mcmc_based_searches.py 94.7 KB
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""" Searches using MCMC-based methods """
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from __future__ import division, absolute_import, print_function
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import sys
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import os
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import copy
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import logging
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from collections import OrderedDict
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import subprocess
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import numpy as np
import matplotlib
import matplotlib.pyplot as plt
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from ptemcee import Sampler as PTSampler
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import corner
import dill as pickle

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import pyfstat.core as core
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from pyfstat.core import tqdm, args, read_par
import pyfstat.optimal_setup_functions as optimal_setup_functions
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import pyfstat.helper_functions as helper_functions
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class MCMCSearch(core.BaseSearchClass):
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    """MCMC search using ComputeFstat
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    Parameters
    ----------
    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.
    tref, minStartTime, maxStartTime: int
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        GPS seconds of the reference time, start time and end time. While tref
        is requirede, minStartTime and maxStartTime default to None in which
        case all available data is used.
    label, outdir: str
        A label and output directory (optional, defaults is `'data'`) to
        name files
    sftfilepattern: str, optional
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        Pattern to match SFTs using wildcards (*?) and ranges [0-9];
        mutiple patterns can be given separated by colons.
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    detectors: str, optional
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        Two character reference to the detectors to use, specify None for no
        contraint and comma separate for multiple references.
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    nsteps: list (2,), optional
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        Number of burn-in and production steps to take, [nburn, nprod]. See
        `pyfstat.MCMCSearch.setup_initialisation()` for details on adding
        initialisation steps.
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    nwalkers, ntemps: int, optional
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        The number of walkers and temperates to use in the parallel
        tempered PTSampler.
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    log10beta_min float < 0, optional
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        The  log_10(beta) value, if given the set of betas passed to PTSampler
        are generated from `np.logspace(0, log10beta_min, ntemps)` (given
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        in descending order to ptemcee).
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    theta_initial: dict, array, optional
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        A dictionary of distribution about which to distribute the
        initial walkers about
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    rhohatmax: float, optional
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        Upper bound for the SNR scale parameter (required to normalise the
        Bayes factor) - this needs to be carefully set when using the
        evidence.
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    binary: bool, optional
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        If true, search over binary parameters
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    BSGL: bool, optional
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        If true, use the BSGL statistic
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    SSBPrec: int, optional
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        SSBPrec (SSB precision) to use when calling ComputeFstat
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    minCoverFreq, maxCoverFreq: float, optional
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        Minimum and maximum instantaneous frequency which will be covered
        over the SFT time span as passed to CreateFstatInput
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    injectSources: dict, optional
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        If given, inject these properties into the SFT files before running
        the search
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    assumeSqrtSX: float, optional
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        Don't estimate noise-floors, but assume (stationary) per-IFO sqrt{SX}
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    transientWindowType: str
        If 'rect' or 'exp',
        compute atoms so that a transient (t0,tau) map can later be computed.
        ('none' instead of None explicitly calls the transient-window function,
        but with the full range, for debugging)
        Currently only supported for nsegs=1.
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    tCWFstatMapVersion: str
        Choose between standard 'lal' implementation,
        'pycuda' for gpu, and some others for devel/debug.
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    Attributes
    ----------
    symbol_dictionary: dict
        Key, val pairs of the parameters (i.e. `F0`, `F1`), to Latex math
        symbols for plots
    unit_dictionary: dict
        Key, val pairs of the parameters (i.e. `F0`, `F1`), and the
        units (i.e. `Hz`)
    transform_dictionary: dict
        Key, val pairs of the parameters (i.e. `F0`, `F1`), where the key is
        itself a dictionary which can item `multiplier`, `subtractor`, or
        `unit` by which to transform by and update the units.

