pyfstat.py 103 KB
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""" Classes for various types of searches using ComputeFstatistic """
import os
import sys
import itertools
import logging
import argparse
import copy
import glob
import inspect
from functools import wraps
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import subprocess
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from collections import OrderedDict
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import numpy as np
import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
import emcee
import corner
import dill as pickle
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import lal
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import lalpulsar

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try:
    from tqdm import tqdm
except ImportError:
    def tqdm(x):
        return x

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plt.rcParams['text.usetex'] = True
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plt.rcParams['axes.formatter.useoffset'] = False
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config_file = os.path.expanduser('~')+'/.pyfstat.conf'
if os.path.isfile(config_file):
    d = {}
    with open(config_file, 'r') as f:
        for line in f:
            k, v = line.split('=')
            k = k.replace(' ', '')
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            v = v.replace(' ', '').replace("'", "").replace('"', '').replace('\n', '')
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            d[k] = v
    earth_ephem = d['earth_ephem']
    sun_ephem = d['sun_ephem']
else:
    logging.warning('No ~/.pyfstat.conf file found please provide the paths '
                    'when initialising searches')
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    earth_ephem = None
    sun_ephem = None

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parser = argparse.ArgumentParser()
parser.add_argument("-q", "--quite", help="Decrease output verbosity",
                    action="store_true")
parser.add_argument("-c", "--clean", help="Don't use cached data",
                    action="store_true")
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parser.add_argument("-u", "--use-old-data", action="store_true")
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parser.add_argument('unittest_args', nargs='*')
args, unknown = parser.parse_known_args()
sys.argv[1:] = args.unittest_args

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logger = logging.getLogger()
logger.setLevel(logging.DEBUG)
stream_handler = logging.StreamHandler()
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if args.quite:
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    stream_handler.setLevel(logging.WARNING)
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else:
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    stream_handler.setLevel(logging.DEBUG)
stream_handler.setFormatter(logging.Formatter(
    '%(asctime)s %(levelname)-8s: %(message)s', datefmt='%H:%M'))
logger.addHandler(stream_handler)
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def initializer(func):
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    """ Decorator function to automatically assign the parameters to self """
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    names, varargs, keywords, defaults = inspect.getargspec(func)

    @wraps(func)
    def wrapper(self, *args, **kargs):
        for name, arg in list(zip(names[1:], args)) + list(kargs.items()):
            setattr(self, name, arg)

        for name, default in zip(reversed(names), reversed(defaults)):
            if not hasattr(self, name):
                setattr(self, name, default)

        func(self, *args, **kargs)

    return wrapper


def read_par(label, outdir):
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    """ Read in a .par file, returns a dictionary of the values """
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    filename = '{}/{}.par'.format(outdir, label)
    d = {}
    with open(filename, 'r') as f:
        for line in f:
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            if len(line.split('=')) > 1:
                key, val = line.rstrip('\n').split(' = ')
                key = key.strip()
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                d[key] = np.float64(eval(val.rstrip('; ')))
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    return d


class BaseSearchClass(object):
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    """ The base search class, provides general functions """
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    earth_ephem_default = earth_ephem
    sun_ephem_default = sun_ephem

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    def add_log_file(self):
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        """ Log output to a file, requires class to have outdir and label """
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        logfilename = '{}/{}.log'.format(self.outdir, self.label)
        fh = logging.FileHandler(logfilename)
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        fh.setLevel(logging.INFO)
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        fh.setFormatter(logging.Formatter(
            '%(asctime)s %(levelname)-8s: %(message)s',
            datefmt='%y-%m-%d %H:%M'))
        logging.getLogger().addHandler(fh)

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    def shift_matrix(self, n, dT):
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        """ Generate the shift matrix

        Parameters
        ----------
        n: int
            The dimension of the shift-matrix to generate
        dT: float
            The time delta of the shift matrix

        Returns
        -------
        m: array (n, n)
            The shift matrix
        """

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        m = np.zeros((n, n))
        factorial = np.math.factorial
        for i in range(n):
            for j in range(n):
                if i == j:
                    m[i, j] = 1.0
                elif i > j:
                    m[i, j] = 0.0
                else:
                    if i == 0:
                        m[i, j] = 2*np.pi*float(dT)**(j-i) / factorial(j-i)
                    else:
                        m[i, j] = float(dT)**(j-i) / factorial(j-i)
        return m

    def shift_coefficients(self, theta, dT):
        """ Shift a set of coefficients by dT

