LnZCKCeny2jbEZ13/+6nt70EoVRqedzSXvrtjxzAUrR7lXO3Ob+uQx384KJ8ajRnjaunqf4uMe3t/dT5617htyzWfGjFbqPKxk0tNfwmsREYY8t8+8n76sVIXm/PvHD+MfvUy1o1PNMNYA7t20UmVW/a5/ybWTQOi7SaIIfoyGeEI1chNavu5FNOVy4LwV+m2l0EwV6gmhrULtOw/RWCX3TtuzspPJDWINbB3nullbzmH4k4E3qD0NWSz1nX76ocb3qQf3oZWpYMXQynkY5FcCRRSRHJc+1c4Uaol2a2ynbDtcpjonEb9uBLJeKV95YiTwfyfTDr5y69xUgalmu5RD7riXvpmlQdqZy1CaJDB1dffwA358UO7Tf5YqdUiIrB0jf67PHQPA3duP4MTEHOZamT0uy3pnrHQuhmTpHfccQDg5+Cs20RAlyAcQTr+Lpm/60yN7T+PI2GxwPJWo7oLOMt8u9uL6O2Ow9e0a9noF/WZizjkOSLv5r0qePSFNwzY8vv8fTAyBXS0UCF9HmbpjNjaDTbwDh4kUP3Hfi/jHp48F19Crb7eKDVZIMtl417Cafhehr+z99XXXNWr2fn6bWFmhXGT5cuL8FfqZNoo1aonNb1H2ggCjhRvvnVam8NCeUbQzTfdsGq6Xcm2+tR8QI6vvcRIKC1/Tl2hhH9qVzn2fnEtxdqaNrzzhqCnfR5q5UzP3vRaeOTJuEsaFcQiZ0pqHnRSVHkxl7pViLEsSWEPevlPT4c5NnuudfWbltBkZWFVgZD4APRCEB2cz8WjPHNf2oiHWS15Ux2RdoSISFJYQcvSOE/aK2e6S9IVHD5mNyp0CUPMknBYkvqYf1kuUDWccDfMFyZ8+jZL5y58CfOqBfWAGRqeb+OxD+63fuhhk8wKzmYorZrEdxqcWpZx8z/PnE7NtvOk/fbfjegkR/vCXrwPgBKm0cd1q8OylRAif39eGtx86G3DyQDgR+QqWYKie2EApgfPgc5sT+asUIKR3NKXYhdM37fvpB/fbthk2NiWfHchr+tFls0/4GkuaKb1crDlNtltWRKEhCECzrfDDA2NIM/39gnV1o/F1DoS8cJf9QqXYqckmvmQ20sg8LVhz6L05/XamMN/OcqHbshLR98rzrx5NiO2HzmrXVYjQN/WaaqKWkNb0zUSVEAXC8IlDZ+3fn3/0EKbm2yapmm5L0b5dGgaydguB76ffTwpc4TdFs2978Q1EzmgsZUXYd0tY5f9Shd6RSTL/nkKNHJg1AmTDUA1t5XIPpUrZegm9owe6MpOX1Ev/Nedp8I7794Q+ijT97taSs7MtvfJkxnQz8yJOXT968eQUzpiV5G33O4qm6MrS15xAdO8gv5L2d4/yo+KJ3AVEyImB2g+46xD65lr+K/7eC273NIGfb0nsJ0lO6PuKkvL6p/VM88ahtEO4wZKsQDsVyYf3nLb3Hp9r6RVEpjX9ekJBm/mGeN3Xo6bfFz5x3x77dytTaKYZ6kli6R3f60UgWRnlJRER5tPMdAAFEOGCdQ2AdJrl/EzsNB39KalS5cVOzLXxKZvPw7xso12RJ7gEzIw7fnDQfm8btz+/zlbbMgJ2tpnh5KTjef2VhiRmE/uBaEm//4XtaCSJ1vRTNsI0pDHue95tjdjOlF35SJIoqZt0WqGrOigtk6ohz/d3g4vCFQO0CiaYmrdKUuyMZGVjppPeqSb0QbCrJOHq/UHqa7jrh2qaExZNP3MBcM4kxMFWgb5Qn22l+D9/7ho7meT39ZWizUCYFtlvXJ2aJkngfbtOBV43QosAOsL2+ITuPz5VWLQYyis5vrthminc8+xxzDSdIdtvS/kmgWqAey/SL0OhH6587jBj1Re+LTsJhfeST6FA/dXBcL0WPKe0obO5hdcr6iqS8K9I6P/A7IfRVmwVzkwx1tVrxl/ftaHUT9ow0juLQDvTu10N1cl6KLQzxrpGEgwaSY0qfF5CWsPI2HmxbByu2/zs+VeSt9A74eTK+APE375RDJU+FHNgvPONtpLzxM/pwQwcGpvFg7tHvWu4TpspoSnITmoCrenrSVFxZ7BYnkYQG4f8nSq2zwvoAay9FsLnUWbp4/tq+xDe14cIe4bTAp2mryWxP3iE0y8bNIyQBelF7xwbn8NXnhgJ9nD91AN77f0Al0hOBv76Rg2tNLMrykwxZlqpde8T6k4oiSQJs2zOtjJc9yOb7POnWXEa5ryXTF4oPTMyge8+fxIzzRRzbZ3r/nGzcrVuhPBsV5kK+m/phRG6Q/qfAHDPcyfw6L4zNhYkn+BO2jx4Q8LpJ4SfuOIi/MaWK035TnrnhFFsfAHeysKVB+DGh+Pqw+fQkeee0Df/ZAUrxm1pbwk8C3JKGUWjyHunZdKHpEZRAmtFabiRoF7Tysp8O8Pzxyc7Nf1I7ywcaSaGXMfpp0o4fvfyLIdpNX3xtdflCY7TH67XOvzsXF4Q/dnKafraYCo8umioPqcfdkjNgbvv0qmnmyl+4G0Soq+nhc58Owuu47vHiaeNBE75nUrnPUFI73jX8WkEaZ8aGa8P5Yzdvqaf15IyT4sq0/T/uiBBlpsU9UTTlsRiWvnuyIYqKRmqej/0Cs5qpQqzrTRI7DVrM0HKfZ0HBqCFvh/U1FaMs7NtvHDCRb0yGN8xLsH5ms62Umfsg0zqnRqnxIK4a3ZeZ2o+xTd2HNdKgxEyfrwKszMM+yvJIBmY4kInAf/Tp4BGp5p49ugE/vK7e4Iy8rd8E8pMt4FboV11yQbceM0lNiOpFfrmPBHUfh9upaojh5XV9JmDsSYYMokFbfvJ5KA84zbce75310nbZv7z1BIKUmfbdjO5qdKM8ezRCXxr5wkw6/s2agm+9MPDGJ9t47H9Y8E7Viq6bPYN8T4BtCATv1+hXCTNglKMX/+kTissnhayBCPoHBmZWZoROU5//VCtU9P3lrdyX99Toa3cPUWA+fXt5PTDgS6D9PDYLB7OCX0RomnO4OcnexIPEAIszSNotpXJcOh4T3/Q+ysixVrYJ2ZJaz1n/GU79HN+1/Cs8rv1aPLq5aPIRdQ+D2tvDzEeMzqNXZmCjS4u40TzE0Uveidj7QiQEJn4g9COIZiYbVslYt1QLZgos0x5thSyK505E/iUGOkmxuK5Vua5IrIVxs54atorVYGQy3vfNNsKM63U26pRnyP2Jnn+PA0ChO/iiUNn8Wgu8M9PLeDXSdDOFGaaWVBWyss9xPsK8Dh9byKoGa8mS++wPFcWnCP3qydJ8E7cStiNp7wht5XX9JlNrI5P8YTPFrrX6tQKxbmvdHunSuHpI+P43gunoFhHvDdqhIf2aPonzcLcVT5NuZw4r4S+/zJl45GG0fQVay+XmjGkPGmyTc62nLeCDu13/L7W9AnvfOPlIIK1vvsopnc8TT9VOHB6Bv/13t1QioON14Wz9sGMnADXn3OtrGPnLvHcyDInTD/38AHsG522HUlcUWEEl6/xzKeZmRSNYTFnyG36Aoy1dl8zAV6+pu8/T96DwxnTRNPvaMLCTIXWpRFC7yg7EIv4eaF3qo4Z5u6+/coIWz88Q08E4Tt485/dbymR9WZrTYGk9fBXdXbFAN3XZBITr7Gax2mL8Pnv