def bls_parallel_pfind(
        times, mags, errs,
        magsarefluxes=False,
        startp=0.1,  # by default, search from 0.1 d to...
        endp=100.0,  # ... 100.0 d -- don't search full timebase
        stepsize=1.0e-4,
        mintransitduration=0.01,  # minimum transit length in phase
        maxtransitduration=0.4,   # maximum transit length in phase
        ndurations=100,
        autofreq=True,  # figure out f0, nf, and df automatically
        blsobjective='likelihood',
        blsmethod='fast',
        blsoversample=5,
        blsmintransits=3,
        blsfreqfactor=10.0,
        nbestpeaks=5,
        periodepsilon=0.1,  # 0.1
        sigclip=10.0,
        verbose=True,
        nworkers=None,
):
    '''Runs the Box Least Squares Fitting Search for transit-shaped signals.

    Breaks up the full frequency space into chunks and passes them to parallel
    BLS workers.

    Based on the version of BLS in Astropy 3.1:
    `astropy.stats.BoxLeastSquares`. If you don't have Astropy 3.1, this module
    will fail to import. Note that by default, this implementation of
    `bls_parallel_pfind` doesn't use the `.autoperiod()` function from
    `BoxLeastSquares` but uses the same auto frequency-grid generation as the
    functions in `periodbase.kbls`. If you want to use Astropy's implementation,
    set the value of `autofreq` kwarg to 'astropy'. The generated period array
    will then be broken up into chunks and sent to the individual workers.

    NOTE: the combined BLS spectrum produced by this function is not identical
    to that produced by running BLS in one shot for the entire frequency
    space. There are differences on the order of 1.0e-3 or so in the respective
    peak values, but peaks appear at the same frequencies for both methods. This
    is likely due to different aliasing caused by smaller chunks of the
    frequency space used by the parallel workers in this function. When in
    doubt, confirm results for this parallel implementation by comparing to
    those from the serial implementation above.

    In particular, when you want to get reliable estimates of the SNR, transit
    depth, duration, etc. that Astropy's BLS gives you, rerun `bls_serial_pfind`
    with `startp`, and `endp` close to the best period you want to characterize
    the transit at. The dict returned from that function contains a `blsmodel`
    key, which is the generated model from Astropy's BLS. Use the
    `.compute_stats()` method to calculate the required stats.

    Parameters
    ----------

    times,mags,errs : np.array
        The magnitude/flux time-series to search for transits.

    magsarefluxes : bool
        If the input measurement values in `mags` and `errs` are in fluxes, set
        this to True.

    startp,endp : float
        The minimum and maximum periods to consider for the transit search.

    stepsize : float
        The step-size in frequency to use when constructing a frequency grid for
        the period search.

    mintransitduration,maxtransitduration : float
        The minimum and maximum transitdurations (in units of phase) to consider
        for the transit search.

    ndurations : int
        The number of transit durations to use in the period-search.

    autofreq : bool or str
        If this is True, the values of `stepsize` and `nphasebins` will be
        ignored, and these, along with a frequency-grid, will be determined
        based on the following relations::

            nphasebins = int(ceil(2.0/mintransitduration))
            if nphasebins > 3000:
                nphasebins = 3000

            stepsize = 0.25*mintransitduration/(times.max()-times.min())

            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(ceil((maxfreq - minfreq)/stepsize))

        If this is False, you must set `startp`, `endp`, and `stepsize` as
        appropriate.

        If this is str == 'astropy', will use the
        `astropy.stats.BoxLeastSquares.autoperiod()` function to calculate the
        frequency grid instead of the kbls method.

    blsobjective : {'likelihood','snr'}
        Sets the type of objective to optimize in the `BoxLeastSquares.power()`
        function.

    blsmethod : {'fast','slow'}
        Sets the type of method to use in the `BoxLeastSquares.power()`
        function.

    blsoversample : {'likelihood','snr'}
        Sets the `oversample` kwarg for the `BoxLeastSquares.power()` function.

    blsmintransits : int
        Sets the `min_n_transits` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    blsfreqfactor : float
        Sets the `frequency_factor` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    periodepsilon : float
        The fractional difference between successive values of 'best' periods
        when sorting by periodogram power to consider them as separate periods
        (as opposed to part of the same periodogram peak). This is used to avoid
        broad peaks in the periodogram and make sure the 'best' periods returned
        are all actually independent.

    nbestpeaks : int
        The number of 'best' peaks to return from the periodogram results,
        starting from the global maximum of the periodogram peak values.

    sigclip : float or int or sequence of two floats/ints or None
        If a single float or int, a symmetric sigma-clip will be performed using
        the number provided as the sigma-multiplier to cut out from the input
        time-series.

