mcmc_based_searches.py 87.6 KB
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""" Searches using MCMC-based methods """

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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 numpy as np
import matplotlib
import matplotlib.pyplot as plt
import emcee
import corner
import dill as pickle

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import core
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from core import tqdm, args, earth_ephem, sun_ephem
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from optimal_setup_functions import get_V_estimate
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from optimal_setup_functions import get_optimal_setup
import helper_functions
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class MCMCSearch(core.BaseSearchClass):
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    """ MCMC search using ComputeFstat"""
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    symbol_dictionary = dict(
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        F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$',
        Delta='$\delta$')
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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')
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    rescale_dictionary = {}


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    @helper_functions.initializer
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    def __init__(self, label, outdir, theta_prior, tref, minStartTime,
                 maxStartTime, sftfilepath=None, nsteps=[100, 100],
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                 nwalkers=100, ntemps=1, log10temperature_min=-5,
                 theta_initial=None, scatter_val=1e-10,
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                 binary=False, BSGL=False, minCoverFreq=None,
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                 maxCoverFreq=None, detectors=None, earth_ephem=None,
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                 sun_ephem=None, injectSources=None, assumeSqrtSX=None):
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        """
        Parameters
        label, outdir: str
            A label and directory to read/write data from/to
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        sftfilepath: str
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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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        theta_prior: dict
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            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.
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        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.
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        tref, minStartTime, maxStartTime: int
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            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].
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        nwalkers, ntemps: int,
            The number of walkers and temperates to use in the parallel
            tempered PTSampler.
        log10temperature_min float < 0
            The  log_10(tmin) value, the set of betas passed to PTSampler are
            generated from np.logspace(0, log10temperature_min, ntemps).
        binary: Bool
            If true, search over binary parameters
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        detectors: str
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            Two character reference to the data to use, specify None for no
            contraint.
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        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

        """

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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 {} on data {}'.format(
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                self.label, self.sftfilepath))
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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.log10temperature_min:
            self.betas = np.logspace(0, self.log10temperature_min, self.ntemps)
        else:
            self.betas = None
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        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")

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        self._log_input()
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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('scatter_val = {}'.format(self.scatter_val))
        logging.info('nsteps = {}'.format(self.nsteps))
        logging.info('ntemps = {}'.format(self.ntemps))
        logging.info('log10temperature_min = {}'.format(
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            self.log10temperature_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, sftfilepath=self.sftfilepath,
            minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq,
            earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem,
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            detectors=self.detectors, BSGL=self.BSGL, transient=False,
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            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
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            binary=self.binary, injectSources=self.injectSources,
            assumeSqrtSX=self.assumeSqrtSX)
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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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        FS = search.compute_fullycoherent_det_stat_single_point(
            *self.fixed_theta)
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        return FS

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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 += [
                'asini', 'period', '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 _check_initial_points(self, p0):
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        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))

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                p0 = self._generate_new_p0_to_fix_initial_points(
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                    p0, nt, initial_priors)

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    def _generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors):
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        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
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    def _OLD_run_sampler_with_progress_bar(self, sampler, ns, p0):
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        for result in tqdm(sampler.sample(p0, iterations=ns), total=ns):
            pass
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        return sampler

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    def setup_convergence_testing(
            self, convergence_period=10, convergence_length=10,
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            convergence_burnin_fraction=0.25, convergence_threshold_number=10,
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            convergence_threshold=1.2, convergence_prod_threshold=2,
            convergence_plot_upper_lim=2):
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        """
        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
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        convergence_plot_upper_lim: float
            the upper limit to use in the diagnostic plot
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        """
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        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
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        self.convergence_prod_threshold = convergence_prod_threshold
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        self.convergence_diagnostic = []
        self.convergence_diagnosticx = []
        self.convergence_threshold_number = convergence_threshold_number
        self.convergence_threshold = convergence_threshold
        self.convergence_number = 0
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        self.convergence_plot_upper_lim = convergence_plot_upper_lim
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    def _get_convergence_statistic(self, i, sampler):
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        s = sampler.chain[0, :, i-self.convergence_length+1:i+1, :]
        within_std = 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)
        between_std = np.sqrt(np.mean((per_walker_mean-mean)**2, axis=0))
        W = within_std
        B_over_n = between_std**2 / self.convergence_period
        Vhat = ((self.convergence_period-1.)/self.convergence_period * W
                + B_over_n + B_over_n / float(self.nwalkers))
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        c = np.sqrt(Vhat/W)
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        self.convergence_diagnostic.append(c)
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        self.convergence_diagnosticx.append(i - self.convergence_length/2)
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        return c