39Oas4iHlkfHiHPBA7vdRDvfzjDdTO07krbvoHc8t0NrfPaEfjNVHZN0J70T/t7OlB1TeXrHrghB9j1ZYza5Y+KZ5ZQO89xW03c2gVaq28yvhTXw+5Sg97skFhTIik3aSFar2uOsc6UlzybZQfPQ1HCYgkMxjNBP7Pmy5anvwrlq6B0iuomIdhPRXiL6UMHvw0T0P8zvjxPR1eb41UQ0R0RPm3+fXtrqh/BfpnhO+EItzVQHbz3rafo6Ilf8+p2h6/pXXAgiwrpGzRqpBNIRxNNFa33uRfqpdVVumUklmr502mdGxu3AnWtnaJoViEA0NH95/vSRcRwZm3O8s9BWCAXmpZuGcNmF61BLyBof8zlmfAEm7SHGK3leTfk4D5X889glNjo9kwRF0Z+KXZoK309fJqd8m4nLZjdB7t85SSjg/7+x43iw9V3G4gpLdjKzwTu5R5B+MmxyF/nHEyIcHZ9DkjgbjKQ4ED99qU/bS/jHYOv+OjUfGpBbXj/QAo/xu3+zzd53Ps0wPe9p+hvjno8AACAASURBVOwEUeBtk4V9BMjlhclUxyTurxT874JWquwYzOcr8r13ZEUm77KWkD0mEdh5d+hmqrBpuI63ve6y4H61JDSIy5izhlIOV4D5nFeS68hP6aAngbBvhqsrTdf4/Xm2leKbzx630cWhUZztHg9yfssoiL6CtiroHSKqAbgNwNsBXA/gPUR0fa7Y7wE4y8yvBvAXAP6z99s+Zn6j+ff+Jap3IXxNX7j0Ri2x1IAMwplWhnUN/eizJmRetFChiCRC0AWPAOsaCT778AE8f9xxtNIxv/bkUXtfxbC+uLL0v2h9o2MPzF759B/YPWqfR/PJYXnpMIqdK+grLloHwA2UDjdJ80C//aZX4nWvuAh1ayQ1htzA3uFp+solOSMC/vqhAwCMYEvctf17iTePGKvyPvyCIg8In3sWTZ8LtDa/TELVOf2hWoJN61wCtpOT87YvyPNqDd1NPpniQu1XhGstCSdNHQuR4AuPHkSNCN9/cRSKGXOtLHgO0XLbOU1ffMZnWymOjM3i0X1ngroBxUn75tvKbD/otHJmOLsIALDv+uv6iM9Rt1J9/7u3H3HPJJOGR+/5aGfhZCLwacCQ05dj7t2JIuLTU7qe+qZXXrLB5VTKROi7OjjaCoW0qr+XhFzf0Tsu2hzMeOdtP/DKhZNYPiBwvq0wclYrXKLpuwRyus/5e1jIfgv2lfDqoXduBLCXmfczcwvAXQDekSvzDgCfN39/BcAv0yCmrBx8q3wrlZmVLE8pg2qm6QxmVtM3nZhgvCYUrN++Pk74P372GgCwmhfQ6e9tE6rBaU4/ffXF2DTc0JRCoOl30iF5Y6cEf4gGqXJCRSYzGXySM97STTmh77+UVCmMzbTsSijxhJYfHCPPmRqt3hesmVLBAPafRyZQiRvoh97xA6NCTb+T09eaPqFe0y6oBbfoePZ1jRp+52deab/Pp1kw+dj+4NM7CnjXpx7p1PTNeZQTwGkmmUv1CvLhvae1pp+GCdfsMysv3TXcymimlWFirm13PfMzmeYFHgD8ydee1ffPU4/KeVZJvwFCjd6ndyTf0ZOHz+IbJlFhns7Mt0UrU5iYa2NsphUEGfqrPE1nhe3rr7zec+OV+M6ukxgzgWTOE60zAExz+qGy4T+3KFEE4H/97w/Z42MzLbdhCjt6VxQ+6bMvnJiy182/q3pCQTCg2NYyZTj9zKWVcJy+oXeYO6jg1UTvXA7giPd9xBwrLMPMKYAJALKD9jVE9BQRPUhEP190AyJ6HxFtJ6Lto6OjRUUqYcgT+qnZTq/uLafEkDvbyrDeCn3jU2waXhszDb2ThZr+yy4YBgBsP+Tyx+QNOSJApW+mSuHXbrjCaop+FGZChL9//FCHwSsIxLKavluRCGzQU8Z28pI+I5fIDxS/ticnmzg93bIC1TeEK84H1zge0xf6QvkUQUf4htphnt4RyiQPNqsuIjI5gfygtzy9o4Vfw7zvqlsh+leZb2WBV5frDxSk1Dg2MV/wzotqpa9RTwjNNEMtIcy3lU2NrLfgBHYdnwxy7Yvg08+qJ/OZZmriJKQdPaFPhB0j48hjXaMWGGqlnkW0jLX7IFx1iaY/Mde2aUDy5xdx+ruOT+LpI2cDhejrO44FqxPpM857x9E7r3jJegAuWaHT9Dv3IhDtWOWeZ3K+7VFKWlF47uikFrSKce/zJ60LqGHvjfcO2/bNOxiMnJ3FDw+MYbaVQrHZqMfr+xJ9rjV9/c/X7IeMEqrrrf34g+SEvHpy7xTVIj+qysocB3AVM98A4IMA7iSiCzsKMt/OzFuYecvmzZsrVKkYftCFaAANr9HbhoqYaXVq+o5vJMuRa03fcY/yQj7+rd0AgKcOn8X2gy5qVe7r85etTGFdI7E8bJ7TPzo+ZyeZmWaKA6dnQ21ROXoHKFgyG41NjH2+j7KUL93oPJhsQu+dVKnQkKv0klUMjv5x/5nyg08mz5pQJAUro6KcSMpo9KLty4TD3JmdUpba9Zr2gy6Ltu02FcynKuCz8xqlfyz/Uz6Ntv+zbORC0HSZCIGH95zGL7x2s9WgZVL1XURFS51t6glJ2l2xe6dJQvjL7+3tqOtwPbHPU6TR5zVjZcuwDYKaN312tpV1TCBO+IeNYXeH8oz9gLY1SbsRPLuM+ahRp3HX7WKlv/sOCz7qSZi4Ls0Yt5v0B0JtJUS4eEMDf3Hfi27LUI9CBIv27WxQ860wHmLX8Sl89YkRnJxsuj7nb8HJbsJoG+8dsu9TK6WyMpAYF9/luShF+HKg3rsIRgBc6X2/AsCxkjIjRFQHcBGAMdY9ogkAzPwEEe0D8BoA2xdb8SL4htxDZ2ZDTR9aa06IMNvMrNAXCkM6gFAu0gEEWusM7zfTzGwgikCnLPY0fRN+3c6aSBUHOd0JJuI2Y3z+kf04cHoGzx2dDISW0DtznpeRQIKDhHr5V597PDAUAZ3aUUjveBNITtMXLc//PVOM4ToFXkx2429Lg/jnyGTBGK7XoJix48iEFeDHJ+as+1oeYnwmEsOeDAgOnqGZ6myQ9URrUY2c+14eqXHlzWOulXWE5ks9RDXyl+HBNUtWFoQwWKyVZvZ7M1W4cP2wvqdZ/SmFgN6BtJ/SMQNCR/h2Gn+RpQw99Ae/eK0JolP2OOBWofb6Xpto4Z6imWY2k+ZcK7M2iKA9grYIn9mPeveb2U/H7HvqkPdptf+8od4qIsUpJxKP4hJPpWaaQQITFes+M1yvYeTsHL6z8ySGaklg6BaaRSgwZrd6ts+QKrvfhDgP+Lz++GzLudlmCkNZ4k0soSG35SkZDMbR8Tn80zPH8f5fuLbgCZcWVTT9bQCuI6JriGgIwLsBbM2V2QrgvebvdwH4HjMzEW02hmAQ0asAXAegMxJniVCvOaH1+UcOWu8dwHnnaHontYLL9+kFXM55ZqNle50yv/RKleqgJmRAWsOY0fQljcFw3fn2JgS0U93Rzky38KUfHunwmPAzfgKd2rl4HADAQ3tOd+QikeCsIvjHv7HjeJDPppUzWIq/fS1J8LIL1uGWX3q1vYa0jVGYOu6RKmW9Vx7df8YKhvm2wtR8Wlg/rdE7ekdWGXlNf+vTx3Dg9Iye4JMEjTqV0jsEnUPoz7/zYkc959tZwGf7wi1PZRRRGlprU/Y+MG1R84R4plwCtlaqXJCQaLLsUWUsAUJae5xuakphyGy753P6ts7mmAgWt2oznwG9457hzHQLR00E8lzL2Tbm2kZwequxvLDPi2Gbclh18u+O3vEEvPnNpw3zypW1NyjVsbIAjKbv1YvZBbBZ7x0iDDcSTM/rKOXheiiQhUrT40VPjnPtLGjftvHImTR9dsjYkD7/yEEAOrldqhSmm6n23glWVqHLZitVXl5952a7Kugdw9HfAuDbAJ4H8GVm3klEtxLRzabY5wC8lIj2QtM44tb5ZgA7iOgZaAPv+5m5WkL1BaBG5C1l9QBrePm5xW/aT+Ga11yE05egGN+7oIhWKHM3lP7ezhhDtZpenqcKG4brVqOsJwlSpWwgGeCFlZtrpTnqoNPFs5OK2HrLz3o2hdCQywDe/8UngmcH9H6r8Nqv6XlPHDozg+mmFoqSx96mFWZNgTVqWrMsckFNMzYBNK5OzIxTk/NaUy8YyNboB/1ehfoYn2vjwnUN+yzN1KXQFsFfIvMBAPtHpwPvD8FcOwtXPp7AzGu5+cunGWPbwbN4fP9Yx++B0ZtdQjEJHJQ8RmC32mLo0H9m19ayG9eQEVa+zSHfZv79dL0d5SnCxS/6taeOWoE2a2wbG4dqertKc688vVMWnGXvXdIXgGKtvsij51fNRinyHGWavnD6LhZENH227piAZgJkg5uhes3TtIG7t49gfK6NNGPcv3sUz4xMYL6dWTlxx+9uQTvT7qj/26cewenplqV3PrJ1p3V8ePHkNB7YPWptiP4mS9dcusFeTwy98ptSbHNbLTeq0Dtg5nsA3JM79mHv73kAv1Fw3lcBfHWRdawMf//QdqawqV4PDCey/G2lfmqEUOhLjhrp6H6npJyoSLMSI6Tnp9/OlHVpbGeMTcN1nJ5u4vKXrLcupr7ftU2b7GlnPjo58c77B7tKFWhc39p5Aq+97IIOWoLgBJbvmvj4/jEcHZ/FK16y3m1TJwPRdNThes1GPgf1NfRE4r2bTGmPlC8+dgivftmmUv6cSHy6YQKXEhwbn8PLjaFPePJ2plA3RrJGjQqvFzxnwcCab7uJ99CZGZsPKMsYXJP2cX3JR2pWM/mQfLFHyDlKOWEnG4b4NIgyExsBePHktLFl6H+S7G24nmDKE9p5Q2LQhjlOvJ0pPHdsEmdn251eN6l+R7NG0//9N78Kn3v4gOWpM++ff80izRsQTj+n6ZvPhJzXi1WqEkf5yAu6zLgfN3M5ePKoJwn+5gcH8MYrX4Ife/mFUMyYb+tJVSmzolZ6u0yhbHxNnwCMzbQw23ITfytVmGtnaNS099WVF2+w6dqlLeu1xNJx4s7r1zGIgFaM3/zpq3Df83ol3jQrf3kuUS5WhZ/+uQR//1DxKql5nL7voSAGGNuJrWHMaaLBIDbCx4esBvLwl9+StEvuu3FIe1U89P/9kt2/t5kqa1twmymbzpeb/aUT/V9vfpU1vOa9Z3xXQN9IZx7Dtkch920O/fm9L9r2apo6ikuhaCZyfYKLkWjUwkbKjMbju9VlShux5tvhhJdvQ6GNEiIjJENBAbj0AuKy2agVc/ps/uWjZgHgP2zdicNjM7bt//O3XsD9JsLV345wuBHmQ7fPqFzyuXz9fI3WT7Ws20p2BNP0QpH/uDgFiJtww3gnKWZ87Ndf37GS8JH3c29nWhvVuajCsq1UoZ0y5toZ5tuZdc31FaBP3r8XB8/ojVikXo8fKF64F7lX2tV04gygvndcnvKRsfXMyASe67L5jmj6k/Nt61nTSpVdKdUSwj89cwzHx+dtcOVQPXF0nAkGk9QJ+pphWgyx9UmddAZfN3lJXI8f6+ErVfJqfE2/7a00fAptuXHeCX0r2FM9s/sucELR+5q+5TjFGVA6uhnEjt4JXRVnWylGzs6hWWAUJOh7vfplm2y95MXqnNpaQ5Dkb800w/is1iylI/gTlG8MlPre/MZXICFCs6060kMIf/6v/+4JO2j97tSokfUcyENKnpx0m1S3Uu3JI376YvgCnEY+ZDaryddFspvWEuf6KMbd+XYWpCJuppnN687M2NDQ+83KRjg6MCyc4JppZq8vgr+D5lDOFXJdI8yPw8zYeWwCYzNtK7SHaonNbe9vJ2g3wSjk9Iv3axBNcKiWIFOwieFaRlP0o6kzFdI1YrNp1BKr6Yt3kuLQ9REAnh2ZsO0nz+3Xt50pNI3Ql2eS85uZQivLjDFX2SA8Pdnra8wHuZi0kNo/OtPxzECYxM09kP7wbW2yeqp5LpvSBL5CNVmQiVUg19KpSrTg9nPoEBHmjLtskaYPwORVcgpIQs7FFqamqXKrwblWFjyHGG/zxl9B3t7SShUelL2thcbrst/HUuL8E/rWkKSFvnSg//0zj3raM3fQOzKO9ZJcNgMJNRFf3HzruRN4ZN/pQk1f9j799Z+83J4rGKprYyMggkCngPb3VQV8j4vQJdKvr2Ltj3zR+kbH/afnUzywexSpYhyfmMe+Ubc/sAhRpUJvIhkkgE4kJlqJcJmpEbziyQM4gTJcN0LfeEX9xBUX4ZpLN1pDrmQXlXNSpWxqCZl8DpyesUnlMma8dNMQTk02Mdxwnhb+SgWApcc0tZOgkbhtFAXjsy28ZEND2wc8molIt+O6Rg2bhmt2QA/Vk2DLQ9H0h0qEvhYwTksEYLcmlMlGc/Ghpl9PnCYtAj6/astYpwMXDbVuPFXEvc8vv/vEJE5ONm2ftZO6t+oT11Q29gU5vZ3KRKysaylBby1ojfheP/z7xw8XRlLbent2B4kSl3bTnlYJrrxkvW1Tn96RiaDttedULv2JD2mDybm2XbGIrUQCnlqpwoahWqDpz7UzjM20QCSJ4lJbnzkzOfr7NEi6dkC7UDfqibUZSkbSuYLN4fPPDuT3LZAdzKLQ7xt+7pg009uT1RPCjddcAsAPUnH5OnLjwkYL+nlC5Np+npB/eOooZltZodAn0hOGdIjESBeG7myyZBSh2ky1F4t4+QAeD5s6m4AMeAFDRwf7Qv8PfvFa1BLCh7c+h0s2DkEpxn27Tlp/cH1fvcJIlR4IAp0TRt9guplad9dW6ugdWbX4QTqTc3qw7Do+aZ/tp155MX7yqouhDL1Tqzmhr6kQtknk7ASXhhklL9k4hGaqsKFR7zDKCZrGja5m3OeE/vBxdraFizcOBe3GcB5HG4ZquGBdw2rqjVqCubbbCESuNlzXbfWp3AbgsmryV053mt3SRJCJZinabDNV1tvM3wFMJvhffO1mNEzu9XWNmhV6IoSkD/sLn1bmeGj3pKH7qaRYZtZ9UfpTK3N9uWnoHSLS3lXM+OKjh4Jn/saO42in4RgJ2sQ817WbN+KdN1xu6qF/E1rktT9yQSBU8xvOiFs1AJyYcJsE5SHnTcy10TJcue4vJt4DOkBu/VAdM2YyH6ol+OT9+/CTH73Xxp7MNFPbf//n08esx5iuE1ltXtq/kZBV4CRBX5mm30HveBMmo3jCXy6cV0JfG25cwNJQvYZLNw3jg7/yGgChIK0nYRSfc6OkjhwqQGiU