        If a list of two ints/floats is provided, the function will perform an
        'asymmetric' sigma-clip. The first element in this list is the sigma
        value to use for fainter flux/mag values; the second element in this
        list is the sigma value to use for brighter flux/mag values. For
        example, `sigclip=[10., 3.]`, will sigclip out greater than 10-sigma
        dimmings and greater than 3-sigma brightenings. Here the meaning of
        "dimming" and "brightening" is set by *physics* (not the magnitude
        system), which is why the `magsarefluxes` kwarg must be correctly set.

        If `sigclip` is None, no sigma-clipping will be performed, and the
        time-series (with non-finite elems removed) will be passed through to
        the output.

    verbose : bool
        If this is True, will indicate progress and details about the frequency
        grid used for the period search.

    nworkers : int or None
        The number of parallel workers to launch for period-search. If None,
        nworkers = NCPUS.

    Returns
    -------

    dict
        This function returns a dict, referred to as an `lspinfo` dict in other
        astrobase functions that operate on periodogram results. This is a
        standardized format across all astrobase period-finders, and is of the
        form below::

            {'bestperiod': the best period value in the periodogram,
             'bestlspval': the periodogram peak associated with the best period,
             'nbestpeaks': the input value of nbestpeaks,
             'nbestlspvals': nbestpeaks-size list of best period peak values,
             'nbestperiods': nbestpeaks-size list of best periods,
             'lspvals': the full array of periodogram powers,
             'frequencies': the full array of frequencies considered,
             'periods': the full array of periods considered,
             'durations': the array of durations used to run BLS,
             'blsresult': Astropy BLS result object (BoxLeastSquaresResult),
             'blsmodel': Astropy BLS BoxLeastSquares object used for work,
             'stepsize': the actual stepsize used,
             'nfreq': the actual nfreq used,
             'durations': the durations array used,
             'mintransitduration': the input mintransitduration,
             'maxtransitduration': the input maxtransitdurations,
             'method':'bls' -> the name of the period-finder method,
             'kwargs':{ dict of all of the input kwargs for record-keeping}}

    '''

    # get rid of nans first and sigclip
    stimes, smags, serrs = sigclip_magseries(times,
                                             mags,
                                             errs,
                                             magsarefluxes=magsarefluxes,
                                             sigclip=sigclip)

    # make sure there are enough points to calculate a spectrum
    if len(stimes) > 9 and len(smags) > 9 and len(serrs) > 9:

        # if we're setting up everything automatically
        if isinstance(autofreq, bool) and autofreq:

            # use heuristic to figure out best timestep
            stepsize = 0.25*mintransitduration/(stimes.max()-stimes.min())

            # now figure out the frequencies to use
            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(npceil((maxfreq - minfreq)/stepsize))

            # say what we're using
            if verbose:
                LOGINFO('min P: %s, max P: %s, nfreq: %s, '
                        'minfreq: %s, maxfreq: %s' % (startp, endp, nfreq,
                                                      minfreq, maxfreq))
                LOGINFO('autofreq = True: using AUTOMATIC values for '
                        'freq stepsize: %s, ndurations: %s, '
                        'min transit duration: %s, max transit duration: %s' %
                        (stepsize, ndurations,
                         mintransitduration, maxtransitduration))

            use_autoperiod = False

        elif isinstance(autofreq, bool) and not autofreq:

            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(npceil((maxfreq - minfreq)/stepsize))