        Parameters
        ----------
        theta: array-like, shape (n,)
            vector of the expansion coefficients to transform starting from the
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            lowest degree e.g [phi, F0, F1,...].
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        dT: float
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            difference between the two reference times as tref_new - tref_old.
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        Returns
        -------
        theta_new: array-like shape (n,)
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            vector of the coefficients as evaluate as the new reference time.
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        """
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        n = len(theta)
        m = self.shift_matrix(n, dT)
        return np.dot(m, theta)

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    def calculate_thetas(self, theta, delta_thetas, tbounds, theta0_idx=0):
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        """ Calculates the set of coefficients for the post-glitch signal """
        thetas = [theta]
        for i, dt in enumerate(delta_thetas):
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            if i < theta0_idx:
                pre_theta_at_ith_glitch = self.shift_coefficients(
                    thetas[0], tbounds[i+1] - self.tref)
                post_theta_at_ith_glitch = pre_theta_at_ith_glitch - dt
                thetas.insert(0, self.shift_coefficients(
                    post_theta_at_ith_glitch, self.tref - tbounds[i+1]))

            elif i >= theta0_idx:
                pre_theta_at_ith_glitch = self.shift_coefficients(
                    thetas[i], tbounds[i+1] - self.tref)
                post_theta_at_ith_glitch = pre_theta_at_ith_glitch + dt
                thetas.append(self.shift_coefficients(
                    post_theta_at_ith_glitch, self.tref - tbounds[i+1]))
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        return thetas


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class ComputeFstat(object):
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    """ Base class providing interface to `lalpulsar.ComputeFstat` """
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    earth_ephem_default = earth_ephem
    sun_ephem_default = sun_ephem

    @initializer
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    def __init__(self, tref, sftfilepath=None, minStartTime=None,
                 maxStartTime=None, binary=False, transient=True, BSGL=False,
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                 detector=None, minCoverFreq=None, maxCoverFreq=None,
                 earth_ephem=None, sun_ephem=None,
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                 ):
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        """
        Parameters
        ----------
        tref: int
            GPS seconds of the reference time.
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        sftfilepath: str
            File patern to match SFTs
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        minStartTime, maxStartTime: float GPStime
            Only use SFTs with timestemps starting from (including, excluding)
            this epoch
        binary: bool
            If true, search of binary parameters.
        transient: bool
            If true, allow for the Fstat to be computed over a transient range.
        BSGL: bool
            If true, compute the BSGL rather than the twoF value.
        detector: str
            Two character reference to the data to use, specify None for no
            contraint.
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        minCoverFreq, maxCoverFreq: float
            The min and max cover frequency passed to CreateFstatInput, if
            either is None the range of frequencies in the SFT less 1Hz is
            used.
        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 earth_ephem is None:
            self.earth_ephem = self.earth_ephem_default
        if sun_ephem is None:
            self.sun_ephem = self.sun_ephem_default

        self.init_computefstatistic_single_point()

    def init_computefstatistic_single_point(self):
        """ Initilisation step of run_computefstatistic for a single point """

        logging.info('Initialising SFTCatalog')
        constraints = lalpulsar.SFTConstraints()
        if self.detector:
            constraints.detector = self.detector
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        if self.minStartTime:
            constraints.minStartTime = lal.LIGOTimeGPS(self.minStartTime)
        if self.maxStartTime:
            constraints.maxStartTime = lal.LIGOTimeGPS(self.maxStartTime)

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        logging.info('Loading data matching pattern {}'.format(
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                     self.sftfilepath))
        SFTCatalog = lalpulsar.SFTdataFind(self.sftfilepath, constraints)
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        names = list(set([d.header.name for d in SFTCatalog.data]))
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        SFT_timestamps = [d.header.epoch for d in SFTCatalog.data]
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        logging.info(
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            'Loaded {} data files from detectors {} spanning {} to {}'.format(
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                len(SFT_timestamps), names, int(SFT_timestamps[0]),
                int(SFT_timestamps[-1])))
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        logging.info('Initialising ephems')
        ephems = lalpulsar.InitBarycenter(self.earth_ephem, self.sun_ephem)

        logging.info('Initialising FstatInput')
        dFreq = 0
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        if self.transient:
            self.whatToCompute = lalpulsar.FSTATQ_ATOMS_PER_DET
        else:
            self.whatToCompute = lalpulsar.FSTATQ_2F

