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stharrold/20150305T195000_SDSS_J160036.83+272117.8_CRTS.ipynb

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20150305T195000_SDSS_J160036.83+272117.8_CRTS.ipynb
{
"metadata": {
"name": "",
"signature": "sha256:3be77af942370429d764473802e206fdcc7154e08cfe735bdc95d4d79098db2e"
},
"nbformat": 3,
"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": 39
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Globals"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"warnings.simplefilter('always')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 40
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Custom functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**TODO:** \n",
"- remove period resolution. resolution is only in frequency, and is (max_freq - min_freq) / (data_duration / data_sampling)"
]
},
{
"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": 41
},
{
"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": 42
},
{
"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": 43
},
{
"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": 44
},
{
"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": 45
},
{
"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": 46
},
{
"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": 47
},
{
"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": 48
},
{
"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": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Load original data.\n"
]
}
],
"prompt_number": 49
},
{
"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": 50,
"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": 50
},
{
"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": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Convert time and magnitude units.\n"
]
}
],
"prompt_number": 51
},
{
"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": 52,
"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": 52
},
{
"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": 53,
"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": 53
},
{
"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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3Am+x9u8Bzow5TqGwI/CNb3xjQUYptwaWFvuBv+1tb1M47M9bvHix9vT0FESy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\niPQkHPP5/P97ReSM7GVWxp49exotIRG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"text": [
"<matplotlib.figure.Figure at 0x1185c3550>"
]
},
{
"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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\n",
"text": [
"<matplotlib.figure.Figure at 0x1185bb890>"
]
}
],
"prompt_number": 54
},
{
"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": [
"Estimate significance levels from periodogram.\n",
"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 0x11870fbd0>"
]
},
{
"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": 55
},
{
"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 0x1186b6450>"
]
}
],
"prompt_number": 56
},
{
"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\nxYW8Fkei+Rfbtm2juLg4sOLYvHkzI0eO5IQTTmDZsmUMHz48rbKng3g5vrJpcp3f3JKmnHPSXFLS\np0r615k0jCSpqqpi9uzZgev7vcmpaujIGq97w2txJHqD3LZtG127dg1lcfTo0YOzzjqL119/PZSM\njUW8XE/ZtNaFXyBFOsK5k6W5RM+liikOI2tIZhU/vze5VCJrvIoj0RtkWIvjo48+omfPnpx11lks\nXrw4aRkzyebNm333ZVMCQb9xrFTGt1KluUTPpUpcxSEibUTknMYSxmjdJLOKn9+bXNjIGm80kdda\nSfQGGVEcQdm8eTM9e/bkzDPPzErFUVVVFTc1e6q5sNLJUUcdFbO8T58+jSzJZ0Si58CZcR90PlBz\nI67icGeI/6GRZDFaOWFX8Yv3JhfWz+1VHB9//HGdBZHoDTKMq+rgwYPs3LmT4uJiTj31VN5//332\n7NkTSs5Mc8stt8Tdn+xqiZlg5MiRDcKHc3NzGTFiRBNJ5BBREm3btm3UVPuNSRBX1Qsi8lXJtuW/\njBZHrAdBLAYNGpTwTS5sbiXvgLCq1mXhLSsrY9q0aQAMHjy4Qb9hFMeWLVsoLi6mTZs25OfnM2jQ\nIN58881QcnqJRHdt2rSJM844gzPOOCNQxFm8KLG1a9fG7XPhwoVJy5tuYmVTPnToUFbJ2FIJMpHv\ne8APgcMiEnEoq6omTAgjImOAu4Ac4D5V/U2MOtOBi4E9wFWqusQt/xkwETiCs+rg1aoa3pdhNBsS\npVVv27YtBw4cYP78+QlzQ4WlTZvP3qGKi4v5+OOP61a8u+CCCwCYMmVKg5nrYcY4IuMbESLjHCNH\njgwtbyTaCxwX35IlS+rt94s4SxQllug81q9fH1rWTOG3cuOKFStiljcWEUV84MABSktLKS8vb3FW\nR5A1xzuqahtVzVPVTu4niNLIAWbizDo/GRgfyX3lqTMWOE5Vjwe+C9zjlg8AvgOcoaqn4Cier4c6\nM6PZkWiMI8y4RSq5lbp161ZvnCOSnj1W4sQwiiMyvhEhlciqRIEEfhFniaLEEo1hNGXEUjQffvhh\nqPLGwKvQVbVVTgAE6gbIrxCRW93tfiISJPh8OPCBqq5V1YPAHJy1PLxcCjwIoKqvAoUi0hP4BDgI\ntBeRXJyZ6huCnpTRPEk0xhFxHwV5SAdJv+4llsURIZ7i2L59e+DB8WiLI5UB8mTXLkkUJTZ16lSK\niop822yuUaVCAAAgAElEQVTKiKXmQGuZABhkjOMPwEggkqRmN8EGzPsAXtW/3i1LWEdVtwF3Av8G\nNuKkcn8hQJ9GMybRzPFo4vnqg2bRjeBdw6Fbt26BFUeYMY7IHI4IQ4YMYfXq1YFXNfQSJJAgVsRZ\noiixsrIyxowZ49tmU0YsReNV9kHKG4PWMgEwyK/rbFUdKiJLAFR1m4gEmQUUdIppg0F3ERmIk/Jk\nALATmCsi31DVv0TXraioqPteUlJCSUlJwG6NbKOsrIy//OUvgeZyxPPVqyqTJk3iF7/4ReAUGV7X\nlJ+rKtqK2bt3L6pKhw4dknJVtW3bliFDhrB06VLOO++8QHJGCLJ2SawFjcrLyxOuO1JdXd3guAhN\nHbHkpV+/fqxevbpBef/+/ZtAGodsnQBYU1Pju8plMgRRHAfc8QoA3KSHQRZy2gAc7dk+GseiiFen\nr1tWAsxX1a1un48D5wBxFYfRvKmoqOCxxx5LWG/cuHGsXLmywexw78Nw2LBh9O/fnzVr1gR6qHvr\nRLuqIokMoy2OiLUhIoEtjiFDhtRtV1VVUVtby1VXXcXAgQPTPogaSwFE2r/uuutYt24dxx9/PNOm\nTavX786dO33bzKaIpSuuuILbbrut3rUXESZOnNhkMo0cOZIXX3yx3ktGNoQIR79Ux0vrE4QgimMG\n8ATQQ0R+CXwV+H8BjlsMHO8OdG/EWd9jfFSdfwCTgDkiMgLHJfWRiKwEbhGRAmAf8HngtQB9Gs2Y\nO++8M26epAjz58+Pu3/evHlMnz495tuoH96B927duvHBBx/Ubfu5qryKIwheV1XEYooM5HqtgCDK\nI8jaJX7jPGVlZTz//PMsXbqU/Pz8Bv3FGx/KJpfLggULYi461ZTKrbWECAeJqpoN3AT8CkcBfEFV\n/xrguEM4SuE54F3gMVVdLiLXisi1bp2ngdUi8gFwL/ADt3wp8BCO8lnmNvk/Ic/NaGYk4+uPxa23\n3ho6dYnXxRB0cDwZiyPiqkp1EDXI4HgiN92oUaNYsGBBvbVIEtHULhcvGzbEjpdpypBhG+NwEZFf\nAC8DD6hqqNVxVPUZ4JmosnujtmPO1FLVO4A7wvRntG569epFbW1tXFeLH96Fn2INjhcVFTV4k4wo\nDggW6eUd40j1ARNkcNw7nhKLoqIijjvuOBYtWsS5554LkDBstKldLl6yMcnhJ598Eqq8uRIk/GA1\nTkTVYhF5TUTuFJEvZlguwwhMhw4dKC0tTSlU1BuJEz04vm3bNnr27JmSxXHkyBG2bNlSt1ZEqoOo\nQSLQ+vbtm7Cd0aNH89JLL9VtJ0o5kk0ul2xMcuhHS0u8EcRVNUtVrwZG4wxOXw4Ez31tGAEJ++OK\nhNx27dqVZ599ls6dE85L9cXr1onlqurevXtKimPbtm106tSpbiwl1SyqkWR68XJyBVFC0YpjzZo1\ncetnk8slG5Mc+v0PRrIQtBSCTAC8X0Tm48zqzgW+AvjPEDKMJAkbfx9xHUWsg7BJEr307NmTqqoq\nDh48yJVXXsmmTZuorKwEHMXRo0ePmIqjqKgokMKLDsWNPPjPO+88CgoKksqiWlZWxmmnnQaQtBI6\n//zzefXVV+sUQqJzyaYxjvLycnr16lWvrFevXk2awjxbw3HTTZBfalcchbED2AZ87M4EN4y0kuyy\npHv27KFbt24xZ3AHVUaHDh1i8uTJqCrz589HVSkvL6eqqqpOcaQyxhE9axycB/+f/vQn+vXrl3QW\n1YjryxuCWlxczMSJEwO116VLFwYPHlznghowYEDc+tm2rkS0BdTUFpGtx+Giql9S1eE4A9WFwEsi\nkj2ZzowWQaq5fLZu3crcuXMblAcJ7wUnQic6ymnNmjXMmDEjLWMc0bPG00VEcXhXTty6dSuzZ88O\nfE297qpLL7007TJmiltuuYUdO3bUK9uxYwe33nprE0lk63HUISKXiMgdwCycRIQvAk13Z4wWyfTp\n01NuI2x+Ki9+CRT37t3Lrl27KC4uTklxRLuq0kWHDh0AUgrt9SqOBQsWxK2bTTmX/LLj+pU3FhEl\nkZeX12LX4wgyAXAM8E/gLlVNfj1Ow4hDmNX/Bg4cyNq1a5N2bcWioKAg5qJKubm5dOzYkfz8/JQm\nAMZyVaWDeH175zNUVVUxffp09u/fT35+Pvn5+XVuqXPPPZc33niDPXv2JLwPTe0K8uI3/ySZlSSN\ncCRUHKp6nYj0AoaJyBnAa6rqvyixYSRB2IHtdIY39urVi2uvvZaZM2fWC8Pt0aMH48ePZ82aNeTl\n5TVQHNu3b69LcBjP4qiqquLBBx+kffv2zJs3r9HWZ1i3bl1d/9F5vbp06VKnyDp27Mhpp53G/Pnz\nE843yKZB3vz8/JhWZipBEkYwgkwAvBz4Lc4kQAFmisiPVbWhQ9kwkqS8vDxucj0vfrPCc3NzGzxI\nunfvzpYtW+q2CwsL6/zibdu2ZfDgwUydOpWysjJqamrYunUrxcXFrF69mosvvpjTTz+doqIi8vLy\nWLduHaWlpXVv7Zs3b6Zr165s27bNV3FEHtqRWc7vv/9+qNQi6SDWLPWdO3cyb968uu3osFw/smmQ\n94QTTmiwgBXAiSee2ATSNKSlzd3wEiTk5P8Bw1T1m6p6BTAMiD9LyDBCkspDNCcnh7y8PG6++eYG\n+37zm88WnSwuLq4X4//Vr36VN954o67v2tpaHnnkEWpqavjWt75Fz54962aNL1u2jNdff53q6mpe\nfvllqqur2bt3L/PmzYs7xtGU6zPk5TlJrP1cN14lG1Ec8ebCtG3bNq3KLl5afHCSXnbr1o3CwkK6\ndevWIKFprLVDioqKuO2229ImYzJEzmP//v0Jl/FtrgRRHAJs8WxvJUYqdMNoKm688UZ69erFsGHD\nGuz73Oc+V/d969atvPPOO3XbTz31VN2P+pNPPmH9+vUMGuQsUllcXMzWrVvrFMdzzz1XLy1JhJkz\nZ8ZVHEFSiwRJV5IMkYeqn+vGu2bJOeecw7Jly+KuY9K+ffu0PQQjlphXEXtXyquoqOD2229n69at\n7Ny5k61bt3L77bc3UB7R59bUbqqqqiquueaauu3q6mquueaaFqc8giiOZ4HnROQqEbkaeJqo/FOG\nkQ5ycnISV4rBMcccw8cff8ykSQ3Tnk2bNs33uF27dtU9rN544w1OO+20ugdnJF9VZBzDL2Jr3759\ncV0SiSaEpcOd4TdXJdJ2eXk53bp1q7evS5cunH/++XXbBQUFnHnmmZx//vm+qUx27NjRwFJKZDX4\nkcgSmzlzZswss94lgWNlCK6trW3SyK9bbrklpkyJUrk0N4IMjv9YRL4MRFaauVdVn8isWEZr49Ch\nQ0lHSbVp04b8/HzWrl3bYN+9997b8AAPkYfV5z//ec4888y68ki+qojFkUgB+FkN5eXlvPLKK/Ws\nlWQnhFVUVNQ9UHNzc2MqSi+RdUTKysro0aMHffv2ZenSpZSWltaN73gZPXo0e/bsYfjw4b7jSF5L\nKd5iWolcWoksMT9F7S3Pxuy47733Xqjy5oqv4hCRE3AGxY/DSW3+Y1W1iX9GRli3bh05OTlJKQ8R\noX379g0mg0Gw8NF9+/bx+uu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G0XX6umUCrFfVRW7533BcXQ3wpmouKSmhpKQk0fkYhmG0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\nwhSHYRiGEYr/D4YcTu7aiOzuAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1165cef50>"