+8AvvRqT86mlJ/KQHZFch3Yv0/fVXW8EbjPVHhUXrmsEfs6AE04AcPHGocAlUwvcUNO/6pINGDLGJ7l/vjM1aol1J9vgDaw5bzNs4SzfffujVpuW7ez8NLnMwP/YfgRz7QzPHZ20vDez5kWFfw40fcXYe2oa82kWxAO0vKhTZsa1mzchIS2UmU0um9yzaM1OAvESNOpJB231xUcP4fqXX2hzAX3qgb24e/sRk/uIsb5Rw6bhutXUfU1f6gs4eud4TgDJJObTO7PNVL87oXfq2qtIVhvjsy3nNKBcvIXI6zdc8RJISu7hes1y+nVPs0woTBr3lSdGMN/O7GoiH7MBIOD0dZ28CTfztNia07zFZdSPWpf3BRRvXCP7+yZEngupKV9z1KagniRWqZKrrff6Zr7Nfcjtx42mL4JflC/J5bNhyEUp12tk+feEtGIy08qCla9fP4Jz2dTP51bJZGxrrUwF/caHvIO6x+kDenKXKPy8PWy5cF4JfXHZnJxPLccrgRlAaBz1l/lAGFYuXhWAW2qSp+k3EsLUXFsbvdLOlyxGH7ubk+GixeBphX5DO0812wpT821cuL7hRSG6ulmKoJbgnmddBCeAgN5p1IzbYo1w2YXr8M4bLg8iiQVDNbdnwHpP05ekblKnoXqCx/aPWWOz248AlkLJ694iGPWqILHURT3H6d/xgwNotsWXWR+XWAYp82s3XI7/5y2vwbqhmtUOh3I2g2bqluF1472TXyZftGEIr37ZJshG9O1MvxvJcrp+qI4L1tVtIJzkyxHI1eS9+Tt9icDw6w4AM60sCM7yDYe1hPDN505YYaHY8y4jlztI6Il1jQTTJgjQ1/Tz9M6LJ6cx13Ka/sUbhmx7SDHxdlLK+fwDZsL1BNpwo2ZXNvk9I2Tikef1kwj+xBU6iV/beO/UEsIf/NK1prxZSZl35Y+/173iQs/orY/5Qn+4nuCnXnkxfvzyjoB+i/HZtjXsZ9KWZuJppuGqtlFznjwHz8wiVaGmL+0vq2wxakvw5+svvwj/7NqXQil9LTHy+oZcH3l6x2UCcIbcfAK35cL5JfQTwuhUE599aD9uvPoSo8m5TukbtPJCXzHjP/3a67FhqI5G3dEoPr0jfbte03zgbCsLZvYfe7nukG+44iXI2L1g8UJRHObf+GfX6vREQu9caLI+Erm63nDVS/Az174Un/6dn0QtIRstKRr15Jyjd9bVa5biEE62lujn9wdQ3XD6vtAnQrDPbjN1Wo2ky5V8Rr5LqrSTeMSIoNBeRcDeU9Nm8Li6z6cZzky3MGdWSmJf2H1iCvtHp3FkbNZqaEP1BOvqCWo1wnBD+46LBsymbhJ3UUvI2knK+kfGjA1DNbzsgnXWy2l9o4aXbhrGrPC9NZ0i+W9+96eDZ/TbRkBEODE5j3/7lR2Bt4z0CxFkw/XEef1I3zJfM5PSO++9IzaldY1aYMgFYI3X+Ql9PtVa+pd+eBj3PX8S6+q1QIvUmr7m2/0JVIKJBOsaic1Em29PG9hohLgzkif4L7/xBhtLcOs/7QIR2T4hk0QtSeyOdoJ/+YZXdOTjefvrL7P5rgDg5159Kd545Uvcs8qmKvDoHaOcSIZLmfCa7SwcA55RVz8/B5y+PLcfMObvJKbtHokd09/ZdbIw7ba9ljXkEn70sgtspl6GScHBLj34cuO8E/rjc22cmWnhLdf/iNXk7OAyA6WVshUAMmYYwGsvuwAACgWHCG5AvzhxbfM7zj//0c24/V/9FN50zSU6NYCn6W8crmGmmQWa/lt+7GUAtLaqw/K18BaNFNBC9JO//ZN42+suQz0hnJycxwd+6Vr86GV6gplqtvGSDQ0M1RMMN2qoJdq4NFRPbERoQgjSCIsbmxYyui4vu2AYx4xQBrQQkAyDf/vIwZzLZmeg0mzTeUVI1LHvOVVPCB/ZuhMAMNNMMTnftt4We09N42tPHcVHtu7E0yMTdqIQr6Ahc811jZrRqhx1JZOTuGs2ugh9mSyu+5ELcOG6OoiAf3jqKP7+8UN42QXDmG1l+PSD+2z+pVdt3mjq7673W2+6KndN97cvxMQ+4nvviKafj61gADe/4RXGp5xsvIR4HV20voFTJte/PHdq+OZGbuUz28pQryU4NdXE7hNT2kip2CYxEzfZVqqwccj1iZY3yTO0AuHoRxdEBMAa62WSSMhx8glpBSNTjDMzLQx52qsT+saDzHtPQZoT8/m6V1yEn7jiouD5bKwEgBtuvTcoL5y+0G3ikJEkmrP3V7W/8zOvxFw7w4+aMT/fzjDTygKKxRf6AmmLOWP3YNbP8tCLo8GkKf1CJhrpQrUkwas2b8QhY+h3+25ETX9BqCWEybk2xqZ1ZxODrNAybeUShonnhLxkxWKhVxiq1+zM7IKzwvvMGS3fF/qKgbe+7jKdFVKxXSomRNg4XLfLR7mnXFs6kkSaEhAY9xo1zXe+5kcuQDtjrKu7zjs9n+J9b74WL904hHUN7aLaqJNdTSRGgL3UM2Q2U2UTcslzXbS+EWwikgczrAdHEOFr/p4VTb+R4Pd//lXIFOPnrtPJ8/Ia7NR8iklDj8mzy3VGJ+cxZzaNFqE2VNMCf11DTwCj0y1cesGw3bRFvLHqCRUKfblzzeyK9pF/eb0OrCHNFTdThT/85esAAAdPz1iOVQa8f7krL96Qu7Z7Lj/YR2vOrn2F02fveiJP6kmCv/jNN9oVkY99p2cw28r+//bOPM6uqsr333XuuWPNY1JJVWWeQ+aEhBAISSAQROYhKoKCoKjo5yHdIDxE/NBO3Y0+pV/bDt22bbeg3f0aW237iQpqg4CCIvRTBEGZDCFjJTXde/f7Yw/3nFu3UjehkkqR/ft86lP3nrvPOevss/faa6+RtTNaTVv9bgfNtVNljGLX/gHqMqHLLXPLWQtIhwFXnTQdKOn0B/JFatKlcRRVTymlXYvtOLMStTXcZlNxD5QgELfrCAPhvRtmuutG38RgXjGhPu3aR9NeBEFpx1CficaMSuw6tnv6TMH3UgvN9O0zPLVtLzv3DzjhYaBMvTOlJUfvQIHV0/Vu++ltPU7St/QXIgJj1I00mRB29w6ycV47Xc05ssmEsydY2PEevac+btRqVmgyfKdYLEVrH2687pi+zeUdJgIEibld2ok8aLZmjz+/uyTdmMUhX1CkEsJDZUEnNgcMaPVIf77I/sECvREdXpQZagOcXtUDEXKpBD3G5zxZNlFtxGF9tqTeKQ97B5wXRNSroac/T1MuqXOLhFqtk0zo7bPTZw4WaYtskwfyRZcALRAxqjAZklLiQ2fFa+XkC8bQqCKBSqrUt6B3JlZfe/z0Zte3Uabf059njzFM2vQCVt/7Sk8/vQMF/vYnz5IIhLRZJNNhQCZM6FD6/jx16RBl3oUz5Ca0O+yQ9Lvmv91BNWaTxl1RB+XUpUNHn1XbWX20Pj8qkcYuHfNciYb12zD7qE7f9kXpnLhAEY0nsE2+9cuX+NFTr3Dnm5cBeoFIhwn68wVE4n76AC/v7qe1Nu12dhcs7yQhpSCiPmM4788XXe0F3f96kbK0pc0CCyWm35cvsOW4iVy7QS+QVn9tGX4QCBMbMmycNwGAazfOYla7lqRvP3ch+WKRd6ybrgWTMkNuNA7m9IUdFftXf9cHduwboDmXcm3+7m0rdUK0fCmv0x/39Ls5UFTxIiaJQKtoG3NJsskEr+4boKdfz0+rLs0XKme9zCQT7O4dJJNMGK+gBLv3612GfR32WXLpcqYfEEYEEzsHC0Wv3jkkWKa/u3dQT+qAmHpHF/bGSfqf+t5v3LlW95cvs6JHV3r7Qq0HiVI4FzD7HUr6e5FSaH2tkfQbcklaIwwYSpJ+nZH0BwslfWvMoGvum4lID4HogKREICbwy0i8YcBnvv9bHnzmVQYKRS5Y3unO6RssGMOipu3DZy9wknwUy6c0AbgttvUYURBTDQCcZxakdKgnTX1W+8XXpkNqIkwVSoweSukFHv19qdyk9XUWsXENmtFZ9c6+/rxjWNpoGDHkBhXy6Uc8s+zOyQZ6DeaLjkFaXfw+46lSCuArXaqSJ5SF9SsXNHO1AWVhIKQSEVtHRE9s6dL3iVQhAydx2kV+SVcjYULIJAMXNVvu8fHynl5aa1OkEgFXnDgN0BKrbdc/WHCJ3srVO/f/RueMUUrf045By5x7Bwqsn9Pu1Dv/8qiuFmfVOnYMdjXnXD9YAScMxBWTse8qquYKJG4QbsqVdr0WKtJXO/eVehT3UQAAG0tJREFU3HAFIZcKyaYSMcGlNh1q25DdrQelDLF2EWyuSblFfSCvmXY6DLhszRTjwVSa61AqiRm1ZaVDvQgoVbJp2XFSPk+uWT8jFjWu1FDHj8ON1xfTF830k6FQmw6NTj/uMmnrbyYCYfX0Ft66Zgpgo3V10rBKrlPR3DvZsi2bhWU2obMXiDNI1pgBOLkxyylz2mPnWXe8lVOb3DE70aOSfiCwalozF68oZbquy5SYXyaZIGG8UmoMjelkQO9AnqVd+tqJQFjS1cj62W3Y3EI2WKscdgBbg7PVpReVIlc2mBH42HnHkQ4DNi+YyC1v0LsEqyqJuvX1RAJt9hqvlBd395IKA2rTYSRQrVT9LB0GZFNa1dPTn6cmnXDeMY88t1OnuTVBP1FJf19/3jEpa7xPmuyI2aR2hbR9iNILTk9/3nnS6OPaHfKl3b3u2I//9BSAmIrE3ra7Occz23q02sn0r1vEiyq2AEPU0SDu/njdaXPcuwW4++o1evcT6qjiIGDIWH1hZy9tdRnyxaJL0xu1L1m98wPPbI8ZLaPeStaWUn7tvsECCybVO0n4x0/pQLr1c9qd7agc9r7bewZ48qU9BKKdExqzKZZPaS71gcTPf/imTY4WR1fk+97+PLVm4a9Jh+RSCWozYUzFUpNO8H+f/KOLmUhIielbptxel3bPrgPKdJ+GiSAm6ZccO7RqzQZe2kycNpGb3QHb91iu3tGCS7Q2Mjzx4h5e3Tfg1TuHgjAI2N07yJKuRhZ1NTqXrejAmdFey0C+yAu7etnbN8j6OVrvrChZ6KOTIapLtO9kCMMzsPw5m0rQP1gsSfzoRSgTVu7u53fuJ5kQNsyd4I5V8pxQSksvUfrs7iBtdN524ORSCc5bNpmaVMiLu/piRuVlU5o4YWarUXfpCV4px3xomK2VVpykr+LMztJ5yapu0smESZKmmd0NZ8yNRWeCZgAW+4wBeOe+QVKJgEmNGX6/Yz+3njXfJaWzRtxMqKXPfQN6wicTJffGhNF1J8O4V9Yfdu5neqs2yNpykKHx9GnIJnl134BjHtlUyK79gxUkfZ3v/P7fbB8Se1GbHjoW5kysY29/3kUw16RLUnO+qJhQryNU7bCMqnfKDYd16dDZjQKxi7se55lQ7+yisSg79g/QkE261M0AL+/pcwbFhAj/9fSrPPjMjphkGd3lzZlYp71SysbrYEGxYFKDe2a7YHc351xEtMW3jGuxVVm8tLvX9duGuROY2JDho+cd59qXp5SwgYFCyU1XRfqsb7BALpXg2o2zmNFWY6Kqw9g47mzK8fCzO1zZRbsT0XQJbXVpNi+YyDQzPmxAmXW2yBdVbBdm3xHAX160BNC7n8DY+KAk2duF3O5IrZBg+8TOh2xSv9+nX+lxz3y48bpi+kGgjTk3nDGPyY1ZY8gtDejLT5jK29dOY7BQ5LE/7OKpbT1smDuBS1dPcYtDoYzpTzQTNBqRW756W9iBUZNO0DtYMAuFZvw16XDYHcKevnzMnQxwRrSoeieasMvCMayk1nmXDEgh126Yxf4B7WVkJ7jdngJOj5gKK0v6yUAbtezzKmWzC0rsWeoyoevjLQsn0lar1VeZZIJL10wdkpjut9v2Oq+JglL8yzUnsKdvkEC0ofTFXb10t2gVwYopTcyZWE8mGbB8ahOrpjXzpctXMr+jnnRYCrbpbMqyfEoTLTWpGNPf119w6psw0Gk6rKTfkE2yY1+/WzhzKb1g7dg3EMtpZK/2SoW8NpWYvs0OaZlGTWShfmFnL4OFIutmtcYyuAIuC2xfvhQZfe8HTo4EEZVUKN/51Us016ZM8FPJJddqTAYLykWLPvHiHpSC7193MhPqM051EvNJj/TZpy5ewqLORvf7dMcU44GDe/vy/PO71pTUcJHrnXlcB4qSeucNiyaZZxjSXe7ZKuWSF4E7LlpC2iT0s8y0d6DgxmAQ6PGoBZxewkD49CVLqMuEbpzZdvZ95dIhe3oHERG+f93J7rm29/QzsT5jvIuK7h3Z3imUCZHOKcL0id012vdx/Wa9W+uMOAAkQ80Tbj93oXuG7T1e0j8khEHA3r5BF2V6ypx2ZrbXssNIlpmkZooDhSL7+0vFOz5yzkLAeLoUtNfNe06ZyfIpTTGVi4gOyihPKgZwycouN1FzqVBLAGaSFpXOTx71uokiX1Q05OL5czLJoW31RI7f2w7iy9dOc8ncQC881mNIh4wHjjbrXlkwxuakCdayOH9ZJ5sXTCAZCu31GVoNE//Djv3OiLpuZqms5SfOX+Q8MVpq00MklnxRxRaV7T0D/P3bV/GLW04jDISmXMolAZvaWsPLu/ucNNxUk6I2HZIOE06v316XIUwEpJMlg1hXc44LV3TR3VwTk1p7+vNuZ9aYTbLf5EhPBNr2sGv/oJug2WSC9ro0v9u+j96IX7crWCKlfnJMP+JpcvfVa/jiZSucgXGwUOTM4zpY1Nnoxsx/PPEy+aJi7cxWN8mdpG92F5+77xkeelY7EtSkIpJ+oO032WSCB5/ZQVMu5VyJSznnI2kCIu9h5/4BwiBgYkOG92/Su4KopG8NjmcvmVQKQjS/u0WsEL9HvqioTSfZMLc9ZgMAqM8m2dM76MaC9ZIZLnWwfY5KxxXKCSu2Se9gwc2nQCCX1Oqd7zz+Msu6m6jLhJy/vJPGXMlrLSGllCy16ZCVU5tjNBWKOk/V5KasiSMo2QNVmaRv8U9XrWZZd4lH1KZDGnNJ6jIhK6c2saizMRZrADi705rpLWTNjn773n6v0z8UBIEpfm5m0TlLJ7NwcgNzO+pYN6vVFdrY05tn30CBpsiAsIbXvEnUZoNTyos8fPO9J1bU+S+YVO/UOzWpkF4zQEW02mc4Sf+RmzeRSgiN2VTsuFXvxMPCi7E0BJ+7dLljOpMbM6STJe+EbDKkIZvkQ29c4IxEV5w4TccLGMkxX1RkTLGMqCfFX1y