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stharrold/20150303T132000_SDSS_J160036.83+272117.8_CRTS.ipynb

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20150303T132000_SDSS_J160036.83+272117.8_CRTS.ipynb
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20150303T132000_SDSS_J160036.83+272117.8_CRTS.ipynb
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"metadata": {
"name": "",
"signature": "sha256:157fb37909f9eccd79d8f13da607e14cda4728b00c9a185484d8b89af0635251"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Discover eclipses of SDSS J160036.83+272117.8 using Catalina Real-Time Transient Survey."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"About Catalina Real-Time Survey: http://crts.caltech.edu/#research\n",
"\n",
"To fetch the data for SDSS J160036.83+272117.8:\n",
"- Navigate to http://nesssi.cacr.caltech.edu/DataRelease/ > click \"Search for photometry in a single `location`.\" \n",
"- Input coordinates:\n",
" - RA: 16 00 36.8\n",
" - DEC: +27 21 17\n",
"- Click download.\n",
"- **Notes:**\n",
" - CRTS photometry is in Vmag (from http://nesssi.cacr.caltech.edu/DataRelease/).\n",
" - The photometry is from the Catalina Sky Survey Schmidt telescope, Steward Observatory, Tucson, Arizona (from http://nesssi.cacr.caltech.edu/DataRelease/ > \"Check image coverage by `location`.\" and from individual coverage maps http://crts.caltech.edu/Telescopes.html). Telescope location (longitude, latitude): (-110 deg 43.9 min West, +32 deg 25 min North) = (-110.731667 deg, 32.4166667 deg) (from http://www.lpl.arizona.edu/css/css_facilities.html).\n",
" - The data timestamp precision is 1e-5 days = ~1 second. Using the telescope location when converting to Barycentric Coordinate Time (TCB) does not improve the timestamp accuracy since the light travel time across the Earth's radius is ~0.02 sec, which is much less than the timestamp precision.\n",
" - Using Barycentric Coordinate Time relative to Unix epoch as time coordinates so that CRTS data can be combined with other data in units of seconds.\n",
"\n",
"For web-based data exploration, also see the VAO:\n",
"- http://www.usvao.org/science-tools-services/time-series-search-tool/ > click \"Launch\"\n",
"- http://vao-web.ipac.caltech.edu/applications/VAOTimeSeries/? > enter Location: 16h00m36.83s +27d21m17.8s, Radius: 10 arcsec\n",
"- A single result appears for CACR archive (http://nesssi.cacr.caltech.edu/DataRelease/). Click \"display\".\n",
"- Read the info message about needing to specifiy columns manually. Click \"periodogram\". An error message will appear \"Problem Processing Request\".\n",
"- Choose the correct data columns. Under Input:\n",
" - Periodogram type: Lomb Scargle\n",
" - Time column: ObsTime\n",
" - Data column: Mag\n",
" - Click \"Create Periodogram\".\n",
"\n"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Initialization"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Imports"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Note:** As of 2015-02-21, code folding from https://github.com/ipython-contrib/IPython-notebook-extensions/wiki/Home_3x\n",
"and https://github.com/ipython-contrib/IPython-notebook-extensions/wiki/Codefolding_v3 is not stable for IPython 2x. Do not import."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Standard libraries.\n",
"from __future__ import absolute_import, division, print_function\n",
"import collections\n",
"import copy\n",
"import os\n",
"import pickle as pkl\n",
"import re\n",
"import StringIO\n",
"import sys\n",
"import warnings\n",
"# Third-party installed packages.\n",
"import astroML.density_estimation as astroML_dens\n",
"import astroML.plotting as astroML_plt\n",
"import astroML.stats as astroML_stats\n",
"import astroML.time_series as astroML_ts\n",
"import astropy.constants as ast_con\n",
"import astropy.time as ast_time\n",
"import astropy.units as ast_units\n",
"import astropysics.phot as astpy_phot\n",
"import binstarsolver as bss\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import scipy.constants as sci_con\n",
"import scipy.signal as sci_sig\n",
"import statsmodels.api as sm\n",
"# IPython magic.\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Globals"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"warnings.simplefilter('always')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Custom functions"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_periodogram(periods, powers, xscale='log', n_terms=1,\n",
" period_unit='seconds', flux_unit='relative', return_ax=False):\n",
" \"\"\"Plot the periods and powers for a generalized Lomb-Scargle\n",
" periodogram. Convenience function for plot formats from [1]_.\n",
"\n",
" Parameters\n",
" ----------\n",
" periods : numpy.ndarray\n",
" 1D array of periods. Unit is time, e.g. seconds or days.\n",
" powers : numpy.ndarray\n",
" 1D array of powers. Unit is Lomb-Scargle power spectral density from flux and angular frequency,\n",
" e.g. from relative flux, angular frequency 2*pi/seconds.\n",
" xscale : {'log', 'linear'}, string, optional\n",
" `matplotlib.pyplot` attribute to plot periods x-scale in 'log' (default) or 'linear' scale.\n",
" n_terms : {1}, int, optional\n",
" Number of Fourier terms used to fit the light curve for labeling the plot.\n",
" Example: n_terms=1 will label the title with\n",
" \"Generalized Lomb-Scargle periodogram\\nwith 1 Fourier terms fit\"\n",
" period_unit : {'seconds'}, string, optional\n",
" flux_unit : {'relative'}, string, optional\n",
" Strings describing period and flux units for labeling the plot.\n",
" Example: period_unit='seconds', flux_unit='relative' will label the x-axis with \"Period (seconds)\"\n",
" and label the y-axis with \"Lomb-Scargle Power Spectral Density\\n\" +\n",
" \"(from flux in relative, ang. freq. in 2*pi/seconds)\".\n",
" return_ax : {False, True}, bool\n",
" If `False` (default), show the periodogram plot. Return `None`.\n",
" If `True`, return a `matplotlib.axes` instance for additional modification.\n",
"\n",
" Returns\n",
" -------\n",
" ax : matplotlib.axes\n",
" Returned only if `return_ax` is `True`. Otherwise returns `None`.\n",
"\n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111, xscale=xscale)\n",
" ax.plot(periods, powers, color='black', linewidth=1)\n",
" ax.set_xlim(min(periods), max(periods))\n",
" ax.set_title((\"Generalized Lomb-Scargle periodogram\\n\" +\n",
" \"with {num} Fourier terms fit\").format(num=n_terms))\n",
" ax.set_xlabel(\"Period ({punit})\".format(punit=period_unit))\n",
" ax.set_ylabel(\n",
" (\"Lomb-Scargle Power Spectral Density\\n\" +\n",
" \"(from flux in {funit}, ang. freq. in 2*pi/{punit})\").format(\n",
" funit=flux_unit, punit=period_unit))\n",
" if return_ax:\n",
" return_obj = ax\n",
" else:\n",
" plt.show()\n",
" return_obj = None\n",
" return return_obj\n",
"\n",
"\n",
"# TODO: Create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_periodogram(times, fluxes, fluxes_err, min_period=None, max_period=None, num_periods=None,\n",
" sigs=(95.0, 99.0), num_bootstraps=100, show_periodogram=True,\n",
" period_unit='seconds', flux_unit='relative'):\n",
" \"\"\"Calculate periods, powers, and significance levels using generalized Lomb-Scargle periodogram.\n",
" Convenience function for methods from [1]_.\n",
" \n",
" Parameters\n",
" ----------\n",
" times : numpy.ndarray\n",
" 1D array of time coordinates for data. Unit is time, e.g. seconds or days.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes. Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" min_period : {None}, float, optional\n",
" Minimum period to sample. Unit is same as `times`.\n",
" If `None` (default), `min_period` = 2x median sampling period,\n",
" (the Nyquist limit from [2]_).\n",
" max_period : {None}, float, optional\n",
" Maximum period to sample. Unit is same as `times`.\n",
" If `None` (default), `max_period` = 0.5x acquisition time,\n",
" (1 / (2x the frequency resolution) adopted from [2]_).\n",
" num_periods : {None}, int, optional\n",
" Number of periods to sample, including `min_period` and `max_period`.\n",
" If `None` (default), `num_periods` = minimum of \n",
" acquisition time / median sampling period (adopted from [2]_), or\n",
" 1e4 (to limit computation time).\n",
" sigs : {(95.0, 99.0)}, tuple of floats, optional\n",
" Levels of statistical significance for which to compute corresponding\n",
" Lomb-Scargle powers via bootstrap analysis.\n",
" num_bootstraps : {100}, int, optional\n",
" Number of bootstrap resamplings to compute significance levels.\n",
" show_periodogram : {True, False}, bool, optional\n",
" If `True` (default), display periodogram plot of Lomb-Scargle power spectral density vs period\n",
" with significance levels.\n",
" period_unit : {'seconds'}, string, optional\n",
" flux_unit : {'relative'}, string, optional\n",
" Strings describing period and flux units for labeling the plot.\n",
" Example: period_unit='seconds', flux_unit='relative' will label the x-axis with \"Period (seconds)\"\n",
" and label the y-axis with \"Lomb-Scargle Power Spectral Density\\n\" +\n",
" \"(from flux in relative, ang. freq. in 2*pi/seconds)\".\n",
" \n",
" Returns\n",
" -------\n",
" periods : numpy.ndarray\n",
" 1D array of periods. Unit is same as `times`.\n",
" powers : numpy.ndarray\n",
" 1D array of powers. Unit is Lomb-Scargle power spectral density from flux and angular frequency,\n",
" e.g. from relative flux, angular frequency 2*pi/seconds.\n",
" sigs_powers : list of tuple of floats\n",
" Powers corresponding to levels of statistical significance from bootstrap analysis.\n",
" Example: [(95.0, 0.05), (99.0, 0.06)]\n",
" \n",
" See Also\n",
" --------\n",
" astroML.time_series.search_frequencies, select_sig_periods_powers\n",
" \n",
" Notes\n",
" -----\n",
" - Minimum period default calculation:\n",
" min_period = 2.0 * np.median(np.diff(times))\n",
" - Maximum period default calculation:\n",
" max_period = 0.5 * (max(times) - min(times))\n",
" - Number of periods default calculation:\n",
" num_periods = int(min(\n",
" (max(times) - min(times)) / np.median(np.diff(times))),\n",
" 1e4)\n",
" - Period sampling is linear in angular frequency space with more samples for shorter periods.\n",
" - Computing periodogram of 1e4 periods with 100 bootstraps takes ~85 seconds for a single 2.7 GHz core.\n",
" Computation time is approximately linear with number of periods and number of bootstraps.\n",
" - Call before `astroML.time_series.search_frequencies`.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" .. [2] http://zone.ni.com/reference/en-XX/help/372416B-01/svtconcepts/fft_funda/\n",
" \n",
" \"\"\"\n",
" # Check inputs.\n",
" median_sampling_period = np.median(np.diff(times))\n",
" min_period_nyquist = 2.0 * median_sampling_period\n",
" if min_period is None:\n",
" min_period = min_period_nyquist\n",
" elif min_period < min_period_nyquist:\n",
" warnings.warn(\n",
" (\"`min_period` is less than the Nyquist period limit (2x the median sampling period).\\n\" +\n",
" \"Input: min_period = {per}\\n\" +\n",
" \"Nyquist: min_period_nyquist = {per_nyq}\").format(per=min_period,\n",
" per_nyq=min_period_nyquist))\n",
" acquisition_time = max(times) - min(times)\n",
" max_period_acqtime = 0.5 * acquisition_time\n",
" if max_period is None:\n",
" max_period = max_period_acqtime\n",
" elif max_period > max_period_acqtime:\n",
" warnings.warn(\n",
" (\"`max_period` is greater than 0.5x the acquisition time.\\n\" +\n",
" \"Input: max_period = {per}\\n\" +\n",
" \"From data: max_period_acqtime = {per_acq}\").format(per=max_period,\n",
" per_acq=max_period_acqtime))\n",
" max_num_periods = int(acquisition_time / median_sampling_period)\n",
" if num_periods is None:\n",
" num_periods = int(min(max_num_periods, 1e4))\n",
" elif num_periods > max_num_periods:\n",
" warnings.warn(\n",
" (\"`num_periods` is greater than acquisition time div. by median sampling period.\\n\" +\n",
" \"Input: num_periods = {num}\\n\" +\n",
" \"From data: max_num_periods = {max_num}\").format(num=num_periods,\n",
" max_num=max_num_periods)) \n",
" comp_time = 85.0 * (num_periods/1e4) * (num_bootstraps/100) # in seconds\n",
" if comp_time > 10.0:\n",
" print(\"INFO: Estimated computation time: {time:.0f} sec\".format(time=comp_time))\n",
" # Compute periodogram.\n",
" max_omega = 2.0 * np.pi / min_period\n",
" min_omega = 2.0 * np.pi / max_period\n",
" omegas = np.linspace(start=min_omega, stop=max_omega, num=num_periods, endpoint=True)\n",
" periods = 2.0 * np.pi / omegas\n",
" powers = astroML_ts.lomb_scargle(t=times, y=fluxes, dy=fluxes_err, omega=omegas, generalized=True)\n",
" dists = astroML_ts.lomb_scargle_bootstrap(t=times, y=fluxes, dy=fluxes_err, omega=omegas, generalized=True,\n",
" N_bootstraps=num_bootstraps, random_state=0)\n",
" sigs_powers = zip(sigs, np.percentile(dists, sigs))\n",
" if show_periodogram:\n",
" # Plot custom periodogram with delta BIC.\n",
" ax0 = \\\n",
" plot_periodogram(\n",
" periods=periods, powers=powers, xscale='log', n_terms=1,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=True)\n",
" xlim = (min(periods), max(periods))\n",
" ax0.set_xlim(xlim)\n",
" for (sig, power) in sigs_powers:\n",
" ax0.plot(xlim, [power, power], color='black', linestyle=':')\n",
" ax0.set_title(\"Generalized Lomb-Scargle periodogram with\\n\" +\n",
" \"relative Bayesian Information Criterion\")\n",
" ax1 = ax0.twinx()\n",
" ax1.set_ylim(\n",
" tuple(\n",
" astroML_ts.lomb_scargle_BIC(\n",
" P=ax0.get_ylim(), y=fluxes, dy=fluxes_err, n_harmonics=1)))\n",
" ax1.set_ylabel(\"delta BIC\")\n",
" plt.show()\n",
" for (sig, power) in sigs_powers:\n",
" print(\"INFO: At significance = {sig}%, power spectral density = {pwr}\".format(sig=sig, pwr=power))\n",
" return (periods, powers, sigs_powers)\n",
"\n",
"\n",
"# TODO: Create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def select_sig_periods_powers(peak_periods, peak_powers, cutoff_power):\n",
" \"\"\"Select the periods with peak powers above the cutoff power.\n",
" \n",
" Parameters\n",
" ----------\n",
" peak_periods : numpy.ndarray\n",
" 1D array of periods. Unit is time, e.g. seconds or days.\n",
" peak_powers : numpy.ndarray\n",
" 1D array of powers. Unit is Lomb-Scargle power spectral density from flux and angular frequency,\n",
" e.g. from relative flux, angular frequency 2*pi/seconds.\n",
" cutoff_power : float\n",
" Power corresponding to a level of statistical significance. Only periods\n",
" above this cutoff power level are returned.\n",
" \n",
" Returns\n",
" -------\n",
" sig_periods : numpy.ndarray\n",
" 1D array of significant periods. Unit is same as `peak_periods`.\n",
" sig_powers : numpy.ndarray\n",
" 1D array of significant powers. Unit is same as `peak_powers`.\n",
"\n",
" See Also\n",
" --------\n",
" calc_periodogram, astroML.time_series.search_frequencies\n",
"\n",
" Notes\n",
" -----\n",
" - Call after `astroML.time_series.search_frequencies`.\n",
" - Call before `calc_best_period`.\n",
" \n",
" \"\"\"\n",
" sig_idxs = np.where(peak_powers > cutoff_power)\n",
" sig_periods = peak_periods[sig_idxs]\n",
" sig_powers = peak_powers[sig_idxs]\n",
" return (sig_periods, sig_powers)\n",
"\n",
"\n",
"# TODO: Create test from numpy example."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_best_period(times, fluxes, fluxes_err, candidate_periods,\n",
" n_terms=6, show_periodograms=False, show_summary_plots=True,\n",
" period_unit='seconds', flux_unit='relative'):\n",
" \"\"\"Calculate the period that best represents the data from a multi-term generalized Lomb-Scargle\n",
" periodogram. Convenience function for methods from [1]_.\n",
" \n",
" Parameters\n",
" ----------\n",
" times : numpy.ndarray\n",
" 1D array of time coordinates for data. Unit is time, e.g. seconds or days.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes. Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" candidate_periods : numpy.ndarray\n",
" 1D array of candidate periods. Unit is same as `times`.\n",
" n_terms : {6}, int, optional\n",
" Number of Fourier terms to fit the light curve. To fit eclipses well often requires ~6 terms,\n",
" from section 10.3.3 of [1]_.\n",
" show_periodograms : {False, True}, bool, optional\n",
" If `False` (default), do not display periodograms (power vs period) for each candidate period.\n",
" show_summary_plots : {True, False}, bool, optional\n",
" If `True` (default), display summary plots of delta BIC vs period and periodogram for best fit period.\n",
" period_unit : {'seconds'}, string, optional\n",
" flux_unit : {'relative'}, string, optional\n",
" Strings describing period and flux units for labeling the plot.\n",
" Example: period_unit='seconds', flux_unit='relative' will label the x-axis with \"Period (seconds)\"\n",
" and label the y-axis with \"Lomb-Scargle Power Spectral Density\\n\" +\n",
" \"(from flux in relative, ang. freq. in 2*pi/seconds)\".\n",
" \n",
" Returns\n",
" -------\n",
" best_period : float\n",
" Period with the highest relative Bayesian Information Criterion. Unit is same as `times`.\n",
"\n",
" See Also\n",
" --------\n",
" astroML.time_series.search_frequencies, calc_num_terms\n",
"\n",
" Notes\n",
" -----\n",
" - Ranges around each candidate period are based on the angular frequency resolution\n",
" of the original data. Adopted from [2]_.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 1000 # chosen to balance fast computation with medium range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.1 # ensure sampling precision is higher than data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" - Calculating best period from 100 candidate periods takes ~61 seconds for a single 2.7 GHz core.\n",
" Computation time is approximately linear with number of candidate periods.\n",
" - Call after `astroML.time_series.search_frequencies`.\n",
" - Call before `calc_num_terms`.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" .. [2] http://zone.ni.com/reference/en-XX/help/372416A-01/svtconcepts/fft_funda/\n",
" \n",
" \"\"\"\n",
" # Check input\n",
" candidate_periods = sorted(candidate_periods) # sort to allow combining identical periods\n",
" comp_time = 61 * len(candidate_periods)/100 \n",
" if comp_time > 10.0:\n",
" print(\"INFO: Estimated computation time: {time:.0f} sec\".format(time=comp_time))\n",
" # Calculate the multiterm periodograms using a range around each candidate angular frequency\n",
" # based on the angular frequency resolution of the original data.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 1000 # chosen to balance fast computation with medium range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.1 # ensure sampling precision is higher than data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" max_period = 0.5 * acquisition_time\n",
" min_omega = 2.0 * np.pi / max_period\n",
" median_sampling_period = np.median(np.diff(times))\n",
" min_period = 2.0 * median_sampling_period\n",
" max_omega = 2.0 * np.pi / (min_period)\n",
" periods_bics = []\n",
" for candidate_period in candidate_periods:\n",
" candidate_omega = 2.0 * np.pi / candidate_period\n",
" range_omegas = \\\n",
" np.clip(\n",
" np.linspace(\n",
" start=candidate_omega - range_omega_halfwidth,\n",
" stop=candidate_omega + range_omega_halfwidth,\n",
" num=num_omegas, endpoint=True),\n",
" min_omega, max_omega)\n",
" range_periods = 2.0 * np.pi / range_omegas\n",
" range_powers = astroML_ts.multiterm_periodogram(t=times, y=fluxes, dy=fluxes_err,\n",
" omega=range_omegas, n_terms=n_terms)\n",
" range_bic_max = max(astroML_ts.lomb_scargle_BIC(P=range_powers, y=fluxes, dy=fluxes_err,\n",
" n_harmonics=n_terms))\n",
" range_omega_best = range_omegas[np.argmax(range_powers)]\n",
" range_period_best = 2.0 * np.pi / range_omega_best\n",
" # Combine identical periods, but only keep the larger delta BIC.\n",
" if len(periods_bics) > 0:\n",
" if np.isclose(last_range_omega_best, range_omega_best, atol=omega_resolution):\n",
" if last_range_bic_max < range_bic_max:\n",
" periods_bics[-1] = (range_period_best, range_bic_max)\n",
" else:\n",
" periods_bics.append((range_period_best, range_bic_max))\n",
" else:\n",
" periods_bics.append((range_period_best, range_bic_max))\n",
" (last_range_period_best, last_range_bic_max) = periods_bics[-1]\n",
" last_range_omega_best = 2.0 * np.pi / last_range_period_best\n",
" if show_periodograms:\n",
" print(80*'-')\n",
" plot_periodogram(periods=range_periods, powers=range_powers, xscale='linear', n_terms=n_terms,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=False)\n",
" print(\"Candidate period: {per} seconds\".format(per=candidate_period))\n",
" print(\"Best period within window: {per} seconds\".format(per=range_period_best))\n",
" print(\"Relative Bayesian Information Criterion: {bic}\".format(bic=range_bic_max))\n",
" # Choose the best period from the maximum delta BIC.\n",
" best_idx = np.argmax(zip(*periods_bics)[1])\n",
" (best_period, best_bic) = periods_bics[best_idx]\n",
" if show_summary_plots:\n",
" # Plot delta BICs after all periods have been fit.\n",
" print(80*'-')\n",
" periods_bics_t = zip(*periods_bics)\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111, xscale='log')\n",
" ax.plot(periods_bics_t[0], periods_bics_t[1], color='black', marker='o')\n",
" ax.set_title(\"Relative Bayesian Information Criterion vs period\")\n",
" ax.set_xlabel(\"Period (seconds)\")\n",
" ax.set_ylabel(\"delta BIC\")\n",
" plt.show()\n",
" best_omega = 2.0 * np.pi / best_period\n",
" range_omegas = \\\n",
" np.clip(\n",
" np.linspace(\n",
" start=best_omega - range_omega_halfwidth,\n",
" stop=best_omega + range_omega_halfwidth,\n",
" num=num_omegas, endpoint=True),\n",
" min_omega, max_omega)\n",
" range_periods = 2.0 * np.pi / range_omegas\n",
" range_powers = astroML_ts.multiterm_periodogram(t=times, y=fluxes, dy=fluxes_err,\n",
" omega=range_omegas, n_terms=n_terms)\n",
" plot_periodogram(periods=range_periods, powers=range_powers, xscale='linear', n_terms=n_terms,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=False)\n",
" print(\"Best period: {per} seconds\".format(per=best_period))\n",
" print(\"Relative Bayesian Information Criterion: {bic}\".format(bic=best_bic))\n",
" return best_period\n",
"\n",
"# TODO: Create test."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_num_terms(times, fluxes, fluxes_err, best_period, max_n_terms=20, show_periodograms=False,\n",
" show_summary_plots=True, period_unit='seconds', flux_unit='relative'):\n",