            # say what we're using
            if verbose:
                LOGINFO('min P: %s, max P: %s, nfreq: %s, '
                        'minfreq: %s, maxfreq: %s' % (startp, endp, nfreq,
                                                      minfreq, maxfreq))
                LOGINFO('autofreq = False: using PROVIDED values for '
                        'freq stepsize: %s, ndurations: %s, '
                        'min transit duration: %s, max transit duration: %s' %
                        (stepsize, ndurations,
                         mintransitduration, maxtransitduration))

            use_autoperiod = False

        elif isinstance(autofreq, str) and autofreq == 'astropy':

            use_autoperiod = True
            minfreq = 1.0/endp
            maxfreq = 1.0/startp

        else:

            LOGERROR("unknown autofreq kwarg encountered. can't continue...")
            return None

        # check the minimum frequency
        if minfreq < (1.0/(stimes.max() - stimes.min())):

            minfreq = 2.0/(stimes.max() - stimes.min())
            if verbose:
                LOGWARNING('the requested max P = %.3f is larger than '
                           'the time base of the observations = %.3f, '
                           ' will make minfreq = 2 x 1/timebase'
                           % (endp, stimes.max() - stimes.min()))
                LOGINFO('new minfreq: %s, maxfreq: %s' %
                        (minfreq, maxfreq))


        #############################
        ## NOW RUN BLS IN PARALLEL ##
        #############################

        # fix number of CPUs if needed
        if not nworkers or nworkers > NCPUS:
            nworkers = NCPUS
            if verbose:
                LOGINFO('using %s workers...' % nworkers)

        # check if autoperiod is True and get the correct period-grid
        if use_autoperiod:

            # astropy's BLS requires durations in units of time
            durations = nplinspace(mintransitduration*startp,
                                   maxtransitduration*startp,
                                   ndurations)

            # set up the correct units for the BLS model
            if magsarefluxes:

                blsmodel = BoxLeastSquares(
                    stimes*u.day,
                    smags*u.dimensionless_unscaled,
                    dy=serrs*u.dimensionless_unscaled
                )

            else:

                blsmodel = BoxLeastSquares(
                    stimes*u.day,
                    smags*u.mag,
                    dy=serrs*u.mag
                )

            periods = nparray(
                blsmodel.autoperiod(
                    durations*u.day,
                    minimum_period=startp,
                    maximum_period=endp,
                    minimum_n_transit=blsmintransits,
                    frequency_factor=blsfreqfactor
                )
            )

            frequencies = 1.0/periods
            nfreq = frequencies.size

            if verbose:
                LOGINFO(
                    "autofreq = 'astropy', used .autoperiod() with "
                    "minimum_n_transit = %s, freq_factor = %s "
                    "to generate the frequency grid" %
                    (blsmintransits, blsfreqfactor)
                )
                LOGINFO('stepsize = %s, nfreq = %s, minfreq = %.5f, '
                        'maxfreq = %.5f, ndurations = %s' %
                        (abs(frequencies[1] - frequencies[0]),
                         nfreq,
                         1.0/periods.max(),
                         1.0/periods.min(),
                         durations.size))

            del blsmodel
            del durations

        # otherwise, use kbls method
        else:

            frequencies = minfreq + nparange(nfreq)*stepsize


        # break up the tasks into chunks
        csrem = int(fmod(nfreq, nworkers))
        csint = int(float(nfreq/nworkers))
        chunk_minfreqs, chunk_nfreqs = [], []

        for x in range(nworkers):

            this_minfreqs = frequencies[x*csint]

            # handle usual nfreqs
            if x < (nworkers - 1):
                this_nfreqs = frequencies[x*csint:x*csint+csint].size
            else:
                this_nfreqs = frequencies[x*csint:x*csint+csint+csrem].size

            chunk_minfreqs.append(this_minfreqs)
            chunk_nfreqs.append(this_nfreqs)


        # populate the tasks list
        #
        # task[0] = times
        # task[1] = mags
        # task[2] = errs
        # task[3] = magsarefluxes

