Source code for stingray.modeling.scripts


import numpy as np
from astropy.modeling import models

from stingray.modeling import PSDParEst, PSDPosterior, PSDLogLikelihood
from stingray.modeling import GaussianPosterior, GaussianLogLikelihood
from stingray import Powerspectrum

__all__ = ["fit_powerspectrum", "fit_crossspectrum", "fit_lorentzians"]


[docs]def fit_powerspectrum(ps, model, starting_pars=None, max_post=False, priors=None, fitmethod="L-BFGS-B"): """ Fit a number of Lorentzians to a power spectrum, possibly including white noise. Each Lorentzian has three parameters (amplitude, centroid position, full-width at half maximum), plus one extra parameter if the white noise level should be fit as well. Priors for each parameter can be included in case `max_post = True`, in which case the function will attempt a Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one entry for each parameter. The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of a total of `N` Lorentzians. The white noise level has a parameter `amplitude_(N+1)`. For example, a model with two Lorentzians and a white noise level would have parameters: [amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2]. Parameters ---------- ps : Powerspectrum A Powerspectrum object with the data to be fit model: astropy.modeling.models class instance The parametric model supposed to represent the data. For details see the astropy.modeling documentation starting_pars : iterable, optional, default None The list of starting guesses for the optimizer. If it is not provided, then default parameters are taken from `model`. See explanation above for ordering of parameters in this list. fit_whitenoise : bool, optional, default True If True, the code will attempt to fit a white noise level along with the Lorentzians. Be sure to include a starting parameter for the optimizer in `starting_pars`! max_post : bool, optional, default False If True, perform a Maximum-A-Posteriori fit of the data rather than a Maximum Likelihood fit. Note that this requires priors to be specified, otherwise this will cause an exception! priors : {dict | None}, optional, default None Dictionary with priors for the MAP fit. This should be of the form {"parameter name": probability distribution, ...} fitmethod : string, optional, default "L-BFGS-B" Specifies an optimization algorithm to use. Supply any valid option for `scipy.optimize.minimize`. Returns ------- parest : PSDParEst object A PSDParEst object for further analysis res : OptimizationResults object The OptimizationResults object storing useful results and quantities relating to the fit Examples -------- We start by making an example power spectrum with three Lorentzians >>> m = 1 >>> nfreq = 100000 >>> freq = np.linspace(1, 1000, nfreq) >>> np.random.seed(100) # set the seed for the random number generator >>> noise = np.random.exponential(size=nfreq) >>> model = models.PowerLaw1D() + models.Const1D() >>> model.x_0_0.fixed = True >>> alpha_0 = 2.0 >>> amplitude_0 = 100.0 >>> amplitude_1 = 2.0 >>> model.alpha_0 = alpha_0 >>> model.amplitude_0 = amplitude_0 >>> model.amplitude_1 = amplitude_1 >>> p = model(freq) >>> power = noise * p >>> ps = Powerspectrum() >>> ps.freq = freq >>> ps.power = power >>> ps.m = m >>> ps.df = freq[1] - freq[0] >>> ps.norm = "leahy" Now we have to guess starting parameters. For each Lorentzian, we have amplitude, centroid position and fwhm, and this pattern repeats for each Lorentzian in the fit. The white noise level is the last parameter. >>> t0 = [80, 1.5, 2.5] Let's also make a model to test: >>> model_to_test = models.PowerLaw1D() + models.Const1D() >>> model_to_test.amplitude_1.fixed = True We're ready for doing the fit: >>> parest, res = fit_powerspectrum(ps, model_to_test, t0) `res` contains a whole array of useful information about the fit, for example the parameters at the optimum: >>> p_opt = res.p_opt """ if not (isinstance(starting_pars, np.ndarray) or isinstance(starting_pars, list)): starting_pars = model.parameters if priors: lpost = PSDPosterior(ps.freq, ps.power, model, priors=priors, m=ps.m) else: lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m) parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post) res = parest.fit(lpost, starting_pars, neg=True) return parest, res
[docs]def fit_crossspectrum(cs, model, starting_pars=None, max_post=False, priors=None, fitmethod="L-BFGS-B"): """ Fit a number of Lorentzians to a cross spectrum, possibly including white noise. Each Lorentzian has three parameters (amplitude, centroid position, full-width at half maximum), plus one extra parameter if the white noise level should be fit as well. Priors for each parameter can be included in case `max_post = True`, in which case the function will attempt a Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one entry for each parameter. The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of a total of `N` Lorentzians. The white noise level has a parameter `amplitude_(N+1)`. For example, a model with two Lorentzians and a white noise level would have parameters: [amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2]. Parameters ---------- cs : Crossspectrum A Crossspectrum object with the data to be fit model: astropy.modeling.models class instance The parametric model supposed to represent the data. For details see the astropy.modeling documentation starting_pars : iterable, optional, default None The list of starting guesses for the optimizer. If it is not provided, then default parameters are taken from `model`. See explanation above for ordering of parameters in this list. max_post : bool, optional, default False If True, perform a Maximum-A-Posteriori fit of the data rather than a Maximum Likelihood fit. Note that this requires priors to be specified, otherwise this will cause an exception! priors : {dict | None}, optional, default None Dictionary with priors for the MAP fit. This should be of the form {"parameter name": probability distribution, ...