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    def _burnin_convergence_test(self, i, sampler, nburn):
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        if i < self.convergence_burnin_fraction*nburn:
            return False
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        if np.mod(i+1, self.convergence_period) != 0:
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            return False
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        c = self._get_convergence_statistic(i, sampler)
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        if np.all(c < self.convergence_threshold):
            self.convergence_number += 1
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        else:
            self.convergence_number = 0
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        return self.convergence_number > self.convergence_threshold_number

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    def _prod_convergence_test(self, i, sampler, nburn):
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        testA = i > nburn + self.convergence_length
        testB = np.mod(i+1, self.convergence_period) == 0
        if testA and testB:
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            self._get_convergence_statistic(i, sampler)
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    def _check_production_convergence(self, k):
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        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)))

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    def _run_sampler(self, sampler, p0, nprod=0, nburn=0):
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        if hasattr(self, 'convergence_period'):
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            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):
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                if self._burnin_convergence_test(i, sampler, nburn):
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                    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):
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                self._prod_convergence_test(j, sampler, nburn)
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                j += 1
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            self._check_production_convergence(k)
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            return sampler
        else:
            for result in tqdm(sampler.sample(p0, iterations=nburn+nprod),
                               total=nburn+nprod):
                pass
            return sampler
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    def run(self, proposal_scale_factor=2, create_plots=True, **kwargs):
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        """ Run the MCMC simulatation """
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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']
            return

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        self._initiate_search_object()
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        sampler = emcee.PTSampler(
            self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp,
            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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        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)
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            logging.info("Mean acceptance fraction: {}"
                         .format(np.mean(sampler.acceptance_fraction, axis=1)))
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            if self.ntemps > 1:
                logging.info("Tswap acceptance fraction: {}"
                             .format(sampler.tswap_acceptance_fraction))
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            if create_plots:
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                fig, axes = self._plot_walkers(sampler,
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                                              symbols=self.theta_symbols,
                                              **kwargs)
                fig.tight_layout()
                fig.savefig('{}/{}_init_{}_walkers.png'.format(
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                    self.outdir, self.label, j), dpi=400)
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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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        logging.info("Mean acceptance fraction: {}"
                     .format(np.mean(sampler.acceptance_fraction, axis=1)))
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        if self.ntemps > 1:
            logging.info("Tswap acceptance fraction: {}"
                         .format(sampler.tswap_acceptance_fraction))
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        if create_plots:
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            fig, axes = self._plot_walkers(sampler, symbols=self.theta_symbols,
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                                          nprod=nprod, **kwargs)
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            fig.tight_layout()
            fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label),
                        dpi=200)
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        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
        lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1))
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        all_lnlikelihood = sampler.lnlikelihood
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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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    def _get_rescale_multiplier_for_key(self, key):
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        """ 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

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    def _get_rescale_subtractor_for_key(self, key):
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        """ 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

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    def _scale_samples(self, samples, theta_keys):
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        """ Scale the samples using the rescale_dictionary """
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        for key in theta_keys:
            if key in self.rescale_dictionary:
                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):
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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]
            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
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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=False,
                    **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)
        add_prior: bool
            If true, plot the prior as a red line
        nstds: float
            The number of standard deviations to plot centered on the mean
        label_offset: float
            Offset the labels from the plot: useful to precent overlapping the
            tick labels with the axis labels
        dpi: int
            Passed to plt.savefig
        rc_context: dict
            Dictionary of rc values to set while generating the figure (see
            matplotlib rc for more details)
        tglitch_ratio: bool
            If true, and tglitch is a parameter, plot posteriors as the
            fractional time at which the glitch occurs instead of the actual
            time
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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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        Note: kwargs are passed on to corner.coner

        """
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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()
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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

            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,
                                         label_kwargs={'fontsize': 8},
                                         data_kwargs={'alpha': 0.1,
                                                      'ms': 0.5},
                                         range=_range,
                                         **kwargs)

            axes_list = fig_triangle.get_axes()
            axes = np.array(axes_list).reshape(self.ndim, self.ndim)
            plt.draw()
            for ax in axes[:, 0]:
                ax.yaxis.set_label_coords(-label_offset, 0.5)
            for ax in axes[-1, :]:
                ax.xaxis.set_label_coords(0.5, -label_offset)
            for ax in axes_list:
                ax.set_rasterized(True)
                ax.set_rasterization_zorder(-10)
            plt.tight_layout(h_pad=0.0, w_pad=0.0)
            fig.subplots_adjust(hspace=0.05, wspace=0.05)

