"""Main Lomb-Scargle Multiband Implementation""" import numpy as np from astropy import units as u from astropy.time import Time, TimeDelta from astropy.timeseries.binned import BinnedTimeSeries from astropy.timeseries.periodograms.lombscargle import LombScargle from astropy.timeseries.sampled import TimeSeries from .implementations import available_methods, lombscargle_multiband from .implementations.mle import construct_regularization, design_matrix, periodic_fit __all__ = ["LombScargleMultiband"] 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) class LombScargleMultiband(LombScargle): """Compute the Lomb-Scargle Periodogram. This implementation is 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 `~astropy.units.Quantity` ['time'] sequence of observation times y : array-like or `~astropy.units.Quantity` sequence of observations associated with times t bands : array-like sequence of passband labels associated with times t, each unique label defines a single band of data. dy : float, array-like, or `~astropy.units.Quantity`, optional error or sequence of observational errors associated with times t normalization : {'standard', 'model', 'log', 'psd'}, optional Normalization to use for the periodogram. nterms_base : int, optional number of frequency terms to use for the base model common to all bands. In the case of the fast algorithm, this parameter is passed along to the single band LombScargle method as the ``nterms`` parameter. nterms_band : int, optional number of frequency terms to use for the residuals between the base model and each individual band reg_base : float or None (default = None) amount of regularization to use on the base model parameters reg_band : float or None (default = 1E-6) amount of regularization to use on the band model parameters regularize_by_trace : bool (default = True) if True, then regularization is expressed in units of the trace of the normal matrix center_data : bool, optional if True, pre-center the data by subtracting the weighted mean of the input data. fit_mean : bool, optional 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. Only applicable to the "fast" method 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, bands, dy=None, normalization="standard", nterms_base=1, nterms_band=1, reg_base=None, reg_band=1e-6, regularize_by_trace=True, center_data=True, fit_mean=True, ): # If t is a TimeDelta, convert it to a quantity. The units we convert # to don't really matter since the user gets a Quantity back at the end # so can convert to any units they like. if isinstance(t, TimeDelta): t = t.to("day") # We want to expose self.t as being the times the user passed in, but # if the times are absolute, we need to convert them to relative times # internally, so we use self._trel and self._tstart for this. self.t = t if isinstance(self.t, Time): self._tstart = self.t[0] trel = (self.t - self._tstart).to(u.day) else: self._tstart = None trel = self.t self._trel, self.y, self.bands, self.dy = self._validate_inputs( trel, y, bands, dy ) self.normalization = normalization self.nterms_base = nterms_base self.nterms_band = nterms_band self.reg_base = reg_base self.reg_band = reg_band self.regularize_by_trace = regularize_by_trace self.center_data = center_data self.fit_mean = fit_mean self.nterms = self.nterms_base # determined by the base model params @classmethod def from_timeseries( cls, timeseries, signal_column=None, uncertainty_column=None, band_labels=None, **kwargs, ): """ Initialize a multiband periodogram from a time series object. If a binned time series is passed, the time at the center of the bins is used. Also note that this method automatically gets rid of NaN/undefined values when initializing the periodogram. Parameters ---------- signal_column : list The names of columns containing the signal values to use. uncertainty_column : list, optional The names of columns containing the errors on the signal. band_labels : list, optional The labels for each band, matched by index. If none, uses the labels of ``signal_column`` as band names. **kwargs Additional keyword arguments are passed to the initializer for this periodogram class. """ if signal_column is None: raise ValueError( "signal_column_name should be set to a list of valid column names" ) if band_labels is not None: if len(band_labels) != len(signal_column): raise ValueError( "band_labels have an