        # task[4] = minfreq
        # task[5] = nfreq
        # task[6] = stepsize

        # task[7] = nphasebins
        # task[8] = mintransitduration
        # task[9] = maxtransitduration

        # task[10] = blsobjective
        # task[11] = blsmethod
        # task[12] = blsoversample

        # populate the tasks list
        tasks = [(stimes, smags, serrs, magsarefluxes,
                  chunk_minf, chunk_nf, stepsize,
                  ndurations, mintransitduration, maxtransitduration,
                  blsobjective, blsmethod, blsoversample)
                 for (chunk_minf, chunk_nf)
                 in zip(chunk_minfreqs, chunk_nfreqs)]

        if verbose:
            for ind, task in enumerate(tasks):
                LOGINFO('worker %s: minfreq = %.6f, nfreqs = %s' %
                        (ind+1, task[4], task[5]))
            LOGINFO('running...')

        # return tasks

        # start the pool
        pool = Pool(nworkers)
        results = pool.map(_parallel_bls_worker, tasks)

        pool.close()
        pool.join()
        del pool

        # now concatenate the output lsp arrays
        lsp = npconcatenate([x['power'] for x in results])
        periods = 1.0/frequencies

        # find the nbestpeaks for the periodogram: 1. sort the lsp array
        # by highest value first 2. go down the values until we find
        # five values that are separated by at least periodepsilon in
        # period
        # make sure to get only the finite peaks in the periodogram
        # this is needed because BLS may produce infs for some peaks
        finitepeakind = npisfinite(lsp)
        finlsp = lsp[finitepeakind]
        finperiods = periods[finitepeakind]

        # make sure that finlsp has finite values before we work on it
        try:

            bestperiodind = npargmax(finlsp)

        except ValueError:

            LOGERROR('no finite periodogram values '
                     'for this mag series, skipping...')

            return {'bestperiod':npnan,
                    'bestlspval':npnan,
                    'nbestpeaks':nbestpeaks,
                    'nbestinds':None,
                    'nbestlspvals':None,
                    'nbestperiods':None,
                    'lspvals':None,
                    'periods':None,
                    'durations':None,
                    'method':'bls',
                    'blsresult':None,
                    'blsmodel':None,
                    'kwargs':{'startp':startp,
                              'endp':endp,
                              'stepsize':stepsize,
                              'mintransitduration':mintransitduration,
                              'maxtransitduration':maxtransitduration,
                              'ndurations':ndurations,
                              'blsobjective':blsobjective,
                              'blsmethod':blsmethod,
                              'blsoversample':blsoversample,
                              'autofreq':autofreq,
                              'periodepsilon':periodepsilon,
                              'nbestpeaks':nbestpeaks,
                              'sigclip':sigclip,
                              'magsarefluxes':magsarefluxes}}

        sortedlspind = npargsort(finlsp)[::-1]
        sortedlspperiods = finperiods[sortedlspind]
        sortedlspvals = finlsp[sortedlspind]

        # now get the nbestpeaks
        nbestperiods, nbestlspvals, nbestinds, peakcount = (
            [finperiods[bestperiodind]],
            [finlsp[bestperiodind]],
            [bestperiodind],
            1
        )
        prevperiod = sortedlspperiods[0]

        # find the best nbestpeaks in the lsp and their periods
        for period, lspval, ind in zip(sortedlspperiods,
                                       sortedlspvals,
                                       sortedlspind):

            if peakcount == nbestpeaks:
                break
            perioddiff = abs(period - prevperiod)
            bestperiodsdiff = [abs(period - x) for x in nbestperiods]

            # this ensures that this period is different from the last
            # period and from all the other existing best periods by
            # periodepsilon to make sure we jump to an entire different
            # peak in the periodogram
            if (perioddiff > (periodepsilon*prevperiod) and
                all(x > (periodepsilon*period)
                    for x in bestperiodsdiff)):
                nbestperiods.append(period)
                nbestlspvals.append(lspval)
                nbestinds.append(ind)
                peakcount = peakcount + 1

