def test_logprior(self): t0 = [10.0] lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) lp_test = lpost.logprior(t0) lp = np.log(scipy.stats.norm(self.countrate, self.cerr).pdf(t0)) assert lp == lp_test
def test_counts_are_nan(self): y = np.nan * np.ones(self.x.shape[0]) t0 = [10.0] self.model.amplitude = t0[0] lpost = GaussianPosterior(self.x, y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) assert np.isclose(lpost(t0), logmin, 1e-5)
def test_negative_loglikelihood(self): t0 = [10.0] self.model.amplitude = t0[0] mean_model = self.model(self.x) loglike = -np.sum(-0.5*np.log(2.*np.pi) - np.log(self.yerr) - \ 0.5*((self.y - mean_model)/self.yerr)**2.0) lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) loglike_test = lpost.loglikelihood(t0, neg=True) assert np.isclose(loglike, loglike_test)
def test_negative_loglikelihood(self): t0 = [10.0] self.model.amplitude = t0[0] mean_model = self.model(self.x) loglike = -np.sum(-0.5*np.log(2.*np.pi) - np.log(self.yerr) - \ 0.5*((self.y - mean_model)/self.yerr)**2.0) lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) loglike_test = lpost.loglikelihood(t0, neg=True) assert np.isclose(loglike, loglike_test)
def test_negative_posterior(self): t0 = [10.0] self.model.amplitude = t0[0] mean_model = self.model(self.x) lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) post_test = lpost(t0, neg=True) loglike = np.sum(-0.5*np.log(2.*np.pi) - np.log(self.yerr) - \ 0.5*((self.y - mean_model)/self.yerr)**2.0) logprior = np.log(scipy.stats.norm(self.countrate, self.cerr).pdf(t0)) post = -loglike - logprior assert np.isclose(post_test, post, atol=1.e-10)
def test_negative_posterior(self): t0 = [10.0] self.model.amplitude = t0[0] mean_model = self.model(self.x) lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) post_test = lpost(t0, neg=True) loglike = np.sum(-0.5*np.log(2.*np.pi) - np.log(self.yerr) - \ 0.5*((self.y - mean_model)/self.yerr)**2.0) logprior = np.log(scipy.stats.norm(self.countrate, self.cerr).pdf(t0)) post = -loglike - logprior assert np.isclose(post_test, post, atol=1.e-10)
def test_correct_number_of_parameters(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) with pytest.raises(IncorrectParameterError): lpost([2, 3])
def test_making_posterior(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) assert lpost.x.all() == self.x.all() assert lpost.y.all() == self.y.all()
def test_logprior_fails_without_prior(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) with pytest.raises(AttributeError): lpost.logprior([10])
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
def test_correct_number_of_parameters(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) with pytest.raises(IncorrectParameterError): lpost([2,3])
def test_making_posterior(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) lpost.logprior = set_logprior(lpost, self.priors) assert lpost.x.all() == self.x.all() assert lpost.y.all() == self.y.all()
def test_logprior_fails_without_prior(self): lpost = GaussianPosterior(self.x, self.y, self.yerr, self.model) with pytest.raises(AttributeError): lpost.logprior([10])