    """
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    symbol_dictionary = dict(
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        F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$',
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        Delta='$\delta$', asini='asini', period='P', ecc='ecc', tp='tp',
        argp='argp')
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    unit_dictionary = dict(
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        F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad',
        asini='', period='s', ecc='', tp='', argp='')
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    transform_dictionary = {}
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    @helper_functions.initializer
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    def __init__(self, theta_prior, tref, label, outdir='data',
                 minStartTime=None, maxStartTime=None, sftfilepattern=None,
                 detectors=None, nsteps=[100, 100], nwalkers=100, ntemps=1,
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                 log10beta_min=-5, theta_initial=None,
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                 rhohatmax=1000, binary=False, BSGL=False,
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                 SSBprec=None, minCoverFreq=None, maxCoverFreq=None,
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                 injectSources=None, assumeSqrtSX=None,
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                 transientWindowType=None, tCWFstatMapVersion='lal'):
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        if os.path.isdir(outdir) is False:
            os.mkdir(outdir)
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        self._add_log_file()
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        logging.info('Set-up MCMC search for model {}'.format(self.label))
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        if sftfilepattern:
            logging.info('Using data {}'.format(self.sftfilepattern))
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        else:
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            logging.info('No sftfilepattern given')
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        if injectSources:
            logging.info('Inject sources: {}'.format(injectSources))
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        self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label)
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        self._unpack_input_theta()
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        self.ndim = len(self.theta_keys)
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        if self.log10beta_min:
            self.betas = np.logspace(0, self.log10beta_min, self.ntemps)
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        else:
            self.betas = None
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        if args.clean and os.path.isfile(self.pickle_path):
            os.rename(self.pickle_path, self.pickle_path+".old")

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        self._set_likelihoodcoef()
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        self._log_input()
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    def _set_likelihoodcoef(self):
        self.likelihoodcoef = np.log(70./self.rhohatmax**4)
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    def _log_input(self):
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        logging.info('theta_prior = {}'.format(self.theta_prior))
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        logging.info('nwalkers={}'.format(self.nwalkers))
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        logging.info('nsteps = {}'.format(self.nsteps))
        logging.info('ntemps = {}'.format(self.ntemps))
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        logging.info('log10beta_min = {}'.format(
            self.log10beta_min))
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    def _initiate_search_object(self):
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        logging.info('Setting up search object')
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        self.search = core.ComputeFstat(
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            tref=self.tref, sftfilepattern=self.sftfilepattern,
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            minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq,
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            detectors=self.detectors, BSGL=self.BSGL,
            transientWindowType=self.transientWindowType,
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            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
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            binary=self.binary, injectSources=self.injectSources,
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            assumeSqrtSX=self.assumeSqrtSX, SSBprec=self.SSBprec,
            tCWFstatMapVersion=self.tCWFstatMapVersion)
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        if self.minStartTime is None:
            self.minStartTime = self.search.minStartTime
        if self.maxStartTime is None:
            self.maxStartTime = self.search.maxStartTime
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    def logp(self, theta_vals, theta_prior, theta_keys, search):
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        H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in
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             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]
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        twoF = search.get_fullycoherent_twoF(
            self.minStartTime, self.maxStartTime, *self.fixed_theta)
        return twoF/2.0 + self.likelihoodcoef
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    def _unpack_input_theta(self):
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        full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta']
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        if self.binary:
            full_theta_keys += [
                'asini', 'period', 'ecc', 'tp', 'argp']
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        full_theta_keys_copy = copy.copy(full_theta_keys)

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        full_theta_symbols = ['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$',
                              r'$\delta$']
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        if self.binary:
            full_theta_symbols += [
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                'asini', 'period', 'ecc', 'tp', 'argp']
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        self.theta_keys = []
        fixed_theta_dict = {}
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        for key, val in self.theta_prior.iteritems():
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            if type(val) is dict:
                fixed_theta_dict[key] = 0
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                self.theta_keys.append(key)
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            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))
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            full_theta_keys_copy.pop(full_theta_keys_copy.index(key))
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        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]

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    def _evaluate_logpost(self, p0vec):
        init_logp = np.array([
            self.logp(p, self.theta_prior, self.theta_keys, self.search)
            for p in p0vec])
        init_logl = np.array([
            self.logl(p, self.search)
            for p in p0vec])
        return init_logl + init_logp