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        FstatOptionalArgs = lalpulsar.FstatOptionalArgsDefaults

        if self.minCoverFreq is None or self.maxCoverFreq is None:
            fA = SFTCatalog.data[0].header.f0
            numBins = SFTCatalog.data[0].numBins
            fB = fA + (numBins-1)*SFTCatalog.data[0].header.deltaF
            self.minCoverFreq = fA + 0.5
            self.maxCoverFreq = fB - 0.5
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            logging.info('Min/max cover freqs not provided, using '
                         '{} and {}, est. from SFTs'.format(
                             self.minCoverFreq, self.maxCoverFreq))
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        self.FstatInput = lalpulsar.CreateFstatInput(SFTCatalog,
                                                     self.minCoverFreq,
                                                     self.maxCoverFreq,
                                                     dFreq,
                                                     ephems,
                                                     FstatOptionalArgs
                                                     )

        logging.info('Initialising PulsarDoplerParams')
        PulsarDopplerParams = lalpulsar.PulsarDopplerParams()
        PulsarDopplerParams.refTime = self.tref
        PulsarDopplerParams.Alpha = 1
        PulsarDopplerParams.Delta = 1
        PulsarDopplerParams.fkdot = np.array([0, 0, 0, 0, 0, 0, 0])
        self.PulsarDopplerParams = PulsarDopplerParams

        logging.info('Initialising FstatResults')
        self.FstatResults = lalpulsar.FstatResults()

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        if self.BSGL:
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            if len(names) < 2:
                raise ValueError("Can't use BSGL with single detector data")
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            else:
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                logging.info('Initialising BSGL')
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            # Tuning parameters - to be reviewed
            numDetectors = 2
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            Fstar0sc = 15.
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            oLGX = np.zeros(10)
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            oLGX[:numDetectors] = 1./numDetectors
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            self.BSGLSetup = lalpulsar.CreateBSGLSetup(numDetectors,
                                                       Fstar0sc,
                                                       oLGX,
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                                                       True,
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                                                       1)
            self.twoFX = np.zeros(10)
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            self.whatToCompute = (self.whatToCompute +
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                                  lalpulsar.FSTATQ_2F_PER_DET)

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        if self.transient:
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            logging.info('Initialising transient parameters')
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            self.windowRange = lalpulsar.transientWindowRange_t()
            self.windowRange.type = lalpulsar.TRANSIENT_RECTANGULAR
            self.windowRange.t0Band = 0
            self.windowRange.dt0 = 1
            self.windowRange.tauBand = 0
            self.windowRange.dtau = 1
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    def compute_fullycoherent_det_stat_single_point(
            self, F0, F1, F2, Alpha, Delta, asini=None, period=None, ecc=None,
            tp=None, argp=None):
        """ Compute the fully-coherent det. statistic at a single point """

        return self.run_computefstatistic_single_point(
            self.minStartTime, self.maxStartTime, F0, F1, F2, Alpha, Delta,
            asini, period, ecc, tp, argp)

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    def run_computefstatistic_single_point(self, tstart, tend, F0, F1,
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                                           F2, Alpha, Delta, asini=None,
                                           period=None, ecc=None, tp=None,
                                           argp=None):
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        """ Returns twoF or ln(BSGL) fully-coherently at a single point """
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        self.PulsarDopplerParams.fkdot = np.array([F0, F1, F2, 0, 0, 0, 0])
        self.PulsarDopplerParams.Alpha = Alpha
        self.PulsarDopplerParams.Delta = Delta
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        if self.binary:
            self.PulsarDopplerParams.asini = asini
            self.PulsarDopplerParams.period = period
            self.PulsarDopplerParams.ecc = ecc
            self.PulsarDopplerParams.tp = tp
            self.PulsarDopplerParams.argp = argp
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        lalpulsar.ComputeFstat(self.FstatResults,
                               self.FstatInput,
                               self.PulsarDopplerParams,
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                               1,
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                               self.whatToCompute
                               )