equal number of elements to signal_column" ) else: band_labels = signal_column # use the flux labels as band labels if isinstance(timeseries, TimeSeries): time = timeseries.time elif isinstance(timeseries, BinnedTimeSeries): time = timeseries.time_bin_center else: raise TypeError( "Input time series should be an instance of " "TimeSeries or BinnedTimeSeries" ) # Build lombscargle_multiband inputs t = [] y = [] dy = [] band = [] for i, col in enumerate(signal_column): if np.ma.is_masked(timeseries[col]): signal_mask = ~timeseries[col].mask else: signal_mask = ~np.isnan(timeseries[col]) if uncertainty_column is not None: dy_col = timeseries[uncertainty_column[i]] if np.ma.is_masked(dy_col): signal_mask &= ~dy_col.mask else: signal_mask &= ~np.isnan(dy_col) t.append(time[signal_mask].mjd * u.day) y.append(timeseries[col][signal_mask]) band.append([band_labels[i]] * sum(signal_mask)) dy.append(timeseries[uncertainty_column[i]][signal_mask]) t = np.hstack(t) y = np.hstack(y) band = np.hstack(band) if uncertainty_column is not None: dy = np.hstack(dy) if len(dy) == 0: dy = None return cls(t, y, band, dy=dy, **kwargs) def _validate_inputs(self, t, y, bands, dy): # Validate shapes of inputs if dy is None: t, y, bands = np.broadcast_arrays(t, y, bands, subok=True) else: t, y, bands, dy = np.broadcast_arrays(t, y, bands, dy, subok=True) if t.ndim != 1: raise ValueError("Inputs (t, y, bands, dy) must be 1-dimensional") # validate units of inputs if any is a Quantity if any(has_units(arr) for arr in (t, y, bands, dy)): t, y = map(u.Quantity, (t, y)) if dy is not None: dy = u.Quantity(dy) try: dy = u.Quantity(dy, unit=y.unit) except u.UnitConversionError: raise ValueError("Units of dy not equivalent " "to units of y") return t, y, bands, dy def autofrequency( self, samples_per_peak=5, nyquist_factor=5, minimum_frequency=None, maximum_frequency=None, return_freq_limits=False, ): """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 The approximate number of desired samples across the typical peak nyquist_factor : float, optional 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. return_freq_limits : bool, optional if True, return only the frequency limits rather than the full frequency grid. Returns ------- frequency : ndarray or `~astropy.units.Quantity` ['frequency'] The heuristically-determined optimal frequency bin """ if hasattr(self._trel, "unit"): unit = self._trel.unit trel = self._trel.to(u.day) # do frequency calculations in days else: trel = self._trel baseline = trel.max() - trel.min() n_samples = trel.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 # Convert back to the input units if hasattr(self._trel, "unit"): df = df.to(1 / unit) minimum_frequency = minimum_frequency.to(1 / unit) maximum_frequency = maximum_frequency.to(1 / unit) n_freq = 1 + int(np.round((maximum_frequency - minimum_frequency) / df)) if return_freq_limits: return minimum_frequency, minimum_frequency + df * (n_freq - 1) else: return minimum_frequency + df * np.arange(n_freq) def autopower( self, method="flexible", sb_method="auto", 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 : str, optional specify the multi-band lomb scargle implementation to use. Options are: - 'flexible': Constructs a common model, and an offset model per individual band. Applies regularization to the resulting model to constrain complexity. - 'fast': Passes each band individually through LombScargle (single-band), combines periodograms at the end by weight. Speed depends on single-band method chosen in 'sb_method'. sb_method : str, optional specify the single-band lomb scargle implementation to use, only in the case of using the 'fast' multiband method. 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. normalization : {'standard', 'model', 'log', 'psd'}, optional If specified, override the normalization specified at instantiation. samples_per_peak : float, optional The approximate number of desired samples across the typical peak nyquist_factor : float, optional The multiple of the average nyquist frequency used to choose the maximum frequency if maximum_frequency is not provided. minimum_frequency : float or `~astropy.units.Quantity` ['frequency'], optional If specified, then use this minimum frequency rather than one chosen based on the size of the baseline. Should be `~astropy.units.Quantity` if inputs to LombScargle are `~astropy.units.Quantity`. maximum_frequency : float or `~astropy.units.Quantity` ['frequency'], optional If specified, then use this maximum frequency rather than one chosen based on the average nyquist frequency. Should be `~astropy.units.Quantity` if inputs to LombScargle are `~astropy.units.Quantity`. Returns ------- frequency, power : ndarray 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, method=method, sb_method=sb_method, normalization=normalization ) return frequency, power def power( self, frequency, method="flexible", sb_method="auto", normalization="standard" ): """Compute the Lomb-Scargle power at the given frequencies. Parameters ---------- frequency : array-like or `~astropy.units.Quantity` ['frequency'] frequencies (not angular frequencies) at which to evaluate the periodogram. Note that in order to use method='fast', frequencies must be regularly-spaced. method : str, optional specify the multi-band lomb scargle implementation to use. Options are: - 'flexible': Constructs a common model, and an offset model per individual band. Applies regularization to the resulting model to constrain complexity. - 'fast': Passes each band individually through LombScargle (single-band), combines periodograms at the end by weight. Speed depends on single-band method chosen in 'sb_method'. sb_method : str, optional specify the single-band lomb scargle implementation to use, only in the case of using the 'fast' multiband method. Options can be found in `~astropy.timeseries.LombScargle`. normalization : {'standard', 'model', 'log', 'psd'}, optional If specified, override the normalization specified at instantiation. Returns ------- power : ndarray The Lomb-Scargle power at the specified frequency """ if normalization is None: normalization = self.normalization frequency = self._validate_frequency(frequency) f_shape = np.shape(frequency) power = lombscargle_multiband( strip_units(self._trel), strip_units(self.y), strip_units(self.bands), dy=strip_units(self.dy), frequency=strip_units(np.ravel(frequency)), method=method, sb_method=sb_method, normalization=normalization, nterms_base=self.nterms_base, nterms_band=self.nterms_band, reg_base=self.reg_base, reg_band=self.reg_band, regularize_by_trace=self.regularize_by_trace, center_data=self.center_data, fit_mean=self.fit_mean, ) return np.reshape(power * self._power_unit(normalization), f_shape) def design_matrix(self, frequency, t_fit=None, bands_fit=None): """Compute the design matrix for a given frequency Parameters ---------- frequency : float the frequency for the model t_fit : array-like, `~astropy.units.Quantity`, or `~astropy.time.Time` (optional) Times (length ``n_samples``) at which to compute the model. If not specified, then the times and uncertainties of the input data are used. bands_fit : array-like, or str Bands to use in fitting, must be subset of bands in input data. Returns ------- ndarray The design matrix for the model at the given frequency. This should have a shape of (``len(t)``, ``n_parameters``). See Also -------- model model_parameters offset """ if t_fit is None: t_fit, dy = strip_units(self._trel, self.dy) else: t_fit, dy = strip_units( self._validate_t(self._as_relative_time("t", t_fit)), None ) if bands_fit is None: bands_fit = np.unique(self.bands) elif type(bands_fit) == str: bands_fit = [bands_fit] unique_bands = np.unique(bands_fit) unique_bands_fit = np.unique(bands_fit) bands_fit = bands_fit[:, np.newaxis] if not set(unique_bands_fit).issubset(set(unique_bands)): raise ValueError( "bands_fit does not match training data: " f"input: {set(unique_bands_fit)} output: {set(unique_bands)}" ) t_fit, bands_fit = np.broadcast_arrays(t_fit, bands_fit) return design_matrix( t_fit.ravel(), bands_fit.ravel(), frequency, dy, nterms_base=self.nterms_base, nterms_band=self.nterms_band, ) def model(self, t, frequency, bands_fit=None): """Compute the Lomb-Scargle model at the given frequency. The model at a particular frequency is a linear model: model = offset + dot(design_matrix, model_parameters) Parameters ---------- t : array-like or `~astropy.units.Quantity` ['time'] Times (length ``n_samples``) at which to compute the model. frequency : float the frequency for the model bands_fit : list or array-like the unique bands to fit in the model Returns ------- y : np.ndarray The model fit corresponding to the input times. Will have shape (``n_bands``,``n_samples``). See