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    def _check_initial_points(self, p0):
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        for nt in range(self.ntemps):
            logging.info('Checking temperature {} chains'.format(nt))
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            num = sum(self._evaluate_logpost(p0[nt]) == -np.inf)
            if num > 0:
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                logging.warning(
                    'Of {} initial values, {} are -np.inf due to the prior'
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                    .format(len(p0[0]), num))
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                p0 = self._generate_new_p0_to_fix_initial_points(
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                    p0, nt)
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    def _generate_new_p0_to_fix_initial_points(self, p0, nt):
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        logging.info('Attempting to correct intial values')
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        init_logpost = self._evaluate_logpost(p0[nt])
        idxs = np.arange(self.nwalkers)[init_logpost == -np.inf]
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        count = 0
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        while sum(init_logpost == -np.inf) > 0 and count < 100:
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            for j in idxs:
                p0[nt][j] = (p0[nt][np.random.randint(0, self.nwalkers)]*(
                             1+np.random.normal(0, 1e-10, self.ndim)))
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            init_logpost = self._evaluate_logpost(p0[nt])
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            count += 1

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        if sum(init_logpost == -np.inf) > 0:
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            logging.info('Failed to fix initial priors')
        else:
            logging.info('Suceeded to fix initial priors')

        return p0
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    def setup_initialisation(self, nburn0, scatter_val=1e-10):
        """ Add an initialisation step to the MCMC run

        If called prior to `run()`, adds an intial step in which the MCMC
        simulation is run for `nburn0` steps. After this, the MCMC simulation
        continues in the usual manner (i.e. for nburn and nprod steps), but the
        walkers are reset scattered around the maximum likelihood position
        of the initialisation step.

        Parameters
        ----------
        nburn0: int
            Number of initialisation steps to take
        scatter_val: float
            Relative number to scatter walkers around the maximum likelihood
            position after the initialisation step

        """

        logging.info('Setting up initialisation with nburn0={}, scatter_val={}'
                     .format(nburn0, scatter_val))
        self.nsteps = [nburn0] + self.nsteps
        self.scatter_val = scatter_val

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#    def setup_burnin_convergence_testing(
#            self, n=10, test_type='autocorr', windowed=False, **kwargs):
#        """ Set up convergence testing during the MCMC simulation
#
#        Parameters
#        ----------
#        n: int
#            Number of steps after which to test convergence
#        test_type: str ['autocorr', 'GR']
#            If 'autocorr' use the exponential autocorrelation time (kwargs
#            passed to `get_autocorr_convergence`). If 'GR' use the Gelman-Rubin
#            statistic (kwargs passed to `get_GR_convergence`)
#        windowed: bool
#            If True, only calculate the convergence test in a window of length
#            `n`
#        **kwargs:
#            Passed to either `_test_autocorr_convergence()` or
#            `_test_GR_convergence()` depending on `test_type`.
#
#        """
#        logging.info('Setting up convergence testing')
#        self.convergence_n = n
#        self.convergence_windowed = windowed
#        self.convergence_test_type = test_type
#        self.convergence_kwargs = kwargs
#        self.convergence_diagnostic = []
#        self.convergence_diagnosticx = []
#        if test_type in ['autocorr']:
#            self._get_convergence_test = self._test_autocorr_convergence
#        elif test_type in ['GR']:
#            self._get_convergence_test = self._test_GR_convergence
#        else:
#            raise ValueError('test_type {} not understood'.format(test_type))
#
#
#    def _test_autocorr_convergence(self, i, sampler, test=True, n_cut=5):
#        try:
#            acors = np.zeros((self.ntemps, self.ndim))
#            for temp in range(self.ntemps):
#                if self.convergence_windowed:
#                    j = i-self.convergence_n
#                else:
#                    j = 0
#                x = np.mean(sampler.chain[temp, :, j:i, :], axis=0)
#                acors[temp, :] = emcee.autocorr.exponential_time(x)
#            c = np.max(acors, axis=0)
#        except emcee.autocorr.AutocorrError:
#            logging.info('Failed to calculate exponential autocorrelation')
#            c = np.zeros(self.ndim) + np.nan
#        except AttributeError:
#            logging.info('Unable to calculate exponential autocorrelation')
#            c = np.zeros(self.ndim) + np.nan
#
#        self.convergence_diagnosticx.append(i - self.convergence_n/2.)
#        self.convergence_diagnostic.append(list(c))
#
#        if test:
#            return i > n_cut * np.max(c)
#
#    def _test_GR_convergence(self, i, sampler, test=True, R=1.1):
#        if self.convergence_windowed:
#            s = sampler.chain[0, :, i-self.convergence_n+1:i+1, :]
#        else:
#            s = sampler.chain[0, :, :i+1, :]
#        N = float(self.convergence_n)
#        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_n/2.)
#
#        if test and np.max(c) < R:
#            return True
#        else:
#            return False
#
#    def _test_convergence(self, i, sampler, **kwargs):
#        if np.mod(i+1, self.convergence_n) == 0:
#            return self._get_convergence_test(i, sampler, **kwargs)
#        else:
#            return False
#
#    def _run_sampler_with_conv_test(self, sampler, p0, nprod=0, nburn=0):
#        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._test_convergence(i, sampler, test=True,
#                                      **self.convergence_kwargs):
#                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
#        iterator = tqdm(sampler.sample(output[0], iterations=nprod),
#                        total=nprod)
#        for result in iterator:
#            self._test_convergence(j, sampler, test=False,
#                                   **self.convergence_kwargs)
#            j += 1
#        return sampler