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        if self.transient is False:
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            if self.BSGL is False:
                return self.FstatResults.twoF[0]

            twoF = np.float(self.FstatResults.twoF[0])
            self.twoFX[0] = self.FstatResults.twoFPerDet(0)
            self.twoFX[1] = self.FstatResults.twoFPerDet(1)
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            log10_BSGL = lalpulsar.ComputeBSGL(twoF, self.twoFX,
                                               self.BSGLSetup)
            return log10_BSGL/np.log10(np.exp(1))
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        self.windowRange.t0 = int(tstart)  # TYPE UINT4
        self.windowRange.tau = int(tend - tstart)  # TYPE UINT4
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        FS = lalpulsar.ComputeTransientFstatMap(
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            self.FstatResults.multiFatoms[0], self.windowRange, False)
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        if self.BSGL is False:
            return 2*FS.F_mn.data[0][0]

        FstatResults_single = copy.copy(self.FstatResults)
        FstatResults_single.lenth = 1
        FstatResults_single.data = self.FstatResults.multiFatoms[0].data[0]
        FS0 = lalpulsar.ComputeTransientFstatMap(
            FstatResults_single.multiFatoms[0], self.windowRange, False)
        FstatResults_single.data = self.FstatResults.multiFatoms[0].data[1]
        FS1 = lalpulsar.ComputeTransientFstatMap(
            FstatResults_single.multiFatoms[0], self.windowRange, False)

        self.twoFX[0] = 2*FS0.F_mn.data[0][0]
        self.twoFX[1] = 2*FS1.F_mn.data[0][0]
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        log10_BSGL = lalpulsar.ComputeBSGL(
                2*FS.F_mn.data[0][0], self.twoFX, self.BSGLSetup)
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        return log10_BSGL/np.log10(np.exp(1))
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    def calculate_twoF_cumulative(self, F0, F1, F2, Alpha, Delta, asini=None,
                                  period=None, ecc=None, tp=None, argp=None,
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                                  tstart=None, tend=None, npoints=1000,
                                  minfraction=0.01, maxfraction=1):
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        """ Calculate the cumulative twoF along the obseration span """
        duration = tend - tstart
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        tstart = tstart + minfraction*duration
        taus = np.linspace(minfraction*duration, maxfraction*duration, npoints)
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        twoFs = []
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        if self.transient is False:
            self.transient = True
            self.init_computefstatistic_single_point()
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        for tau in taus:
            twoFs.append(self.run_computefstatistic_single_point(
                tstart=tstart, tend=tstart+tau, F0=F0, F1=F1, F2=F2,
                Alpha=Alpha, Delta=Delta, asini=asini, period=period, ecc=ecc,
                tp=tp, argp=argp))

        return taus, np.array(twoFs)

    def plot_twoF_cumulative(self, label, outdir, ax=None, c='k', savefig=True,
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                             title=None, **kwargs):
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        taus, twoFs = self.calculate_twoF_cumulative(**kwargs)
        if ax is None:
            fig, ax = plt.subplots()
        ax.plot(taus/86400., twoFs, label=label, color=c)
        ax.set_xlabel(r'Days from $t_{{\rm start}}={:.0f}$'.format(
            kwargs['tstart']))
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        if self.BSGL:
            ax.set_ylabel(r'$\log_{10}(\mathrm{BSGL})_{\rm cumulative}$')
        else:
            ax.set_ylabel(r'$\widetilde{2\mathcal{F}}_{\rm cumulative}$')
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        ax.set_xlim(0, taus[-1]/86400)
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        ax.set_title(title)
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        if savefig:
            plt.savefig('{}/{}_twoFcumulative.png'.format(outdir, label))
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            return taus, twoFs
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        else:
            return ax

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class SemiCoherentSearch(BaseSearchClass, ComputeFstat):
    """ A semi-coherent search """

    @initializer
    def __init__(self, label, outdir, tref, nsegs=None, sftfilepath=None,
                 binary=False, BSGL=False, minStartTime=None,
                 maxStartTime=None, minCoverFreq=None, maxCoverFreq=None,
                 detector=None, earth_ephem=None, sun_ephem=None):
        """
        Parameters
        ----------
        label, outdir: str
            A label and directory to read/write data from/to.
        tref, tstart, tend: int
            GPS seconds of the reference time, and start and end of the data.
        nsegs: int
            The (fixed) number of segments
        sftfilepath: str
            File patern to match SFTs

