Source code for astropy.stats.lombscargle.core

"""Main Lomb-Scargle Implementation"""
from __future__ import print_function, division

import numpy as np

from .implementations import lombscargle, available_methods
from .implementations.mle import periodic_fit
from ... import units
from ...utils.compat.numpy import broadcast_arrays
from ...extern.six.moves import map


def has_units(obj):
    return hasattr(obj, 'unit')


def get_unit(obj):
    return getattr(obj, 'unit', 1)


def strip_units(*arrs):
    strip = lambda a: None if a is None else np.asarray(a)
    if len(arrs) == 1:
        return strip(arrs[0])
    else:
        return map(strip, arrs)


[docs]class LombScargle(object): """Compute the Lomb-Scargle Periodogram This implementations here are based on code presented in [1]_ and [2]_; if you use this functionality in an academic application, citation of those works would be appreciated. Parameters ---------- t : array_like or Quantity sequence of observation times y : array_like or Quantity sequence of observations associated with times t dy : float, array_like or Quantity (optional) error or sequence of observational errors associated with times t fit_mean : bool (optional, default=True) if True, include a constant offset as part of the model at each frequency. This can lead to more accurate results, especially in the case of incomplete phase coverage. center_data : bool (optional, default=True) if True, pre-center the data by subtracting the weighted mean of the input data. This is especially important if fit_mean = False nterms : int (optional, default=1) number of terms to use in the Fourier fit Examples -------- Generate noisy periodic data: >>> rand = np.random.RandomState(42) >>> t = 100 * rand.rand(100) >>> y = np.sin(2 * np.pi * t) + rand.randn(100) Compute the Lomb-Scargle periodogram on an automatically-determined frequency grid & find the frequency of max power: >>> frequency, power = LombScargle(t, y).autopower() >>> frequency[np.argmax(power)] 1.0016662310392956 Compute the Lomb-Scargle periodogram at a user-specified frequency grid: >>> freq = np.arange(0.8, 1.3, 0.1) >>> LombScargle(t, y).power(freq) array([ 0.0204304 , 0.01393845, 0.35552682, 0.01358029, 0.03083737]) 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.s >>> y = y * u.mag >>> frequency, power = LombScargle(t, y).autopower() >>> frequency.unit Unit("1 / s") >>> power.unit Unit(dimensionless) Note here that the Lomb-Scargle power is always a unitless quantity, because it is related to the :math:`\\chi^2` of the best-fit periodic model at each frequency. References ---------- .. [1] Vanderplas, J., Connolly, A. Ivezic, Z. & Gray, A. *Introduction to astroML: Machine learning for astrophysics*. Proceedings of the Conference on Intelligent Data Understanding (2012) .. [2] VanderPlas, J. & Ivezic, Z. *Periodograms for Multiband Astronomical Time Series*. ApJ 812.1:18 (2015) """ available_methods = available_methods() def __init__(self, t, y, dy=None, fit_mean=True, center_data=True, nterms=1): self.t, self.y, self.dy = self._validate_inputs(t, y, dy) self.fit_mean = fit_mean self.center_data = center_data self.nterms = nterms def _validate_inputs(self, t, y, dy): # Validate shapes of inputs if dy is None: t, y = broadcast_arrays(t, y, subok=True) else: t, y, dy = broadcast_arrays(t, y, dy, subok=True) if t.ndim != 1: raise ValueError("Inputs (t, y, dy) must be 1-dimensional") # validate units of inputs if any is a Quantity if any(has_units(arr) for arr in (t, y, dy)): t, y = map(units.Quantity, (t, y)) if dy is not None: dy = units.Quantity(dy) try: dy = units.Quantity(dy, unit=y.unit) except units.UnitConversionError: raise ValueError("Units of dy not equivalent " "to units of y") return t, y, dy def _validate_frequency(self, frequency): frequency = np.asanyarray(frequency) if has_units(self.t): frequency = units.Quantity(frequency) try: frequency = units.Quantity(frequency, unit=1./self.t.unit) except units.UnitConversionError: raise ValueError("Units of frequency not equivalent to " "units of 1/t") else: if has_units(frequency): raise ValueError("frequency have units while 1/t doesn't.") return frequency def _validate_t(self, t): t = np.asanyarray(t) if has_units(self.t): t = units.Quantity(t) try: t = units.Quantity(t, unit=self.t.unit) except units.UnitConversionError: raise ValueError("Units of t not equivalent to " "units of input self.t") return t def _power_unit(self, norm): if has_units(self.y): if self.dy is None and norm == 'psd': return self.y.unit ** 2 else: return units.dimensionless_unscaled else: return 1
[docs] def autofrequency(self, samples_per_peak=5, nyquist_factor=5, minimum_frequency=None, maximum_frequency=None): """Determine a suitable frequency grid for data. Note that this assumes the peak width is driven by the observational baseline, which is generally a good assumption when the baseline is much larger than the oscillation period. If you are searching for periods longer than the baseline of your observations, this may not perform well. Even with a large baseline, be aware that the maximum frequency returned is based on the concept of "average Nyquist frequency", which may not be useful for irregularly-sampled data. The maximum frequency can be adjusted via the nyquist_factor argument, or through the maximum_frequency argument. Parameters ---------- samples_per_peak : float (optional, default=5) The approximate number of desired samples across the typical peak nyquist_factor : float (optional, default=5) The multiple of the average nyquist frequency used to choose the maximum frequency if maximum_frequency is not provided. minimum_frequency : float (optional) If specified, then use this minimum frequency rather than one chosen based on the size of the baseline. maximum_frequency : float (optional) If specified, then use this maximum frequency rather than one chosen based on the average nyquist frequency. Returns ------- frequency : ndarray or Quantity The heuristically-determined optimal frequency bin """ baseline = self.t.max() - self.t.min() n_samples = self.t.size df = 1.0 / baseline / samples_per_peak if minimum_frequency is None: minimum_frequency = 0.5 * df if maximum_frequency is None: avg_nyquist = 0.5 * n_samples / baseline maximum_frequency = nyquist_factor * avg_nyquist Nf = 1 + int(np.round((maximum_frequency - minimum_frequency) / df)) return minimum_frequency + df * np.arange(Nf)