    def _run_sampler(self, sampler, p0, nprod=0, nburn=0, window=50):
        for result in tqdm(sampler.sample(p0, iterations=nburn+nprod),
                           total=nburn+nprod):
            pass
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        self.mean_acceptance_fraction = np.mean(
            sampler.acceptance_fraction, axis=1)
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        logging.info("Mean acceptance fraction: {}"
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                     .format(self.mean_acceptance_fraction))
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        if self.ntemps > 1:
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            self.tswap_acceptance_fraction = sampler.tswap_acceptance_fraction
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            logging.info("Tswap acceptance fraction: {}"
                         .format(sampler.tswap_acceptance_fraction))
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        self.autocorr_time = sampler.get_autocorr_time(window=window)
        logging.info("Autocorrelation length: {}".format(
            self.autocorr_time))
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        return sampler

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    def _estimate_run_time(self):
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        """ Print the estimated run time

        Uses timing coefficients based on a Lenovo T460p Intel(R)
        Core(TM) i5-6300HQ CPU @ 2.30GHz.

        """
        # Todo: add option to time on a machine, and move coefficients to
        # ~/.pyfstat.conf
        if (type(self.theta_prior['Alpha']) == dict or
                type(self.theta_prior['Delta']) == dict):
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            tau0LD = 5.2e-7
            tau0T = 1.5e-8
            tau0S = 1.2e-4
            tau0C = 5.8e-6
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        else:
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            tau0LD = 1.3e-7
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            tau0T = 1.5e-8
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            tau0S = 9.1e-5
            tau0C = 5.5e-6
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        Nsfts = (self.maxStartTime - self.minStartTime) / 1800.
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        if hasattr(self, 'run_setup'):
            ts = []
            for row in self.run_setup:
                nsteps = row[0]
                nsegs = row[1]
                numb_evals = np.sum(nsteps)*self.nwalkers*self.ntemps
                t = (tau0S + tau0LD*Nsfts) * numb_evals
                if nsegs > 1:
                    t += (tau0C + tau0T*Nsfts)*nsegs*numb_evals
                ts.append(t)
            time = np.sum(ts)
        else:
            numb_evals = np.sum(self.nsteps)*self.nwalkers*self.ntemps
            time = (tau0S + tau0LD*Nsfts) * numb_evals
            if getattr(self, 'nsegs', 1) > 1:
                time += (tau0C + tau0T*Nsfts)*self.nsegs*numb_evals