        For all other parameters, see pyfstat.ComputeFStat.
        """

        self.fs_file_name = "{}/{}_FS.dat".format(self.outdir, self.label)
        if self.earth_ephem is None:
            self.earth_ephem = self.earth_ephem_default
        if self.sun_ephem is None:
            self.sun_ephem = self.sun_ephem_default
        self.transient = True
        self.init_computefstatistic_single_point()
        self.init_semicoherent_parameters()

    def init_semicoherent_parameters(self):
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        logging.info(('Initialising semicoherent parameters from {} to {} in'
                      ' {} segments').format(
            self.minStartTime, self.maxStartTime, self.nsegs))
        if self.nsegs == 1:
            self.transient = False
            self.whatToCompute = lalpulsar.FSTATQ_2F
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        self.tboundaries = np.linspace(self.minStartTime, self.maxStartTime,
                                       self.nsegs+1)

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    def run_semi_coherent_computefstatistic_single_point(
            self, F0, F1, F2, Alpha, Delta, asini=None,
            period=None, ecc=None, tp=None, argp=None):
        """ Returns twoF or ln(BSGL) semi-coherently at a single point """
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        self.PulsarDopplerParams.fkdot = np.array([F0, F1, F2, 0, 0, 0, 0])
        self.PulsarDopplerParams.Alpha = Alpha
        self.PulsarDopplerParams.Delta = Delta
        if self.binary:
            self.PulsarDopplerParams.asini = asini
            self.PulsarDopplerParams.period = period
            self.PulsarDopplerParams.ecc = ecc
            self.PulsarDopplerParams.tp = tp
            self.PulsarDopplerParams.argp = argp

        lalpulsar.ComputeFstat(self.FstatResults,
                               self.FstatInput,
                               self.PulsarDopplerParams,
                               1,
                               self.whatToCompute
                               )

        if self.transient is False:
            if self.BSGL is False:
                return self.FstatResults.twoF[0]

            twoF = np.float(self.FstatResults.twoF[0])
            self.twoFX[0] = self.FstatResults.twoFPerDet(0)
            self.twoFX[1] = self.FstatResults.twoFPerDet(1)
            log10_BSGL = lalpulsar.ComputeBSGL(twoF, self.twoFX,
                                               self.BSGLSetup)
            return log10_BSGL/np.log10(np.exp(1))

        detStat = 0
        for tstart, tend in zip(self.tboundaries[:-1], self.tboundaries[1:]):
            self.windowRange.t0 = int(tstart)  # TYPE UINT4
            self.windowRange.tau = int(tend - tstart)  # TYPE UINT4

            FS = lalpulsar.ComputeTransientFstatMap(
                self.FstatResults.multiFatoms[0], self.windowRange, False)

            if self.BSGL is False:
                detStat += 2*FS.F_mn.data[0][0]
                continue
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            FstatResults_single = copy.copy(self.FstatResults)
            FstatResults_single.lenth = 1
            FstatResults_single.data = self.FstatResults.multiFatoms[0].data[0]
            FS0 = lalpulsar.ComputeTransientFstatMap(
                FstatResults_single.multiFatoms[0], self.windowRange, False)
            FstatResults_single.data = self.FstatResults.multiFatoms[0].data[1]
            FS1 = lalpulsar.ComputeTransientFstatMap(
                FstatResults_single.multiFatoms[0], self.windowRange, False)

            self.twoFX[0] = 2*FS0.F_mn.data[0][0]
            self.twoFX[1] = 2*FS1.F_mn.data[0][0]
            log10_BSGL = lalpulsar.ComputeBSGL(
                    2*FS.F_mn.data[0][0], self.twoFX, self.BSGLSetup)

            detStat += log10_BSGL/np.log10(np.exp(1))

        return detStat
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class SemiCoherentGlitchSearch(BaseSearchClass, ComputeFstat):
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    """ A semi-coherent glitch search

    This implements a basic `semi-coherent glitch F-stat in which the data
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    is divided into segments either side of the proposed glitches and the
    fully-coherent F-stat in each segment is summed to give the semi-coherent
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    F-stat
    """

