BoxLeastSquares¶

class
astropy.stats.
BoxLeastSquares
(t, y, dy=None)[source]¶ Bases:
object
Compute the box least squares periodogram
This method is a commonly used tool for discovering transiting exoplanets or eclipsing binaries in photometric time series datasets. This implementation is based on the “box least squares (BLS)” method described in [1] and [2].
Parameters:  t : arraylike or Quantity
Sequence of observation times.
 y : arraylike or Quantity
Sequence of observations associated with times
t
. dy : float, arraylike or Quantity, optional
Error or sequence of observational errors associated with times
t
.
References
[1] (1, 2) Kovacs, Zucker, & Mazeh (2002), A&A, 391, 369 (arXiv:astroph/0206099) [2] (1, 2) Hartman & Bakos (2016), Astronomy & Computing, 17, 1 (arXiv:1605.06811) Examples
Generate noisy data with a transit:
>>> rand = np.random.RandomState(42) >>> t = rand.uniform(0, 10, 500) >>> y = np.ones_like(t) >>> y[np.abs((t + 1.0)%2.01)<0.08] = 1.0  0.1 >>> y += 0.01 * rand.randn(len(t))
Compute the transit periodogram on a heuristically determined period grid and find the period with maximum power:
>>> model = BoxLeastSquares(t, y) >>> results = model.autopower(0.16) >>> results.period[np.argmax(results.power)] 1.9923406038842544
Compute the periodogram on a userspecified period grid:
>>> periods = np.linspace(1.9, 2.1, 5) >>> results = model.power(periods, 0.16) >>> results.power array([0.01421067, 0.02842475, 0.10867671, 0.05117755, 0.01783253])
If the inputs are AstroPy Quantities with units, the units will be validated and the outputs will also be Quantities with appropriate units:
>>> from astropy import units as u >>> t = t * u.day >>> y = y * u.dimensionless_unscaled >>> model = BoxLeastSquares(t, y) >>> results = model.autopower(0.16 * u.day) >>> results.period.unit Unit("d") >>> results.power.unit Unit(dimensionless)
Methods Summary
autoperiod
(duration[, minimum_period, …])Determine a suitable grid of periods autopower
(duration[, objective, method, …])Compute the periodogram at set of heuristically determined periods compute_stats
(period, duration, transit_time)Compute descriptive statistics for a given transit model model
(t_model, period, duration, transit_time)Compute the transit model at the given period, duration, and phase power
(period, duration[, objective, method, …])Compute the periodogram for a set of periods transit_mask
(t, period, duration, transit_time)Compute which data points are in transit for a given parameter set Methods Documentation

autoperiod
(duration, minimum_period=None, maximum_period=None, minimum_n_transit=3, frequency_factor=1.0)[source]¶ Determine a suitable grid of periods
This method uses a set of heuristics to select a conservative period grid that is uniform in frequency. This grid might be too fine for some user’s needs depending on the precision requirements or the sampling of the data. The grid can be made coarser by increasing
frequency_factor
.Parameters:  duration : float, arraylike or Quantity
The set of durations that will be considered.
 minimum_period, maximum_period : float or Quantity, optional
The minimum/maximum periods to search. If not provided, these will be computed as described in the notes below.
 minimum_n_transits : int, optional
If
maximum_period
is not provided, this is used to compute the maximum period to search by asserting that any systems with at leastminimum_n_transits
will be within the range of searched periods. Note that this is not the same as requiring thatminimum_n_transits
be required for detection. The default value is3
. frequency_factor : float, optional
A factor to control the frequency spacing as described in the notes below. The default value is
1.0
.
Returns:  period : arraylike or Quantity
The set of periods computed using these heuristics with the same units as
t
.
Notes
The default minimum period is chosen to be twice the maximum duration because there won’t be much sensitivity to periods shorter than that.
The default maximum period is computed as
maximum_period = (max(t)  min(t)) / minimum_n_transits
ensuring that any systems with at least
minimum_n_transits
are within the range of searched periods.The frequency spacing is given by
df = frequency_factor * min(duration) / (max(t)  min(t))**2
so the grid can be made finer by decreasing
frequency_factor
or coarser by increasingfrequency_factor
.