            if add_prior:
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                self._add_prior_to_corner(axes, self.samples)
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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):
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        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            xlim = ax.get_xlim()
            s = samples[:, i]
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            prior = self._generic_lnprior(**self.theta_prior[key])
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            x = np.linspace(s.min(), s.max(), 100)
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            multiplier = self._get_rescale_multiplier_for_key(key)
            subtractor = self._get_rescale_subtractor_for_key(key)
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            ax2 = ax.twinx()
            ax2.get_yaxis().set_visible(False)
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            ax2.plot((x-subtractor)*multiplier, [prior(xi) for xi in x], '-r')
            ax2.set_xlim(xlim)
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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
            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']))
            priorln = ax.plot(x, prior, 'r', label='prior')
            ax.set_xlabel(self.theta_symbols[i])

            s = self.samples[:, i]
            while len(s) > 10**4:
                # random downsample to avoid slow calculation of kde
                s = np.random.choice(s, size=int(len(s)/2.))
            kde = gaussian_kde(s)
            ax2 = ax.twinx()
            postln = ax2.plot(x, kde.pdf(x), 'k', label='posterior')
            ax2.set_yticklabels([])
            ax.set_yticklabels([])

        lns = priorln + postln
        labs = [l.get_label() for l in lns]
        axes[0].legend(lns, labs, loc=1, framealpha=0.8)

        fig.savefig('{}/{}_prior_posterior.png'.format(
            self.outdir, self.label))

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

        """

        def logunif(x, a, b):
            above = x < b
            below = x > a
            if type(above) is not np.ndarray:
                if above and below:
                    return -np.log(b-a)
                else:
                    return -np.inf
            else:
                idxs = np.array([all(tup) for tup in zip(above, below)])
                p = np.zeros(len(x)) - np.inf
                p[idxs] = -np.log(b-a)
                return p

        def halfnorm(x, loc, scale):
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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':
            return lambda x: logunif(x, kwargs['lower'], kwargs['upper'])
        elif kwargs['type'] == 'halfnorm':
            return lambda x: halfnorm(x, kwargs['loc'], kwargs['scale'])
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        elif kwargs['type'] == 'neghalfnorm':
            return lambda x: 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'])
        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=0.4, color="k",
                      temp=0, lw=0.1, nprod=0, add_det_stat_burnin=False,
                      fig=None, axes=None, xoffset=0, plot_det_stat=False,
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                      context='ggplot', subtractions=None, labelpad=0.05):
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        """ Plot all the chains from a sampler """

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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
            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, :, :, :]

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        if subtractions is None:
            subtractions = [0 for i in range(ndim)]
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        else:
            if len(subtractions) != self.ndim:
                raise ValueError('subtractions must be of length 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
            if hasattr(self, 'convergence_idx'):
                convergence_idx = self.convergence_idx
            else:
                convergence_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[:convergence_idx+1],
                                     cs[:convergence_idx+1]-subtractions[i],
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                                     color="r", alpha=alpha,
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                                     lw=lw)
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                        axes[i].axvline(xoffset+convergence_idx,
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                                        color='k', ls='--', lw=0.25)
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                    axes[i].plot(xoffset+idxs[burnin_idx:],
                                 cs[burnin_idx:]-subtractions[i],
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                                 color="k", alpha=alpha, lw=lw)
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                    if symbols:
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                        if subtractions[i] == 0:
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                            axes[i].set_ylabel(symbols[i], labelpad=labelpad)
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                        else:
                            axes[i].set_ylabel(
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                                symbols[i]+'$-$'+symbols[i]+'$_0$',
                                labelpad=labelpad)
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                    if hasattr(self, 'convergence_diagnostic'):
                        ax = axes[i].twinx()
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                        c_x = np.array(self.convergence_diagnosticx)
                        c_y = np.array(self.convergence_diagnostic)
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                        break_idx = np.argmin(np.abs(c_x - burnin_idx))
                        ax.plot(c_x[:break_idx], c_y[:break_idx, i], '-b')
                        ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-b')
                        ax.set_ylabel('PSRF')
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                        ax.ticklabel_format(useOffset=False)
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                        ax.set_ylim(1, self.convergence_plot_upper_lim)
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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],
                                 color="r", alpha=alpha, lw=lw)
                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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            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.lnlikelihood[temp, :, :]
                if burnin_idx and add_det_stat_burnin:
                    burn_in_vals = lnl[:, :burnin_idx].flatten()
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                    try:
                        axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)],
                                      bins=50, histtype='step', color='r')
                    except ValueError:
                        logging.info('Det. Stat. hist failed, most likely all '
                                     'values where the same')
                        pass
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                else:
                    burn_in_vals = []
                prod_vals = lnl[:, burnin_idx:].flatten()
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                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
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                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)