    @initializer
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    def __init__(self, label, outdir, tref, tstart, tend, nglitch=0,
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                 sftfilepath=None, theta0_idx=0, BSGL=False, minStartTime=None,
                 maxStartTime=None, minCoverFreq=None, maxCoverFreq=None,
                 detector=None, earth_ephem=None, sun_ephem=None):
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        """
        Parameters
        ----------
        label, outdir: str
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            A label and directory to read/write data from/to.
        tref, tstart, tend: int
            GPS seconds of the reference time, and start and end of the data.
        nglitch: int
            The (fixed) number of glitches; this can zero, but occasionally
            this causes issue (in which case just use ComputeFstat).
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        sftfilepath: str
            File patern to match SFTs
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        theta0_idx, int
            Index (zero-based) of which segment the theta refers to - uyseful
            if providing a tight prior on theta to allow the signal to jump
            too theta (and not just from)
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        For all other parameters, see pyfstat.ComputeFStat.
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        """

        self.fs_file_name = "{}/{}_FS.dat".format(self.outdir, self.label)
        if self.earth_ephem is None:
            self.earth_ephem = self.earth_ephem_default
        if self.sun_ephem is None:
            self.sun_ephem = self.sun_ephem_default
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        self.transient = True
        self.binary = False
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        self.init_computefstatistic_single_point()

    def compute_nglitch_fstat(self, F0, F1, F2, Alpha, Delta, *args):
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        """ Returns the semi-coherent glitch summed twoF """
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        args = list(args)
        tboundaries = [self.tstart] + args[-self.nglitch:] + [self.tend]
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        delta_F0s = args[-3*self.nglitch:-2*self.nglitch]
        delta_F1s = args[-2*self.nglitch:-self.nglitch]
        delta_F2 = np.zeros(len(delta_F0s))
        delta_phi = np.zeros(len(delta_F0s))
        theta = [0, F0, F1, F2]
        delta_thetas = np.atleast_2d(
                np.array([delta_phi, delta_F0s, delta_F1s, delta_F2]).T)

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        thetas = self.calculate_thetas(theta, delta_thetas, tboundaries,
                                       theta0_idx=self.theta0_idx)
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        twoFSum = 0
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        for i, theta_i_at_tref in enumerate(thetas):
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            ts, te = tboundaries[i], tboundaries[i+1]

            twoFVal = self.run_computefstatistic_single_point(
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                ts, te, theta_i_at_tref[1], theta_i_at_tref[2],
                theta_i_at_tref[3], Alpha, Delta)
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            twoFSum += twoFVal

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        if np.isfinite(twoFSum):
            return twoFSum
        else:
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            return -np.inf
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    def compute_glitch_fstat_single(self, F0, F1, F2, Alpha, Delta, delta_F0,
                                    delta_F1, tglitch):
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        """ Returns the semi-coherent glitch summed twoF for nglitch=1

        Note: used for testing
        """
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        theta = [F0, F1, F2]
        delta_theta = [delta_F0, delta_F1, 0]
        tref = self.tref

        theta_at_glitch = self.shift_coefficients(theta, tglitch - tref)
        theta_post_glitch_at_glitch = theta_at_glitch + delta_theta
        theta_post_glitch = self.shift_coefficients(
            theta_post_glitch_at_glitch, tref - tglitch)

        twoFsegA = self.run_computefstatistic_single_point(
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            self.tstart, tglitch, theta[0], theta[1], theta[2], Alpha,
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            Delta)

        if tglitch == self.tend:
            return twoFsegA

        twoFsegB = self.run_computefstatistic_single_point(
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            tglitch, self.tend, theta_post_glitch[0],
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            theta_post_glitch[1], theta_post_glitch[2], Alpha,
            Delta)

        return twoFsegA + twoFsegB


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class MCMCSearch(BaseSearchClass):
    """ MCMC search using ComputeFstat"""
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    @initializer
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    def __init__(self, label, outdir, sftfilepath, theta_prior, tref,
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                 tstart, tend, nsteps=[100, 100, 100], nwalkers=100, ntemps=1,
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                 log10temperature_min=-5, theta_initial=None, scatter_val=1e-10,
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                 binary=False, BSGL=False, minCoverFreq=None,
                 maxCoverFreq=None, detector=None, earth_ephem=None,
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                 sun_ephem=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
            File patern to match SFTs
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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, tstart, tend: int
            GPS seconds of the reference time, start time and end time
        nsteps: list (m,)
            List specifying the number of steps to take, the last two entries
            give the nburn and nprod of the 'production' run, all entries
            before are for iterative initialisation steps (usually just one)
            e.g. [1000, 1000, 500].
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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
        detector: str
            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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        self.minStartTime = tstart
        self.maxStartTime = tend