Also -------- design_matrix offset model_parameters """ if bands_fit is None: bands_fit = np.unique(self.bands) frequency = self._validate_frequency(frequency) t = self._validate_t(self._as_relative_time("t", t)) y_fit = periodic_fit( *strip_units(self._trel, self.y, self.dy), bands=self.bands, frequency=strip_units(frequency), t_fit=strip_units(t), bands_fit=bands_fit, center_data=self.center_data, nterms_base=self.nterms_base, nterms_band=self.nterms_band, reg_base=self.reg_base, reg_band=self.reg_band, regularize_by_trace=self.regularize_by_trace, ) return y_fit * get_unit(self.y) def offset(self, t_fit=None, bands_fit=None): """Return the offset array of the model The offset array of the model is the (weighted) mean of the y values in each band. Note that if self.center_data is False, the offset is 0 by definition. Parameters ---------- t_fit : array-like, `~astropy.units.Quantity`, or `~astropy.time.Time` (optional) Times (length ``n_samples``) at which to compute the model. If not specified, then the times and uncertainties of the input data are used. bands_fit : array-like, or str Bands to use in fitting, must be subset of bands in input data. Returns ------- offset : array See Also -------- design_matrix model model_parameters """ if bands_fit is None: bands_fit = np.unique(self.bands) if t_fit is None: on_fit = False t_fit = self.t else: on_fit = True bands_fit = bands_fit[:, np.newaxis] unique_bands = np.unique(self.bands) unique_bands_fit = np.unique(bands_fit) if not set(unique_bands_fit).issubset(set(unique_bands)): raise ValueError( "bands_fit does not match training data: " f"input: {set(unique_bands_fit)} output: {set(unique_bands)}" ) y, dy = strip_units(self.y, self.dy) if np.shape(t_fit) != np.shape( bands_fit ): # No need to broadcast if bands map to timestamps t_fit, bands_fit = np.broadcast_arrays(t_fit, bands_fit) # need to make sure all unique filters are represented u, i = np.unique( np.concatenate([bands_fit.ravel(), unique_bands]), return_inverse=True ) if not self.center_data: return 0 if dy is None: dy = 1 dy = np.broadcast_to(dy, y.shape) # Calculate ymeans -- per band ymeans = np.zeros(y.shape) # filter specific means for band in unique_bands: mask = self.bands == band ymeans[mask] = np.average(y[mask], weights=1 / dy[mask] ** 2) ymeans_fit = ymeans[i[: -len(unique_bands)]] if on_fit: return ymeans_fit * get_unit(self.y) else: return ymeans * get_unit(self.y) def model_parameters(self, frequency, units=True): r"""Compute the best-fit model parameters at the given frequency. The model described by these parameters is: .. math:: y(t; f, \vec{\theta}) = \theta_0 + \sum_{n=1}^{\tt nterms_base} [\theta_{2n-1}\sin(2\pi n f t) + \theta_{2n}\cos(2\pi n f t)] + \theta_0^{(k)} + \sum_{n=1}^{\tt nterms_band} [\theta_{2n-1}^{(k)}\sin(2\pi n f t) + where :math:`\vec{\theta}` is the array of parameters returned by this function. Parameters ---------- frequency : float the frequency for the model units : bool If True (default), return design matrix with data units. Returns ------- theta : np.ndarray (n_parameters,) The best-fit model parameters at the given frequency. See Also -------- design_matrix model offset """ frequency = self._validate_frequency(frequency) t, y, dy = strip_units(self._trel, self.y, self.dy) if self.center_data: y = y - strip_units(self.offset()) dy = np.ones_like(y) if dy is None else np.asarray(dy) X = design_matrix( t, self.bands, frequency, dy=dy, nterms_base=self.nterms_base, nterms_band=self.nterms_band, ) regularization = construct_regularization( self.bands, nterms_base=self.nterms_base, nterms_band=self.nterms_band, reg_base=self.reg_base, reg_band=self.reg_band, ) M = np.dot(X.T, X) if regularization is not None: # M is being affected by operations on diag diag = M.ravel(order="K")[:: M.shape[0] + 1] if self.regularize_by_trace: diag += diag.sum() * np.asarray(regularization) else: diag += np.asarray(regularization) try: parameters = np.linalg.solve(M, np.dot(X.T, y / dy)) except np.linalg.LinAlgError: parameters = np.dot(M, np.linalg.lstsq(X.T, y / dy)[0]) if units: parameters = get_unit(self.y) * parameters return parameters def false_alarm_probability(self): """Not Implemented""" raise NotImplementedError def false_alarm_level(self): """Not Implemented""" raise NotImplementedError def distribution(self): """Not Implemented""" raise NotImplementedError