""" Searches using MCMC-based methods """ import sys import os import copy import logging from collections import OrderedDict import numpy as np import matplotlib import matplotlib.pyplot as plt import emcee import corner import dill as pickle import core from core import tqdm, args, earth_ephem, sun_ephem from optimal_setup_functions import get_V_estimate from optimal_setup_functions import get_optimal_setup import helper_functions class MCMCSearch(core.BaseSearchClass): """ MCMC search using ComputeFstat""" symbol_dictionary = dict( F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$', Delta='$\delta$', asini='asini', period='P', ecc='ecc', tp='tp', argp='argp') unit_dictionary = dict( F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad', asini='', period='s', ecc='', tp='', argp='') rescale_dictionary = {} @helper_functions.initializer def __init__(self, label, outdir, theta_prior, tref, minStartTime, maxStartTime, sftfilepath=None, nsteps=[100, 100], nwalkers=100, ntemps=1, log10temperature_min=-5, theta_initial=None, scatter_val=1e-10, binary=False, BSGL=False, minCoverFreq=None, maxCoverFreq=None, detectors=None, earth_ephem=None, sun_ephem=None, injectSources=None, assumeSqrtSX=None): """ Parameters label, outdir: str A label and directory to read/write data from/to sftfilepath: str Pattern to match SFTs using wildcards (*?) and ranges [0-9]; mutiple patterns can be given separated by colons. theta_prior: dict Dictionary of priors and fixed values for the search parameters. For each parameters (key of the dict), if it is to be held fixed the value should be the constant float, if it is be searched, the value should be a dictionary of the prior. theta_initial: dict, array, (None) Either a dictionary of distribution about which to distribute the initial walkers about, an array (from which the walkers will be scattered by scatter_val, or None in which case the prior is used. tref, minStartTime, maxStartTime: int GPS seconds of the reference time, start time and end time nsteps: list (m,) List specifying the number of steps to take, the last two entries give the nburn and nprod of the 'production' run, all entries before are for iterative initialisation steps (usually just one) e.g. [1000, 1000, 500]. nwalkers, ntemps: int, The number of walkers and temperates to use in the parallel tempered PTSampler. log10temperature_min float < 0 The log_10(tmin) value, the set of betas passed to PTSampler are generated from np.logspace(0, log10temperature_min, ntemps). binary: Bool If true, search over binary parameters detectors: str Two character reference to the data to use, specify None for no contraint. minCoverFreq, maxCoverFreq: float Minimum and maximum instantaneous frequency which will be covered over the SFT time span as passed to CreateFstatInput earth_ephem, sun_ephem: str Paths of the two files containing positions of Earth and Sun, respectively at evenly spaced times, as passed to CreateFstatInput If None defaults defined in BaseSearchClass will be used """ if os.path.isdir(outdir) is False: os.mkdir(outdir) self._add_log_file() logging.info( 'Set-up MCMC search for model {} on data {}'.format( self.label, self.sftfilepath)) self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label) self._unpack_input_theta() self.ndim = len(self.theta_keys) if self.log10temperature_min: self.betas = np.logspace(0, self.log10temperature_min, self.ntemps) else: self.betas = None if earth_ephem is None: self.earth_ephem = self.earth_ephem_default if sun_ephem is None: self.sun_ephem = self.sun_ephem_default if args.clean and os.path.isfile(self.pickle_path): os.rename(self.pickle_path, self.pickle_path+".old") self._log_input() def _log_input(self): logging.info('theta_prior = {}'.format(self.theta_prior)) logging.info('nwalkers={}'.format(self.nwalkers)) logging.info('scatter_val = {}'.format(self.scatter_val)) logging.info('nsteps = {}'.format(self.nsteps)) logging.info('ntemps = {}'.format(self.ntemps)) logging.info('log10temperature_min = {}'.format( self.log10temperature_min)) def _initiate_search_object(self): logging.info('Setting up search object') self.search = core.ComputeFstat( tref=self.tref, sftfilepath=self.sftfilepath, minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq, earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem, detectors=self.detectors, BSGL=self.BSGL, transient=False, minStartTime=self.minStartTime, maxStartTime=self.maxStartTime, binary=self.binary, injectSources=self.injectSources, assumeSqrtSX=self.assumeSqrtSX) def logp(self, theta_vals, theta_prior, theta_keys, search): H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in zip(theta_vals, theta_keys)] return np.sum(H) def logl(self, theta, search): for j, theta_i in enumerate(self.theta_idxs): self.fixed_theta[theta_i] = theta[j] FS = search.compute_fullycoherent_det_stat_single_point( *self.fixed_theta) return FS def _unpack_input_theta(self): full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta'] if self.binary: full_theta_keys += [ 'asini', 'period', 'ecc', 'tp', 'argp'] full_theta_keys_copy = copy.copy(full_theta_keys) full_theta_symbols = ['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$', r'$\delta$'] if self.binary: full_theta_symbols += [ 'asini', 'period', 'ecc', 'tp', 'argp'] self.theta_keys = [] fixed_theta_dict = {} for key, val in self.theta_prior.iteritems(): if type(val) is dict: fixed_theta_dict[key] = 0 self.theta_keys.append(key) elif type(val) in [float, int, np.float64]: fixed_theta_dict[key] = val else: raise ValueError( 'Type {} of {} in theta not recognised'.format( type(val), key)) full_theta_keys_copy.pop(full_theta_keys_copy.index(key)) if len(full_theta_keys_copy) > 0: raise ValueError(('Input dictionary `theta` is missing the' 'following keys: {}').format( full_theta_keys_copy)) self.fixed_theta = [fixed_theta_dict[key] for key in full_theta_keys] self.theta_idxs = [full_theta_keys.index(k) for k in self.theta_keys] self.theta_symbols = [full_theta_symbols[i] for i in self.theta_idxs] idxs = np.argsort(self.theta_idxs) self.theta_idxs = [self.theta_idxs[i] for i in idxs] self.theta_symbols = [self.theta_symbols[i] for i in idxs] self.theta_keys = [self.theta_keys[i] for i in idxs] def _check_initial_points(self, p0): for nt in range(self.ntemps): logging.info('Checking temperature {} chains'.format(nt)) initial_priors = np.array([ self.logp(p, self.theta_prior, self.theta_keys, self.search) for p in p0[nt]]) number_of_initial_out_of_bounds = sum(initial_priors == -np.inf) if number_of_initial_out_of_bounds > 0: logging.warning( 'Of {} initial values, {} are -np.inf due to the prior' .format(len(initial_priors), number_of_initial_out_of_bounds)) p0 = self._generate_new_p0_to_fix_initial_points( p0, nt, initial_priors) def _generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors): logging.info('Attempting to correct intial values') idxs = np.arange(self.nwalkers)[initial_priors == -np.inf] count = 0 while sum(initial_priors == -np.inf) > 0 and count < 100: for j in idxs: p0[nt][j] = (p0[nt][np.random.randint(0, self.nwalkers)]*( 1+np.random.normal(0, 1e-10, self.ndim))) initial_priors = np.array([ self.logp(p, self.theta_prior, self.theta_keys, self.search) for p in p0[nt]]) count += 1 if sum(initial_priors == -np.inf) > 0: logging.info('Failed to fix initial priors') else: logging.info('Suceeded to fix initial priors') return p0 def _OLD_run_sampler_with_progress_bar(self, sampler, ns, p0): for result in tqdm(sampler.sample(p0, iterations=ns), total=ns): pass return sampler def setup_convergence_testing( self, convergence_period=10, convergence_length=10, convergence_burnin_fraction=0.25, convergence_threshold_number=10, convergence_threshold=1.2, convergence_prod_threshold=2, convergence_plot_upper_lim=2, convergence_early_stopping=True): """ If called, convergence testing is used during the MCMC simulation This uses the Gelmanr-Rubin statistic based on the ratio of between and within walkers variance. The original statistic was developed for multiple (independent) MCMC simulations, in this context we simply use the walkers Parameters ---------- convergence_period: int period (in number of steps) at which to test convergence convergence_length: int number of steps to use in testing convergence - this should be large enough to measure the variance, but if it is too long this will result in incorect early convergence tests convergence_burnin_fraction: float [0, 1] the fraction of the burn-in period after which to start testing convergence_threshold_number: int the number of consecutive times where the test passes after which to break the burn-in and go to production convergence_threshold: float the threshold to use in diagnosing convergence. Gelman & Rubin recomend a value of 1.2, 1.1 for strict convergence convergence_prod_threshold: float the threshold to test the production values with convergence_plot_upper_lim: float the upper limit to use in the diagnostic plot convergence_early_stopping: bool if true, stop the burnin early if convergence is reached """ if convergence_length > convergence_period: raise ValueError('convergence_length must be < convergence_period') logging.info('Setting up convergence testing') self.convergence_length = convergence_length self.convergence_period = convergence_period self.convergence_burnin_fraction = convergence_burnin_fraction self.convergence_prod_threshold = convergence_prod_threshold self.convergence_diagnostic = [] self.convergence_diagnosticx = [] self.convergence_threshold_number = convergence_threshold_number self.convergence_threshold = convergence_threshold self.convergence_number = 0 self.convergence_plot_upper_lim = convergence_plot_upper_lim self.convergence_early_stopping = convergence_early_stopping def _get_convergence_statistic(self, i, sampler): s = sampler.chain[0, :, i-self.convergence_length+1:i+1, :] N = float(self.convergence_length) M = float(self.nwalkers) W = np.mean(np.var(s, axis=1), axis=0) per_walker_mean = np.mean(s, axis=1) mean = np.mean(per_walker_mean, axis=0) B = N / (M-1.) * np.sum((per_walker_mean-mean)**2, axis=0) Vhat = (N-1)/N * W + (M+1)/(M*N) * B c = Vhat/W self.convergence_diagnostic.append(c) self.convergence_diagnosticx.append(i - self.convergence_length/2) return c def _burnin_convergence_test(self, i, sampler, nburn): if i < self.convergence_burnin_fraction*nburn: return False if np.mod(i+1, self.convergence_period) != 0: return False c = self._get_convergence_statistic(i, sampler) if np.all(c < self.convergence_threshold): self.convergence_number += 1 else: self.convergence_number = 0 if self.convergence_early_stopping: return self.convergence_number > self.convergence_threshold_number def _prod_convergence_test(self, i, sampler, nburn): testA = i > nburn + self.convergence_length testB = np.mod(i+1, self.convergence_period) == 0 if testA and testB: self._get_convergence_statistic(i, sampler) def _check_production_convergence(self, k): bools = np.any( np.array(self.convergence_diagnostic)[k:, :] > self.convergence_prod_threshold, axis=1) if np.any(bools): logging.warning( '{} convergence tests in the production run of {} failed' .format(np.sum(bools), len(bools))) def _run_sampler(self, sampler, p0, nprod=0, nburn=0): if hasattr(self, 'convergence_period'): logging.info('Running {} burn-in steps with convergence testing' .format(nburn)) iterator = tqdm(sampler.sample(p0, iterations=nburn), total=nburn) for i, output in enumerate(iterator): if self._burnin_convergence_test(i, sampler, nburn): logging.info( 'Converged at {} before max number {} of steps reached' .format(i, nburn)) self.convergence_idx = i break iterator.close() logging.info('Running {} production steps'.format(nprod)) j = nburn k = len(self.convergence_diagnostic) for result in tqdm(sampler.sample(output[0], iterations=nprod), total=nprod): self._prod_convergence_test(j, sampler, nburn) j += 1 self._check_production_convergence(k) return sampler else: for result in tqdm(sampler.sample(p0, iterations=nburn+nprod), total=nburn+nprod): pass return sampler def run(self, proposal_scale_factor=2, create_plots=True, **kwargs): """ Run the MCMC simulatation """ self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use() if self.old_data_is_okay_to_use is True: logging.warning('Using saved data from {}'.format( self.pickle_path)) d = self.get_saved_data_dictionary() self.samples = d['samples'] self.lnprobs = d['lnprobs'] self.lnlikes = d['lnlikes'] return self._initiate_search_object() sampler = emcee.PTSampler( self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp, logpargs=(self.theta_prior, self.theta_keys, self.search), loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor) p0 = self._generate_initial_p0() p0 = self._apply_corrections_to_p0(p0) self._check_initial_points(p0) ninit_steps = len(self.nsteps) - 2 for j, n in enumerate(self.nsteps[:-2]): logging.info('Running {}/{} initialisation with {} steps'.format( j, ninit_steps, n)) sampler = self._run_sampler(sampler, p0, nburn=n) logging.info("Mean acceptance fraction: {}" .format(np.mean(sampler.acceptance_fraction, axis=1))) if self.ntemps > 1: logging.info("Tswap acceptance fraction: {}" .format(sampler.tswap_acceptance_fraction)) if create_plots: fig, axes = self._plot_walkers(sampler, symbols=self.theta_symbols, **kwargs) fig.tight_layout() fig.savefig('{}/{}_init_{}_walkers.png'.format( self.outdir, self.label, j), dpi=400) p0 = self._get_new_p0(sampler) p0 = self._apply_corrections_to_p0(p0) self._check_initial_points(p0) sampler.reset() if len(self.nsteps) > 1: nburn = self.nsteps[-2] else: nburn = 0 nprod = self.nsteps[-1] logging.info('Running final burn and prod with {} steps'.format( nburn+nprod)) sampler = self._run_sampler(sampler, p0, nburn=nburn, nprod=nprod) logging.info("Mean acceptance fraction: {}" .format(np.mean(sampler.acceptance_fraction, axis=1))) if self.ntemps > 1: logging.info("Tswap acceptance fraction: {}" .format(sampler.tswap_acceptance_fraction)) if create_plots: fig, axes = self._plot_walkers(sampler, symbols=self.theta_symbols, nprod=nprod, **kwargs) fig.tight_layout() fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label), dpi=200) samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim)) lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1)) lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1)) all_lnlikelihood = sampler.lnlikelihood self.samples = samples self.lnprobs = lnprobs self.lnlikes = lnlikes self.all_lnlikelihood = all_lnlikelihood self._save_data(sampler, samples, lnprobs, lnlikes, all_lnlikelihood) def _get_rescale_multiplier_for_key(self, key): """ Get the rescale multiplier from the rescale_dictionary Can either be a float, a string (in which case it is interpretted as a attribute of the MCMCSearch class, e.g. minStartTime, or non-existent in which case 0 is returned """ if key not in self.rescale_dictionary: return 1 if 'multiplier' in self.rescale_dictionary[key]: val = self.rescale_dictionary[key]['multiplier'] if type(val) == str: if hasattr(self, val): multiplier = getattr( self, self.rescale_dictionary[key]['multiplier']) else: raise ValueError( "multiplier {} not a class attribute".format(val)) else: multiplier = val else: multiplier = 1 return multiplier def _get_rescale_subtractor_for_key(self, key): """ Get the rescale subtractor from the rescale_dictionary Can either be a float, a string (in which case it is interpretted as a attribute of the MCMCSearch class, e.g. minStartTime, or non-existent in which case 0 is returned """ if key not in self.rescale_dictionary: return 0 if 'subtractor' in self.rescale_dictionary[key]: val = self.rescale_dictionary[key]['subtractor'] if type(val) == str: if hasattr(self, val): subtractor = getattr( self, self.rescale_dictionary[key]['subtractor']) else: raise ValueError( "subtractor {} not a class attribute".format(val)) else: subtractor = val else: subtractor = 0 return subtractor def _scale_samples(self, samples, theta_keys): """ Scale the samples using the rescale_dictionary """ for key in theta_keys: if key in self.rescale_dictionary: idx = theta_keys.index(key) s = samples[:, idx] subtractor = self._get_rescale_subtractor_for_key(key) s = s - subtractor multiplier = self._get_rescale_multiplier_for_key(key) s *= multiplier samples[:, idx] = s return samples def _get_labels(self): """ Combine the units, symbols and rescaling to give labels """ labels = [] for key in self.theta_keys: label = None