[docs] def autopower(self, method='auto', method_kwds=None, normalization='standard', samples_per_peak=5, nyquist_factor=5, minimum_frequency=None, maximum_frequency=None): """Compute Lomb-Scargle power at automatically-determined frequencies Parameters ---------- method : string (optional) specify the lomb scargle implementation to use. Options are: - 'auto': choose the best method based on the input - 'fast': use the O[N log N] fast method. Note that this requires evenly-spaced frequencies: by default this will be checked unless ``assume_regular_frequency`` is set to True. - 'slow': use the O[N^2] pure-python implementation - 'cython': use the O[N^2] cython implementation. This is slightly faster than method='slow', but much more memory efficient. - 'chi2': use the O[N^2] chi2/linear-fitting implementation - 'fastchi2': use the O[N log N] chi2 implementation. Note that this requires evenly-spaced frequencies: by default this will be checked unless ``assume_regular_frequency`` is set to True. - 'scipy': use ``scipy.signal.lombscargle``, which is an O[N^2] implementation written in C. Note that this does not support heteroskedastic errors. method_kwds : dict (optional) additional keywords to pass to the lomb-scargle method normalization : string (optional, default='standard') Normalization to use for the periodogram. Options are 'standard', 'model', or 'psd'. samples_per_peak : float (optional, default=5) The approximate number of desired samples across the typical peak nyquist_factor : float (optional, default=5) The multiple of the average nyquist frequency used to choose the maximum frequency if maximum_frequency is not provided. minimum_frequency : float (optional) If specified, then use this minimum frequency rather than one chosen based on the size of the baseline. maximum_frequency : float (optional) If specified, then use this maximum frequency rather than one chosen based on the average nyquist frequency. Returns ------- frequency, power : ndarrays The frequency and Lomb-Scargle power """ frequency = self.autofrequency(samples_per_peak=samples_per_peak, nyquist_factor=nyquist_factor, minimum_frequency=minimum_frequency, maximum_frequency=maximum_frequency) power = self.power(frequency, normalization=normalization, method=method, method_kwds=method_kwds, assume_regular_frequency=True) return frequency, power
[docs] def power(self, frequency, normalization='standard', method='auto', assume_regular_frequency=False, method_kwds=None): """Compute the Lomb-Scargle power at the given frequencies Parameters ---------- frequency : array_like or Quantity frequencies (not angular frequencies) at which to evaluate the periodogram. Note that in order to use method='fast', frequencies must be regularly-spaced. method : string (optional) specify the lomb scargle implementation to use. Options are: - 'auto': choose the best method based on the input - 'fast': use the O[N log N] fast method. Note that this requires evenly-spaced frequencies: by default this will be checked unless ``assume_regular_frequency`` is set to True. - 'slow': use the O[N^2] pure-python implementation - 'cython': use the O[N^2] cython implementation. This is slightly faster than method='slow', but much more memory efficient. - 'chi2': use the O[N^2] chi2/linear-fitting implementation - 'fastchi2': use the O[N log N] chi2 implementation. Note that this requires evenly-spaced frequencies: by default this will be checked unless ``assume_regular_frequency`` is set to True. - 'scipy': use ``scipy.signal.lombscargle``, which is an O[N^2] implementation written in C. Note that this does not support heteroskedastic errors. assume_regular_frequency : bool (optional) if True, assume that the input frequency is of the form freq = f0 + df * np.arange(N). Only referenced if method is 'auto' or 'fast'. normalization : string (optional, default='standard') Normalization to use for the periodogram. Options are 'standard', 'model', 'log', or 'psd'. fit_mean : bool (optional, default=True) if True, include a constant offset as part of the model at each frequency. This can lead to more accurate results, especially in the case of incomplete phase coverage. center_data : bool (optional, default=True) if True, pre-center the data by subtracting the weighted mean of the input data. This is especially important if fit_mean = False method_kwds : dict (optional) additional keywords to pass to the lomb-scargle method Returns ------- power : ndarray The Lomb-Scargle power at the specified frequency """ frequency = self._validate_frequency(frequency) power = lombscargle(*strip_units(self.t, self.y, self.dy), frequency=strip_units(frequency), center_data=self.center_data, fit_mean=self.fit_mean, nterms=self.nterms, normalization=normalization, method=method, method_kwds=method_kwds, assume_regular_frequency=assume_regular_frequency) return power * self._power_unit(normalization)
[docs] def model(self, t, frequency): """Compute the Lomb-Scargle model at the given frequency Parameters ---------- t : array_like or Quantity, length n_samples times at which to compute the model frequency : float the frequency for the model Returns ------- y : np.ndarray, length n_samples The model fit corresponding to the input times """ frequency = self._validate_frequency(frequency) t = self._validate_t(t) y_fit = periodic_fit(*strip_units(self.t, self.y, self.dy), frequency=strip_units(frequency), t_fit=strip_units(t), center_data=self.center_data, fit_mean=self.fit_mean, nterms=self.nterms) return y_fit * get_unit(self.y)