0mHefMpPGrI7oTIUBd121mnxRGX166CRxiCcxGw79+SJ3XLzYfW+vz9CQS9KfL1KXCRksaIn/g1vmxVQgFpUW2lTEIJaMqK+KMUm/pPttqU3TUpNykn5bXZptkcmWSSVIJxNcuU67N7rSheZyP7/lVMeA7eIblfRXTWtm47wJBIGwuLOBfEHR3ZJj68ou0mFAXTrkjosX87a1U7lgeaeTCqM52a3e2eqZs8kEl66eEntmKxA05pIuKrfc28umzLDY3qMTi02sz7BwsjbMWwHh4hVdNBo9/acuXlK6l3nve/viyQBba9Mcb5hnfTZk4eQGHU8RmRettSle6ekfIr0OVxkqk0zQWCb4gFbvKKXVl/35gju/b7CgVYnmmtlUgqZckqtPnk4QaHvUjLba2A46CIQtx3Vw1mK96/iHK4+P3atQVPz7e0+MJUW0iHqp2eIuoN2sayLzuqU2xSM3baIhm6THCFcP3Lgxdq0N89qdrdEKJNt7+l2E/uFGVUxfRE4XkV+LyG9F5IYKv6dF5C7z+09FZGrktxvN8V+LyObRI30oorqyKDqbciztbiI01vjfm8CIWBIuVWLsWgJOOL9kgOOnNzs9tmXE5yyZRDoMaMolXUQlEIlyFersdjJVeVC31qbpaMjy/k3aDe6uq1ZTlwmZarbU0YmUL8Q9izYvmOiu31abobMp55j+xIY0qTDgjYsnGQYQ8D/fMJ/aiI545/4B2mrTLhdPFIs6G8mmEs44eryR1Hr6CzFXP8B4YgzP9N98fDf7BwpkkyHXb54zpPCG3brPNgm4OhoyTlp2bZJDh2o6qfX9z37sTDd5yvMmzeuop6kmafo6RVtd2i3+Exsy3H7uQvc+s8kEfQMF57MfhYhm8L2DBf7k9DlMNsFOl6zq5qTZbXz3/SfF2l92wlRXGjEIdKTwW0+YwrlLO+loyNJam3b9GPUQEYF7rzvZSdNBINy4ZZ67btJ470xtyZEOE84bJhrkU6JZX/dnN2/iohWdZFMJl+77+GnNjiE35pJOIo5K4qlEgta6ND39eWZPKBW7mT2hzunjbWxJIogHik1vreXpbT28fe20WL8Mp8Foq0uzJcJMSw+hVSvnL5vMB06bE9HpF7nv19v4+e93uviAjoYs1502hz/u6Xe7k1wqwX3Xr9c0mr56w6Kh9zlxZisFpVg4uUE/S1DynrvhjLl0NFg1L3z2Tcti50aFuY6GLGEioDGXirm0RrGsu8m5BJ9rvN529Q4OqzYebYzI9E2N2zuBM4D5wFYRmV/W7Apgp1JqJnAH8HFz7nx0Td0FwOnAX9mauYcDVodfCXnjpmlzZ1x54rSY77oNxFgxtZn5k+pZ1NkQS+26YFKD82aZWJ9h1bRmPnHBYh695VQevmkTF63o4uYz9eS0fumBwNffeQIz22sREeffXI5JjVnHAI6f3sLPbj6VdSawKR1RCdkc7FFYabG7JcfVJ01nvkkFcdVJpQLL0Wi/XKrkHaOMv7114fvFLadx5YnxSWqrUQFsXdUdk5ytd0hdJjkkvXMUt597HH2DWgdrPYHi9ygVtAetlisPUkpXUI1ZL5Yoyncd/2vrUtrr9ITtas5x3jKdj8hKy2cvmewmmy1qE8Wp8ycwrbWGx245DdASppUeP3nBIrqacqyb2eqiuS0WdzVyvfG+mTexnkVdjUMSk9kF/KTZ+l03mniLzqYc/3rN2iHPa89JBOJ2eJeunsKSrkaXv6hSTv+W2jQttWlaa9Mu1uOuq9cQGp/0xlyKhmySq00Al7tXKNRlQvb2DfKx8xfFigpNb9OLh+27ZCJgSnNp9ze3o463rJ4SE6xgeEl/OLTWpMglE+RSIS21aXd+72CB7T0DfGbrUhZ3NRCI8D6zWL+wq5dJDXpRziQTZJMJ7nzTMhKBHh+VEsR9+OwFboeYTSbobNLn9+eLbJzb7ubno2YcRDF7QundbzRR9o255LAZN6EUr7HYpJUoFtUQ54jDhWr2E6uA3yqlngEQka8BZwNPRtqcDdxqPn8D+KxokeFs4GtKqX7gd6aG7irggdEhP44DlRpryqWoy4S012X40FnzedvaaTHmYJO1XXHiNJRSPP7C7mHzhTfVpLj76jUApCLrpv28rLuJL1y2gkDiCcLKGZnFpMZMTBqw57x/0yz+uKdkPMwXikMiMNsjapByCdwdNwnLACPpa6b/lStW8dNndhAEwpmLOmjIJbn5DfH13Bp6AT563nH85xMvM9lMiBvOmEsYCCunNrM8oteshH39eTJh3Mce4FvXnmgKsJTexdvLFh6orN7ZtqeP5to4U+luzvGOddOHtAXNmDoMMzh1fslTyjLx8p0UwOffuiIW1b1/IO8Y3YUrunhpd2/FAJ4ZhikCNOSSpCOqwnKcbJj+f92wwS3qw2VctBHHqYiufPX0Fpfuuas5V/G8SkiHAZeunsI7T57Op+99iotXdsV+z4QJ6tJJ7dpLqdZuFPaZwoTw5kiKimQi4C0RtRTA2pktLOlu5GBw6xsXxPrNTpP6TEjSSNRRrzeA+65f76TvbCpBJpVg3exWntuxj5pUWHFhDIPSgl+XSXLGcR18ZutS/vulPfF3WUG4OWl2G3dfvYaLPveAE9Y2zZvAd594edjnKo9SzxdVxR3m4UA1TH8y8IfI9+eB44dro5TKi8huoMUcf7Ds3MmHTG0V+MzWpRWPX7lOMxIR4W1myxnt9Hetn+EkWCsJJg4xQi4IhEWTGyoWca6EdbPaKhpx3rdxViwwaMuiDlfEweKa9TMYCY/cfKqbOB2NGacKWTerzUlsd5ZtWS1aalMxF9XTFkyM/f4B450w3IJmsXVVNw25JC/t6ovp6xdM0vrlhz64cbhTgVIVsig2L5zIlrL7NteknM72QLCBZ0AsmKjZSKZbjis9Z5TpCOK8fUALE0tHWPBAM5X2+vSQ41EjXzUue621KZZ2N/K77fGKVVedNJ2TZ7cxr0NLndFYjuFwzSkzeHb7fkSEyY3ZIbup92yYSTIR8MCNG9ne08/1m+fGfrdqE4CPn7/IqXqGw1evXD0iTeUoXyhtfeSHbto07K7BLuwA8zvq3aK+vLuJ+ZMqZ+nMpULOWRJnTWctnhQbS39+4eLy0xxWTWvmr9+y3H3fvGACa2ZsGLb9CTNaXX9/cMtcHnxmxxC73uGCDFfY2DUQuRDYrJS60ny/FFillHpvpM0Tps3z5vvTaIn+NuABpdQ/mONfBL5tCqZH73EVcBVAd3f38ueee26UHu/QoUyoeiUvGo9Dhw3WOlI+yQeDamizuVdGq4B1NN1DNYjuOjw8ohCRnymlVozUrpqZ9zwQFRs6gReHayMiIdAA7KjyXJRSf6OUWqGUWtHW1lb+85ggqvf1GD2IyFHJ8KE62nQJztFjugdbLckzfI/Ximpm38PALBGZJiIptGH2nrI29wCXmc8XAN9XegtxD3CJ8e6ZBswCHhod0j08PDw8DhYj6vSNjv49wHeBBPAlpdQTInIb8IhS6h7gi8BXjKF2B3phwLS7G230zQPvVkoNb9L28PDw8DisGFGnf6SxYsUK9cgjj4w1GR4eHh7jCqOp0/fw8PDweJ3AM30PDw+PYwie6Xt4eHgcQ/BM38PDw+MYgmf6Hh4eHscQjjrvHRF5BXgtIbmtwPZRIudwYzzRCuOL3vFEK4wvescTrTC+6H0ttE5RSo0Y3XrUMf3XChF5pBq3paMB44lWGF/0jidaYXzRO55ohfFF75Gg1at3PDw8PI4heKbv4eHhcQzh9cj0/2asCTgIjCdaYXzRO55ohfFF73iiFcYXvYed1tedTt/Dw8PDY3i8HiV9Dw8PD49hMC6ZfhWF2v+HiDwpIr8UkXtFZEql6xwpVEHvO0XkcRF5TER+XKEG8RHDSLRG2l0gIkpExtQrooq+vVxEXjF9+5iIXDkWdBpaRuxbEbnIjN0nROQfjzSNZbSM1Ld3RPr1NyKyayzoNLSMRGu3iPxARB41fGHLWNAZoWckeqcY3vVLEfmhiHSO2s2VUuPqD53e+WlgOpACfgHML2tzCpAzn98F3HWU01sf+fxG4D+OVlpNuzrgfnQpzBVHed9eDnx2rGg8SFpnAY8CTeZ7+9FMb1n796LTrh+VtKJ15e8yn+cDzx7NfQt8HbjMfN4AfGW07j8eJX1XqF0pNQDYQu0OSqkfKKX2m68Poit2jRWqoXdP5GsNVF1ed7QxIq0GHwE+AfQdSeIqoFp6jwZUQ+s7gDuVUjsBlFLbjjCNURxs324F/umIUDYU1dCqAFsgt4EKFfyOIKqhdz5wr/n8gwq/HzLGI9OvVKj9QMXWrwC+c1gpOjCqoldE3m1qC38CuPYI0VaOEWkVkaVAl1Lq348kYcOg2rFwvtkmf0NERq4YfnhQDa2zgdki8hMReVBETj9i1A1F1fPMqE+nAd8/AnRVQjW03gq8RUSeB76N3pmMFaqh9xfA+ebzuUCdiLSMxs3HI9OvVCS0omQsIm8BVgCfPKwUHRhV0auUulMpNQP4U+Dmw05VZRyQVhEJgDuA644YRQdGNX37TWCqUmoR8D3gy4edqsqohtYQreJZj5acvyAijYeZruFQ9TxDV8r7hhq7qnjV0LoV+DulVCewBV3pb6z4XzX0fgA4WUQeBU4GXkBXH3zNGI9Mv6pi6yKyCbgJeKNSqv8I0VYJVdEbwdeAcw4rRcNjJFrrgIXAD0XkWWA1cM8YGnNH7Ful1KuR9/95YPkRoq0c1YyD54F/U0oNKqV+B/wavQiMBQ5m3F7C2Kl2oDparwDuBlBKPQBk0HluxgLVjNsXlVLnKaWWovkYSqndo3L3sTJmvAYjSAg8g95OWiPIgrI2S9GGklnjhN5Zkc9noWsPH5W0lrX/IWNryK2mbzsin88FHjyKaT0d+LL53IpWAbQcrfSadnOAZzExP0crrWgV7+Xm8zw0kx0TmquktxUIzOfbgdtG7f5j9aJeY6dtAX5jGPtN5thtaKke9Db+j8Bj5u+eo5zeTwNPGFp/cCBGO9a0lrUdU6ZfZd9+1PTtL0zfzj2KaRXgL4EngceBS47mvjXfbwU+NpZ0Vtm384GfmHHwGHDaUU7vBcBTps0XgPRo3dtH5Hp4eHgcQxiPOn0PDw8Pj0OEZ/oeHh4exxA80/fw8PA4huCZvoeHh8cxBM/0PTw8PI4heKbvMa4gIgWT1fFXIvJ1Eckd5PlfOJgspiZL52eH+e0cEbllmN96DoauKuj4nog0jeY1PY5NeKbvMd7Qq5RaopRaCAwA76z2RBFJKKWuVEo9OUq0/AnwV6N0rZHwFeCaI3Qvj9cxPNP3GM/4ETATdJ4lEXnI7AI+JyIJc7xHRG4TkZ8Ca0xu8hXmt62mjsGvROTj9qIi8jaTH/4+YG2lG4vIbKBfKbXdfJ8mIg+IyMMi8pFIu1qTF/3n5l5nm+MfEZH3RdrdLiLXikiHiNwf2c2sM03uQeeP8fB4TfBM32NcQkRC4AzgcRGZB1wMrFVKLQEKwJtN0xrgV0qp45VSP46cPwn4ODpX+RJgpVHXdAAfRjP7U9GRnJWwFvh55Pungf+tlFoJvBw53gecq5Rahq7z8BciIsAXgcsMLQE6f81XgTcB3zXPsRgdPYrS6ZbTo5Vp0ePYRTjWBHh4HCSyIvKY+fwjNPO8Cp1I7WHNT8kCNhd9AfjnCtdZCfxQKfUKgIh8FTjJ/BY9fhc65XE5OoBXIt/XUkqF+xX0ggI6tcKfichJQBGdQneCUupZEXnVpKqeADyqlHpVRB4GviQiSeD/KKUei9xjGzAJeHXY3vHwGAGe6XuMN/QaKdjBSM5fVkrdWKF9n6qc8rdSeluLanKT9KKLcYx03puBNmC5UmrQZCfNmN++gK7sNRH4EoBS6n6zQJyJTv/7SaXU35v2GXNfD49DhlfveLwecC9wgYi0A4hIs4xcF/mn6HzlrUb/vxW4zxxfLyItRtq+cJjz/xtjTzD4CVpFAyXVEuiFYZth+KcAUbr+FZ1ZcyXwXUP7FNP+8+hdzDJzXNCLw7MjPJeHxwHhJX2PcQ+l1JMicjPwn0Y/Pgi8G3juAOe8JCI3ojNvCvBtpdS/AYjIrcADwEtovX2iwiXux+jnlc5a+D7gH41xNqpO+irwTRF5BK2f/38RGgZE5AfArshuZD1wvYgMAj3AW83x5ei00KNSSMPj2IXPsunhcYgQkU8D31RKfe8Qzw/Qi8qFSqmnqrjXPUqpew/UzsNjJHj1jofHoePPgIMKDrMwAWK/Be4dieEb/MozfI/RgJf0PTw8PI4heEnfw8PD4xiCZ/oeHh4exxA80/fw8PA4huCZvoeHh8cxBM/0PTw8PI4heKbv4eHhcQzh/wPln2iFE8t2DQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3aca7d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Single band Lomb-Scargle for band u\n",
    "from gatspy import periodic\n",
    "periods = np.linspace(0.2, 0.9, 1000)\n",
    "P = periodic.LombScargleAstroML().fit(times_u,mags_u,dmags_u).periodogram(periods)\n",
    "plt.plot(periods, P, lw=0.5)\n",
    "plt.xlabel('Period (days)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Period (days)')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3abc7cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Single band Lomb-Scargle for band z\n",
    "from gatspy import periodic\n",
    "periods = np.linspace(0.2, 0.9, 1000)\n",
    "P = periodic.LombScargleAstroML().fit(times_z,mags_z,dmags_z).periodogram(periods)\n",
    "plt.plot(periods, P, lw=0.5)\n",