]
}
],
"prompt_number": 57
},
{
"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 0x1186ab210>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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YbWijwzGscRqGo1CIM6f3bLyAud2B24ASPHPT4WkOuRB4WtISf30GcM62NtTh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\nFI7AcHBwcHAICkdgODg4ODgExf8HflOjFVk1rCYAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x116856150>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best period: 86691.1081704 seconds\n",
"Relative Bayesian Information Criterion: 582.303992687\n"
]
}
],
"prompt_number": 58
},
{
"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": 59
},
{
"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 0x11949a850>"
]
},
{
"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 0x11955cf90>"
]
},
{
"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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\nBkNU+P/+0dIvw8A2TAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1196c6e90>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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dvbNAIGCnVePs2ZaVlVFcXMyAAQPIzc2lT58+rFixgpycHFfF5nRB1ofatKnz\nytlz1WVWN2B0A003JkL16cz3cNrMzc1lxIgRdu8kKyuL/Px8wF3Ra30CJCQkcOWVV9K2bVtWr15t\nG9dWrVoxZMiQOvXppDZ96mvrfRpDm+Goq8fwKbAFaAdMB1Tw971Yr/1sUQwaNMg2An6/nw8//JBH\nH32U119/nZ07d5KRkWFXynl51e9iveGGG2xL7/RTrlixwm4ROSueGTNmEBMTw5YtWwDo0qULw4YN\ns9PxxhtvMGTIEK655hq6desWtvXnbCE40xzu9X9er9fVMtSFXxuGUHcBVA8G15dQcTkLY+g0UD3I\npl0/ANHR0VRUVOD3+7nuuutYu3YtBQUFVFZa0dmnT59OWloaADt27LB91/ffb70ufObMmfa5dH6n\npqZy5513smzZMioqKgArr0eMGGFXXD179nRVuE888QRdu3Z15ZfzPpwVlDNOfm5ubo3WcX3i6DcE\n53MeNmyY3YpduXKlq9FQWFjo0uewYcOIj49n2bJlNbT5+OOP10ub+l5Ctanzx6lP53RW5zTqs88+\nmzFjxjB37lz7npza1L2M0J6W09UK7oq8Phys56krSY12wWgjGB0dTceOHQkEAvj9fkaNGkUgELAH\n1pcsWQJYWsrPz2fXrl1AtTZnzJhB27Zt7fPrhkiHDh0488wzAWyd+/1+rrzySnw+H1u3biUzM5Pb\nbrvNbkBVVFRw/vnn12i4hWoTatenfta19TQai7rGGAJAABjUZFdvZPSMgGHDhtnd6tDFY3reenx8\nPFlZWbZR0H5UPfMCrK55aEvv22+/tYW5aNEibrnlFvscAL/4xS9c3cjU1FQ7LX6/n7POOouqqqqw\naQ638EgXOBFYv74HY8bsJSEhgdLS7hx33AZbZIc6LW/x4sWsWbMGgD179titwhNOOAGoNpa5ubmu\nFurtt9/OfffdB8D5559PdnY2w4YNs2cA6cpff9ctOT1oXlRUZFeOPXv2tP3WzufVvn17evXqxfDh\nw1FK2d14J86BvuLiYp588knefPNN2zCGGrVQdMUS2jrWlWOoYTzU1lltz9nZ83SuyygoKLDToNPu\nfMa1aROwtRmaX507d67h4gBqjO+Epvnqq692aVyjtQmwZ08C//1vf9auhR07fs5bb30E1Ky4G0Je\nXh4ff/wxBQUFlJWVUVlZabtS9aB9ba3pu+++m3vvvZdrrrmGmJgYO+/1bCitzxtvvNEeC+ncuTOV\nlZXs3r393jvfAAAgAElEQVTb1qa+zrp16wC3Tvbt20dWVhbTpk1zuYbAcqHl5eXZRkOjNeTUYm3a\nhOrxntBnnZWV1WjaDEd9Vj6fCjwGnAh4gUhgn4i0qvPAI0CoX1BP+3TinPd+1VVX1bpUXbd8Vq9e\nbVdSq1evZvduK2agUori4mLb3aSvFVpgwlXQCxYs4PTTT2fYsGFUVVXVsP4HW3BUWRnJokVDWbHC\nOYPlKn7+86WccYaVbmcvIdRYhBso0wwZMoQhQ4YA1T5gzZdffuna1yng/fv3ExcXx86dO3nzzTft\nVowuaKGEdtWdOA1O6GK/Rx991M7rBx54gC1bttj5VlZWxsiRI3niiScoLi62KzbnM9Cui2+++Sbs\n/f/444+u6+rBxccff5x9+/YRGRnJqlWr7BZ2famPNsEd/O6mm26yn1VohQfYvQmwfN/htJmUlGRf\n66STTnIZhlDXE1jP5e2337b16fP5auhTp1HP9Anl++9P4F//Gsn+/dHBX87nu++Kufjir7DaltU4\n5/zr/2ur1MJpxqnPcJNKnL2j1q1b29rUeR/ag9GEzhjUhJad0F4UYBur+fPn23m2detWkpKS8Pv9\nrF+/nl69ejF06FDyHOseNLVpE6qNr7PHuXXrVv785z8fsjbrQ30Gn5/ACqD3CjAAuApIb/SUHAL6\ngeUFZ5I40RWCc957YWEhc+fOJdUxk0GjK1ZtFMDyoSYmJrJnzx5EpEarLhzOwrNgwQJOOaUPe/dG\ncOmlWUREWK6Sb7/91h4EfPzxx/H7/YwcOZLs7Owa3UURWLDgIlauPBmPp4LzzltBaWk5ubmD+Pzz\nQTzyyJf87GfuQu+swLU7y+lLrQtnhaYZOnQoK1eudPmgA4FA2FbM0qVL7eOcFcyECRNqnU2hz7Fw\n4ULKy8uJi4vjsssuq1ER6dlP+npJSUlkZ2fb40WjRo2y06av7fP5uOiii+y83r17NyJC165dOf/8\nm3nvvYtZv74THs9Z+HzX25Xjvn377Gf0i1/8osZA7cHQea3907Whp22+9NJL7Nq1K6zv2elP1xVX\nUVHRQbUZ+hxDtdmnTx/at09l27YisrKy7Dxzjh088cQTzJ8/n0AgwMsvv8xnn33m0ue6dd2ZP/8y\nRCI44YTvycjYwCef9GPjxvb8859juO6654mJqZ6S7XRHOt1Zzvusi3D6DOdmcdYJWpvOa4W6DmtD\n95h1qAs9o2vy5Mn2s8rMzKxRFpKSkvjPf/5jN6Duvvtuvv/+e1JTU+1zOSciLFy4kDVr1lBSUoLH\n48Hv74Lf/xRff30alZV7iI/fQVzcFkaNGsXMmTNtbQ4aNMh2HTYm9Q2i94NSKlJEDgCzlVLLgd83\nemoOgdCumW7pRUXFM3bsNbRvH2fP4dbdQu2HrA9OX7rH47Etvl70px9oZWWl7cP0+XxUVHj47LMR\nXH89FBRAdPTvOfnk/7F9+39caxdKSkpYu3Ytjz/+OFVVVXaBfOSRR+jYsSOlpTdQUHAy0dHljBs3\nl1mzxjN16lQCgVdYt+5vvPlmf1q3/sJVWEKNREO6mXpfPSDp8XhITEwM62YJbbGWlpa6Kh9nYbn8\n8st58803XdcKLdA7d+60K+DZs2dz5513uirVUD99eXm565js7Gw7bc5rb9y4Eb/fz969e203XiAA\nzzxzBSJ+AMrLfwn8mzfeGMOvf30xkZGR9jWdA7UNxZnvCxcu5Pvvv6ey8gAdOvTk17/+FQsWLCAr\nK4tWrVq5VnHXh1Bt/vDDD3z11Vf2b3fddRfbt29n165dJCUl4fV67YpTqRGMGgX//S9AN7p0uZry\n8u/Zvv0l1zWKi4u5/fbbqaqqYs+ePfYzf/jhh+nU6TQKCpYgEsGpp37KeedloxT07Pk1M2aMoqAg\njaeeSuWmm5bbLpZQbeq/h6PP8vJyWwPaCOh0RkREUFRUxIsvvsjIkSPt1nqo6zB0XUJoo8app4yM\nDHu2m76ncNoUETtdL7zwAgMHDmT58uWuc+mGYXl5uT0WUV5ezoYNf2DDhnODqYlj167HgDVkZ2e7\ntOlsiDUm9TEMxUopL7BCKfUQsJXqgegWQV5env0gd+3ahchNlJc/zFNPeenf/2suuGCJPWhbX1at\n6smnn57G9u2/x+PZishL7N8/jVWrVvHqq6+6KiD9QNevX8+iRYs477zreemlX6M7H7GxUFLiZdmy\nAURGvgNcCHxhX0spRUlJiev6lZWVbNrUA5gEQKtWE3j//fd46qnK4PaFWC/Vm8Qrr5zDoEE5tlG8\n7777SElJ4cUXX+Sqq65i9erV9OnTx542WB/0dF6orpDj4uI499xz7X1CW6zOlpnzOL/fzz//+c8a\n13AWkFmzZtlGMSUlpYZLyMrHWGJjY9mzZw/z5s3D6/W6pq86/eP62tHR0bbx1ftCBErNDxqFXCIj\nb+XAgVeBDHbvvorZsx+jbdu27Nq1i2uvvfawu+rulnhX4DU2bjyJRx9dw+efn0AgMLVB/uHCwlZ8\n8MGZ/PjjHUREVAK57N9/Pz/88F+WLl1qx+ravn27nb967Gfhwjdp0+ZppkzR+WSNX23a1BWYB5wE\n/J99La/Xi9/v55NPPnGloaoqmk2bZgBxxMTksH37DZSVXYzP5yMmpoLWrW/gxx8Xs2fPr3n55TfZ\nu/ctlzZ9Ph8REREkJCRQUlLSYP+4U5/6uWrdQLU2q6qq2Lx5M2AZjRtvvJG5c+eGdQk5cWrzwgsv\ntAelvV4v5557rmt2VWpqKiNHjmTWrFkUFRXx6KOP4vf76dGjB2Bp88ILL2THjh0uI+LUZlxcnOPq\nVwPXAMXApSj1S0T+CDxOYeF5Lm02VbSi+hiGq4AI4FbgN0BnoO6J2EeY1NRUx4M8D3jS3rZs2QBK\nS31cc00egUAe4B4QC+1Ser0+liw5ny+++LnjCt2wOkhXkpLyO4YN62pvcQ5+pqSk0KfP7TzzzBWU\nlMRx/PHwj3/AoEFw661P8sYbFxIIpALvAyOAdwFr9sjGjRtJSUlxzObphOW9iyIi4mEKCmZRUGC1\nAtPS0oIur6lERIyhvDydd9/91uX+0IXh/fffZ/LkyaxevdqueENbaOFmIWnB+f1+lFJs3ryZ4uJi\nnnnmP3To0IGsrExXi9Xn87F37167Zebz+VwDrs64/zrP9fhMbGwsJSUl9uyjxMRE2x3gpKioyDag\n2hj7fD7i4uJo3bq1y8erjYjzPoYPH86LL76I1/sndu4cBGzG5xvDgQMFHDjwG+Attm3LAu4CDpCe\nnk5ycvJhx6Sp1mYMsABruA7Ky0/g9NNLueaa1nW6SJzujkCgK/Pmjaa83Lno7CJgGJGRjzBwYDTF\nxdYMF61Nr9dLeXk5KSnpVFS8wscfn0hkJEybBrfcAgcOwPDh75OTMzhYAXUAxgNVdOnSxZ6Q0Lp1\na7uChKeA/sB6ysouYd263Tz22GNERUUFpzPvBP4C/InKynvZu/dVKirc2lyyZAkPPPCAy+8eLo+d\n+RKqT4/HY6+jKSw8wMsvf8LIkWfY2tT3Hhsby969exk+fDhDhgyxtfn888/z+uuv25NOQrXp9/tJ\nS0vjv1bXivLycrKzs10r1hcsWIDP57N71mA1EouLi4OGMob33nuPZcuW0apVKy688ELmzp1rL3RL\nSUnhsssuY8mSJZSVdWDTpsewOrY3EBv7Ifv3f8T+/ZcB6fz44ynAIpc2m2IAuj4v6skLfi0FpjTK\nVZsAqxAodAQPpe7G6/2AsrLFrFrVi3//u4Q77kit0VV3dilzcnLweh+jsPDnQDlK3YXIPCADmAac\nytatL7J06UcMHpxLRIQwcuRInn76afbtK6ag4FLmzbsG8HDccWv5/PM0kpOt67RrV8BVV73AwoXD\ngoPIbwCjuPHGTiQmJjJr1iw8Hk/Q1eHDim7eHsimquoPdnqLi4tZs2aNXcm3b/80W7c+SE5OJhER\n3mC6FSLiWmhTV5A5pztO73f//fczceJEhg0bxssvfwj8FriC0tL25OXBQw8VkJzcn+jov+DxrCYp\nKcnuNj/22GN06tQp7MB6IBBg+/ZK8vMvB85BqVQqKqqorPwfsBilXqekpIQXX3yR2NhYioqK7Mo+\ntKKLjo62C9e6devs74sWLaK4uNg2Inpuuc/n48orH2LmzGuD57mF1q0VmzdXAEtQ6ntE0oELgDfI\nz8+ntLT0sKcF6nQnJNzB3r0nAquAM1DqBYqLL+DVV0fwyCNdasxOCdXmRx/t47PPHkYkhqiot1Bq\nEvv3F2G9gv0ODhz4Hffeu4prrnmH5OQiuxVbUVGBUj0pKFjE1q1p+HwlvPFGLMHlOwAMHvwRHTtu\n4aWXLkbkWiCOdu3uYOTIkbz//vv4fD7HLKRbsVq1JVgR+XejlLLzX/dO4uNnceDAHeTnd8fr/RWw\n0KXNyy+/3NZEXW//c/4eCATo2bOnveCstLScDRtOQ6kJlJX1JS8vgkceqSAy8nw8nr/TocOH+Hwe\nSkpK2LRpE5s2bWLt2rW2Pp2uN2sa6042bjwFGE1ERF/27WvPa69toKKiJ/AqsJzS0lL+9re/2dqc\nMGECK1asqNFIPO644/jkk09Yv349e/bssafIHjhwgMTERHuKamJiIsnJyVx22WheeOFKqqri8fkW\no9QCkpOTg4b0Kay67Xpgka3N+gaPbDAiEvYD/K+Ozze1HRdyjr8D24D/1bHPY8APWGsj+tayj9TF\nhg0bZNKkSdK163VidYw3CngEELhUQCQyslTWrBGZMmWK/enXr5/ExMQIIHFxcQJjgsdXCJwbPF5/\nIiUy8gFRqkpAxOtdKp07XyS9e58i0dEnCrwSPFakTZvn5U9/miobNmyw09ivXz/p1q2bHHfc8XLS\nSe8LiEREVMqoUa/IlClTpFu3bvZ14OXgudYJtHGlw+v12vv6/X45+eS+EhW1VkAkMfG3EhkZKVdf\nfbVkZGTIpEmT5NFHH5UPPvhApkyZ4kpPOHS+ONPctu0NEhGx27432Cmwy/H/AYG/i893vADi8Xjs\ntEZEREhCQoJ06dJFBg4cKB99tFLOOCNHoNBxfOinXOBVgQvF50uwz5WYmChJSUmilJKYmBg5/vjj\npXv37nY+9OjRw/4+adIkSUtLc/3fr18/iY1NEqW+Dl7nacdzR2JiYuTUU98IbnvWvm5GRoZ88MEH\nB827g2nzxBMzJDFxZ/D8w4PnbyWQJyAyebL7GdTUZlt7X3hRICJEn6dJRES+gIhSRdKu3R/k5JN/\nJtHRiQI3C+wN6vZ7uf32GTXuR+uzY8dREhFh7Xv88Svl7rvvc2gTgQsEKoPp+LX9u1JKAImOjnbl\ne6dOfwum6XOJiHBrc8qUKfL000/LlClTDprHznKrOemkX4nX+4lDO2UCPwY1qX9bKV7vJdK9ew9b\nkzrNcXFxcsopp0i3bt3kjDMGyyWXzBGvd2Ud2hSBbwR+Iz5fdZ4kJyfLKaecInFxcaKUktjYWJkw\nYYIMHDjQzotzzjlHABkwYEANfepjo6J+E6wXdgSfd7U+vd6uwfsqFYiztXmwch2sOw9aV4d+6qrU\nU+v61Ovk8Eugb22GARgCLA5+/znW+x4abBi0cPr0+Sr48P5kC9Uq9K8JiPziFyJ/+lN1wfN6vfY+\nsbGnCZQIiERF3eqq5KKiouz9Bg78vSi1xSGUfY7veyQx8SZb9E6xOwuXzxcrHs/fgsdUSmTkH0Wp\nOIFOopSunIoEMuxjIiMj7e/p6el24bKEMzp4zFqBSFswzoLkLFDhSExMFKWUREREyIoVK0REJDn5\nHvveIiLeloEDb5aIiMhg3vSRiIinghW5BPPuz6JUUkiFhUCywJ/E43Hm1dsCFwmkSWTkKRIdfaP4\nfDmOSkckMnKbwF8EzhEYGPw7WuA34vH8TXr1WibJyS9Jp05TxO/vI1FRUdKpUydJS0uTCRMmuCog\nK/8flGqDGy9+v1969eolsbGx0r17d7nmmr8Gt28TsAp4ly5d5IILLpDdu3cfVIN1afPaa58NVpD5\nAtXaTEu7Lqg5ka++krDajI9PEng3+By+EPDa+nbqPC1toHg8bzryuFysRo71f0zMv2XixHtsbdam\nT6/3F1Jt/N8XOEHAI5GRtzqe9732/s7ykZaWZud7v379JDo6OZifInBuDW2GVvbhuP766yUqKkqU\nUuLz+SQvL09++EEkMnJT8LxbJDr6BklIaBc0pq0kMvKm4HPWefGeREQMlFatWrm0GRMTKzBU4AvH\nvpsFfitwikAPad/+KomKmimw3bFPhcACgcsEfi7R0ecE9XyDwGRJTp4vZ565SWJi7pcOHS6U1q3b\niM/ns/Nm0qRJ9ncr70+06x+v1zK4sbGx0qlTJ4mLi5MJEyaI368bBiNsbaalpdWpzUY3DK6dLGNw\nTvB7LJBQ7wtYx9ZmGGYClzn+Xw10CLPfQYXTtWuaRERYLdHY2P5y4403Snp6uqSnp8tDDz0nrVuX\nCYgkJ0+VtLQ06dKli6MgdJDExB3Bgvd3+/dWrVqJz+cTn88n2rovWrRIvN7OAo84hLJHIiL+Iamp\nZ9kVkbbkugCefPLJYSrMyQ6hOVs5uwROc+2rWzq6JaavYRWESIE1AiJJSbdJ7969pVu3bpKWliaT\nJk0SkYMbBqfhiYmJkZkzq1tJkZF/sLfpvNDChR7i7C1ZaZ8lcJ3ADRIRMVd0a9WqnD4WON0+h1LK\n1cvo0eOX0r79X6V1a2chrM9nv8Dfg+mxWlrOfOrY8fpgHldKZOQZdkXjriR8EhW1UUCke/dRLo0M\nGTKkzvyrS5vdunWTxMTnBUT69v1A4uPjpXv37pKeni6LFi2Sc875VkAkIWG9dO2aZvcU9LMYMOCd\nYN7tFo8n1aUJpzYnTZokrVolitWSX+bImy+kffub5K67JrkqYqc+k5OT7edhnb+3VFfoVgOm+vsj\n4jRu+hOqzWpjM0lAxONZKnfdNcnunWh9HkybgwcPdl2nY8f+0rGjTstnolvXlh6rDZRSMQK/EauX\na+2v1PsCdwiMlbi4v4rH84O9LSJim8DtAtX57/F4JDExMfi/R2JiRkta2reilDM/6vNZIXCJ6AaH\n8967d+8jVk9EJCJitvTs2dNVHnW5a916erCMv1pvbTaZYcAahfoSWBf8/wTgvXpfoG7DsAg4zfH/\nu0D/MPvVQzi/CD6Ab21L6hTdf/6jH1CxwIl2RRsdHSepqVb3MTr6GwGvXeh0txiQhIQEmTRpkrz+\n+uu228IqHK0EIiU9Pd1u7WnROy357t27XQ+7ugCeGxS3SGRkhWRkrJRx46ZKQkKC6/o6DbrbGRMT\nI927d5euXbsGt90uINK69Tbp2rW7fUxGRoaIhDcMzorBmbbp0z+ViIj9wTy5zb7GgAEDXO6bCRMm\nOO5joEBOrQXj7LMrJDdX7C50dHS0xMfHS6dOnVyVoG5pdu3aTTp1ulR69/5QYmOXSkzMNwLvCcwX\nmCHwe1HqWomKulMiIhaLZRi0gXhOIFWSkpIkPj5elBoh1T27e2pUaO6PVYG3bXu//ZzT09PtXlRD\nqa7UVgXz8yzp0aOHS5v79okcd5zOqwfttHi9Xhky5O/BCu2AnHLK7WHTrLU5ZcoUOf300+0KzeNJ\ntCu5jIyMWrUpIvZx+mNpr0MwL/cIiLRrt02GD/+nnHBCuqsSBqvXEKpNrZXo6Da2O3LcuNmu3onu\nQdSlTWejKjIyVvr2tRp5Xu9SiYhoZevRqc1JkyZJQoJ2RSYJTBPdIg/9REX9KA88UCI9epwkgLRv\n396+j1DDpxtdqamD5Be/WCDx8R9Ijx47RKmPBBaK1SiaKkrdLK1aTQz2qqs9DEotF+1K9Pl8EhnZ\nSZTS7rBVAgkud5f7MzCY3rV2/vv9/jq1eaiGoT6zkm4BBgJLgzX0GqVU+3ocV19Cp75KuJ2m6Pl1\nWOsQag4I6v/fswdB9RzhCRMmMHx4En7/e/z449nAO1RVXQhsIjr6FfLyeuHzldC+/e0EAuXExMTQ\npk0be/ZETEwM3bt3Z/78+cyePRuPx0NERERwoHgPERERnH/++TUWrznfTJWUlITH47GX2qemprJ7\n926Ki3PYv/9UwMMJJ/QkK8ua8HX88cfbIQ7AGswaO3Ys8+fPt5fzb9iwgdjY2OBq3Tiee243u3a1\nx+MZCjxeYyXwzJkz7dAfzvAXZWVlXH/99Tz33HOMHn0H06efGpwVMYOKisfx+azAddnZ2UybNo1Z\ns2YRGRnJm2++SVRUVHBWyBdAJu3bn0Vl5YWIHMf+/aV4vRsZMSKS556zBsFDQ0O8+OKLdh7fcMMN\n+Hw+du7cycaNASBAYuIq7rori88//5y33nrLLRQBK+LAdOLietO16zN8911/4FpgLCUl/8Oa6NQ3\neMRzwH3h5OXgI+AaCgoyaNPGQ0ZGRq0vBao/7bFmIhVTUfEh69dXurSZlJTE7NlwxhlVwB+AQuAR\nkpN/w5IlVwFwzjnvEhX1AytWYA/g6ny7+eab7cWRxcXFKKWCz8QaLE5JSSEqKqpWbQI1AuR17dqV\n9evXU1V1HTCe44/vxeWXW9rs1280//73v+0Vu1FRUdxyyy0sWLAgrDZHjBjB559/TU7OmeTmnlFj\nzj+4tVlWVkZKSoq9knvIkCGUlpaydetWUlPf5uuvvXi92ygvHwrssScXgDXxwOPxMH/+fHu2kpWf\nv8frnUFq6gQKCrpRVhaDx7OTc86J5MQT8/njH+9hz54LWbSoyqXNtWvX0rdvX0pKShgxYoS92A8C\nxMb+kTvvzGLy5Ezi4n7lmnIuAnv26P8mkpHxN9asGUll5SlYb0rOo7R0A1bVGgdswpr0sBdHxJwQ\nvgaKqaw8jsrKOBISIrnyyitdC/RycnIa5a11Sgus1h2U+kJEBiqlvhaRvkqpKOArEal9uaD7+FRg\nkYicHGbbTCBHROYH/18NDBaRbSH7SV3pLCwspE2br6mqOpOoqF9TWfmyHdgNrILx3XffUVICaWnr\nKC3tHzyyCojA6y3jqqteoHXrdXal9dprr7F27Vq7wlqwYEGdC4/S09MpKyuz99HBzJyvXDzrrLPY\nsGEDYE2zbN26tcv4TJgwwS7gztWn8fHx3HLLLS6xOomKiqJjx46UlY1lx477UGolIr1Ryjrvd999\nZ0/Rdb6wxvkdoLIygjlzxpGf34XWrb9h167++P3t7Rk9X375JStXrqzxvgiNni0E1VNQwVoQ9OST\nT5KamuoKwgZQWlrqMhQffPABn3/+uV05jB07Fp/Px4QJExg0aBCbNm2ipKSkxvPt0KEDhYWFHDjQ\nnW3bbmD//kupnnRXBNxLu3YvUlJSTHFxMTExMZSXWzO4qlwl8ThgLbCDu+56hNhYH4MHDz7kqYCF\nhYWcdNK9bN78V+Ad4FeuKZZam0lJScyYUcJvfhMbPPIAVvQZ7MVjEydO4PTTT6e0tJQNGzbY2kxO\nTmb27Nm16jM2NpY2bdrYDaZw2ly5ciUXX3wxlZWVKKXo2rUrW7dutZ9neno6o0ePDrs6Oi0tjSuu\nuCKsNn0+Hx6Ph4SELmze/AmQCJwGfEZERATjx4+3X6oVTpv6f4Bly/qxaNEwvF7o338Cn376mB24\nrmfPnnZQwfz8fLsBVlt+OLWZlZXF2LFja9Wmjjm1cOFCVq1aVUObkydPZuLEiTz//PMcOHDAnp2V\nkJDA3r178fv9nHzyyXz33Qa2bh1GRcVvAb/jSguJjLwFr3cXJSUlpKSkUFJSwt69e6lZ770LnE1y\n8nWMH98Wn8/H2LFja9VmsBHR4HVnEQffhVyl1P8BsUqpc7HmbC06yDH1ZSHWOgmUUoOAwlCjUB98\nviQiIk4HoG3bVcTFxdGxY0d7+9atWxk/fjx+fxITJ75Nv36fopT18I47bi3jxz9Lp04/2jFm9Bz8\njIwMTjjhBBYsWGCH23UupnGyadMme5susM5WZmpqKllZWfaKad0Ccu6vW8uBQMAudEoprrjiCnvl\nqDN2jcZaDLeJHTseQql8RE4ChiMilJaWkp6ezuzZs3nxxRdrRHF0MnPmieTndyE6ehsPPriOjIwT\naNu2LfPnz7ePdaYtFF2J+P1+OnToYH8fNmwYmZmZPPjgg3Y6dOFx5rnGGbHztddeo7S0lLvuuouy\nsjI6dOhAeno6xx9/PD6fj9jYWC677DLWrVtHIBAgPz+HAwcuB9pg9SLPAPzExc3immuu5tZbbyUj\nI4N27dohIlRVVREfH09iYmLw2azDmkjXjoULv2H27Nk89NBDh9xjSEpKomPH0QB4vUvx+Xx25E+o\n1ibAxImxXHzxC3g8G4FIWrUq4qKL/mOvKNZvYsvKyiIjI4MJEybw0UcfMXv27Br6dFJSUuJqgITT\n5tChQ+0yI2ItWNQrbFNSUuwFoqH6bN++vR3WIVSbHo+H0tJS9uzZw+bN3wKPB7fcDUBVVRUzZ86s\nlzY3berEG2/8CgC//15uu+1UMjIybH3OmTOHHTt2EAgEXEYhND969+5dQ5tAndrUIdJ37twZVpvj\nx49nwYIFpKSkMH78eFq1aoXP56Nfv36kp6dz5ZVXsmLFCjZuXENFxSNYS8H6Yq256gpcRPfuMdx2\n221kZGQwduxYkpOTbaMQHx/vuI9Pg3nXnyVLljB79mxuvvnmOvPuUKiPK2kScB3WNNUbgMVYffKD\nopR6CRgMtFVKbQImAx4AEZklIouVUkOUUmuxlvldfbBzhgYnS0pK4quvIqmsHIbH8wNbt/4PcEf3\ndL5X9u23X2Pnzmfo0cPHiBGXkJAQXeMaUC2K0JaYrkjGjh3LjBkz7MqwpKSEqKgo+10B4SKl+nw+\nfD6fHQ/l2muv5cMPP3TtH/paQBHh2Wef5c4777R7Ex06dKCgoIDi4mKqqqrs1nNsbBQVFX+lsvKv\nwD1YXVY47rjjWLVqFYD9UiKdf7ql8dVXfSkoGA6UUVExlPfe605WVhbTp0+3F5PpedgpKSns2bOH\nki2Qh9wAACAASURBVJIS/H4/Xq+XDRs22Pfg9XoZPnw42dnZdrf+m2++Yc+ePWHj12i6detmF0pd\nqaxdu5ZFixbRrl07V0iCyspKe9/s7OwaUSxhD86XDHbunO6KRaUrZ7/fT9u2bfn+++8drbOvgAtY\nvz6RioqGvbDeqU/9Qp38fKtCS0r6H9u2lbr2P+mkk1zvPA4EZtCx4z1ERbXi0kuHEBsbXkfhQn+A\npc+EhARatWplGwPn7zfffHNYbebl5bkWLHbs2JGsrCw7am5t+ty5s/rVLNnZ2bRp0wawerG6bGh9\nKvUYIhOxJiP2B5bh9Xpdbz3T70pwBtfbuzeOV17JQiQaeJwNGybzwgtDiImJsd1jgUDAXj2sr6dX\nWDu12b59e84880yXNj0eDx06dKhTm1DtbqtLm9nZ2SQnJxMIBMjNzSUjIwOfz+cKg2N5y6tDx8TE\nxBAbG2unxZnPWp/VgfasMBxFRT1Ys2aNvZahvvqsL3X2GIJuo1Ui8oyIXBr8PFunX8eBiIwWEb+I\nRItIFxH5e9AgzHLsc6uIpInIKSLyVV3nA6t1o8cYAoEAI0aMoFMny+rHxHxbY/+oqCjXe2V1QVq3\nbjVvvWUta68r5IF+QLqlD9CpUyd8Ph9+v9+17+bNm2s1Cprrr7+ehIQEfvjhB1JSUuzW8sKFC3n4\n4YfJz88nNjbW9TrFAwcOsHjxYjvtGzZsoLKy0naBREREEBcXR3JyMpWVT2NFLekPXIDH47Fbkzrs\ntx6f0UYhP9/Pm28OCV7tJgYMwK6snBVuz5497RaNbt1ceeWVdgu2bdu2tpsjOzubmJgYVq9eTSAQ\n4K233rLDe+uWmn5HtG6lpaamcs8995CRkUGXLl1c+2q3kf5f97Z0iAL9LFJSUmr0qHSL9/vvvycQ\nCLB27Vq2bNlCXFwco0aNoqioKKTgfhXMd2t1a69ever9wnqnPrdt28bo0ePYvr09SkFc3Joa++s4\nRho9vrJ+/f94441FLm2Gi44aqrX4+PiwlX9ERATXXHNNrdrUYR3S09NJT09n1apVJCcn2/p8/PHH\n+fOf/8zmzZtdZUFrU9+LdvXt37/fztOoqCjS09MZOLAH1kIt0L0GvU9KSgqvv/666z0EqampVFTA\nq6+OYu/eVsTEfAn8lgEDBvDPf/6TnTt32sfHx8dz3XXXkZGRwU033WTrNFSb7777bg1trl271qXN\nW265xaVN3TB68MEH66VNvTrc5/PZIWR0byzUsHq9Xm644QaKiorstDzyyCOUlpa69FmNriL7oWth\nZ8O3sajTMIhIJfC9Uqr2mrMFoBcv/uxnUa6YI85BMf1i9HADX7qCDGcgtEupa1crDEbfvn3tbnVW\nVparEiopKeGxxx5zdUdDSU5O5o477nBdSw9aFxcXU1ZWRklJCZ07d7a78n6/nwcffNBOuzPUg8fj\nsd+eZXUny7DeqwRwD/v372fPnj2u1b9OtmyBl1++jAMHoujb9zMyMr5wGVJnXJcJEybYrcj58+fb\nBUK3YHWLMzXVepets+AmJyfz5Zdf2sbE6TbTLS/Afk/GqFGjyMjI4I477sDn8/HHP/7Rdaw2nOXl\n5SxZssTeX3fDNQkJCYwdO5bs7GzX4KDOM91yhGq3g8ezEoADB06x8/9QXUnffgtVVZF06VLKqFEX\n1NDnddddZ2vTmd9an05thjMMDz/8sH3OmJgYVq5cabtCndeqqqrimWeeqVObPp+P0aNHM3r0aPt+\ndQWpXwtaWlpKbGxsDW3qNDrvQVNSUkJkZGSwB/NXrCAKI4DqYcfExMSwg6YTJ8LGjd1ISNjDtde+\nTUbGCbY+nYHyXnnlFduQLV++nOLiYl577TUAlzZ1WHWnNmNiYlzavPnmm13afPrpp4H6a1M32EpL\nS+0XAX3yySdkZGRw8803u+qM1NRUPvroI1dU58rKSjsEjVOfAG3alAIFQDvKytqSkJDgKq+NRX3G\nGFoD3yql3ldKLQp+FjZqKg4TbRi6dCng1ltvJS0tzR6wTU5OZty4cYwYMcJuFTkfYrdu3Zg+fTqz\nZ8/mmWeesQuNFrmuhKqqqoiLi2PMmDF25erz+bjttttcXVhnFxOw48Dk5OSEbf2FzmQCq/U0cuRI\n7rzzTjutQ4cOtdPepk0b29cZHW25wvTb0yxmYonnVOA8UlJSwrYiS0thxAjYu7cVXbsGuPDCd+0X\ntOtCqv2xFRUVvPDCCwCuQqNbi1BtRH/3u9/Rtm1bW9AxMTFMmzaNr7/+2m6Ber1eV9r1OITuzWhj\n069fP5KTk1m7dq1rLEKHXdDo/bOzs+04N3369KFHjx7Mnz+f5cuX28ZUt3j1dXW6dbc/JUW7YPoT\nHe3l2Wef5VDR2jz9dMuNGKrPqVOn2tp05qEeUHVqM/RVqmCFH2ndujVxcXHccMMNfP3113Z+3Hrr\nrXVqE9z6dKLjBn377bcEAgE776Kjo7nuuutc2jzppJOA6phB+/fvp7S01GU8qlvW2wDdurUGmHWP\nLjTQ5ZNPwtNPQ2RkJZdd9grt2h1w6TMxMRGwjJ52j4Ll8gxtcOh8vf3220lJSXFp8+6772bDhg22\nvmbMmOHS5vDhwwHCarNDhw7k5+f/f3vnHh9Vdfb778p9EiATBBNAyKDEBLA0UNSo9G1ahXrDUqkI\nXgpeyovWIhzpR2vt0fS8tWKrL4oera0YPQq8XqNYWgtKYqsCKgatCohhYhS5JJBIrpBknT/2rM3e\nk0kySSY3eL6fTz6Zy5691977t/azLs96Hpc2Q018e71eEhISXMH3zCR4cXGxa94uOHHSzJkz7fhh\nycmDiI62MuDFxORw7bXXRtwoQHiG4TfAxcBvsYJ1mL8+wZEj8JE1rUBa2h48Hg9XXXUVS5YscbUc\nDcGTnT6fjy+//JLS0lLeeecd1qyxuu/OWX4T2rmmpobNmze32J+Z0DTpK80Nzc/Pt1P8BXu1/P3v\nfyc+Pt7VcomKimLMmDHMnTuXrKwsV1kLCwvJyspytX6MMTAVNC0tLfDQqwH+AEBMzAouv3yByyjk\n5+fT2BjFlCmlbN4McXG7aW6+lNWrn6Kuro6CggK7dZ2RkWEf64YbbgCOjrUOHz6c6667zt6vaVEl\nJiYyZcoUuzLefPPNTJs2zRZweno6OTk53Hnnna6HYKgHVG5uLgsXLrQTtJgWrDNT1owZM2yj65wg\n9Pl89oS50/No9OjRrsaBuc6HDh2irq6OsrJ/Yrk4DuXwYS/z5s1zZfbrCIHnNJMmWf/b0qffkdDH\n4/G00OZ9991nXz/DN998Y2tz3bp1rodre9rcuHGjPfQV7NVSUFDAwYMHbW16PB4GDBjAk08+SUpK\niqucfr+f9PR0iouLGTFihH0cc+zrr7/eznFhcS9Wr2Emw4Ytsr17nPc+L+/fLFxo3TOvdwlvvvkH\nu4f697//nYSEBFc9cGamM5+np6fbowJObebk5Li0aWI2md9kZ2dz//332xrJzMxskQsdLG0uWLCA\nBQsWAEe1aRoeGRkZ9v0oLCy0G1S1tbUMHDjQ9hRzanPAgAEsWLCghT69Xi91dXWUlJTQ1GS1Nhob\ns1i3bl2ntdkWrRoGFTg7rXVhiL8i5za9yVNPvUtDA5x44jesW/dcC88CCN1qNzfx3nvvtb0OMjMz\n+fnPf96ikji79z/9qeVXvmHDBvtYYHVXTXfReEo8++yzdiJ2UwENCxYs4LbbbnO1XH7xi1/YHkih\n3M/M752tSuc48OzZs+0hr6FDn2bYsDIaG0ewZs1VHDly1M9g1aq/ct99OWzZkk5S0mFOOOEavvxy\ni93CWrRokZ3VbeXKla5eC8Cbb75pf3bzzTfb+73jDmvceN68eeTk5LR4yJnyz5s3D5/Px6pVq6ip\nqWHt2rV2Xt1QkTWdBsNUroqKCnuYyFSc4Hv1k5/8xDUUBtYDbu/evZSUlPDcc8+5vFbcQyDWfNUJ\nJ/wHt9xyiz2pHG4lNNsUFlrjw88/f3tIbTrP0TxgjTbvuusuhg4dCljaNEOQzmtkkhQ516w4x8eh\nfW2Guu6LFi2yvzcuz0uWLGk1dLvp7YXSpnE3nTjRWk8SH1/B979vteQrKu6hvHyMXYZXXnmF5cur\nuOuuTJqbo0hN/RMVFQ+wY8cOPvvsM8CqO86Hu1ObAK+//jrjxo2juPhoHoiOatOZle3WW29lyJAh\nIeukMzKs0WZdXR0DBw5k8+bN9vErKytd2rzxxhttA2a0mZaWRlxcHI8++ih+v9/Vi3Br0xrqHDQo\nxzZ8po5Eyki05ZVUqJR6FXhZa+2aNVNKZWINEl6E5Q/Ya3zzjQ+Ak0+uZv/+qpCeBaa1bi5YaWkp\nNTU1duTKqVOnhlzIZCJdOhdlmXSJe/bsaXGswsJCZs2axapVq1x5fH/zm9+wbds24Kiv/4MPPthi\n385WvdP9LDk5mW3bttn7ML2JYHw+H7Nnz7b3V1f3Eo8/fi0lJadw//2X4fE8gVKDqK5eTkNDGnCQ\n5OS5HDjwJmBV3GnTptlCN63AYA8N0y1evXo1a9euJSYmhgMHDvDCCy/YBqU9fD4f1dXV9jV86qmn\n7Hzc5tilpaX4/X4SEhLsyWZn5br66qtJSkqiubnZ/t55PY8cOWK/nzp1KuvWrePQoUO2P39JSQkv\nvPACs2fPpqGhwZUm1OPxU1d3DhMnXsmAAQPspCxOHbW1rsHn86E1+P0DAaioeKNVrxezH+Ml5oyq\n2p42TQY4p35CZdYzCYGCtfnwww9TXFxMZWUlycnJ9kTnH//4R8477zxKS0uZPn06GzZsCHnO8fHx\nbNu2jeLiYoYMGeLymArm1VdftcuakPAp5eUf8tFHE1ix4ioGDvwLL7zwAp99dg/19daE7Qkn/IWY\nmP8CrDrwhz/8gfz8fFufznrgfBjecMMN1NTU8B//YYXf3r9/v61NpydeW/cu+D488sgjdnY8o83C\nwkKXk4izB3P11Vfz0EMP2d9VVla2qOvB2pw+fbrL03HFihXcfvvtxMTEuLR5wgl7qaiAwYOn4PFY\n6XfN/Q5Xn+3RlmGYBlwJPKyUOg04hLVKeQCWyXoGOK/TR+4gxhKakzX/DxywWlTnnjucLVtO5fPP\nP7dbT84baG62LxDa+OSTT2b79u1MnjyZZ599lgceeMBOVO+sKMYrx4i9sLCQpKQkl7ujsdrZ2dls\n3brVte9nnnkGr9framnl5eWxcOFC+3WoijRjxgy2brXGEs0wit/vt1OTtraYyVkxPZ6DzJ37JKtW\nzeHgwVOpq/u9Y8stnHjiQkaPht27rZbJqFGj8Hg8duvJ6Xrp7Er7/X7Xw8cZp7+pqcluaaamptqT\naqEqpJmEM14VXq/Xvj8mN6+zl7V169YWlausrIx//OMfjBs3jt27d7taZsZzbdasWaSmppKSkmK3\nosFqoT311FNMmDCBvLw8e+hlzZo1pKUl88YbUFk5nNzc010hyQ3BrtNObfp8Pr75ZiC1tVEMHQoZ\nGYPZubNlQqFgbYI7r3Bb2gRYvXq1Sz/btm1rMUZtrsWTTz4ZUpvO+2Ja90uWLAGOzuW0liv5tttu\nc12Lzz//vMU2BrMOwzBjRgExMY188MEkvvnmJntIGGpITr6T666L4a230vnqqy+pqqril7/8JePH\njyc3N9fVyDPHNzhTwHZWm+C+D+ZatabNoqIiNm3axDnnnMNbb73FAw88wB133MF3vvMdKioqbH2a\nSXGTs8SpTcCVne3aa6+1r29eXp6tzR/+8Az++79h9+5BNDUpOy1xJENwt2oYtNYNWGGzVyilooEh\nga/KtZXis0cx6TiDTzzQiCYrC5YscbeeQt1Ag2lpBc/oB88FgDtBuDn+9ddf36KlZsR54403Ulpa\nyuOPP96piaHk5GRXMiFnMg7ncZykpKSQn5/vSjUaGxuL1+slJeVRoqJ+TEVFJomJUfzhD+fx0ENz\nueSSi2z/6OHDh5Ofn88DDzzQ4lqYymDSKW7atMkWcGZmJklJSRw4cMD2+HCOWZtrF6riOe9BZWWl\nncwn2Ag5fxvcIjWZvEpLS/F4PK6cDOeff769XVZWFnv37mXmzJn2BOCMGTOYMGGCKz2i2f/OnZbH\ny/79Q1uUO/j6mPMM1mZ5+ZDAsUO37IGQ2jTGLxxtmmMbFixYwOzZsyOuTfP7goICV8+ioKDA7kEG\n93LNNk8//TTJyck8+OCDLXIbjxjxJMOGncHXX3+XlJQxjB17mPLypfz4x+fg8Xjs+SzTeDD6dGoT\nrOtrUn2aa9QVbcLR+/D444+HpU1j+ILdj1vTp9Gx0SZY7uwrVqzg2muvJSUlhY0bN9ojBU7tJydX\nUlXl5eDBweHcvg4Tbs7nJix3gj6DeUgdOPBTYDSZmS1bJGZOIVR2qFA30YlpAQV3sQsKCqiurqa6\nutqeCHa6vQF2PlhnDBPnDY6NjWXZsmWA9UA3bncG00Mwwg1+eJjWHxzt1k6YMIGEhARXqtH6+vpA\ni6+MiRNjaWpazsCBA3n22ZO55JKL8Hg89oNi+vTpdqU3ld15vQoLC3n77bdtkWdmWvGTli5dyqhR\no5gzZ47dUgpV0ZzDU877Ye6BOZ7T6JmhrMLCQrxeL+np6XbYA5O8x0ySjxkzhubmZkpKSuyWsnNf\nplVlXDLN/gsKCuwHmrmWAEOHWp5NFRVpnYo9M3/+fP76V8uja/TohhbaDHUtzHUzD4C2HtxOfRqS\nk5Ntv/tZs2a5dGu2C6XNUL3kZcuWuYZJzLU0k6lGm8GeRKaXm52dbT+0TzrpJE466SQSEhK4//77\nXbmNS0pKyMyMJSXlQ0aOHMm2bdtc4+lGn5deemlIfRo2b95s37uBAwcybtw4br/9dpKTk7n11ls7\npU1zH8y1ak+b06ZNY8eOHbz44otccMEF5Ofn24Z59OjRKKUoKSlhxIgRrl6j0SYcdWc3xzBDpMEM\nHbqfqiovMC4isZGCCcsw9CVMS3r9+vWUlpYB1sKRffv+SWGhuyPjC5rw7QjOeQnThUxPT7cfYrW1\ntezdu5e0tDQ7pox58IciJyen1Ym74C76o48+Sn19PdHR0cTExLBs2TKGDBnClClT7LIZnL0iv2Od\nhpO0tDTeeOMNsrOzKS0tDYTP2M+sWbNcSc2dLd6NGze6BOf3++2JWhMYzXiqHDhwoMWDLHgYytBW\npi5zbq19P3/+fJdr75o1a1i1ahVz5sxh6dKlfPHFFzz88MMteoytYa6Z1+ttEeZj0KBDxMU1UF2d\nwPjxua7Maq3hNP7r16/nwIHFALz55p8pLDzNvhbBi7g6g3NewuzXfJaQkMBrr71m34+qqirbMITq\nbbZ1zZ2Nk6Kioja16dyH82HnHJoM1mdcXBznn38+KSkpbNiwocXciNHn4cOHbX0aQ2b0mZycbHv2\njBkzht/+9re8//77todUT2gT4Fe/+pX9IDfPg0mTJrXQp4m91B7B+nSudRg6dD87d2YQFzeR3NyU\nsPTZEfqdYTDi+N3vfocVZySBYcOaGT9+JP/6178AaxKosbGRgoICEhISyM7OJi0trdXx8nDEYIZT\nnLz77rv2Z2Yooa0HUTg4K3hrQgzVwjGtqMWLF/Pggw/yxRdf2N3WvXv34vP57MrRWgJ0J05DZs5t\nxowZrjFUOCreoqIiu4dmWuGmJdXe+bSHqcibN2929c7MKtNZs2Zx2mmncfHFF9trGMx1Mg9i59Cc\nE+d4NVhj1iZQnFI/ArJ55pkPwiqn85pZ+swE4Pe/n4fPV05RURGVlZVh6dM5N9YabWnztddeC6nN\nzhoi54Sv89htbW/Owwzdeb1eeyjPxFs6fPgwy5cvx+fz2auDg+dhWjtvc26LFi1i3rx5tja9Xi/v\nv/9+j2gTjuozeG2NqZPGwAHs37/f9oIM1qaz0WDKZPZvhpuMNuvq6oGzKS4+HNLYd5V2DYNSapzW\n+pOgz3K11oURL00HmDlzJitXHqSsDLKyouwbm5eXZ0/YBBN844uKijotBkOoh3RHblRw9zSUUFtr\n4TjXBZjXpoViIl2aEM1VVVU0NTXZ4bPPPfdcV6L5tsJ4OI8XaojDlDPc3pnzfODoNWytcprPhw8f\nztatW+1AcE53y1CY8pgHYmlpqWt4pbi42G4YmG2LioocE+tbgGzi4ydixXsMn5kzZ3Lffd+isREm\nTx6Az2c9DMwwYSic597a3FhH6Ko2g2ktdEywPo03mdGJ+W+GZ5z6BOwhwG9961t2rDET1ypcfXaH\nNkM5r4TCfJednc1bb73FmDFjmDFjRqtDgaY35eztP/nkk3i9XiorK6mqqgo5pOvWpuUlVlGRShcf\nYSEJp8fwrFLq/2GtSvEAS4HTgdDjIt2EEbb57/F4GDfu+wHD0D3HDBZJqAdYcIvTGbqgrd5IKAGa\n/Qb/xnwWfBwjvNzcXPbs2eMayjITZ7t27bJXoSYnJ9uLhJyTYsZzJ5zrAe7WYHut2lA4z7GoqCjs\nShs8gWtaxMbAB1+fwsLCFlEnnWPfZnzc7/BFh6PeKF7vHiorYf36L5kQIsh8WwYuOnoQjY3DiI2l\nWypuT2vT7K81wx28T/M/O9uKN+Uc+gFc7pdgXfOamhr73nZGn4DrGJ0Zew+ufx0x0MYd1/SonY0N\naFl/TE/KTGx7vV5bn05PRPOXmppqa3PkyFrKyuDTT5soKSnr8Hm2RziG4UwsY/AOlqvqSqyA6j2K\nsbLOi11ebkVyzMzs/H5bm3hq7SEdilDbtdcbCVWZzHvn9+0dx4kZJzceELNmzeLgwYOsWLGCU045\nxRbgtGnT7AnvxMREO9CX8/ydZQle9elsiXe1VRsupnIEOxe01qsy7p0xMTEkJyfj9/tJTk4OGZ44\n2FAZo3rHHQu54grYtKmK99+3EjSZxDqhfue8FhUVljYzMiCmkwO2x4o2Te/BXDejz5tuuomCggJ7\n2HP9+vXs3r2bhIQEezw9IyPDtYgrXG0GPyu6E6f2TKwm87kpr7OMRoPV1dW2Js3/UD2eYEO/Zs0a\n3nrrTcaOhT17ovn1r//EO++saqHPrhCOZBux1q97gASgRGvdao6hnsS4A3q9eygstFrLrbWeWqOj\nD7ZwWmrh0pnfhLMvZ0UwXg6bNm2iuLjYjrB68OBBO3T2unXrmDVrVotrEaps3V3JWsOcX1FRkT3O\numnTJlauXNni+/Z8uY3njBPnfTULp5qaPgbOpLx8CA0NVqt57NixdmKdtjDaHDmyhsJCaxGSaNPC\nzMMFDysZl9KCggJXWBMzjOS8Hn1Rm6YMxnXWqU+nkQr25Aom+Dyc99U0+IqLi/H5zmTPHg8ff9xk\n9+rC1Wd7hGMYNmMNsE7GWsvwJ6XUTK31ZV06cgQwrbLc3DTS09Pa2dqiq5UnkhWmJwkehsnIyGDn\nzp1hTURHmq7eA+cww/z58xk/fnxYxwxeHJafn293330+H3fffbe9WG7ChAnMnn0m110HDQ2pWOkX\na+zEOu3Fvje92UmTkjo9vn28aNP00MwQjFmEN3z4cHuBX0/S1fuwY8eODuvT6dEWHx9vT0hnZWWR\nk5ODz+ezXfRNz2DiRA8bN8KRI2Ps/YSrz/YIxzBcr7V+N/D6a+ASpdRPu3TUCFBXF0919UA8HgiE\nRw+L/lp5ukpwaIvFixdTWlrKnXfeaUejbG+SzWAqSmpqqi3g1NTUsCtQZ+6Bs7KacdbMzEzuuOMO\nXnrppXZ/H84xnRW6tLSUe+65h4wMK3R2QsK3qa9/O+zY987FbeFyvGrT2QoGuOeee+y1NcXFxWFP\nAkPXtRnuNk6C55qMN+CECRNci/Laoi13doPRJ1iu21OmWA//M8+cS1nZ/6KmpiZiuRnCMQx7lVKj\ngj7r8T6bc+LG7/dTUWGCrh0mKip0FjbhKE6/coCpU6fabnTOFc2m69vevpz/ewLnUJGzhen1ennp\npZfaHI8PF2eIDtOLysqyDMPUqTfx+eeVIWPfB2vT5/NRXm5ZhK7Mfx1vGI1OmDDBbsTk5uZ2SJ+9\nqU2whoFee+01zjnnHIqKimytRFKfw4cP57HHHsMEet61K94OlxGp3AzhGIa1WLnowJpjGA1sB