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                xfmt = matplotlib.ticker.ScalarFormatter()
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                xfmt.set_powerlimits((-4, 4))
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                axes[-1].xaxis.set_major_formatter(xfmt)

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            axes[-2].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)
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        return fig, axes

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    def _apply_corrections_to_p0(self, p0):
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        """ Apply any correction to the initial p0 values """
        return p0

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    def _generate_scattered_p0(self, p):
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        """ Generate a set of p0s scattered about p """
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        p0 = [[p + self.scatter_val * p * np.random.randn(self.ndim)
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               for i in xrange(self.nwalkers)]
              for j in xrange(self.ntemps)]
        return p0

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    def _generate_initial_p0(self):
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        """ Generate a set of init vals for the walkers """

        if type(self.theta_initial) == dict:
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            logging.info('Generate initial values from initial dictionary')
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            if hasattr(self, 'nglitch') and self.nglitch > 1:
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                raise ValueError('Initial dict not implemented for nglitch>1')
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            p0 = [[[self._generate_rv(**self.theta_initial[key])
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                    for key in self.theta_keys]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
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        elif type(self.theta_initial) == list:
            logging.info('Generate initial values from list of theta_initial')
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            p0 = [[[self._generate_rv(**val)
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                    for val in self.theta_initial]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
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        elif self.theta_initial is None:
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            logging.info('Generate initial values from prior dictionary')
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            p0 = [[[self._generate_rv(**self.theta_prior[key])
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                    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:
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            p0 = self._generate_scattered_p0(self.theta_initial)
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        else:
            raise ValueError('theta_initial not understood')

        return p0

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    def _get_new_p0(self, sampler):
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        """ 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`.

        """
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        temp_idx = 0
        pF = sampler.chain[temp_idx, :, :, :]
        lnl = sampler.lnlikelihood[temp_idx, :, :]
        lnp = sampler.lnprobability[temp_idx, :, :]
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        # General warnings about the state of lnp
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        if np.any(np.isnan(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are nan".format(
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                    np.shape(lnp), np.sum(np.isnan(lnp))))
        if np.any(np.isposinf(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are +np.inf".format(
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                    np.shape(lnp), np.sum(np.isposinf(lnp))))
        if np.any(np.isneginf(lnp)):
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            logging.warning(
                "Of {} lnprobs {} are -np.inf".format(
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                    np.shape(lnp), np.sum(np.isneginf(lnp))))
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        lnp_finite = copy.copy(lnp)
        lnp_finite[np.isinf(lnp)] = np.nan
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        idx = np.unravel_index(np.nanargmax(lnp_finite), lnp_finite.shape)
        p = pF[idx]
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        p0 = self._generate_scattered_p0(p)
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        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]))

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        return p0

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    def _get_data_dictionary_to_save(self):
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        d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers,
                 ntemps=self.ntemps, theta_keys=self.theta_keys,
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                 theta_prior=self.theta_prior, scatter_val=self.scatter_val,
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                 log10temperature_min=self.log10temperature_min,
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                 BSGL=self.BSGL)
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        return d

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    def _save_data(self, sampler, samples, lnprobs, lnlikes, all_lnlikelihood):
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        d = self._get_data_dictionary_to_save()
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        d['samples'] = samples
        d['lnprobs'] = lnprobs
        d['lnlikes'] = lnlikes
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        d['all_lnlikelihood'] = all_lnlikelihood
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        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)

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    def get_saved_data_dictionary(self):
        """ Returns dictionary of the data saved as pickle """
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        with open(self.pickle_path, "r") as File:
            d = pickle.load(File)
        return d

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    def _check_old_data_is_okay_to_use(self):
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        if args.use_old_data:
            logging.info("Forcing use of old data")
            return True

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        if os.path.isfile(self.pickle_path) is False:
            logging.info('No pickled data found')
            return False

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        if self.sftfilepath is not None:
            oldest_sft = min([os.path.getmtime(f) for f in
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                              self._get_list_of_matching_sfts()])
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            if os.path.getmtime(self.pickle_path) < oldest_sft:
                logging.info('Pickled data outdates sft files')
                return False
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        old_d = self.get_saved_data_dictionary().copy()
        new_d = self._get_data_dictionary_to_save().copy()
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        old_d.pop('samples')
        old_d.pop('lnprobs')
        old_d.pop('lnlikes')

        mod_keys = []
        for key in new_d.keys():
            if key in old_d:
                if new_d[key] != old_d[key]:
                    mod_keys.append((key, old_d[key], new_d[key]))
            else:
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                raise ValueError('Keys {} not in old dictionary'.format(key))
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        if len(