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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)
        self.unpack_input_theta()
        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()

    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 inititate_search_object(self):
        logging.info('Setting up search object')
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        self.search = 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,
            detector=self.detector, BSGL=self.BSGL, transient=False,
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            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
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            binary=self.binary)
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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

    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]

    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))

                p0 = self.generate_new_p0_to_fix_initial_points(
                    p0, nt, initial_priors)

    def generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors):
        logging.info('Attempting to correct intial values')
        idxs = np.arange(self.nwalkers)[initial_priors == -np.inf]
        count = 0
        while sum(initial_priors == -np.inf) > 0 and count < 100:
            for j in idxs:
                p0[nt][j] = (p0[nt][np.random.randint(0, self.nwalkers)]*(
                             1+np.random.normal(0, 1e-10, self.ndim)))
            initial_priors = np.array([
                self.logp(p, self.theta_prior, self.theta_keys,
                          self.search)
                for p in p0[nt]])
            count += 1

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

        return p0
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    def 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

    def run(self, proposal_scale_factor=2):
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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))
            d = self.get_saved_data()
            self.sampler = d['sampler']
            self.samples = d['samples']
            self.lnprobs = d['lnprobs']
            self.lnlikes = d['lnlikes']
            return

        self.inititate_search_object()

        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)
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        self.check_initial_points(p0)

        ninit_steps = len(self.nsteps) - 2
        for j, n in enumerate(self.nsteps[:-2]):
            logging.info('Running {}/{} initialisation with {} steps'.format(
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                j, ninit_steps, n))
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            sampler = self.run_sampler_with_progress_bar(sampler, n, p0)
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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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            fig, axes = self.plot_walkers(sampler, symbols=self.theta_symbols)
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            fig.savefig('{}/{}_init_{}_walkers.png'.format(
                self.outdir, self.label, j))

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            p0 = self.get_new_p0(sampler)
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            p0 = self.apply_corrections_to_p0(p0)
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            self.check_initial_points(p0)
            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_with_progress_bar(sampler, nburn+nprod, p0)
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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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        fig, axes = self.plot_walkers(sampler, symbols=self.theta_symbols,
                                      burnin_idx=nburn)
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        fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label))

        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
        lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1))
        self.sampler = sampler
        self.samples = samples
        self.lnprobs = lnprobs
        self.lnlikes = lnlikes
        self.save_data(sampler, samples, lnprobs, lnlikes)

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    def plot_corner(self, figsize=(7, 7),  tglitch_ratio=False,
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                    add_prior=False, nstds=None, label_offset=0.4,
                    dpi=300, rc_context={}, **kwargs):

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        if self.ndim < 2:
            with plt.rc_context(rc_context):
                fig, ax = plt.subplots(figsize=figsize)
                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):
            fig, axes = plt.subplots(self.ndim, self.ndim,
                                     figsize=figsize)

            samples_plt = copy.copy(self.samples)
            theta_symbols_plt = copy.copy(self.theta_symbols)
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            theta_symbols_plt = [s.replace('_{glitch}', r'_\textrm{glitch}')
                                 for s in theta_symbols_plt]
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            if tglitch_ratio:
                for j, k in enumerate(self.theta_keys):
                    if k == 'tglitch':
                        s = samples_plt[:, j]
                        samples_plt[:, j] = (s - self.tstart)/(
                                             self.tend - self.tstart)
                        theta_symbols_plt[j] = r'$R_{\textrm{glitch}}$'

            if type(nstds) is int and 'range' not in kwargs:
                _range = []
                for j, s in enumerate(samples_plt.T):
                    median = np.median(s)
                    std = np.std(s)
                    _range.append((median - nstds*std, median + nstds*std))
            else:
                _range = None

            fig_triangle = corner.corner(samples_plt,
                                         labels=theta_symbols_plt,
                                         fig=fig,
                                         bins=50,
                                         max_n_ticks=4,
                                         plot_contours=True,
                                         plot_datapoints=True,
                                         label_kwargs={'fontsize': 8},
                                         data_kwargs={'alpha': 0.1,
                                                      'ms': 0.5},
                                         range=_range,
                                         **kwargs)