s = self.symbol_dictionary[key] s.replace('_{glitch}', r'_\textrm{glitch}') u = self.unit_dictionary[key] if key in self.rescale_dictionary: if 'symbol' in self.rescale_dictionary[key]: s = self.rescale_dictionary[key]['symbol'] if 'label' in self.rescale_dictionary[key]: label = self.rescale_dictionary[key]['label'] if 'unit' in self.rescale_dictionary[key]: u = self.rescale_dictionary[key]['unit'] if label is None: label = '{} \n [{}]'.format(s, u) labels.append(label) return labels def plot_corner(self, figsize=(7, 7), add_prior=False, nstds=None, label_offset=0.4, dpi=300, rc_context={}, tglitch_ratio=False, fig_and_axes=None, save_fig=True, **kwargs): """ Generate a corner plot of the posterior Using the `corner` package (https://pypi.python.org/pypi/corner/), generate estimates of the posterior from the production samples. Parameters ---------- figsize: tuple (7, 7) Figure size in inches (passed to plt.subplots) add_prior: bool If true, plot the prior as a red line nstds: float The number of standard deviations to plot centered on the mean label_offset: float Offset the labels from the plot: useful to precent overlapping the tick labels with the axis labels dpi: int Passed to plt.savefig rc_context: dict Dictionary of rc values to set while generating the figure (see matplotlib rc for more details) tglitch_ratio: bool If true, and tglitch is a parameter, plot posteriors as the fractional time at which the glitch occurs instead of the actual time fig_and_axes: tuple fig and axes to plot on, the axes must be of the right shape, namely (ndim, ndim) save_fig: bool If true, save the figure, else return the fig, axes Note: kwargs are passed on to corner.coner """ if 'truths' in kwargs and len(kwargs['truths']) != self.ndim: logging.warning('len(Truths) != ndim, Truths will be ignored') kwargs['truths'] = None if self.ndim < 2: with plt.rc_context(rc_context): if fig_and_axes is None: fig, ax = plt.subplots(figsize=figsize) else: fig, ax = fig_and_axes ax.hist(self.samples, bins=50, histtype='stepfilled') ax.set_xlabel(self.theta_symbols[0]) fig.savefig('{}/{}_corner.png'.format( self.outdir, self.label), dpi=dpi) return with plt.rc_context(rc_context): if fig_and_axes is None: fig, axes = plt.subplots(self.ndim, self.ndim, figsize=figsize) else: fig, axes = fig_and_axes samples_plt = copy.copy(self.samples) labels = self._get_labels() samples_plt = self._scale_samples(samples_plt, self.theta_keys) if tglitch_ratio: for j, k in enumerate(self.theta_keys): if k == 'tglitch': s = samples_plt[:, j] samples_plt[:, j] = ( s - self.minStartTime)/( self.maxStartTime - self.minStartTime) labels[j] = r'$R_{\textrm{glitch}}$' if type(nstds) is int and 'range' not in kwargs: _range = [] for j, s in enumerate(samples_plt.T): median = np.median(s) std = np.std(s) _range.append((median - nstds*std, median + nstds*std)) elif 'range' in kwargs: _range = kwargs.pop('range') else: _range = None fig_triangle = corner.corner(samples_plt, labels=labels, fig=fig, bins=50, max_n_ticks=4, plot_contours=True, plot_datapoints=True, label_kwargs={'fontsize': 8}, data_kwargs={'alpha': 0.1, 'ms': 0.5}, range=_range, **kwargs) axes_list = fig_triangle.get_axes() axes = np.array(axes_list).reshape(self.ndim, self.ndim) plt.draw() for ax in axes[:, 0]: ax.yaxis.set_label_coords(-label_offset, 0.5) for ax in axes[-1, :]: ax.xaxis.set_label_coords(0.5, -label_offset) for ax in axes_list: ax.set_rasterized(True) ax.set_rasterization_zorder(-10) plt.tight_layout(h_pad=0.0, w_pad=0.0) fig.subplots_adjust(hspace=0.05, wspace=0.05) if add_prior: self._add_prior_to_corner(axes, self.samples) if save_fig: fig_triangle.savefig('{}/{}_corner.png'.format( self.outdir, self.label), dpi=dpi) else: return fig, axes def _add_prior_to_corner(self, axes, samples): for i, key in enumerate(self.theta_keys): ax = axes[i][i] xlim = ax.get_xlim() s = samples[:, i] prior = self._generic_lnprior(**self.theta_prior[key]) x = np.linspace(s.min(), s.max(), 100) multiplier = self._get_rescale_multiplier_for_key(key) subtractor = self._get_rescale_subtractor_for_key(key) ax2 = ax.twinx() ax2.get_yaxis().set_visible(False) ax2.plot((x-subtractor)*multiplier, [prior(xi) for xi in x], '-r') ax2.set_xlim(xlim) def plot_prior_posterior(self, normal_stds=2): """ Plot the posterior in the context of the prior """ fig, axes = plt.subplots(nrows=self.ndim, figsize=(8, 4*self.ndim)) N = 1000 from scipy.stats import gaussian_kde for i, (ax, key) in enumerate(zip(axes, self.theta_keys)): prior_dict = self.theta_prior[key] prior_func = self._generic_lnprior(**prior_dict) if prior_dict['type'] == 'unif': x = np.linspace(prior_dict['lower'], prior_dict['upper'], N) prior = prior_func(x) prior[0] = 0 prior[-1] = 0 elif prior_dict['type'] == 'norm': lower = prior_dict['loc'] - normal_stds * prior_dict['scale'] upper = prior_dict['loc'] + normal_stds * prior_dict['scale'] x = np.linspace(lower, upper, N) prior = prior_func(x) elif prior_dict['type'] == 'halfnorm': lower = prior_dict['loc'] upper = prior_dict['loc'] + normal_stds * prior_dict['scale'] x = np.linspace(lower, upper, N) prior = [prior_func(xi) for xi in x] elif prior_dict['type'] == 'neghalfnorm': upper = prior_dict['loc'] lower = prior_dict['loc'] - normal_stds * prior_dict['scale'] x = np.linspace(lower, upper, N) prior = [prior_func(xi) for xi in x] else: raise ValueError('Not implemented for prior type {}'.format( prior_dict['type'])) priorln = ax.plot(x, prior, 'r', label='prior') ax.set_xlabel(self.theta_symbols[i]) s = self.samples[:, i] while len(s) > 10**4: # random downsample to avoid slow calculation of kde s = np.random.choice(s, size=int(len(s)/2.)) kde = gaussian_kde(s) ax2 = ax.twinx() postln = ax2.plot(x, kde.pdf(x), 'k', label='posterior') ax2.set_yticklabels([]) ax.set_yticklabels([]) lns = priorln + postln labs = [l.get_label() for l in lns] axes[0].legend(lns, labs, loc=1, framealpha=0.8) fig.savefig('{}/{}_prior_posterior.png'.format( self.outdir, self.label)) def plot_cumulative_max(self, **kwargs): """ Plot the cumulative twoF for the maximum posterior estimate See the pyfstat.core.plot_twoF_cumulative function for further details """ d, maxtwoF = self.get_max_twoF() for key, val in self.theta_prior.iteritems(): if key not in d: d[key] = val if hasattr(self, 'search') is False: self._initiate_search_object() if self.binary is False: self.search.plot_twoF_cumulative( self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'], Alpha=d['Alpha'], Delta=d['Delta'], tstart=self.minStartTime, tend=self.maxStartTime, **kwargs) else: self.search.plot_twoF_cumulative( self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'], Alpha=d['Alpha'], Delta=d['Delta'], asini=d['asini'], period=d['period'], ecc=d['ecc'], argp=d['argp'], tp=d['argp'], tstart=self.minStartTime, tend=self.maxStartTime, **kwargs) def _generic_lnprior(self, **kwargs): """ Return a lambda function of the pdf Parameters ---------- kwargs: dict A dictionary containing 'type' of pdf and shape parameters """ def logunif(x, a, b): above = x < b below = x > a if type(above) is not np.ndarray: if above and below: return -np.log(b-a) else: return -np.inf else: idxs = np.array([all(tup) for tup in zip(above, below)]) p = np.zeros(len(x)) - np.inf p[idxs] = -np.log(b-a) return p def halfnorm(x, loc, scale): if x < loc: return -np.inf else: return -0.5*((x-loc)**2/scale**2+np.log(0.5*np.pi*scale**2)) def cauchy(x, x0, gamma): return 1.0/(np.pi*gamma*(1+((x-x0)/gamma)**2)) def exp(x, x0, gamma): if x > x0: return np.log(gamma) - gamma*(x - x0) else: return -np.inf if kwargs['type'] == 'unif': return lambda x: logunif(x, kwargs['lower'], kwargs['upper']) elif kwargs['type'] == 'halfnorm': return lambda x: halfnorm(x, kwargs['loc'], kwargs['scale']) elif kwargs['type'] == 'neghalfnorm': return lambda x: halfnorm(-x, kwargs['loc'], kwargs['scale']) elif kwargs['type'] == 'norm': return lambda x: -0.5*((x - kwargs['loc'])**2/kwargs['scale']**2 + np.log(2*np.pi*kwargs['scale']**2)) else: logging.info("kwargs:", kwargs) raise ValueError("Print unrecognise distribution") def _generate_rv(self, **kwargs): dist_type = kwargs.pop('type') if dist_type == "unif": return np.random.uniform(low=kwargs['lower'], high=kwargs['upper']) if dist_type == "norm": return np.random.normal(loc=kwargs['loc'], scale=kwargs['scale']) if dist_type == "halfnorm": return np.abs(np.random.normal(loc=kwargs['loc'], scale=kwargs['scale'])) if dist_type == "neghalfnorm": return -1 * np.abs(np.random.normal(loc=kwargs['loc'], scale=kwargs['scale'])) if dist_type == "lognorm": return np.random.lognormal( mean=kwargs['loc'], sigma=kwargs['scale']) else: raise ValueError("dist_type {} unknown".format(dist_type)) def _plot_walkers(self, sampler, symbols=None, alpha=0.4, color="k", temp=0, lw=0.1, nprod=0, add_det_stat_burnin=False, fig=None, axes=None, xoffset=0, plot_det_stat=False, context='ggplot', subtractions=None, labelpad=0.05): """ Plot all the chains from a sampler """ if context not in plt.style.available: raise ValueError(( 'The requested context {} is not available; please select a' ' context from `plt.style.available`').format(context)) if np.ndim(axes) > 1: axes = axes.flatten() shape = sampler.chain.shape if len(shape) == 3: nwalkers, nsteps, ndim = shape chain = sampler.chain[:, :, :] if len(shape) == 4: ntemps, nwalkers, nsteps, ndim = shape if temp < ntemps: logging.info("Plotting temperature {} chains".format(temp)) else: raise ValueError(("Requested temperature {} outside of" "available range").format(temp)) chain = sampler.chain[temp, :, :, :] if subtractions is None: subtractions = [0 for i in range(ndim)] else: if len(subtractions) != self.ndim: raise ValueError('subtractions must be of length ndim') if plot_det_stat: extra_subplots = 1 else: extra_subplots = 0 with plt.style.context((context)): plt.rcParams['text.usetex'] = True if fig is None and axes is None: fig = plt.figure(figsize=(4, 3.0*ndim)) ax = fig.add_subplot(ndim+extra_subplots, 1, 1) axes = [ax] + [fig.add_subplot(ndim+extra_subplots, 1, i) for i in range(2, ndim+1)] idxs = np.arange(chain.shape[1]) burnin_idx = chain.shape[1] - nprod if hasattr(self, 'convergence_idx'): convergence_idx = self.convergence_idx else: convergence_idx = burnin_idx if ndim > 1: for i in range(ndim): axes[i].ticklabel_format(useOffset=False, axis='y') cs = chain[:, :, i].T if burnin_idx > 0: axes[i].plot(xoffset+idxs[:convergence_idx+1], cs[:convergence_idx+1]-subtractions[i], color="r", alpha=alpha, lw=lw) axes[i].axvline(xoffset+convergence_idx, color='k', ls='--', lw=0.25) axes[i].plot(xoffset+idxs[burnin_idx:], cs[burnin_idx:]-subtractions[i], color="k", alpha=alpha, lw=lw) if symbols: if subtractions[i] == 0: axes[i].set_ylabel(symbols[i], labelpad=labelpad) else: axes[i].set_ylabel( symbols[i]+'$-$'+symbols[i]+'$_0$', labelpad=labelpad) if hasattr(self, 'convergence_diagnostic'): ax = axes[i].twinx() c_x = np.array(self.convergence_diagnosticx) c_y = np.array(self.convergence_diagnostic) break_idx = np.argmin(np.abs(c_x - burnin_idx)) ax.plot(c_x[:break_idx], c_y[:break_idx, i], '-b') ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-b') ax.set_ylabel('PSRF') ax.ticklabel_format(useOffset=False) ax.set_ylim(0.5, self.convergence_plot_upper_lim) else: axes[0].ticklabel_format(useOffset=False, axis='y') cs = chain[:, :, temp].T if burnin_idx: axes[0].plot(idxs[:burnin_idx], cs[:burnin_idx], color="r", alpha=alpha, lw=lw) axes[0].plot(idxs[burnin_idx:], cs[burnin_idx:], color="k", alpha=alpha, lw=lw) if symbols: axes[0].set_ylabel(symbols[0], labelpad=labelpad) if plot_det_stat: if len(axes) == ndim: axes.append(fig.add_subplot(ndim+1, 1, ndim+1)) lnl = sampler.lnlikelihood[temp, :, :] if burnin_idx and add_det_stat_burnin: burn_in_vals = lnl[:, :burnin_idx].flatten() try: axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)], bins=50, histtype='step', color='r') except ValueError: logging.info('Det. Stat. hist failed, most likely all ' 'values where the same') pass else: burn_in_vals = [] prod_vals = lnl[:, burnin_idx:].flatten() try: axes[-1].hist(prod_vals[~np.isnan(prod_vals)], bins=50, histtype='step', color='k') except ValueError: logging.info('Det. Stat. hist failed, most likely all ' 'values where the same') pass if self.BSGL: axes[-1].set_xlabel(r'$\mathcal{B}_\mathrm{S/GL}$') else: axes[-1].set_xlabel(r'$\widetilde{2\mathcal{F}}$') axes[-1].set_ylabel(r'$\textrm{Counts}$') combined_vals = np.append(burn_in_vals, prod_vals) if len(combined_vals) > 0: minv = np.min(combined_vals) maxv = np.max(combined_vals) Range = abs(maxv-minv) axes[-1].set_xlim(minv-0.1*Range, maxv+0.1*Range) xfmt = matplotlib.ticker.ScalarFormatter() xfmt.set_powerlimits((-4, 4)) axes[-1].xaxis.set_major_formatter(xfmt) axes[-2].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2) return fig, axes def _apply_corrections_to_p0(self, p0): """ Apply any correction to the initial p0 values """ return p0 def _generate_scattered_p0(self, p): """ Generate a set of p0s scattered about p """ p0 = [[p + self.scatter_val * p * np.random.randn(self.ndim) for i in xrange(self.nwalkers)] for j in xrange(self.ntemps)] return p0 def _generate_initial_p0(self): """ Generate a set of init vals for the walkers """ if type(self.theta_initial) == dict: logging.info('Generate initial values from initial dictionary') if hasattr(self, 'nglitch') and self.nglitch > 1: raise ValueError('Initial dict not implemented for nglitch>1') p0 = [[[self._generate_rv(**self.theta_initial[key]) for key in self.theta_keys] for i in range(self.nwalkers)] for j in range(self.ntemps)] elif type(self.theta_initial) == list: logging.info('Generate initial values from list of theta_initial') p0 = [[[self._generate_rv(**val) for val in self.theta_initial] for i in range(self.nwalkers)] for j in range(self.ntemps)] elif self.theta_initial is None: logging.info('Generate initial values from prior dictionary') p0 = [[[self._generate_rv(**self.theta_prior[key]) for key in self.theta_keys] for i in range(self.nwalkers)] for j in range(self.ntemps)] elif len(self.theta_initial) == self.ndim: p0 = self._generate_scattered_p0(self.theta_initial) else: raise ValueError('theta_initial not understood') return p0 def _get_new_p0(self, sampler): """ Returns new initial positions for walkers are burn0 stage This returns new positions for all walkers by scattering points about the maximum posterior with scale `scatter_val`. """ temp_idx = 0 pF = sampler.chain[temp_idx, :, :, :] lnl = sampler.lnlikelihood[temp_idx, :, :] lnp = sampler.lnprobability[temp_idx, :, :] # General warnings about the state of lnp if np.any(np.isnan(lnp)): logging.warning( "Of {} lnprobs {} are nan".format( np.shape(lnp), np.sum(np.isnan(lnp)))) if np.any(np.isposinf(lnp)): logging.warning( "Of {} lnprobs {} are +np.inf".format( np.shape(lnp), np.sum(np.isposinf(lnp)))) if np.any(np.isneginf(lnp)): logging.warning( "Of {} lnprobs {} are -np.inf".format( np.shape(lnp), np.sum(np.isneginf(lnp)))) lnp_finite = copy.copy(lnp) lnp_finite[np.isinf(lnp)] = np.nan idx = np.unravel_index(np.nanargmax(lnp_finite), lnp_finite.shape) p = pF[idx] p0 = self._generate_scattered_p0(p) self.search.BSGL = False twoF = self.logl(p, self.search) self.search.BSGL = self.BSGL logging.info(('Gen. new p0 from pos {} which had det. stat.