9rv\nH0UQcwFzc3MZMmQIVVU/Aq7n5JOPAGIYnEMlSUlJNDY20tDQQFJSEjU1NW16aAR3fSOZIjBShJoD\nsMZZfUBkHgTOEB2mlTd2rPVdVdWIVlcjO8uQl5fH73+/lL17rQVMHs8XWOttjm+MPvfs2WPHcnJn\nzWudvq7P4B6D6Z07J5Mjqc/p06fj9XptbW7bBj/4Qfur5TtCu4ZBW5nlbZRSk4CfR+ToncDv91Nd\nXU1j4ykAbNjwCIWFk4/bbrgh1Pnn5eWxZMkS16I7Z7fcEBzMri8SPLncHR5RoXzhzVCQmTMIByt4\nayKwh/POswLhiT5D69NJsEu6oa/rM7jHYHo+kb7fwWFVRoyApCTYtw9qaxNITKxv49cdo8OOdFrr\nLUqpMyNWgjBxLtCxAriZVaVzyc1tPdDZ8YZpvXz55ZfEx8ezbNkyoqOjXSG7S0tLXUNLrQUUFJyG\nYUiL74Jbikaj0dHjAIiK2sG7777bZk7x441QPQeweg/GjTN42FP0GZqoKGuocssWS5+jRn0ZsX2H\ns/L5FsfbKGAS8FUrm3cbznUMP/vZz1i+fBzNzTBlihgFJ221TPPy8lixYoU9XmuCg7UXUPB4xswR\nVFScQFOTcn3XWkvxllv+TF4eXH75RNLTB/Zwifs2rekzLy+PtWvXurRp3FRFn62TldVLhgEYyNE5\nhkbgVeCFiJUgTJwTfIMGDUYpK+VkfHwpIC2ycHGGqS4tLXWFphZaMmCA5fVWVhZDZaXXNcEMbn96\n02MoLra8Uk455UgPl7Z/E+wV9stf/rJTq5ePJ8w8Q3m51UDOz88Pqc2OEs4cw12d3nsEOVrpiqms\n9NLUFMOwYY2MHy9GoS2CfbJNUvcJEyZwwQUX9Njq0P6As/Hh9B4ZNiybsjIv5eVD8Pv9dviSOJDS\nfwAAF3JJREFUhIQEe8IfjoY2KCmxnCHOOqt7YuUfKwRr0+nmecEFF7gWKh7v+mxtbcXgweOAE+05\nMKPNrtKqYVBKrWnjd1prfUmXj94BzIRjVVUV5eVWb2H8+H4XHLbHCe66myB7v/vd7ygvLw+rRRbJ\nFbV9mWAPJ3PeI0ZUA17Ky4dSWvq2axuD0SZARYXVeuuuGF7HCuFqsy2NHU/adDpfgHXuu3aVAidS\nWTmsxbZdoa0n631tfKfb+K7bMWsYxEe84xgfcWfydGi7RdZXKllrLfruwpxzerqVDKi+Ph142y5L\nqGvS0BDH7t0QHd1Iero0XDpCa9psi76iTegdfZ59NkRFacrLBzJ8+Gh2795ll6O7hpJ2aa1LO73n\nbsJKDWhZBKvCJvZugYQeo7U1C905zODz+bjkEli2DJqaTm1RFievvPIKu3dbyWEGD95PdPSwFtsI\nxy69oc/MTB8nnww7d8JZZ/2UF16IjBt3W4ahAJgIoJR6QWs9s8tHiwBW6sqTAHj11T/yy1/+714u\nUf/leOmGdxUzJPTppzB1KigVeruKigr27LFcVRsatmKyCwqdQ/QZHllZlmFoI4Fkhwm3r3ty5A7Z\nNaw4OVZNfeSRm3u3MP0cqWAW7T2A0tJg0CA4eBBqahIZMKDWztntDCft1OZpp8kwUlcRfVq0p8+s\nLHj1VXjppU849VRc2uws/Ua9c+bM4Z133kHrIcAQ4uLqee21J3jzTSs1YnsBqHoCaeH0T9q7P0pZ\nboGbNln+4gMGfGFPNC9atMiO5RMVFcWAAadTXQ0jRhxi2bJldurO3tanaLP/0t49Mi6rSlm9Vac2\nr7nmmk4dsy3DMEEpZZKYehyvwfJKGtSpI3aSXbt2BSILWqFUTz75MBMnZvcpYfelsgiRJSvrqGHw\n+b5wfWfWhgDExVmhWqZNG8l5503sM3oQbR67OIc6MzIis89WDYPWOjoyh4gMgwdbPuHJyWdRVQVn\nnDGoRyMoCn2Lnm4BHw2N0XKlvdHmsGGj2LvXB2iuuGIyieIXcdzSk/o02ty2DS6+2AqV0VWUWfDU\nl1FK6YMHD3LOOeeQmPgo7733Xe6+G371q94uWf/BKdTglbt9vSXZF8r+8sswYwZER/+D2NgfMXz4\ncC677DKysrKIjY3l7rvv5uyzr+Evf1mC13uQgwdTeqRcxwJ94f52hb5Q/tRUK5heXNwYYmK+5mc/\n+xk+n4/FixejtW7FXaJ1+s0cg9frJSEhgX//uxGwUiZaWbWEcOgvlSwUvV12v99PVdVe4EyamjJo\naqqnpKSENWvW2CFFEhISePnl7QCkpOwDxDCES2/f367S2+X3+/2kpXnZt8/L4cOjOXz4c1asWMEt\nt9zS/o9bIQKdjp6joqKC+nofAE8//eveLYxw3ODz+TjrrFSUasSKy+UhLS2N6dOn4/P5yM3NpaKi\ngv37rbAEVVUbe7W8wvHHqFG1gVdjiY2N5dprr+3S/vqNYSgsLCQ6OhmrYh5h3753+PDDD3u7WMJx\nQkaGj4wMBUSRnj6NuXPn2tE/CwsLA66qVu4qpbaLNoUew+fz8YMfDAcgNnYCN954IykpXeux9hvD\ncNddd1FdPRqryB/zwQebWbx4cW8XSziOGD3aSoQyefJVtlF4/vnnuf322wPZyL4NQEXFem644QZX\nrgZB6E4GD94LwIgR53bZKEA/Mgz19fXs22dWkhaTmZnJ4sWLpfIJPcakSdacljNpT01NDc3NzZSV\n7QPGAk2kpVXwK/GMEHqQ730vFQidUKoz9JvJZ8slMBuAoUN3s3HjRkncIfQYfr8freuAsZSXD+GV\nV16hoqKC2NjYwMTjOCCWuLidzJ17WYcCwQlCV/D7/ZSU+ImP/y7V1QN58cU3qKoqDQxvdo5+02M4\n/fTT8Xis1aNRUR9xxRVX2HHwBaG78fl8XHqptcT088/j+fjjjyktLWXnzp3s2bOHYcMuBCApaSer\nV6/mwgsvFH0KPYI1x5DL2LHW0rNPP9W2NjtLvzEMWkdz5Ii15Hvv3tf429/+xvz583u5VMLxRFnZ\nayjVTH39aBoarM52QkICF110ESNHWulJtN5KaWmp6FPoUTZu3Ehc3CcAHDlizXUlJCR0en/9xjDs\n3ZtGY2MssbG7gINMnjyZxx57rLeLJRxHXHrpD0lL24M1Ans6AEOHWiuhy8qsiL+JiR8BiD6FHiUn\nJ4frrhsXeHc2AF1ZvNxvDMMXX4wCIDOzgnHjxrFu3TqZYxB6nJEjywKvzgGgrKyMgoLX2bMnjaio\nJi6/fLToU+gV0tO/AkCpKQABT7nO0W8mn7/4wgTP282kSbOk0gk9igl7MHJkOZs3n4lplcXFxTF2\n7DVs3x7FsGFfkZwcw6xZok+h5zDajI2F+PgTaGgYCZwEfNnpffabWEmJidXU1ibh8WSj9XamTJnC\nc889JxVQ6HZMxbv77rt5660vqK3dBhwChgINnHDCn6mouJ6YmAeJibmVYcOGsWXLFtGm0CP4/X6K\ni4u54YYb2LdvBc3NFwDXAPkAnYqV1G+Gkmprk4iJ2UVd3Vbq6+tZv349V155ZW8XSzgOMGEvDh8+\nTG3tdmALMBA4j7S0NLS2Jp4bGwuor69n165dok2hx/D5fMyYMYO6ujqamwsCn15KWlpap/fZbwwD\nwIABr9uvs7OzeeaZZ3qxNMLxRqIdR/vFwP/LOXgwnQMHTiQqqgr4JwBpaWmiTaHHsdYtvAw0A9Oo\nrOz8471fGYaEhNUkJiYyZswYNmzYIF11oUdZuXIlmZmZeDwvA03AHBoa/gyAUk+TmBjHmDFjmDt3\nrmhT6HHee+89oqPLgXVAPPX1Szq9r241DEqp85VS25RSnymlbg3xfa5Sqkop9UHg747W9pWY+Cp7\n9rxObW0tcXFxUvGEHsfr9TJnzhwWLrwIr/clLN+NbwGHaGpaamvTxFEShJ4kPT2dJUuW4PPlBz7p\nfCy5bvNKUkpFAw8B5wFfAe8qpV7RWn8atGmRNoO0bdDUZC0WMuGOBaE3MKEwBg9ey7Bho/D744A7\nqasrIz4+nqlTp/Z2EYXjlDlz5vDOO+8QGxvLtGnP8PrrP6SpqXP76k531TOAnVprP4BSajXwIyDY\nMIQ1Y97Q8DUAe/fuZfny5WRnZ5OWltbrSTKE44uKigo7v3NU1FkkJSXZ/uINDQ0sX74cn8/Hd77z\nHU477TTRptBjfP3117Y2S0p+Snr6qeza1bl9dedQ0gigzPH+y8BnTjRwtlJqq1JqrVJqHO2gtaa2\ntpaFCxdGsKiCEB7OwGTNzc0cOnSIw4cPuz4rKSnhvvvuc6V8FITuJtGRZLy5uZldu7Z1el/daRjC\nWSCxBRiptf42sBwoaGd7m3fffZfc3FxpkQk9xsaNG5k5c2a7202cOJGXXnpJ9Cn0GH6/nyuvvJKo\nqMg80rvTMHwFjHS8H0nQUjyt9SGtdW3g9d+AWKXU4FA7S0qyYuFHRUWxYMEC0tPTu6XQgtAaOTk5\neDyeVoOTxcfHk5GRwRtvvCHOEUKP4vP5uPLKKxkxInhQpnN05xzDe0CGUsoH7AYuB+Y4N1BKpQL7\ntNZaKXUG1krsA6F2lpqaSmxsLDNmzMDj8eD3+6U1JvQKMTHuahMfH09MTAzXX389KSkpVFZWimEQ\neoVIhXrvth6D1roRuAl4DfgE+B+t9adKqf9USv1nYLOfAB8ppYqBZcDs1vZXUlJCdHS07QooRkHo\nLZypE5VSNDQ0UFNTw7p16wDRptA7+P3+iDVIujWIXmB46G9Bn/3J8fph4OFw9jV8+HCXm2phYaF4\nJAk9gnMSOT09nfj4eMCKd5+amkppaalLn6JNoSdx6tNoMy0tjeTkZLZv396pffablc9XX321a+GQ\nTOwJPYV5yJtu+syZMxk3bhynnnoqzc3NJCUlcdlll9n6FG0KPU1lZSV+v9/W5ty5c+152c7QbwyD\nrCYVehMTqGzevHl4PB5mzZpFVVUVZWVlrmEkQehpQmnT4/FQUVHR6X32m3wMTtLT0yksLASQLrvQ\na5g1DaGGOUG0KfQuzjU3HaVfGoZ58+b1dhEEgZkzZ7JmzRqmT5/eYphTEHqbmTNnsnTp0k79tl8a\nBkHoSUwilMrKSiorK0lOTqaqqsrutgtCb7Jx40a2bbNWOcfHx9shWroy/N5v5hicSJgBoSdxjuFW\nVVWxaNGiNrcXfQo9SU5ODvPmzWPevHldyvPspN/0GEwrDaC4uBgQf3GhZzEP/Pz8/F4thyAEY3q1\nkaLf9BicrbQZM2aIURB6jW+++abN70WbQk/j8/nIzs6O2P76jWEQhL7CoEGDersIguAiuMeQnJzc\npf31G8NgXAAFobcwPQHz31S+rlZCQegqZh7MkJ2d3aVAo/1mjsG55NuM8WZlZZGTk9N7hRKOK5yT\nyunp6fh8PoqKihgyZAhVVVW2gcjPz8fr9ZKdnS3DSkKPEBy2Bbo2pNlvDMO8efPIy8vjtttu6+2i\nCMcppqI51ykUFRVx1VVXkZeX1663kiB0F2YxZVFRUUTWefWboSRBEAShZ+g3PQZB6CsEd9vN/Jfk\nCBH6ApFIKSuGQRA6SKgYSEVFRWIUhD5BJGJ0yVCSIAiC4EIMgyAIguBCDIMghMn8+fN54oknuPDC\nCyOWW1cQIkUk9dlv5hjMBJ/Euhd6ix07dlBaWkppaSnz58/n3nvvdU3yiTaF3iRYn88++2yn99Vv\nDENubi5FRUUS617oNRITEwGYPHkyjz32GF6v1zYAok2htwnWZ1eQoSRBCJOVK1cybtw41q1bh9fr\n7e3iCIKLSOpTDIMghInX62XWrFliFIQ+SST1KYZBEARBcNFv5hgKCwtdq0xlgk/obVpbAS3aFPo7\n/cYwyMSe0NcQAyAcq8hQkiAIguBCDIMgCILgQgyDIAiC4EIMgyAIguBCDIMgCILgQgyDIAiC4EIM\ngyAIguBCDIMgCILgQmmte7sM7aKU0v2hnMKxiXOFszOvsyxwE/oCbelz9OjRaK1VR/cphkEQBOEY\nRSnVKcMgQ0mCIAiCCzEMgiAIggsxDIIgCIILMQyCIAiCCzEMgiAIggsxDIIgCIILMQyCIAiCCzEM\ngiAIggsxDIIgCIILMQyCIAiCCzEMgiAIgotuNQxKqfOVUtuUUp8ppW5tZZsHA99vVUpN7M7yCIIg\nCO3TbYZBKRUNPAScD4wD5iilxgZtcyEwRmudAcwHHumu8ghHKSws7O0iHDPItYwscj37Bt3ZYzgD\n2Km19mutjwCrgR8FbXMJ8CSA1noT4FVKpXZjmQSk8kUSuZaRRa5n36A7DcMIoMzx/svAZ+1tc1I3\nlkkQBEFoh+40DOEmUAiOFS6JFwRBEHqRbkvUo5TKAe7SWp8feP8roFlrvdSxzaNAodZ6deD9NuB7\nWuu9QfsSYyEIgtAJOpOoJ6Y7ChLgPSBDKeUDdgOXA3OCtnkFuAlYHTAklcFGATp3YoIgCELn6DbD\noLVuVErdBLwGRAOPa60/VUr9Z+D7P2mt1yqlLlRK7QRqgGu6qzyCIAhCePSLnM+CIAhCz9GnVj7L\ngrjI0d61VErlKqWqlFIfBP7u6I1y9geUUiuUUnuVUh+1sY3oMkzau56izfBRSo1USm1QSn2slPq3\nUmphK9t1TJ9a6z7xhzXctBPwAbFAMTA2aJsLgbWB12cCG3u73H3xL8xrmQu80ttl7Q9/wHeBicBH\nrXwvuozs9RRthn8t04DswOsBwPZIPDf7Uo9BFsRFjnCuJbR0FRZCoLX+J3CwjU1Elx0gjOsJos2w\n0Frv0VoXB15XA58Cw4M267A++5JhkAVxkSOca6mBswNdy7VKqXE9VrpjD9FlZBFtdoKAB+hEYFPQ\nVx3WZ3e6q3YUWRAXOcK5JluAkVrrWqXUBUABcGr3FuuYRnQZOUSbHUQpNQB4Hrg50HNosUnQ+zb1\n2Zd6DF8BIx3vR2JZtra2OSnwmeCm3WuptT6kta4NvP4bEKuUGtxzRTymEF1GENFmx1BKxQIvAE9r\nrQtCbNJhffYlw2AviFNKxWEtiHslaJtXgJ+CvbI65II4of1rqZRKVUqpwOszsFyXD/R8UY8JRJcR\nRLQZPoHr9DjwidZ6WSubdViffWYoScuCuIgRzrUEfgLcoJRqBGqB2b1W4D6OUmoV8D1giFKqDLgT\ny9tLdNkJ2rueiDY7wjnAVcCHSqkPAp/dDoyCzutTFrgJgiAILvrSUJIgCILQBxDDIAiCILgQwyAI\ngiC4EMMgCIIguBDDIAiCILgQwyAIgiC4EMMgdBtKqZOUUi8rpXYopXYqpZYFVmmG2jZXKbWmle/+\nqpQapJRKVkrdEOaxQ4UFaGt7f0+urlVK/Y9S6pQQn89TSi3v5D7/qpQaFIGy2fdCKXWJUuo3Xd2n\n0L8QwyB0C4EVmS8CL2qtT8WKdTMA+F2IbdtcaKm1vkhr/Q2QAtwYZhE6ukBH00MRPZVSY4AkrfXn\nkdyv4zpFkleBma0ZdOHYRAyD0F38AKjTWptwv83AYuBapZQn0DJ+RSn1OrAe68GcrJR6NZBg6BFH\nWAS/UuoE4B7glEDylqVKqSSl1Hql1PtKqQ+VUpe0VaBAiJBtSqmnlVKfKKWeU0p5HJv8wrGvzMBv\nzlBKva2U2qKUekspdWrg8/FKqU2Bsmw1rX+l1FWOzx9VSoWqY7NxhChRSl2jlNqulNoEnO34fKhS\n6nml1ObA39mBzwcopZ4IlHOrUurHjus02HGeTwT2+4xSalqg/DuUUqe3dW5OAvftHWBaW9dWOMbo\n7UQT8nds/gELgftDfL4F+BYwDysUsDfweS5Qh5VcKAr4BzAz8N0uYDCQjiO5C1a4j4GB10OAzxzf\nHQpxbB/QDJwVeP84cIvjGD8PvL4B+HPg9UAgOvD6POD5wOvlwBWB1zFAAjAW64Fvtv+/wNUhyvE3\nYFLg9TCgFDgBKyzEv4AHA9+tBM4JvB6FFQ8HYKnz2jquoblOPuAIMB6rF/QeVlgUsGLzv9TOueUC\naxz7vwZY2tuakr+e++szsZKEY462hnJ04G+d1rrS8flmrbUf7Hg6U7CiRhqCh3qigN8rpb6L9cAf\nrpQ6UWu9r41jl2mt3wm8fhrLgN0XeP9i4P8W4NLAay/wVGD4R3M0vtjbwK+VUidhDZftVEqdC3wH\neC/Q2fEAe0KUIR34OvD6TGCD1roicN7/w9EQ0+cBYwP7AhiolEoCzsUKjAhA0DU07NJafxzY58dY\nvTKAf2MZjlDn1tpw0W7g/Fa+E45BxDAI3cUnWMHQbAITo6Ow0o5Oxgro5cRpTBTWw74trsTqKUzS\nWjcppXZhtdzbIvgYzvcNgf9NHK0b/wd4XWv9Y6VUOlAIoLVepZTaCFwMrFWBAIXAk1rr29spgzm2\nKY8K+lw7Xp+ptT7s+mFghK2d/Tc4XjcDhx2v2zy3EETR8TkboR8jcwxCt6C1fh1IVEpdDaCUisZq\nmT+hta5v5WdnBMbHo7BaxP8K+v4Q1vCHYRCwL2AUvo/VEm+PUcoKPQxwBfDPdrYfhNViBkdUSqXU\nyVrrXVrr5cDLWMNjrwM/UUoNDWwzWCk1KsQ+S7GGkAA2A98LbBsLXObY7h9YPRpzzG8HXq4Dfu74\n3NvOOXTo3EJghruE4wQxDEJ38mPgMqXUDqwk5bVYIYHh6HASjvfvAg9h9TY+11q/5PiOwHDLW0qp\nj5RSS4FngMlKqQ+Bq7Hy3Tr3F4rtwM+VUp8AycAjIbZ3lu1erOGqLVhzGubzWUqpfysr1PF44Cmt\n9afAHcA/lFJbsR7saSHK8C+sHhNa66+Bu7AmeP8FfOzYbmHg/LYGhoNMr+S/gJTAdSjGmhMIJvj8\ng8+vrXML3v4M4M0QxxCOUSTstnDcoKycuGu01t/q5XKcDCzXWl/Um+UIh0DvbQswWWvd2NvlEXoG\n6TEIxxu93hLSWpcAh1SIBW59kIuxvJXEKBxHSI9BEARBcCE9BkEQBMGFGAZBEATBhRgGQRAEwYUY\nBkEQBMGFGAZBEATBhRgGQRAEwcX/B02Vy3uZs7G/AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x11936c110>"