    "plt.xlabel('Period (days)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now do it using the Multi Band periodogram, which takes advantage of the information in all filters, by calculating an overall variability, and then deviations from that overall variability in each filter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Period (days)')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a12232908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_multi = periodic.LombScargleMultiband(Nterms_base=1, Nterms_band=0).fit(times,mags,dmags,filters).periodogram(periods)\n",
    "plt.plot(periods, P_multi, lw=0.5)\n",
    "plt.xlabel('Period (days)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's fit to find the best period:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finding optimal frequency:\n",
      " - Estimated peak width = 0.00189\n",
      " - Using 5 steps per peak; omega_step = 0.000378\n",
      " - User-specified period range:  0.2 to 0.9\n",
      " - Computing periods at 64577 steps\n",
      "Zooming-in on 5 candidate peaks:\n",
      " - Computing periods at 1000 steps\n",
      "Best period:  0.6010505641943096\n"
     ]
    }
   ],
   "source": [
    "ls = periodic.LombScargleMultiband(fit_period=True,Nterms_base=1, Nterms_band=0)\n",
    "ls.optimizer.period_range = (0.2, 0.9)\n",
    "ls.fit(times,mags,dmags,filters)\n",
    "period = ls.best_period\n",
    "print ('Best period: ', period)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "foldTimes =  times / period  # divide by period to convert to phase\n",
    "foldTimes = foldTimes % 1   # take fractional part of phase only (i.e. discard whole number part)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1b19e128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now we plot the light curve\n",
    "# plot folded lightcurve\n",
    "plt.scatter(foldTimes[filters == 'u'],mags[filters == 'u'],marker='o',color='b',label='u')\n",
    "plt.scatter(foldTimes[filters == 'g'],mags[filters == 'g'],marker='o',color='r',label='g')\n",
    "plt.scatter(foldTimes[filters == 'r'],mags[filters == 'r'],marker='o',color='g',label='r')\n",
    "plt.scatter(foldTimes[filters == 'i'],mags[filters == 'i'],marker='o',color='orange',label='i')\n",
    "plt.scatter(foldTimes[filters == 'z'],mags[filters == 'z'],marker='o',color='purple',label='z')\n",
    "#plt.ylim(18,20.5)\n",
    "plt.xlim(0.,1.)\n",
    "plt.title('Light Curve',size=15)\n",
    "plt.xlabel('phase (period = 0.60105 d)',size=15)\n",
    "plt.ylabel('mag',size=15)\n",
    "plt.legend(loc=4)\n",
    "plt.gca().invert_yaxis()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "1. Find the periods for the remianing light curves of the dataset, using both single-band periodogram and the multi-band periodogram. What is the range of periods you find? Are all light curves similar?\n",
    "\n",
    "2. Plot the periodograms. So you see any other significant period peaks? Try to fold the light curves with the highest and second and third hightst peaks. \n",
    "\n",
    "3. Using bootstrapping, find the significance of the main peak in each case. How likely is it to find the periodicity if the null hypothesis is assumed?\n",
    "\n",
    "4. Suppose that you have the following magnitude limits in the different bands:\n",
    "\n",
    "* $r$, $i$, $z$ bands: 18 mag\n",
    "* $g$ band: 18.5 mag\n",
    "* $u$ babd: 19 mag.\n",
    "\n",
    "Repeat the period finding analysos under these conditions. What do you find?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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