            prevperiod = period


        # generate the return dict
        resultdict = {
            'bestperiod':finperiods[bestperiodind],
            'bestlspval':finlsp[bestperiodind],
            'nbestpeaks':nbestpeaks,
            'nbestinds':nbestinds,
            'nbestlspvals':nbestlspvals,
            'nbestperiods':nbestperiods,
            'lspvals':lsp,
            'frequencies':frequencies,
            'periods':periods,
            'durations':[x['durations'] for x in results],
            'blsresult':[x['blsresult'] for x in results],
            'blsmodel':[x['blsmodel'] for x in results],
            'stepsize':stepsize,
            'nfreq':nfreq,
            'mintransitduration':mintransitduration,
            'maxtransitduration':maxtransitduration,
            'method':'bls',
            'kwargs':{'startp':startp,
                      'endp':endp,
                      'stepsize':stepsize,
                      'mintransitduration':mintransitduration,
                      'maxtransitduration':maxtransitduration,
                      'ndurations':ndurations,
                      'blsobjective':blsobjective,
                      'blsmethod':blsmethod,
                      'blsoversample':blsoversample,
                      'autofreq':autofreq,
                      'periodepsilon':periodepsilon,
                      'nbestpeaks':nbestpeaks,
                      'sigclip':sigclip,
                      'magsarefluxes':magsarefluxes}
        }

        return resultdict


    else:

        LOGERROR('no good detections for these times and mags, skipping...')
        return {'bestperiod':npnan,
                'bestlspval':npnan,
                'nbestinds':None,
                'nbestpeaks':nbestpeaks,
                'nbestlspvals':None,
                'nbestperiods':None,
                'lspvals':None,
                'periods':None,
                'durations':None,
                'blsresult':None,
                'blsmodel':None,
                'stepsize':stepsize,
                'nfreq':None,
                'nphasebins':None,
                'mintransitduration':mintransitduration,
                'maxtransitduration':maxtransitduration,
                'method':'bls',
                'kwargs':{'startp':startp,
                          'endp':endp,
                          'stepsize':stepsize,
                          'mintransitduration':mintransitduration,
                          'maxtransitduration':maxtransitduration,
                          'ndurations':ndurations,
                          'blsobjective':blsobjective,
                          'blsmethod':blsmethod,
                          'blsoversample':blsoversample,
                          'autofreq':autofreq,
                          'periodepsilon':periodepsilon,
                          'nbestpeaks':nbestpeaks,
                          'sigclip':sigclip,
                          'magsarefluxes':magsarefluxes}}
def bls_parallel_pfind(
        times, mags, errs,
        magsarefluxes=False,
        startp=0.1,  # by default, search from 0.1 d to...
        endp=100.0,  # ... 100.0 d -- don't search full timebase
        stepsize=1.0e-4,
        mintransitduration=0.01,  # minimum transit length in phase
        maxtransitduration=0.4,   # maximum transit length in phase
        ndurations=100,
        autofreq=True,  # figure out f0, nf, and df automatically
        blsobjective='likelihood',
        blsmethod='fast',
        blsoversample=5,
        blsmintransits=3,
        blsfreqfactor=10.0,
        nbestpeaks=5,
        periodepsilon=0.1,  # 0.1
        sigclip=10.0,
        verbose=True,
        nworkers=None,
):
    '''Runs the Box Least Squares Fitting Search for transit-shaped signals.

    Breaks up the full frequency space into chunks and passes them to parallel
    BLS workers.

    Based on the version of BLS in Astropy 3.1:
    `astropy.stats.BoxLeastSquares`. If you don't have Astropy 3.1, this module
    will fail to import. Note that by default, this implementation of
    `bls_parallel_pfind` doesn't use the `.autoperiod()` function from
    `BoxLeastSquares` but uses the same auto frequency-grid generation as the
    functions in `periodbase.kbls`. If you want to use Astropy's implementation,
    set the value of `autofreq` kwarg to 'astropy'. The generated period array
    will then be broken up into chunks and sent to the individual workers.

    NOTE: the combined BLS spectrum produced by this function is not identical
    to that produced by running BLS in one shot for the entire frequency
    space. There are differences on the order of 1.0e-3 or so in the respective
    peak values, but peaks appear at the same frequencies for both methods. This
    is likely due to different aliasing caused by smaller chunks of the
    frequency space used by the parallel workers in this function. When in
    doubt, confirm results for this parallel implementation by comparing to
    those from the serial implementation above.