" \"\"\"Calculate the number of Fourier terms that best represent the data's underlying\n",
" variability for representation by a multi-term generalized Lomb-Scargle periodogram.\n",
" Convenience function for methods from [1]_.\n",
" \n",
" Parameters\n",
" ----------\n",
" times : numpy.ndarray\n",
" 1D array of time coordinates for data. Unit is time, e.g. seconds or days.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes. Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" best_period : float\n",
" Period that best represents the data. Unit is same as `times`.\n",
" max_n_terms : {20}, int, optional\n",
" Maximum number of terms to attempt fitting.\n",
" Example: From 10.3.3 of [1]_, many light curves of eclipses are well represented\n",
" with ~6 terms and are best fit with ~10 terms.\n",
" show_periodograms : {False, True}, bool, optional\n",
" If `False` (default), do not display periodograms (power vs period) for each candidate number of terms.\n",
" show_summary_plots : {True, False}, bool, optional\n",
" If `True` (default), display summary plots of delta BIC vs number of terms, periodogram and\n",
" phased light curve for best fit number of terms.\n",
" period_unit : {'seconds'}, string, optional\n",
" flux_unit : {'relative'}, string, optional\n",
" Strings describing period and flux units for labeling the plots.\n",
" Example: period_unit='seconds', flux_unit='relative' will label the x-axis with \"Period (seconds)\"\n",
" and label the y-axis with \"Lomb-Scargle Power Spectral Density\\n\" +\n",
" \"(from flux in relative, ang. freq. in 2*pi/seconds)\".\n",
" \n",
" Returns\n",
" -------\n",
" best_n_terms : int\n",
" Number of Fourier terms that best fit the light curve. The number of terms\n",
" is determined by the maximum relative Bayesian Information Criterion, from\n",
" section 10.3.3 of [1]_.\n",
" phases : ndarray\n",
" The phase coordinates of the best-fit light curve. Unit is decimal orbital phase.\n",
" fits_phased : ndarray\n",
" The relative fluxes for the `phases` of the best-fit light curve. Unit is same as `fluxes`.\n",
" times_phased : ndarray\n",
" The phases of the corresponding input `times`. Unit is decimal orbital phase.\n",
"\n",
" See Also\n",
" --------\n",
" calc_best_period, refine_best_period\n",
"\n",
" Notes\n",
" -----\n",
" - Range around the best period is based on the angular frequency resolution\n",
" of the original data. Adopted from [2]_.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 1000 # chosen to balance fast computation with medium range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.1 # ensure sampling precision is higher than data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" - Call after `calc_best_period`.\n",
" - Call before `refine_best_period`.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" # Calculate the multiterm periodograms and choose the best number of terms from the maximum relative BIC.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 1000 # chosen to balance fast computation with medium range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.1 # ensure sampling precision is higher than data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" max_period = 0.5 * acquisition_time\n",
" min_omega = 2.0 * np.pi / max_period\n",
" median_sampling_period = np.median(np.diff(times))\n",
" min_period = 2.0 * median_sampling_period\n",
" max_omega = 2.0 * np.pi / (min_period)\n",
" best_omega = 2.0 * np.pi / best_period\n",
" range_omegas = \\\n",
" np.clip(\n",
" np.linspace(\n",
" start=best_omega - range_omega_halfwidth,\n",
" stop=best_omega + range_omega_halfwidth,\n",
" num=num_omegas, endpoint=True),\n",
" min_omega, max_omega)\n",
" range_periods = 2.0 * np.pi / range_omegas\n",
" nterms_bics = []\n",
" for n_terms in range(1, max_n_terms+1):\n",
" range_powers = astroML_ts.multiterm_periodogram(t=times, y=fluxes, dy=fluxes_err,\n",
" omega=range_omegas, n_terms=n_terms)\n",
" range_bic_max = max(astroML_ts.lomb_scargle_BIC(P=range_powers, y=fluxes, dy=fluxes_err,\n",
" n_harmonics=n_terms))\n",
" nterms_bics.append((n_terms, range_bic_max))\n",
" if show_periodograms:\n",
" print(80*'-')\n",
" plot_periodogram(periods=range_periods, powers=range_powers, xscale='linear', n_terms=n_terms,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=False)\n",
" print(\"Number of Fourier terms: {num}\".format(num=n_terms))\n",
" print(\"Relative Bayesian Information Criterion: {bic}\".format(bic=range_bic_max))\n",
" # Choose the best number of Fourier terms from the maximum delta BIC.\n",
" best_idx = np.argmax(zip(*nterms_bics)[1])\n",
" (best_n_terms, best_bic) = nterms_bics[best_idx]\n",
" mtf = astroML_ts.MultiTermFit(omega=best_omega, n_terms=best_n_terms)\n",
" mtf.fit(t=times, y=fluxes, dy=fluxes_err)\n",
" (phases, fits_phased, times_phased) = mtf.predict(Nphase=1000, return_phased_times=True, adjust_offset=True)\n",
" if show_summary_plots:\n",
" # Plot delta BICs after all terms have been fit.\n",
" print(80*'-')\n",
" nterms_bics_t = zip(*nterms_bics)\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
" ax.plot(nterms_bics_t[0], nterms_bics_t[1], color='black', marker='o')\n",
" ax.set_xlim(min(nterms_bics_t[0]), max(nterms_bics_t[0]))\n",
" ax.set_title(\"Relative Bayesian Information Criterion vs\\n\" +\n",
" \"number of Fourier terms\")\n",
" ax.set_xlabel(\"number of Fourier terms\")\n",
" ax.set_ylabel(\"delta BIC\")\n",
" plt.show()\n",
" range_powers = astroML_ts.multiterm_periodogram(t=times, y=fluxes, dy=fluxes_err,\n",
" omega=range_omegas, n_terms=best_n_terms)\n",
" plot_periodogram(periods=range_periods, powers=range_powers, xscale='linear', n_terms=best_n_terms,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=False)\n",
" print(\"Best number of Fourier terms: {num}\".format(num=best_n_terms))\n",
" print(\"Relative Bayesian Information Criterion: {bic}\".format(bic=best_bic))\n",
" return (best_n_terms, phases, fits_phased, times_phased)\n",
"\n",
"# TODO: Create test"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_phased_light_curve(phases, fits_phased, times_phased, fluxes, fluxes_err, n_terms=1,\n",
" flux_unit='relative', return_ax=False):\n",
" \"\"\"Plot a phased light curve. Convenience function for\n",
" plot formats from [1]_.\n",
"\n",
" Parameters\n",
" ----------\n",
" phases : ndarray\n",
" The phase coordinates of the best-fit light curve. Unit is decimal orbital phase.\n",
" fits_phased : ndarray\n",
" The relative fluxes for corresponding `phases` of the best-fit light curve.\n",
" Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" times_phased : ndarray\n",
" The phases of the time coordinates for the observed data. Unit is decimal orbital phase.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes corresponding to `times_phased`. Unit is integrated flux,\n",
" e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" n_terms : {1}, int, optional\n",
" Number of Fourier terms used to fit the light curve.\n",
" flux_unit : {'relative'}, string, optional\n",
" String describing flux units for labeling the plot.\n",
" Example: flux_unit='relative' will label the y-axis with \"Flux (relative)\".\n",
" return_ax : {False, True}, bool\n",
" If `False` (default), show the periodogram plot. Return `None`.\n",
" If `True`, return a `matplotlib.axes` instance for additional modification.\n",
"\n",
" Returns\n",
" -------\n",
" ax : matplotlib.axes\n",
" Returned only if `return_ax` is `True`. Otherwise returns `None`.\n",
" \n",
" See Also\n",
" --------\n",
" plot_periodogram\n",
" \n",
" Notes\n",
" -----\n",
" - The phased light curve is plotted through two complete cycles to illustrate the primary minimum.\n",
"\n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
" ax.errorbar(np.append(times_phased, np.add(times_phased, 1.0)), np.append(fluxes, fluxes),\n",
" np.append(fluxes_err, fluxes_err), fmt='.k', ecolor='gray', linewidth=1)\n",
" ax.plot(np.append(phases, np.add(phases, 1.0)), np.append(fits_phased, fits_phased), color='blue', linewidth=2)\n",
" ax.set_title((\"Phased light curve\\n\" +\n",
" \"with {num} Fourier terms fit\").format(num=n_terms))\n",
" ax.set_xlabel(\"Orbital phase (decimal)\")\n",
" ax.set_ylabel(\"Flux ({unit})\".format(unit=flux_unit))\n",
" if return_ax:\n",
" return_obj = ax\n",
" else:\n",
" plt.show()\n",
" return_obj = None\n",
" return return_obj\n",
"\n",
"\n",
"# TODO: Create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def refine_best_period(times, fluxes, fluxes_err, best_period, n_terms=6,\n",
" show_plots=True, period_unit='seconds', flux_unit='relative'):\n",
" \"\"\"Refine the best period to a higher precision from a multi-term generalized Lomb-Scargle\n",
" periodogram. Convenience function for methods from [1]_.\n",
" \n",
" Parameters\n",
" ----------\n",
" times : numpy.ndarray\n",
" 1D array of time coordinates for data. Unit is time, e.g. seconds or days.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes. Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" best_period : float\n",
" Period that best represents the data. Unit is same as `times`.\n",
" n_terms : {6}, int, optional\n",
" Number of Fourier terms to fit the light curve. To fit eclipses well often requires ~6 terms,\n",
" from section 10.3.3 of [1]_.\n",
" show_plots : {True, False}, bool, optional\n",
" If `True`, display plots of periodograms and phased light curves.\n",
" period_unit : {'seconds'}, string, optional\n",
" flux_unit : {'relative'}, string, optional\n",
" Strings describing period and flux units for labeling the plot.\n",
" Example: period_unit='seconds', flux_unit='relative' will label a periodogram\n",
" x-axis with \"Period (seconds)\" and label a periodogram y-axis with \n",
" \"Lomb-Scargle Power Spectral Density\\n(from flux in relative, ang. freq. in 2*pi/seconds)\".\n",
"\n",
" \n",
" Returns\n",
" -------\n",
" refined_period : float\n",
" Refined period. Unit is same as `times`.\n",
" refined_period_resolution : float\n",
" Precision of refined period. Unit is same as `times`.\n",
" phases : ndarray\n",
" The phase coordinates of the best-fit light curve. Unit is decimal orbital phase.\n",
" fits_phased : ndarray\n",
" The relative fluxes for the `phases` of the best-fit light curve. Unit is same as `fluxes`.\n",
" times_phased : ndarray\n",
" The phases of the corresponding input `times`. Unit is decimal orbital phase.\n",
" mtf : astroML.time_series.MultiTermFit\n",
" Instance of the `astroML.time_series.MultiTermFit` class for the best fit model.\n",
"\n",
" See Also\n",
" --------\n",
" calc_best_period, calc_num_terms\n",
"\n",
" Notes\n",
" -----\n",
" - Range around the best period is based on the angular frequency resolution\n",
" of the original data. Adopted from [2]_.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 2000 # chosen to balance fast computation with small range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.01 # ensure sampling precision very high relative to data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" - Resolution of refined period (period precision) is based on time resolution of original data.\n",
" max_period = 0.5 * acquisition_time\n",
" min_omega = 2.0 * np.pi / max_period\n",
" median_sampling_period = np.median(np.diff(times))\n",
" min_period = 2.0 * median_sampling_period\n",
" max_omega = 2.0 * np.pi / (min_period)\n",
" period_resolution = 2.0 * np.pi / (max_omega - min_omega)\n",
" - Call after `calc_num_terms`.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" .. [2] http://zone.ni.com/reference/en-XX/help/372416A-01/svtconcepts/fft_funda/\n",
" \n",
" \"\"\"\n",
" # Calculate the multiterm periodogram and choose the best period from the maximal power.\n",
" acquisition_time = max(times) - min(times)\n",
" omega_resolution = 2.0 * np.pi / acquisition_time\n",
" num_omegas = 2000 # chosen to balance fast computation with medium range\n",
" anti_aliasing = 1.0 / 2.56 # remove digital aliasing\n",
" sampling_precision = 0.01 # ensure sampling precision very high relative to data precision\n",
" range_omega_halfwidth = (num_omegas/2.0) * omega_resolution * anti_aliasing * sampling_precision\n",
" max_period = 0.5 * acquisition_time\n",
" min_omega = 2.0 * np.pi / max_period\n",
" median_sampling_period = np.median(np.diff(times))\n",
" min_period = 2.0 * median_sampling_period\n",
" max_omega = 2.0 * np.pi / (min_period)\n",
" refined_period_resolution = 2.0 * np.pi / (max_omega - min_omega)\n",
" best_omega = 2.0 * np.pi / best_period\n",
" range_omegas = \\\n",
" np.clip(\n",
" np.linspace(\n",
" start=best_omega - range_omega_halfwidth,\n",
" stop=best_omega + range_omega_halfwidth,\n",
" num=num_omegas, endpoint=True),\n",
" min_omega, max_omega)\n",
" range_periods = 2.0 * np.pi / range_omegas\n",
" range_powers = astroML_ts.multiterm_periodogram(t=times, y=fluxes, dy=fluxes_err,\n",
" omega=range_omegas, n_terms=n_terms)\n",
" refined_omega = range_omegas[np.argmax(range_powers)]\n",
" refined_period = 2.0 * np.pi / refined_omega\n",
" mtf = astroML_ts.MultiTermFit(omega=refined_omega, n_terms=n_terms)\n",
" mtf.fit(t=times, y=fluxes, dy=fluxes_err)\n",
" (phases, fits_phased, times_phased) = mtf.predict(Nphase=1000, return_phased_times=True, adjust_offset=True)\n",
" if show_plots:\n",
" plot_periodogram(periods=range_periods, powers=range_powers, xscale='linear', n_terms=n_terms,\n",
" period_unit=period_unit, flux_unit=flux_unit, return_ax=False)\n",
" plot_phased_light_curve(phases=phases, fits_phased=fits_phased, times_phased=times_phased,\n",
" fluxes=fluxes, fluxes_err=fluxes_err, n_terms=n_terms,\n",
" flux_unit=flux_unit, return_ax=False)\n",
" print(\"Refined period: {per} seconds\".format(per=refined_period))\n",
" print(\"Refined period resolution: {per_res} seconds\".format(per_res=refined_period_resolution))\n",
" return (refined_period, refined_period_resolution, phases, fits_phased, times_phased, mtf)\n",
"\n",
"# TODO: Create test."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_flux_fits_residuals(phases, fits_phased, times_phased, fluxes):\n",
" \"\"\"Calculate the fluxes and their residuals at phased times from a fit\n",
" to a light curve.\n",
" \n",
" Parameters\n",
" ----------\n",
" phases : numpy.ndarray\n",
" The phase coordinates of the best-fit light curve. Unit is decimal orbital phase.\n",
" Required: numpy.shape(phases) == numpy.shape(fits_phased)\n",
" fits_phased : numpy.ndarray\n",
" The relative fluxes for the `phases` of the best-fit light curve. Unit is relative flux.\n",
" Required: numpy.shape(phases) == numpy.shape(fits_phased)\n",
" times_phased : numpy.ndarray\n",
" The phases coordinates of the `fluxes`. Unit is decimal orbital phase.\n",
" Required: numpy.shape(times_phased) == numpy.shape(fluxes)\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes. Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" Required: numpy.shape(times_phased) == numpy.shape(fluxes)\n",
"\n",
" Returns\n",
" -------\n",
" fit_fluxes : numpy.ndarray\n",
" 1D array of `fits_phased` resampled at `times_phased`.\n",
" numpy.shape(fluxes_fit) == numpy.shape(fluxes)\n",
" residuals : numpy.ndarray\n",
" 1D array of the differences between `fluxes` and `fits_phased` resampled at `times_phased`:\n",
" residuals = fluxes - fits_phased_resampled\n",
" numpy.shape(residuals) == numpy.shape(fluxes)\n",
" \n",
" \"\"\"\n",
" fit_fluxes = np.interp(x=times_phased, xp=phases, fp=fits_phased)\n",
" residuals = np.subtract(fluxes, fit_fluxes)\n",
" return (fit_fluxes, residuals)\n",
"\n",
"\n",
"# TODO: create test\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Analyze SDSS J160036.83+272117.8 light curve"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Load light curve"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Load original data.\")\n",
"path_project = os.path.abspath(r'/Users/harrold/Google Drive/ccd.utexas/Projects/20140630_SDSS_J160036.83+272117.8')\n",
"path_crts = \\\n",
" os.path.join(\n",
" path_project,\n",
" os.path.relpath(r'Work_Logs/20141203_CRTS_data/result_web_fileovSSl4.csv'))\n",
"df_crts = (pd.DataFrame.from_csv(path=path_crts)).reset_index()\n",
"df_crts.sort(columns='MJD', ascending=True, inplace=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df_crts.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>MasterID</th>\n",
" <th>Mag</th>\n",
" <th>Magerr</th>\n",
" <th>RA</th>\n",
" <th>Dec</th>\n",
" <th>MJD</th>\n",
" <th>Blend</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.45</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15338</td>\n",
" <td> 27.35499</td>\n",
" <td> 53470.38932</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.41</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15344</td>\n",
" <td> 27.35494</td>\n",
" <td> 53470.39657</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.36</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15339</td>\n",
" <td> 27.35497</td>\n",
" <td> 53470.40384</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.39</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15336</td>\n",
" <td> 27.35496</td>\n",
" <td> 53470.41115</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.49</td>\n",
" <td> 0.09</td>\n",
" <td> 240.15342</td>\n",
" <td> 27.35490</td>\n",
" <td> 53479.38284</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 12,
"text": [
" MasterID Mag Magerr RA Dec MJD Blend\n",
"0 1126078052790 17.45 0.10 240.15338 27.35499 53470.38932 0\n",
"1 1126078052790 17.41 0.10 240.15344 27.35494 53470.39657 0\n",
"2 1126078052790 17.36 0.10 240.15339 27.35497 53470.40384 0\n",
"3 1126078052790 17.39 0.10 240.15336 27.35496 53470.41115 0\n",
"4 1126078052790 17.49 0.09 240.15342 27.35490 53479.38284 0"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Transform light curve units"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- **Notes:**\n",
" - CRTS photometry is in Vmag (from http://nesssi.cacr.caltech.edu/DataRelease/).\n",
" - The photometry is from the Catalina Sky Survey Schmidt telescope, Steward Observatory, Tucson, Arizona (from http://nesssi.cacr.caltech.edu/DataRelease/ > \"Check image coverage by `location`.\" and from individual coverage maps http://crts.caltech.edu/Telescopes.html). Telescope location (longitude, latitude): (-110 deg 43.9 min West, +32 deg 25 min North) = (-110.731667 deg, 32.4166667 deg) (from http://www.lpl.arizona.edu/css/css_facilities.html).\n",
" - The data timestamp precision is 1e-5 days = ~1 second. Using the telescope location when converting to Barycentric Coordinate Time (TCB) does not improve the timestamp accuracy since the light travel time across the Earth's radius is ~0.02 sec, which is much less than the timestamp precision.\n",
" - Using Barycentric Coordinate Time relative to Unix epoch as time coordinates so that CRTS data can be combined with other data in units of seconds.\n",
" - Using relative flux so that CRTS data can be combined with other data that is differential photometry, not absolute."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Convert time and magnitude units.\")\n",
"# For telescope location, see notes above and http://nesssi.cacr.caltech.edu/DataRelease/\n",
"telescope_location = (-110.731667*ast_units.deg, 32.4166667*ast_units.deg)\n",
"df_crts['datetime_TCB'] = ast_time.Time(df_crts['MJD'].values, format='mjd', scale='utc',\n",
" location=telescope_location, precision=6).tcb.datetime\n",
"df_crts['unixtime_TCB'] = map(lambda dt: np.datetime64(dt).astype(np.int64) / 1e9,\n",
" df_crts['datetime_TCB'].values)\n",
"df_crts['flux_rel'] = \\\n",
" map(lambda mag_1: \\\n",
" bss.utils.calc_flux_intg_ratio_from_mags(\n",
" mag_1=mag_1,\n",
" mag_2=df_crts['Mag'].median()),\n",
" df_crts['Mag'].values)\n",
"df_crts['flux_rel_err'] = \\\n",
" map(lambda mag_1, mag_2: \\\n",
" abs(1.0 - bss.utils.calc_flux_intg_ratio_from_mags(\n",
" mag_1=mag_1,\n",
" mag_2=mag_2)),\n",
" (df_crts['Mag'] + df_crts['Magerr']).values,\n",
" df_crts['Mag'])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df_crts.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>MasterID</th>\n",
" <th>Mag</th>\n",
" <th>Magerr</th>\n",
" <th>RA</th>\n",
" <th>Dec</th>\n",
" <th>MJD</th>\n",
" <th>Blend</th>\n",
" <th>datetime_TCB</th>\n",
" <th>unixtime_TCB</th>\n",
" <th>flux_rel</th>\n",
" <th>flux_rel_err</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.45</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15338</td>\n",
" <td> 27.35499</td>\n",
" <td> 53470.38932</td>\n",
" <td> 0</td>\n",
" <td>2005-04-10 09:21:55.267443</td>\n",
" <td> 1.113125e+09</td>\n",
" <td> 0.972747</td>\n",
" <td> 0.087989</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.41</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15344</td>\n",
" <td> 27.35494</td>\n",
" <td> 53470.39657</td>\n",
" <td> 0</td>\n",
" <td>2005-04-10 09:32:21.667452</td>\n",
" <td> 1.113126e+09</td>\n",
" <td> 1.009253</td>\n",
" <td> 0.087989</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.36</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15339</td>\n",
" <td> 27.35497</td>\n",
" <td> 53470.40384</td>\n",
" <td> 0</td>\n",
" <td>2005-04-10 09:42:49.795462</td>\n",
" <td> 1.113126e+09</td>\n",
" <td> 1.056818</td>\n",
" <td> 0.087989</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.39</td>\n",
" <td> 0.10</td>\n",
" <td> 240.15336</td>\n",
" <td> 27.35496</td>\n",
" <td> 53470.41115</td>\n",
" <td> 0</td>\n",
" <td>2005-04-10 09:53:21.379472</td>\n",
" <td> 1.113127e+09</td>\n",
" <td> 1.028016</td>\n",
" <td> 0.087989</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 1126078052790</td>\n",
" <td> 17.49</td>\n",
" <td> 0.09</td>\n",
" <td> 240.15342</td>\n",
" <td> 27.35490</td>\n",
" <td> 53479.38284</td>\n",
" <td> 0</td>\n",
" <td>2005-04-19 09:12:35.407440</td>\n",
" <td> 1.113902e+09</td>\n",
" <td> 0.937562</td>\n",
" <td> 0.079550</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
" MasterID Mag Magerr RA Dec MJD Blend \\\n",
"0 1126078052790 17.45 0.10 240.15338 27.35499 53470.38932 0 \n",
"1 1126078052790 17.41 0.10 240.15344 27.35494 53470.39657 0 \n",
"2 1126078052790 17.36 0.10 240.15339 27.35497 53470.40384 0 \n",
"3 1126078052790 17.39 0.10 240.15336 27.35496 53470.41115 0 \n",
"4 1126078052790 17.49 0.09 240.15342 27.35490 53479.38284 0 \n",
"\n",
" datetime_TCB unixtime_TCB flux_rel flux_rel_err \n",
"0 2005-04-10 09:21:55.267443 1.113125e+09 0.972747 0.087989 \n",
"1 2005-04-10 09:32:21.667452 1.113126e+09 1.009253 0.087989 \n",