autopower
(duration, objective=None, method=None, oversample=10, minimum_n_transit=3, minimum_period=None, maximum_period=None, frequency_factor=1.0)[source]¶ Compute the periodogram at set of heuristically determined periods
This method calls
BoxLeastSquares.autoperiod()
to determine the period grid and thenBoxLeastSquares.power()
to compute the periodogram. See those methods for documentation of the arguments.

compute_stats
(period, duration, transit_time)[source]¶ Compute descriptive statistics for a given transit model
These statistics are commonly used for vetting of transit candidates.
Parameters:  period : float or Quantity
The period of the transits.
 duration : float or Quantity
The duration of the transit.
 transit_time : float or Quantity
The midtransit time of a reference transit.
Returns:  stats : dict
A dictionary containing several descriptive statistics:
depth
: The depth and uncertainty (as a tuple with two values) on the depth for the fiducial model.
depth_odd
: The depth and uncertainty on the depth for a model where the period is twice the fiducial period.
depth_even
: The depth and uncertainty on the depth for a model where the period is twice the fiducial period and the phase is offset by one orbital period.
depth_half
: The depth and uncertainty for a model with a period of half the fiducial period.
depth_phased
: The depth and uncertainty for a model with the fiducial period and the phase offset by half a period.
harmonic_amplitude
: The amplitude of the best fit sinusoidal model.
harmonic_delta_log_likelihood
: The difference in log likelihood between a sinusoidal model and the transit model.
If
harmonic_delta_log_likelihood
is greater than zero, the sinusoidal model is preferred.
transit_times
: The midtransit time for each transit in the baseline.
per_transit_count
: An array with a count of the number of data points in each unique transit included in the baseline.
per_transit_log_likelihood
: An array with the value of the log likelihood for each unique transit included in the baseline.

model
(t_model, period, duration, transit_time)[source]¶ Compute the transit model at the given period, duration, and phase
Parameters:  t_model : arraylike or Quantity
Times at which to compute the model.
 period : float or Quantity
The period of the transits.
 duration : float or Quantity
The duration of the transit.
 transit_time : float or Quantity
The midtransit time of a reference transit.
Returns:  y_model : arraylike or Quantity
The model evaluated at the times
t_model
with units ofy
.

power
(period, duration, objective=None, method=None, oversample=10)[source]¶ Compute the periodogram for a set of periods
Parameters:  period : arraylike or Quantity
The periods where the power should be computed
 duration : float, arraylike or Quantity
The set of durations to test
 objective : {‘likelihood’, ‘snr’}, optional
The scalar that should be optimized to find the best fit phase, duration, and depth. This can be either
'likelihood'
(default) to optimize the loglikelihood of the model, or'snr'
to optimize the signaltonoise with which the transit depth is measured. method : {‘fast’, ‘slow’}, optional
The computational method used to compute the periodogram. This is mainly included for the purposes of testing and most users will want to use the optimized
'fast'
method (default) that is implemented in Cython.'slow'
is a bruteforce method that is used to test the results of the'fast'
method. oversample : int, optional
The number of bins per duration that should be used. This sets the time resolution of the phase fit with larger values of
oversample
yielding a finer grid and higher computational cost.
Returns:  results : BoxLeastSquaresResults
The periodogram results as a
BoxLeastSquaresResults
object.
Raises:  ValueError
If
oversample
is not an integer greater than 0 or ifobjective
ormethod
are not valid.

transit_mask
(t, period, duration, transit_time)[source]¶ Compute which data points are in transit for a given parameter set
Parameters:  t_model : arraylike or Quantity
Times where the mask should be evaluated.
 period : float or Quantity
The period of the transits.
 duration : float or Quantity
The duration of the transit.
 transit_time : float or Quantity
The midtransit time of a reference transit.
Returns:  transit_mask : arraylike
A boolean array where
True
indicates and in transit point andFalse
indicates and outoftransit point.