={:2.1f},' ' twoF={:2.1f} and lnp={:2.1f}') .format(idx[1], lnl[idx], twoF, lnp_finite[idx])) return p0 def _get_data_dictionary_to_save(self): d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers, ntemps=self.ntemps, theta_keys=self.theta_keys, theta_prior=self.theta_prior, scatter_val=self.scatter_val, log10temperature_min=self.log10temperature_min, BSGL=self.BSGL) return d def _save_data(self, sampler, samples, lnprobs, lnlikes, all_lnlikelihood): d = self._get_data_dictionary_to_save() d['samples'] = samples d['lnprobs'] = lnprobs d['lnlikes'] = lnlikes d['all_lnlikelihood'] = all_lnlikelihood if os.path.isfile(self.pickle_path): logging.info('Saving backup of {} as {}.old'.format( self.pickle_path, self.pickle_path)) os.rename(self.pickle_path, self.pickle_path+".old") with open(self.pickle_path, "wb") as File: pickle.dump(d, File) def get_saved_data_dictionary(self): """ Returns dictionary of the data saved as pickle """ with open(self.pickle_path, "r") as File: d = pickle.load(File) return d def _check_old_data_is_okay_to_use(self): if args.use_old_data: logging.info("Forcing use of old data") return True if os.path.isfile(self.pickle_path) is False: logging.info('No pickled data found') return False if self.sftfilepath is not None: oldest_sft = min([os.path.getmtime(f) for f in self._get_list_of_matching_sfts()]) if os.path.getmtime(self.pickle_path) < oldest_sft: logging.info('Pickled data outdates sft files') return False old_d = self.get_saved_data_dictionary().copy() new_d = self._get_data_dictionary_to_save().copy() old_d.pop('samples') old_d.pop('lnprobs') old_d.pop('lnlikes') mod_keys = [] for key in new_d.keys(): if key in old_d: if new_d[key] != old_d[key]: mod_keys.append((key, old_d[key], new_d[key])) else: raise ValueError('Keys {} not in old dictionary'.format(key)) if len(mod_keys) == 0: return True else: logging.warning("Saved data differs from requested") logging.info("Differences found in following keys:") for key in mod_keys: if len(key) == 3: if np.isscalar(key[1]) or key[0] == 'nsteps': logging.info(" {} : {} -> {}".format(*key)) else: logging.info(" " + key[0]) else: logging.info(key) return False def get_max_twoF(self, threshold=0.05): """ Returns the max likelihood sample and the corresponding 2F value Note: the sample is returned as a dictionary along with an estimate of the standard deviation calculated from the std of all samples with a twoF within `threshold` (relative) to the max twoF """ if any(np.isposinf(self.lnlikes)): logging.info('twoF values contain positive infinite values') if any(np.isneginf(self.lnlikes)): logging.info('twoF values contain negative infinite values') if any(np.isnan(self.lnlikes)): logging.info('twoF values contain nan') idxs = np.isfinite(self.lnlikes) jmax = np.nanargmax(self.lnlikes[idxs]) maxlogl = self.lnlikes[jmax] d = OrderedDict() if self.BSGL: if hasattr(self, 'search') is False: self._initiate_search_object() p = self.samples[jmax] self.search.BSGL = False maxtwoF = self.logl(p, self.search) self.search.BSGL = self.BSGL else: maxtwoF = maxlogl repeats = [] for i, k in enumerate(self.theta_keys): if k in d and k not in repeats: d[k+'_0'] = d[k] # relabel the old key d.pop(k) repeats.append(k) if k in repeats: k = k + '_0' count = 1 while k in d: k = k.replace('_{}'.format(count-1), '_{}'.format(count)) count += 1 d[k] = self.samples[jmax][i] return d, maxtwoF def get_median_stds(self): """ Returns a dict of the median and std of all production samples """ d = OrderedDict() repeats = [] for s, k in zip(self.samples.T, self.theta_keys): if k in d and k not in repeats: d[k+'_0'] = d[k] # relabel the old key d[k+'_0_std'] = d[k+'_std'] d.pop(k) d.pop(k+'_std') repeats.append(k) if k in repeats: k = k + '_0' count = 1 while k in d: k = k.replace('_{}'.format(count-1), '_{}'.format(count)) count += 1 d[k] = np.median(s) d[k+'_std'] = np.std(s) return d def check_if_samples_are_railing(self, threshold=0.01): """ Returns a boolean estimate of if the samples are railing Parameters ---------- threshold: float [0, 1] Fraction of the uniform prior to test (at upper and lower bound) """ return_flag = False for s, k in zip(self.samples.T, self.theta_keys): prior = self.theta_prior[k] if prior['type'] == 'unif': prior_range = prior['upper'] - prior['lower'] edges = [] fracs = [] for l in ['lower', 'upper']: bools = np.abs(s - prior[l])/prior_range < threshold if np.any(bools): edges.append(l) fracs.append(str(100*float(np.sum(bools))/len(bools))) if len(edges) > 0: logging.warning( '{}% of the {} posterior is railing on the {} edges' .format('% & '.join(fracs), k, ' & '.join(edges))) return_flag = True return return_flag def write_par(self, method='med'): """ Writes a .par of the best-fit params with an estimated std """ logging.info('Writing {}/{}.par using the {} method'.format( self.outdir, self.label, method)) median_std_d = self.get_median_stds() max_twoF_d, max_twoF = self.get_max_twoF() logging.info('Writing par file with max twoF = {}'.format(max_twoF)) filename = '{}/{}.par'.format(self.outdir, self.label) with open(filename, 'w+') as f: f.write('MaxtwoF = {}\n'.format(max_twoF)) f.write('tref = {}\n'.format(self.tref)) if hasattr(self, 'theta0_index'): f.write('theta0_index = {}\n'.format(self.theta0_idx)) if method == 'med': for key, val in median_std_d.iteritems(): f.write('{} = {:1.16e}\n'.format(key, val)) if method == 'twoFmax': for key, val in max_twoF_d.iteritems(): f.write('{} = {:1.16e}\n'.format(key, val)) def write_prior_table(self): with open('{}/{}_prior.tex'.format(self.outdir, self.label), 'w') as f: f.write(r"\begin{tabular}{c l c} \hline" + '\n' r"Parameter & & & \\ \hhline{====}") for key, prior in self.theta_prior.iteritems(): if type(prior) is dict: Type = prior['type'] if Type == "unif": a = prior['lower'] b = prior['upper'] line = r"{} & $\mathrm{{Unif}}$({}, {}) & {}\\" elif Type == "norm": a = prior['loc'] b = prior['scale'] line = r"{} & $\mathcal{{N}}$({}, {}) & {}\\" elif Type == "halfnorm": a = prior['loc'] b = prior['scale'] line = r"{} & $|\mathcal{{N}}$({}, {})| & {}\\" u = self.unit_dictionary[key] s = self.symbol_dictionary[key] f.write("\n") a = helper_functions.texify_float(a) b = helper_functions.texify_float(b) f.write(" " + line.format(s, a, b, u) + r" \\") f.write("\n\end{tabular}\n") def print_summary(self): """ Prints a summary of the max twoF found to the terminal """ max_twoFd, max_twoF = self.get_max_twoF() median_std_d = self.get_median_stds() logging.info('Summary:') if hasattr(self, 'theta0_idx'): logging.info('theta0 index: {}'.format(self.theta0_idx)) logging.info('Max twoF: {} with parameters:'.format(max_twoF)) for k in np.sort(max_twoFd.keys()): print(' {:10s} = {:1.9e}'.format(k, max_twoFd[k])) logging.info('Median +/- std for production values') for k in np.sort(median_std_d.keys()): if 'std' not in k: logging.info(' {:10s} = {:1.9e} +/- {:1.9e}'.format( k, median_std_d[k], median_std_d[k+'_std'])) logging.info('\n') def _CF_twoFmax(self, theta, twoFmax, ntrials): Fmax = twoFmax/2.0 return (np.exp(1j*theta*twoFmax)*ntrials/2.0 * Fmax*np.exp(-Fmax)*(1-(1+Fmax)*np.exp(-Fmax))**(ntrials-1)) def _pdf_twoFhat(self, twoFhat, nglitch, ntrials, twoFmax=100, dtwoF=0.1): if np.ndim(ntrials) == 0: ntrials = np.zeros(nglitch+1) + ntrials twoFmax_int = np.arange(0, twoFmax, dtwoF) theta_int = np.arange(-1/dtwoF, 1./dtwoF, 1./twoFmax) CF_twoFmax_theta = np.array( [[np.trapz(self._CF_twoFmax(t, twoFmax_int, ntrial), twoFmax_int) for t in theta_int] for ntrial in ntrials]) CF_twoFhat_theta = np.prod(CF_twoFmax_theta, axis=0) pdf = (1/(2*np.pi)) * np.array( [np.trapz(np.exp(-1j*theta_int*twoFhat_val) * CF_twoFhat_theta, theta_int) for twoFhat_val in twoFhat]) return pdf.real def _p_val_twoFhat(self, twoFhat, ntrials, twoFhatmax=500, Npoints=1000): """ Caluculate the p-value for the given twoFhat in Gaussian noise Parameters ---------- twoFhat: float The observed twoFhat value ntrials: int, array of len Nglitch+1 The number of trials for each glitch+1 """ twoFhats = np.linspace(twoFhat, twoFhatmax, Npoints) pdf = self._pdf_twoFhat(twoFhats, self.nglitch, ntrials) return np.trapz(pdf, twoFhats) def get_p_value(self, delta_F0, time_trials=0): """ Get's the p-value for the maximum twoFhat value """ d, max_twoF = self.get_max_twoF() if self.nglitch == 1: tglitches = [d['tglitch']] else: tglitches = [d['tglitch_{}'.format(i)] for i in range(self.nglitch)] tboundaries = [self.minStartTime] + tglitches + [self.maxStartTime] deltaTs = np.diff(tboundaries) ntrials = [time_trials + delta_F0 * dT for dT in deltaTs] p_val = self._p_val_twoFhat(max_twoF, ntrials) print('p-value = {}'.format(p_val)) return p_val def compute_evidence(self): """ Computes the evidence/marginal likelihood for the model """ betas = self.betas mean_lnlikes = np.mean(np.mean(self.all_lnlikelihood, axis=1), axis=1) mean_lnlikes = mean_lnlikes[::-1] betas = betas[::-1] fig, (ax1, ax2) = plt.subplots(nrows=2, figsize=(6, 8)) if any(np.isinf(mean_lnlikes)): print("WARNING mean_lnlikes contains inf: recalculating without" " the {} infs".format(len(betas[np.isinf(mean_lnlikes)]))) idxs = np.isinf(mean_lnlikes) mean_lnlikes = mean_lnlikes[~idxs] betas = betas[~idxs] log10evidence = np.trapz(mean_lnlikes, betas)/np.log(10) z1 = np.trapz(mean_lnlikes, betas) z2 = np.trapz(mean_lnlikes[::-1][::2][::-1], betas[::-1][::2][::-1]) log10evidence_err = np.abs(z1 - z2) / np.log(10) ax1.semilogx(betas, mean_lnlikes, "-o") ax1.set_xlabel(r"$\beta$") ax1.set_ylabel(r"$\langle \log(\mathcal{L}) \rangle$") print("log10 evidence for {} = {} +/- {}".format( self.label, log10evidence, log10evidence_err)) min_betas = [] evidence = [] for i in range(len(betas)/2): min_betas.append(betas[i]) lnZ = np.trapz(mean_lnlikes[i:], betas[i:]) evidence.append(lnZ/np.log(10)) ax2.semilogx(min_betas, evidence, "-o") ax2.set_ylabel(r"$\int_{\beta_{\textrm{Min}}}^{\beta=1}" + r"\langle \log(\mathcal{L})\rangle d\beta$", size=16) ax2.set_xlabel(r"$\beta_{\textrm{min}}$") plt.tight_layout() fig.savefig("{}/{}_beta_lnl.png".format(self.outdir, self.label)) class MCMCGlitchSearch(MCMCSearch): """ MCMC search using the SemiCoherentGlitchSearch """ symbol_dictionary = dict( F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$', Delta='$\delta$', delta_F0='$\delta f$', delta_F1='$\delta \dot{f}$', tglitch='$t_\mathrm{glitch}$') unit_dictionary = dict( F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad', delta_F0='Hz', delta_F1='Hz/s', tglitch='s') rescale_dictionary = dict( tglitch={ 'multiplier': 1/86400., 'subtractor': 'minStartTime', 'unit': 'day', 'label': 'Glitch time \n days after minStartTime'} ) @helper_functions.initializer def __init__(self, label, outdir, sftfilepath, theta_prior, tref, minStartTime, maxStartTime, nglitch=1, nsteps=[100, 100], nwalkers=100, ntemps=1, log10temperature_min=-5, theta_initial=None, scatter_val=1e-10, dtglitchmin=1*86400, theta0_idx=0, detectors=None, BSGL=False, minCoverFreq=None, maxCoverFreq=None, earth_ephem=None, sun_ephem=None): """ Parameters ---------- label, outdir: str A label and directory to read/write data from/to sftfilepath: str File patern to match SFTs theta_prior: dict Dictionary of priors and fixed values for the search parameters. For each parameters (key of the dict), if it is to be held fixed the value should be the constant float, if it is be searched, the value should be a dictionary of the prior. theta_initial: dict, array, (None) Either a dictionary of distribution about which to distribute the initial walkers about, an array (from which the walkers will be scattered by scatter_val), or None in which case the prior is used. scatter_val, float or ndim array Size of scatter to use about the initialisation step, if given as an array it must be of length ndim and the order is given by theta_keys nglitch: int The number of glitches to allow tref, minStartTime, maxStartTime: int GPS seconds of the reference time, start time and end time nsteps: list (m,) List specifying the number of steps to take, the last two entries give the nburn and nprod of the 'production' run, all entries before are for iterative initialisation steps (usually just one) e.g. [1000, 1000, 500]. dtglitchmin: int The minimum duration (in seconds) of a segment between two glitches or a glitch and the start/end of the data nwalkers, ntemps: int, The number of walkers and temperates to use in the parallel tempered PTSampler. log10temperature_min float < 0 The log_10(tmin) value, the set of betas passed to PTSampler are generated from np.logspace(0, log10temperature_min, ntemps). theta0_idx, int Index (zero-based) of which segment the theta refers to - uyseful if providing a tight prior on theta to allow the signal to jump too theta (and not just from) detectors: str Two character reference to the data to use, specify None for no contraint. minCoverFreq, maxCoverFreq: float Minimum and maximum instantaneous frequency which will be covered over the SFT time span as passed to CreateFstatInput earth_ephem, sun_ephem: str Paths of the two files containing positions of Earth and Sun, respectively at evenly spaced times, as passed to CreateFstatInput If None defaults defined in BaseSearchClass will be used """ if os.path.isdir(outdir) is False: os.mkdir(outdir) self._add_log_file() logging.info(('Set-up MCMC glitch search with {} glitches for model {}' ' on data {}').format(self.nglitch, self.label, self.sftfilepath)) self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label) self._unpack_input_theta() self.ndim = len(self.theta_keys) if self.log10temperature_min: self.betas = np.logspace(0, self.log10temperature_min, self.ntemps) else: self.betas = None if earth_ephem is None: self.earth_ephem = self.earth_ephem_default if sun_ephem is None: self.sun_ephem = self.sun_ephem_default if args.clean and os.path.isfile(self.pickle_path): os.rename(self.pickle_path, self.pickle_path+".old") self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use() self._log_input() def _initiate_search_object(self): logging.info('Setting up search object') self.search = core.SemiCoherentGlitchSearch( label=self.label, outdir=self.outdir, sftfilepath=self.sftfilepath, tref=self.tref, minStartTime=self.minStartTime, maxStartTime=self.maxStartTime, minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq, earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem, detectors=self.detectors, BSGL=self.BSGL, nglitch=self.nglitch, theta0_idx=self.theta0_idx) def logp(self, theta_vals, theta_prior, theta_keys, search): if self.nglitch > 1: ts = ([self.minStartTime] + list(theta_vals[-self.nglitch:]) + [self.maxStartTime]) if np.array_equal(ts, np.sort(ts)) is False: return -np.inf if any(np.diff(ts) < self.dtglitchmin): return -np.inf H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in zip(theta_vals, theta_keys)] return np.sum(H) def logl(self, theta, search): if self.nglitch > 1: ts = ([self.minStartTime] + list(theta[-self.nglitch:]) + [self.maxStartTime]) if np.array_equal(ts, np.sort(ts)) is False: return -np.inf for j, theta_i in enumerate(self.theta_idxs): self.fixed_theta[theta_i] = theta[j] FS = search.compute_nglitch_fstat(*self.fixed_theta) return FS def _unpack_input_theta(self): glitch_keys = ['delta_F0', 'delta_F1', 'tglitch'] full_glitch_keys = list(np.array( [[gk]*self.nglitch for gk in glitch_keys]).flatten()) if 'tglitch_0' in self.theta_prior: full_glitch_keys[-self.nglitch:] = [ 'tglitch_{}'.format(i) for i in range(self.nglitch)] full_glitch_keys[-2*self.nglitch:-1*self.nglitch] = [ 'delta_F1_{}'.format(i) for i in range(self.nglitch)] full_glitch_keys[-4*self.nglitch:-2*self.nglitch] = [ 'delta_F0_{}'.format(i) for i in range(self.nglitch)] full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta']+full_glitch_keys full_theta_keys_copy = copy.copy(full_theta_keys) glitch_symbols = ['$\delta f$', '$\delta \dot{f}$', r'$t_{glitch}$'] full_glitch_symbols = list(np.array( [[gs]*self.nglitch for gs in glitch_symbols]).flatten()) full_theta_symbols = (['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$', r'$\delta$'] + full_glitch_symbols) self.theta_keys = [] fixed_theta_dict = {} for key, val in self.theta_prior.iteritems(): if type(val) is dict: fixed_theta_dict[key] = 0 if key in glitch_keys: for i in range(self.nglitch): self.theta_keys.append(key) else: self.theta_keys.append(key) elif type(val) in [float, int, np.float64]: fixed_theta_dict[key] = val else: raise ValueError( 'Type {} of {} in theta not recognised'.format( type(val), key)) if key in glitch_keys: for i in range(self.nglitch): full_theta_keys_copy.pop(full_theta_keys_copy.index(key)) else: full_theta_keys_copy.pop(full_theta_keys_copy.index(key)) if len(full_theta_keys_copy) > 0: raise ValueError(('Input dictionary `theta` is missing the' 'following keys: {}').format( full_theta_keys_copy)) self.fixed_theta = [fixed_theta_dict[key] for key in full_theta_keys] self.theta_idxs = [full_theta_keys.index(k) for k in self.theta_keys] self.theta_symbols = [full_theta_symbols[i] for i in self.theta_idxs] idxs = np.argsort(self.theta_idxs) self.theta_idxs = [self.theta_idxs[i] for i in idxs] self.theta_symbols = [self.theta_symbols[i] for i in idxs] self.theta_keys = [self.theta_keys[i] for i in idxs] # Correct for number of glitches in the idxs self.theta_idxs = np.array(self.theta_idxs) while np.sum(self.theta_idxs[:-1] == self.theta_idxs[1:]) > 0: for i, idx in enumerate(self.theta_idxs): if idx in self.theta_idxs[:i]: self.theta_idxs[i] += 1 def _get_data_dictionary_to_save(self): d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers, ntemps=self.ntemps, theta_keys=self.theta_keys, theta_prior=self.theta_prior, scatter_val=self.scatter_val, log10temperature_min=self.log10temperature_min, theta0_idx=self.theta0_idx, BSGL=self.BSGL) return