    In particular, when you want to get reliable estimates of the SNR, transit
    depth, duration, etc. that Astropy's BLS gives you, rerun `bls_serial_pfind`
    with `startp`, and `endp` close to the best period you want to characterize
    the transit at. The dict returned from that function contains a `blsmodel`
    key, which is the generated model from Astropy's BLS. Use the
    `.compute_stats()` method to calculate the required stats.

    Parameters
    ----------

    times,mags,errs : np.array
        The magnitude/flux time-series to search for transits.

    magsarefluxes : bool
        If the input measurement values in `mags` and `errs` are in fluxes, set
        this to True.

    startp,endp : float
        The minimum and maximum periods to consider for the transit search.

    stepsize : float
        The step-size in frequency to use when constructing a frequency grid for
        the period search.

    mintransitduration,maxtransitduration : float
        The minimum and maximum transitdurations (in units of phase) to consider
        for the transit search.

    ndurations : int
        The number of transit durations to use in the period-search.

    autofreq : bool or str
        If this is True, the values of `stepsize` and `nphasebins` will be
        ignored, and these, along with a frequency-grid, will be determined
        based on the following relations::

            nphasebins = int(ceil(2.0/mintransitduration))
            if nphasebins > 3000:
                nphasebins = 3000

            stepsize = 0.25*mintransitduration/(times.max()-times.min())

            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(ceil((maxfreq - minfreq)/stepsize))

        If this is False, you must set `startp`, `endp`, and `stepsize` as
        appropriate.

        If this is str == 'astropy', will use the
        `astropy.stats.BoxLeastSquares.autoperiod()` function to calculate the
        frequency grid instead of the kbls method.

    blsobjective : {'likelihood','snr'}
        Sets the type of objective to optimize in the `BoxLeastSquares.power()`
        function.

    blsmethod : {'fast','slow'}
        Sets the type of method to use in the `BoxLeastSquares.power()`
        function.

    blsoversample : {'likelihood','snr'}
        Sets the `oversample` kwarg for the `BoxLeastSquares.power()` function.

    blsmintransits : int
        Sets the `min_n_transits` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    blsfreqfactor : float
        Sets the `frequency_factor` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    periodepsilon : float
        The fractional difference between successive values of 'best' periods
        when sorting by periodogram power to consider them as separate periods
        (as opposed to part of the same periodogram peak). This is used to avoid
        broad peaks in the periodogram and make sure the 'best' periods returned
        are all actually independent.

    nbestpeaks : int
        The number of 'best' peaks to return from the periodogram results,
        starting from the global maximum of the periodogram peak values.

    sigclip : float or int or sequence of two floats/ints or None
        If a single float or int, a symmetric sigma-clip will be performed using
        the number provided as the sigma-multiplier to cut out from the input
        time-series.

        If a list of two ints/floats is provided, the function will perform an
        'asymmetric' sigma-clip. The first element in this list is the sigma
        value to use for fainter flux/mag values; the second element in this
        list is the sigma value to use for brighter flux/mag values. For
        example, `sigclip=[10., 3.]`, will sigclip out greater than 10-sigma
        dimmings and greater than 3-sigma brightenings. Here the meaning of
        "dimming" and "brightening" is set by *physics* (not the magnitude
        system), which is why the `magsarefluxes` kwarg must be correctly set.

        If `sigclip` is None, no sigma-clipping will be performed, and the
        time-series (with non-finite elems removed) will be passed through to
        the output.

    verbose : bool
        If this is True, will indicate progress and details about the frequency
        grid used for the period search.

    nworkers : int or None
        The number of parallel workers to launch for period-search. If None,
        nworkers = NCPUS.

