Time series analysis (MSAP4-02) =============================== .. code:: ipython3 import matplotlib.pyplot as plt import numpy as np import pandas as pd .. code:: ipython3 import star_privateer as sp import plato_msap4_demonstrator_datasets.plato_sim_dataset as plato_sim_dataset .. code:: ipython3 sp.__version__ .. parsed-literal:: '1.3.0' K2: Preprocessing ----------------- This first part include preprocessing tasks that are not actually included in MSAP4-02 but are useful for the subsequent analysis. .. code:: ipython3 t, s0, dt = sp.load_k2_example () .. code:: ipython3 fig, ax = plt.subplots (1, 1, figsize=(8,4)) ax.scatter (t[s0!=0]-t[0], s0[s0!=0], color='black', marker='o', s=1) ax.set_xlabel ('Time (day)') ax.set_ylabel ('Flux (ppm)') fig.tight_layout () plt.savefig ('figures/k2_lc.png', dpi=300) .. image:: timeseries_analysis_files/timeseries_analysis_7_0.png .. code:: ipython3 pcutoff = 60 pthresh = 60 K2: Rotation period analysis ---------------------------- In the next step, we compute the ACF and the WPS. We also analyse the characteristic periodicities obtained from the function, considering only periods below :math:`P_\mathrm{cutoff}`. .. code:: ipython3 p_acf, acf = sp.compute_acf (s0, dt, normalise=True) (_, _, _, _, prots, hacf, gacf, acf_smooth) = sp.find_period_acf (p_acf, acf, pcutoff=pcutoff, return_smoothed_acf=True) fig = sp.plot_acf (p_acf, acf, prot=prots, acf_additional=acf_smooth, color_additional="darkorange", filename='figures/acf_k2.png') .. image:: timeseries_analysis_files/timeseries_analysis_11_0.png We can take a look at the values we have extracted from the ACF. Most often, the rotation period can be linked to the first value of the ``prots`` array. .. code:: ipython3 prots[0], hacf[0], gacf[0] .. parsed-literal:: (2.6765510971308686, 1.219105626528322, 0.8085280511689089) We now turn to the wavelet analysis .. code:: ipython3 (periods, wps, gwps, _, _) = sp.compute_wps(s0, dt*86400, normalise=True) (prot_ps, E_prot_ps, param_gauss) = sp.compute_prot_err_gaussian_fit (periods, gwps, n_profile=1) .. code:: ipython3 fig = sp.plot_wps(t-t[0], periods, wps, gwps, shading='auto', color_coi='darkgrey', ylogscale=True, lw=1, normscale='log', filename='figures/wps_k2.png', dpi=300, figsize=(8,4), ylim=(1, 100), show_contour=False, param_gauss=param_gauss) .. image:: timeseries_analysis_files/timeseries_analysis_16_0.png Let’s take a look at the result of the fit performed on the GPWS ! .. code:: ipython3 prot_ps, E_prot_ps .. parsed-literal:: (2.6075837141864864, 0.3868209325802026) Note that, due to the short length of this light curve, we do not show for this first case the analysis of long term modulations. PLATO simulation: Preprocessing ------------------------------- This first part include preprocessing tasks that are not actually included in MSAP4-02 but are useful for the subsequent analysis. .. code:: ipython3 filename = sp.get_target_filename (plato_sim_dataset, '040', filetype='csv') t, s0, dt = sp.load_resource (filename) t, s0, dt = sp.rebin (t, 12), sp.rebin (s0, 12), dt*12 .. code:: ipython3 fig, ax = plt.subplots (1, 1, figsize=(8,4)) ax.scatter (t[s0!=0]-t[0], s0[s0!=0], color='black', marker='o', s=1) ax.set_xlabel ('Time (day)') ax.set_ylabel ('Flux (ppm)') fig.tight_layout () plt.savefig ('figures/plato_lc.png', dpi=300) .. image:: timeseries_analysis_files/timeseries_analysis_23_0.png .. code:: ipython3 s = sp.preprocess (t, s0, cut=60) pcutoff = 60 pthresh = 60 PLATO simulation: Rotation period analysis ------------------------------------------ This first part include preprocessing task that are not actually included in MSAP4-02 but are useful for the subsequent analysis. .. code:: ipython3 fig, ax = plt.subplots (1, 1, figsize=(8,4)) ax.scatter (t[s!=0]-t[0], s[s!=0], color='black', marker='o', s=1) ax.set_xlabel ('Time (day)') ax.set_ylabel ('Flux (ppm)') fig.tight_layout () plt.savefig ('figures/plato_lc_filtered.png', dpi=300) .. image:: timeseries_analysis_files/timeseries_analysis_27_0.png .. code:: ipython3 p_acf, acf = sp.compute_acf (s, dt, normalise=True) (_, _, _, _, prots, hacf, gacf, acf_smooth) = sp.find_period_acf (p_acf, acf, pcutoff=pcutoff, return_smoothed_acf=True) fig = sp.plot_acf (p_acf, acf, prot=prots, acf_additional=acf_smooth, color_additional="darkorange", filename='figures/acf_plato_short.png') .. image:: timeseries_analysis_files/timeseries_analysis_28_0.png .. code:: ipython3 (periods, wps, gwps, _, _) = sp.compute_wps(s, dt*86400, normalise=True) (prot_ps, E_prot_ps, param_gauss) = sp.compute_prot_err_gaussian_fit (periods, gwps, n_profile=1) fig = sp.plot_wps(t-t[0], periods, wps, gwps, shading='auto', color_coi='darkgrey', ylogscale=True, lw=1, normscale='log', filename='figures/wps_plato.png', dpi=300, figsize=(8,4), ylim=(1, 100), show_contour=False, param_gauss=param_gauss) .. image:: timeseries_analysis_files/timeseries_analysis_29_0.png Let’s take a look at the result of the fit performed on the GPWS ! PLATO simulation: Long term modulation analysis ----------------------------------------------- This time, we do not consider filtered out the data in order to consider long term modulations. We put a period threshold at 60 days to consider only long period in the postprocessing of our analysis. In the figure below, note that a Gaussian smoothing window is applied before looking for local maxima, shown in orange in the figure below. .. code:: ipython3 s0 = sp.preprocess (t, s0, cut=60, desired=[1,1,0,0]) p_acf, acf = sp.compute_acf (s0, dt, normalise=True, pthresh=pthresh, use_scipy_correlate=True, verbose=True) (_, hacf, gacf, _, pmods, hacf, gacf, acf_smooth) = sp.find_period_acf (p_acf, acf, pthresh=pthresh, return_smoothed_acf=True) fig = sp.plot_acf (p_acf, acf, prot=pmods, acf_additional=acf_smooth, color_additional="darkorange", filename="figures/acf_plato_long.png") .. image:: timeseries_analysis_files/timeseries_analysis_33_0.png