"2 2005-04-10 09:42:49.795462 1.113126e+09 1.056818 0.087989 \n",
"3 2005-04-10 09:53:21.379472 1.113127e+09 1.028016 0.087989 \n",
"4 2005-04-19 09:12:35.407440 1.113902e+09 0.937562 0.079550 "
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df_crts.describe()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>MasterID</th>\n",
" <th>Mag</th>\n",
" <th>Magerr</th>\n",
" <th>RA</th>\n",
" <th>Dec</th>\n",
" <th>MJD</th>\n",
" <th>Blend</th>\n",
" <th>unixtime_TCB</th>\n",
" <th>flux_rel</th>\n",
" <th>flux_rel_err</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td> 3.880000e+02</td>\n",
" <td> 388.000000</td>\n",
" <td> 388.000000</td>\n",
" <td> 388.000000</td>\n",
" <td> 388.000000</td>\n",
" <td> 388.000000</td>\n",
" <td> 388</td>\n",
" <td> 3.880000e+02</td>\n",
" <td> 388.000000</td>\n",
" <td> 388.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 17.478428</td>\n",
" <td> 0.103067</td>\n",
" <td> 240.153367</td>\n",
" <td> 27.355005</td>\n",
" <td> 55001.961761</td>\n",
" <td> 0</td>\n",
" <td> 1.245453e+09</td>\n",
" <td> 0.965972</td>\n",
" <td> 0.090177</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td> 0.000000e+00</td>\n",
" <td> 0.228205</td>\n",
" <td> 0.032256</td>\n",
" <td> 0.000084</td>\n",
" <td> 0.000071</td>\n",
" <td> 913.646033</td>\n",
" <td> 0</td>\n",
" <td> 7.893902e+07</td>\n",
" <td> 0.169248</td>\n",
" <td> 0.025432</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 16.730000</td>\n",
" <td> 0.080000</td>\n",
" <td> 240.152930</td>\n",
" <td> 27.354740</td>\n",
" <td> 53470.389320</td>\n",
" <td> 0</td>\n",
" <td> 1.113125e+09</td>\n",
" <td> 0.291072</td>\n",
" <td> 0.071034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 17.370000</td>\n",
" <td> 0.090000</td>\n",
" <td> 240.153320</td>\n",
" <td> 27.354960</td>\n",
" <td> 54257.247355</td>\n",
" <td> 0</td>\n",
" <td> 1.181109e+09</td>\n",
" <td> 0.952804</td>\n",
" <td> 0.079550</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 17.420000</td>\n",
" <td> 0.090000</td>\n",
" <td> 240.153370</td>\n",
" <td> 27.355000</td>\n",
" <td> 54923.401175</td>\n",
" <td> 0</td>\n",
" <td> 1.238665e+09</td>\n",
" <td> 1.000000</td>\n",
" <td> 0.079550</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 17.472500</td>\n",
" <td> 0.100000</td>\n",
" <td> 240.153410</td>\n",
" <td> 27.355040</td>\n",
" <td> 55830.152332</td>\n",
" <td> 0</td>\n",
" <td> 1.317008e+09</td>\n",
" <td> 1.047129</td>\n",
" <td> 0.087989</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td> 1.126078e+12</td>\n",
" <td> 18.760000</td>\n",
" <td> 0.320000</td>\n",
" <td> 240.153650</td>\n",
" <td> 27.355340</td>\n",
" <td> 56568.132160</td>\n",
" <td> 0</td>\n",
" <td> 1.380770e+09</td>\n",
" <td> 1.887991</td>\n",
" <td> 0.255268</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
" MasterID Mag Magerr RA Dec \\\n",
"count 3.880000e+02 388.000000 388.000000 388.000000 388.000000 \n",
"mean 1.126078e+12 17.478428 0.103067 240.153367 27.355005 \n",
"std 0.000000e+00 0.228205 0.032256 0.000084 0.000071 \n",
"min 1.126078e+12 16.730000 0.080000 240.152930 27.354740 \n",
"25% 1.126078e+12 17.370000 0.090000 240.153320 27.354960 \n",
"50% 1.126078e+12 17.420000 0.090000 240.153370 27.355000 \n",
"75% 1.126078e+12 17.472500 0.100000 240.153410 27.355040 \n",
"max 1.126078e+12 18.760000 0.320000 240.153650 27.355340 \n",
"\n",
" MJD Blend unixtime_TCB flux_rel flux_rel_err \n",
"count 388.000000 388 3.880000e+02 388.000000 388.000000 \n",
"mean 55001.961761 0 1.245453e+09 0.965972 0.090177 \n",
"std 913.646033 0 7.893902e+07 0.169248 0.025432 \n",
"min 53470.389320 0 1.113125e+09 0.291072 0.071034 \n",
"25% 54257.247355 0 1.181109e+09 0.952804 0.079550 \n",
"50% 54923.401175 0 1.238665e+09 1.000000 0.079550 \n",
"75% 55830.152332 0 1.317008e+09 1.047129 0.087989 \n",
"max 56568.132160 0 1.380770e+09 1.887991 0.255268 "
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Plot light curve using pandas plotting utilities.\")\n",
"df_plot = df_crts.set_index(keys='datetime_TCB', inplace=False)\n",
"ax = pd.DataFrame.plot(df_plot[['flux_rel', 'flux_rel_err']], yerr='flux_rel_err', marker='.', linestyle='', color='black')\n",
"ax.set_title(\"Light curve\")\n",
"plt.show(ax)\n",
"print(\"Plot light curve using matplotlib.\")\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.errorbar(df_crts['unixtime_TCB'], df_crts['flux_rel'], df_crts['flux_rel_err'],\n",
" fmt='.k', ecolor='gray', linewidth=1)\n",
"ax.set_title(\"Light curve\")\n",
"ax.set_xlabel(\"Unixtime (TCB)\")\n",
"ax.set_ylabel(\"Flux (relative)\")\n",
"plt.show(ax)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot light curve using pandas plotting utilities.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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jDn/0odh8iBpNCXXhpzlsBLkjLOdxcsalL+yBRpX5OMcN5FaCuqO+vl7Pnj17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\nHkYhIDURhwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11954e3d0>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot light curve using matplotlib.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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/fn3Uc11++eVRyxkL9vyXX365ueiii5zz+P1+U1JS4vwW+TdmzJgmr2vvT0vu\n0/HHH28A07NnT9O3b1/nmt26dXPu0XPPPWcqKyvNJZdcYnJzc83IkSOj1r21z8ndXvPz853POTk5\nYW3ymmuuiel88ZTHfW33+W+44Qbnmbn3AUyPHj3MoEGDDGCKi4s924z7uJKSkpjLZIwxK1euNFVV\nVaa4uDjqvcnKynI+d+nSxQwYMMD5XlpaGvbu2vuRm5vrHOtV5pYS6jub7aub+mtKk4junxgfVcDD\nHE0WGIaIjAIGm6NLpD5GAuIyfD4fBw4cYP/+/Xz00Ufs3LnTCdsfNGgQzz77LKeffjr33HMPvXv3\n5qabbmqVmhfNIyMrK8sJlOnbty+jRo0K85uOdOGLpo7b81qNB+DLL78kSlbeMLxGb9Zkkpuby4UX\nXkhVVRVZWVlhJrCdO3cyc+ZM5s2bx6hRo5KSgdSO4Lds2RKmxdjJvvfff5///M//ZNu2bTQ0NBAI\nBLj77rsbjbD8fj8333wzgUCA733ve04ivFhHhO75oYEDBzojw549e1JeXs5HH31E165dOXz4MHl5\nec5IUUQazUm417gGnJw+8a5xXVRUxNatW9m9e7fTXgCnLe3bt4//+Z//4ayzzqKhoYF9+/axYsWK\npIxArTZeWFjIgAEDePvtt535I8upp56aUC0m0oyYl5cXZkZ0j7rHjBkTduyePXvYs2cPWVlZzJs3\nz9OE9M9//hMIzgO6g1djITLAdfjw4XTt2pUVK1ZQXFzMvn37nPQ3Bw8edMzJNuiutraW6urqMIcL\nE7IuHDlyhCuuuCIsfU67IBZJAviAi0Kfc4HusUqh0LFRNQngN8C3XN8/APpF2S8u6bl582ZnFNa1\na1dz5plnho047MjEa7TSUtyjnDfeeMN07tzZDBs2zLnGyJEjTUlJiZk6dapZvny52bx5szMydx8b\nOSr0+/1h5T/++ONjLpN79ObWnM4777ywc0aO6q+55hrnWLemFMvoPhr2HFdccYXJz88P07Si/fXp\n08f53KtXrya1hJZoNzfccIMRkajXs3Xv379/mOYFmKFDhzpl8bpmZWVli9uWW0Ox5xg6dKgpKCgI\nK2tRUZHp3LmzAUxeXl5Ubbi1msT48eNNVlaW6dq1q7ngggtMz549HY2mV69eJicnx1x00UUxa3Dx\nlOfYY4916jt27Fjnd/f9GT9+fNgzdH+O9o7YNnj66aeHaRLxaOYWt+bv/my15Mi/M888M+x9cbeP\nLl26OFpO1MFRAAAgAElEQVRia60akZAATaJTc0JERCqA54HHQz8dDyzwPiIuBgBusbk1dP5WYW3V\nEIzira2tdUbRQ4cOdUY+iV6sxo5yXn31VWbNmsXPfvYzx4Y9fPhwXn75ZcrLyxu5EQKOLfrVV19t\nFC9RVFTklDU3N5c333yzReVzR2Bbu21OTg49evQgKyvL2c99j6CxO24gEGD16tXcfPPNMU9g+kIR\ns2vXrqWuri4sHUEkZ511FkOHDgWCo/aW+q83xcaNG50RXM+ePZ3ruduCnQcCOOmkkygpKeGuu+5i\n3bp1zda7pW1rzpw5lJSUsHTpUoqKisjJyaFPnz6ceeaZQPDe2Il1a5Ovr69n0qRJMV8jVpYsWcKR\nI0doaGhwbO52onjPnj3s37/fccn2wh9Kp+FeXKu6urrZ++fWMI0xznneffddRISNGzfy9ttvO8+w\nU6dOzjsO0KdPHzZs2BB2TtsG7dzF8OHDKSsra5GzitX8161bx7p165zPeXl5UT2Y1q9fz9133+18\nd6c5efTRR+nevTtPPfUUmzdvjtspINnE4t00ATgXWAVgjNkoIscmsAyRthMTbafKykrnc2lpabOu\ndzaZXmFhIccff7zTKZ5wwgmO6p9oN0Z3x2C9UQ4dOkROTk6j87u9GrKzs52G6tWp3HDDDTz99NNh\neZhiJVpMQa9evdi2bZtjOrAvf35+Pq+99lpYRLE7NbV7sjA3NzfuF8zd8UYjKyuLhx9+mNNPP51j\njjmGI0eOOMFykQnUWoN9Vt26dePll1/m7rvvJicnh3379jlCuKSkhBUrVpCdnU1+fj4XXHBBs2tW\n2EnRPn36UFxczLRp01i3bl3MJjC32fH55593OmLrZrl8+XIGDRrU6LjmTJDxYNuLNXFabIcMRyfy\nmxOC0by2YjHtDhs2jGXLlnHWWWc5nnQ+n4+9e/dijHEyHEPQ/TXS+WL9+vXccccdvPLKK43O7X7v\nE73aX21trfMuuYkceEWuWLl169aYnC6awy2QE0ZzqgawOvT/ndD/zsQ4cW1iMzdd6/qeEHOTMUfV\nwalTpzoqanZ2diP1uLUqebRr7tq1q9GkGmBOPPFEZwJ90aJFYWYwa4qKnLieP3++qaqqckwqVVVV\nZv78+TGryO76ucuUk5PjTLrZibeuXbuaSZMmmeXLl4eZo9zmEjsx6Da7xMPIkSPD7onbROC+3g03\n3BD226hRo5qsY7zP0d0+jDFhpqX8/HzTtWtX07t3b8e8gss0EemkYE2HkecpLi6O+/64zY7uSdDC\nwkKnjoWFhWGTpNGeRVPmy1hxT9zbNmKfV+/eveMyN8Vrfot05LD33ZpFRcTccccdpqSkJGyy2n5u\nypHhlVdeMZWVleahhx5y/j/00EPmlVdeiev+2OfhvtfWBOj+y83NNW+88UbYsZHPJ5H9kBsSYG6K\npZN/APhP4EPgYmA+8IuYL9C0kBgFLA59HgGs8tgvrhuzcuVKc8EFFzgd8tChQ8M6I3eHk+iHY89n\nBVOPHj0MYIYMGRJmC+3Vq5c55phjnM7Z7/c3WZaWehW5j3Hbc92eM+75gby8PE/vphtuuMEMHDjQ\n0wbeHJs3bzaLFi0yxcXFZvDgwaa4uNiceuqpRkScMhQWFpq77rrLnHTSSWEv2sUXXxz1nPZli/Rc\na64ckfMrbg+VaPMlubm5jgB1zydF0qtXr1YJCXdnaoVAly5dHI8mY4zp169fWOcdrd6tnW9zP6vi\n4mLz3HPPmZKSEjNp0iRTUlISJuxjOX9LvNCi3V/7zhCaq6isrDRTp041JSUl5uSTTzZdunRp1kvI\n3UHbQUKsRBskRM55Rvvr379/WL3dgwlbj2SQCCHR7JwEMBXYQdD19UZgMfCzGI5DRJ4jmHK8WES2\niMj3ReRGEbkx1PMvBj4SkU0E5zxujuW8zWH9qQOBAJs2bWLLli2OqtyrVy9uvfVWZs+eTWlpKVVV\nVQwZMoRHH32UVatWJeLywFHb8oYNGygpKeF3v/udEx0KwTQcBw8eBHAWBYqGtcVaYrXpNlWmpUuX\nRg36gaB9+9lnn+WUU05xvH0sGzduZMuWLdTX1zNixIio2VKbwufzMXr0aMaNG8d3v/tdxo0bx8cf\nf4wxxpmj2LlzJ6+//jonnniic9yQIUOieja5F+PZtGkTV155ZUz3xdqmbTTx6tWrHfNT//79nUh4\ntwln3759LF261DF1epmOhg0bBgTNCy1Jl+H2vLn88svp1KkT559/vpOuBXBMfwDHHXecE+jorntr\n59vss8rLy+PAgQNMmTKFvXv38sorr1BWVuaYc2M9vzuuIB5se589ezbV1dVhiwt9/PHHACxdupT6\n+no2bdrEwYMHOXLkCMOHD280J2Fxzx0uWrQo6j5e2LZjzd2lpaVOnbp06eLsJyJhZuFt27aFLULl\nNrvavqm90qSQEJHOwPvGmCeMMd8M/f3WxFgrY8w4Y0yhMaaLMWagMeZpY8zjxpjHXftMNMYMNsac\naYz5Wyvr43Qe1taenZ3tdMZ2EvScc85xgsECgQDvvvsu1dXVrc7hXlFRQVVVlbN+bnl5OUVFRZSX\nlzNkyBBnMh2Cwurcc88FjkaCQ2MhYBulpblOqinc9u7BgwcDQRdDt6tl//79nQnmffv2sWzZMqfz\ndacH2bZtW5MTltGIFHhAo2VMGxoaWLZsmbMIU3FxMTU1NZ4Lttj1MLp27cqNN94YNb2FF+6I65kz\nZ1JSUsJ1113H448/Tvfu3cOe1wknnEBZWRmLFy9uciL2+eefp6SkhNdeey3m9BBw9N7Yeu7Zs4c3\n3niDL7/8kpqaGq688krneu7XzxgTtU24BwStmW+zgnTr1q1s2bKFTZs28cgjj/DYY4/Fdf5AIOC0\np3jaja2bzVvlboOffPIJVVVVvP/++wQCgbD7cujQIU/HCnuOY445hr179zJq1Ki4BzxuFixYQElJ\nCWeccYbzW//+/enUqRN5eXlAUJj+4Q9/cLbbwcTgwYOdYNvWDACTSZMT18aYwyLyoYgUmeD6Eu0e\nd66YwsJC9u/fz6FDh+jUqZPzwlmf8kR5N9mOyWZ1DQQCfO1rX+Ob3/ym4y//0ksvha0U9+ijj1JS\nUuJEFY8ePZq1a9eGCQS3733Xrl1paGiImie/OSJ9+GfPns21115LfX09nTp1cpKPde7cmezsbF5+\n+WWOO+44/v73v4ethDZnzhyOP/546uvrW3TP7LNx54867rjj2Lx5s5MSBHBiFQ4cOBAmwNzYe25z\nKjU0NHDzzTc3uWpcJO6I64KCAicFx4gRI5g8eTLDhg3jtttuA+CWW25hx44dTpux9Yh0oGhp+gl7\nbwYOHMh7771HcXEx+fn5rF27luLiYiZPnuy0j7y8PGdE7fZKc98XwPG4cZ8/Xuz9z8vLcyay6+vr\nKS8vj+v8sb5rXjE+lnPOOYdly5Zx2mmnISJhifPsO2Lp27dvWJnsuW1sjW370VLhNIc7wd+dd95J\neXk5gwcPZuLEiezbt8+Jj+jZs2dUx5Xnn38+bOI68t1vT8Ti3dQb+LuIrAasu4MxxnwjecVqPQUF\nBU7gT25uLn379iUQCFBcXMzPfha0liXKu8m+IO6RTM+ePYGgt4P1rBozZgz79++nrKzM8WRwL7oT\niTsVAbQ8F0/kanl2Zbq9e/eyePFiIKjNZGVlsWXLFrZs2cKYMWMajRRvv/12evfuDcALL7yQEI+w\n8vJyFi1a5AS1de3alccee4wZM2Y0WqDJTWSnCkETXrSgu0hsZ2FXxbMdnfvcgCO4Iejp5Pf7ncWK\n7MgzUQkQIzuwCRMmALB//34mTJjgrMNRXV3tCIbc3Fwuu+yyRmWIDOxsaVngqCCdNGkSN910k2MW\n/Nvf/sb5558fc71jfde8vKFqamqorq5m0qRJfPrpp/z4xz/moYceAoIDjR49emCMYePGjUDQRFlV\nVeV57vr6ekfoxTPgsffGnT7FJod87rnn2L9/v2O56NatGz169GDLli2ORm4TVdrcX1//+tedJYLT\nbmU6F3dG+a3dGtHcDbxnz57s2bOHffv20a1bN8el0UY9QmJGWxa3297LL7/MzJkzKSwsZP369Qwf\nPpzZs2fH7XIXqU3E0pCiaQ72GAgfnd1yyy3cc889lJWV8eKLLwJB88tdd93VKCmZnZMAEpZksKam\nxtFobP6mQCDArl27gKDwKg2tHxwtmWBrtRsIroTndlu098s9oo3W2dqFidzYY9zmKGi+bbm3r127\nlptvDk7P2TxFbtzR13/605+YMWNG2PWjjcTjaduRgqa8vJyKigruvfdeNm/eDARdoZ9++umwazdF\nrBpWtE74yiuvDJsHWLt2LTfeeCPf+ta3GDlyJDNmzOCvf/0rS5cuZcuWLYgI//7v/84HH3wQdWU6\ne27AiU+IdcBj7437vbY52D7//HNHk+nUqRM33nij44I7ZMiQsPfJvUKjTXGedivTiYiEJsirm9sn\nKSVrIe4GbhOguZPHRQqERK5MZ0c5P//5z53rtFZbidQm4jnGjsZKSkqirqZWU1PDd77zHTZt2gQ0\nNr/Mnz8/rI42VYKIsGHDBh599FE6derkCJ+mOiJ/aLWzyAWF3GnDS0pKyMnJYerUqdx4443OAk22\nw4xGQUEBEydOZNGiRTHf40izl10Jb/LkyezcuZM+ffpw8cUXh2kYbjNWU52w3SfWVNqxELnwTmRM\nQOTKdK3VJNzXslRXVzuT1RDUYr7//e+36Nyx4H53rakNopt5rEns8OHDzlzk6tWrHVOhJVoHf+GF\nF7YoWDPae2217G7dunHjjTfSq1cv552y82r2vkamPLcZl9MtC2y1iLwM/NEYs9G9QUSKgbHAFcDX\nk1i+uImmKk+YMMFZ/hMStzZCtPOtXbuW0aNH4/f7qampCYvG9ContG69XS+aWk3Njs7cOaSs+cVr\nSUpr/zfG8OGHHzJ79myuuOIKR0jEis2H5J60zs7OdvJt2XvQlCkOvM1GzQkre99t5Lm9nnvthAMH\nDoR5FFli7YRbm/452uJHNpL3pJNOYsOGDZxwwglcd911cZ23pdh1wS0nnngivXr1Svh6I/Y8ketP\nrF27NsybLRAI8Mtf/pJLLrnEOdaamrp27cpVV13lmdk1EcF00ZYvtQGUdkCalZXltM25c+fSv39/\nZ41rd/3cGYjbYxbYpoTEJcB3gF+LyOnAXoLR0fnAe8AfgIuSXsI4iaYq33zzzU6K67aaHIo2orSC\nA46OTO3qaHZ93EQKLztZOGTIEMaPH8/Pf/5zIHx0Zlc3cxMpwGx93Pb/oUOHsmTJEmbOnBnTPY18\nWe2Ldfzxx7N161YnGeOiRYsYMWJEo1F8tHNEagQtKYetuz9ifYlo62/bexLLM0pG+uf+/fs79W3N\nAj7NEc1holu3bmEJKu+9917Wrl3brHBoqfnLyzzl1jDuuOMOZ8K3pqbGMSc3NDTw0ksved7z1q5t\nEYn7WVttGOBnP/uZ077svEO0MiQ6PVCi8RQSxpgGgqm+nxaRLOCY0KbPTXAZU8UD+yIUFRV5agh2\nnejIlb/uvffehJXDjpisqvvVr36VkSNHct999zmxAG5NwgqshQsXOo3b/VLbvP4Ar732WqteMveL\nZd0Es7Ky2LRpE9ddd52zsA4E711bqOA/+MEP+N3vfkdeXh5z585l8eLFjBo1ipycnLgHF/G++JGd\naaSQhqML74D3XFoi5iSiOUz86Ec/wu/3s2jRojBvvObOmSjzl+XOO+9k6tSpYW3Y4k7F05adrftZ\nX3jhhXEfn+j0QIkm1jWujxBcFyItmT17Nj179mT37t0tXlEtHqzW4CZaPpXa2tpGo9dEmpsiR0z2\nu325+vXr5+zbr1+/MIFll8u0dbH1GTduHICTj6i1FBcXc9lll7F06VInGOrgwYPcf//9TJgwgaKi\nomav49bGYjHtRJqcLNdeey0NDQ0sX77cmSc5cuQIU6ZMabaztee0JpnRo0cTCAS49dZbY8rdFNmZ\n2knM6dOnN5qTaIpEd8purOkEgu3ZPQhKtAnXTbR5CLeAsEGwu3fvJicnh27dujFnzhzOPvvsqBPX\nlkSYeKurqx2PtKuuusrxbAKYMWMGvXr1YteuXc3OaSVSs0k0MQmJdCKazdk24GeeeabNPAiivax+\nv59AIEC/fv3Yvn07tbW13HTTTTz11FMMHDiQuXPnsmHDhqRPXrmjRf1+P8888wynnHKKMxKzbsJ2\n4jqyLu5zNIf7ebhfxlmzZjFu3Diee+455s+fT3l5Offffz8HDx6ka9euvPTSS/zlL3+J6Xm5hVss\npp1YO7Ti4mImTJjg7BvLcQUFBY5gKy8vZ+TIkTFdy32f+vXr52h4/fr1azQn0R5oyfNviVCJnIew\n7qZu8+2BAwcoKiqivr7eMVvazttNtHeypqamVcLNlqO8vJzzzz/fcX7Izs6msrKSAQMGOO+M3+9v\nV88wVjJOSLiltc/nc0aEkap8axquF01NVrqv5/P52L59u/Oi7d27l/nz54dNKlt/6mQRbTR9zz33\nMHXqVE/vpmgjoOZw31N3nId9sT766CNn34kTJ/LYY4/xX//1X05cQCzld2tjNgamNSxYsKBZm3/k\ns47WduLpgNzHe3XAsWgSXuWLd9Dh1ox69uwZpo3b7bHUrbXvVGlpqeON5J5Lc7c/n89HbW2t4xrc\nnNt0onE/N7e33h//+EfmzZvnqdG5f3cHmLY3mhUSIlJijHk/4rfSplxjU020kS8kViC4sS9UpG+3\nu6OPbCSRHUik33WyVU+v+q9du9axdUfeLzvyAlrduO21x44dy/r16wG47777yM3NdVwX7e9NHe/3\n+x0vtvvuu48vvviixeYDd8fqtba2JRXrEsdjSmpt+dzXcgsn96jY7pdsItNqW3dYCLZRW5apU6dy\nzz33MGHChEaxJW7s/ok2mfldzg8+n4/x48fHPJhqz8SiScwTkd8B9wM5wH3AOSRgmdFk4WVzbmnO\no1iJ9O1uqlwQPhpvT5NX0QLEopU9Wfcy2sR/5AvsLs8pp5xCTk4O+fn5rXrR3R1rc04EqfBI8Wo/\n0ersThT4wAMPtEn5kkU0byQvAblp0ybPuJpo/YK9d7G2GS8rhN1mByw//elP+fzzzzl8+HCbzd0k\ni1iExHkEBcNKgu6vc4B/S2ahWktbPwh7Pbfvc21trdOgojWSSFUz0W558dBc5xNNMyt1LZrUEpNG\n5GguEAg4122pK2trA8dssGBubi4XX3xxkxpJKoR6PJqEXSt7z549rY6O9/l8bNu2Lcwt1t6zRKeQ\naKoTjuUYaN5lujVEO4edG4GjA5YBAwZ47httENSeiUVIHAb2E9QiugEfGWO8157swLg7ehsB2x5o\nbg6muc4n8njboS9YsIAdO3YQCATiXjku0gxnO/mWmK9aa3+32GBBmxb81ltv9dw3FUI9nrm0eFN5\nN4d1i50+fTo/+clPWn0+L7w68qbaRTzCMxl4tWWvfeOtX6qJRUisBhYCwwnGSjwuIlcbY65JasmU\nhNHaEZTbNu0+j00tAIldPjNeEmV/t8GC1t+9qXuWKMHUknLGQiI1nXiEUzKJxQyZTrSX+9ocsQiJ\nHxpj3g59/gz4hoiMT2KZOhRus4v7f3trKNHKM2LECJYtW8bQoUMbZdyMlVgCD5sjUfMD8aRr8BJM\n8cwbJJNEajrtpS3G6vXVVve8JaYxN+3lvjZHLEJiu4icEPFb+9WN0gy3qpoKVbk12Jz4TUVfR77A\nCxYscHJDRXMqaInfeqJGzfF0rF6Cyb74qdA0OiqpMjelo+moJcQiJBZzNDV4N+BEgutdn5asQinp\nQSydamSnaTPSuo9ZtWqVMwqLNR06hAugRKR8j8c1sjnBlAoX2UxFBW5qaVZIGGNOd38XkbOBCUkr\nkZKRNNVptiQdOiR+BBk5AdkUzQnI9p60LR2wg4Cm4o/c+0H7tu2nK3FHXBtj/iYi5yWjMOlKrI20\nqTiJTKejdZqpintpL3MiicCWublA0/ZQt0wWVLFEXLujwjoBZwOfJK1EaUisDcFr5JtpNsxotKdg\nQS8SadZIVdxLquzzySQd2k4mCAMvYtEkunN0TuIw8DLwYtJKpLRr/H6/swCNzXgaS2bdVAYLNkes\nZg0lNbTnttMRiGVOorINytEhyARzk+003VGm6d6RxmrWgPZvzskks0d7v9cdhabWuF7UxHHGGPON\nJJQno2mv5qZM6lhagq2/XRdg2rRpnmtAtHdzTiY9s/Z+rzsKTWkSDzaxzTSxTUkz0rVjSZRwc+9v\n1yhXFCVIU0JiszEm0GYlUdIG26nGswBRMnzd01W4KUo60ZSQWAAMBRCRF40xV7dNkZRMpKMEl3V0\n052SecQaJzEoqaVQMp5MiZOIJ6NuIlm1apWTqnvbtm30798faD4qXVFaS8YtX5oORJpeEk17Gs3G\nMymcDqSq3O6odPcysJmMWzACMadrURJLU0JiiIjsDX3OcX2GoHdTjySWK6OJNL2cdlpi02AlsyOL\ndEuEo6vURbumTgorLaUjCsb2iKeQMMZktWVBOhLW9FJcXMz48eP5/PPPW5wmu62JdEuE2CauFUVJ\nT9TclALcC7vbZU7h6KLuVlC0Z2EB8PDDD1NXV8cjjzzCmjVrwlJ/pxPtyTynJA+d12kZHU5IuDsE\n96i9LTuE9rrMabzU1dXR0NBAQ0MDX/3qV9myZUvU/dz3fPbs2Sm5503RXsqhRCdR7tNqvmoZHU5I\nuDuEVDSU9t5hxkNWVtAimZuby5tvvum5nzuuwq6HrSix0lHcp9srHU5IpJpM6TArKiro1asXDQ0N\nrFy50tPUFO9Et6JEkinu0+mKCokUYNXn7OxsJk2alFbZLa1d9/XXX+eTT4IZ43/4wx8ya9asqHZd\nKwgiBYX9roJCaY5EpQrXhIEtQ4VECrDqM5B26rO1686bN48PP/yQwsJClixZEvMa1xZ9MZVYSVSq\ncE0Y2DJUSKQAqz4XFhamrfpsR3dlZWUxrXEN6jLbUtyCtrKyEr/fz+LFi/ntb3/LkCFDUls4JeNR\nIdHGuKOPy8rKWLduHZB+I2s7umsOnZNoPe57tWbNGurr653o9fnz56e2cG1AMpJDKrHT4YREe7BL\n5ufnx9TBZgI+n49t27aFpVewz0D902PD3WaPHDni/F5fX5+iErUt6t2UWjqckFC7ZNtj5zGmT58O\nkLYeXanCPfl/3HHHsXnzZgYPHswtt9zS7iP0E0GivZtOOeUU/H5/2geBthUdTkikWpNwu8CC2ueV\n2LDtpry8nEWLFrFixYoOY3ZJlHeTZdu2bTEFgSpBOpyQUE2i9bRU0C5cuJCdO3eqbTlO3Pc7JyeH\n8vLytM6kGy+J8m6yZGdnA80HgSpBOqW6AKmioqKCqqoqRo0aRW1tbZtff+HChSm9fmv51a9+RVVV\nFS+++CJ1dXXN7l9RUcHf//53AoEAr776KhUVFW1QSkVpzJo1a+jevTvvv/++mppioMNpEnZUtnr1\namcy7Morr6SqqqpNR2U7d+5M28k4n89HXV2dE+vx7LPPNlv+jRs30tDQAEDnzp154IEHkl7OTKGj\nuhEn2jTsPt/kyZPZvHkzmzdv7jAaWUvpcELCNojCwkLWr1/P8OHDmT9/fpubPqzKm66pBuKdTLT7\nAxw+fJgpU6aklWBU2p5Em4bt+dSlNj46rLlpzpw5lJSUJGwyLB4qKipoaGggLy+PF154IS0babz3\nb86cOeTl5QHpKxiVzMC61KrZMzaSKiRE5DIR+UBE/ldEpkbZXioiu0XkndDfz5JZHjeJngyLh40b\nN7Jlyxbq6+uZMmVKm18/EcR7/woKCpg4cWLKBLOiWDRhYHwkzdwkIlnAI8BFwCfA2yKy0Bjzj4hd\na4wx30hWOdojmZCWI17cSQ2V+PH7/UycOJH33nuP7Oxshg0bRn5+vtrTW0CiXWoznWRqEucCm4wx\nfmPMIWAuMCbKfpLEMniSSu8mawfNysri29/+dlp5N/n9fqqrqznhhBP45S9/SUFBAXPnzo2axM+N\nVfE3bdqkKn4L8Pl8rF271rmHTz75JKWlpSogWkAqrQjpSDInrgcA7iiVrcB5EfsY4N9EZD1BbeM2\nY8z7SSyTQypD/W+//Xb27NlDbW0tW7Zs4Xvf+17a5OCxI9c9e/Y4AUlTpkxpNiDJPXH92muvEQgE\n1P0wTqx3GMDKlSupra3N6I5Ol5VtHyRTSJgY9vkbMNAYs09ELgcWAF+JtmNlZaXzubS0tNWeDv/8\n5z8B6NGjR5u7Y27cuJEvv/zS+X7w4ME2vX4iiDcgac6cOfTu3RtjDDt37tRI1zjx+/0MGjSItWvX\nAvCvf/0rJa7bbUmihYF7jWsIrgwJmbXGdXV1tSNME4YxJil/wAjgT67vdwBTmzlmM9A7yu8m0Ywc\nOdIQFGTmmmuuSfj5m+Lyyy93rg2YMWPGtOn1E4Hf7zfdu3c3fr8/5mNyc3MNYHJzc+M6Tgkyfvx4\n06lTJwOYoUOHml27dqW6SGlLZWVlqovQJoT6zlb15cmck1gDnCwiPhHpAnwLWOjeQUT6iYiEPp8L\niDHmiySWyaFHjx5A23o4WHv+zTff7JhfBg8ezF133dUm108kRUVFTJ48OS6T0Q033KCRrq1gyZIl\njgZ63HHHZbSpKZmkOttCupE0c5Mx5rCITAT+DGQBTxlj/iEiN4a2Pw58E7hJRA4D+4Brk1WeSFLh\n4eBWn3/84x93mERt1rbcq1cvjXRtBe45CfUSazmaejw+khpxbYx5FXg14rfHXZ9/Dfw6mWWIxD0Z\nZhOlQdtPhtlEbR1FQESiAiJ+hg0bxrJly+jfv79jT1fiR+Mk4qPDpuVIVWh+qlOVtzXutRDc2O+Z\nWOdk8fzzz8e0ZKzSNBonER8dTkhYUqVydsT1JDpinZNBrEvGKtFpL1aEdKPDCglVOVtGR9OElMxB\n1wlo3JYAAAr8SURBVJJpGR1WSKjK2TL0RVOUjkWHFRIamq+kC36/n3Xr1oW5a86ePZuCggLOOuss\n1eCUpNJhhYTSNkSmVggEAlRXV6t5Kg7c92r69OkAXH/99akrkNKh6HBCIpU29Y44Ioy8r9OnT1cT\nVZxEcyNWQau0FR1OSKTSpu52B7VLf3aEl9ydM6dr164ZmTMnmagbsZJKOpyQaE/eOR0lNcWIESNU\nGLQSdSNWUkWHExKp9s5xv+xqV1ZiQc1NiUFTj7eMDicklNahpqPUYif/lfhRYdAyVEgocaGmo7ZH\nJ/+VVJLMVOGKoihKmtPhNAm1SyqKosROhxMSKgwURVFiR81NiqIoiicqJBRFURRPVEgoShqh6zMr\nbU2Hm5NIJe0p2ltJT3R9ZqWtUSHRhqQ62ltJf3SxLKWtUXOToqQRc+bMoaSkRBfLUtoMFRKKkkbo\nYllKW6NCQlEURfFE5yTaEI32VhQl3VAh0YaoMFAUJd1Qc5OiKIriiQoJRVEUxRMVEoqiKIonKiQU\nRVEUT1RIKIqiKJ6okFAURVE8USGhKIqieKJCQlEURfFEjDGpLkOziIhJh3IqSrJwR+v7/X4nKFMD\nNJWmEBGMMdKqc6RD56tCQlEUJX4SISTU3KQoiqJ4okJCURRF8USFhKIoiuKJCglFURTFExUSiqIo\niicqJBRFURRPVEgoiqIonqiQUBRFUTxRIaEoiqJ4okJCURRF8USFhKIoiuJJUoWEiFwmIh+IyP+K\nyFSPfWaFtq8XkaHJLI+iKIoSH0kTEiKSBTwCXAaUAONE5NSIfUYBg40xJwMVwGPJKk97prq6OtVF\nSBqZXDfQ+qU7mV6/RJBMTeJcYJMxxm+MOQTMBcZE7PMN4BkAY8xbQIGI9EtimdolmdxQM7luoPVL\ndzK9fokgmUJiALDF9X1r6Lfm9jk+iWVSFEVR4iCZQiLWBSAic53rwhGKoijthKQtOiQiI4BKY8xl\noe93AF8aY+5z7fMboNoYMzf0/QPgAmPM9ohzqeBQFEVpAa1ddKhzogoShTXAySLiAz4FvgWMi9hn\nITARmBsSKrWRAgJaX0lFURSlZSRNSBhjDovIRODPQBbwlDHmHyJyY2j748aYxSIySkQ2AfXA95JV\nHkVRFCV+0mKNa0VRFCU1pDTiWkSeFpHtIvKux/ZTRGSliBwQkckR25oN1EslraybX0Q2iMg7IrK6\nbUocHzHU7zuhAMkNIrJCRIa4trXrZwetrl8mPL8xofq9IyJrReT/urZlwvNrqn7t+vk1VzfXfueI\nyGERudr1W/zPzhiTsj/ga8BQ4F2P7X2B4cDdwGTX71nAJsAHZAPrgFNTWZdE1S20bTPQO9V1aGX9\nzgd6hj5fBqxKl2fXmvpl0PPLc30+g2DMUyY9v6j1S4fn11zdXM/pNeBl4OrWPLuUahLGmDeAXU1s\n32GMWQMcitgUS6BeSmlF3SzterI+hvqtNMbsDn19i6PxL+3+2UGr6mdJ9+dX7/qaD3we+pwpz8+r\nfpZ2+/yaq1uIHwMvADtcv7Xo2aVrgr9YAvXSGQMsE5E1InJDqguTAH4ALA59zsRn564fZMjzE5Gx\nIvIP4FXgltDPGfP8POoHaf78RGQAwc7fpjmyE88tenbJdIFNJpk+2z7SGPOZiPQFlorIB6HRQ9oh\nIv8H+D4wMvRTRj27KPWDDHl+xpgFwAIR+RrwOxE5JdVlSiSR9QOKQ5vS/fnNAH5ijDEiIhzVilr0\n7qWrJvEJMND1fSBBqZgRGGM+C/3fAcwnqCamHaHJ3N8C3zDGWPU4Y56dR/0y5vlZQh1kZ6A3wWeV\nEc/PYusnIn1C39P9+Q0jGHu2GbgaeFREvkEL3710ERKR9kEnUE9EuhAM1FvY9sVKCGF1E5FcEeke\n+pwHXAI06cXQHhGRE4CXgO8aYza5NmXEs/OqXwY9v5NCo1BE5GwAY8xOMuf5Ra1fJjw/Y8wgY8yJ\nxpgTCc5L3GSMWUgLn11KzU0i8hxwAXCMiGwBphGcdccY87iI9AfeBnoAX4rIJKDEGFMnUQL1UlIJ\nD1paN+BY4KVQ++0M/MEYsyQFVWiS5uoH/BfQC3gsVJdDxphzjUeQZSrq0BQtrR/Qn8x4flcD40Xk\nEFAHXBvalinPL2r9SIPnF0PdotLSZ6fBdIqiKIon6WJuUhRFUVKACglFURTFExUSiqIoiicqJBRF\nURRPVEgoiqK0Q2JN5Bfat0hE/hJKWrg8FHWdEFRIKIqitE+qCCaPjIVfAbONMWcCdwG/TFQhVEgo\naUMoCOjdiN8qJSLVepTjhonIzGb2GSMip7q+TxeRC1tXYs9rLRORE0KpqN8Rkc9EZGvo899EJFtE\nbhORf9h01SLy76Fjq0Opnt8RkffduYVCI8nuySiz0vZES+QXCgJ8NZRX6nURsalETiWY9RWgmgQm\nXVQhoaQ7zQb6GGPWGmMmNbPblQSDGe0x04wxf2lt4SKR4LoFHxpjPjbGDDXGDAV+A/x36PvZBBMG\nXgicE9p+IeH5d74d+n0kcJ+I2KDYuUDaJaRT4uIJ4MfGmOHAFODR0O/rCQYIQrAtdxeRXom4oAoJ\nJRMw4Iyy7xWRt0TkQxH5auj3UhFZFPo8Q0TuDH2+VERqROR8oAx4IDSSHyQisyW0WIsEF6G5JzR6\nXyMiZ4vIEhHZJKHleEP7TQmN+teLSKVHWb8N/DHK7+70LHcQTKVQB2CM2WuMeTbKvj0IRgsfCX1f\nyNHIYSXDEJF8guuYPC8i7xAcXPQPbb4NuEBE/gZ8nWCepiNRTxQn6ZoFVlGiYYAsY8x5InI5wXQF\nF0fscwfwtoi8CcwELjfGbBaRhcAiY8xLACJiOKqlGCBgjBkqIv8NzCb4suYA7wGPi8glwGBjzLki\n0gn4o4h8LUr20JHA7V4VEJEeQHdjjN9rF+APItIAnAxMMqG0CcaY7SJyjIjkRayXoGQGnYDakBYZ\nRigpoR3U5BNcaGhPoi6qKOmCl2nJ/ftLof9/I7gCV/iOxuwnaJJZCjxsjNns2tzUQjM2Edq7wEpj\nTL0x5nOgQUR6EkwEd0lohLeWYNrpwVHOU2iM+aKJ6zSHNTedCZwATJFgskHLdsIzfSoZQqjT3ywi\n3wSQIENCn/uEBicQHAg9lajrqpBQ0omdBJPquelD+KpiDaH/R/DWlIcQXLEr0k2wqfkNe94vgYOu\n3790XeeXdp7BGPMVY0xVE+eLSqgjqBORE2PY93OCwvA8189Chq3Z0VEJJfL7K1AsIltE5HvAd4Af\niMg6glrsN0K7/x/gAxH5kODSyL9IVDlUSChpQ8hG/5kEF/pBRHoDlwJvxnoOESkC/oPgGsGXi4hd\nK2AvQRt/s6eIVjSCmTW/L8H00ojIAAkuWhPJpxJat6AJfgn8Wo6mrM633k3uMohIbqge7lTs/Ujz\n9R2UIMaYccaYQmNMF2PMQGNMVWjp0cuNMWcZY04zxtwd2veF0MCk2BhTEVqeNCGokFDSjfHAnSGz\nzl+AygiTkRsT5fOTwGRjzDaCXkRPSjC3/lyCppu1IjKoieu75yqc8xpjlgJzgJUisgGYR3Dt5Eje\nBIY3VVZjzGPAcoJzJ+8CrxM+CfmHUP3XAFXGmHcAJJh+fqfORyiJRFOFK0obIiKlwLeMMTcl4dwV\nQJ4x5qFEn1vpuKgmoShtiDGmmuDqYMkIevsWweVUFSVhqCahKIqieKKahKIoiuKJCglFURTFExUS\niqIoiicqJBRFURRPVEgoiqIonqiQUBRFUTz5/+nQcGaUJMTVAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x117f09f90>"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Search for a single period."
]
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"Calculate the significance level cutoff for power spectral density"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Estimate significance levels from periodogram.\")\n",
"# Note: This cell takes ~1.5 minutes to execute.\n",
"(_, powers, sigs_powers) = \\\n",
" calc_periodogram(\n",
" times=df_crts['unixtime_TCB'].values, fluxes=df_crts['flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values, min_period=None, max_period=None, num_periods=None,\n",
" sigs=(95.0, 99.0), num_bootstraps=100, show_periodogram=True, period_unit='seconds', flux_unit='relative')\n",
"print()\n",
"print(\"NOTE: This periodogram has low resolution in period spacing\\n\" +\n",