    Returns
    -------

    dict
        This function returns a dict, referred to as an `lspinfo` dict in other
        astrobase functions that operate on periodogram results. This is a
        standardized format across all astrobase period-finders, and is of the
        form below::

            {'bestperiod': the best period value in the periodogram,
             'bestlspval': the periodogram peak associated with the best period,
             'nbestpeaks': the input value of nbestpeaks,
             'nbestlspvals': nbestpeaks-size list of best period peak values,
             'nbestperiods': nbestpeaks-size list of best periods,
             'lspvals': the full array of periodogram powers,
             'frequencies': the full array of frequencies considered,
             'periods': the full array of periods considered,
             'durations': the array of durations used to run BLS,
             'blsresult': Astropy BLS result object (BoxLeastSquaresResult),
             'blsmodel': Astropy BLS BoxLeastSquares object used for work,
             'stepsize': the actual stepsize used,
             'nfreq': the actual nfreq used,
             'durations': the durations array used,
             'mintransitduration': the input mintransitduration,
             'maxtransitduration': the input maxtransitdurations,
             'method':'bls' -> the name of the period-finder method,
             'kwargs':{ dict of all of the input kwargs for record-keeping}}

    '''

    # get rid of nans first and sigclip
    stimes, smags, serrs = sigclip_magseries(times,
                                             mags,
                                             errs,
                                             magsarefluxes=magsarefluxes,
                                             sigclip=sigclip)

    # make sure there are enough points to calculate a spectrum
    if len(stimes) > 9 and len(smags) > 9 and len(serrs) > 9:

        # if we're setting up everything automatically
        if isinstance(autofreq, bool) and autofreq:

            # use heuristic to figure out best timestep
            stepsize = 0.25*mintransitduration/(stimes.max()-stimes.min())

            # now figure out the frequencies to use
            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(npceil((maxfreq - minfreq)/stepsize))

            # say what we're using
            if verbose:
                LOGINFO('min P: %s, max P: %s, nfreq: %s, '
                        'minfreq: %s, maxfreq: %s' % (startp, endp, nfreq,
                                                      minfreq, maxfreq))
                LOGINFO('autofreq = True: using AUTOMATIC values for '
                        'freq stepsize: %s, ndurations: %s, '
                        'min transit duration: %s, max transit duration: %s' %
                        (stepsize, ndurations,
                         mintransitduration, maxtransitduration))

            use_autoperiod = False

        elif isinstance(autofreq, bool) and not autofreq:

            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(npceil((maxfreq - minfreq)/stepsize))

            # say what we're using
            if verbose:
                LOGINFO('min P: %s, max P: %s, nfreq: %s, '
                        'minfreq: %s, maxfreq: %s' % (startp, endp, nfreq,
                                                      minfreq, maxfreq))
                LOGINFO('autofreq = False: using PROVIDED values for '
                        'freq stepsize: %s, ndurations: %s, '
                        'min transit duration: %s, max transit duration: %s' %
                        (stepsize, ndurations,
                         mintransitduration, maxtransitduration))

            use_autoperiod = False

        elif isinstance(autofreq, str) and autofreq == 'astropy':

            use_autoperiod = True
            minfreq = 1.0/endp
            maxfreq = 1.0/startp

        else:

            LOGERROR("unknown autofreq kwarg encountered. can't continue...")
            return None

        # check the minimum frequency
        if minfreq < (1.0/(stimes.max() - stimes.min())):

            minfreq = 2.0/(stimes.max() - stimes.min())
            if verbose:
                LOGWARNING('the requested max P = %.3f is larger than '
                           'the time base of the observations = %.3f, '
                           ' will make minfreq = 2 x 1/timebase'
                           % (endp, stimes.max() - stimes.min()))
                LOGINFO('new minfreq: %s, maxfreq: %s' %
                        (minfreq, maxfreq))


        #############################
        ## NOW RUN BLS IN PARALLEL ##
        #############################

        # fix number of CPUs if needed
        if not nworkers or nworkers > NCPUS:
            nworkers = NCPUS
            if verbose:
                LOGINFO('using %s workers...' % nworkers)

        # check if autoperiod is True and get the correct period-grid
        if use_autoperiod:

            # astropy's BLS requires durations in units of time
            durations = nplinspace(mintransitduration*startp,
                                   maxtransitduration*startp,
                                   ndurations)