]
},
{
"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 0x1194bb3d0>"
]
},
{
"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 0x117666dd0>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solid line is residual median: -0.0122890252007\n",
"Rank-based standard deviation, sigmaG = 0.0634401456816\n"
]
}
],
"prompt_number": 60
},
{
"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.\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: Thu, 05 Mar 2015 Prob (F-statistic): nan\n",
"Time: 20:35:09 Log-Likelihood: 382.41\n",
"No. Observations: 388 AIC: -762.8\n",
"Df Residuals: 387 BIC: -758.9\n",
"Df Model: 0 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"const -0.0043 0.005 -0.932 0.352 -0.013 0.005\n",
"==============================================================================\n",
"Omnibus: 333.466 Durbin-Watson: 2.057\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 12206.953\n",
"Skew: 3.363 Prob(JB): 0.00\n",
"Kurtosis: 29.643 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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ZIScJMzMr5CRhZmaFnCTMzKyQk4SZmRVykjAzs0JOEmZmVshJwszMCjlJmJlZ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\nrND/B5FW1j9ofkijAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x1176b12d0>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Number of outliers detected: 5\n"
]
}
],
"prompt_number": 61
},
{
"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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pA6MuXbrQo0cP7rnnHpYvX560GJJ68ZV0IHAa8DgQu51R3HC8M4FnzGybmS0H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\nrghPDs4554rw5OCcc66I/w8cQ/aYhm7hZwAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x118196510>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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DODMc6Q2ApEmS/i/H81ybvYjHMzrxJinPaCGOwNjbzDa7BTPbBOyfy0nMLFOy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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x116bcbd50>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Best number of Fourier terms: 10\n",
"Relative Bayesian Information Criterion: 544.796832514\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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afwt09ds5HA2WeBaMi8E4GgJBFMw9/jwst+ANmGwF/DpO+47AIklfAHv8fWZm\nZ1dJUoejjhHPgmnatCn79u2jpKSEtLS0GpbM4agZ4ioYv+bXQDN7E9gKZAboc0LVxXI46j7xFIwk\n0tPT2bNnT0wrx+Go68RVMGZWIulSKlBQMtokZQ5HQySeiwwOxGGcgnHUV4K4yD6V9DBeJlkR3qBL\nM7N54Y0kzTKzkZIKKT8Q08ysVVIkdjjqCPEsGHBxGEf9J4iCOQpPYdwdsf/k8A0zG+n/TVg52eFo\nCCRSMC5V2VHfCaJgrjGzFeE7JPWtJnkcjnpDUBeZw1FfaRSgzStR9r2cbEEcjvqGc5E5GjrxqikP\nxisP00bS+fixF7w05WY1I57DUXdxFoyjoRPPRTYQOAto7f8NsQP4SXUK5XDUB3bt2kXbtrHHJLsY\njKO+E6+a8lRgqqTvmdlnVbmIpMfNzCklR4Ni165ddOvWLeZxZ8E46jtBYjA/90fyAyCpraT/VPA6\nkxI3cTjqF4lcZC4G46jvBFEwQ81sa2jDzLYAR1fkImYWrzhmKZJGS1oiabmk26Mcz5S0TdJX/vL7\nisjhcNQkLk3Z0dAJkqYsSe3MbLO/0Q6IWTxJ0ht4yQChWTDLrMeqSeaXpXkYOA3IBeZImmZmiyOa\nfuTqmjnqAjt37kyoYJwF46jPBFEwDwKfSXoJT1H8EPhjnPYrgc7As377S4E8YEqC6wwHss0sB0DS\nZOAcIFLBRE7f7HDUSnbt2uWyyBwNmoQKxsyekfQlB0bun2dmi+KcMtLMhoVtT5P0pZndlOBS3YE1\nYdtrgRGR4gDHS5qPZ+XcmkAWhyNluHEwjoZOEAsGoB1QZGZPSuooqY+ZrYzR9iBJ/czsOygd9R+k\nml+QCcrmAT3NbKekM4HX8dKpyzFhwoTS9czMTDIzMwN073AkjyDjYFwMxpEqsrKyyMrKqtZrJFQw\nkibgzVJ5CPAk0BTP/TUyxim/Bj6UFFJAvYGfBpAlF+gZtt0Tz4opxcx2hK2/LenR8PhQOOEKxuFI\nBUGC/EVFRTUokcNxgMgX74kTJyb9GkEsmPPwCl5+CWBmuZJaxmpsZjMkDcRTSABLzGxPrPZhzAUG\nSOqNNxvmxXjxm1IkdQY2mplJGg4omnJxOGoDQVxkBQUFNSiRw1GzBFEwe8xsv+TF1iU1j9fYP34z\n0MvMfiJpgKRD/EnLYmJmxZKuB97By1J7wswWS7rOPz4JuBBvXE4xsBO4JID8DkdKcKViHA2dIArm\nZUmT8GrdTAKzAAAgAElEQVSS/RS4Bvh3nPZP4lk7x/vb6/AKZsZVMOC5vYC3I/ZNClt/BHgkgMwO\nR8px42AcDZ0gWWT3SzodrwbZQOAPZjYzzin9zOwiSZf45xeFrB+HoyHhLBhHQydoFtk3QAZeptc3\nCdrukVT62iapHxAkBuNw1BtKSkooLi6madOmMdu4NGVHfSdhqRhJPwZmA+cDFwCzJV0b55QJwAyg\nh6TngQ+AcmVfHI76TMg9Fs96dxaMo74TxIK5DTjKzAoAJLUHPgOeiGwoqRHQFk8RHefv/pWZbUqO\nuA5H3SCRewxcDMZR/wmiYPKBwrDtQn9fOfxss9vM7EUCBPUdjvpKogA/OAvGUf8JomC+Az6XNNXf\nPgdYIOkWvOKVf41oP1PSrcCLQOkoMjdexdGQCKJgXAzGUd8JqmC+40Apl6n+eosY7S/xj/8ybJ8B\nfSspo8NR53AuMocjWJryhNC6X6p/q5ntj2wn6Ydm9jJwipmtSKqUDkcdI4gFc9BBBzkF46jXxMwi\nkzRe0mB/PV3Sh0A2sEHSqCin/Nb/+0ryxXQ46hZBLJiMjAx27txZQxI5HDVPPAvmYuBuf/0qvHlY\nOuINtnwGiBxsWSBpJtDXn3QsnJgTjTkc9RFnwTgc8RXMHjMLxV1GA5PNrARYLCnaeT/Am0r5v8AD\nlJ0YLEgpfoej3hA0yL9r1y7MLO54GYejrhJXwUg6HNgAZAK3hh0rZ/ub2V68bLORZrYxqVI6HHWM\nIC6yRo0a0bRpU/bs2UOzZs1qSDKHo+aIN5L/Jrx4ylLgb6HAvaQxeBN/RcUpF4cjmAUDLg7jqN/E\ntGDM7HMOzOkSvv8t4K3qFMrhqOvs3LkzkII56KCD2LlzJ+3atasBqRyOmiVhLTKHw1Fxdu3aldBF\nBgfiMA5HfaRGFIyks2riOg5HbSGoiyxkwTgc9ZG4CkZSI0nHx2sTkGOS0IfDUWcoLCykZcuYM4uX\n4iwYR30mroLxR+w/WtWLmNn4qvbhcNQltm3bRqtWrRK2cxaMoz4TpBbZe5IuBF4NGxcTE0kXUH7c\nyzbgG5dh5mgobN++PZCCcRaMoz4TJAbzM+AlYK+kHf6yPU77a4B/A5f7y+PAHcD/JF0Z70KSRkta\nImm5pJiTlEk6VlKxpPMDyO9w1DhBFYyzYBz1mSDFLmNVTY5FE2CwmeUBSOqMN7p/BPAxXpmZckhK\nAx4GTgNygTmSppnZ4ijt/ow3a6Yb/uyolQRVMC1atKCwsDBhO4ejLhJkyuRGkn4k6S5/u5ek4XFO\n6RlSLj4b/X0FwN445w0Hss0sx8z2AZPx5p6J5Aa8AaBulkxHrSWogmnVqhXbt8dzCDgcdZcgLrJH\nge8Bl/nbhcQP/H8o6S1JV0kaB0wDsiQ1B7bGOa87sCZse62/rxRJ3fGUzj/9Xa7GmaNWsn37dlq3\nbp2wnVMwjvpMkCD/CDM7StJX4M1MKalJnPbXA+cD38dTAE9zIEHg5DjnBVEWDwF3mJnJqw4Y00U2\nYcKE0vXMzEwyMzMDdO9wJIegWWStW7dm40aX++KoebKyssjKyqrWayhRYpik2cDxwFxf0XQE3jWz\no5IqiHQcMMHMRvvbdwL7zezPYW1WcECpdAB2Aj8xs2kRfQVJeHM4qoV9+/bRrFkziouLE1ZJnjRp\nEvPmzWPSpEk1JJ3DER1JmFlS49pBXGT/AKYAnST9CZgF3BursaQL/Cyw7QGzzkLMBQZI6i2pKd58\nNGUUh5n1NbM+ZtYHLw7z80jl4nCkmh07dtCqVatAJfhbtWrFtm3bakAqh6PmCZJF9qykL4FT/V3n\nRGZ2RfAXYGyCNtGuUyzpeuAdIA14wswWS7rOP+5e8Rx1gqABfoAOHTqwadMmcnJyKCgoYNiwYdUs\nncNRcyRUMJLuAT4CnjSzogB9bqiocglhZm8Db0fsi6pYzOzqylzD4ahuKqJgunfvTm5uLpdeeimf\nf/45xcXFpKWlVbOEDkfNECTIvwIvg+zvknYAnwCfmNnrMdrPlfQi8DoH0pLNzF6rsrQORx2gIgqm\nW7duLF26lLZt29K/f3/mz5/P0UcfXc0SOhw1QxAX2X+A/0jqghcXuRW4Dog1ALM1sAs4PWK/UzCO\nBsG2bdsCpSgDpe1GjhxJ8+bNWbx4sVMwjnpDEBfZE8BgIA/4FLgA+CpWezMblyzhHI66SEUsGElM\nmTKFwYMH8/zzz7NkyZJqls7hqDmCuMja+e22ApuBfH+kfVQkZQDXAocCGfjjW8zsmipLm0Q++OAD\n0tPTGTlyZKpFcdQzKqJgAM4991wADjnkEKZOnVpdYjkcNU4QF9l5AJIGA6PxRuqnmVmPGKf8F1js\nt50IXOFv1ypOPfVUunTpwvr161MtiqOeUVEFE6Jnz56sXbu2GiRyOFJDEBfZWcAJ/tIG+AAv0B+L\n/mZ2oaRzzOxpSc/judZqDXl5eTRv3pyCggL27dtHkybxChM4HBWjsgqma9eu7oXHUa8IMtByNPAl\ncIGZDTazq/3AfyxCmWPbJB2Op5Q6VlHOpLJo0SKOOuooevToQU5OTqrFcdQztm7dGjjIH05Iwbgq\nFI76QkIFY2a/xBsHM0zSWEmdEpzyuKR2wO/xRuIvwht8WWtYsmQJgwYNon///ixfvjzV4jjqGVu2\nbKFt27YVPq958+Y0adLEFb901BuCuMguAu7HUzICHpb0GzN7OVp7M3vcX/0I6JMsQZPJ0qVLOeSQ\nQ0hLS2PlypWpFsdRz9i6dStt2rSp1LmhuGBlLCCHo7YRxEX2e+BYM7vSzH4EHAv8oXrFql6WLVvG\nwIED6dSpE5s2uWllHMmlshYMuDiMo34RRMGIspN7FVDHZ5Jcvnw5AwYMoGPHjuTn56daHEc9wykY\nh8MjiIKZAbwjaZykq4HpRNQLq0vs27eP1atX07dv39JCgw5HMqmKi6x9+/Zs3rw5yRI5HKkhyDiY\n30gKTSAGMMnMpgS9gKRjgVwzW1dJGZNKTk4O3bp1Iz093VkwjmqhKhZM27Zt2bJlS5IlcjhSQ0wF\nI2kgXnC/P7AA+I2ZVWYU2A3A4ZKWmdnFlRMzeYTcY+CVSncKxpFMdu/eTUlJCQcddFClzm/Xrh1r\n1qxJ3NDhqAPEc5H9B3gTr/bYPODvlbmAnxxwFPCTypyfbCIVjHOROZJJyD0WZLKxaDgLxlGfiOci\naxGWcrxEUswCl+FIagRcDvQxs7sl9QK6mNkXVZQ1KWRnZ5ezYMys0g8EhyOcqrjHwCkYR/0ingXT\nTNLR/jIMyAitS4pXT/xR4Ht4c8gAFPr7agXLli0rVTDNmjUjPT2dHTt2pFgqR32hqgqmXbt2Lsjv\nqDfEs2A2AA/G2T45xnkjzOyokMVjZpsl1YpiX2bGvHnzOPLII0v3hdxklakd5XBEUpUMMnAWjKN+\nEVPBmFlmJfvcK6l0zldJHYH9lewrqaxYsYJmzZrRvXv30n2hTLJ+/fqlUDJHfcG5yByOAwQZB1NR\n/gFMATpJ+hMwC7g3yImSRktaImm5pNujHD9H0nxJX0n6UtIpFRHss88+47jjjiuzz2WSOZKJc5E5\nHAcIMuFYhTCzZyV9CZzq7zrHzBLOB+NbPQ8DpwG5wBxJ0yLOfc/MpvrtD8dTZP2DyvbGG28watSo\nMvs6duzoMskcSaOqLrKMjAz279/P7t27adasWRIlczhqnqRbMJL+AbQ1s4f9JehkY8OBbDPL8WfM\nnAycE97AzIrCNlsAgU2PnTt3MmPGDM4777wy+50F40gmVbVgJDk3maPekFDBSGok6UeS7vK3e0ka\nHueUL4HfS1oh6QFJxwSUpTsQPsJsrb8vUp5zJS3GK1dzY8C+efPNNxk+fDgdO5admsYpGEcyqaqC\nAecmc9QfgrjIHsUL0p8C3M2BtOOoisPMngKektQeOB/4i6ReZpbIlRVoliUzex14XdIJeNMzHxKt\n3YQJE0rXMzMzeeGFF7jsssvKtevYsSPZ2dlBLu1wJKSqLjJwgX5Hcpg+fTr//ve/ee2116Iez8rK\nIisrq1plCKJgKpt23B8YBByMN+lYInKBnmHbPfGsmKiY2SeSGktqb2YFkcfDFcyWLVv44IMPeOqp\np8r14ywYRzJJhgXTUBXM9OnTadq0KaeddlqqRakXvPTSS0yZMoWcnBx69+5d7nhmZiaZmZml2xMn\nTky6DEFiMBVKO5b0F0nL8aydb4FhZnZWgOvMBQZI6i2pKXAx3oyY4X33kz/kPjTYM5pyieS9997j\nhBNOiDqJk1MwjmTiXGSVY/Xq1Vx88cVcdtllfPFFrSj6Uef57rvvaNy4MUuWLEmZDEEsmMi04wvx\nJiGLxXfA98ysQk9tMyuWdD3wDpAGPGFmiyVd5x+fhFcX7UpJ+/BcdZcE6XvOnDnl0pNDuCwyRzJx\nLrLKMX36dC644AJGjBjBfffdF9Ot4whOdnY2Y8aMYenSpYwePTolMgQp1x8o7VjSYH//XKCXX4Ms\nvJ95Aa71NhFzzfiKJbT+F+AvifqJZO7cudx2221RjzkF40gmzkVWOebOncvw4cO55JJLuP32212a\ndhXZv38/+fn5nHjiiSxdujRlcsR0kUlqF1qAPOAFf8nz90Vys//3wRhLyli+fDmDBg2KeqxNmzYU\nFRWxZ8+eGpbKEcmKFSsYPXo0GzZsSLUolaKkpITCwsIqlx1qiC6y0P9o27ZtOeKII6o9+Fzf2bx5\nMy1btmTIkCEsW7YsZXLEs2DmET+zq0/4hpmFyvGPNrPd4cckpexVZPfu3WzcuJEePXpEPd6oUSM6\nduzIxo0b6dmzZ9Q2jurDzBg3bhy7d+8mJyeHL774gueff56bb7458cm1jM2bN9O6dWvS0tISN45D\nQ7RgVq5cSZ8+3iPlxBNPZPbs2Slz69QHNm3aRKdOnTjkkENqpwVjZr3NrE+sJU6f/wu4r0ZYtWoV\nPXv2pHHj2Lq0c+fObNy4sQalcoSYM2cOWVlZ9OjRg8GDB/Ovf/2LBQsWpFqsSrFhwwa6du1a5X4a\nmoIpKSlh/fr1pS+BQ4cOZf78+SmWqm6zceNGOnXqRK9evSgoKKCoqCjxSdVAwhhMjNL824BVZlYc\n1q4r0A04yD9HeBZQK6By0/slgfA3o1h06tSJvLy8GpLIEc6MGTO46KKLuP/++wGYPXs2jz32WIql\nqhzr169PioJpaC6ygoICWrduTZMm3uiHoUOH8rvf/S7FUtVtNm7cSMeOHWnUqBH9+vVj+fLlZarI\n1xRB0pQfBWYDj/vL58ArwDJJZ4S1Ox14AG/0/YP++oN4sZnfJlHmCrFmzRp69eoVt03nzp2dgkkR\nc+fOZcSIEaXbgwYNYvny5SmUqPLUJgtmz549vPjii1WWpSbIy8ujc+fOpdsDBgxg/fr1FBYWplCq\nuk1IwQApdZMFUTDrgCPNbJiZDQOOBFYAowjL6DKzp83sZOBqMzs5bDnbzFKWc7hmzZqY8ZcQTsGk\nji+//JJjjjlQFKJVq1YUFxenzKSvCuvXr6dLly5V7icZCuaVV17hkksuYe7cuVWWp7oJuXNCNG7c\nmMGDB/PNN9+kUKq6TUFBAe3btwdqv4I5xMwWhjbMbBEwyMy+I0oSgJm9ImmspNsk3RVakihzhVi7\ndm3C4L1TMKlh27ZtbNu2jYMPPrh0nyS6dOnC+vXrUyhZ5UiWi6xt27Zs3rwZs0DVk6IyZ84cAGbN\nmlVleaqbSAsGPDdZXY3F1QbCFczAgQNTlkkWRMEslPRPSSdJypT0KLBIUjqwL7KxpEnARXiFKOWv\nHxzZrqZYs2ZNQgXTq1cvVq1aVUMSOUIsX76cAQMG4BdnKKVr1651MlU5WS6y9PR0mjZtWiUrbuHC\nhZx99tl1wgqItGAAjjjiCBforwJ1yYK5Cm90/k3Ar/DcY1fhKZdoE34db2ZXApvNbCJwHDEKUtYE\na9euTegi69u3LytWrKj0NXbv3s1zzz1XpT4aIsuWLWPAgAHl9nft2rVOWjA5OTkJ431BqaqbbO3a\ntZxwwgmsXr06KfJUJ6GU2nCGDh1aJ5RjbSWaBVMVi7iyxFUwkhoD083sATM7z18eMLOdZrbfzHZE\nOW2X/3enpO5AMVB1x3QlMLNAFkxIwZgZW7duZebMmYG/DDPjwgsv5KGHHuKUU06huLg48UkOwLNg\nBg4cWG5/XXSRmRmLFi1i8ODBSemvKplkod/9iBEjWLduXVLkqU7y8/Pp0KFDmX2HH344CxYsSMlD\nsT4QrmDatWuHpJSkvsdVMH4a8n5JFSmu9KaktsD9eHPD5OBVAKhxtm7dSlpaWsKR1W3btqVx48bk\n5eVx8cUXc/rpp/P222/HPSfEV199xcKFC/nf//5H+/bt+fTTT5MheoNg2bJlURVMXbRg1q5dS/Pm\nzWnXLlqRi4pTFQtm+/btSGLw4MHk5uYmRZ7qJJqC6dChAy1atKgTFlhtpKCgoMw97d27Nzk5OTUu\nRxAXWRHwjaT/SPqHv/w9VmMzu9vMtpjZq0BvvISAPyRJ3goRxD0W4thjj2X8+PGsXr2a++67j6lT\npwY678UXX+Tyyy+nSZMmnHnmmbz//vtVEblBUZ9cZJ999hlHHx1tyFjlqIqCyc3NpXv37rRv355d\nu3axc+fOpMlVHURTMOAGXFaFcAsGUqdgglRTfs1fwilnt0q6IGy/wttIIhWpykHcYyHOPvtsrr/+\neqZNm8bAgQM59dRTMbNyAehIPvroI/785z8DcNhhh/HKK69UWe5I9u7dS5MmTRLKUpcwM5YuXcoh\nh5QPz9VFBTNt2jTGjh2btP6q4iILJRtIolu3bqxbt47+/RPN95c6YimYY445htmzZ3P22WenQKq6\nS3FxMYWFhWWqetdaBePPUBmEs4hfu6xWK5jrrruOI488kuOPPx6AZs2aMX/+/LijX4uKivjmm284\n9thjARg8eDCLF5crNF1lhg4dyumnn87f/x7TcIzK3r172bJlS7kU0NrAhg0bSE9Pj+pS6tKlS53K\nItuyZQtvvvkmf/3rX5PWZ1UsmPAHdvfu3cnNza2TCiYzM5M//CElzo86zebNm2nTpg2NGh1wUPXp\n04fvvvuuxmUJUipmIPAn4FAgw99tZtY3vJ2ZjUu6dFWkIi6yxo0bM3LkyNLtsWPH8tZbb8VVMHPm\nzOHwww/noIO8SjgDBw4kOzs7kOUTlO3bt7N06dJKFVC88cYbeeyxx9i/P+b8cCkjlvUCngVTm4PT\nRUVFrFq1ikMPPRSAZ555hh/84AflMqGqQrIUTMiCqa3s37+fzZs3l3HnhDj++ONZsGABhYWFtGjR\nIgXS1U0i3WPgWTDvvfdejcsSJAbzJPAvvGywTOBp4LlYjSV1kfSEpBn+9qGSrk2CrBWmIhZMJGPG\njOHNN9+M22b27NllJjLLyMggIyODrVu3Vuqa0Vi0aBFDhgxhxYoV7NtXbthRQvnMjO3btydNnmSx\nbNmymAqmY8eObN26lb1799awVMG46qqrGDJkCB999BFmxqRJk/jZz36W1GtUxUW2adOmchZMbWXb\ntm00b968tA5ZOBkZGQwbNswlzlSQWAqmtgb5M8zsPUBmtsrMJgBj4rR/CngXr/AlwHLg11URsrJU\nRcGceOKJLF68mLy8PJ599ln+8Ic/lEuZnD17dpk6WpD8wpkrV65k8ODBdOjQoUJxiaKiIpYtW8ah\nhx5aLW67qhLPgklLS6u1BUg3b97Mu+++yxNPPMEdd9zBvHnz2LNnDyeccEJSr1NVCyZUh6q2K5hw\nZRiNzMxMPvrooxqUqO4TTcEcfPDB5OTk1HjadxAFs1tSGpAt6XpJ5wPN47TvYGYvAiUAZrYPz/qp\ncSriIoskPT2ds846i9tvv52bbrqJyZMnlyseGE3BJLv0f6gadPfu3Vm7dm3g8z799FOGDRvGwIED\na+UDZunSpVFTlEPU1kD/rFmzOO6447jqqqvIz8/n2muv5dJLL016AkZVLJi65CKLFX8JcdJJJ7nJ\nxypINAXTpk0bGjduXONVuoMomJvwyu3fCBwDXIE3kj8WhZJKP52k4/DK+9coQQdZxuOmm27ihRde\n4O9//zv33nsvjz/+eOmxtWvXsnfv3nJTAST7zTsnJ4c+ffrQo0ePCimK6dOnc+qpp9K5c+eYAfNP\nPvmECy64gBkzZiRL3MAsXLiwNIYRjdqqYL7++muGDRtGWloaDz74ILt27eLHP/5x0q+TLAVT2y2Y\ncGsrGiNGjODrr7+mpKSkQv025AGa0RQMpMZNllDBmNkXZrbDzNaY2TgzO9/MPo9zyi3AG0BfSf8D\n/ounnBIiabSkJZKWS7o9yvHLJc2XtEDSLElDY/W1efNm0tPTqxQcHDZsGHv27OGyyy5j7NixfPXV\nV6X/rCHrJfLNNdmFM3Nzc+nRo0dMC2b16tXl/vmWL1/Os88+y7XXXkuXLl2iyrNnzx4uuugihg4d\nytVXX12j8Y5t27axadMm+vXrF7NNbX3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nnnsYP358SMfffPPNXL582efDZfXq1XTv3r1g\nLJKTk33GVJsxYwb79+/nr3/1XO/bpk0bJkyYwGuvvVYoG6X3Qs+SnuCHwhrMpUuXWLduHZMmTfLr\nXedPwHTq1ImpU6dSr1494uPjw07iFchE5nIAAEtjSklJ4dKlS0W+sQdDMGt5cnJy+Pnnnz1+MwMH\nDgzL/TdSvPPOO/Tp08dngjUXcXFxHD16lLNnz/qtk5eXx5dffknv3r1DOr+IkJiYWGKBQEMVMMEw\nEbgbK83yX+3NuWTlQVLaAsbfw9rl9dG2bduAk235+fnk5OR4aBq1atWiWrVqHm/hLipVqsTkyZML\nCR7wNJEdOXKEhg0bFqoTKQ0mLS2N5ORkGjduzPTp0z1+/MEgIrRr185nKJvNmzfTseMVR8Lk5GQ2\nb97soRnm5+czZcoU5s6d69O8NW7cOJ5+urAF15eAKWkNpm7dupw8ebIgHtnOnTupW7cu3bp1IzMz\n0+d8kz8B407//v1ZtsxvlKWAuAeR9dZg3B0A6tatS8OGDdm2bZsjAiaYtTxbtmyhbdu2HnMQAwcO\n9KsBlySffvoprVu3ZtasWUyePDlg3ejoaBISEgKashYvXkxiYmJYWqG/F7FIEKqAeayoCqq6ytcW\nXvfCJxKLLIPF38P67NmzZGRk0LVr1yK9OVzeQN4Lpnbu3Mn7778fUn/cJ/mPHj3q86asWbMm586d\ncyR0hTvp6em0b9++WG20a9fO5xvXli1bPNp2TRq7u2F+9dVXNG3aNGDuGV94C5jSMJFVqFCBRo0a\nFZjq1q9fT5cuXahatarPhbEXLlzgl19+oVq1agHb7dmzZ1hZIvPy8jhz5kyBtle7dm1yc3MLvPy8\nhfAdd9zBZ599xpo1azxWjIeDy4MyEGlpaYXutV//+tdERUWxa9euYp2/OLz99ts89dRTzJgxg337\n9gVlvi/KTDZr1qyw03SXKQEjIlVE5N9F5FNgvIj8HxEp9CooIin233MictZrK/Gk8KFMfDmNv/hf\nKSkptG/fnuuuu65IAeNtHnMRGxtL9erVQ+qPtwbjS8BERUVFJE3xnj17ih3evnXr1j7TPmdmZhZy\navD+8SxevJjf//73IZ/T21W5NExkYJlFXQLTJWDA98JYV9iVotaVtG/fnm+//TbkxcBHjx6lQYMG\nBb8t77Uw3gJm4MCB/PnPfyYpKSlkzdWbcAWMiBRLYysumZmZvPjii6xZs4aePXsG/VwKJGB27drF\n3r17ueuuu3zuL4rk5GQ2bdpU5BywEwRzte9j5WeZgZWvpRVWEjEPVLWr/TdGVW/w2gK/Ul1j1K9f\n32cIjdWrV9OjRw8AEhISAr5V+RMw4eA+ye/PRAaRMZNlZmbSokWLYrXhKwpsXl4eWVlZhbQK99X/\nly5dYsmSJQwaNCjkc5YFExlYC+NciyRTU1Pp3Lkz4NurKhjzGFghQ1q1ahWyHf7w4cOFXk4CCZhe\nvXoxc+ZMZs2aFdJ5fFG7dm3Onz9Pbm6uz/2XLl3y6/5bmgJmwYIF3HfffSEHSQ0kYGbNmsWIESMC\nzuMEon79+jRq1IhNmzZx6tQpPvrooyLXmoVLMAKmlaqOUNWvVfUrVX0ES8gY/FCjRg0uXLhQ6A3R\nXcDExcVx6NAhLly44LMNJwWM+yS/Pw0GnJ/oP3PmDD///LNHNIJw8BVZ2RXDynsxbadOnQq8htav\nX0+DBg3CioDsOqeqoqqlJmASEhLYsWMH2dnZnDhxosDU58urKlgBA9C5c2dSU1ND6osru6o7LgFz\n8eJFsrKyPPaLCKNGjXIkArWIBJyHSU9PL0jM583tt99Oeno6Z844k7k9Pz+fFStWBKUBLFu2jAED\nBoR8jrZt25KRkVEoW21ubi4ffvghjz76aMhtujNo0CCmTJlC165dmThxIqNHjy5We/4IRsBsEZHO\nri8i0gkon7lIg0RECmkDubm57Nixo+ANtGLFijRv3tzvSmMnBUxMTAz5+fmcP38+oIBxWoNxaS/B\nRtv1R+3atbl48aJHbhR/mlGHDh04duwY+/fvZ8GCBWFpLwDVqlWjatWqHD9+nBMnThATE+PTgSLS\ndOvWjdWrV/P111/TuXPngjm54mgwEJ6A8afBHDlyhKNHj1KnTh0qVYpEHFyLm266yW9O+RUrVtC3\nb1+f+6pWrUqPHj2YOnWqI6GHpk+fTr9+/YqMQpCbm8vWrVt95o0qiurVq1O/fv1CIX4+/vhjunbt\nWuwwWM888wynT59m+PDhbNiwIeiICqESKJpyhohkYC2cTBGRH0TkALAea3W+IQDe8zArV66kQ4cO\nHomgEhIS/M7DOClgRIQ6depw4sSJEtVgMjMzHfHmExFuvvlmj0ltf8FMo6OjGT58OIMHD2b+/Pk8\n/PDDYZ83Li6O3bt3l5r2Atb8U8WKFXnyySc9XNBdD3Z3srOzC7lb+8MlYELxrvJ177g0qQMHDkR8\njupXv/qV3xcyl3emP8aOHcu8efPo27dvWHHZZs+ezbZt21BVZs+ezRNPPFHooXz58mX27dtX4N2X\nkpJCu3btPH7zoeDLe/Lvf/972JP77tx4442sXr2a5557jlq1anmkrnCSQBrMnfb2b8DNQA/gNvtz\nP38HiUghdx0Rua04nbwa8X4AzJ07lwceeMCjjitIpS8OHz7sd64kHGJjY9mzZw/nz5/3m3/DaQ1m\n7969jiXo8o4CGyh18aRJkxg1ahRr164tVmiXxMREtmzZUiIPT3+ICHPnzuXRRx/1EDDFNZE1adIE\nEfGrEfjCl4ksNjaWgwcPsm/fvognY4uPj/fp7HH27Fm2bdvmETzSm1tvvZX9+/czcuTIkN/Wt23b\nxmOPPcaDDz7IunXriIqK4oUXXuDLL7/k4sWLHDhwgD59+lCnTh2Sk5MLYoEV1z27Q4cOHlpmWloa\n2dnZAQVpuESiTQi8kv+AawPOANWAWvZWOOHzFT4RkefEoqqIvAVMcbLTVwPu+a9//PFHVq1axR/+\n8AePOoE8yfbu3evoWp7Y2FhSU1Np3LixX5OV0xrMnj17fIauCQfv+GDff/+934d+5cqVeeSRR4p9\n7qSkJDZt2sS2bdscu45wSE5OZvLkyR7mJ18mMl+BLv0hIiGbyXyZyJo1a8YPP/xQIgImISHB5+Lk\nNWvWFLIO+OPee+8NKs6XO4sXL2bcuHHUrFmTAQMGMHLkSBo2bEiTJk3YsGEDTz/9dMGcyZEjR9i6\ndStffPFFsQVMz549PVJKvP3224wcOTLsxGSBCDUiQLAE46b8MrADeIsrCycDpUBOxspGmQpsArKA\nLsXu6VWGu+fT/PnzGTBgQKH1Ca1atfL5g3Gp2sX1vnKnUaNGpKamBrTdhqvBXLhwgT/96U98+OGH\nHuW7d+927MHsS4OJdPKvXr16sWzZMt59912/GUxLi7p163L69GmPiMWhaDBgpUNYv3590PV9aTCu\n+HglIWA6duzI9u3bCznPfPHFF0GbeLp06cLJkyd9akL++Pzzz+nXrx9z587lmWee4YknngCsMEbj\nx48nIyODl19+mYYNG1K5cmXeeOMNhgwZwt69e+nUqVPwF+hF27Ztyc7O5tChQ5w5c4aFCxcWhEVy\nmkilNglmkv9eoLmq9lDV211bgPoXgfNAFeA6YH8wIf6vNdznDP75z38WMo+Btcbh2LFjhbxbDh06\nRM2aNR2dVI6NjWXdunUBb6RwNZjp06eTnp7OmDFjCmzGqsru3bsdiwnnLrBVtUQETOPGjRkzZgz3\n3HNP0BGgS4oKFSpQt25dj//X8ePHQ/LY69atW9AhY86fP8+JEycKaTD16tXjp59+YseOHY6+EPki\nJiaGxMREPvvsM49yVyrmYIiKimLw4MFBm8l++eUXduzYQYcOHWjatCmvvPJKQTqM4cOHk5KSwqRJ\nkzxC7999992MHz+e999/v1jBUaOiorjzzjtZuHAhH3zwAX369Cm2R2aJ43LD9LcBnwL1iqrnVn87\nVsyyilhBL5cCC4I93onNuqzSZe/evdq4cWPds2eP1qtXT/Pz833WS05O1tWrV3uUzZ8/XwcOHOho\nf5YtW6aATps2zW+d06dPa7Vq1UJu+ze/+Y2uW7dOp0yZosOHD1dV1WPHjmmtWrXC7q83e/bs0WbN\nmqmqanZ2ttaoUcOxtq9WOnbsqOvXry/43qRJE92/f3/Qx+fl5en111+vOTk5RdZNS0vTNm3a+NzX\nqlUrBfTUqVNBnztcli1bpi1bttRffvlFVa17NiYmRvPy8oJuIyUlRePj4/Xy5ctF1t28ebO2bt3a\n7/5QzhsOy5cv17Zt22pCQoJ+9dVXET2X/dx09FkcjAYzGdgaQvDKR1T1z6qar6pZqjoQ8B9v/Rql\nefPmnDt3jsmTJzN06FC/yc86d+5cEHXWxZo1a+jevbuj/XG5R/fs2dNvnerVq5OXlxfSCu8TJ05w\n4MABkpOTefjhh1myZAknT550dP4FLBfVI0eOkJ+fXyLay9WA+yJHVeXYsWMeCeqKolKlSnTv3p3l\ny5cXWTcjI6NQigcXAwYMoFWrVtSsWTPoc4dLv379aNq0acHizfXr19OhQ4eQ3KM7d+5MXl5eUAtN\nN23a5BHvzptIumUD9O7dmypVqhAVFVXscDulQbAr+afYWzBzMMdFpIn7BoQe+OgqR0T47W9/y3vv\nveeRg8Sb/v37s2TJkgJ30by8PBYuXBh2GAh/1KhRg8uXLxfKI+PdZ3czWWZmZqGFXt644oFFR0dT\np04d7rzzTubMmcOGDRtITEx0rP+VKlWiQYMGHDx40AgYG3cBc+rUKapWrRqySWbIkCG88cYbPPnk\nk9x3331+5+BWrlzpdz3HlClT2LZtW2idDxMRYfLkyUydOpX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laq7BUGyMgDFcy6wDWohI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\nBkNEMALGYDAYDBHh/wPcAcrlvyWJogAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x118dbe550>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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lvRiOSdT+2hzI/OPPGd3RkOPjLT3rMW7cOCZOnMjEiROJiYnRxl1Khg0NDZoj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\n",
"text": [
"<matplotlib.figure.Figure at 0x119370f10>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Refined period: 86691.2179111 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 = 0.9572569763\n",
"Departure from Gaussian tail: number of sigma, Z2 = 0.923504933385\n",
"Plot histogram of residuals:\n",
"Optimization terminated successfully."
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Current function value: -166.321107\n",
" Iterations: 17\n",
" Function evaluations: 48\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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B3hsZe7VjPzXbRi7WiLgDGCVpbMGynYxpTM3n7f4bahpTRDwfEXcDbw60bEVx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\n5TgxmJlZzv8CEvDt2WDXxQIAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x1196c6e50>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting phased light curve residuals:\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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WL1/Oc889x8aNG0PuxzwGdP1cvOXujn32BMxzGTduHOXl5cyaNUv3/Dv67caN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\nDkEQBCEh/j/Cjodkw7cwiAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x1174e8410>"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Solid line is residual median: -0.00471242445348\n",
"Rank-based standard deviation, sigmaG = 0.0592058615313\n"
]
}
],
"prompt_number": 62
},
{
"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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PTJky5ajz1zzO3ppevXq1NS748MMPU1RURE1NDWFhYQCkpKRYi/+a0oOZl2YZ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\neln7FRUVMX36dMsIhyI+Pp577rnHCtpohohYt26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2A6C5B7fRp7OhYO7dsWPHmD59um0A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\nEFz8f9HVRPh8cGdGAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x118cdfc10>"
]
},
{
"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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\ngvWryD6BGgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11ad56050>"
]
}
],
"prompt_number": 63
},
{
"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> 0.520761</td>\n",
" <td> primary_minimum</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 0.5</td>\n",
" <td> 0.878454</td>\n",
" <td> secondary_minimum</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 64,
"text": [
" phase_dec flux_rel event\n",
"0 0.0 0.520761 primary_minimum\n",
"1 0.5 0.878454 secondary_minimum"
]
}
],
"prompt_number": 64
},
{
"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": 65
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# CHECKPOINT: Load saved data from previous calculations of phased light curve.\n",
"path_phot = os.path.join(path_project,\n",
" r'Work_Logs/20150216_light_curve_solution/phot_crts.csv')\n",
"df_crts = pd.DataFrame.from_csv(path=path_phot)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 66
},
{
"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": 67
},
{
"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. Assumes that phased lightcurve\n",
" is symmetrical about phase=0.5. Convenience function for 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",
" - The phased light curve is assumed to be symmetrical about phase=0.5 since the phased\n",
" lightcurve is folded at phase=0.5. This allows proper fitting for unevenly sampled data.\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",
" # Fold the phased light curve at phase=0.5 to enforce symmetry to\n",
" # accommodate irregular data sampling.\n",
" tfmask_lt05 = times_phased < 0.5\n",
" tfmask_gt05 = np.logical_not(tfmask_lt05)\n",
" phases_folded = np.append(times_phased[tfmask_lt05], np.subtract(1.0, times_phased[tfmask_gt05]))\n",
" phases_mirrored = np.append(phases_folded, np.subtract(1.0, phases_folded))\n",
" fluxes_folded = np.append(fluxes[tfmask_lt05], fluxes[tfmask_gt05])\n",
" fluxes_mirrored = np.append(fluxes_folded, fluxes_folded)\n",
" fluxes_err_folded = np.append(fluxes_err[tfmask_lt05], fluxes_err[tfmask_gt05])\n",
" fluxes_err_mirrored = np.append(fluxes_err_folded, fluxes_err_folded)\n",
" # Append the data to itself (tesselate) 2 times for total of 3 cycles to compute\n",
" # histogram without edge effects.\n",
" tess_phases = phases_mirrored\n",
" tess_fluxes = fluxes_mirrored\n",
" tess_fluxes_err = fluxes_err_mirrored\n",
" for begin_phase in xrange(0, 2):\n",
" tess_phases = np.append(tess_phases, np.add(phases_mirrored, begin_phase + 1.0))\n",
" tess_fluxes = np.append(tess_fluxes, fluxes_mirrored)\n",
" tess_fluxes_err = np.append(tess_fluxes_err, fluxes_err_mirrored)\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=phases_mirrored, fluxes=fluxes_mirrored, fluxes_err=fluxes_err_mirrored,\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": 68
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print(\"Compute Bayesian blocks histogram for folded, 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 folded, phased light curve.\n"
]
},
{
"metadata": {},
"output_type": "display_data",
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OpkFmZ2czadIkS/90yDFYv3491157raNpuaO9BL3ODRs2sH//fvVd55+e4M1I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