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semi_coherent_glitch_search.py

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  • mcmc_based_searches.py 93.16 KiB
    """ Searches using MCMC-based methods """
    
    import sys
    import os
    import copy
    import logging
    from collections import OrderedDict
    import subprocess
    
    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, read_par
    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, rhohatmax=1000,
                     binary=False, BSGL=False, minCoverFreq=None, SSBprec=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).
            rhohatmax: float
                Upper bound for the SNR scale parameter (required to normalise the
                Bayes factor) - this needs to be carefully set when using the
                evidence.
            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.lnlikelihoodcoef = np.log(70./self.rhohatmax**4)
    
            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, SSBprec=self.SSBprec)
    
        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 + self.lnlikelihoodcoef
    
        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 = np.sqrt(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']
                self.all_lnlikelihood = d['all_lnlikelihood']
                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[:, :, nburn:]
            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, str
                If true, plot the prior as a red line. If 'full' then for uniform
                priors plot the full extent of the prior.
            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.corner
    
            """
    
            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
    
                hist_kwargs = kwargs.pop('hist_kwargs', dict())
                if 'normed' not in hist_kwargs:
                    hist_kwargs['normed'] = True
    
                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,
                                             hist_kwargs=hist_kwargs,
                                             **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, add_prior)
    
                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, add_prior):
            for i, key in enumerate(self.theta_keys):
                ax = axes[i][i]
                s = samples[:, i]
                lnprior = self._generic_lnprior(**self.theta_prior[key])
                if add_prior == 'full' and self.theta_prior[key]['type'] == 'unif':
                    lower = self.theta_prior[key]['lower']
                    upper = self.theta_prior[key]['upper']
                    r = upper-lower
                    xlim = [lower-0.05*r, upper+0.05*r]
                    x = np.linspace(xlim[0], xlim[1], 1000)
                else:
                    xlim = ax.get_xlim()
                    x = np.linspace(s.min(), s.max(), 1000)
                multiplier = self._get_rescale_multiplier_for_key(key)
                subtractor = self._get_rescale_subtractor_for_key(key)
                ax.plot((x-subtractor)*multiplier,
                        [np.exp(lnprior(xi)) for xi in x], '-C3',
                        label='prior')
    
                for j in range(i, self.ndim):
                    axes[j][i].set_xlim(xlim[0], xlim[1])
                for k in range(0, i):
                    axes[i][k].set_ylim(xlim[0], xlim[1])
    
        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'] == 'log10unif':
                    upper = prior_dict['log10upper']
                    lower = prior_dict['log10lower']
                    x = np.linspace(lower, upper, N)
                    prior = [prior_func(xi) for xi in x]
                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, 'C3', 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 log_of_unif(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 log_of_log10unif(x, log10lower, log10upper):
                log10x = np.log10(x)
                above = log10x < log10upper
                below = log10x > log10lower
                if type(above) is not np.ndarray:
                    if above and below:
                        return -np.log(x*np.log(10)*(log10upper-log10lower))
                    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(x*np.log(10)*(log10upper-log10lower))
                    return p
    
            def log_of_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: log_of_unif(x, kwargs['lower'], kwargs['upper'])
            if kwargs['type'] == 'log10unif':
                return lambda x: log_of_log10unif(
                    x, kwargs['log10lower'], kwargs['log10upper'])
            elif kwargs['type'] == 'halfnorm':
                return lambda x: log_of_halfnorm(x, kwargs['loc'], kwargs['scale'])
            elif kwargs['type'] == 'neghalfnorm':
                return lambda x: log_of_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 == "log10unif":
                return 10**(np.random.uniform(low=kwargs['log10lower'],
                                              high=kwargs['log10upper']))
            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=0.8, 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="C3", 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()
                            axes[i].set_zorder(ax.get_zorder()+1)
                            axes[i].patch.set_visible(False)
                            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], '-C0',
                                    zorder=-10)
                            ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-C0',
                                    zorder=-10)
                            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="C3", 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)
    
                axes[-1].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)
    
                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='C3')
                        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)
    
            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')
            old_d.pop('all_lnlikelihood')
    
            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 - self.lnlikelihoodcoef
    
            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 generate_loudest(self):
            self.write_par()
            params = read_par(self.label, self.outdir)
            for key in ['Alpha', 'Delta', 'F0', 'F1']:
                if key not in params:
                    params[key] = self.theta_prior[key]
            cmd = ('lalapps_ComputeFstatistic_v2 -a {} -d {} -f {} -s {} -D "{}"'
                   ' --refTime={} --outputLoudest="{}/{}.loudest" '
                   '--minStartTime={} --maxStartTime={}').format(
                        params['Alpha'], params['Delta'], params['F0'],
                        params['F1'], self.sftfilepath, params['tref'],
                        self.outdir, self.label, self.minStartTime,
                        self.maxStartTime)
            subprocess.call([cmd], shell=True)
    
        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, write_to_file='Evidences.txt'):
            """ 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)
    
            logging.info("log10 evidence for {} = {} +/- {}".format(
                  self.label, log10evidence, log10evidence_err))
    
            if write_to_file:
                EvidenceDict = self.read_evidence_file_to_dict(write_to_file)
                EvidenceDict[self.label] = [log10evidence, log10evidence_err]
                self.write_evidence_file_from_dict(EvidenceDict, write_to_file)
    
            ax1.semilogx(betas, mean_lnlikes, "-o")
            ax1.set_xlabel(r"$\beta$")
            ax1.set_ylabel(r"$\langle \log(\mathcal{L}) \rangle$")
            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))
    
        @staticmethod
        def read_evidence_file_to_dict(evidence_file_name='Evidences.txt'):
            EvidenceDict = OrderedDict()
            if os.path.isfile(evidence_file_name):
                with open(evidence_file_name, 'r') as f:
                    for line in f:
                        key, log10evidence, log10evidence_err = line.split(' ')
                        EvidenceDict[key] = [
                            float(log10evidence), float(log10evidence_err)]
            return EvidenceDict
    
        def write_evidence_file_from_dict(self, EvidenceDict, evidence_file_name):
            with open(evidence_file_name, 'w+') as f:
                for key, val in EvidenceDict.iteritems():
                    f.write('{} {} {}\n'.format(key, val[0], val[1]))
    
    
    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, rhohatmax=1000,
                     dtglitchmin=1*86400, theta0_idx=0, detectors=None,
                     BSGL=False, minCoverFreq=None, maxCoverFreq=None,
                     earth_ephem=None, sun_ephem=None, injectSources=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
            rhohatmax: float
                Upper bound for the SNR scale parameter (required to normalise the
                Bayes factor) - this needs to be carefully set when using the
                evidence.
            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()
    
            self.lnlikelihoodcoef = (self.nglitch+1)*np.log(70./self.rhohatmax**4)
    
        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,
                injectSources=self.injectSources)
    
        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 + self.lnlikelihoodcoef
    
        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, rhohatmax=1000,
                     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()
    
            self.lnlikelihoodcoef = self.nsegs * np.log(70./self.rhohatmax**4)
    
        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 + self.lnlikelihoodcoef
    
    
    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.all_lnlikelihood = d['all_lnlikelihood']
                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,
                injectSources=self.injectSources)
    
        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 + self.lnlikelihoodcoef
    
        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]