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        logging.info('Estimated run-time = {} s = {:1.0f}:{:1.0f} m'.format(
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            time, *divmod(time, 60)))
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    def run(self, proposal_scale_factor=2, create_plots=True, window=50,
            **kwargs):
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        """ Run the MCMC simulatation

        Parameters
        ----------
        proposal_scale_factor: float
            The proposal scale factor used by the sampler, see Goodman & Weare
            (2010). If the acceptance fraction is too low, you can raise it by
            decreasing the a parameter; and if it is too high, you can reduce
            it by increasing the a parameter [Foreman-Mackay (2013)].
        create_plots: bool
            If true, save trace plots of the walkers
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        window: int
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            The minimum number of autocorrelation times needed to trust the
            result when estimating the autocorrelation time (see
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            ptemcee.Sampler.get_autocorr_time for further details.
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        **kwargs:
            Passed to _plot_walkers to control the figures

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        Returns
        -------
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        sampler: ptemcee.Sampler
            The ptemcee ptsampler object
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        """
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        self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use()
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        if self.old_data_is_okay_to_use is True:
            logging.warning('Using saved data from {}'.format(
                self.pickle_path))
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            d = self.get_saved_data_dictionary()
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            self.samples = d['samples']
            self.lnprobs = d['lnprobs']
            self.lnlikes = d['lnlikes']
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            self.all_lnlikelihood = d['all_lnlikelihood']
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            return

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        self._initiate_search_object()
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        self._estimate_run_time()
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        sampler = PTSampler(
            ntemps=self.ntemps, nwalkers=self.nwalkers, dim=self.ndim,
            logl=self.logl, logp=self.logp,
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            logpargs=(self.theta_prior, self.theta_keys, self.search),
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            loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor)
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        p0 = self._generate_initial_p0()
        p0 = self._apply_corrections_to_p0(p0)
        self._check_initial_points(p0)
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        # Run initialisation steps if required
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        ninit_steps = len(self.nsteps) - 2
        for j, n in enumerate(self.nsteps[:-2]):
            logging.info('Running {}/{} initialisation with {} steps'.format(
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                j, ninit_steps, n))
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            sampler = self._run_sampler(sampler, p0, nburn=n, window=window)
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            if create_plots:
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                fig, axes = self._plot_walkers(sampler,
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                                               **kwargs)
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                fig.tight_layout()
                fig.savefig('{}/{}_init_{}_walkers.png'.format(
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                    self.outdir, self.label, j))
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            p0 = self._get_new_p0(sampler)
            p0 = self._apply_corrections_to_p0(p0)
            self._check_initial_points(p0)
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            sampler.reset()

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        if len(self.nsteps) > 1:
            nburn = self.nsteps[-2]
        else:
            nburn = 0
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        nprod = self.nsteps[-1]
        logging.info('Running final burn and prod with {} steps'.format(
            nburn+nprod))
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        sampler = self._run_sampler(sampler, p0, nburn=nburn, nprod=nprod)
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        if create_plots:
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            fig, axes = self._plot_walkers(sampler, nprod=nprod, **kwargs)
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            fig.tight_layout()
            fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label),
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                        )
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        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
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        lnprobs = sampler.logprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.loglikelihood[0, :, nburn:].reshape((-1))
        all_lnlikelihood = sampler.loglikelihood[:, :, nburn:]
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        self.samples = samples
        self.lnprobs = lnprobs
        self.lnlikes = lnlikes
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        self.all_lnlikelihood = all_lnlikelihood
        self._save_data(sampler, samples, lnprobs, lnlikes, all_lnlikelihood)
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        return sampler
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    def _get_rescale_multiplier_for_key(self, key):
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        """ Get the rescale multiplier from the transform_dictionary
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        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
        """
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        if key not in self.transform_dictionary:
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            return 1