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

            if add_prior:
                self.add_prior_to_corner(axes, samples_plt)

            fig_triangle.savefig('{}/{}_corner.png'.format(
                self.outdir, self.label), dpi=dpi)
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    def add_prior_to_corner(self, axes, samples):
        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            xlim = ax.get_xlim()
            s = samples[:, i]
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            prior = self.generic_lnprior(**self.theta_prior[key])
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            x = np.linspace(s.min(), s.max(), 100)
            ax2 = ax.twinx()
            ax2.get_yaxis().set_visible(False)
            ax2.plot(x, [prior(xi) for xi in x], '-r')
            ax.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]
            prior_func = self.generic_lnprior(**prior_dict)
            if prior_dict['type'] == 'unif':
                x = np.linspace(prior_dict['lower'], prior_dict['upper'], N)
                prior = prior_func(x)
                prior[0] = 0
                prior[-1] = 0
            elif prior_dict['type'] == 'norm':
                lower = prior_dict['loc'] - normal_stds * prior_dict['scale']
                upper = prior_dict['loc'] + normal_stds * prior_dict['scale']
                x = np.linspace(lower, upper, N)
                prior = prior_func(x)
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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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        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:
            self.inititate_search_object()
        if self.binary is False:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
                Alpha=d['Alpha'], Delta=d['Delta'], tstart=self.tstart,
                tend=self.tend, **kwargs)
        else:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
                Alpha=d['Alpha'], Delta=d['Delta'], asini=d['asini'],
                period=d['period'], ecc=d['ecc'], argp=d['argp'], tp=d['argp'],
                tstart=self.tstart, tend=self.tend, **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):
            if x < 0:
                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,
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                     lw=0.1, burnin_idx=None, add_det_stat_burnin=False,
                     fig=None, axes=None, xoffset=0, plot_det_stat=True):
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        """ Plot all the chains from a sampler """

        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, :, :, :]

        with plt.style.context(('classic')):
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            if fig is None and axes is None:
                fig = plt.figure(figsize=(8, 4*ndim))
                ax = fig.add_subplot(ndim+1, 1, 1)
                axes = [ax] + [fig.add_subplot(ndim+1, 1, i, sharex=ax)
                               for i in range(2, ndim+1)]
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            idxs = np.arange(chain.shape[1])
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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
                    if burnin_idx:
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                        axes[i].plot(xoffset+idxs[:burnin_idx],
                                     cs[:burnin_idx], color="r", alpha=alpha,
                                     lw=lw)
                    axes[i].plot(xoffset+idxs[burnin_idx:], cs[burnin_idx:],
                                 color="k", alpha=alpha, lw=lw)
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                    if symbols:
                        axes[i].set_ylabel(symbols[i])
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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:
                    axes[0].set_ylabel(symbols[0])
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        if len(axes) == ndim:
            axes.append(fig.add_subplot(ndim+1, 1, ndim+1))

        if plot_det_stat:
            lnl = sampler.lnlikelihood[temp, :, :]
            if burnin_idx and add_det_stat_burnin:
                burn_in_vals = lnl[:, :burnin_idx].flatten()
                axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)], bins=50,
                              histtype='step', color='r')
            else:
                burn_in_vals = []
            prod_vals = lnl[:, burnin_idx:].flatten()
            axes[-1].hist(prod_vals[~np.isnan(prod_vals)], bins=50,
                          histtype='step', color='k')
            if self.BSGL:
                axes[-1].set_xlabel(r'$\mathcal{B}_\mathrm{S/GL}$')
            else:
                axes[-1].set_xlabel(r'$2\mathcal{F}$')
            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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        return fig, axes

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    def apply_corrections_to_p0(self, p0):
        """ Apply any correction to the initial p0 values """
        return p0

    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')
            p0 = [[[self.generate_rv(**val)
                    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]