d def _apply_corrections_to_p0(self, p0): p0 = np.array(p0) if self.nglitch > 1: p0[:, :, -self.nglitch:] = np.sort(p0[:, :, -self.nglitch:], axis=2) return p0 def plot_cumulative_max(self): fig, ax = plt.subplots() d, maxtwoF = self.get_max_twoF() for key, val in self.theta_prior.iteritems(): if key not in d: d[key] = val if self.nglitch > 1: delta_F0s = [d['delta_F0_{}'.format(i)] for i in range(self.nglitch)] delta_F0s.insert(self.theta0_idx, 0) delta_F0s = np.array(delta_F0s) delta_F0s[:self.theta0_idx] *= -1 tglitches = [d['tglitch_{}'.format(i)] for i in range(self.nglitch)] elif self.nglitch == 1: delta_F0s = [d['delta_F0']] delta_F0s.insert(self.theta0_idx, 0) delta_F0s = np.array(delta_F0s) delta_F0s[:self.theta0_idx] *= -1 tglitches = [d['tglitch']] tboundaries = [self.minStartTime] + tglitches + [self.maxStartTime] for j in range(self.nglitch+1): ts = tboundaries[j] te = tboundaries[j+1] if (te - ts)/86400 < 5: logging.info('Period too short to perform cumulative search') continue if j < self.theta0_idx: summed_deltaF0 = np.sum(delta_F0s[j:self.theta0_idx]) F0_j = d['F0'] - summed_deltaF0 taus, twoFs = self.search.calculate_twoF_cumulative( F0_j, F1=d['F1'], F2=d['F2'], Alpha=d['Alpha'], Delta=d['Delta'], tstart=ts, tend=te) elif j >= self.theta0_idx: summed_deltaF0 = np.sum(delta_F0s[self.theta0_idx:j+1]) F0_j = d['F0'] + summed_deltaF0 taus, twoFs = self.search.calculate_twoF_cumulative( F0_j, F1=d['F1'], F2=d['F2'], Alpha=d['Alpha'], Delta=d['Delta'], tstart=ts, tend=te) ax.plot(ts+taus, twoFs) ax.set_xlabel('GPS time') fig.savefig('{}/{}_twoFcumulative.png'.format(self.outdir, self.label)) class MCMCSemiCoherentSearch(MCMCSearch): """ MCMC search for a signal using the semi-coherent ComputeFstat """ @helper_functions.initializer def __init__(self, label, outdir, theta_prior, tref, sftfilepath=None, nsegs=None, nsteps=[100, 100, 100], nwalkers=100, binary=False, ntemps=1, log10temperature_min=-5, theta_initial=None, scatter_val=1e-10, detectors=None, BSGL=False, minStartTime=None, maxStartTime=None, minCoverFreq=None, maxCoverFreq=None, earth_ephem=None, sun_ephem=None, injectSources=None, assumeSqrtSX=None): """ """ if os.path.isdir(outdir) is False: os.mkdir(outdir) self._add_log_file() logging.info(('Set-up MCMC semi-coherent search for model {} on data' '{}').format( self.label, self.sftfilepath)) self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label) self._unpack_input_theta() self.ndim = len(self.theta_keys) if self.log10temperature_min: self.betas = np.logspace(0, self.log10temperature_min, self.ntemps) else: self.betas = None if earth_ephem is None: self.earth_ephem = self.earth_ephem_default if sun_ephem is None: self.sun_ephem = self.sun_ephem_default if args.clean and os.path.isfile(self.pickle_path): os.rename(self.pickle_path, self.pickle_path+".old") self._log_input() def _get_data_dictionary_to_save(self): d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers, ntemps=self.ntemps, theta_keys=self.theta_keys, theta_prior=self.theta_prior, scatter_val=self.scatter_val, log10temperature_min=self.log10temperature_min, BSGL=self.BSGL, nsegs=self.nsegs) return d def _initiate_search_object(self): logging.info('Setting up search object') self.search = core.SemiCoherentSearch( label=self.label, outdir=self.outdir, tref=self.tref, nsegs=self.nsegs, sftfilepath=self.sftfilepath, binary=self.binary, BSGL=self.BSGL, minStartTime=self.minStartTime, maxStartTime=self.maxStartTime, minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq, detectors=self.detectors, earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem, injectSources=self.injectSources, assumeSqrtSX=self.assumeSqrtSX) def logp(self, theta_vals, theta_prior, theta_keys, search): H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in zip(theta_vals, theta_keys)] return np.sum(H) def logl(self, theta, search): for j, theta_i in enumerate(self.theta_idxs): self.fixed_theta[theta_i] = theta[j] FS = search.run_semi_coherent_computefstatistic_single_point( *self.fixed_theta) return FS class MCMCFollowUpSearch(MCMCSemiCoherentSearch): """ A follow up procudure increasing the coherence time in a zoom """ def _get_data_dictionary_to_save(self): d = dict(nwalkers=self.nwalkers, ntemps=self.ntemps, theta_keys=self.theta_keys, theta_prior=self.theta_prior, scatter_val=self.scatter_val, log10temperature_min=self.log10temperature_min, BSGL=self.BSGL, run_setup=self.run_setup) return d def update_search_object(self): logging.info('Update search object') self.search.init_computefstatistic_single_point() def get_width_from_prior(self, prior, key): if prior[key]['type'] == 'unif': return prior[key]['upper'] - prior[key]['lower'] def get_mid_from_prior(self, prior, key): if prior[key]['type'] == 'unif': return .5*(prior[key]['upper'] + prior[key]['lower']) def init_V_estimate_parameters(self): if 'Alpha' in self.theta_keys: DeltaAlpha = self.get_width_from_prior(self.theta_prior, 'Alpha') DeltaDelta = self.get_width_from_prior(self.theta_prior, 'Delta') DeltaMid = self.get_mid_from_prior(self.theta_prior, 'Delta') DeltaOmega = np.sin(np.pi/2 - DeltaMid) * DeltaDelta * DeltaAlpha logging.info('Search over Alpha and Delta') else: logging.info('No sky search requested') DeltaOmega = 0 if 'F0' in self.theta_keys: DeltaF0 = self.get_width_from_prior(self.theta_prior, 'F0') else: raise ValueError("You aren't searching over F0?") DeltaFs = [DeltaF0] if 'F1' in self.theta_keys: DeltaF1 = self.get_width_from_prior(self.theta_prior, 'F1') DeltaFs.append(DeltaF1) if 'F2' in self.theta_keys: DeltaF2 = self.get_width_from_prior(self.theta_prior, 'F2') DeltaFs.append(DeltaF2) logging.info('Searching over Frequency and {} spin-down components' .format(len(DeltaFs)-1)) if type(self.theta_prior['F0']) == dict: fiducial_freq = self.get_mid_from_prior(self.theta_prior, 'F0') else: fiducial_freq = self.theta_prior['F0'] return fiducial_freq, DeltaOmega, DeltaFs def read_setup_input_file(self, run_setup_input_file): with open(run_setup_input_file, 'r+') as f: d = pickle.load(f) return d def write_setup_input_file(self, run_setup_input_file, R, Nsegs0, nsegs_vals, V_vals, DeltaOmega, DeltaFs): d = dict(R=R, Nsegs0=Nsegs0, nsegs_vals=nsegs_vals, V_vals=V_vals, DeltaOmega=DeltaOmega, DeltaFs=DeltaFs) with open(run_setup_input_file, 'w+') as f: pickle.dump(d, f) def check_old_run_setup(self, old_setup, **kwargs): try: truths = [val == old_setup[key] for key, val in kwargs.iteritems()] return all(truths) except KeyError: return False def init_run_setup(self, run_setup=None, R=10, Nsegs0=None, log_table=True, gen_tex_table=True): if run_setup is None and Nsegs0 is None: raise ValueError( 'You must either specify the run_setup, or Nsegs0 from which ' 'the optimial run_setup given R can be estimated') fiducial_freq, DeltaOmega, DeltaFs = self.init_V_estimate_parameters() if run_setup is None: logging.info('No run_setup provided') run_setup_input_file = '{}/{}_run_setup.p'.format( self.outdir, self.label) if os.path.isfile(run_setup_input_file): logging.info('Checking old setup input file {}'.format( run_setup_input_file)) old_setup = self.read_setup_input_file(run_setup_input_file) if self.check_old_run_setup(old_setup, R=R, Nsegs0=Nsegs0, DeltaOmega=DeltaOmega, DeltaFs=DeltaFs): logging.info('Using old setup with R={}, Nsegs0={}'.format( R, Nsegs0)) nsegs_vals = old_setup['nsegs_vals'] V_vals = old_setup['V_vals'] generate_setup = False else: logging.info( 'Old setup does not match requested R, Nsegs0') generate_setup = True else: generate_setup = True if generate_setup: nsegs_vals, V_vals = get_optimal_setup( R, Nsegs0, self.tref, self.minStartTime, self.maxStartTime, DeltaOmega, DeltaFs, fiducial_freq, self.search.detector_names, self.earth_ephem, self.sun_ephem) self.write_setup_input_file(run_setup_input_file, R, Nsegs0, nsegs_vals, V_vals, DeltaOmega, DeltaFs) run_setup = [((self.nsteps[0], 0), nsegs, False) for nsegs in nsegs_vals[:-1]] run_setup.append( ((self.nsteps[0], self.nsteps[1]), nsegs_vals[-1], False)) else: logging.info('Calculating the number of templates for this setup') V_vals = [] for i, rs in enumerate(run_setup): rs = list(rs) if len(rs) == 2: rs.append(False) if np.shape(rs[0]) == (): rs[0] = (rs[0], 0) run_setup[i] = rs if args.no_template_counting: V_vals.append([1, 1, 1]) else: V, Vsky, Vpe = get_V_estimate( rs[1], self.tref, self.minStartTime, self.maxStartTime, DeltaOmega, DeltaFs, fiducial_freq, self.search.detector_names, self.earth_ephem, self.sun_ephem) V_vals.append([V, Vsky, Vpe]) if log_table: logging.info('Using run-setup as follows:') logging.info('Stage | nburn | nprod | nsegs | Tcoh d | resetp0 |' ' V = Vsky x Vpe') for i, rs in enumerate(run_setup): Tcoh = (self.maxStartTime - self.minStartTime) / rs[1] / 86400 if V_vals[i] is None: vtext = 'N/A' else: vtext = '{:1.0e} = {:1.0e} x {:1.0e}'.format( V_vals[i][0], V_vals[i][1], V_vals[i][2]) logging.info('{} | {} | {} | {} | {} | {} | {}'.format( str(i).ljust(5), str(rs[0][0]).ljust(5), str(rs[0][1]).ljust(5), str(rs[1]).ljust(5), '{:6.1f}'.format(Tcoh), str(rs[2]).ljust(7), vtext)) if gen_tex_table: filename = '{}/{}_run_setup.tex'.format(self.outdir, self.label) if DeltaOmega > 0: with open(filename, 'w+') as f: f.write(r'\begin{tabular}{c|cccccc}' + '\n') f.write(r'Stage & $\Nseg$ & $\Tcoh^{\rm days}$ &' r'$\Nsteps$ & $\V$ & $\Vsky$ & $\Vpe$ \\ \hline' '\n') for i, rs in enumerate(run_setup): Tcoh = float( self.maxStartTime - self.minStartTime)/rs[1]/86400 line = r'{} & {} & {} & {} & {} & {} & {} \\' + '\n' if V_vals[i][0] is None: V = Vsky = Vpe = 'N/A' else: V, Vsky, Vpe = V_vals[i] if rs[0][-1] == 0: nsteps = rs[0][0] else: nsteps = '{},{}'.format(*rs[0]) line = line.format(i, rs[1], '{:1.1f}'.format(Tcoh), nsteps, helper_functions.texify_float(V), helper_functions.texify_float(Vsky), helper_functions.texify_float(Vpe)) f.write(line) f.write(r'\end{tabular}' + '\n') else: with open(filename, 'w+') as f: f.write(r'\begin{tabular}{c|cccc}' + '\n') f.write(r'Stage & $\Nseg$ & $\Tcoh^{\rm days}$ &' r'$\Nsteps$ & $\Vpe$ \\ \hline' '\n') for i, rs in enumerate(run_setup): Tcoh = float( self.maxStartTime - self.minStartTime)/rs[1]/86400 line = r'{} & {} & {} & {} & {} \\' + '\n' if V_vals[i] is None: V = Vsky = Vpe = 'N/A' else: V, Vsky, Vpe = V_vals[i] if rs[0][-1] == 0: nsteps = rs[0][0] else: nsteps = '{},{}'.format(*rs[0]) line = line.format(i, rs[1], '{:1.1f}'.format(Tcoh), nsteps, helper_functions.texify_float(Vpe)) f.write(line) f.write(r'\end{tabular}' + '\n') if args.setup_only: logging.info("Exit as requested by setup_only flag") sys.exit() else: return run_setup def run(self, run_setup=None, proposal_scale_factor=2, R=10, Nsegs0=None, create_plots=True, log_table=True, gen_tex_table=True, fig=None, axes=None, return_fig=False, **kwargs): """ Run the follow-up with the given run_setup Parameters ---------- run_setup: list of tuples """ self.nsegs = 1 self._initiate_search_object() run_setup = self.init_run_setup( run_setup, R=R, Nsegs0=Nsegs0, log_table=log_table, gen_tex_table=gen_tex_table) self.run_setup = run_setup self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use() if self.old_data_is_okay_to_use is True: logging.warning('Using saved data from {}'.format( self.pickle_path)) d = self.get_saved_data_dictionary() self.samples = d['samples'] self.lnprobs = d['lnprobs'] self.lnlikes = d['lnlikes'] self.nsegs = run_setup[-1][1] return nsteps_total = 0 for j, ((nburn, nprod), nseg, reset_p0) in enumerate(run_setup): if j == 0: p0 = self._generate_initial_p0() p0 = self._apply_corrections_to_p0(p0) elif reset_p0: p0 = self._get_new_p0(sampler) p0 = self._apply_corrections_to_p0(p0) # self._check_initial_points(p0) else: p0 = sampler.chain[:, :, -1, :] self.nsegs = nseg self.search.nsegs = nseg self.update_search_object() self.search.init_semicoherent_parameters() sampler = emcee.PTSampler( self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp, logpargs=(self.theta_prior, self.theta_keys, self.search), loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor) Tcoh = (self.maxStartTime-self.minStartTime)/nseg/86400. logging.info(('Running {}/{} with {} steps and {} nsegs ' '(Tcoh={:1.2f} days)').format( j+1, len(run_setup), (nburn, nprod), nseg, Tcoh)) sampler = self._run_sampler(sampler, p0, nburn=nburn, nprod=nprod) logging.info("Mean acceptance fraction: {}" .format(np.mean(sampler.acceptance_fraction, axis=1))) if self.ntemps > 1: logging.info("Tswap acceptance fraction: {}" .format(sampler.tswap_acceptance_fraction)) logging.info('Max detection statistic of run was {}'.format( np.max(sampler.lnlikelihood))) if create_plots: fig, axes = self._plot_walkers( sampler, symbols=self.theta_symbols, fig=fig, axes=axes, nprod=nprod, xoffset=nsteps_total, **kwargs) for ax in axes[:self.ndim]: ax.axvline(nsteps_total, color='k', ls='--', lw=0.25) nsteps_total += nburn+nprod samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim)) lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1)) lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1)) all_lnlikelihood = sampler.lnlikelihood self.samples = samples self.lnprobs = lnprobs self.lnlikes = lnlikes self.all_lnlikelihood = all_lnlikelihood self._save_data(sampler, samples, lnprobs, lnlikes, all_lnlikelihood) if create_plots: try: fig.tight_layout() except (ValueError, RuntimeError) as e: logging.warning('Tight layout encountered {}'.format(e)) if return_fig: return fig, axes else: fig.savefig('{}/{}_walkers.png'.format( self.outdir, self.label), dpi=200) class MCMCTransientSearch(MCMCSearch): """ MCMC search for a transient signal using the ComputeFstat """ symbol_dictionary = dict( F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$', Delta='$\delta$', transient_tstart='$t_\mathrm{start}$', transient_duration='$\Delta T$') unit_dictionary = dict( F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad', transient_tstart='s', transient_duration='s') rescale_dictionary = dict( transient_duration={'multiplier': 1/86400., 'unit': 'day', 'symbol': 'Transient duration'}, transient_tstart={ 'multiplier': 1/86400., 'subtractor': 'minStartTime', 'unit': 'day', 'label': 'Transient start-time \n days after minStartTime'} ) def _initiate_search_object(self): logging.info('Setting up search object') self.search = core.ComputeFstat( tref=self.tref, sftfilepath=self.sftfilepath, minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq, earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem, detectors=self.detectors, transient=True, minStartTime=self.minStartTime, maxStartTime=self.maxStartTime, BSGL=self.BSGL, binary=self.binary) def logl(self, theta, search): for j, theta_i in enumerate(self.theta_idxs): self.fixed_theta[theta_i] = theta[j] in_theta = copy.copy(self.fixed_theta) in_theta[1] = in_theta[0] + in_theta[1] if in_theta[1] > self.maxStartTime: return -np.inf FS = search.run_computefstatistic_single_point(*in_theta) return FS def _unpack_input_theta(self): full_theta_keys = ['transient_tstart', 'transient_duration', 'F0', 'F1', 'F2', 'Alpha', 'Delta'] if self.binary: full_theta_keys += [ 'asini', 'period', 'ecc', 'tp', 'argp'] full_theta_keys_copy = copy.copy(full_theta_keys) full_theta_symbols = [r'$t_{\rm start}$', r'$\Delta T$', '$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$', r'$\delta$'] if self.binary: full_theta_symbols += [ 'asini', 'period', 'period', 'ecc', 'tp', 'argp'] self.theta_keys = [] fixed_theta_dict = {} for key, val in self.theta_prior.iteritems(): if type(val) is dict: fixed_theta_dict[key] = 0 self.theta_keys.append(key) elif type(val) in [float, int, np.float64]: fixed_theta_dict[key] = val else: raise ValueError( 'Type {} of {} in theta not recognised'.format( type(val), key)) full_theta_keys_copy.pop(full_theta_keys_copy.index(key)) if len(full_theta_keys_copy) > 0: raise ValueError(('Input dictionary `theta` is missing the' 'following keys: {}').format( full_theta_keys_copy)) self.fixed_theta = [fixed_theta_dict[key] for key in full_theta_keys] self.theta_idxs = [full_theta_keys.index(k) for k in self.theta_keys] self.theta_symbols = [full_theta_symbols[i] for i in self.theta_idxs] idxs = np.argsort(self.theta_idxs) self.theta_idxs = [self.theta_idxs[i] for i in idxs] self.theta_symbols = [self.theta_symbols[i] for i in idxs] self.theta_keys = [self.theta_keys[i] for i in idxs]