" \"and does not show all periods at their acutal power levels.\\n\" +\n",
" \"This periodogram is only used to estimate the significance levels.\")\n",
"(sig, power) = sigs_powers[-1]\n",
"if np.any(powers > power):\n",
" print()\n",
" print(\n",
" (\"NOTE: There are power spectral density values above the\\n\" +\n",
" \"{sig}% significance level. This means the object should\\n\" +\n",
" \"be flagged for follow up.\").format(sig=sig))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INFO: Estimated computation time: 85 sec\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Dc18Hf/Znf67ec62hQv+qJW0GHAtsFosmASPN7M089f8KXEFwnzyxwrI2GknW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\nXWGatbG4onecVKwu6ZQYYrD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0AEG5js0eJKm8mpJNNtkEKHyjzc5U3BxUQ9H85z//SZ16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\n2o1/8AAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x115ca9b90>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INFO: At significance = 95.0%, power spectral density = 0.0545247548728\n",
"INFO: At significance = 99.0%, power spectral density = 0.0624013991858\n",
"\n",
"NOTE: This periodogram has low resolution in period spacing\n",
"and does not show all periods at their acutal power levels.\n",
"This periodogram is only used to estimate the significance levels.\n",
"\n",
"NOTE: There are power spectral density values above the\n",
"99.0% significance level. This means the object should\n",
"be flagged for follow up.\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Show that power spectral density values are invariant to time units.\")\n",
"# Note: This cell takes ~1.5 minutes to execute.\n",
"calc_periodogram(\n",
" times=df_crts['MJD'].values, fluxes=df_crts['flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values, min_period=None, max_period=None, num_periods=None,\n",
" sigs=(95.0, 99.0), num_bootstraps=100, show_periodogram=True, period_unit='days', flux_unit='relative')\n",
"print()\n",
"print(\"NOTE: This periodogram shows that the power spectral density values\\n\" +\n",
" \"are not affected when using days for time units instead of seconds.\\n\" +\n",
" \"As of 2015-02-24, astroML.time_series.search_frequencies (used later)\\n\" +\n",
" \"expects time units in days.\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Show that power spectral density values are invariant to time units.\n",
"INFO: Estimated computation time: 85 sec\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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LtpDuv/9+9thjj7ztH3zwQXbddde8x9dYYw3mzJlT1vnfeOMN1l9//ZLbOY7T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\nJ0+eRJ8+fdzaGvmS1GpjdLve62AKlrfnDvS9MLItUPdCLTQeDgRSvO6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"text": [
"<matplotlib.figure.Figure at 0x115cb3a50>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INFO: At significance = 95.0%, power spectral density = 0.0544800156721\n",
"INFO: At significance = 99.0%, power spectral density = 0.062406956977\n",
"\n",
"NOTE: This periodogram shows that the power spectral density values\n",
"are not affected when using days for time units instead of seconds.\n",
"As of 2015-02-24, astroML.time_series.search_frequencies (used later)\n",
"expects time units in days.\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Show that power spectral density is dependent on flux units.\")\n",
"# Note: This cell takes ~1.5 minutes to execute.\n",
"calc_periodogram(\n",
" times=df_crts['unixtime_TCB'].values, fluxes=df_crts['Mag'].values,\n",
" fluxes_err=df_crts['Magerr'].values, min_period=None, max_period=None, num_periods=None,\n",
" sigs=(95.0, 99.0), num_bootstraps=100, show_periodogram=True, period_unit='seconds', flux_unit='mag')\n",
"print()\n",
"print(\"NOTE: Using different flux units can bias different periods.\\n\" +\n",
" \"Using magnitudes instead of relative flux increases the significance\\n\" +\n",
" \"of several longer periods. Using the Bayesian Information Criterion\\n\" +\n",
" \"(shown later) reduces the bias.\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Show that power spectral density is dependent on flux units.\n",
"INFO: Estimated computation time: 85 sec\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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2xwYCgaaRxCx4F3A5q+bT3qdxnjNwMSHPl/SOpPskneAThAZaOGbGhAkTmlsM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\nWTU7UH8fRCQP+BuQCLyklPqTnz6zgKHAMeAWpdRmo/1lYDh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jgw8+yLnnnmsdZ2dnW9cp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\nRqOJG7SoaTQajSZu0KKm0Wg0mrjh/wMHu0IovbjTCAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x117ada650>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"INFO: At significance = 95.0%, power spectral density = 0.0486328583589\n",
"INFO: At significance = 99.0%, power spectral density = 0.0553166926785\n",
"\n",
"NOTE: Using different flux units can bias different periods.\n",
"Using magnitudes instead of relative flux increases the significance\n",
"of several longer periods. Using the Bayesian Information Criterion\n",
"(shown later) reduces the bias.\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"Find for periods at which power spectral density peaks above significance level."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Calculate periods at which power spectral density peaks.\")\n",
"# Note: This cell takes ~1 minute to execute.\n",
"# Note: As of 2015-02-24, astroML.time_series.search_frequencies search range expects the time units to be days.\n",
"# From above, the power spectral density values are invariant to the choice of time units.\n",
"print(\"INFO: Iteratively find peak periods.\")\n",
"(peak_omegas_mjd, peak_powers) = astroML_ts.search_frequencies(t=df_crts['MJD'].values,\n",
" y=df_crts['flux_rel'].values,\n",
" dy=df_crts['flux_rel_err'].values)\n",
"peak_periods = (2.0 * np.pi / peak_omegas_mjd) * sci_con.day\n",
"print(\"Number of peak periods: {num}\".format(num=len(peak_periods)))\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, xscale='log')\n",
"ax.plot(peak_periods, peak_powers, color='black', marker='o')\n",
"ax.set_title(\"Peak powers vs period\")\n",
"ax.set_xlabel(\"Period (seconds)\")\n",
"ax.set_ylabel(\"Lomb-Scargle Power Spectral Density\")\n",
"# Save xlim, ylim for plot of selected significant powers.\n",
"xlim = ax.get_xlim()\n",
"ylim = ax.get_ylim()\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Calculate periods at which power spectral density peaks.\n",
"INFO: Iteratively find peak periods.\n",
"Number of peak periods: 801"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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mVnJuCDsndecKcsCAAU3uW11dnVKBo3R6VdneXdu2bWPcuHGMGzcukMeZn5fY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\nl7/8pf73f/+3/v3vf9dwOKzf/e53FdD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"text": [
"<matplotlib.figure.Figure at 0x117abad10>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Reduce the number of periods fit by requiring that\\n\" +\n",
" \"the periods be above a significance level.\")\n",
"(cutoff_sig, cutoff_power) = sigs_powers[-1]\n",
"print()\n",
"print(\"At significance = {sig}%, power spectral density = {pwr}\".format(sig=cutoff_sig, pwr=cutoff_power))\n",
"(sig_periods, sig_powers) = select_sig_periods_powers(peak_periods=peak_periods, peak_powers=peak_powers,\n",
" cutoff_power=cutoff_power)\n",
"print()\n",
"print(\n",
" (\"Number of peak periods above {sig}% significance level: {num}\".format(\n",
" sig=cutoff_sig, num=len(sig_periods))))\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, xscale='log')\n",
"ax.plot(sig_periods, sig_powers, color='black', marker='o')\n",
"ax.set_title(\"Significant powers vs period\")\n",
"ax.set_xlabel(\"Period (seconds)\")\n",
"ax.set_ylabel(\"Lomb-Scargle Power Spectral Density\")\n",
"# Use xlim, ylim from plot of peak powers.\n",
"ax.set_xlim(xlim)\n",
"ax.set_ylim(ylim)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Reduce the number of periods fit by requiring that\n",
"the periods be above a significance level.\n",
"\n",
"At significance = 99.0%, power spectral density = 0.0624013991858\n",
"\n",
"Number of peak periods above 99.0% significance level: 510\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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fnPHkzzStJSW9r12qqgtxFm+KLq8CWpb6NLKCsrIyFi1aFHet8N27d9ctL5up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\noX379g0mg0Gw8NF9+/bx+uu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G0XX6umUCrFfVRW7533BcXQ3wpmouKSmhpKQk0fkYhmG0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\nwhSHYRiGEYr/D4YcTu7aiOzuAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1166e1850>"
]
}
],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Select the best period from the relative Bayesian Information Criteria.\")\n",
"# Note: This cell takes ~5 minutes to execute.\n",
"best_period = calc_best_period(times=df_crts['unixtime_TCB'].values, fluxes=df_crts['flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values, candidate_periods=sig_periods,\n",
" n_terms=6, show_periodograms=False, show_summary_plots=True,\n",
" period_unit='seconds', flux_unit='relative')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Select the best period from the relative Bayesian Information Criteria.\n",
"INFO: Estimated computation time: 311 sec\n",
"--------------------------------------------------------------------------------"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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qKyvZt28fubm5vuu29fU4kaQ8WIhIZ5xAsUxVn3Jn14jIAFWtFpGBQK07vxIY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\njInJgoUxxpiYLFgYY4yJyYKFMcaYmP4/U/sWodiSIBUAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x116334e10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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YbWijwzGscRqGo1CIM6f3bLyAud2B24ASPHPT4WkOuRB4WtISf30GcM62NtTh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\nFI7AcHBwcHAICkdgODg4ODgExf8HflOjFVk1rCYAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1166d6d50>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best period: 86691.1081704 seconds\n",
"Relative Bayesian Information Criterion: 582.303992687\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Calculate number of terms, refine best period, before and after removing outliers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**TODO:** determine ephimeris and uncertainties from lomb-scargle fit."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_z1_z2(dist):\n",
" \"\"\"Calculate a rank-based measure of Gaussianity in the core and tail of a distribution.\n",
" \n",
" Parameters\n",
" ----------\n",
" dist : array_like\n",
" Distribution to evaluate. 1D array of `float`.\n",
" \n",
" Returns\n",
" -------\n",
" z1 : float\n",
" Departure of distribution core from that of a Gaussian in number of sigma.\n",
" z2 : float\n",
" Departure of distribution tails from that of a Gaussian in number of sigma.\n",
" \n",
" Notes\n",
" -----\n",
" - From section 4.7.4 of [1]_:\n",
" z1 = 1.3 * (abs(mu - median) / sigma) * sqrt(num_dist)\n",
" z2 = 1.1 * abs((sigma / sigmaG) - 1.0) * sqrt(num_dist)\n",
" where mu = mean(residuals), median = median(residuals),\n",
" sigma = standard_deviation(residuals), num_dist = len(dist)\n",
" sigmaG = sigmaG(dist) = rank_based_standard_deviation(dist) (from [1]_)\n",
" - Interpretation:\n",
" For z1 = 1.0, the probability of a true Gaussian distribution also with\n",
" z1 > 1.0 is ~32% and is equivalent to a two-tailed p-value |z| > 1.0.\n",
" The same is true for z2.\n",
" \n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" (mu, sigma) = astroML_stats.mean_sigma(dist)\n",
" (median, sigmaG) = astroML_stats.median_sigmaG(dist)\n",
" num_dist = len(dist)\n",
" z1 = 1.3 * (abs(mu - median) / sigma) * np.sqrt(num_dist)\n",
" z2 = 1.1 * abs((sigma / sigmaG) - 1.0) * np.sqrt(num_dist)\n",
" return (z1, z2)\n",
"\n",
"\n",
"# TODO: create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Computing best number of Fourier terms, best fit period, and fit residuals for all data points.\")\n",
"(best_n_terms, phases, fits_phased, df_crts['phase_dec']) = \\\n",
" calc_num_terms(times=df_crts['unixtime_TCB'].values,\n",
" fluxes=df_crts['flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values,\n",
" best_period=best_period, max_n_terms=20, show_periodograms=False, show_summary_plots=True,\n",
" period_unit='seconds', flux_unit='relative')\n",
"(best_period, best_period_resolution, phases, fits_phased, df_crts['phase_dec'], multi_term_fit) = \\\n",
" refine_best_period(times=df_crts['unixtime_TCB'].values,\n",
" fluxes=df_crts['flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values,\n",
" best_period=best_period, n_terms=best_n_terms, show_plots=True,\n",
" period_unit='seconds', flux_unit='relative')\n",
"(df_crts['fit_flux_rel'], df_crts['res_flux_rel']) = \\\n",
" calc_flux_fits_residuals(phases=phases, fits_phased=fits_phased,\n",
" times_phased=df_crts['phase_dec'].values,\n",
" fluxes=df_crts['flux_rel'].values)\n",
"print()\n",
"print(\"Evaluating distribution of light curve residuals:\")\n",
"(z1, z2) = calc_z1_z2(dist=df_crts['res_flux_rel'].values)\n",
"print(\"Departure from Gaussian core: number of sigma, Z1 = {z1}\".format(z1=z1))\n",
"print(\"Departure from Gaussian tail: number of sigma, Z2 = {z2}\".format(z2=z2))\n",
"print(\"Plot histogram of residuals:\")\n",
"astroML_plt.hist(df_crts['res_flux_rel'].values, bins='knuth', histtype='step')\n",
"plt.title(\"Residuals to light curve fit\")\n",
"plt.xlabel(\"Residual relative flux\")\n",
"plt.ylabel(\"Number of observations\")\n",
"plt.show()\n",
"print(\"Plotting phased light curve residuals:\")\n",
"(median, sigmaG) = astroML_stats.median_sigmaG(df_crts['res_flux_rel'].values)\n",
"ax = plot_phased_light_curve(phases=phases,\n",
" fits_phased=np.multiply(np.ones(len(phases)), median),\n",
" times_phased=df_crts['phase_dec'].values,\n",
" fluxes=df_crts['res_flux_rel'].values,\n",
" fluxes_err=df_crts['flux_rel_err'].values,\n",
" n_terms=best_n_terms, flux_unit='relative', return_ax=True)\n",
"plt.show(ax)\n",
"print(\"Solid line is residual median: {med}\".format(med=median))\n",
"print(\"Rank-based standard deviation, sigmaG = {sig}\".format(sig=sigmaG))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Computing best number of Fourier terms, best fit period, and fit residuals for all data points.\n",
"--------------------------------------------------------------------------------"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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5wv8TPmsucAXwIFFH8jKiTumULtX0iofVruyQ3bHtvgb8lmi48E+JHnh0cdwiVxA9Z+Iz\nomdFv1nBNuOP71ZgUNjeGmAt0XDt+6UYM5Qaztvdv6qGbcaWS7YfbUhtuHWphdI6tpJFj857Nq6o\nC9Efz9+IfgV2JLqy5CJ33xLWuRm4nOgXxgh3n5q2AEVEJKkaG3gvXN+9hughLsOBz9z9XjO7kegS\nwpssevrTeKJLFNsT/Qrt5iUfUCMiImlWk81KZwDL3f0ToksGnwzlTxI9nxWip6M94+473b2A6Cll\nfUtvSERE0qsmk8PFRB12AG3cPXb523r2XDrXjpIPA19N6pcBiohINamR5GBm+wHnEHVOlRBugKqo\n809ERGpQTd3ncCYwN1zOB7DezA5x93Vh7JnYzVBrgA5x6x3KnmvbATAzJQsRkSpw95QvT66pZqUf\nsqdJCaLxVi4L05cBE+PKLzaz/cysM3AEMLv0xjI95khtfd12220ZjyGbXzq+Or51+VVZaa85hLtE\nzyC6xjvmbmBCGJGyALgIwN2XmNkEomuii4BrvCp7JSIieyXtycGj8WUOKlW2iShhJFv+TqI7S0VE\nJEN0h3QWycnJyXQIWU3HN710fGuXGrsJrrqYmVqaREQqyczwWtghLSIidYiSg4iIJFByEBGRBEoO\nIiKSQMlBREQSKDmIiEgCJQcREUmg5CAiIgmUHEREJIGSg4iIJFByEBGRBEoOIiKSQMlBREQSKDmI\niEgCJQcREUmg5CAiIgmUHEREJIGSg4iIJFByEBGRBEoOIiKSQMlBREQSKDmIiEgCJQcREUmg5CC1\nTl5eHoMHDyYnJ4fBgweTl5eX0e2I1EcNMx2ASLy8vDxGjhzJihUristi00OHDq3x7YjUV+bumY6h\nUszM61rMkrrBgwczderUhPIBAwbwl7/8BXcn9v8fm05WdvXVV/P2228n3f7kyZMrFVNeXh65ubns\n2LGDRo0aMWLECCUYqXPMDHe3VJdPe83BzFoCfwGOBhz4KbAM+DvQESgALnL3LWH5m4HLgV3ACHdP\nPFNI1tqxY0fS8nfeeYdzzjkHMyt+ASXex5fF1xjivf766xx//PG0adOG1q1b07p16zKnGzVqpBqI\n1FtprzmY2ZPANHf/q5k1BJoBtwCfufu9ZnYjcIC732RmPYDxwIlAe+BVoJu7747bnmoOWWrTpk30\n6tWLVatWJcyr7C/+smogAwcO5P7772f9+vVs2LCh+BX/PjbdpEkTioqK2LZt217HI5Jpla05JFTN\nq/MFfAv4KEn5B0CbMH0I8EGYvhm4MW65yUC/Uuu6ZJcdO3b4n/70Jz/44IN9yJAh3qlTJyeqZTrg\nXbt29UmTJlVqm5MmTfKuXbtWeTu7d+/2zZs3+4knnlhiG7FXkyZNfNiwYf7II4/4ggULfOfOnVXZ\ndZEaE86dKZ+/092s1BnYaGaPA8cBc4Ffh8SwPiyzHmgTptsBM+PWX01Ug5As5O48//zz3HjjjRx5\n5JG88cYbHH300eTl5TF27FgKCwtp3Lgxw4cPr3QTTmz5qm7HzGjZsiUHHHBA0vm9evWiX79+zJw5\nkwceeIDVq1fTp08f+vXrR//+/TnppJNo06ZN8fLqt5C6Jq3NSmbWB3gbONnd55jZA8BW4FfufkDc\ncpvcvZWZjQVmuvvTofwvwEvu/nzcsp7OmKVmzJo1i+uvv56tW7fyxz/+kTPOOCPTISWVrM+ha9eu\njBkzpsTJfdOmTcyePZuZM2cyc+ZMZs2axQEHHEC/fv1o0aIFL730EqtXry53GyLpVNs6pFcDq919\nTnj/D6Kmo3Vmdoi7rzOztsCGMH8N0CFu/UNDWQmjR48uns7JySEnJ6f6I5e0+Pjjj7n55pv5z3/+\nw+23385PfvITGjRokOmwypRqDaRVq1YMGTKEIUOGALB7926WLl3K22+/zahRo0okBog6tW+55RYO\nO+wwDj/8cJo0aZJSPKqBSKry8/PJz8+v8vo10SE9Hfi5uy81s9FA0zDrc3e/x8xuAlp6yQ7pvuzp\nkD48vqqgmkPdtGXLFu644w7++te/MnLkSK6//nqaNWuW6bBqRE5ODtOmTUsoP/DAA2ndujUfffQR\nbdq0oVu3bnTr1o0jjzyyeLpjx47FyTPVWoxIMrWt5gAwHHjazPYDVhBdytoAmGBmPyNcygrg7kvM\nbAKwBCgCrlEmqFtK/7K9+uqrWbVqFXfccQfnnXceixcvpm3btpkOs0Y1atQoaXmfPn2YPHkyRUVF\nrFq1ig8//JClS5fy4Ycf8uKLL/Lhhx+yceNGunTpQrdu3ViwYAEFBQUltrFixQrGjh2r5CDVrzK9\n17Xhha5WqrWSXSHUsGFD7927ty9atCjT4WXM3lw59fXXX/u7777rzz33XMJVXLFXly5dfNq0ab51\n69Ya2Bupq6jk1Uq6Q1qqTVn3FuieAKrlCqyyjm+HDh1o27YtixcvpnPnzvTp04cTTzyRPn36cNxx\nx9G4ceOk8ajvon6pjc1KkuU2bdrE5MmTmT9/ftL5hYWFNRxR7TN06NC9PvmOGDGCFStWlNnn8M03\n37B48WLmzJnDO++8w2OPPcbSpUs56qijihPGiSeeSEFBAddff73u+pZyqeYglebuvP/++0yaNIlJ\nkybx7rvvctppp7Fs2TKWLFmSsLxqDtWnsjWQ7du3s2DBguKEMWfOHJYuXcru3bsTlj311FOZMmWK\nrpzKUpWtOSg5CFDxH/qOHTuYPn16cULYuXMn55xzDmeffTY5OTk0adJEV9PUEQMGDODNN99MKG/U\nqBHuTrNmzWjfvj3t2rWjffv2JaZj/86ZM4frrrtO/9d1iJqVpNLKGlxu8+bN7Ny5k0mTJvHaa6/R\no0cPzjnnHCZOnMgxxxxTPNBdzN7elSw1o6xLiHNycnj55Zf5/PPPWbNmDWvWrOHTTz9lzZo1LFiw\ngLy8vOL3GzZsSFh/xYoV3H333QwZMqRW37siqVHNQcrs6GzYsCEXXHABZ599NmeeeSYHH3xwBqKT\n6lYdNbz/+q//YsaMGQnljRo1okGDBnTv3p2ePXtyzDHHcMwxx9CzZ0/atWuX8IMiFo+ap9JPNQep\ntLKGye7fvz8TJkyo4Wgk3aqjhldWv0ROTg7PPfccS5YsYdGiRSxevJiXX36ZxYsX88033xQniti/\nn376Kbfccos6x2sh1RxEl6BKpVWl9rFhwwYWL15c/Fq0aBFz5sxh165dCct+5zvfSfqdlKpTh7RU\nWl5eHr/4xS80MJxUSnXcuzFw4ECmT5+eUG5mxU1T8a9OnTqxzz77JI1FTVPlU7OSVNrQoUPp3r07\nTZo0oV27dupIlpRUx70byW7QAzjjjDP4wx/+wKJFi1i4cCGPPvooixYtYsuWLcVNUj179uTYY49l\n7dq13HrrrWqaqmaqOQifffYZRxxxBMuWLeOggw7KdDhSj1S2eWrz5s0sWrSo+LVw4UJmz56dtGlK\nzaIlqVlJKu3uu+/mww8/5PHHH890KFIP7W3zVFlNU82bN+fqq68mJyeHAQMGsP/++1dn2HWOkoNU\nSlFREV27duX555/nhBNOyHQ4IpVW1gUVffv2ZejQoeTn5zN79mx69OjBaaedVpwsWrRokbBONvdd\nqM9BKuXFF1+kffv2SgxSZ5U15tSoUaMYOnQoo0aNorCwkFmzZpGfn8+9997LhRdeyNFHH12cLE45\n5RSmT5+e9GZQqJ99F6o51HPf/va3ueKKK/jhD3+Y6VBEqqyyTVOFhYXMnDmz+Glp77zzDg0aNODL\nL79MWDZb+i7UrCQpW7x4MYMGDaKgoID99tsv0+GIZMz27dvp378/7777bsK8Ll268Nhjj9GrVy8O\nOOCADERXPdSsJCl76KGHuOqqq5QYpN5r0qQJbdq0STqvqKiIUaNG8e6779K6dWt69+7NCSecQO/e\nvendu3fSK/yyoe9CyaGe2rJlC88++2zSIbZF6qOKnpexa9culi1bxty5c5k3bx533nkn8+fPp2XL\nliUSxueff87vfve7Ot93oWaleur+++9nzpw5jB8/PtOhiNQale272L17NytWrGDevHnMmzePuXPn\nMm3aNIqKihKWzXTfhfocpEK7d++mW7dujBs3jv79+2c6HJGsUt59F5dffjknn3wyJ598Mh06dKjR\nuCqbHBIHKZGsN3nyZFq2bEm/fv0yHYpI1ilrSJAePXrQvn17nnnmGXr37s1hhx3GxRdfTG5uLnPn\nzmXnzp0lls/Ly2Pw4MHk5OQwePBg8vLyaiL8YupzqIfGjh3Lr371q6Rj64vI3qnovguIHrW7fPly\n3nrrLd566y3+/Oc/s3LlSvr06cMpp5xCw4YNeeqpp/j444+Lt1HVfotY53hlqVmpnlm6dCkDBgxg\n1apVZf7CEZG9U5UhQTZv3sysWbN48803eeihh9i8eXPCMl27duWqq66iadOmNGvWrPhV+n2s7PXX\nX+fXv/51cWJRn4OUaeTIkTRr1ow777wz06GISBlycnKYNm1aQnnHjh258MIL+frrr4tf27ZtK/E+\nvqywsLDE+rrPQZLaunUr48aNS3qjj4jUHo0aNUpa3r17d+67776Ut1NW53gq1CFdj4wbN47TTjut\nxq+SEJHKGTFiBF27di1R1rVrV4YPH16p7exN07FqDvWEu/Pggw/y8MMPZzoUEalAdTznG5J3jqdK\nfQ71xKuvvsq1117LwoULdZWSSD0S6xyfMmWKOqQl0fnnn89ZZ53FlVdemelQRCQDat0d0mZWAHwJ\n7AJ2untfM2sF/B3oCBQAF7n7lrD8zcDlYfkR7j611PaUHCqpoKCAPn36sHLlSpo1a5bpcEQkA2rj\nHdIO5Lh7L3fvG8puAl5x927Aa+E9ZtYD+AHQAxgCPGxm6jTfSw8//DCXXXaZEoOIpKymOqRLZ6tz\ngYFh+kkgnyhBnAc84+47gQIzWw70BWbWUJxZZ9u2bTz++OPMmjUr06GISB1SUzWHV83sHTO7IpS1\ncff1YXo9EBtIvR2wOm7d1UD7Gogxaz3zzDP069ePLl26ZDoUEalDaqLmcIq7rzWzg4FXzOyD+Jnu\n7mZWXidCwrzRo0cXT+fk5JCTk1NNoWYXd2fs2LHce++9mQ5FRGpY7BGoVVWjVyuZ2W3AV8AVRP0Q\n68ysLfCGu3c3s5sA3P3usPxk4DZ3nxW3DXVIp2jGjBn8/Oc/5/3332effdR1I1Kf1aoOaTNramYt\nwnQzYBCwCHgBuCwsdhkwMUy/AFxsZvuZWWfgCGB2OmPMZrHRV5UYRKSy0lpzCCf4f4W3DYGn3f2u\ncCnrBOAwEi9l/Q3RpaxFwEh3n1Jqm6o5pGDNmjX07NmTgoIC9t9//0yHIyIZVuvuc6huSg6p+e1v\nf8uWLVsYO3ZspkMRkVpAyUHYsWMHHTt2JD8/n+7du2c6HBGpBWpVn4NkxoQJEzj22GOVGESkypQc\nstCDDz5Y6aF9RUTiKTlkmdmzZ7Nx40bOOuusTIciInWYkkOWGTt2LNdccw0NGjTIdCgiUoepQzqL\nrF+/nu7du7NixQpatWqV6XBEpBZRh3Q99thjj3HhhRcqMYjIXlNyyAJ5eXkMGjSI22+/ncWLF5OX\nl5fpkESkjlOzUh2Xl5fHyJEjSzwjtmvXrowZM6bSz5sVkeylZqV6Jjc3N+Hh4StWrNCd0SKyV5Qc\n6rht27YlLS8sLKzhSEQkm5SZHMxsiJldmKT8+2b2nfSGJan46quveO+995LOa9y4cQ1HIyLZpLya\nwyhgWpLyacDt6QlHUvXFF18wZMgQTjjhBLp27VpiXteuXXWHtIjslfKeBNfI3TeULnT3jeHZDJIh\nmzZtYvDgwfTr148xY8bw8ssvM3bsWAoLC2ncuDHDhw9XZ7SI7JUyr1Yys6XA0e6+s1T5vsASdz+i\nBuJLFle9vlppw4YNfOc732Hw4MHcc889mKV88YGI1GPVebXS88Cfzax53MZbAI+GeVLD1qxZw8CB\nA7nggguUGEQkrcpLDr8F1gMFZjbPzOYBHwMbgVtrIjjZY+XKlQwcOJBhw4YxevRoJQYRSasKb4Iz\ns6bA4YADy919e00EVk489a5Zafny5Zx++unccMMN6mgWkSqptifBmdn3iBICQGyDxQu7e0aalupb\ncliyZAm9M/JDAAAW3ElEQVSDBg3itttu44orrsh0OCJSR1U2OZR3tdI5xCWDJNTvkGYLFizgzDPP\n5L777uNHP/pRpsMRkXpEYyvVUrNnz+acc87hoYce4vvf/36mwxGROq7aag4W9Xj+F7DZ3Rea2Q/C\n++XAw+6+Y6+jlaRmzJjB9773PR5//HHdryAiGVFen8PDQE+gMfAh0ByYDAwI611aU0GWiiuraw6v\nvvoql1xyCePHj+eMM87IdDgikiWqs0P6faAHUXJYA7R296JQo1jk7sdUR8CVlc3JIS8vj5/+9Kf8\n85//5NRTT810OCKSRaqzQ7ownIW3m9lKdy8CcHc3s53lrCcpysvLIzc3lx07drBlyxYKCgqYMmUK\nJ510UqZDE5F6rrzkcLCZXUd0GWv8NMDBaY8syyV7SM+hhx7KZ599lsGoREQi5TUrjabkfQ4lFnT3\n36U1sjJkS7PS4MGDmTp1atLyyZMnZyAiEclm1das5O6jqyUiSWrHjuQXe+khPSJSG6T9SXBm1sDM\n5pvZi+F9KzN7xcyWmtlUM2sZt+zNZrbMzD4ws0Hpji2TGjVqlLRcD+kRkdqgJh4TOhJYwp5mqZuA\nV9y9G/BaeI+Z9QB+QHSF1BDgYTPL2seYjhgxgkMOOaREmR7SIyK1RXkd0nvNzA4FzgLuAK4LxecC\nA8P0k0A+UYI4D3gmPD+iwMyWA32BmemMMVOGDh3Kcccdx/7770/btm31kB4RqVVSSg5mdjZwNNE9\nDw7g7r9PYdX7gf8G9o8ra+Pu68P0eqBNmG5HyUSwGmifSnx1kbvz3nvv8corr9C9e/dMhyMiUkKF\nycHMHgWaAN8GHgMuAmalsN7ZwAZ3n29mOcmWCfdMlHfpUdJ5o0ePLp7OyckhJyfp5mu1RYsWsd9+\n+3HkkUdmOhQRyUL5+fnk5+dXef1UnuewyN17mtlCdz82PBlusrsPqGC9O4EfA0VENY79iUZyPRHI\ncfd1ZtYWeMPdu5vZTQDufndYfzJwm7vPKrXdrLiU9a677mLt2rXk5uZmOhQRqQeq8zGhMbGH+2wz\ns/ZEJ/tDylkeAHf/jbt3cPfOwMXA6+7+Y+AF4LKw2GXAxDD9AnCxme1nZp2BI4DZqe5IXZOXl6f+\nBRGptVLpc5hkZgcA9wFzQ9ljVfis2M/9u4EJZvYzoIComQp3X2JmE4iubCoCrsmKKkISn3/+OQsX\nLmTgwIEVLywikgGpNCs1dvfC2DRRE1FhrKymZUOz0vjx43n22Wd54YUXMh2KiNQT6WhWeis24e6F\n7r4lvkwq76WXXlKTkojUauWNrdSW6PLSp4FL2DO+0v7AI+6ekesv63rNYdeuXbRp04b58+fToUOH\nTIcjIvVEdQ7ZPRgYRnSvwR/jyrcCv6lSdMKsWbNo3769EoOI1GrlDbz3BPCEmX3P3f9ZcyFlt7y8\nPM4666xMhyEiUq7ympWuJ2pGKj1ctxHdv/an9IeXNK463ax0/PHH8+CDDzJgQLm3iYiIVKvqbFZq\nQRl3KEvVrF69mk8++YR+/fplOhQRkXLpeQ416OWXX2bw4ME0bJjW8Q5FRPZahZeymtmRZvaamb0X\n3h9rZremP7Tso7uiRaSuSOUmuOlEI6s+4u69zMyAxe5+dE0EmCSeOtnnsGPHDlq3bs2KFSs46KCD\nMh2OiNQz6bgJrmn84HfhzLyzKsHVZ9OmTePoo49WYhCROiGV5LDRzA6PvTGz7wNr0xdSdlKTkojU\nJan0jP4K+DPQ3cw+BT4GLk1rVFnopZde4rnnnst0GCIiKakwObj7CuB0M2sG7OPuW9MfVnZZunQp\n27Zt47jjjst0KCIiKSkzOYSb4GI8rjwqyNBNcHVR7K7o2LETEantyutzaAE0B04AriYaY+lQ4BdA\n7/SHlj3U3yAidU0ql7LOAM6KNSeZWQvgJXc/tQbiSxZPnbqUdevWrbRr1461a9fSvHnzTIcjIvVU\nOi5lbU3JS1d3hjJJwauvvkr//v2VGESkTknlaqWngNlm9jzRoHvnA0+mNaosoiYlEamLKmxWAjCz\nE4BTiTqmp7v7/HQHVk4sdaZZyd1p374906dP5/DDD694BRGRNKnOUVmLuftcYG6Vo6qn5s+fT/Pm\nzZUYRKTOSaXPQapITUoiUlcpOaSRkoOI1FUp9TnUJnWlz2Hjxo0cfvjhbNy4kf322y/T4YhIPZeO\nS1mlCiZPnszpp5+uxCAidZKSQ5rEhswQEamL1KyUBkVFRbRu3ZrFixfTrl27TIcjIqJmpdrgrbfe\nolOnTkoMIlJnKTmkwUsvvaSrlESkTktbcjCzxmY2y8wWmNkSM7srlLcys1fMbKmZTTWzlnHr3Gxm\ny8zsAzMblK7Y0k2XsIpIXZfWPgcza+ru28ysIfAf4AbgXOAzd7/XzG4EDnD3m8ysBzAeOJFoePBX\ngW7uvrvUNmt1n8OqVas44YQTWLduHQ0aNMh0OCIiQC3rc3D3bWFyP6ABsJkoOcQG7nuSaCA/gPOA\nZ9x9p7sXAMuBvumMLx3y8vIYMmSIEoOI1GlpTQ5mto+ZLQDWA2+4+3tAG3dfHxZZD7QJ0+2A1XGr\nryaqQdQpalISkWyQ0sB7VRWahI43s28BU8zstFLz3czKayNKOm/06NHF0zk5OeTk5Ox9sNVg+/bt\nTJ8+nXHjxmU6FBGp5/Lz88nPz6/y+jV2n4OZ/RbYDvwcyHH3dWbWlqhG0d3MbgJw97vD8pOB29x9\nVqnt1No+h5dffpm77rqL6dOnZzoUEZESak2fg5kdFLsSycyaAN8B5gMvAJeFxS4DJobpF4CLzWw/\nM+sMHAHMTld86aC7okUkW6SzWakt8KSZ7UOUhMa5+2tmNh+YYGY/AwqAiwDcfYmZTQCWAEXANbW2\nipCEu5OXl8cLL7yQ6VBERPaahs+oJkuWLGHIkCGsXLkSs5RrbiIiNaLWNCvVN7G7opUYRCQbKDlU\nE13CKiLZRM1K1eCLL77g0EMPZd26dTRr1izT4YiIJFCzUgZMnTqVAQMGKDGISNZQcqgGalISkWyj\nZqW9tHv3btq2bcvMmTPp3LlzpsMREUlKzUo1bO7cuRx44IFKDCKSVZQc9pLuihaRbKTksJfU3yAi\n2Uh9Dnth3bp1HHXUUWzYsIF999030+GIiJRJfQ41IC8vj8GDBzNw4EAaNWrE1KlTMx2SiEi1Suvz\nHLJRXl4eI0eOZMWKFcVlI0eOBFDzkohkDdUcKik3N7dEYgBYsWIFY8eOzVBEIiLVT8mhknbs2JG0\nvLCwsIYjERFJHyWHStq5c2fS8saNG9dwJCIi6aPkUAlTp05l8eLFtG7dukR5165dGT58eIaiEhGp\nfuqQTtHDDz/M73//eyZNmsSXX37J2LFjKSwspHHjxgwfPlyd0SKSVXSfQwWKioq47rrreOWVV5g0\naRJdu3atsc8WEakulb3PQTWHcnzxxRdcfPHF7Nq1i7fffpuWLVtmOiQRkRqhPocyfPzxx5xyyil0\n7tyZvLw8JQYRqVeUHJJ46623OPnkk7nqqqt46KGHNDSGiNQ7alYq5emnn+baa6/lySef5Mwzz8x0\nOCIiGaHkEOzevZvRo0czbtw4Xn/9dY455phMhyQikjFKDsD27dsZNmwYn3zyCbNmzUq4j0FEpL6p\n930Oa9euJScnh4YNG/L6668rMYiIUA9rDnl5eeTm5rJjxw6++eYbli9fzvDhw7n11lsxS/kSYBGR\nrFavkkOy4bbbtGlD7969lRhEROLUq2alZMNtr1+/XsNti4iUktbkYGYdzOwNM3vPzBab2YhQ3srM\nXjGzpWY21cxaxq1zs5ktM7MPzGxQdcaj4bZFRFKT7prDTuBadz8a6Af80syOAm4CXnH3bsBr4T1m\n1gP4AdADGAI8bGbVFmOjRo2Slmu4bRGRktKaHNx9nbsvCNNfAe8D7YFzgSfDYk8C54fp84Bn3H2n\nuxcAy4G+1RXPL3/5Sxo2LNnNouG2RUQS1ViHtJl1AnoBs4A27r4+zFoPtAnT7YCZcautJkom1aZz\n58506dJFw22LiJSjRpKDmTUH/gmMdPet8VcGububWXljcFfb+Ny5ubncdtttXHrppdW1SRGRrJT2\n5GBm+xIlhnHuPjEUrzezQ9x9nZm1BTaE8jVAh7jVDw1lJYwePbp4Oicnh5ycnArjWLx4MUuWLOHC\nCy+sym6IiNQp+fn55OfnV3n9tD7sx6IqwpPA5+5+bVz5vaHsHjO7CWjp7jeFDunxRP0M7YFXgcPj\nn+5T1Yf9XHnllRx66KGMGjVq73ZKRKQOquzDftKdHAYA04GF7GkeuhmYDUwADgMKgIvcfUtY5zfA\n5UARUTPUlFLbrHRy+Pzzzzn88MP54IMPaNOmTcUriIhkmVqVHNKhKsnhnnvu4f333+eJJ55IT1Ai\nIrWckkMpRUVFdOnShYkTJ9K7d+80RiYiUntVNjlk/fAZEydOpGPHjkoMIiKVkPXJYcyYMYwYMSLT\nYYiI1ClZnRzmzZvHypUrueCCCzIdiohInZLVySE3NzfpkBkiIlK+rO2Q3rBhA0ceeSTLly/nwAMP\nrIHIRERqL3VIB48++igXXnihEoOISBVkZc3hm2++oVOnTkyZMoWePXvWUGQiIrWXag7AP/7xD446\n6iglBhGRKsrK5DBmzBhGjhyZ6TBEROqsrEsOM2fOZOPGjXpGg4jIXsi65JCbm8vw4cNp0KBBpkMR\nEamzsqpDes2aNfTs2ZOPPvqIli1b1nBkIiK1V73ukH7kkUe45JJLlBhERPZS1tQcCgsL6dixI9On\nT+fII4/MQGQiIrVXva05PPPMM/Tu3VuJQUSkGmRFcnB3cnNzdfmqiEg1yYrkMGPGDLZt28agQYMy\nHYqISFbIiuSQm5vLiBEj2GefrNgdEZGMq/Md0itXrqR3796sXLmS5s2bZzAyEZHaq951SD/00ENc\ndtllSgwiItWoTtccvv76azp27Mjs2bPp0qVLhiMTEam96lXN4W9/+xunnHKKEoOISDWrs8/PjF2+\nOnbs2EyHIiKSdepszeG1115jn3324bTTTst0KCIiWafOJocxY8YwYsQIzFJuQhMRkRTVyQ7pZcuW\n0b9/f1auXEnTpk0zHZKISK1XLzqkH3zwQX7+858rMYiIpElaaw5m9ldgKLDB3XuGslbA34GOQAFw\nkbtvCfNuBi4HdgEj3H1qkm16q1atWLBgAR06dEhb7CIi2aS21RweB4aUKrsJeMXduwGvhfeYWQ/g\nB0CPsM7DZpY0vn333ZeFCxemLei6Kj8/P9MhZDUd3/TS8a1d0poc3H0GsLlU8bnAk2H6SeD8MH0e\n8Iy773T3AmA50DfZdtevX8/IkSPJy8ur/qDrMP1xpZeOb3rp+NYumehzaOPu68P0eqBNmG4HrI5b\nbjXQvqyNrFixQvc4iIikSUY7pMM4GOV1epTbIVJYWFi9AYmICFADl7KaWSfgxbgO6Q+AHHdfZ2Zt\ngTfcvbuZ3QTg7neH5SYDt7n7rFLbq1vX3oqI1BKV6ZDOxPAZLwCXAfeEfyfGlY83sz8RNScdAcwu\nvXJldk5ERKomrcnBzJ4BBgIHmdknwCjgbmCCmf2McCkrgLsvMbMJwBKgCLjG69odeiIiWaLO3SEt\nIiLpVyfvkJaSzKzAzBaa2XwzS2iKk8oxs7+a2XozWxRX1srMXjGzpWY21cxaZjLGuqyM4zvazFaH\n7/B8Myt9f5SkyMw6mNkbZvaemS02sxGhvFLfYSWH7OBEnfy93D3pvSFSKSnfvClVkuz4OvCn8B3u\n5e6TMxBXttgJXOvuRwP9gF+a2VFU8jus5JA91FFfTSp586ZUUhnHF/Qdrhbuvs7dF4Tpr4D3iS7y\nqdR3WMkhOzjwqpm9Y2ZXZDqYLFXWzZtSfYab2btm9n9qtqse4VaCXsAsKvkdVnLIDqe4ey/gTKIq\n5KmZDiibpXDzplTe/wKdgeOBtcAfMxtO3WdmzYF/AiPdfWv8vFS+w0oOWcDd14Z/NwL/oowxqWSv\nrDezQwDCzZsbMhxPVnH3DR4Af0Hf4b1iZvsSJYZx7h67l6xS32ElhzrOzJqaWYsw3QwYBCwqfy2p\ngtjNm1Dy5k2pBuFkFXMB+g5XmUWPx/w/YIm7PxA3q1LfYd3nUMeZWWei2gJENzU+7e53ZTCkOi/+\n5k2ittlRwL+BCcBhlHoOiVROkuN7G5BD1KTkwMfAVXHt41IJZjYAmA4sZE/T0c1EI06k/B1WchAR\nkQRqVhIRkQRKDiIikkDJQUREEig5iIhIAiUHERFJoOQgIiIJlBykTjKzfDM7oQY+Z4SZLTGzcaXK\nc8zsi7ghpqdW0+edY2Y37sX6Hc3sh9URi9RvmXhMqEh1qPINOmbW0N2LUlz8auB0d/80ybxp7n5u\nVeNIElcDd38ReLES65Tel87AJcAze7ENEdUcJH3MrJOZvW9mfw4PHZliZo3DvOJf/mZ2kJl9HKaH\nmdnE8DCSj83sV2Z2g5nNM7O3zeyAuI/4cfjVvsjMTgzrNwsPk5kV1jk3brsvmNlrwCtJYr0ubGeR\nmY0MZY8AXYDJZvbrZLuYZDs/DA9eWmRmd8eVfxU3/X0zezxMP2Fmj5jZTOBeM7vMzMaGeQeb2T/M\nbHZ4nRzKR5vZODP7D3uGYI65Gzg1HJeRZraPmd0X1n/XzK4M28gxsxlm9m/gPTMbaGbTwrFfYWZ3\nm9mPw3oLzaxLWO/CsG8LzGxa8v95yQrurpdeaXkBnYgePHJseP934NIw/QbQO0wfBHwcpocBy4Bm\nofwL4Mow709EI0wC5AOPhulTgUVh+s64z2gJfAg0Ddv9BGiZJM4TiIYaaBI+dzFwXJj3MdAqyTo5\nwBZgfnjdDLQDVgIHAg2IHqhyXlh+a9y63wMeD9NPEI15Exut4DJgbJgeTzTiLkRDHiwJ06OBOUCj\nJHENBF6Me38lcEuYbhTW6xTi/wroGLc/m4mGcd4PWAOMDvNGAPeH6YVA2zC9f6a/Y3ql76VmJUm3\nj919YZieS3Riqsgb7v418LWZbWFPM8si4Ngw7YSmE3efYWb7m9m3iAYePMfMbgjLNSI6sTrRU7CS\njSUzAHje3bcDmNnzwH8B71YQ5wx3Pyf2xszOC7F/Ht4/Hbbz73K24cBz7p6smewM4KhoHDUAWoTB\nFR14wd13JFmndG1mENDTzL4f3u8PHA4UAbPdfWXcsnM8jGdkZsuBKaF8MXBamH4TeNLMJgDPl7Nf\nUscpOUi6xZ/AdgGNw3QRe5o1G1NS/Dq7497vpvzvbOwE+113XxY/w8xOAr4uZ734k6pRtT6N8rYT\nv70mpdbbVsb2DDjJ3b8pURgli7LWSeZX7l6iKc3Mckg8HhUed3e/2sz6AkOBuWZ2grtvqkQsUkeo\nz0FqWuzkWQD0CdPfT75omevGpn8AxaNQbnH3L4l+7Y4oXsisV5J1S5sBnG9mTcIv8/NDWWXNAQaa\n2YFm1gC4GIi1y683s+5mtg/RkNRlJZ/4OKdScl+OSyGGL4EWce+nANeYWcOwjW5m1jSlvUkWnFlX\nd5/t7rcBG4FDq7otqd1Uc5B0K30SjL3/AzAhdJDmUfIXtidZvvQ8BwrNbB7R9/jyUH478ICZLST6\n8fMR0bNzy3zylbvPN7MniIY0BnjM3WNNSmWdxBO25+5rzewmov4UAyZ5dPURRA9zn0R0Qn2HqG+j\non0cATxkZu+GfZwGXFNBXAuBXWa2AHgcyCVqyptnUZVjA3uSU1mfW96+3mtmR4T9ezWuyVCyjIbs\nFhGRBGpWEhGRBEoOIiKSQMlBREQSKDmIiEgCJQcREUmg5CAiIgmUHEREJIGSg4iIJPj/tyZ/dWZQ\ntzMAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x115dcb490>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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/BrAWuK9vVfV4hiZeMDzDhR4Fw8zukLSA7SO7P2FmC7PscpiZRcdoPCBpgZl9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\n6xpkp06dXFOPO3FeV5mZmRw8eJC+ffvyyCPNl+txCoyGhgaefPLJiG3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"text": [
"<matplotlib.figure.Figure at 0x116343a10>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best number of Fourier terms: 9\n",
"Relative Bayesian Information Criterion: 612.071808489\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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RdQB+BtTz/4bIAX5VnEI5HBWBWNYLOAvGUTmIV035Q+BDSaeY2bdFuYik583M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\n4Vjs1Smcjp4JPO3xeQb4AFgW5rk3Y6nTdgIT7bKHgIfs722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bBOQBV2PlXAdrPWp1gOsx\nGCLGhOs3GKKAiHQEXlfVX9R0X8JFRF4EvlbVT2u6L4a6gZnBGAxRQFV3A6dqi6NlKGz1WBZW9kOD\nwRHMDMZgMBgMUcHMYAwGg8EQFYyAMRgMBkNUMALGYDAYDFHBCBiDwWAwRAUjYAwGg8EQFYyAMRgM\nBkNU+P/+0dIvw8A2TAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1179e4c50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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dvbNAIGCnVePs2ZaVlVFcXMyAAQPIzc2lT58+rFixgpycHFfF5nRB1ofatKnz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\nBkEQBMGFGAZBEATBhRgGQRAEwcX/B02Vy3uZs7G/AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x116766510>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Refined period: 86691.0533001 seconds\n",
"Refined period resolution: 1280.46027175 seconds\n",
"\n",
"Evaluating distribution of light curve residuals:\n",
"Departure from Gaussian core: number of sigma, Z1 = 2.27076145401\n",
"Departure from Gaussian tail: number of sigma, Z2 = 9.17657024728\n",
"Plot histogram of residuals:\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: -468.233712\n",
" Iterations: 17\n",
" Function evaluations: 47\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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6/ltu/7c5UPWV+j36KHzpS9Xnn3ZaduDaUVtb9XV22AEefrhn8SiacHFa0q5A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\nmRlOBmZmBvx/HJyC3f4K2JcAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1179d6710>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting phased light curve residuals:\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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KqfftH0RkFFAKnA+c3e2z9yJa/ACVlZVdij9R0Y0aNYqSkpIIAcfaPxpBH3BQ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\ntiI9+eSTrFy5ki9/+ctRBJj9Tdzf0OJOtLL7tbgtPEtDQwM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"text": [
"<matplotlib.figure.Figure at 0x117f01250>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solid line is residual median: -0.0122890252007\n",
"Rank-based standard deviation, sigmaG = 0.0634401456816\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Remove outliers from the residuals using the Bonferroni corrected p-values.\")\n",
"model = sm.OLS(endog=df_crts['res_flux_rel'], exog=np.ones(len(df_crts)))\n",
"fit = model.fit()\n",
"print(\"Fit a constant to the residuals.\")\n",
"print(fit.summary())\n",
"outlier_test = fit.outlier_test()\n",
"astroML_plt.hist(outlier_test['bonf(p)'].values, bins='scott', histtype='step')\n",
"plt.title(\"Histogram of Bonferroni corrected p-values\")\n",
"plt.xlabel(\"Corrected p-value\")\n",
"plt.ylabel(\"Number of data points\")\n",
"plt.show()\n",
"df_crts['is_inlier'] = np.isclose(outlier_test['bonf(p)'], 1.0)\n",
"print((\"Number of outliers detected: {num}\").format(\n",
" num=len(df_crts.loc[np.logical_not(df_crts['is_inlier'].values)])))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Remove outliers from the residuals using the Bonferroni corrected p-values.\n",
"Fit a constant to the residuals."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: res_flux_rel R-squared: -0.000\n",
"Model: OLS Adj. R-squared: -0.000\n",
"Method: Least Squares F-statistic: -inf\n",
"Date: Tue, 03 Mar 2015 Prob (F-statistic): nan\n",
"Time: 15:27:12 Log-Likelihood: 395.80\n",
"No. Observations: 388 AIC: -789.6\n",
"Df Residuals: 387 BIC: -785.6\n",
"Df Model: 0 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"const 0.0017 0.004 0.380 0.704 -0.007 0.010\n",
"==============================================================================\n",
"Omnibus: 352.705 Durbin-Watson: 2.055\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 15300.456\n",
"Skew: 3.611 Prob(JB): 0.00\n",
"Kurtosis: 32.904 Cond. No. 1.00\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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ykjAzs0JOEmZmVshJwszMCjlJmJlZIScJMzMr5CRhZmaFnCTMzKyQk4SZmRVy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\nk4SZmRVykjAzs0JOEmZmVshJwszMCv0/Gqcaq07CcAsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1191511d0>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of outliers detected: 5\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"For inliers, recomputing best number of Fourier terms, best fit period, and fit residuals.\")\n",
"tfmask_inliers = df_crts['is_inlier'].values\n",
"(best_n_terms, phases, fits_phased, df_crts.loc[tfmask_inliers, 'phase_dec']) = \\\n",
" calc_num_terms(times=df_crts.loc[tfmask_inliers, 'unixtime_TCB'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'flux_rel'].values,\n",
" fluxes_err=df_crts.loc[tfmask_inliers, 'flux_rel_err'].values,\n",
" best_period=best_period, max_n_terms=20, show_periodograms=False, show_summary_plots=True,\n",
" period_unit='seconds', flux_unit='relative')\n",
"(best_period, best_period_resolution, phases, fits_phased, df_crts.loc[tfmask_inliers, 'phase_dec'], multi_term_fit) = \\\n",
" refine_best_period(times=df_crts.loc[tfmask_inliers, 'unixtime_TCB'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'flux_rel'].values,\n",
" fluxes_err=df_crts.loc[tfmask_inliers, 'flux_rel_err'].values,\n",
" best_period=best_period, n_terms=best_n_terms, show_plots=True,\n",
" period_unit='seconds', flux_unit='relative')\n",
"(df_crts.loc[tfmask_inliers, 'fit_flux'], df_crts.loc[tfmask_inliers, 'res_flux_rel']) = \\\n",
" calc_flux_fits_residuals(phases=phases, fits_phased=fits_phased,\n",
" times_phased=df_crts.loc[tfmask_inliers, 'phase_dec'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'flux_rel'].values)\n",
"# Evaluate gaussianity of residuals\n",
"print()\n",
"print(\"Evaluating distribution of light curve residuals:\")\n",
"(z1, z2) = calc_z1_z2(dist=df_crts.loc[tfmask_inliers, 'res_flux_rel'].values)\n",
"print(\"Departure from Gaussian core: number of sigma, Z1 = {z1}\".format(z1=z1))\n",
"print(\"Departure from Gaussian tail: number of sigma, Z2 = {z2}\".format(z2=z2))\n",
"print(\"Plot histogram of residuals:\")\n",
"astroML_plt.hist(df_crts.loc[tfmask_inliers, 'res_flux_rel'].values, bins='knuth', histtype='step')\n",
"plt.title(\"Residuals to light curve fit\")\n",
"plt.xlabel(\"Residual relative flux\")\n",
"plt.ylabel(\"Number of observations\")\n",
"plt.show()\n",
"print(\"Plotting phased light curve residuals:\")\n",
"tfmask_outliers = np.logical_not(tfmask_inliers)\n",
"(median, sigmaG) = astroML_stats.median_sigmaG(df_crts.loc[tfmask_inliers, 'res_flux_rel'].values)\n",
"ax = plot_phased_light_curve(phases=phases,\n",
" fits_phased=np.multiply(np.ones(len(phases)), median),\n",
" times_phased=df_crts.loc[tfmask_inliers, 'phase_dec'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'res_flux_rel'].values,\n",
" fluxes_err=df_crts.loc[tfmask_inliers, 'flux_rel_err'].values,\n",
" n_terms=best_n_terms, flux_unit='relative', return_ax=True)\n",
"ax.errorbar(np.append(df_crts.loc[tfmask_outliers, 'phase_dec'].values,\n",
" np.add(df_crts.loc[tfmask_outliers, 'phase_dec'].values, 1.0)),\n",
" np.append(df_crts.loc[tfmask_outliers, 'res_flux_rel'].values,\n",
" df_crts.loc[tfmask_outliers, 'res_flux_rel'].values),\n",
" np.append(df_crts.loc[tfmask_outliers, 'flux_rel_err'].values,\n",
" df_crts.loc[tfmask_outliers, 'flux_rel_err'].values),\n",
" fmt='or', ecolor='gray', linewidth=1)\n",
"plt.show(ax)\n",
"print(\"Solid line is residual median: {med}\".format(med=median))\n",
"print(\"Rank-based standard deviation, sigmaG = {sig}\".format(sig=sigmaG))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For inliers, recomputing best number of Fourier terms, best fit period, and fit residuals.\n",
"--------------------------------------------------------------------------------"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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gtgMDzKzY4LKeHJK3ZcsWDjnkEMaMGUP79u3THY5zLgnr1q2jU6dOzJw5s9iy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\nENjNzNbtSoA13ZtvvkmXLl0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"text": [
"<matplotlib.figure.Figure at 0x115d79510>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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pWjPzQsazU+Kd3p6RQhwfxjnhSG8AJE2S9Is8r3NN7iQez8jEO709I4U4AuNA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\nQiYWemXao0ePCB8GWELAGW6pP8/p0HaapJzk5eUZh6kfzmQ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e9w3E6kl+XVud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\nkJCQQIQCIyQkJCQkEKHACAkJCQkJxP8CtLsJdJR7zoEAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x117a48c50>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best number of Fourier terms: 10\n",
"Relative Bayesian Information Criterion: 543.143185107\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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+USNJHY4GhrNgHE2dhArGr/k1xMxeB3YAeSH6nFBzsRyOhk+8QpcALVq04ODB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\njMFgMBgiwv8Hd9eYIVUJvYAAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1163eb5d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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kxowZw0MPPQRoqyK11B8zZoxX2eZZVk1NTZO+Bm1WqgYfm81GdXU127dv91qt\nqPvhy1XTeK+amzWfCBhXAEaotpq5aexzX9xMTU3Vr1X8nDRpEpMmTaK0tBS32016ejq///3vfZaj\nykpOTva7IjPLbea2kZvtNXM1w9w//mbUxpX7yJEjffITtOfZHz/VcVUvNN6vyZMnU1VVRWpqqt7X\nxnurXJHVQNOxY0euv/76JvfW6MbcHMz3ur1xVq0Y/MFoDxg9ejR/+MMfmpyjdKJG9zdfukPwHVik\nfvf1gMyePVufUbz++usnplH4TqjVGuTn57Nu3ToKCwuprq6mvr6eiIgI7HZ7i26Ivmas0Dhr9VWX\nv1mlWXbzLMufG2tOTg6TJ08mOzubqqoqcnNzyczMZNKkSU3ug6/+ee655/TPX331VbN1tpcu19hW\nIzeNfeWLm9nZ2U3sU7Nnz252teEL+fn5uteOeUUG3n3U3KrAvCLzZatpLdrCT1WfUR7jbNxfkJ8/\nfiqeq+vM3PQXAa2ui46OpqysjGPHjpGVldXkHdHSSstcLzS+iwJNNd8WnNEDg/FmNtfBalaZmJjI\n/fff7/MFbozWVDdA6WGDgoLYvXs3ixYtYsqUKV7XGvW8/shl9KSpqKjw6YkUHx/frM7YF4yGN+Pn\nQA2oxt+U54OaIYGmRvCH1NRU/vznPzdph/JOMcNYl9kjw9xnxpgIY9TyY489xoEDB/T6qqur6d+/\nP926dWPXrl26jteo0lNlJyQ0dYGtqKjQP6sZYq9evUhJSeHFF1+kvLycl156iW+++SYgRwJzm4zc\n9PfQqraauWnkgi9uJiQkUFysbZEuhKCiosKnW6URvl7O6r5s2rSJ2traZj37mnvGzK6sio/GFfna\ntWtbZdxvCz9VfV999ZXuKbRx40Y9utgsp6+6jDxRNkFVrpmbqk989Zvy1APtHTB8+HDy8/NbNUge\nPHjQq16n08nBgwd5+umnCQ4O5vvvv281NwPBGa1KMi4rm3upqkjDnJwcRo4c6VM9YlYtgRbQEh4e\njtvtpqamhtzc3GYjGgM1uBojJDMzM/W2BAqzV5IvOeDEG1CNWLhwoc92tAXme6cyVJqjlg8cOOBV\nn2qXOl9FpRrvr3pwlT+5P6xfv56kpCQ2btyIw+GgvLycmpoaCgsLGTp0aKvbZOamP14o2VvLzezs\nbKKiogAtF5TK4W+GP5WUPzR3TwPhkPnF70+e9uQmwBdffKG3Y/To0W0upyVuKtnN/ZaamkpycrJX\ntlWjI4FHlFUcAAAgAElEQVRCSysGpW41cryiooKamhoqKyvbxM1AcEavGKB5FYWC0pOWlJToAS6B\n5I05cuQITqdTzzgZFxfH448/7veFbMxLA74jQ1esWKF73TgcDsrKynjrrbcYNGiQz5WEL6g2GN0F\njX1g/GyOhm3pIfRn/DTL5nK5fHpUGVVMRv/u5nLHKJjrMAcYmuubPXs2H3zwgb6KMOKGG25g586d\nLFu2jFtuuYXXXnuNnTt3UllZic1mo1u3btx+++16H19//fVUVFRwxRVXcOuttxIcHAxo9yiQeBR/\naMn4bczGaVQT+SrDCJfLpc9GQePmq6++2uRc4/0wqlSM3DTOen1xU3HxscceY/369T75qepRnDS/\nUH2t7FvLTXW92fjs67lRK0Cn08mll16qn6/UcsacW4GmbzfWo3ZqVPL74qbdbicrK4uKigp++ctf\ncvXVV5Ofn+9VTufOnfWy/fHTeD6gc9Nms7F06dKAZG8tzugVA3gbSltzbqBqm7S0NBITE0lMTGTc\nuHEMGDDAb33GvDTQaIAyEr6oqMgrzXNBQQG7du1i0aJFAc/A1XLaqAox1mH8PH78eH3mGsiD58/4\n6Us280xdtVlB2XZayh2jYK7D3M/m+mpqavTZsrnPamtrcblcbN++nczMTIqKiigvL/da/RnPP3Lk\nCC6Xi507d5KZmcmECROIjIzkhx9+OK6leqDGb+N3X0ZiXzBzU0V8G2HOaWX8XXFT1eePm6qfzCs2\nX/UYOemrDcfDTXW92fjcEjeNqe2VG60x51agq11jPf/4xz/0+s31KW6mpqbq12zYsIHMzEwSEhK8\nylEDS3P8NLdPcXPy5MnWiiFQrFixgh07dtDQ0EDXrl11Iw20LS+Lw+Fg1KhRrFixgmXLlrFq1Spu\nv/12r/p27txJfX097733HsOHD2/WHVGN+uHh4fqsJi4uDofD4TVbU4Ytp9PpNbNV7VB1q5nEoEGD\n9ONmo3RbDFPmiFdfq4OsrCz27NnD3LlzdTmNxufCwkL9Gl+7rZlner7qMELNro1Q/vrma1RfhoeH\nU1ZWRlFRkdd1cXFxhISEsGDBAmw2G0FBQV7lOBwOpk6dekL1t2ZuqtkitC3PvpmbH3zwARMmTPA6\nZ/DgwXz33XfU19f75BI08skfN1U/qZe+0ebmqzzVVuO9VSuKE8FNaOTnmjVrmtw71TeHDh1izpw5\nBAcHM2HCBGJiYnQ5jLadlJSUJu8GX6uQ5vjpi5sJCQleO7oNHz6chYZd3pxOJ7m5uWzYsIEjR440\nKU+t2Pxxsz1x1gwM6kYeOnRIn/Xk5eXp3hqB5mVxuwV1dSGEhdV5/W70CmhoaNBJoEZ60KJN6+vr\nm91TNy0tjXnz5lFaWoqUEoDIyEhcLpcut5RSfwhzc3OZN28eUVFROknNek2Ahx56iCNHjlBfX8+r\nr75KcHAwYWFhAalwfMEYH5Camkp9fT0dOnTwehEY265mOMa2jxw5EiklKSkpPpfrRvnnzZtHZGQk\ndvtIoqKeYO3aBvbtayqXcSB2Op18/vnnjBgxokl8wPr167nyyispKyvT81VFREQQFxdHcHAwqamp\nLFu2TK8/KiqK8PBwjh07xpIlSwgLC2sxdUVrMHHiRL777jtdZ5yXl0d2dra+P3igq96amlBstlqC\nDGt9Yz+q/P4KBw8ebPYeQeMs3h83S0tL9fKDgoK8ZrWKm0olY+SG0YtGRUA//fTTxMbG4nA42sxN\n8PY0dDgcTbgJ6HYigPnz5zN16lQ9VYeKH/rPf/7D3Llzm7wbzPLb7XYqK6Ow2f5Gx46/oKBgJ336\n7PK6xszNKVOm6PWsXbuWuXPnMn78eH0Vm5KS4sVBIz8rKyt13ipuhoWF8fHHH1NSUhJQapXjwVkx\nMOTn53vdSIW4uDi/udN94bvvkli5cgSVlR3o3Xsnt9zyARERlYB/Txmjbrt3794t1udwOIiKivKy\nRQQZnnKn04ndbteDx+Li4rDZbE2CuIx1O51OhBD6C2D//v16ecOGDeP+++9n4MCB+jI6EChPLqfT\nSYcOHdi2bRugrRLUi8XYdl997WsWZYRR/uDgYAoKbgXm8sMP2vF+/WoZO/YcYmMbZ/vmwWjy5Mk+\n61i2bBnp6el68JzT6WySMrlp/dqDqMr35/raFmzYsMFrUyZlrzLHtfhDWVkE776bhsuVQGTkMVJS\nPqRPnx+btMOc37+le2SEP26qMnr16oXb7fbJTbObr3l2PXfuXL39+zwj/rBhw7jnnnvo06cPI0aM\nCKgffMms/PqN3ARvXfy9994LNNpCWtoJ0Cz/v/61nv37FwPnsX07bN/+M6699lOva8zcnDhxIv36\n9dMzqYLmzm18Loz1GPlp5K3iZl5enld7TyQ/zTgrBgbjki0uLo7IyEiCgoJITU3F4XCwatUqwLcX\nj1pprFxZw8aNT6LMLj/+2IfFi0fTpcvt7N69lbq6Ojp06MDw4cN1wgFey+S33347oAfd+LB26dKF\n1NRUHn30Uc4//3yCg4M5cuQIYWFh+taKyvitlpcPPfQQ0dHR2Gw2EhMTSU1NZfny5XqZoaGh1NbW\n4nQ6+ctf/qL7gftbupvjMhISEnTf9pSUFLZu3cq2bdt0tYwySBrbHhYWxrJly/wazlXfz5w5k/x8\nLX32TTfdRFZWFjabjR9+CAX+DsAVV2Rz6FA8+fnns2zZHUyaNI+QkIYmfRcXF0d9fT0LFizg6NGj\nuntgWloa8+fP5/DhwwQFBel9ZJZJzZCDg4N1VZOaEYeFhXH99dd7qXjaqvaARtfnsLAwunfvTlpa\nGp9//rnXPTAbqhU3v/rqW779dh6FhVpajbKyjixdeicXXPAAdXUfUVRUhMPhICwsjJUrVzZpo7pH\nvvrADF/cBO0ldNlll7F8+XKEEDgcDi9udurUibKyMv72t7814abD4dAnP0IIpJQ4nU4eeeQRunXr\n5uXCae5jX8Zm0KLpR40ahdPp5NNPP23CTYfDwYQJE5g/fz733nsvX375JUVFRZx77rl6UkFVvio3\nPz+fd999l23btulp8+12O0uXLuPgwaXAedhs33DZZaWsX38Nn312HX/6U6Njgpmb+/fvZ8OGDdhs\nNnr37s33339Px44dGTFiBFlZWRQVFfnlp1pp2Gw2duzYAWjPv9vt1ss3u2YfDz/NOCsGBmjsyOuu\nS2fTpuuw2WoJDv4KqGfEiBFs3LiRZFMKaVBLxkO4XL8Bghg6dB2XX/41Cxbcw4EDTsrLJ1JePh7Q\nXMeWL1/uNStRel4Au30Ab78dzK5d2j4IGzfC1Klg1hKYH1aIobg4mo4dO7FnT65+Xk1NDbt3725i\nEAT0NAdJSUk4HA6vMo0pKkaOHNniFoZGMqlMo4Ce/kClczCqZZRKQrV9wYIFPoMBFYzuo+o8NcOb\nP38BtbVvAEFERy9i+PA8amttzJs3kcLCznz11c+56qovffZdTk6OXp7qk8zMTCoqKvTfVR+ZoWbI\n6rzIyEg6duzIvn37qKmpISsri5iYmDZtcGNGRkYGV155JT17PsHBg70oKdnE7Nm/0X3q1UNt9P1v\nDKa6D4jjnHMKueeeBaxbN5ScnCHk5v4Jt/vfgDZLzcvL44MPPvBSJSl+1tcH8dVXV/Ltt5dw7FhH\n3nkH7r0XJk4ET4Zon/1rs0VQVhbJzTePYf361bqKs7Ky0oubQgi/3AT0l/To0aP54osvSElJ0d1I\nm+OnsV/AW+WWnp7OlClT/HIzJiZG18UbA9OMSS+NBv9Zs2Z5beGZlJRESUkJe/ZcDgxBiMM88EAm\n0dFBhIUFkZ19Nf/611DuvHMNISHuJn1nVBOp/VJAU0W3xE+1qliwYIHX869WXVFRUbot8kTw04yz\nZmBwOBzcfns6f/nLtdTXXwnAF19UY7Pdxrp163TjrHlE1Ub50UA8Ntv3HDjwaz79NAy7/VNgBWVl\nY4FXgBy/S/EXX3yRY8f6MnPmVKDxoVy5UvtLToYLLjiP7t336rKmpo5ny5aBLFo0gAMHnDzzDMBG\nYC7wFFCPEEKfaYWFhdGlSxfdTbGmpqaJsU29pKFxU5G2ZgnNycmhoSGI4uIY5sxZ4KWWUekn3nvv\nPUpLS72Mt75mbqr+xv72NuDV1f0SuBYhinE6X2PBggJsNhtRUXkUFb1GdvbPuOiiL4mJadpOpfIy\n94laQfkyFBoNi0bD3tixY/XrVBtPVPqB6OhoLrxwFsuX/wqAb75JZPnyK3E4CvzagrS+ikCIKUgJ\ndvsDfPLJdkpKXiY4+F80NAwFniU09AF9hXj33Xd75TPSDN55VFW9h9udrP/+3XfapOWZZ+D//g/q\n64MJCWnA4XBwxx2jyM3tyYcfXsKOHYnU19sAN0JcDOwHNBWWskOEhoZSX18PNL0PCsaXtJGbio+t\ncQxRm/8cOxbJ008v5fbb01m8WOOm4t/zzz9PVFSUvoJUvIuNjfXip7/IbCX/O+9kAs8AcMMN6/ji\niw8pKiri6NEXCQlZz65dvdm4sR9DhvyvCTeNXE9KSuLTTz/VVdFt4adSMdtsNurq6qiqqmpxBdhW\nnBUDg1oO5uUlUF8/FKgC3Ljdw6mpuZFPP81g//79PsPXb7stjblz76OmBurq/sLu3TsIDw+nsnIr\n8BzwGPAKHToMY9y4cT5vRFlZJ+rq3gUiCAnJ4MEH8wkObiA6eirPPw/Z2ZCdfR/nn59L164HKC2N\nYufOPtTVaVlJQ0LqkPIoDQ3nArOAa4CbkLKCykrNxlFTU4PdbicpKYnrr79eXxG0RIxAsjT6Qm3t\nYObOvZBjx6IQws2ll/6X4cMFr78+W08/ofWTJl98/C107PgSlZUXUFCQB7zGihWZ3HGH994J5qSB\nDQ1B1NRoCcuuuWYdu3YV6DKHh+8H7sDtvo533nEyceJ+s5j6asbcJ80lJzTaoxITE0lKSuLKK8dT\nWxtCWloaL7zwgleKjbZs/K6guLlmTTbZ2cmeXw8B51JY+EdAS6o2ceJEr01zVF+9+WYkBw92BNay\nb9/bFBerPv81sAX4NV26fEbHjlv1FaJxYCgsLKKi4nkgGdhPjx4zGD36fAYP/n/85S+wYQNMmQId\nO/6WxMQdgGD37p4cPXqOXkZw8H4aGmKRcgTwC2Ak8AXV1dUEBQVRW1tLbW0tkZGR3Hvvva3iZlv2\nwejffzDPPjsYpbWNizvA1VfHERr6gtfK4dixYwBkZHzGuee+zN69cVRUCAoLM4DnyczM1GVUkdlq\nZafk7979OXJzz6dz5wNcccU23nzTaMv8P+BtPvtsCL/6VTn79uU1uX+Kg48++ihXXnklWVlZzJ07\nt1X8TEy8gp//fBSxsQd56aW5XtxszoZ3PDgrBgZFqv/97yLPL88CR4CXgBkMHOjil7+8ocl1K1as\nYO/evtTU9CY0tIja2ndwOp2EhYWRl5dHaOiz1NbeCVyMzfY7li/XZhlKP2iz2bDbu1Bb+y4QhxCf\nMWnSF0RHaxGpQ4dmM3BgCB9/3J9//jOUvLye5OX11Ovv2XM3gwZ9S58+O/j3v99k167zgLeAYcCH\nwI04nbHs27dPfwmHhYVht9t1QqjZRXFxsdcMyZeOP9AVw48/wvDhUFkZRVDQEdzuGDZtGsQPP/Sl\nY8dCqqpexOl0elQGPQgKehqX604aw2ISgRvZufMt3nnnOcrLS1i1ahWvvfaa7kb417/+FSkl0dFP\nUFzcmU6dihgyZDMuV+MsS7sPM4HrOHToLubMuYiqqv1e7oebN2/W+8Ks4jN+N7qKqj0QtNnabXzy\nyR289trFgOTGG1fTrdtynyk22qK/VddERCSjmTEOAQOAncAvgUtwOg812TRnxYoVFBYepago2/PL\nHC9uhoXlU1MzG5jBoUMzCAvTNtExbxpz8OB4YDxQQUzM3YwadRlhYXW43RnMnh3Nrl0XMn16PcXF\n3di48XK9/o4dSxk0aBMXX7yFDz98mV27igkKmofbnQasBG7AZvsGp9OJy+XSPY1Wrlzpxb+W+Nna\nLVSlhLvugsxMEKIaIao5eLArS5f+hkGDLqOq6tdAgWfl0kBw8GR+/PEJduyINZTSHxjD7t1pvPvu\nu5SVlbFmzRoGDx5MdHS0zk+3OxYhtCSEN974KUFBUl8FaOW/S3DwD9TXX8gf/vADdXUv0tDQ4OUW\nrDhYUlLiZew2HjO7MSsbptPppH//x8jMvJMdO8I477wCunZdRW7uVq+VRlvc8FvCGR/gpiAlum4/\nPDyLCRMEwcGFwECefnqtz9lLUVERhw9rS79zzllGUlJvxo4dS3p6OklJSdx//zi6d/8rACUlv2fX\nrko9WEoLOMnj++//iPag/0BCwiPExkbp5ScnJzNy5FBeeikap3MoMAZ4lK5d/8hDD83l7rvfol+/\n77HZGjwBMocZN24BsA9threYkpIykpKSOOecc5oEHIE2I3S5Cjh27JjP40ZZAiXP/fdDZSWEh6/E\n7Y4D+hMe/jWVlR04dOgFIiKySUr6Jw0NrwM7cbvvAhoYPDiHu+9+CZgCVNDQMIbvvvsdLtceNmzY\noKcyVoE8UkZRXKxls7zhhk90Pa0KFNIyVn4LZNHQ0IGSkvF6KoD58+f7lH3btiTmzZvAM8/8gbfe\nuov9++P0e11RUaGrhyIjIxk7dizr1qWwdas2KIBg9eobGDZsklew0olI2/Dhh9r/iy/eQUREJVFR\nmiohKmomY8eObaJGKioqYs+e/tTVxRMauo8LL9zlxc1JkybRt+8HBAe7qKvry+7dN5GZmalv0LNr\n1y4WL66htnYm4AZG06XLXq9AxKuvTmbChHO56KKxwLXANM4991nGjVvIlClzGTbsS6Kjj3nuybk8\n8MA6goPfAiKAD6mru0BfxSYmJvrhZzEul8svP1u7P8O772qDQnBwOVJehNvdlc6dXyIoqIFNmwZx\n5Eg2nTv/nUsueQ8hfqShYS5udywOx3+5667FvPdeObABSKCmJpPvvqvC5XKxdu1aXS7FT5iFlJFE\nRGRzwQWa7U/xc9KkSSQlXUivXloEdEnJJCoqaqmurm4SPAnay7u4OJrLL8/j2Wen8dJLk/n668tx\nu725mZeXh81mIykpiRtueISMjNHU1moR7nv3dic29oUmQaVnnFeSEGI+cBNwWEp5kZ9zXgCGA5XA\neCnlf9tSV2FhLGVlHYmIKGPq1OsRAoYM+YF1637BW29F0ru39/krVqzgwIFItGVxFb/61VHOOSfd\nS79nt9u5774Y/vrXT6iouAG7/TVGjvyCf/7zZQCCgl7G7f4lUEiXLveRnn69X/ns9jJgMU6nk9jY\nWObPz6W+vl6fwYaEhHhmwQ3Y7alUV2cBaUAFNTV/1qM31UxBSvjvfwdSULAOOA/IBn6N01nVKhdd\naEw53dDQgM12FbW1M4iJgejoWeTluQkPL6BTp3Q6dBhLUdGjlJcP41PdU8+NEMsICnqCb7/dw9at\nIdjtbqqrNwCfAuOAvVx2WQavvvoq1157rSGD5wzgHHr02M2OHc+xfn3TdCBagrxZwPXAQ8Dz2GyV\nuvthcnIyU6dOpaioiAMHHqS2tjH4cNeu3uTlnU9qakYTj5Fx48axZ8/F5OQMAero1m00sbFT2bLl\nCrZsGYbdvkT3sjoef3sFlVWjb98D3HrrNIqLj/Hii1BWdhP19Tu9zm1MTaENfkOH/perrvpVE27e\neectzJv3Jw4ceAMhZvGLX3Rhz55sAIKDr2Lfvqc9JT6C07mR1NSxPmXr0MEOfITTuZ3Y2Fiys0s5\nevQobrebqqoqbDYbTqeT8PAwEhKeZPfujsDNwGoqK+/grruGsXXrVqCRn4WFnXjzzcspK3sCOERw\n8AwaGl7zG7zYHBQ/6+sbCA7+FdCPxMSFfP/9Ls/z9BohIR9w6NDTlJdfRnn5wzTGi21HiMeBj3jv\nPTeHDy/Ebv+G6ur3gKsJDl5Nff3lXHZZT6699lomTpzo4Wd/YAJQj9M5hwULNuvcNK5Qc3I2sGPH\nNs/544HXvGyR6p69/PLXFBYuxu3WNvCqrOzARx8NJzf3fEJCGlWIcXFxpKamEhQUxbx5Y2hoCCEi\nYinR0e+wd+97bN48mKlTR7N69XKdCyeCn00gpWy3PzSF5CXA//wcHwGs8ny+Asjxc55sDhMmTJDn\nnPOQBCn79PmfnDlzppw5c6acMuXvEtzSZmuQc+culWvWrJE33XSTjI+Pl3a7XcKLEqSMivq3nDlz\nprz00ktlWFiYRJs+yujoaBkfHy979LhSClEuQcrBg7+STuclEl6S2jqlStrt18kpU6bo9aq/vLw8\nuWbNGrlmzRr5j3/8Q0ZHR8vu3bt76qbJX2RkpEfuKdLh+KWEKk8d/yeDgoJkr1695PTp0+X06bNl\nUtI2z7HGPyH2yt/+9k96W+Lj4/VrmsOwYcMMcvxbgpSPPSbl9OnTZVJSkuzevbt+3G7vKWGqhJdl\nbOzfZVjYgCbt6NChg4yMjJS33PJPKUS9BClfeKFCSillfHy857yLJdRLqJdduw736pOkpCS9D5UM\ncXGqvX+UoaGh8vzzz5fTp0+Xa9as8ZQ5xXO8VsJk6XD0lQMHrvf0S4O8+ebFMioqStrtdtmzZ0/Z\nt+/1Ego910yVgAwLu0yClA5HmezRI0GXZ8SIEc32X0vc7NHjAhkcrN3LadP+qrdt6NDDEqRMTf3W\nBzcHeGQvl48++rRfbvbs2VNGRHwkQcrY2MPy/fe3y9DQ2yQUS5AyJGS+7NMnUU6fPt2Lm1JKnZ+Z\nmZktclPdl+nTp8vevS+WQUHrPX23VQrRSW7ZskUmJSXJRx6ZLm++OUPabDVN+Ol0PianT5/uxc3i\n4mJdnpb5eY0EKYOCDspDh4p1eRo5FSQhTcIc2anTQhkbe6/nN+929OrVS0ZEOGVs7F7P/f5GHjig\nyaHVJSR8KUHKiIj5frk5c+ZMuWXLFtmt2+89bcyTYPPipybb+RIOes5ZKe32i2Rc3APSbq+QIOUF\nF3wvO3bsrHNzwIABMiRksef8LRK0+oOCciRImZ7+b0Obm+en593Z6nd3u6qSpJRfAsXNnHIz8Kbn\n3K+BaCHEua2tZ+fOnRQVdQeguDhb/z0mppQ+fXZSVxdEaemdJCcnU1hY6IkytqON8JCWpgXcFBUV\n6e5gdrtdj0jes+c/nHfeIwjhJidnCPv3fws8ANQB6VRXf0pWVlYTuYx5XSZPnkxUVBQFBQVe7mdK\n320MwomJiWH69CHExU0FGoAncbsf48CBBnbvHsTLL9/P99/3IzS0hi5d/gDEYLN9g5TdWLv2Zr0t\nLeVdUv7jjZ43kcDNCCGZPLlRD2rc3rFrVwn8DafzSe677yDdu1c2acevf/1rpk6dyiWXHOKmm7QY\nkt/9LpxPPmn0tAkJWQoEExn5JgcOfKT3iXlGqWSIiXnR88vD1NZ20KPaExISqKkZDjzvOT4eeJmq\nqu3U1t7HsGHZSBlEZuadBAdP9Cz1D7Fz55+Bc4BV+rU1Nd8AeVRVReB2X6rLs3jxYp/9Fwh27tzJ\nnj12Ghrs2GwFREQ05hKaNUtLifH115dw5ZVGblYDWj6sSy/djN1e45ebubm5dOs2ky5dDlFY2Jlb\nb02ktnY5EA28Q339BEJCgn2qUhU/R44c2YSbxgR90Og373A4GD36VuLjfwt8D1yElJnccMPvuPrq\nyXzwwXhWrLiFurpQIiJWAJ3o2PGPABQWzqC+PtaLm/5yaCluZmdn65vdaKpY+O1vw+jSpXEDoUa9\nvw1YjtP5LBMm/EB09BeA26stAwcOJC0tjWnTJjJ27L+JjDxGVdUgfve7aNxu5eU2HRhKUNBhyst/\n55eboKW6uO++KMLCdgMJwD3U1tbq/AwK6oRmkzkXyMJmS6e6+n8cPPgPnM7ROByV7N59IbW171Jd\nHUJubi4//HAt9fV3ARXAHYBWv9ut2WN+/LGXl8fT8fDTH061jaEbUGD4vhdNL9IqaDdTyxRZXv4F\nb7zxhr7T0eDBXwPw8stQW9uYWyco6LdABD16bKdHD817QXW23W7nggsu0POXxMXFcdddkYwd+y+6\ndt1PSEgdwcE5hIZeA2Q2WTqqnZbM+zur/PmhoaGcf/75REVF6SHw9913n9c+0QDjxkUixEOeb09S\nUZHLu+/eTllZR0JDN9G163BGjaojKcnJvfd+TlBQA1u3DqCwsFOLeYeg8cWwevVqevXqRVjY7YCd\nX/xC8Kc/TdTbcdNNN3np/Y06zvDwcIKDgwkJCfHZjssu+5ahQ9fR0AAjR0JExL8IC9tEff2FxMYe\noXPnF/Q+TkxMZOzYsWRlZTXZrSoy8r9oqqkY4EWEEOzevZvLL5/IoUPPAUFcfnkGHTp8oLfbZrPx\nzTcpCDETKYM4evRZYDXwLW73FWjUG4828dIQHKwN8BUVQ3R5Nm/e3GIGX3/QuJkEgNu9hdmzZ7No\n0SKqqqq4+mro3PkwBw7Ae+81cjMsrBeaC3UDgwb9B2iem6mpyYwfv5CBA/9LRISbyMgSgoIeBe4k\nLCyE66/XVJyBcrNXr15MmjSJqKgo7HY7HTp04I477vAaXNLTr0WIEWiP7M85dOgz/vGPB9ixoy9w\njE6dptCly+9ITOzCpEm19O69k9raMNavH9IkUtsXjJOqESNGcMEFFwKagX3SpGhdvWTkp6b3b+Rm\nWloaoaGhuN1ugoKC6NmzJ2vWrNHbERVVxujRSwgNrWHZMnjzzXFERmYATwNuzj33CaDUi5sq26mq\ne+vWrQQFSc477w2P5M+gvdbA5TrA/v3PAxfSq1cViYn/x3nnddF5UVe3idraq4DDVFdfBfwPIT6k\nrk5NciYD2/U+sdk+A2Dr1i40NDToMpnv5YnA6eCVJEzfpa+TZs6cqX82Z/98+unZfPSRdjOqqr6i\noEBbAWRmZnL77Q7694dt22DJEs29sWvX3lRX/1arXDwLxAPe7mXLli3TZwoqmKRnz3x+85vXAO+A\nLn32SokAACAASURBVHUcvF3NzC6IUVFRHDt2jNraWhwOB9HR0fq5X3zxRRPXM4fDwUMPVfPqq78i\nOvpZDh7sgpR5wCvU1r6Cy+UmK+uQ57oqBg7czLffDmL9+iGkpe3zcofLzs5m+/bt2O12QHPl69ix\nI6BtBDNmzBiWLr2DHTsgPR3eeacxV5I51YDxc2lpKQ0NDXrSNV/tuOaazxg0aChz58LmzVpajpiY\no9x111IcjhvJzKzzctvztVvV6tWrufTSdPLzf46Uo5HyADU1WzlyZA7QAVhEWdkzPPjgg173sKKi\nHM0FeD8wB1DeaTsJD7+dhoZjGDJVEBS0noaGiRQX96Jr12Dd+NxWzJ49m40b11FYCA0N/6OhodrL\nDfbyyzeycuVNzJkDq1YtYejQK9mz5/fU1IQCy1i37k3S09Nb5CZUk5q6gmHDSlm7di1vvLGEggK3\nHqiXnp4eMDdDQ0OJiYnx4qeZAxo3U3n99WuJj19EYeEVFBYewe3+AJjJ0aP7OHpUC94KD3eQnJzN\njz/24ZtvLuOBB0axevVyUlJS9NTqr7zyis7N6upq4uLiKCkpITo6GofDwRVXPM7u3dEkJtbSt2+o\nVy4vo2xmGYUQuk3ryJEjTVK5x8UdYtSopaxcOR6XKwGXC4RwM2LER/TvH0NmZlITl1JjPz755JP0\n69ePjRsfoXv3NVRUXI3mUfhHKioeRHMiOUyfPrO4/PKbqKqqIjMz0+BWWwAMAd4HBiBlAlBLaOij\nCPFvL27W1W0CymhoOI+8vAqSkhxee0IA+irreHGqB4Z9QHfD9/M8vzWBcWAww+lUCdpKCA0tpLa2\nMdBl8eK3mDp1Gvff34H/9/8gNTWasLC/Ul3dGZttE3fc0UUvx18OE7W/rhbYoqVeUCkUjMEmWVlZ\nelZPlR9fIT8/30slYwzCCg0NpaqqqknAiqqzWzcbaWmvsny55kap0jaonbvUdYMHf8233w5i27b+\n3Hjjx14PifLTnjFjBqBFm6r9bWfNmkVtbYjHq0uSliZYuTLcS1ZA32XOVwCO6j8VPBQeHq4Hv6Wl\npZGamk1ych9eeGE7ERHl9O+/zZOo0NutND4+3udqJzo6mnHjruR//1vF8uW3AtMMDPiArl1ncPPN\nd/i8hxpeo3PnHOAGjhzZRdeuW7n77nSWL6/0SjnS0KDtJxAUdEWrjaS+MGDAALp0CUYLev3eq59G\njBhB376XkZNzEzk58OGH0fziF79l3ry7ATedO8/3CmD0x01o5Mrrr7+OEELPl6VSexj3WgiEm9C4\nilBlGKHq69rVRkrK+8yefQW9e//cwE+8+Nmt2wG6d99DQUEP8vMvIT1dc8lUvDx06JAXNydNmqTX\ntWXLFn74QcsPNnq0FvtjzOUVSICYEIKOHTsyc+ZMBg8e7OVynpaWxurVe3jiiW0MHTqCvXv/SZcu\nhZi5qeArN1VMTDT33/8Nc+fGU1c3EFjhObuQ2Ni7Wbx4GXPnztXvowoW1VKE5BIScjmdOt3J4cOC\nLl2+5557rmb58u7s2rVLDxoMD7dTVfVfpLyK6OgbSEnp1kQ286TZ1251geBUDwwrgAeBZUKIwUCJ\nlPJQawvZvVv7b7fv4ze/mURWVpZXoMsTT/TkZz/bx8aNIfTqBaWl44F6Ro1aT3i47yAccwCKcZag\nQv6DgoKoq6sjNzeXl156iU6dOnnN5IyeAgkJ2k5jzz//PIWFhbz44ovcfffd7N+/n8rKSl0nabfb\ndcLW1NR4hfkrmUpLS9m3b5++F8Hf/vY3unbtSlhYGA7H1VRVXchf/rIZId7DbrcHtBfCnj3xNDSE\n4HTuY/v2H71yJanBSm2XaMxg26FDBzp27EhdXR1ut1uX1xj8ZgwS27LltWbl+Oqrr6ipqfGZLRPg\noou+IyysiBUreuF2d+Cxx3qzZMnj3HzzHWRlZXlltwwPD8dutxMUFITT6SQtbYRHnh8JCYlk2bJl\nBAcH06tXL4KDg9m7dy9VVd8BJbjdXamv7wyUH1ccA8CRI5otIT6+Ars9Uc+cWVBQwNq1a+nZM4ai\not9x330gxD2AjZiYZdx776U+bQO+gqN8JZEELTDy9ddfD4ibKrOqSqMeGRnJsWPHvFYdvrIYq/vb\nEj8PHz4KzOX99zuQkTELu90eUDoHKSE3V4v/ueSS/WRn72zCT+NgcODAAT11h8qbZrPZ2LdvH/v2\n7ePIkSNeKSkaV28LGDUqiTffLPQph6rDmN/I2I8REZXcf/9b/OtfPaiuvohevaqprn6C2267nDFj\nxrBt2zZ9YllSUoLdbqdz584UFxdz3333Ybfb9fualZWlPwdjx45l2bJlVFZWopliryI4+AocDm1y\nesbFMQghlgJfAYlCiAIhxL1CiN8IIX4DIKVcBeQKIXYB89CUaq2GGhh69tQMt0aDKUBh4WE6d36I\nXr2gqAiCghq45ZaV9OxZ5KfExhmaevCMgS2gzRaMuforKip0I5lxJmcuU0WKVlZWsnix5r6qrklJ\nSfEyzBnLUw+AUSaF+vp63Ue8vn6B59c7kVJSVVXF/PnzvXby8gX14PXsmacbJM11qeW70XheUVFB\nfX09VVVVunHU6XRy7rnneskeKHbu3ElBQQEVFRU+DfoAffocZNq0dTzyyGoef/wc7rjjV/rgXV5e\nrvuS5+bmUl1dTWVlJaGhoTgcDr0PVSrp3NxcQkNDGTVqlEcdJoH/AY0v9OOJY3C74ehRzXYwevRl\njBo1SudQREQElZWVbNv2e3r1+oi6OqitDaNnz91MnrzLb+SwLx4ofir1oJH/gXIzKipK96fPzc3V\nddfGe6j46csg2xI/a2oWATXAdUh5DlVVVVx88cX6ef7sOEePdqK0NBqHo5IRI5w++Wl8boxpTOrr\n6/U04aBlR05JSfFrg2vuPqs68vLyCA72bdDv1EkyZYqL6dM/JC3tU0aPHobD4dBzMKkJa1lZGdXV\n1RQUFNCjRw9iYmK8+q+oqEh/Dr744guioqI8KjHNLTg29qqAZG4rml0xCPH/23v3+Kiqc+H/u3Ih\nGZKQAbmEIGZAohhvqFSp2jpotYigaCqKQIvVAkVb6Vs95XjKT3L6O31r1R60Wq1aiRattaIxqYKi\nJVhUsCIglpuBzIjchJALuZDrev/Ys3b27Oy55DoJrO/nk09m9uzZe+01z97PWs96LiIRwyj7bYwl\ndwn4gfeBt6WUTeG+L6WcEe7zwD53R9tYJ3w+H++9J4FRlJX9yyy8ct111/Hss89SU1PD+PHjefHF\nX5OUBOvXQ2HhY7jdVVGfo7CwkPr6ehISEhg0aBBVVVXcfPPNrFmzxtynX79+zJ4920wQFuqmtqcC\nto4SrB4WqtZ0XFxcUAUqaE109tVXX1FTUxOUnyY+fj3GoP0aIBFoZMCAATz99NNhSxju2TMKgF27\n/sDkyb82Sxeq6y8rKzMfFBkZGVRVVVFbWxsUjZuRkUF6enpQRk5rX9ijcp36SN3U9pxL9u8qU8Bb\nb73FxIkTg8x4qn+tHjZ2U4j9wVBYWGjm/hFiF1J+i/fe28fatcvYsGEDL730Uod8xT/+eC/NzSMZ\nOLCBVatWBI04R44caebPWb36m+zdC48++idGjPgqqN5COKwmTpfLxQUXXMDBgweZNGkSTzzxBE1N\nRs6tQYMGceqpp4bNsGo1vakiV/b0Fmof5YVml00ILZ9JSXXU16/BSANyLfBnMjMzzXv2nnvucWyX\nGrQI8Q+mTPkDL730kimL6vrVYrxyOvD7/WYBLKtshkpJoeTLXlfCilK6VtlUbZ4xY0ZQ2VO7qWq3\nGr0GUFlmQ5mR7fL5hz/8IfCJkZO+tLQfr7/+OhUVFZ2Sz1DEh7LdCyEWY+RB7o+RlOV9DHVVj5HM\n57/z8vIGL1my5P0ua00I8vLylqh2+nw+00tELbKsXDmc3btTSUp6mYMH3+To0aMcO3aM2bNnU15e\nTnFxcSAVMIwaBRs2vNOu83/44Yd8+eWXtLS0UF1dTWNjI8eOHePYsWNmucTm5mZqa2uZPn26+aPa\nFy3Xrl1LTk4O27ZtY+7cuQwcOJDExETOPvts8zvZ2dmUl5ebqaCllFRWVlJeXm5mzUxMTOTcc8/l\nwgsvpLy8nFtuuYVjx45x8803c+65I/nwwwyMpZtikpMPUF5eTklJCeXl5aSkpFBRUYHf78fj8eB2\nu3nzzX/xzjvfRYjj1NT8gJKSHezZs4ehQ4ea1+/3+6mvryctLY0f/ehHXHLJJZSXl3PzzTdz9tln\nU15ezvTp07ngggtITExsc11er5dHHnmELVu2cPTo0aDrsfL4449TVFRk5qBX+x4/fjzou2rEv2/f\nPvO9NXV2c3Oz+aBvbm7m2LFjQedT/azMVR9++KGlytsY4LvU1n5OeflLlJSUsGfPnqDKfaGwy2dp\naRorVw7njDOaKC//LX6/n4qKCoYNG8aqVasoKioy5XPYMNi0qQhhd8cIg/ptGhoaaGpqwu/3M2zY\nMMaPH88XX3xh5guqqqpi2LBhZp1nJ9nMzs7myJEjDB48mE2bNrFly5ag31D126ZNm2hsNApZKdm8\n6667zAyooeTzlltuobS0nJqaKzBcvV+ltraWI0eOcPToUTZs2GAeU+F2u/nVr5o5cmQIjY0PUVLy\nCnv27OFHP/oRa9euNa+/sbGRtLQ07rzzTs455xxTHu2yOWnSJNauXdtGPjdu3MiWLVvM+8RJNv/4\nxz+2kU11n2zdutVRPtX7jIwM08yqiI+Pp6mpiYqKijbntMvn9u3bA7/lMeB+mptTqaxcRFnZ4bDy\nmZeXx5IlS9q90BBuXLIFuEBK+WMp5TIp5dtSypVSyueklPOBC1Hzmh7E6sbm9/vxer3U1BhpD5KT\njQU3IQTbtm3joYce4tvf/naQJrW6uanRaaTyjUqTq1GSck+13jD9+vVrMyp1QmWZtLumWs9lN4X1\n69ePKVOmAK0uh4888ggvvfQSDQ0NZu6k1atXB+zmqwBISbmV4cOHA8Yi6NSpU80+U30JUFpqzBaS\nkz8B6hk/fry5OGldtBwzZgwLFiwIMslYXzu5mar2er1es4iJk3lJ/QYq95HTYqj1ver7UaNGtTEN\nqGPZj2F1MwTM9luv0fiNtwf6/Tyz70K5Vdqxy+cppxjxEGeemRQkL9u3b2fMmDFcffXVQfJpbWNd\nXV27ZXPMmDFmf1ndGIcOHRpVEakZM2YwY8aMkKNPl8tlmj+hVe4ffvhhs+0vv/wyr7/+Oi+//HKQ\nfP7zn/8kIeHtwDe/y/DhWUEmx9dffz0o6aPH46G5uVU+4d2QspmRkRGVbF5yySVtZHP58uVmdlhV\n6tNKONlUbVHHtMuneq8UtPW7p512mvk6MTEx6He3XkNhYaFZ3EiIGgwX4WSGDPkGQFCfdBUhFYOU\nslCqIRcghOhv+7xFSlnY9ps9j5qlXX/92eTk5JgjxZaWFp599tmgfa0F6lXgV6QFsI8++giXy2Ue\nV7kI5ubmmi52DQ0NPPvssx1O01xYWMhDDz3Eb37zG55//nmuu+4686ZXATPQaudUtsqSkhIee+wx\nli9fbha0b2oy0k7W1V3Fvn37iI+P589//nNIE4Kaql9ySRU5OTmsXr3afDBYC8Sfc845YTNm2oPq\nCgsL+fe//23mojn11FOD/MytN6YyP4Uqrv7YY8E5YlJSUoIeUtb909LS6N+/P8OGDQvyP9+5c6fZ\nPtVndXV1Qddo/MY7Av1+OikpKRQWFnZ4mq7M5llZRhuVN42UkrKysjY5n+x92F7ZtP5G1jYrpdxR\nrPKpHvZgyObq1au59957zbbv2LEj6D57/PHHzX7ev/8D4HMgncOHx3Lw4EGys7Md80UBbNwI9fXJ\nuN1l5OT0DymbVpdxJ1TbPv744zayWVJSwuDBg8nJyWH9+vXtkk3VlsWLFzvKp+qn999/34y1cLvd\npknZGoug2vLQQw+ZsS6q7apAj5QSIXYG+v50zjzzzKA+6SoiWjKFEJcKIbYBOwPvxwkh/hDhaz3G\n8eNw4ICxoDx0aD3Tp08PcqG88847yc/PN2vOOrm5KZNUqNHZ5s2bGTFihPk9JSgul4tTT22Nx6up\nqQkZZRwJeyKt1atXB53z+9//PtB2ETwxMZG6urqgxerhw78kObmGlpbRNDScRnNzc0hffKvHxxln\n7G1T7tA68rnjjjvCXoPa1+PxmAvpatFv4MCB5Ofnh1wwVEVb1G+hRkxqVnP06NGg71ZUVFBXV8cH\nH3xgpk9Wn1dWVlJbW8uXX34ZtEioYi0As89UlSxrnw4f3gg00tycQU1NMwsWdMgnAmhVDFKWthlt\nq3WmgoICs4KYfaTZXtlctmyZ+Zl11llbW9th2QSj/5V8qn5V57zrrrsoLi422z5+/Hhzpgqt94X6\nPDXVMDk1NX2Huro6Dh48iMvlcnSQUDm5Tj/dF1Y2rQvqTn2l9j3zzDO566672kSSK9m0Kh17dLb6\nLTIyMpg+fToZGRlmm8855xxH+VQxK2632ywepKLMrYvY1tmkKp+qfi97nq/+/Y3Zw6FDRnBpl+dJ\nIjqvpKUYq0VHAKSUmzHyQvcKVHnj1NRq4uKMUdPcuXNJSEhg/vz5ZGRkMGfOHKZNm4bH4+Gll15q\nk51QPTStD0+rcCl3Pvv3wBg9pKSkAB0v7mKdEkOrqcp6TmVKys3Nxe12M3jwYFJSUoK8mu68807c\nbjeVlUdpaAik82QyiYmJbNrknJuwtBQqK90kJ9eRkXGwzef9+/c3C5FffvnlZnvtJiPVtpycHDZt\n2hQk7MnJyWzatClEIZrgsH67AlP+7PbtSgkOGDAg5MKy8kBRbVajavvDNzhjZg7f//5MEhKMvhg6\n9BudSjmgPEgnTjTMIbm5uYwZM4bU1FS++OILBg4cyLRp00zTiV3O2iub1j62ymZqaqq5YNoe+VS/\ntXXGkZGRwZ133mmec/LkyXi9XrMdOTk5NDY2BhWZmTp1KikpKcTHx1Nf/0bgSJODUsE4eUup6qej\nRu1p85lVNq28+uqrLFu2jBUrVpjXqtq2fv16FixYECSb8+bNCyubykyjfoOFCxea/52yw9pNXHbT\nlJPjQ319fVDJYOv3cnNzA3UZzuQHP/gBycnGsVNSzumSWBsnovJ9kFJ+adsU1hupJ1GKIS3tmLlN\nFVrPyMhos7/S3OrhnpWV5RgpaJ3C+3y+kK54LpeLu+++G5fLZcY0WEdm1pwvoUZ91ilxamqqWRDI\n6ZzKrXDfvn3U1NSYaY9nz55tjkZqa2tpaTEUgxCTWbBgQchzt954paYnjHVhX6W5Li0tNUf11tGU\ntW6xam9BQYHpjZGTk8M999xDaWmpadsHY+HttttuM9seKqy/uLiYgQMHsnTp0qDt6kauqqpq49aq\nzrt69eqg2YkaIWZlZQU9fFW7lauzMbI3omW93h90akRmNSWpPpo1axb33nuv429i/c07IpvWUbeS\nzZycHDweT5u019HKpt/v58iRI6SmppoPJ2tf2dvu9/vZu3cvLS0tZnpzl8tFRUUFzc3NNDauAaqA\nHGbN+q+Q623Hj8MHRkYQRo3ytWmzmhmqGCCFyjm1detWc7tVNvPz87n11ltN2Rw9enRQLWkgKPXL\n31XOdBvFxcUUFBSQkpISJJ+RTFx25a9cU5ubm4P6WH3Puvbjcrm49FJjhjhixKVhzWedIZoAty+F\nEJcBCCH6YeQ+3t4trekAgTUZBgyIzv3U7ivt8Xh4+OGH+fzzz03Xx7FjxwbdkC+99FJYN0uXyxVI\nD13SZrHUGhjl8/l4/vnnASMwrKmpib/97W9BowslECrKWKFuXr/f32YKrdqTlJRkRqsaOYFaiIu7\nkpSUTxz7oKCggMcfPwPIYdQonxlRvWrVKtN7ZfTo0ezcuZPMzEx+/OMfs3HjRtNtLzMzk5kzZ5oP\n9fj4eNNcc+WVV/L222+3qa27e/dusrKyzPdqVOnz+RwfhNZITmsUpxol2hcLrYFO1vdfffWV+b3r\nrrvO8WFkdf1sbj4LOJ3KSneHA9ykBOWIElhnDEtXyOa0adPYsmWL+bl6IG7YsIHPP/88SD5DySbA\n0qVLg+TJ5XI55vNS31W/n1r/gtZyqW63m/r6eovybyIp6X3q66fw9dcXkZW1sc0xi4uLKSys4vjx\n6xk27CBudyONjYbMJicnM27cOMdYhKysLNNjatSoUdx6662mfV7hdru54447TFfbn/70p2Yt+PPO\nO88MGOvXz4iyPvXUU2lqajL7Xf1O9lmskk8nE5dxPYVBLqzKpdUqm059nJWVxe9//3uLXE8AbmPv\nXkFdXV2nAzCdiGbG8GOMVKIjMNJVXBB43ytQisE6YwiHvfOUt4x1YWrOnDlBP7rTgrUdJ1NTfn4+\n69evdzz3vffey6JFi0KOLuyLjl6v19wWyqy1aNEi0tNVoaDDJCd/TnNzIj7fqKCHiRLsG26YRkmJ\n8cTavPkRPvroI+rq6pg/fz4TJhg5jaymN2XOUgtps2fPDvI9/+Uvf2m2XX3feu2qT1X/WvtYXV+k\nvETKtKGSiKnFQoXdNqzeK4WlonidsC7s19Ya6Ss2bjzS4QC3hoZ+1NUZpVvT0iLv312yCTBz5swg\nmbGuuzmde+HChUHypFK+OKF+SyWf7733XtC5Fi1aBBh2eIXbbdwXX3zRWijFKqNer5eNG41z19a+\nybp166irq2PhwoWmfDrdB3PmzDHP/+mnn7J48eKgtlrNylbUeyc5tG8LJQt22bSbq+2OBdHK5pw5\nc4K+u3u3MUuvqxtKUVFRpwIwQxFVSgwp5W1detYuZMOGvcBITjst/KWoUY3TdoVamLKPWp0WrO0j\nejUysxJNuH+oBTR7G9SoINS5FFZ3OI/naz780EjT6/EMNf3MFb/+dQE1NdOIjz/E/v3/YP9+ow6v\ntcaxMr1ZcdrWXqy/h3WmYBdw++9mTf2Qk5MT1jZ8ww03mGsroYrUp6SkmOkTgnMrGecYOvTioJGi\nal+kEZrP56OmxrDvp6fXs3btB1H3hbq+jshmqARqM2fONHNCQXSyCa3ypIrYO2EfsYaSD2uxqRtu\n6M+TTxquqE1N8SQkNOPxeEwZzc/Pp7T0SgCOHStg5cqVbWQz1H2gzt9xT7JgmQslm/Z97bJpHbAo\n86q6fmuutFCyqXj44YeDZFPKAxjhZEP47ndvMh0XopXNaIhGMXwohCgF/gq8JqUMV1+hx4mLM3Lw\nXX/9RSxdOjdoqmb9YaydtXbtWnNat2HDBp5//nkmT57MBx98ECRMSkhVwXmnvEFO57IeO1REohKo\nUEXBVXIx6/tosB6vrMwXUAzZZGW1Tk+V+aGm5g5gGi7Xeqqrw9/8XY3H4+HXv/4177zzDjk5OSH7\nyf67hfLaUVivf+bMmaad+eqrr2b16tUkJCSYEcGZmZls3LiRRx991Pzu448/Tk1NDYmJB2hshOrq\nQXi9FwCGqSDaB6rH46G62lAMp5+eGtYcab+RL7roog7LptdS0a6jsglt5fOBBx5g48a2Jh+IXjYL\nCgosbW1k2LCDHDqUgd9/GqefXorH4zHbFx/vZt++2QjRjJRre1w2PR6P2Y/h+sr624VLde92u9vc\n6+q9ks2pU6fy7LPPUl1dHVTX/N577+XIkSOmbGZkDKOs7ACNjR7q6zPwer3tks1oiKgYpJTZQohL\ngFuB/wq4rv5VSvnnLmtFJ9i9+ziQTGnpOjPaEFrTNVuxaneVRMvv97NgwYKwIwynEdD7778f8lzW\nY8+cOZPFixezY4fhG69GBwUFBQwePJixY8c6LiBZTVCJiYnm4tbAgQMt6whtsY6iMjP343LVUlEx\nkFtuWczHH/+ZxMREhg0bFmi7Ufy9X7+1pKSk8Oqrr5Kfnx/kIuk0ArWmpxgyZAirVq3iwIEDrFix\ngsmTJweNXsKhzCB+v5+5c+fy29/+ts3Iubi4mOTkZNPcduutt/Laa6+ZN5e1n+zXn5+fH/R++vTp\nQR42e/bswev1cuutt1JfX28u1hYVFXH55Vfy9NNQUeEOkpv8/PyoR2ZqxtDSctBRXuwzWHUeNfL0\n+/3MmTOnXbK5fv16x7TlauE/GtkEWLduHaeeeqrZf6mpqY7nT0pK4qmnnuL48eMMHjwYaDvbDdXW\nMWNKOHQog7ffjsPlMlKPHD58OBAhfBEQz5AhX1BT02xef6jZlRUlnytWrGD+/PlBtv1LL700qkBU\nIOh3UPJpvT71Pzk5mYMHDzoO8lT2ZWg7w7HLJhjxJuo3eO6557j//vt56qmngmRz6tSpvPJKi+lR\nqNrRHtmMRLReSRuklD/DeJKUE6i61hs4etQIILnllss544wzgGA3RStWO/fo0aPNfa3uiD6fz/Rc\nSE9PJz09nfz8/DbHUt93Gh3Yjz1hwgTmzJnDnDlzTHvrwoULmTVrVkgtb7XR33///aZrXLh8R3bi\n4iRjxhjmg08/HWaxUe7GqNY2EWjm6NEXqKmp4b777gNabcb2kaASQGvB+eLiYpKSkoK8QKIVSGUG\nUZGb9nUI1ZYJEyaY23/1q18FecOo/nTC2n4VYWv3CX/hhReCjqFu1qFDjZvz2LE0Ro5sbZeKHI/G\nrqsUw3nnZTjKi5Od2+v1Brnbvv766+bn0cjmhAkTHEeus2YZ1c+ikU21v93O7sSiRYuYP38+Cxcu\nNN2Z7TiZcAGysw3ZPHp0An6/n5UrV5puyC7XrQCkpr5HbW0t7777rilbTvKpvKqKi4tN+dy6dSvF\nxcVB9vlnngmf3deK9XdQ8mntC9WGCRMmmE4gdk+t+++/P+g7TijZhNZcaklJSfzwhz80+9fok9bj\nu91G2pDKyvQOyWYkIs4YhBDpGKWTbsFIIvM68I1OnbUDONnRpGxdfM7MbJ1Wq2mvddRp16BqX3vU\noH0/NUKxjkxSUlL4zne+0yYtdaRjdxbVNvtaQTiys0vYuvU8KiqMmzYzM5MPP/yQyy9fyldfEHaZ\nbAAAIABJREFU9SM5+V8cP14WlFs+1PmUeUtVGlPfUWsjykNIPayGDRtmelw5zSK6qp/stTKSkpLI\nzc0NOt/8+fPJy8szE7wBYRVtQkIL/fvXUFubwtdfgyVeKwjrCNYun0oxDB0KjzzS1hzptHYBreaw\nSLKpvmv1Jnrqqae47bbbePXVV5k1a5ZZpEa1sbtkU7UP2ppBQz2kRo7cS1LScerrxwCjGT9+EJdd\ndhnvvPMePp+RIv3UUzdRWups5rQed86cOeTl5eH1ek35HD9+PL/85S/Jzc0FWted8vPzg67dun5n\nJdTv0B6syfn2799PRUVFGxOfkk2AH/3oRzz33HNs3brVcUCqUM42x445z+Q6SzRrDJuBN4D/BtZb\n02T0JE52tLq6ZI4fh7Q0Al4fxlR1ypQpbNy4MUhY7ES7QOX0ML73XqNIjHLLs5KVlWXmVFEVqNrL\nsGHDgoTCPmV1QkUWWx+SLS0tNDUNQIjrOHr0fMaMuYrc3PFkZWWRkjIPgG9+82sOHTKqVEVqqxLy\n7OxsMx/95s2buffeezl8+DAPPvggGzduDBqxKIF3uvGsv0GoxehozFJOtTKKioqCZl3WiOoZM4KT\n/trNUYq0tGPU1qawf39oxWB9WNvls6bmawCGDXM2R6oHqP361MgwGtmxf1eNLuPi4vjP//xPs/9V\n33ZUNq2j/vT0dDPRXUFBAW63O6gd9gfaY489RkpKCo899hiFhYVmzYzExETi488GbuKUU/4Pq1fP\n5NFHH+WCCxaxfXsKp5xyhDfeeJDLL19nZkUNhfUB/OSTTzJ58mQeeOABjh49ys9+9jOeeOIJpk6d\nymWXXWa2Vbn1hhrNq9+hoqLCrPzWXtlUsxe/34/L5TID7oqKirjvvvvMgatC5VJTMyBfICmjndRU\npRiicHfrANEohtGxUgaRUJ1iyTIQc9SDwemGjxZ1c6ub2i64Vj91harGtmTJEpvdtQZYAdzGiBGL\ncbmKOXgQdu06g7i4Zi68cDtpacYDK5LAW9cElNeFatvGjRtNhdyR63YaDUfbh9aUFlbvDqtPv30U\na2XChAm8/fbbbbanpR3j0KEMDhxo37UoamoMU9nQoRF27AHU9YdSRpGw7r9w4UJTNp2ildWATKFk\nE+B3v/uducZjrBs9BtxEZWUuqamGotq0yVjsHzduC1u2xJuBadDWA0phlc377rvPHCCqa1dpuXta\nNq2zF5WNVcmndeAaSjbVue33vJoxVFf38IxBCPGolPIeoFBlbrQgpZTXd0uLomTu3Lm88UY1sIDB\ng5uwXooa3aigMKu7WXsEQ41irVG56enpLF++3BRu6+hJfcfpHOvXrw9a5LMv2HUU+yKt/SEJMHDg\nCsrLb+ODD85jz56f8Pzz5yBlLmeeuZ20tJo2x1PXbe8vNRr3eDxBeaai6VOnBW2n79lnDgUFBebo\nNisri2uuuYZdu3aZ0/H8/Hx++MMfsnz58iDvDuWrH6nv1PGtfalISzN+4zVrdpKa2j7tMHfuXEpK\nbgegf/9qoO0N3Bn5DCWbBQUFpmxarz9cX6hRaUVFBenp6TQ1NbF06VKSk5NNc2CoBeVQx7NSXFxs\nttOekbihYS3x8XtoahrNRRf9L4cP/5MDB36JEM2cf/5mPJ5c1q5di9/vDxpFQ7D8qJG4J7AGcfjw\n4bByZm8ftF82rdfldrtZs2YNvkC+K2UqmjJlCn6/n1mzZnHgwAGKior43ve+R1xcXNjfRMmGVT6t\nKNmsrz+lXb9NtISbMbwQ+P+Iw2cxn0Hs2rWLr782Ul7s3v0RxcWtCdKsghOtK50T1htVaWyVJ0XZ\ndseNGxeVzX/ChAltgr4U9rqsShiU0lE20XHjxrURWOuow+peePXVV7NqlZF++4Ybslm/Ht5/fyB7\n974AGHnfr7giuJSGva98ltQYWVlZ5OXl8Ytf/IL777+fkpKSNjdqOKL9HSI9HPPz84M8bubPn4/P\n56OhoYGsrKygqFH7yNWO1eyTl5eHx+MJUgxquj5gwJl4vWe2a21n165d1NcbEeKPPPIfuN3GrMyq\nfDojn+Fk0+l61Gun3ypSn9tHtWrxO5Rs2o+lrlHJpxr9T5o0idWrVzN69Mf8/e+j2bbtTpqapgLx\nuN0vM2BAddCx7KlArLK5ePFiUzZHjBjRrt+qq2QTaOMNNnnyZA4fPsz5559vBrBeccUVrF27Nqx8\n2ttk30/NGOrq3GFnHB0lpGKQUiqn5XFSyqBENUKIhUDXtiRKlJY9cOAAYCwcXnxxFl6vEcHbmemy\nE6Fs3yqdrtru5DbXUcaNG+e4oBkJj8dj2kULCws5fvw4iYmJCAFPPgnnnltFS4uR6uLii9cyfLjz\neoU6r/Uhotowffp0Zs6c2caebhfMUP3W3lmbHVUJS1VlU8eLdKM5YW+jHXXzqXxc0RAsn4a3yU9+\ncgteb9uHQWflsyOy2RX3hDpGe2RTfU+lpC4rK+PNN98kNzeXpKSd7Nq1k127zgTSiI/3MXv2rpDH\niSSb0PociPT97pRNa9tUWyKZjsK1M9gBxpgxHDmSgCVpcJcRzRrDDzAyrFqZ47CtR1APox07dvCn\nP43iyBG46CJDKbz11luAkedFCGH6/p9xxhnk5OR0aHHT/uCx8vbbbwf94Gr/zqBMOepYTqN4677q\nOtQioBIg64LsQw89xFNPPcWtt/6E1auH8NBDd1BaWhy2HdabxHqTOQm03XRnN/9YR5Kd7Z9hw4bx\n1VdfmekDwk2jVXv8fn/IabuaaTkxcqThOrh16xF8vujqGSgZ2bZtFw89NBghJDfddIV5DpWDyGqu\nGTduHBkZGW0eApHMdO2Rzc6OKq2jc0Uot0jrvn6/35wh2FNaQ2tU7/Dhf+E3v/mA3/1uGbfcUsug\nQaGNEu2VzXCmya6UzaysrCDZvO+++xyfM9b7BVoHE6G8+NRrq2JISGjB7W6goqIfGzcGV4brCsKt\nMcwAbgNGCSGsSVjSgDLnb/UcLpeL004bz5EjrYt7kydP5l//+lfQlNqK/YfvqllFVxIpetFpar12\n7dqgRcC8vLyg2rwtLS1UVlZSVPQoP//5z/nBD1Jox8A6IvZRUXegbnBrHYCpU6cGPRztWB+MTrMJ\np4eCNSo+M7MCmERDw2A8nvatBbW0GIuOp5wiSEhoPVco2bS2R7W5O/uzvSjFEk10rXXfvLy8INm0\nRq8bawwNNDc3U1q6k40bf8yCBW1LanaGcMqzq1CyqQLZlGwqxWl/zljvF2s/Wd1WI8lmYmIiI0b8\nkooKiI8f2eXXFG7G8CFwABgCPAyoFehjGGU/Y47yEx8yJHZtsI+Ool2MVYSaAdhHME7TSmXfdVo0\nU2sNpaWl1NXVmQEzvQG7KSCaqbz67JlnnmHGjBlMnTqVsWPHtjlWKNQ5QrlaWs/bGvH6KvC/7TIl\nKWpqjMVmS+xSj+O0qBpNX1mxzwadfiunUTkY/RtONgG2bTOSFWZkZLSJo4kFTvdZKE8ohZNsulyu\nqGVT7RNp7QaCZ1sZGZ8BF3TYay4c4dYY/BiZxJxXTHsYexg6QG1t97oDRmOL9Hg8bcxR0QqDXQDV\ncZ0E0D6ttG5TKbI3b95stlFVmSovLw8ZMGNPAxxNm6Htb9HeWVcoU0A0nHfeeWY8gH2Nw0nJ2j06\nrM4CaiTrCyxk2j1nTj89jd274dAhSXOzwIlQSs4a3NYdRCObdjOZ1UwZyYTq9FALJZ9qm/1cbrcb\nt9ttxt9YY0mmT5/OmDFj+NWvfgUYv4W99rXKU3TeeedFXXfA+nzoiHzar689MzerbAJtTFxOJlfA\njFOw3hNKtpVsgmFqUrKZlZVFdvYpHDwIn312JOrri5ZoIp+/ieFsfBaQBMQD1VLKAV3emjBY/bDB\n6LzuvvnCjRIi7RPJntsRAYzUHvVZXl6e6WuuAmYWLVrERx99ZOY3Atrk1LFmrgx3fPtv0Vuw9o1V\naWzZsqWNH7/9e+q7W7ZsMUe0H3zwAWecAYcPC77+OvQ5nZTc73//GhBb2Qy1XzQm1I4o72jaZDXn\nqYyvhYWFvPzyy6xZs4aJEyeaxWtUXILf7486m6/1+dBb5dPari1btpjxNk5rJU6KXsnmww+7efdd\naGzsnMu7E9EsPj+OkUDvFWA88H3gzC5vSQfoCsUQyoe5vaPgjtCV3hGhRq6KAwcOmErgiSeeYPr0\n6SEzlVpnJ/a2xQqnEax9im/9LdUiY0JCgplTSPn5R8IaeZyRAYcPQ4iA85Ao2eyMKelElE2ntOJW\nJVBdXR0km9ZCTFYzbW+XTbXdLptAWNmMFI1ul00wZNOhWGWniLYewxdCiHgpZTOwTAixGQidvawH\naGyMp74+mYQE6EzKl1iOKrryJnca4VlHHva8/arObEpKCjfffHNQFLP1mHa62l86WuzXB21/u2gX\nSJ0ix0MxbBhs3Qr337+U7duXkZiYyD333BPxBlYptzszaDkRZRPaevBZk9VdddVVQbL59ttvmyZQ\na3/0dtlU2xXW2YBTtLiVaK9DDTpWrfoUKaOXzWiIRjHUCCGSgC1CiN8CB2ldiI4ZtbWtC89+f/f4\nJTvRlSOpnsSet7+mpiaQ3hhWr17d6cI7PUm0NQXaQ6hFx5SU8UAqPl+NOdI966yz2L59e9jzqhlD\nXNwRios/N4+rZbMt9poPqgYywIIFC7j44otj3ML2YZfPzhJqttzcfCYwnKNHE6iqil42oyEaxfB9\njPTcdwM/A04FIq9UdjPWPDTtEfzO3jy9/SYLhT2Jm7WWs1OK8u6ks7+BPU/+K6+8EtU5rWkfgDae\nHx5PcKCc1+vljTfUEVqH/gcPHox4XqUYcnIGRz3yP1llU5lHVK4tq4nzxRdf7HFPpa6Wz7PPjuyC\na0+Zo2ZJY8eOZcKECY6z5e3bje82NZ1iHica2YyGaAr1+AIv64AlnTpbF9LR9YW+evN0NU5V6XqK\nztqprfZnVWe6K85pzdCp0nEr+br66tns3fszampqzPz84ejIGoOWTQNrwZuuTg0eDZ2VzwEDDL8c\nJZ/WmhqhCJcyR2EtkHXPPfcwdKjRNwkJmWaJ2mhkMxrCBbhtDfM9KaWMWDFGCDEJI0I6HnhWSvmg\n7fPBwHIgI9CWh6WU+VG0u9s9kk407At0O3bsMGcQ0fprO7nbWaNIu9N0YT2m1WuoKx8c1gydqr6w\nkq+qqmSzglY0+fm1fEbGyTwCwZXNrNHrkeTTeoxYyefatWt5//33ueyyy0z5jEYxRIOSTzCUxMsv\nv0JCAlRVCX7+83tYubKgy+pshJsxdMq+IISIx/Bo+g6wD/iXEKJQSrndstvdwCYp5X8GlMROIcRy\nKWVTpOPrG6992Bejrammw9WtsKJupli7AdrrFdgVVkcfANaKcqoojBrxf/01jBoVXZ0EKbV8RoP9\nt3FyJban9YhErGUTnGu9dIWHmdWB5OmnnyYuzlhjPXAAWlpOibqGRzSEC3DzqddCCA8wRkr5rhCi\nP8YMIBIXAyXqOEKIl4EbAKtiaM2EBwOAslBKwXrz+3w+amqyAUhMLAcGOn1FEyVWE0pXLeb2JF2l\nsKzVzZRdWz3YQ8UxQLAZIT8/n6FDT6ep6VskJjaQmtqvU23S9H35hK5RWFbzr+qDoUMNxVBTk0p6\netvCYR0lmgC3ucCPgEHA6RiLz08CV4X7HjACsGZ3+gq4xLbPM8A/hBD7MXIwhXSNsd78eXl51Nae\nD8AZZ2ilAK0Pp4qKClJSUswEgsr2GM5/32pC6YqFq+4gmjiGzuI00otGMVjNCH6/n8svnwNASkoN\noBUDBC/+K5lUMmrdx4neLp+hYogiRZe3F6cqgEo+1Qy1q4jGK+kujNH/egAp5S4hRDQT5GhqNtwP\nbJZSeoUQpwOrhRDnSynbqL4lS5ZQXFxMeXk5y5Yto7racGHbseN9iotbTvqFO6frz8vL49577yUv\nL8982FnttQqrCaUrFq66A+v1hYpj6A7UjXfokGEiElE4al922Y3A61RVlfDyy7vJyMjQ8ukQy2Ct\nBAfGg9QphX1vl0+7bHZl2v9IKFOnUgzFxcVdEvAXF8U+9VLKevVGCJFAdA/9fYA17d9IjFmDlUuB\nvwFIKXcDpYSIql6yZAkTJ05k6dKl1NfX09JihIE///xDIdP/alpRD1EV/GV9qL700kvk5OR0S4H4\nvk7//pCaCg0NUF+fFNV3qquNB1lLywHuu+8+LZ9R4vV6HYMTtXyGxj5j8Hq9LFmyxPzrKNHMGNYK\nIf4L6C+EuBpYABRF+A7AJ0B2YH1iP3ALMMO2zw6MxekPhBDDMJTCHqeDWRO3GamXjR557bWnomjK\nyUMoH+xQ03RwNqFoWhk6FKqrjZsvOdkcIwX1dXD/GrIZH3+UdevW9VxDezmhZDMSWj5DoxSDirTv\nKqKZMfwCOAxsBeYBbwERnccDi8h3A28D24C/Sim3CyHmCSHmBXb7NTBeCLEFeBf4DynlUafjqRGu\n1+vlzjt/hLr5LrhgRBSXcPLg8RjFfVQVL5/PR1JSknkTrl+/Poat65uEsuOqvvZ6vUHmj/nzHwBg\n3rwbHSvDnayo/vJ4PLjdbnw+H+np6WbAYUFBQdgBjKYtMVljCJiNPpdSjgXabdyTUq4EVtq2/dHy\n+ggdcItNSRkKuHC5IKVr++OEwSlgJi8vL8hNVRMd7b35GhqMkW12dnp3NalPE2o9LFIOIU1b7GsM\nXUXYGUNg1L9TCBHzYY/VXVV1woABx/UIQ9PttHe6vmFDKQBlZdu0fGq6lVh6JQ0C/i2E+BioCWyT\nUsrru7QlEbC6qy5fXgLAyJHJelGvnSif8LfeeouJEycyduzYbnOvO1Gwj8ry8/PNfnIa/R4+bPz3\nenPQ3dk+ZsyYYdYN+dnPfhbzlNq9HbtiUHFenb2Po1EMix22ReOV1G2ozKo6qrT9WH3Cq6urzeI8\nvbH+dW8hPr4MOMW8+SJV26uuNsp6avlsP9a6IcXFxSxYsACIXUrt3o5VMUhpDO6s8tlRwuVKEtKg\nONI+HT57O1DZBpcuXUpNzWgA+vc/hhEXpwmF3ROkrq4OMMoQXnvttTFsWe8jVGqNwYON7JjW6bqq\npqXy8VjpiiI9JwNOXkpKPlXaB41BuIyvAwZ4qKqK5/jxZFOpdjbGJ9yMoVgI8XfgDSnlLusHQogz\ngWnAdcC3O9WCKFH5fCorK82U26NGaaUQCfvI4cILL2TGjBn8z//8D0eOHIlqqt5X8/y3F6fUGj6f\nj08/3QcMobn5lKDt1utXgVrNzYK6uv6A5JRTYl62pFdjlx+fz8fixYv5xS9+wV133dWmFrITJ5Ns\nquh6az1on89HWtpQqqr6U1OTgst1vEvOF04xXAPMBJ4QQpwDHMMo0JMKfA68iBGD0OOoEVmgdLGm\nHaiC5VOmTAnaHm6qfqLdZO3B4/Hw3e/Cz38OQmQEbXdCmTn7968lPl67zLUHJWcbN240TUjRfudk\nRF17Vhbs22c4RwweXNYlxw6XRK8eeA54LpApVVWcPhIo8Rkzamtbi/RoTh7CjQ67k+PHvwROY//+\nRnNbqDxNatBi5EnSiuFkIpQpsrvPaQxAhtC/vwf40tzeLWsMVgKK4FCHz9LF6BnDyYnTdLonGDfu\nNOLioKoqkebmOOLjW0LacJVspqZWY636pjnxcTJFQvcunHs8HnJy4J//hLPPnsjhw+8HtaWjRBP5\n3KsoLCxk717Djpac3HVpZjWaUMTHw+DAfFnNVp0oLCzkrbc+ASA5uaonmqbRRJUBuL30OcVQVlZG\nQ4MRUfrII7+IcWs0JwvRBLmVlZVRVmaUKjl0KFwBRI2m67BmAO4qoqnHkCOl3Gbb5g3nxtqdJCQk\noqbozzzz61g04YThZPHoiEQ0/ZCRAZ9/bhRECWVVNWpRG7J5zjnaztlZtHwaROoH5RZ96JAhp11B\nNGsMrwgh/gz8FnABDwLfAMJXru4mpk69jaVLk0hMrCczU2db7Awn2w0Wimj6Qd18KnhNFZlxu91m\n1s/c3Fz++MczqKiA9PSGbmvvyYKWT4NI/aCUwbZtZZxv1C9j6dKlncpGG41iuARDGXyE4ar6EkYd\nhZjQ0mL4kqek1ALR5cfvKfQI58SlVTEYpqTKykoAFi5cCMCWLVtwuVwMGXIOFRXKK6n3oGXzxEXJ\nZmNja5xNZWUlCxcu5Pbbb+/QMaNRDE1AHcZsIRnYI6Vs6dDZOoHKodLU9A3gp6Sk1LJ06fMkJycz\nbty4NplEY4G+yU5cWvMlpTp+XlhYSFlZGQcP3ggYCR6XLl3aa+RTy+aJi9WU1FVEoxg+BgqB8Rix\nDH8UQuRKKW/uumZEpjWHynkAjBs3whytaTTdjZquh1p8LisrC8in4RixaNHtjBrVQ43TnNQMGABJ\nSVBTAw0NifTr1xj5SxGIxivpTinlYillo5TyQCCrajQV3LqF9PRsAJqbD5iZBDWa7iZc3nufzxdY\neAa1+Lxjx/taNjU9ghBtTZ2dJZoZwyEhxGm2bT2e6rCgoIDLLruMwYOv5v334dxzh+P1Du/pZmh6\nET1pN7cvPlvxeDzk5uZSUPAPdu50kZjYwLXX9kgKMU0vpafXdDIy4MsvDfkcNKgi8hciEI1ieIvW\nNNvJwChgJ3B2p8/eDlTd11WrjKm6TodxchHrxdNwigHA5XJxzTWz2LlTLTz36/Y2aXoHsZZNiLwG\n1l4iKgYp5TnW90KIC4G7uuTsHUCnw+gYvUF4O0Os2zlkCAghqa118dxzL9CvXxy5ubnk5+ebboFK\naRjpMAbGrK19kb4sn72hjUoxfPjhbtavX0ZiYiJDOvGQjCpXkhUp5adCiEs6fMZOohPodYzeILx9\nma++8pGY6Kahwc2XX9YAhygqKmL+/Pl4PB62bNliUwya9qDls+P4fD6OHxdAFvv3N9PcbNRkePPN\nNzt8zGgin39ueRsHXAjs6/AZO4GRJykXUHmSdD0GTc8RF3cYcAMZJCdXMnXqVDZv3ozP56OwsJDS\n0mZgOsnJlTFuqeZkY+BAI6CyudlI6pWcnMxVV13FW2+91aHjReOVlIYR2JaKYTj9O3BDh87WSYw8\nScYU/ZFH/iMWTdCcpHg8HlJSjJlAYuJI5s2bh8vlYtq0aXi9XsrKyigvNzyT9u37JJZN1ZxkeDwe\nvvWt7MC7YSQnJzNv3jyOHet4ktFo1hiWdPjoXUhxcTEJCUmAYUy7446puni9pkeZOPFsXn0Vrrlm\nNgMHbgdabeOGu6oR7HDhhZlaNjU9ilpjcLlG8dOf3oPL5erU8ULOGIQQRWH+Cjt11g7g9Xq59trZ\nQAJxceU888zjncoFotG0l9NOMzyN1KwVjNGa1+slNzeX1FRj1PbppytZsGBBm1rQGk13oRRDcnJW\np5UChJ8xPBLmMxnms24hPz+fxkbDftbSso+VK1eSm5vLe++919NN0ZykJCYeBQYFBREVFBRQXV2N\ny+ViwIBsqqvh8OHPWLnyY2bOnNmpBUCNJlrq640qg04BmB0hnGIolVL6u+QsXcCcOXN4993lgXcH\nGD9+PCtWrIhpmzQnF2edNQgIjmWoqKjA4/Gwe/duy/aDjB8/nhdffDEGrdScjJx77mn06wcNDUld\nkhYj3OJzgXohhIj5E3jGjBmsWrUFgAEDanjggQdMjxCNpidwSovh9/vxeDy88UYhVVXGFD47O50H\nHnhAm5I0PUZXp8WINo5hdKfP1EkOHDhAWZmRlSwxsYwpU+6IcYs0JxutifSCo0s9Hg+HDzdhOO1V\nkJjYzJQpU3q8fZqTm4wM2Lu3a9JitDvArT0IISYBS4F44Fkp5YMO+3iB/wUSgSNSSq/Tsfr37w8Y\nuZHOP19Ht2l6FsP7aB9wGVVVA8w024mJidxzzz3ExWUCkJBwhKlTp8a2sZqTCuUZl5R0NjCENWt2\n0dLyV0tix/YTTjGcJ4RQjrAuy2sAKaUcEO7AQoh44HHgOxgBcf8SQhRKKbdb9nEDTwDflVJ+JYQY\nHOp4CxYsYN26fhw7BgMH1mt3QE2P4vF4yMryEB/fxPHjLg4frmXvXmMJ7sYbb+TSS2/jyy9h+PC4\nLvEK0WiiRUWNjxsH69ZBRUUq5eWdWx4OucYgpYyXUqYF/hIsr9MiKYUAFwMlUkqflLIReJm2gXG3\nASuklF8Fznkk1MGOHDmC2z0WgHXr/qbdATU9jt/vY8CAKgAOHTJcVzMyMrjyyiuprzfGNNXVu1i2\nbBmTJ0/W8qnpMXw+H1VVnwNQVWUkGs3oRAHoaCKfO8oIYK/l/VeBbVaygUFCiDVCiE+EELNDHczv\n93PsmJEC49ChTaxcuZK5c+d2dZs1mpAcPHiQ9HQj3UVDg5GgLD09nZaWFiorjbFSc7MPv9+v5VPT\no3g8Hk4/3Sh13NxsmNzT09M7fLzuVAzRxDokYuRemgx8F1gshMh22vEf/1hDRcX/AksAP+PHj+fp\np5/uqrZqNBGZMGGCOWOAkWRmZjJt2jQAKiuNm7BfP6O+opZPTU8zcWI2UAysIjU1lcGDQ1rmI9Kd\nimEfMNLyfiTGrMHKXuAdKWWdlLIMeB843+lg48dPBf6b/v3vJSdnDKtXr9aRz5oeRykGIbIoKyvj\nb3/7G3V1dVRVGTOGb397FDk5OVo+NT3OyJEAXiCPhoYGNm3a1OFjdadi+ATIFkJ4hBD9gFswakdb\neQO4XAgRL4ToD1wCbHM6WGWlcZO53ZVMnz5d33SamJCebigGKTOpr69nz549FBUVmTOGIUPqtHxq\nYkJmJhiGmuE0NDRTW1vb4WN1m2KQUjYBdwNvYzzs/yql3C6EmCeEmBfYZwewCvgM2AA8I6UMoRiM\nG0/ZeDWaWGA1JYGxwDd16lRzxjBggJZPTWzo10/VAokHhnebu2qnkVKuBFbatv3R9v5h4OFIx6qo\n0IpBE3vUg79fvzGMGnUm06ZNIy4unePHXSQkNNK/f12MW6g5mRkwoIrq6jRcrrHMnZvBovo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"text": [
"<matplotlib.figure.Figure at 0x1165fed90>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Refined period: 86691.1630407 seconds\n",
"Refined period resolution: 1282.18830406 seconds\n",
"\n",
"Evaluating distribution of light curve residuals:\n",
"Departure from Gaussian core: number of sigma, Z1 = 1.22421453942\n",
"Departure from Gaussian tail: number of sigma, Z2 = 0.695089047762\n",
"Plot histogram of residuals:\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: -160.814336\n",
" Iterations: 15\n",
" Function evaluations: 42\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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5n/rbRsU6hwLT0vSewO15y7Y7pjT/KDC6xf9DeWJ6HbA7cBZwciNly4ir5H21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\nTgxmZlbFicHMzKr8f9PfJdeAllM0AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x117a57610>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting phased light curve residuals:\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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V1fH5z3+eYDDIVVddRXl5ecTzKMwYDsDWrVvJyspi3759gDO7r6ioiJtuukmP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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x117a73790>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solid line is residual median: -0.00531364390857\n",
"Rank-based standard deviation, sigmaG = 0.0598060584015\n"
]
}
],
"prompt_number": 42
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Plot phased light curve with outliers.\")\n",
"tfmask_inliers = df_crts['is_inlier'].values\n",
"tfmask_outliers = np.logical_not(tfmask_inliers)\n",
"ax = plot_phased_light_curve(phases=phases,\n",
" fits_phased=fits_phased,\n",
" times_phased=df_crts.loc[tfmask_inliers, 'phase_dec'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'flux_rel'].values,\n",
" fluxes_err=df_crts.loc[tfmask_inliers, 'flux_rel_err'].values,\n",
" n_terms=best_n_terms, flux_unit='relative', return_ax=True)\n",
"ax.errorbar(np.append(df_crts.loc[tfmask_outliers, 'phase_dec'].values,\n",
" np.add(df_crts.loc[tfmask_outliers, 'phase_dec'].values, 1.0)),\n",
" np.append(df_crts.loc[tfmask_outliers, 'flux_rel'].values,\n",
" df_crts.loc[tfmask_outliers, 'flux_rel'].values),\n",
" np.append(df_crts.loc[tfmask_outliers, 'flux_rel_err'].values,\n",
" df_crts.loc[tfmask_outliers, 'flux_rel_err'].values),\n",
" fmt='or', ecolor='gray', linewidth=1)\n",
"plt.show(ax)\n",
"print(\"Plot unphased light curve with outliers.\")\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
"ax.errorbar(df_crts.loc[tfmask_inliers, 'unixtime_TCB'],\n",
" df_crts.loc[tfmask_inliers, 'flux_rel'],\n",
" df_crts.loc[tfmask_inliers, 'flux_rel_err'],\n",
" fmt='.k', ecolor='gray', linewidth=1)\n",
"ax.errorbar(df_crts.loc[tfmask_outliers, 'unixtime_TCB'],\n",
" df_crts.loc[tfmask_outliers, 'flux_rel'],\n",
" df_crts.loc[tfmask_outliers, 'flux_rel_err'],\n",
" fmt='or', ecolor='gray', linewidth=1)\n",
"ax.set_title(\"Light curve\")\n",
"ax.set_xlabel(\"Unixtime (TCB)\")\n",
"ax.set_ylabel(\"Flux (relative)\")\n",
"plt.show(ax)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot phased light curve with outliers.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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nHqy8tMZynJoKp88ff/wRqNEmwKJFiwCj52a5hoPPFaqMBvcMnDi12lzUNcZw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\nMQyCIAiCi/8P3HHt6ey6GIsAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x11654f890>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plot unphased light curve with outliers.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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tC/e7oHM8B2wDPmrgmBnA/+KbezEgzDEmGjZv3myGDRtmMjMzzUknnWSGDRtm\n8vPzTd++fc3OnTud4zwej+nUqZPxeDxRnT/U9ZYvX26WL19uysrKzPLly027du0MvhxXpn379sYY\nYy688EJn26hRo4wxxpSVlZmysjKzc+dOU1RUFCCfPW92drbzu+7du5vNmzdHLFtZWZnzuUuXLs55\nevToYcrKypzv9i8vL88sXLjQnHvuuQYwgwYNCpDJytsc+vbtawCTnp4ecO2srCzTsWNHU1RUZP74\nxz+as88+2+Tn55tzzz3XrF27NuS5LrvsspByRoI9/2WXXWYuvvhi5zwej8cUFRU524L/Ro0a1eB1\n7f1pyn06/vjjDWC6dOlievTo4VyzY8eOzj168cUXTVlZmRk6dKjJysoyQ4YMCVn25j4nd33Nyclx\nPmdmZgbUyauvvjqi80Ujj/va7vPfcMMNzjNzHwOYzp07m5NOOskAprCwMGydcf+uqKgoYpmMMea9\n994zFRUVprCwMOS9SUtLcz536NDB9O7d2/leXFwc8O7a+5GVleX8NpzMTcXfdjbaVjf015AlETo+\nMToqgJkcTRYYgIgMB/qao0ukPkkM5mUUFBRw4MAB9u/fz2effcaOHTucafsnnXQSL7zwAqeffjoP\nPPAA3bp146abbmqWmRcqIiMtLc2ZKNOjRw+GDx8eEDcdHMIXyhy357UWD8C3335LiKy8AYTrvVmX\nSVZWFhdddBEVFRWkpaUFuMB27NjB9OnTmTt3LsOHD49LBlLbg6+urg6wYuxg3yeffMJdd93F1q1b\nqaurw+v1ct9999XrYXk8Hm6++Wa8Xi8//elPnUR4kfYI3eNDffr0cXqGXbp0obS0lM8++4yMjAwO\nHz5Mdna201MUkXpjEu41rgEnp0+0a1zn5+ezZcsWdu3a5dQXwKlL+/bt489//jNnnXUWdXV17Nu3\nj3fffTcuPVBrjefl5dG7d28++OADZ/zIcuqpp8bUigl2I2ZnZwe4Ed297lGjRgX8dvfu3ezevZu0\ntDTmzp0b1oW0adMmwDcOeMkll0QlX/AE10GDBpGRkcG7775LYWEh+/btc9LfHDx40HEn20l3NTU1\nVFZWBgRcGL934ciRI4wYMSIgfU6rIBJNAhQAF/s/ZwGdItVC/t+GtCSA3wE/dH1fD/QMcVxU2nPz\n5s1OLywjI8OceeaZAT0O2zMJ11tpKu5ezttvv23at29vBg4c6FxjyJAhpqioyEyZMsUsX77cbN68\n2emZu39Sbmx0AAAgAElEQVQb3Cv0eDwB8h9//PERy+Tuvbktp/POOy/gnMG9+quvvtr5rdtSiqR3\nHwp7jhEjRpicnJwASyvUX/fu3Z3PXbt2bdBKaIp1c8MNNxgRCXk9W/ZevXoFWF6AGTBggCNLuGuW\nlZU1uW65LRR7jgEDBpjc3NwAWfPz80379u0NYLKzs0Naw821JMaMGWPS0tJMRkaGufDCC02XLl0c\ni6Zr164mMzPTXHzxxRFbcNHIc+yxxzrlvfzyy53t7vszZsyYgGfo/hzqHbF18PTTTw+wJKKxzC1u\ny9/92VrJwX9nnnlmwPvirh8dOnRwrMTmejWCIQaWRLvGlIiIjAVeAp7ybzoemB/+F1HRG3CrzS3+\n8zcL66sG3yzempoapxc9YMAAp+cT68VqbC/n9ddfZ8aMGdx9992OD3vQoEG89tprlJaW1gsjBBxf\n9Ouvv15vvkR+fr4ja1ZWFu+8806T5HPPwLZ+28zMTDp37kxaWppznPseQf1wXK/Xy8qVK7n55psj\nHsAs8M+YXb16NXv37g1IRxDMWWedxYABAwBfr72p8esNsWHDBqcH16VLF+d67rpgx4EATj75ZIqK\nirj33ntZs2ZNo+Vuat2aPXs2RUVFLF26lPz8fDIzM+nevTtnnnkm4Ls3dmDd+uRra2uZOHFixNeI\nlCVLlnDkyBHq6uocn7sdKN69ezf79+93QrLD4fGn03AvrlVZWdno/XNbmMYY5zwfffQRIsKGDRv4\n4IMPnGfYrl075x0H6N69O+vWrQs4p62Dduxi0KBBlJSUNClYxVr+a9asYc2aNc7n7OzskBFMa9eu\n5b777nO+u9OcPPHEE3Tq1Ilnn32WzZs3Rx0UEG8iiW4aB5wLrAAwxmwQkWNjKEOw78SEOqisrMz5\nXFxc3GjonU2ml5eXx/HHH+80iieccIJj+sc6jNHdMNholEOHDpGZmVnv/O6ohvT0dKeihmtUbrjh\nBp577rmAPEyREmpOQdeuXdm6davjOrAvf05ODm+++WbAjGJ3amr3YGFWVlbUL5i74Q1FWloaM2fO\n5PTTT+eYY47hyJEjzmS54ARqzcE+q44dO/Laa69x3333kZmZyb59+xwlXFRUxLvvvkt6ejo5OTlc\neOGFja5ZYQdFu3fvTmFhIVOnTmXNmjURu8DcbseXXnrJaYhtmOXy5cs56aST6v2uMRdkNNj6Yl2c\nFtsgw9GB/MaUYKiorUhcuwMHDmTZsmWcddZZTiRdQUEBe/bswRjjZDgGX/hrcPDF2rVrueOOO1i0\naFG9c7vf+1iv9ldTU+O8S26CO17BK1Zu2bIloqCLxnAr5JjRmKkBrPT//9D/vz0RDlybyNxN17i+\nx8TdZMxRc3DKlCmOiZqenl7PPG6uSR7qmjt37qw3qAaYE0880RlAX7hwYYAbzLqiggeu582bZyoq\nKhyXSkVFhZk3b17EJrK7fG6ZMjMznUE3O/CWkZFhJk6caJYvXx7gjnK7S+zAoNvtEg1DhgwJuCdu\nF4H7ejfccEPAtuHDhzdYxmifo7t+GGMCXEs5OTkmIyPDdOvWzXGv4HJNBAcpWNdh8HkKCwujvj9u\nt6N7EDQvL88pY15eXsAgaahn0ZD7MlLcA/e2jtjn1a1bt6jcTdG634IDOex9t25RETF33HGHKSoq\nChistp8bCmRYtGiRKSsrM4899pjz/7HHHjOLFi2K6v7Y5+G+19YF6P7Lysoyb7/9dsBvg59PLNsh\nN8TA3RRJI/8IcBfwKXAJMA+4P+ILNKwkhgOL/Z8HAyvCHBfVjXnvvffMhRde6DTIAwYMCGiM3A1O\nrB+OPZ9VTJ07dzaA6d+/f4AvtGvXruaYY45xGmePx9OgLE2NKnL/xu3PdUfOuMcHsrOzw0Y33XDD\nDaZPnz5hfeCNsXnzZrNw4UJTWFho+vbtawoLC82pp55qRMSRIS8vz9x7773m5JNPDnjRLrnkkpDn\ntC9bcORaY3IEj6+4I1RCjZdkZWU5CtQ9nhRM165dm6Uk3I2pVQIdOnRwIpqMMaZnz54BjXeocjd3\nvM39rAoLC82LL75oioqKzMSJE01RUVGAso/k/E2JQgt1f+07g3+soqyszEyZMsUUFRWZU045xXTo\n0KHRKCF3A207CZESqpMQPOYZ6q9Xr14B5XZ3Jmw54kEslESjYxLAFGA7vtDXG4HFwN0R/A4ReRFf\nyvFCEakWketF5EYRudHf8i8GPhORjfjGPG6O5LyNYeOpvV4vGzdupLq62jGVu3btyq233sqsWbMo\nLi6moqKC/v3788QTT7BixYpYXB446ltet24dRUVF/OEPf3Bmh4IvDcfBgwcBnEWBQmF9sZZIfboN\nybR06dKQk37A599+4YUX6NevnxPtY9mwYQPV1dXU1tYyePDgkNlSG6KgoICRI0cyevRofvKTnzB6\n9Gg+//xzjDHOGMWOHTt46623OPHEE53f9e/fP2Rkk3sxno0bN3LFFVdEdF+sb9rOJl65cqXjfurV\nq5czE97twtm3bx9Lly51XJ3hXEcDBw4EfO6FpqTLcEfeXHbZZbRr147zzz/fSdcCOK4/gOOOO86Z\n6Ogue3PH2+yzys7O5sCBA0yePJk9e/awaNEiSkpKHHdupOd3zyuIBlvfZ82aRWVlZcDiQp9//jkA\nS5cupba2lo0bN3Lw4EGOHDnCoEGD6o1JWNxjhwsXLgx5TDhs3bHu7uLiYqdMHTp0cI4TkQC38Nat\nWwMWoXK7XW3b1FppUEmISHvgE2PM08aYH/j/fm8iLJUxZrQxJs8Y08EY08cY85wx5iljzFOuY8Yb\nY/oaY840xvyjmeVxGg/ra09PT3caYzsIes455ziTwbxeLx999BGVlZXNzuE+duxYKioqnPVzS0tL\nyc/Pp7S0lP79+zuD6eBTVueeey5wdCY41FcCtlJaGmukGsLt7+7bty/gCzF0h1r26tXLGWDet28f\ny5Ytcxpfd3qQrVu3NjhgGYpghQfUW8a0rq6OZcuWkZ2dTWFhIYWFhVRVVYVdsMWuh5GRkcGNN94Y\nMr1FONwzrqdPn05RURHXXnstTz31FJ06dQp4XieccAIlJSUsXry4wYHYl156iaKiIt58882I00PA\n0Xtjy7l7927efvttvv32W6qqqrjiiiuc67lfP2NMyDrh7hA0Z7zNKtItW7ZQXV3Nxo0befzxx3ny\nySejOr/X63XqUzT1xpbN5q1y18EvvviCiooKPvnkE7xeb8B9OXToUNjACnuOY445hj179jB8+PCo\nOzxu5s+fT1FREWeccYazrVevXrRr147s7GzAp0z/9Kc/OfttZ6Jv377OZNvmdADjSYMD18aYwyLy\nqYjkG9/6Eq0ed66YvLw89u/fz6FDh2jXrp3zwtmY8lhFN9mGyWZ19Xq9fO973+MHP/iBEy//6quv\nBqwU98QTT1BUVOTMKh45ciSrV68OUAju2PuMjAzq6upC5slvjOAY/lmzZnHNNddQW1tLu3btnORj\n7du3Jz09nddee43jjjuOf/7znwEroc2ePZvjjz+e2traJt0z+2zc+aOOO+44Nm/e7KQEAZy5CgcO\nHAhQYG7sPbc5lerq6rj55psbXDUuGPeM69zcXCcFx+DBg5k0aRIDBw7ktttuA2DChAls377dqTO2\nHMEBFE1NP2HvTZ8+ffj4448pLCwkJyeH1atXU1hYyKRJk5z6kZ2d7fSo3VFp7vsCOBE37vNHi73/\n2dnZzkB2bW0tpaWlUZ0/0nct3BwfyznnnMOyZcs47bTTEJGAxHn2HbH06NEjQCZ7bju3xtb9UKlw\nGsOd4O+ee+6htLSUvn37Mn78ePbt2+fMj+jSpUvIwJWXXnopYOA6+N1vTUQS3dQN+KeIrARsuIMx\nxnw/fmI1n9zcXGfiT1ZWFj169MDr9VJYWMjdd/u8ZbGKbrIviLsn06VLF8AX7WAjq0aNGsX+/fsp\nKSlxIhnci+4E405FAE3PxRO8Wp5dmW7Pnj0sXrwY8FkzaWlpVFdXU11dzahRo+r1FG+//Xa6desG\nwMsvvxyTiLDS0lIWLlzoTGrLyMjgySefZNq0afUWaHIT3KiCz4UXatJdMLaxsKvi2YbOfW7AUdzg\ni3TyeDzOYkW25xmrBIjBDdi4ceMA2L9/P+PGjXPW4aisrHQUQ1ZWFpdeemk9GYIndjZVFjiqSCdO\nnMhNN93kuAX/8Y9/cP7550dc7kjftXDRUFVVVVRWVjJx4kS+/PJLbrnlFh577DHA19Ho3Lkzxhg2\nbNgA+FyUFRUVYc9dW1vrKL1oOjz23rjTp9jkkC+++CL79+93PBcdO3akc+fOVFdXOxa5TVRpc39d\ncMEFzhLBSbcynYt7QmxrtU40dwXv0qULu3fvZt++fXTs2NEJabSzHiE2vS2LO2zvtddeY/r06eTl\n5bF27VoGDRrErFmzog65C7YmIqlIoSwH+xsI7J1NmDCBBx54gJKSEl555RXA536599576yUls2MS\nQMySDFZVVTkWjc3f5PV62blzJ+BTXsX+9YNDJRNsrnUDvpXw3GGL9n65e7ShGlu7MJEb+xu3Owoa\nr1vu/atXr+bmm33DczZPkRv37Ou//vWvTJs2LeD6oXri0dTtYEVTWlrK2LFjefDBB9m8eTPgC4V+\n7rnnAq7dEJFaWKEa4SuuuCJgHGD16tXceOON/PCHP2TIkCFMmzaNv//97yxdupTq6mpEhP/8z/9k\n/fr1IVems+cGnPkJkXZ47L1xv9c2B9vXX3/tWDLt2rXjxhtvdEJw+/fvH/A+uVdotCnOk25lOhER\n/wB5ZWPHxEWyJuKu4DYBmjt5XLBCiOXKdLaX86tf/cq5TnOtlWBrIprf2N5YUVFRyNXUqqqq+PGP\nf8zGjRuB+u6XefPmBZTRpkoQEdatW8cTTzxBu3btHOXTUEPk8a92FrygkDtteFFREZmZmUyZMoUb\nb7zRWaDJNpihyM3NZfz48SxcuDDiexzs9rIr4U2aNIkdO3bQvXt3LrnkkgALw+3GaqgRtsdEmko7\nEoIX3gmeExC8Ml1zLQn3tSyVlZXOYDX4rJjrr7++SeeOBPe7a11tENrNY11ihw8fdsYiV65c6bgK\nLaEa+IsuuqhJkzVDvdfWyu7YsSM33ngjXbt2dd4pO65m72twynObcTnZssBWishrwF+MMRvcO0Sk\nELgcGAFcEEf5oiaUqTxu3Dhn+U+I3doIoc63evVqRo4cicfjoaqqKmA2Zjg5oXnr7YajodXUbO/M\nnUPKul/CLUlp/f/GGD799FNmzZrFiBEjHCURKTYfknvQOj093cm3Ze9BQ644CO82akxZ2ftuZ57b\n67nXTjhw4EBARJEl0ka4uemfQy1+ZGfynnzyyaxbt44TTjiBa6+9NqrzNhW7LrjlxBNPpGvXrjFf\nb8SeJ3j9idWrVwdEs3m9Xn79618zdOhQ57fW1ZSRkcGVV14ZNrNrLCbThVq+1E6gtB3StLQ0p27O\nmTOHXr16OWtcu8vnzkDcGrPANqQkhgI/Bn4rIqcDe/DNjs4BPgb+BFwcdwmjJJSpfPPNNzsprltq\ncChUj9IqDjjaM7Wro9n1cWOpvOxgYf/+/RkzZgy/+tWvgMDemV3dzE2wArPlcfv/BwwYwJIlS5g+\nfXpE9zT4ZbUv1vHHH8+WLVucZIwLFy5k8ODB9Xrxoc4RbBE0RQ5bdk/Q+hKh1t+29ySSZxSP9M+9\nevVyytucBXwaI1TARMeOHQMSVD744IOsXr26UeXQVPdXOPeU28K44447nAHfqqoqx51cV1fHq6++\nGvaeN3dti2Dcz9pawwB33323U7/suEMoGWKdHijWhFUSxpg6fKm+nxORNOAY/66vjW8ZUyUM9kXI\nz88PayHYdaKDV/568MEHYyaH7TFZU/e73/0uQ4YM4aGHHnLmArgtCauwFixY4FRu90tt8/oDvPnm\nm816ydwvlg0TTEtLY+PGjVx77bXOwjrgu3ctYYL/7Gc/4w9/+APZ2dnMmTOHxYsXM3z4cDIzM6Pu\nXET74gc3psFKGo4uvAPhx9JiMSYRKmDiF7/4BR6Ph4ULFwZE4zV2zli5vyz33HMPU6ZMCajDFncq\nnpZsbN3P+qKLLor697FODxRrIl3j+gi+dSGSklmzZtGlSxd27drV5BXVosFaDW5C5VOpqamp13uN\npbspuMdkv9uXq2fPns6xPXv2DFBYdrlMWxZbntGjRwM4+YiaS2FhIZdeeilLly51JkMdPHiQhx9+\nmHHjxpGfn9/oddzWWCSunWCXk+Waa66hrq6O5cuXO+MkR44cYfLkyY02tvac1iUzcuRIvF4vt956\na0S5m4IbUzuIWV5eXm9MoiFi3Si7sa4T8NVndyco1i5cN6HGIdwKwk6C3bVrF5mZmXTs2JHZs2dz\n9tlnhxy4tsTCxVtZWelEpF155ZVOZBPAtGnT6Nq1Kzt37mx0TCuWlk2siUhJJBOhfM62Aj///PMt\nFkEQ6mX1eDx4vV569uzJtm3bqKmp4aabbuLZZ5+lT58+zJkzh3Xr1sV98Mo9W9Tj8fD888/Tr18/\npydmw4TtwHVwWdznaAz383C/jDNmzGD06NG8+OKLzJs3j9LSUh5++GEOHjxIRkYGr776Kn/7298i\nel5u5RaJayfSBq2wsJBx48Y5x0byu9zcXEexlZaWMmTIkIiu5b5PPXv2dCy8nj171huTaA005fk3\nRakEj0PYcFO3+/bAgQPk5+dTW1vruC1t4+0m1DtZVVXVLOVm5SgtLeX88893gh/S09MpKyujd+/e\nzjvj8Xha1TOMlJRTEm5tXVBQ4PQIg0355lTccDQ0WOm+XkFBAdu2bXNetD179jBv3ryAQWUbTx0v\nQvWmH3jgAaZMmRI2uilUD6gx3PfUPc/DvlifffaZc+z48eN58skn+e///m9nXkAk8rutMTsHpjnM\nnz+/UZ9/8LMOVXeiaYDcvw/XAEdiSYSTL9pOh9sy6tKlS4A1bvdHUrbmvlPFxcVONJJ7LM1d/woK\nCqipqXFCgxsLm4417ufmjtb7y1/+wty5c8NadO7t7gmmrY1GlYSIFBljPgnaVtxQaGyiCdXzhdgq\nBDf2hQqO7XY39MGVJLgBCY67jrfpGa78q1evdnzdwffL9ryAZldue+3LL7+ctWvXAvDQQw+RlZXl\nhC7a7Q393uPxOFFsDz30EN98802T3QfuhjXc2tqWRKxLHI0rqbnyua/lVk7uXrE9Lt4Ep9W24bDg\nq6NWlilTpvDAAw8wbty4enNL3NjjY+0y87iCHwoKChgzZkzEnanWTCSWxFwR+QPwMJAJPAScQwyW\nGY0X4XzOTc15FCnBsd0NyQWBvfHWNHgVaoJYKNnjdS9DDfwHv8Buefr160dmZiY5OTnNetHdDWtj\nQQSJiEgJV39CldmdKPCRRx5pEfniRahopHAKcuPGjWHn1YRqF+y9i7TOhPNC2H22w3LnnXfy9ddf\nc/jw4RYbu4kXkSiJ8/Aphvfwhb/OBv4jnkI1l5Z+EPZ67tjnmpoap0KFqiTBpmasw/KiobHGJ5Rl\nVuxaNKkpLo3g3pzX63Wu29RQ1uZOHLOTBbOysrjkkksatEgSodSjsSTsWtm7d+9u9uz4goICtm7d\nGhAWa+9ZrFNINNQIR/IbaDxkujmEOocdG4GjHZbevXuHPTZUJ6g1E4mSOAzsx2dFdAQ+M8aEX3uy\nDeNu6O0M2NZAY2MwjTU+wb+3Dfr8+fPZvn07Xq836pXjgt1wtpFvivuquf53i50saNOC33rrrWGP\nTYRSj2YsLdpU3o1hw2LLy8v55S9/2ezzhSNcQ95QvYhGecaDcHU53LHRli/RRKIkVgILgEH45ko8\nJSJXGWOujqtkSsxobg/K7Zt2n8emFoDYLp8ZLbHyv9vJgjbevaF7FivF1BQ5IyGWlk40yimeROKG\nTCZay31tjEiUxM+NMR/4P38FfF9ExsRRpjaF2+3i/t/aKkooeQYPHsyyZcsYMGBAvYybkRLJxMPG\niNX4QDTpGsIppmjGDeJJLC2d1lIXI436aql73hTXmJvWcl8bIxIlsU1ETgja1nptoyTDbaomwlRu\nDjYnfkOzr4Nf4Pnz5zu5oUIFFTQlbj1WveZoGtZwism++ImwNNoqiXI3JaPrqClEoiQWczQ1eEfg\nRHzrXZ8WL6GU5CCSRjW40bQZad2/WbFihdMLizQdOgQqoFikfI8mNLIxxZSIENlURRVuYmlUSRhj\nTnd/F5GzgXFxk0hJSRpqNJuSDh1i34MMHoBsiMYUZGtP2pYM2E5AQ/OP3MdB6/btJytRz7g2xvxD\nRM6LhzDJSqSVtKF5EqlOW2s0EzXvpbWMicQCK3NjE01bQ9lSWVFFMuPaPSusHXA28EXcJEpCIq0I\n4Xq+qebDDEVrmiwYjli6NRI17yVR/vl4kgx1JxWUQTgisSQ6cXRM4jDwGvBK3CRSWjUej8dZgMZm\nPI0ks24iJws2RqRuDSUxtOa60xaIZEyirAXkaBOkgrvJNpruWabJ3pBG6taA1u/OSSW3R2u/122F\nhta4XtjA74wx5vtxkCelaa3uplRqWJqCLb9dF2Dq1Klh14Bo7e6cVHpmrf1etxUasiQebWCfaWCf\nkmQka8MSK+XmPt6uUa4oio+GlMRmY4y3xSRRkgbbqEazAFE8Yt2TVbkpSjLRkJKYDwwAEJFXjDFX\ntYxISirSViaXtXXXnZJ6RDpP4qS4SqGkPKkyTyKajLqxZMWKFU6q7q1bt9KrVy+g8VnpitJcUm75\n0mQg2PUSa1pTbzaaQeFkIFFyu2elu5eBTWXcihGIOF2LElsaUhL9RWSP/3Om6zP4ops6x1GulCbY\n9XLaabFNgxXPhiw4LBGOrlIX6po6KKw0lbaoGFsjYZWEMSatJQVpS1jXS2FhIWPGjOHrr79ucprs\nliY4LBEiG7hWFCU5UXdTAnAv7G6XOYWji7pbRdGalQXAzJkz2bt3L48//jirVq0KSP2dTLQm95wS\nP3Rcp2m0OSXhbhDcvfaWbBBa6zKn0bJ3717q6uqoq6vju9/9LtXV1SGPc9/zWbNmJeSeN0RrkUMJ\nTazCp9V91TTanJJwNwiJqCitvcGMhrQ0n0cyKyuLd955J+xx7nkVdj1sRYmUthI+3Vppc0oi0aRK\ngzl27Fi6du1KXV0d7733XlhXU7QD3YoSTKqETycrqiQSgDWf09PTmThxYlJlt7R+3bfeeosvvvBl\njP/5z3/OjBkzQvp1rSIIVhT2uyoKpTFilSpcEwY2DVUSCcCaz0DSmc/Wrzt37lw+/fRT8vLyWLJk\nScRrXFv0xVQiJVapwjVhYNNQJZEArPmcl5eXtOaz7d2VlJREtMY1aMhsU3Er2rKyMjweD4sXL+b3\nv/89/fv3T6xwSsqjSqKFcc8+LikpYc2aNUDy9axt764xdEyi+bjv1apVq6itrXVmr8+bNy+xwrUA\n8UgOqUROm1MSrcEvmZOTE1EDmwoUFBSwdevWgPQK9hlofHpkuOvskSNHnO21tbUJkqhl0eimxNLm\nlIT6JVseO45RXl4OkLQRXYnCPfh/3HHHsXnzZvr27cuECRNa/Qz9WBDr6KZ+/frh8XiSfhJoS9Hm\nlESiLQl3CCyof16JDFtvSktLWbhwIe+++26bcbvEKrrJsnXr1ogmgSo+2pySUEui+TRV0S5YsIAd\nO3aobzlK3Pc7MzOT0tLSpM6kGy2xim6ypKenA41PAlV8tEu0AIli7NixVFRUMHz4cGpqalr8+gsW\nLEjo9ZvLb37zGyoqKnjllVfYu3dvo8ePHTuWf/7zn3i9Xl5//XXGjh3bAlIqSn1WrVpFp06d+OST\nT9TVFAFtzpKwvbKVK1c6g2FXXHEFFRUVLdor27FjR9IOxhUUFLB3715nrscLL7zQqPwbNmygrq4O\ngPbt2/PII4/EXc5Uoa2GEcfaNew+36RJk9i8eTObN29uMxZZU2lzSsJWiLy8PNauXcugQYOYN29e\ni7s+rMmbrKkGoh1MtMcDHD58mMmTJyeVYlRanli7hu35NKQ2Otqsu2n27NkUFRXFbDAsGsaOHUtd\nXR3Z2dm8/PLLSVlJo71/s2fPJjs7G0hexaikBjakVt2ekRFXJSEil4rIehH5XxGZEmJ/sYjsEpEP\n/X93x1MeN7EeDIuGDRs2UF1dTW1tLZMnT27x68eCaO9fbm4u48ePT5hiVhSLJgyMjri5m0QkDXgc\nuBj4AvhARBYYY/4VdGiVMeb78ZKjNZIKaTmixZ3UUIkej8fD+PHj+fjjj0lPT2fgwIHk5OSoP70J\nxDqkNtWJpyVxLrDRGOMxxhwC5gCjQhwncZQhLImMbrJ+0LS0NH70ox8lVXSTx+OhsrKSE044gV//\n+tfk5uYyZ86ckEn83FgTf+PGjWriN4GCggJWr17t3MNnnnmG4uJiVRBNIJFehGQkngPXvQH3LJUt\nwHlBxxjgP0RkLT5r4zZjzCdxlMkhkVP9b7/9dnbv3k1NTQ3V1dX89Kc/TZocPLbnunv3bmdC0uTJ\nkxudkOQeuH7zzTfxer0afhglNjoM4L333qOmpialGzpdVrZ1EE8lYSI45h9AH2PMPhG5DJgPfCfU\ngWVlZc7n4uLiZkc6bNq0CYDOnTu3eDjmhg0b+Pbbb53vBw8ebNHrx4JoJyTNnj2bbt26YYxhx44d\nOtM1SjweDyeddBKrV68G4N///ndCQrdbklgrA/ca1+BbGRJSa43ryspKR5nGDGNMXP6AwcBfXd/v\nAKY08pvNQLcQ202sGTJkiMGnyMzVV18d8/M3xGWXXeZcGzCjRo1q0evHAo/HYzp16mQ8Hk/Ev8nK\nyjKAycrKiup3io8xY8aYdu3aGcAMGDDA7Ny5M9EiJS1lZWWJFqFF8LedzWrL4zkmsQo4RUQKRKQD\n8ENggfsAEekpIuL/fC4gxphv4iiTQ+fOnYGWjXCw/vybb77Zcb/07duXe++9t0WuH0vy8/OZNGlS\nVP2Dg9QAAAxuSURBVC6jG264QWe6NoMlS5Y4Fuhxxx2X0q6meJLobAvJRtzcTcaYwyIyHngDSAOe\nNcb8S0Ru9O9/CvgBcJOIHAb2AdfES55gEhHh4Dafb7nlljaTqM36lrt27aozXZuBe0xCo8SajqYe\nj464zrg2xrwOvB607SnX598Cv42nDMG4B8NsojRo+cEwm6itrSiIYFRBRM/AgQNZtmwZvXr1cvzp\nSvToPInoaLNpORI1NT/RqcpbGvdaCG7s91Qsc7x46aWXIloyVmkYnScRHW1OSVgSZXK2xfUk2mKZ\n40GkS8YqoWktXoRko80qCTU5m0Zbs4SU1EHXkmkabVZJqMnZNPRFU5S2RZtVEjo1X0kWPB4Pa9as\nCQjXnDVrFrm5uZx11llqwSlxpc0qCaVlCE6t4PV6qaysVPdUFLjvVXl5OQDXXXdd4gRS2hRtTkkk\n0qfeFnuEwfe1vLxcXVRREiqMWBWt0lK0OSWRSJ+6OxzULv3ZFl5yd86cjIyMlMyZE080jFhJJG1O\nSbSm6Jy2kppi8ODBqgyaiYYRK4mizSmJREfnuF929SsrkaDuptigqcebRptTEkrzUNdRYrGD/0r0\nqDJoGqoklKhQ11HLo4P/SiKJZ6pwRVEUJclpc5aE+iUVRVEip80pCVUGiqIokaPuJkVJEt5atIi7\nhw1jc0UFdw8bxluLFiVaJKUN0OYsCUVJRt5atIg3Jk7k/k2bfBu8Xu7yf75gxIgESqakOmpJKEoS\nsGTGjKMKws/9mzaxdObMBEmktBXUkmhBWtNsbyW5aO9a39pN2oEDLSyJ0tZQJdGCJHq2t5K8HM7I\nCLn9SMeOLSyJ0tZQd5OiJAFDJ0zgrpNPDth258knc8kttyRIIqWtoJaEoiQBdnD6npkzqV6/nj79\n+nHpLbfooLUSd1RJKEqScMGIEVwwYgTl5eVMnTo10eIobQRVEi2IzvZWFCXZUCXRgqgyUBQl2dCB\na0VRFCUsqiQURVGUsKiSUBRFUcKiSkJRFEUJiyoJRVEUJSyqJBRFUZSwqJJQFEVRwqJKQlEURQmL\nGGMSLUOjiIhJBjkVJV64Z+t7PB5nUqZO0FQaQkQwxkizzpEMja8qCUVRlOiJhZJQd5OiKIoSFlUS\niqIoSlhUSSiKoihhUSWhKIqihEWVhKIoihIWVRKKoihKWFRJKIqiKGFRJaEoiqKERZWEoiiKEhZV\nEoqiKEpYVEkoiqIoYYmrkhCRS0VkvYj8r4hMCXPMDP/+tSIyIJ7yKIqiKNERNyUhImnA48ClQBEw\nWkRODTpmONDXGHMKMBZ4Ml7ytGYqKysTLULcSOWygZYv2Un18sWCeFoS5wIbjTEeY8whYA4wKuiY\n7wPPAxhj3gdyRaRnHGVqlaRyRU3lsoGWL9lJ9fLFgngqid5Atev7Fv+2xo45Po4yKYqiKFEQTyUR\n6QIQwbnOdeEIRVGUVkLcFh0SkcFAmTHmUv/3O4BvjTEPuY75HVBpjJnj/74euNAYsy3oXKo4FEVR\nmkBzFx1qHytBQrAKOEVECoAvgR8Co4OOWQCMB+b4lUpNsIKA5hdSURRFaRpxUxLGmMMiMh54A0gD\nnjXG/EtEbvTvf8oYs1hEhovIRqAW+Gm85FEURVGiJynWuFYURVESQ0JnXIvIcyKyTUQ+CrO/n4i8\nJyIHRGRS0L5GJ+olkmaWzSMi60TkQxFZ2TISR0cE5fuxf4LkOhF5V0T6u/a16mcHzS5fKjy/Uf7y\nfSgiq0Xk/7r2pcLza6h8rfr5NVY213HniMhhEbnKtS36Z2eMSdgf8D1gAPBRmP09gEHAfcAk1/Y0\nYCNQAKQDa4BTE1mWWJXNv28z0C3RZWhm+c4Huvg/XwqsSJZn15zypdDzy3Z9PgPfnKdUen4hy5cM\nz6+xsrme05vAa8BVzXl2CbUkjDFvAzsb2L/dGLMKOBS0K5KJegmlGWWztOrB+gjK954xZpf/6/sc\nnf/S6p8dNKt8lmR/frWurznA1/7PqfL8wpXP0mqfX2Nl83ML8DKw3bWtSc8uWRP8RTJRL5kxwDIR\nWSUiNyRamBjwM2Cx/3MqPjt3+SBFnp+IXC4i/wJeByb4N6fM8wtTPkjy5ycivfE1/jbNkR14btKz\ni2cIbDxJ9dH2IcaYr0SkB7BURNb7ew9Jh4j8H+B6YIh/U0o9uxDlgxR5fsaY+cB8Efke8AcR6Zdo\nmWJJcPmAQv+uZH9+04BfGmOMiAhHraImvXvJakl8AfRxfe+DTyumBMaYr/z/twPz8JmJSYd/MPf3\nwPeNMdY8TplnF6Z8KfP8LP4Gsj3QDd+zSonnZ7HlE5Hu/u/J/vwG4pt7thm4CnhCRL5PE9+9ZFES\nwf5BZ6KeiHTAN1FvQcuLFRMCyiYiWSLSyf85GxgKNBjF0BoRkROAV4GfGGM2unalxLMLV74Uen4n\n+3uhiMjZAMaYHaTO8wtZvlR4fsaYk4wxJxpjTsQ3LnGTMWYBTXx2CXU3iciLwIXAMSJSDUzFN+qO\nMeYpEekFfAB0Br4VkYlAkTFmr4SYqJeQQoShqWUDjgVe9dff9sCfjDFLElCEBmmsfMB/A12BJ/1l\nOWSMOdeEmWSZiDI0RFPLB/QiNZ7fVcAYETkE7AWu8e9LlecXsnwkwfOLoGwhaeqz08l0iqIoSliS\nxd2kKIqiJABVEoqiKEpYVEkoiqIoYVEloSiKooRFlYSiKEorJNJEfv5j80Xkb/6khcv9s65jgioJ\nRVGU1kkFvuSRkfAbYJYx5kzgXuDXsRJClYSSNPgnAX0UtK1MglKth/jdQBGZ3sgxo0TkVNf3chG5\nqHkSh73WMhE5wZ+K+kMR+UpEtvg//0NE0kXkNhH5l01XLSL/6f9tpT/V84ci8ok7t5C/J9kpHjIr\nLU+oRH7+SYCv+/NKvSUiNpXIqfiyvgJUEsOki6oklGSn0Yk+xpjVxpiJjRx2Bb7JjPY3U40xf2uu\ncMGIb92CT40xnxtjBhhjBgC/A/7H//1sfAkDLwLO8e+/iMD8Oz/ybx8CPCQidlLsHCDpEtIpUfE0\ncIsxZhAwGXjCv30tvgmC4KvLnUSkaywuqEpCSQUMOL3sB0XkfRH5VES+699eLCIL/Z+nicg9/s/D\nRKRKRM4HSoBH/D35k0RklvgXaxHfIjQP+Hvvq0TkbBFZIiIbxb8cr/+4yf5e/1oRKQsj64+Av4TY\n7k7Pcge+VAp7AYwxe4wxL4Q4tjO+2cJH/N8XcHTmsJJiiEgOvnVMXhKRD/F1Lnr5d98GXCgi/wAu\nwJen6UjIE0VJsmaBVZRQGCDNGHOeiFyGL13BJUHH3AF8ICLvANOBy4wxm0VkAbDQGPMqgIgYjlop\nBvAaYwaIyP8As/C9rJnAx8BTIjIU6GuMOVdE2gF/EZHvhcgeOgS4PVwBRKQz0MkY4wl3CPAnEakD\nTgEmGn/aBGPMNhE5RkSyg9ZLUFKDdkCN34oMwJ+U0HZqcvAtNLQ7VhdVlGQhnGvJvf1V//9/4FuB\nK/BAY/bjc8ksBWYaYza7dje00IxNhPYR8J4xptYY8zVQJyJd8CWCG+rv4a3Gl3a6b4jz5Bljvmng\nOo1h3U1nAicAk8WXbNCyjcBMn0qK4G/0N4vIDwDER3//5+7+zgn4OkLPxuq6qiSUZGIHvqR6broT\nuKpYnf//EcJbyv3xrdgVHCbY0PiGPe+3wEHX9m9d1/m1HWcwxnzHGFPRwPlC4m8I9orIiREc+zU+\nZXiea7OQYmt2tFX8ifz+DhSKSLWI/BT4MfAzEVmDz4r9vv/w/wOsF5FP8S2NfH+s5FAloSQNfh/9\nV+Jb6AcR6QYMA96J9Bwikg/8F741gi8TEbtWwB58Pv5GTxFKNHyZNa8XX3ppRKS3+BatCeZL8a9b\n0AC/Bn4rR1NW59joJrcMIpLlL4c7FXtPknx9B8WHMWa0MSbPGNPBGNPHGFPhX3r0MmPMWcaY04wx\n9/mPfdnfMSk0xoz1L08aE1RJKMnGGOAev1vnb0BZkMvIjQnx+RlgkjFmK74oomfEl1t/Dj7XzWoR\nOamB67vHKpzzGmOWArOB90RkHTAX39rJwbwDDGpIVmPMk8ByfGMnHwFvETgI+Sd/+VcBFcaYDwHE\nl35+h45HKLFEU4UrSgsiIsXAD40xN8Xh3GOBbGPMY7E+t9J2UUtCUVoQY0wlvtXB4jHp7Yf4llNV\nlJihloSiKIoSFrUkFEVRlLCoklAURVHCokpCURRFCYsqCUVRFCUsqiQURVGUsKiSUBRFUcLy/wF4\ngvWryD6BGgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x116316810>"
]
}
],
"prompt_number": 53
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Classify the light curve as an eclipse if deepest and 2nd deepest minima occur at\\n\" +\n",
" \"phase=0 and phase=0.5, respectively, with tolerance of maximum 0.001 phase (0.1%) or\\n\" +\n",
" \"presison of fit light curve.\")\n",
"lombscargle_minima = \\\n",
" np.asarray(\n",
" zip(\n",
" np.append(phases, phases),\n",
" np.append(fits_phased, fits_phased)),\n",
" dtype=[('phase_dec', float), ('flux_rel', float)])\n",
"idxs_min = sci_sig.argrelmin(lombscargle_minima['flux_rel'])\n",
"df_lombscargle = pd.DataFrame(np.sort(np.unique(lombscargle_minima[idxs_min]),\n",
" order=['flux_rel', 'phase_dec'])[:2])\n",
"df_lombscargle['phase_dec'] = np.mod(df_lombscargle['phase_dec'], 1.0)\n",
"df_lombscargle['event'] = ['primary_minimum', 'secondary_minimum']\n",
"tol_phase = max(0.001, 1.0/len(phases))\n",
"if (np.isclose(\n",
" df_lombscargle.loc[df_lombscargle['event'] == 'primary_minimum', 'phase_dec'],\n",
" 0.0, atol=tol_phase) and\n",
" np.isclose(\n",
" df_lombscargle.loc[df_lombscargle['event'] == 'secondary_minimum', 'phase_dec'],\n",
" 0.5, atol=tol_phase)):\n",
" print((\"INFO: Light curve may be an eclipse.\\n\" +\n",
" \" Deepest minima do occur at phases 0.0 and 0.5\\n\" +\n",
" \" within phase tolerance {tol}\").format(tol=tol_phase))\n",
"else:\n",
" print((\"INFO: Light curve does NOT appear to be an eclipse.\\n\" +\n",
" \" Deepest minima do not occur at phases 0.0 and 0.5\\n\" +\n",
" \" within phase tolerance {tol}\\n\" +\n",
" \" Method for determining minima may not apply to stars with\\n\" +\n",
" \" intrinsic variablity that exceeds the flux varability due to an eclipse.\").format(tol=tol_phase))\n",
"print(\"INFO: From Lomb-Scargle fit:\")\n",
"df_lombscargle"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Classify the light curve as an eclipse if deepest and 2nd deepest minima occur at\n",
"phase=0 and phase=0.5, respectively, with tolerance of maximum 0.001 phase (0.1%) or\n",
"presison of fit light curve.\n",
"INFO: Light curve may be an eclipse.\n",
" Deepest minima do occur at phases 0.0 and 0.5\n",
" within phase tolerance 0.001\n",
"INFO: From Lomb-Scargle fit:\n"
]
},
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>phase_dec</th>\n",
" <th>flux_rel</th>\n",
" <th>event</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 0.0</td>\n",
" <td> 0.520348</td>\n",
" <td> primary_minimum</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 0.5</td>\n",
" <td> 0.878776</td>\n",
" <td> secondary_minimum</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 61,
"text": [
" phase_dec flux_rel event\n",
"0 0.0 0.520348 primary_minimum\n",
"1 0.5 0.878776 secondary_minimum"
]
}
],
"prompt_number": 61
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"Save results"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"path_phot = os.path.join(path_project,\n",
" r'Work_Logs/20150216_light_curve_solution/phot_crts.csv')\n",
"df_crts.to_csv(path_phot)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 55
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# CHECKPOINT: Load saved data from previous calculations of phased light curve.\n",
"df_crts = pd.DataFrame.from_csv(path=path_phot)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 56
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**NOTE:** \n",
"* Results _above_ this point were computed without human intervention and can be included as part of a automated pipeline.\n",
"* Results _below_ this point were computed with human intervention and are not yet suitable as part of an automated pipeline."
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Determine relative fluxes of eclipe events for inliers"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_phased_histogram(hist_phases, hist_fluxes, hist_fluxes_err, times_phased, fluxes, fluxes_err,\n",
" flux_unit='relative', return_ax=False):\n",
" \"\"\"Plot a Bayesian blocks histogram for a phased light curve. Convenience function for\n",
" methods from [1]_.\n",
"\n",
" Parameters\n",
" ----------\n",
" hist_phases : numpy.ndarray\n",
" 1D array of the phased times of the right edge of each histogram bin.\n",
" Unit is decimal orbital phase.\n",
" hist_fluxes : numpy.ndarray\n",
" 1D array of the median fluxes corresponding to the histogram bins\n",
" with right edges of `hist_phases`. Unit is integrated flux,\n",
" e.g. relative flux or magnitudes.\n",
" hist_fluxes_err : np.ndarray\n",
" 1D array of the rank-based standard deviation of the binned fluxes\n",
" (sigmaG from section 4.7.4 of [1]_). Unit is same as `hist_fluxes`.\n",
" times_phased : ndarray\n",
" The phases of the time coordinates for the observed data.\n",
" Unit is same as `hist_phases`.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes corresponding to `times_phased`.\n",
" Unit is same as `hist_fluxes`.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `hist_fluxes_err`.\n",
" flux_unit : {'relative'}, string, optional\n",
" String describing flux units for labeling the plot.\n",
" Example: flux_unit='relative' will label the y-axis with \"Flux (relative)\".\n",
" return_ax : {False, True}, bool\n",
" If `False` (default), show the periodogram plot. Return `None`.\n",
" If `True`, return a `matplotlib.axes` instance for additional modification.\n",
"\n",
" Returns\n",
" -------\n",
" ax : matplotlib.axes\n",
" Returned only if `return_ax` is `True`. Otherwise returns `None`.\n",
" \n",
" See Also\n",
" --------\n",
" plot_phased_light_curve, calc_phased_histogram\n",
" \n",
" Notes\n",
" -----\n",
" - The phased light curve is plotted through two complete cycles to illustrate the primary minimum.\n",
"\n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
" ax.errorbar(x=np.append(times_phased, np.add(times_phased, 1.0)), y=np.append(fluxes, fluxes),\n",
" yerr=np.append(fluxes_err, fluxes_err), fmt='.k', ecolor='gray')\n",
" plt_hist_phases = np.append(hist_phases, np.add(hist_phases, 1.0))\n",
" plt_hist_fluxes = np.append(hist_fluxes, hist_fluxes)\n",
" plt_hist_fluxes_upr = np.add(plt_hist_fluxes,\n",
" np.append(hist_fluxes_err, hist_fluxes_err))\n",
" plt_hist_fluxes_lwr = np.subtract(plt_hist_fluxes,\n",
" np.append(hist_fluxes_err, hist_fluxes_err))\n",
" ax.step(x=plt_hist_phases, y=plt_hist_fluxes, color='blue', linewidth=2)\n",
" ax.step(x=plt_hist_phases, y=plt_hist_fluxes_upr, color='blue', linewidth=3, linestyle=':')\n",
" ax.step(x=plt_hist_phases, y=plt_hist_fluxes_lwr, color='blue', linewidth=3, linestyle=':')\n",
" ax.set_title(\"Phased light curve\\n\" +\n",
" \"with Bayesian block histogram\")\n",
" ax.set_xlabel(\"Orbital phase (decimal)\")\n",
" ax.set_ylabel(\"Flux ({unit})\".format(unit=flux_unit))\n",
" if return_ax:\n",
" return_obj = ax\n",
" else:\n",
" plt.show()\n",
" return_obj = None\n",
" return return_obj\n",
"\n",
"\n",
"# TODO: Create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 57
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def calc_phased_histogram(times_phased, fluxes, fluxes_err, flux_unit='relative', show_plot=True):\n",
" \"\"\"Calcluate a Bayesian blocks histogram for a phased light curve. Convenience function for\n",
" methods from [1]_.\n",
"\n",
" Parameters\n",
" ----------\n",
" times_phased : numpy.ndarray\n",
" 1D array of the phases of the time coordinates for the observed data.\n",
" Unit is decimal orbital phase.\n",
" fluxes : numpy.ndarray\n",
" 1D array of fluxes corresponding to `times_phased`.\n",
" Unit is integrated flux, e.g. relative flux or magnitudes.\n",
" fluxes_err : numpy.ndarray\n",
" 1D array of errors for fluxes. Unit is same as `fluxes`.\n",
" Errors are used only for determining bin widths, not for determining flux\n",
" flux_unit : {'relative'}, string, optional\n",
" String describing flux units for labeling the plot.\n",
" Example: flux_unit='relative' will label the y-axis with \"Flux (relative)\".\n",
" show_plot : {True, False}, bool, optional\n",
" If `True`, display plot of phased light curve with histogram.\n",
"\n",
" Returns\n",
" -------\n",
" hist_phases : numpy.ndarray\n",
" 1D array of the phased times of the right edge of each Bayesian block bin.\n",
" Unit is same as `times_phased`.\n",
" hist_fluxes : numpy.ndarray\n",
" 1D array of the median fluxes corresponding to the Bayesian block bins\n",
" with right edges of `hist_phases`. Unit is same as `fluxes`.\n",
" hist_fluxes_err : np.ndarray\n",
" 1D array of the rank-based standard deviation of the binned fluxes\n",
" (sigmaG from section 4.7.4 of [1]_). Unit is same as `fluxes`.\n",
" \n",
" See Also\n",
" --------\n",
" plot_phased_histogram\n",
" \n",
" Notes\n",
" -----\n",
" - Phased times for each bin are defined by the right edge since `matplotlib.pyplot.step`\n",
" constructs plots expecting coordinates for the right edges of bins.\n",
" - Because Bayesian blocks have variable bin width, the histogram is computed from\n",
" three complete cycles to prevent the edges of the data domain from affecting the\n",
" computed bin widths.\n",
" - Binned fluxes are combined using the median rather than a weighted average.\n",
" Errors in binned flux are the rank-based standard deviation of the binned fluxes\n",
" (sigmaG from section 4.7.4 of [1]_).\n",
"\n",
" References\n",
" ----------\n",
" .. [1] Ivezic et al, 2014, Statistics, Data Mining, and Machine Learning in Astronomy\n",
" \n",
" \"\"\"\n",
" # Append the data to itself (tesselate) 2 times for total of 3 cycles to compute\n",
" # histogram without edge effects.\n",
" tess_phases = times_phased\n",
" tess_fluxes = fluxes\n",
" tess_fluxes_err = fluxes_err\n",
" for begin_phase in xrange(0, 2):\n",
" tess_phases = np.append(tess_phases, np.add(times_phased, begin_phase + 1.0))\n",
" tess_fluxes = np.append(tess_fluxes, fluxes)\n",
" tess_fluxes_err = np.append(tess_fluxes_err, fluxes_err)\n",
" # Compute edges of Bayesian blocks histogram.\n",
" # Note: number of edges = number of bins + 1\n",
" tess_bin_edges = \\\n",
" astroML_dens.bayesian_blocks(t=tess_phases, x=tess_fluxes,\n",
" sigma=tess_fluxes_err, fitness='measures')\n",
" # Determine the median flux and sigmaG within each Bayesian block bin.\n",
" tess_bin_fluxes = []\n",
" tess_bin_fluxes_err = []\n",
" for idx_start in xrange(len(tess_bin_edges) - 1):\n",
" bin_phase_start = tess_bin_edges[idx_start]\n",
" bin_phase_end = tess_bin_edges[idx_start + 1]\n",
" tfmask_bin = np.logical_and(bin_phase_start <= tess_phases,\n",
" tess_phases <= bin_phase_end)\n",
" if tfmask_bin.any():\n",
" (bin_flux, bin_flux_err) = astroML_stats.median_sigmaG(tess_fluxes[tfmask_bin])\n",
" else:\n",
" (bin_flux, bin_flux_err) = (np.nan, np.nan)\n",
" tess_bin_fluxes.append(bin_flux)\n",
" tess_bin_fluxes_err.append(bin_flux_err)\n",
" tess_bin_fluxes = np.asarray(tess_bin_fluxes)\n",
" tess_bin_fluxes_err = np.asarray(tess_bin_fluxes_err)\n",
" # Fix number of edges = number of bins. Values are for are right edge of each bin.\n",
" tess_bin_edges = tess_bin_edges[1:]\n",
" # Crop 1 complete cycle out of center of of 3-cycle histogram.\n",
" # Plot and return histogram.\n",
" tfmask_hist = np.logical_and(1.0 <= tess_bin_edges, tess_bin_edges <= 2.0)\n",
" hist_phases = np.subtract(tess_bin_edges[tfmask_hist], 1.0)\n",
" hist_fluxes = tess_bin_fluxes[tfmask_hist]\n",
" hist_fluxes_err = tess_bin_fluxes_err[tfmask_hist]\n",
" if show_plot:\n",
" plot_phased_histogram(\n",
" hist_phases=hist_phases, hist_fluxes=hist_fluxes, hist_fluxes_err=hist_fluxes_err,\n",
" times_phased=times_phased, fluxes=fluxes, fluxes_err=fluxes_err,\n",
" flux_unit=flux_unit, return_ax=False)\n",
" return (hist_phases, hist_fluxes, hist_fluxes_err)\n",
" \n",
"\n",
"# TODO: Create test from astroml book."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 58
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Compute Bayesian blocks histogram for phased light curve.\")\n",
"tfmask_inliers = df_crts['is_inlier'].values\n",
"(hist_phases, hist_fluxes, hist_fluxes_err) = \\\n",
" calc_phased_histogram(times_phased=df_crts.loc[tfmask_inliers, 'phase_dec'].values,\n",
" fluxes=df_crts.loc[tfmask_inliers, 'flux_rel'].values,\n",
" fluxes_err=df_crts.loc[tfmask_inliers, 'flux_rel_err'].values,\n",
" flux_unit='relative', show_plot=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Compute Bayesian blocks histogram for phased light curve.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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t8J7TCC/L0vsazPFcu3YtJSUlPPnkk7S2tkZt6NSNeDrkb05j7tFCbhijc3Px\n4sXKg8dZjuSnlD7DGcnDQV8Ryz6bNWsWs2fPZvbs2bZJQeenvqoASExMVPWW8SUScpKBXsO0rJ9U\nH+Xn59v4KY8P18pM9os0EMfHx/PVr35VtUHn50Dq4TxPGvXz8/MVP/VnOGgZsTds2EBJSQn33nsv\nra2tUZen8y9SW4erH0+aFQPYdXyRIjz12dxtZpbH3IxxK1euxOfzcdFFF1FbW8tVV12lpJFwxian\nvlgf7P7qLFcJxxLO/nEj380338zOnTsBmDFjBps3byYvL0/12bJly9Tkef/99zNx4kT27NmjUlrc\nc889KrjvySefdK2HHJNLL720T1+DKZXKlRuY0tr48eNt9XWOs7Odxwr6CiBabkpEy0250mpra+Or\nX/0qtbW1zJ49W63mwhnqw63IAJ5//nlV7wsuuIC33npLHdO5eaz6Mpwk7sQDDzygVu7/+q//yoED\nB/rwE8w2xMTEuPJTHpflOusB5jjIvtbHVhrm9dxJtbW1zJgxw3YfWZ+ReM4j4aRZMUBv1KHzwXNK\n7HI2B/eZWb5YNm3aZJNGARYuXMiCBQuIi4ujsLCQn/zkJ+o6txlc6ouhV2KJps4ScpVwLOHsHzep\nRZc+MzIyVBukZNjZ2cnChQsBqK+vJzc3l2uuuYZbb70VMFdFcql/zTXX2O7tlLLa29v79DWYUqmc\nfOLj42lra2Pbtm221YocDzdXTX2sIknNQwF9BaBDttXJTb3P3biZn5+vrpX8XLBgAQsWLKCxsZGe\nnh4KCwv54Q9/6Hofea/c3NywKzJnvZ3c1rk5XJKrE87+CSdR6yv3WbNmufITzOc5HD/lcVku9I7X\nzTffTGtrK/n5+aqv9bGVrshyohk1ahTTp0/vM7a6G3MkOMd6uHFSrRjCQbcHzJkzhx/96Ed9zpE6\nUd39zU13CO6BRfJ3twdk+fLlSqJ47LHHhqZRuCfUGghCoRAvv/wyBw8epK2tja6uLlJSUvD5fP26\nIbpJrNArtbqVFU6qdNbdKWWFc2Otqqri5ptvpqKigtbWVnbu3MnGjRtZsGBBn3Fw658VK1aoz6++\n+mrEModLl6u3Veem3ldu3KyoqOhjn1q+fHnE1YYbQqGQ8tpxrsjA3keRVgXOFZmbrWagGAw/ZXl6\nfXRpPFyQXzh+Sp7L65zcDBcBLa9LT0+nqamJw4cPs3nz5j7viP5WWs5yofddFG2q+cHghJ4Y9MGM\n1MFSqsxRbBpMAAAgAElEQVTOzuZ73/ue6wtcj9aUAyD1sDExMezYsYMnnniC2267zXatrucNRy7d\nk6a5udnVEykrKyuiztgNuuFN/xytAVX/TXo+SAkJTDVCOOTn53P33Xf3aYf0TnFCL8vpkeHsMz0m\nQo9a/slPfsK+fftUeW1tbVxwwQWceeaZ1NTUKB2vrtKT9w4G+7rANjc3q89SQjzvvPPIy8vjgQce\n4MiRIzz44IO8+eabUTkSONukczPcQyvb6uSmzgU3bgaDQerrzS3ShRA0Nze7ulXqcHs5y3F56623\n6OjoiOjZF+kZc7qySj7qK/LKysoBGfcHw09Z3quvvqo8hd544w0VXeysp1tZOk+kTVDe18lN2Sdu\n/SY99cB8B3zzm98kFAoNaJLcv3+/rdxAIMD+/fv52c9+RmxsLB988MGAuRkNTmhVkr6sjPRSlZGG\nVVVVzJo1y1U94lQtgRnQkpSURE9PD+3t7ezcuTNiRGO0Blc9QnLjxo2qLdHC6ZXkVg8YegOqjtLS\nUtd2DAbOsZMZKp1Ry/v27bOVJ9slz5dRqfr4ygdX+pOHw2uvvUZOTg5vvPEGfr+fI0eO0N7ezsGD\nB/n6178+4DY5uRmOF7LuA+VmRUUFaWlpgJkLSubwdyKcSiocIo1pNBxyvvjD1Wc4uQnw0ksvqXbM\nmTNn0Pfpj5uy7s5+y8/PJzc315ZtVXckkOhvxSDVrTrHm5ubaW9vp6WlZVDcjAYn9IoBIqsoJKSe\ntKGhQQW4RJM35sCBAwQCAZVxMjMzkzvvvDPsC1nPSwPukaEbNmxQXjd+v5+mpiaefPJJLrroIteV\nhBtkG3R3Qb0P9M/OaNj+HsJwxk9n3Wpra109qnQVk+7fHSl3jISzDGeAobO85cuX8+c//1mtInRc\nfvnlbN++nXXr1vGtb32LRx99lO3bt9PS0kJ8fDxnnnkm3/72t1UfT58+nebmZv7pn/6JK6+8ktjY\nWMAco2jiUcKhP+O3no1TVxO53UNHbW2tkkbB5OYjjzzS51x9PHSVis5NXep146bk4k9+8hNee+01\nV37KciQnnS9Ut5X9QLkpr3can92eG7kCDAQCfPnLX1bnS7WcnnMr2vTtejlyp0ZZfzdu+nw+Nm/e\nTHNzM//2b//GtGnTCIVCtvuMHTtW3TscP/XzAcXN+Ph4/vCHP0RV94HihF4xgN1QOpBzo1XbFBQU\nkJ2dTXZ2NvPmzWPixIlhy9Pz0kCvAUonfF1dnS3N8+7du6mpqeGJJ56IWgKXy2ldFaKXoX8uKipS\nkms0D14446db3ZySumyzhLTt9Jc7RsJZhrOfneW1t7cradnZZx0dHdTW1rJt2zY2btxIXV0dR44c\nsa3+9PMPHDhAbW0t27dvZ+PGjdx4442kpqby4YcfHtVSPVrjt/7dzUjsBic3ZcS3DmdOK/13yU1Z\nXjhuyn5yrtjcytE56daGo+GmvN5pfO6Pm3pqe+lGq+fcina1q5fz0EMPqfKd5Ulu5ufnq2u2bNnC\nxo0bCQaDtvvIiSUSP53tk9y8+eabvRWDG5Yssf8vL59KdXU1TU23093djc+3nAkTJpCVVQrAwoUN\npKenI0Tv+QDTplVG/D57tjlrr16dSUnJb7jlloO28o4cWURXVxe//vXpnH/+15g+/ZWw9Tt8OAO4\njaSkJNrbfwJ0kZn5MH6/nz17bgC68Pvvpba2lrvvjiU1NZWbbtqH3+9X9Zk3LwTA6tWZtLa2Mnbs\nQ1x00UXq+NSpFaq8XbtCLFkSnRqgvHwqhmHW19xaMIeYmBiuvPIdS1opJiUllby8AwCsWXMudXVz\nWLXqbgKBAOPGPcwbb7zJJZeY9/vgg0Igl0DgUe68807VD7L/9foXFBRw+PAPgUMEAo+Sl5fHkiVQ\nUTFVjUdV1QzGjp2B3987PnV15wGvEwgEyMhYRXl5HNOmVVqSbzFxcfE0NT1MXV0dUGy1dCmZmZkc\nPHgLv/pVO2PHPkRMTIytfX6/ny9/eQMlJVmq3gOFW3vr6uqIjb2bcePGsWXLTJqbzfZVVFRQVjaZ\nrVunYmVdV+Pp/K73R2bmDJqabmfdunU89thZXHTRRfzzP/ee/+ijj9HYuMLKoWU+D05+FhWFAFT/\nJyXdZ0ncxSQnpxAX9ztKSkr47LObgVxiYu5mx44drFyZbrufXr8NGzawY8dcYmJimD//E8rKyhQf\nzz3XLHegAVpu/CwpKbXGDlJSVpCRMQl4Bb/fz65d81ixooPExJ9x4403snVrPh9+uI0vfhHF59NO\nG0Ne3h5CoRClpUE1Xs76+/3+PvyU9RHCXGGNHfsQVVW941NaGrSuuY2JEyeSmvoL8vO3Ksk/JWUF\nL7+cypYtyzhw4AA6P+X7YNWqWNLT7e3LyHiF22+/nfLyqSxZwqD5GQkn9MSgwxzINI4cOUJ3tym1\ntLXVU11dTVHR91m6dOlRpcSuq6ujsdFUE61b97QyJre2tmoRwJ/S09PD9Onh75OTk8P776fT2NiI\nYXQBkJqaSm1tLd3d5hNjGIYleXXR0FDPww8/TFpaGocPZ5CTk6MepNbWVhobG2hsrOHWW29lz54b\n6OnpYc6c3xAbG8uRIxlMmTKFYNA34PZu376dxkbTjTE/P99KfZHAhAkT8PtfV+V3dnbQ2dnGzp07\nOXy42rbf9Re+8AUMw2Du3LlMnDiRP/3JXoZe/4cffpienv8mPj5BLaENo2+9qqureest+aJLZ968\neWzenENeXh5VVb10fu211zj//N/T0dGh8lXFxyeQkpLC6adnk5+fz+rV7ar8tLQ04uLiaW9vZ+3a\ntSQmJnLGGV8bcL+Fw/z58zlw4By6u7vo7Gxj165d+P0hpUrIzc1lsLtQ9nqsHGTPnj22Y3p+JPk8\nOPkp+ZSTk8Obb75Ja2srhtX5iYmJNDY2WvdvAYSSatvb63nzzTfZs6eE119/na6uHyrpXH9eNm7c\naG0CdA0vv/wymZmP0tLyY1pbp+Dz+Qb1YpP8bGxswO/fT3JyMhMmTLCtDjo6Ouju7qKlpYXHH3+c\nL385X+UqKigo4Le/Hct3v/td/P6f95mcnPX3+Xx0d19j46cT1dXVlnpqOYFAgG9/+w5ycnKorzdt\nDPn5W5k8eTLjx5uxSxkZk3jvvffYt08atnv52dLSwu7d5gqvp+cQSUlJxMXFUVNTw549JVZGh6Hj\npxMnvCoJTL2jHMju7i71e3JyCtnZ2UNShpzlx42z52OX0grA6NGn9VteXFwcaWlp6sFz3iMlJdUW\nVZycnKImjvr6Q1RXVyt9tbwuEAgghKCz03wQPvnkE3bv3k19/SFKSkpYvXq10q1GC+nJlZKSSnJy\nMrt376azs4MdO3a41jszM7NP2+Pi4qyJxN1Wotc/NTWVw4cb6ezsYPPmzYC7bl1OxG1tbTQ01POX\nv/zFNT5g3bp1TJgwQeljA4EAX/nKV5g4cSKzZ8/G7/fbyh81ahRdXZ10dnYoFUp1dXWfSPXBYsuW\nLTZuZmZmcumllw7JvXsl0NQ+cQj6GPX3PMTFxeHz+WzcFEKo+2dkjLYJV8nJKSQmJiqVTHV1ddg6\nmYJPF93dXezdu1dxs6qqik2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