} fitmethod : string, optional, default "L-BFGS-B" Specifies an optimization algorithm to use. Supply any valid option for `scipy.optimize.minimize`. Returns ------- parest : PSDParEst object A PSDParEst object for further analysis res : OptimizationResults object The OptimizationResults object storing useful results and quantities relating to the fit """ if not (isinstance(starting_pars, np.ndarray) or isinstance(starting_pars, list)): starting_pars = model.parameters if priors: lgauss = GaussianPosterior(cs.freq, np.abs(cs.power), cs.power_err, model, priors) else: lgauss = GaussianLogLikelihood(cs.freq, np.abs(cs.power), model=model, yerr=cs.power_err) parest = PSDParEst(cs, fitmethod=fitmethod, max_post=max_post) res = parest.fit(lgauss, starting_pars, neg=True) return parest, res
[docs]def fit_lorentzians(ps, nlor, starting_pars, fit_whitenoise=True, max_post=False, priors=None, fitmethod="L-BFGS-B"): """ Fit a number of Lorentzians to a power spectrum, possibly including white noise. Each Lorentzian has three parameters (amplitude, centroid position, full-width at half maximum), plus one extra parameter if the white noise level should be fit as well. Priors for each parameter can be included in case `max_post = True`, in which case the function will attempt a Maximum-A-Posteriori fit. Priors must be specified as a dictionary with one entry for each parameter. The parameter names are `(amplitude_i, x_0_i, fwhm_i)` for each `i` out of a total of `N` Lorentzians. The white noise level has a parameter `amplitude_(N+1)`. For example, a model with two Lorentzians and a white noise level would have parameters: [amplitude_0, x_0_0, fwhm_0, amplitude_1, x_0_1, fwhm_1, amplitude_2]. Parameters ---------- ps : Powerspectrum A Powerspectrum object with the data to be fit nlor : int The number of Lorentzians to fit starting_pars : iterable The list of starting guesses for the optimizer. If it is not provided, then default parameters are taken from `model`. See explanation above for ordering of parameters in this list. fit_whitenoise : bool, optional, default True If True, the code will attempt to fit a white noise level along with the Lorentzians. Be sure to include a starting parameter for the optimizer in `starting_pars`! max_post : bool, optional, default False If True, perform a Maximum-A-Posteriori fit of the data rather than a Maximum Likelihood fit. Note that this requires priors to be specified, otherwise this will cause an exception! priors : {dict | None}, optional, default None Dictionary with priors for the MAP fit. This should be of the form {"parameter name": probability distribution, ...} fitmethod : string, optional, default "L-BFGS-B" Specifies an optimization algorithm to use. Supply any valid option for `scipy.optimize.minimize`. Returns ------- parest : PSDParEst object A PSDParEst object for further analysis res : OptimizationResults object The OptimizationResults object storing useful results and quantities relating to the fit Examples -------- We start by making an example power spectrum with three Lorentzians >>> np.random.seed(400) >>> nlor = 3 >>> x_0_0 = 0.5 >>> x_0_1 = 2.0 >>> x_0_2 = 7.5 >>> amplitude_0 = 150.0 >>> amplitude_1 = 50.0 >>> amplitude_2 = 15.0 >>> fwhm_0 = 0.1 >>> fwhm_1 = 1.0 >>> fwhm_2 = 0.5 We will also include a white noise level: >>> whitenoise = 2.0 >>> model = (models.Lorentz1D(amplitude_0, x_0_0, fwhm_0) + ... models.Lorentz1D(amplitude_1, x_0_1, fwhm_1) + ... models.Lorentz1D(amplitude_2, x_0_2, fwhm_2) + ... models.Const1D(whitenoise)) >>> freq = np.linspace(0.01, 10.0, 1000) >>> p = model(freq) >>> noise = np.random.exponential(size=len(freq)) >>> power = p*noise >>> ps = Powerspectrum() >>> ps.freq = freq >>> ps.power = power >>> ps.df = ps.freq[1] - ps.freq[0] >>> ps.m = 1 Now we have to guess starting parameters. For each Lorentzian, we have amplitude, centroid position and fwhm, and this pattern repeats for each Lorentzian in the fit. The white noise level is the last parameter. >>> t0 = [150, 0.4, 0.2, 50, 2.3, 0.6, 20, 8.0, 0.4, 2.1] We're ready for doing the fit: >>> parest, res = fit_lorentzians(ps, nlor, t0) `res` contains a whole array of useful information about the fit, for example the parameters at the optimum: >>> p_opt = res.p_opt """ model = models.Lorentz1D() if nlor > 1: for i in range(nlor - 1): model += models.Lorentz1D() if fit_whitenoise: model += models.Const1D() return fit_powerspectrum(ps, model, starting_pars, max_post=max_post, priors=priors, fitmethod=fitmethod)