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        if 'multiplier' in self.transform_dictionary[key]:
            val = self.transform_dictionary[key]['multiplier']
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            if type(val) == str:
                if hasattr(self, val):
                    multiplier = getattr(
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                        self, self.transform_dictionary[key]['multiplier'])
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                else:
                    raise ValueError(
                        "multiplier {} not a class attribute".format(val))
            else:
                multiplier = val
        else:
            multiplier = 1
        return multiplier

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    def _get_rescale_subtractor_for_key(self, key):
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        """ Get the rescale subtractor from the transform_dictionary
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        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
        """
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        if key not in self.transform_dictionary:
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            return 0

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        if 'subtractor' in self.transform_dictionary[key]:
            val = self.transform_dictionary[key]['subtractor']
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            if type(val) == str:
                if hasattr(self, val):
                    subtractor = getattr(
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                        self, self.transform_dictionary[key]['subtractor'])
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                else:
                    raise ValueError(
                        "subtractor {} not a class attribute".format(val))
            else:
                subtractor = val
        else:
            subtractor = 0
        return subtractor

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    def _scale_samples(self, samples, theta_keys):
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        """ Scale the samples using the transform_dictionary """
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        for key in theta_keys:
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            if key in self.transform_dictionary:
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                idx = theta_keys.index(key)
                s = samples[:, idx]
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                subtractor = self._get_rescale_subtractor_for_key(key)
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                s = s - subtractor
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                multiplier = self._get_rescale_multiplier_for_key(key)
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                s *= multiplier
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                samples[:, idx] = s

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        return samples

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    def _get_labels(self, newline_units=False):
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        """ Combine the units, symbols and rescaling to give labels """
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        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]
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            if key in self.transform_dictionary:
                if 'symbol' in self.transform_dictionary[key]:
                    s = self.transform_dictionary[key]['symbol']
                if 'label' in self.transform_dictionary[key]:
                    label = self.transform_dictionary[key]['label']
                if 'unit' in self.transform_dictionary[key]:
                    u = self.transform_dictionary[key]['unit']
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            if label is None:
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                if newline_units:
                    label = '{} \n [{}]'.format(s, u)
                else:
                    label = '{} [{}]'.format(s, u)
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            labels.append(label)
        return labels
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    def plot_corner(self, figsize=(7, 7), add_prior=False, nstds=None,
                    label_offset=0.4, dpi=300, rc_context={},
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                    tglitch_ratio=False, fig_and_axes=None, save_fig=True,
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                    **kwargs):
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        """ 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)
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        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.
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        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
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        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
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        **kwargs:
            Passed to corner.corner
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        Returns
        -------
        fig, axes:
            The matplotlib figure and axes, only returned if save_fig = False
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        """
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        if 'truths' in kwargs and len(kwargs['truths']) != self.ndim:
            logging.warning('len(Truths) != ndim, Truths will be ignored')
            kwargs['truths'] = None

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        if self.ndim < 2:
            with plt.rc_context(rc_context):
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                if fig_and_axes is None:
                    fig, ax = plt.subplots(figsize=figsize)
                else:
                    fig, ax = fig_and_axes
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                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

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        with plt.rc_context(rc_context):
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            if fig_and_axes is None:
                fig, axes = plt.subplots(self.ndim, self.ndim,
                                         figsize=figsize)
            else:
                fig, axes = fig_and_axes
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            samples_plt = copy.copy(self.samples)
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            labels = self._get_labels(newline_units=True)
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            samples_plt = self._scale_samples(samples_plt, self.theta_keys)
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            if tglitch_ratio:
                for j, k in enumerate(self.theta_keys):
                    if k == 'tglitch':
                        s = samples_plt[:, j]
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                        samples_plt[:, j] = (
                            s - self.minStartTime)/(
                                self.maxStartTime - self.minStartTime)
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                        labels[j] = r'$R_{\textrm{glitch}}$'
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            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))
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            elif 'range' in kwargs:
                _range = kwargs.pop('range')
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            else:
                _range = None

