.. _timeseries-analysis: Manipulation and Analysis of Time Series **************************************** Combining Time Series ===================== The :func:`~astropy.table.vstack` and :func:`~astropy.table.hstack` functions from the :mod:`astropy.table` module can be used to stack time series in different ways. Examples -------- .. EXAMPLE START: Stacking Time Series Row-Wise Using table.vstack Time series can be stacked "vertically" or row-wise using the :func:`~astropy.table.vstack` function (although note that sampled time series cannot be combined with binned time series and vice versa):: >>> from astropy.table import vstack >>> from astropy import units as u >>> from astropy.timeseries import TimeSeries >>> ts_a = TimeSeries(time_start='2016-03-22T12:30:31', ... time_delta=3 * u.s, ... data={'flux': [1, 4, 5, 3, 2] * u.mJy}) >>> ts_b = TimeSeries(time_start='2016-03-22T12:50:31', ... time_delta=3 * u.s, ... data={'flux': [4, 3, 1, 2, 3] * u.mJy}) >>> ts_ab = vstack([ts_a, ts_b]) >>> ts_ab time flux mJy Time float64 ----------------------- ------- 2016-03-22T12:30:31.000 1.0 2016-03-22T12:30:34.000 4.0 2016-03-22T12:30:37.000 5.0 2016-03-22T12:30:40.000 3.0 2016-03-22T12:30:43.000 2.0 2016-03-22T12:50:31.000 4.0 2016-03-22T12:50:34.000 3.0 2016-03-22T12:50:37.000 1.0 2016-03-22T12:50:40.000 2.0 2016-03-22T12:50:43.000 3.0 Note that :func:`~astropy.table.vstack` does not automatically sort, nor get rid of duplicates — this is something you would need to do explicitly afterwards. .. EXAMPLE END .. EXAMPLE START: Stacking Time Series Column-Wise Using table.vstack Time series can also be combined "horizontally" or column-wise with other tables using the :func:`~astropy.table.hstack` function, though these should not be time series (as having multiple time columns would be confusing):: >>> from astropy.table import Table, hstack >>> data = Table(data={'temperature': [40., 41., 40., 39., 30.] * u.K}) >>> ts_a_data = hstack([ts_a, data]) >>> ts_a_data time flux temperature mJy K Time float64 float64 ----------------------- ------- ----------- 2016-03-22T12:30:31.000 1.0 40.0 2016-03-22T12:30:34.000 4.0 41.0 2016-03-22T12:30:37.000 5.0 40.0 2016-03-22T12:30:40.000 3.0 39.0 2016-03-22T12:30:43.000 2.0 30.0 .. EXAMPLE END Sorting Time Series =================== .. EXAMPLE START: Sorting Time Series Sorting time series in place can be done using the :meth:`~astropy.table.Table.sort` method, as for |Table|:: >>> ts = TimeSeries(time_start='2016-03-22T12:30:31', ... time_delta=3 * u.s, ... data={'flux': [1., 4., 5., 3., 2.]}) >>> ts time flux Time float64 ----------------------- ------- 2016-03-22T12:30:31.000 1.0 2016-03-22T12:30:34.000 4.0 2016-03-22T12:30:37.000 5.0 2016-03-22T12:30:40.000 3.0 2016-03-22T12:30:43.000 2.0 >>> ts.sort('flux') >>> ts time flux Time float64 ----------------------- ------- 2016-03-22T12:30:31.000 1.0 2016-03-22T12:30:43.000 2.0 2016-03-22T12:30:40.000 3.0 2016-03-22T12:30:34.000 4.0 2016-03-22T12:30:37.000 5.0 .. EXAMPLE END Resampling ========== We provide a :func:`~astropy.timeseries.aggregate_downsample` function that can be used to bin values from a time series into equal-size or uneven bins, and contiguous and non-contiguous bins, using a custom function (mean, median, etc.). This operation returns a |BinnedTimeSeries|. Note that this is a basic function in the sense that it does not, for example, know how to treat columns with uncertainties differently from other values, and it will blindly apply the custom function specified to all columns. Example ------- .. EXAMPLE START: Creating a BinnedTimeSeries with even contiguous bins The following example shows how to use :func:`~astropy.timeseries.aggregate_downsample` to bin a light curve from the Kepler mission into 20 minute contiguous bins using a median function. First, we read in the data using: .. plot:: :include-source: :context: reset :nofigs: from astropy.timeseries import TimeSeries from astropy.utils.data import get_pkg_data_filename example_data = get_pkg_data_filename('timeseries/kplr010666592-2009131110544_slc.fits') kepler = TimeSeries.read(example_data, format='kepler.fits') (See :ref:`timeseries-io` for more details about reading in data). We can then downsample using: .. plot:: :context: :nofigs: import warnings warnings.filterwarnings('ignore', message='All-NaN slice encountered') .. plot:: :include-source: :context: :nofigs: import numpy as np from astropy import units as u from astropy.timeseries import aggregate_downsample kepler_binned = aggregate_downsample(kepler, time_bin_size=20 * u.min, aggregate_func=np.nanmedian) We can take a look at the results: .. plot:: :include-source: :context: import matplotlib.pyplot as plt plt.plot(kepler.time.jd, kepler['sap_flux'], 'k.', markersize=1) plt.plot(kepler_binned.time_bin_start.jd, kepler_binned['sap_flux'], 'r-', drawstyle='steps-pre') plt.xlabel('Julian Date') plt.ylabel('SAP Flux (e-/s)') .. EXAMPLE END .. EXAMPLE START: Creating a BinnedTimeSeries with uneven contiguous bins The :func:`~astropy.timeseries.aggregate_downsample` can also be used to bin the light curve into custom bins. The following example shows the case of uneven-size contiguous bins: .. plot:: :context: reset :nofigs: import numpy as np from astropy import units as u import matplotlib.pyplot as plt from astropy.timeseries import TimeSeries from astropy.timeseries import aggregate_downsample from astropy.utils.data import get_pkg_data_filename example_data = get_pkg_data_filename('timeseries/kplr010666592-2009131110544_slc.fits') kepler = TimeSeries.read(example_data, format='kepler.fits') import warnings warnings.filterwarnings('ignore', message='All-NaN slice encountered') .. plot:: :include-source: :context: kepler_binned = aggregate_downsample(kepler, time_bin_size=[1000, 125, 80, 25, 150, 210, 273] * u.min, aggregate_func=np.nanmedian) plt.plot(kepler.time.jd, kepler['sap_flux'], 'k.', markersize=1) plt.plot(kepler_binned.time_bin_start.jd, kepler_binned['sap_flux'], 'r-', drawstyle='steps-pre') plt.xlabel('Julian Date') plt.ylabel('SAP Flux (e-/s)') To learn more about the custom binning functionality in :func:`~astropy.timeseries.aggregate_downsample`, see :ref:`timeseries-binned-initializing`. Folding ======= .. EXAMPLE START: Phase Folding a Time Series The |TimeSeries| class has a :meth:`~astropy.timeseries.TimeSeries.fold` method that can be used to return a new time series with a relative and folded time axis. This method takes the period as a :class:`~astropy.units.Quantity`, and optionally takes an epoch as a :class:`~astropy.time.Time`, which defines a zero time offset: .. plot:: :context: reset :nofigs: import numpy as np from astropy import units as u import matplotlib.pyplot as plt from astropy.timeseries import TimeSeries from astropy.utils.data import get_pkg_data_filename example_data = get_pkg_data_filename('timeseries/kplr010666592-2009131110544_slc.fits') kepler = TimeSeries.read(example_data, format='kepler.fits') .. plot:: :include-source: :context: kepler_folded = kepler.fold(period=2.2 * u.day, epoch_time='2009-05-02T20:53:40') plt.plot(kepler_folded.time.jd, kepler_folded['sap_flux'], 'k.', markersize=1) plt.xlabel('Time from midpoint epoch (days)') plt.ylabel('SAP Flux (e-/s)') Note that in this example we happened to know the period and midpoint from a previous periodogram analysis. See the example in :doc:`index` for how you might do this. .. EXAMPLE END Arithmetic ========== .. EXAMPLE START: Arithmetic with Time Series Since |TimeSeries| objects are subclasses of |Table|, they naturally support arithmetic on any of the data columns. As an example, we can take the folded Kepler time series we have seen in previous examples, and normalize it to the sigma-clipped median value. .. plot:: :context: reset :nofigs: import numpy as np from astropy import units as u import matplotlib.pyplot as plt from astropy.timeseries import TimeSeries from astropy.utils.data import get_pkg_data_filename example_data = get_pkg_data_filename('timeseries/kplr010666592-2009131110544_slc.fits') kepler = TimeSeries.read(example_data, format='kepler.fits') kepler_folded = kepler.fold(period=2.2 * u.day, epoch_time='2009-05-02T20:53:40') .. plot:: :context: :nofigs: import warnings warnings.filterwarnings('ignore', message='Input data contains invalid values') .. plot:: :include-source: :context: from astropy.stats import sigma_clipped_stats mean, median, stddev = sigma_clipped_stats(kepler_folded['sap_flux']) kepler_folded['sap_flux_norm'] = kepler_folded['sap_flux'] / median plt.plot(kepler_folded.time.jd, kepler_folded['sap_flux_norm'], 'k.', markersize=1) plt.xlabel('Time from midpoint epoch (days)') plt.ylabel('Normalized flux') .. EXAMPLE END