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            hist_kwargs = kwargs.pop('hist_kwargs', dict())
            if 'normed' not in hist_kwargs:
                hist_kwargs['normed'] = True

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            fig_triangle = corner.corner(samples_plt,
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                                         labels=labels,
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                                         fig=fig,
                                         bins=50,
                                         max_n_ticks=4,
                                         plot_contours=True,
                                         plot_datapoints=True,
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                                         label_kwargs={'fontsize': 12},
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                                         data_kwargs={'alpha': 0.1,
                                                      'ms': 0.5},
                                         range=_range,
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                                         hist_kwargs=hist_kwargs,
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                                         **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)
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                for tick in ax.xaxis.get_major_ticks():
                    tick.label.set_fontsize(8)
                    tick.label.set_rotation('horizontal')
                for tick in ax.yaxis.get_major_ticks():
                    tick.label.set_fontsize(8)
                    tick.label.set_rotation('vertical')

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            plt.tight_layout(h_pad=0.0, w_pad=0.0)
            fig.subplots_adjust(hspace=0.05, wspace=0.05)

            if add_prior:
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                self._add_prior_to_corner(axes, self.samples, add_prior)
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            if save_fig:
                fig_triangle.savefig('{}/{}_corner.png'.format(
                    self.outdir, self.label), dpi=dpi)
            else:
                return fig, axes
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    def _add_prior_to_corner(self, axes, samples, add_prior):
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        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            s = samples[:, i]
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            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)
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            multiplier = self._get_rescale_multiplier_for_key(key)
            subtractor = self._get_rescale_subtractor_for_key(key)
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            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])
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    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]
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            prior_func = self._generic_lnprior(**prior_dict)
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            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
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            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]
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            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)
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            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]
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            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]
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            else:
                raise ValueError('Not implemented for prior type {}'.format(
                    prior_dict['type']))
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            priorln = ax.plot(x, prior, 'C3', label='prior')
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            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))

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    def plot_cumulative_max(self, **kwargs):
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        """ Plot the cumulative twoF for the maximum posterior estimate

        See the pyfstat.core.plot_twoF_cumulative function for further details
        """
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        d, maxtwoF = self.get_max_twoF()
        for key, val in self.theta_prior.iteritems():
            if key not in d:
                d[key] = val
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        if 'add_pfs' in kwargs:
            self.generate_loudest()

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        if hasattr(self, 'search') is False:
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            self._initiate_search_object()
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        if self.binary is False:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
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                Alpha=d['Alpha'], Delta=d['Delta'],
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                tstart=self.minStartTime, tend=self.maxStartTime,
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                **kwargs)
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        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'],
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                tstart=self.minStartTime, tend=self.maxStartTime, **kwargs)
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    def _generic_lnprior(self, **kwargs):
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        """ Return a lambda function of the pdf

        Parameters
        ----------
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        **kwargs:
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            A dictionary containing 'type' of pdf and shape parameters

        """

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        def log_of_unif(x, a, b):
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            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

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        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):
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            if x < loc:
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                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':
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            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'])
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        elif kwargs['type'] == 'halfnorm':
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            return lambda x: log_of_halfnorm(x, kwargs['loc'], kwargs['scale'])
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        elif kwargs['type'] == 'neghalfnorm':
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            return lambda x: log_of_halfnorm(
                -x, kwargs['loc'], kwargs['scale'])
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        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")

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    def _generate_rv(self, **kwargs):
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        dist_type = kwargs.pop('type')
        if dist_type == "unif":
            return np.random.uniform(low=kwargs['lower'], high=kwargs['upper'])
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        if dist_type == "log10unif":
            return 10**(np.random.uniform(low=kwargs['log10lower'],
                                          high=kwargs['log10upper']))
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        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']))
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        if dist_type == "neghalfnorm":
            return -1 * np.abs(np.random.normal(loc=kwargs['loc'],
                                                scale=kwargs['scale']))
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        if dist_type == "lognorm":
            return np.random.lognormal(
                mean=kwargs['loc'], sigma=kwargs['scale'])
        else:
            raise ValueError("dist_type {} unknown".format(dist_type))

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    def _plot_walkers(self, sampler, symbols=None, alpha=0.8, color="k",
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                      temp=0, lw=0.1, nprod=0, add_det_stat_burnin=False,
                      fig=None, axes=None, xoffset=0, plot_det_stat=False,
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                      context='ggplot', labelpad=5):
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        """ Plot all the chains from a sampler """

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        if symbols is None:
            symbols = self._get_labels()
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        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))

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        if np.ndim(axes) > 1:
            axes = axes.flatten()

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        shape = sampler.chain.shape
        if len(shape) == 3:
            nwalkers, nsteps, ndim = shape
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            chain = sampler.chain[:, :, :].copy()
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        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))
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            chain = sampler.chain[temp, :, :, :].copy()
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        samples = chain.reshape((nwalkers*nsteps, ndim))
        samples = self._scale_samples(samples, self.theta_keys)
        chain = chain.reshape((nwalkers, nsteps, ndim))
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        if plot_det_stat:
            extra_subplots = 1
        else:
            extra_subplots = 0
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        with plt.style.context((context)):
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            plt.rcParams['text.usetex'] = True
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            if fig is None and axes is None:
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                fig = plt.figure(figsize=(4, 3.0*ndim))
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                ax = fig.add_subplot(ndim+extra_subplots, 1, 1)
                axes = [ax] + [fig.add_subplot(ndim+extra_subplots, 1, i)
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                               for i in range(2, ndim+1)]
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            idxs = np.arange(chain.shape[1])
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            burnin_idx = chain.shape[1] - nprod
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            #if hasattr(self, 'convergence_idx'):
            #    last_idx = self.convergence_idx
            #else:
            last_idx = burnin_idx
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            if ndim > 1:
                for i in range(ndim):
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                    axes[i].ticklabel_format(useOffset=False, axis='y')
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                    cs = chain[:, :, i].T
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                    if burnin_idx > 0:
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                        axes[i].plot(xoffset+idxs[:last_idx+1],
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                                     cs[:last_idx+1],
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                                     color="C3", alpha=alpha,
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                                     lw=lw)
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                        axes[i].axvline(xoffset+last_idx,
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                                        color='k', ls='--', lw=0.5)
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                    axes[i].plot(xoffset+idxs[burnin_idx:],
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                                 cs[burnin_idx:],
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                                 color="k", alpha=alpha, lw=lw)
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                    axes[i].set_xlim(0, xoffset+idxs[-1])
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                    if symbols:
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                        axes[i].set_ylabel(symbols[i], labelpad=labelpad)
                        #if subtractions[i] == 0:
                        #    axes[i].set_ylabel(symbols[i], labelpad=labelpad)
                        #else:
                        #    axes[i].set_ylabel(
                        #        symbols[i]+'$-$'+symbols[i]+'$^\mathrm{s}$',
                        #        labelpad=labelpad)
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#                    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)
#                        if self.convergence_test_type == 'autocorr':
#                            ax.set_ylabel(r'$\tau_\mathrm{exp}$')
#                        elif self.convergence_test_type == 'GR':
#                            ax.set_ylabel('PSRF')
#                        ax.ticklabel_format(useOffset=False)
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            else:
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                axes[0].ticklabel_format(useOffset=False, axis='y')
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                cs = chain[:, :, temp].T
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                if burnin_idx:
                    axes[0].plot(idxs[:burnin_idx], cs[:burnin_idx],
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                                 color="C3", alpha=alpha, lw=lw)
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                axes[0].plot(idxs[burnin_idx:], cs[burnin_idx:], color="k",
                             alpha=alpha, lw=lw)
                if symbols:
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                    axes[0].set_ylabel(symbols[0], labelpad=labelpad)
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            axes[-1].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)

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            if plot_det_stat:
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                if len(axes) == ndim:
                    axes.append(fig.add_subplot(ndim+1, 1, ndim+1))

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                lnl = sampler.loglikelihood[temp,