            # set up the correct units for the BLS model
            if magsarefluxes:

                blsmodel = BoxLeastSquares(
                    stimes*u.day,
                    smags*u.dimensionless_unscaled,
                    dy=serrs*u.dimensionless_unscaled
                )

            else:

                blsmodel = BoxLeastSquares(
                    stimes*u.day,
                    smags*u.mag,
                    dy=serrs*u.mag
                )

            periods = nparray(
                blsmodel.autoperiod(
                    durations*u.day,
                    minimum_period=startp,
                    maximum_period=endp,
                    minimum_n_transit=blsmintransits,
                    frequency_factor=blsfreqfactor
                )
            )

            frequencies = 1.0/periods
            nfreq = frequencies.size

            if verbose:
                LOGINFO(
                    "autofreq = 'astropy', used .autoperiod() with "
                    "minimum_n_transit = %s, freq_factor = %s "
                    "to generate the frequency grid" %
                    (blsmintransits, blsfreqfactor)
                )
                LOGINFO('stepsize = %s, nfreq = %s, minfreq = %.5f, '
                        'maxfreq = %.5f, ndurations = %s' %
                        (abs(frequencies[1] - frequencies[0]),
                         nfreq,
                         1.0/periods.max(),
                         1.0/periods.min(),
                         durations.size))

            del blsmodel
            del durations

        # otherwise, use kbls method
        else:

            frequencies = minfreq + nparange(nfreq)*stepsize


        # break up the tasks into chunks
        csrem = int(fmod(nfreq, nworkers))
        csint = int(float(nfreq/nworkers))
        chunk_minfreqs, chunk_nfreqs = [], []

        for x in range(nworkers):

            this_minfreqs = frequencies[x*csint]

            # handle usual nfreqs
            if x < (nworkers - 1):
                this_nfreqs = frequencies[x*csint:x*csint+csint].size
            else:
                this_nfreqs = frequencies[x*csint:x*csint+csint+csrem].size

            chunk_minfreqs.append(this_minfreqs)
            chunk_nfreqs.append(this_nfreqs)


        # populate the tasks list
        #
        # task[0] = times
        # task[1] = mags
        # task[2] = errs
        # task[3] = magsarefluxes

        # task[4] = minfreq
        # task[5] = nfreq
        # task[6] = stepsize

        # task[7] = nphasebins
        # task[8] = mintransitduration
        # task[9] = maxtransitduration

        # task[10] = blsobjective
        # task[11] = blsmethod
        # task[12] = blsoversample

        # populate the tasks list
        tasks = [(stimes, smags, serrs, magsarefluxes,
                  chunk_minf, chunk_nf, stepsize,
                  ndurations, mintransitduration, maxtransitduration,
                  blsobjective, blsmethod, blsoversample)
                 for (chunk_minf, chunk_nf)
                 in zip(chunk_minfreqs, chunk_nfreqs)]

        if verbose:
            for ind, task in enumerate(tasks):
                LOGINFO('worker %s: minfreq = %.6f, nfreqs = %s' %
                        (ind+1, task[4], task[5]))
            LOGINFO('running...')

        # return tasks

        # start the pool
        pool = Pool(nworkers)
        results = pool.map(_parallel_bls_worker, tasks)

        pool.close()
        pool.join()
        del pool

        # now concatenate the output lsp arrays
        lsp = npconcatenate([x['power'] for x in results])
        periods = 1.0/frequencies

        # find the nbestpeaks for the periodogram: 1. sort the lsp array
        # by highest value first 2. go down the values until we find
        # five values that are separated by at least periodepsilon in
        # period
        # make sure to get only the finite peaks in the periodogram
        # this is needed because BLS may produce infs for some peaks
        finitepeakind = npisfinite(lsp)
        finlsp = lsp[finitepeakind]
        finperiods = periods[finitepeakind]

        # make sure that finlsp has finite values before we work on it
        try:

            bestperiodind = npargmax(finlsp)

        except ValueError:

            LOGERROR('no finite periodogram values '
                     'for this mag series, skipping...')

            return {'bestperiod':npnan,
                    'bestlspval':npnan,
                    'nbestpeaks':nbestpeaks,
                    'nbestinds':None,
                    'nbestlspvals':None,
                    'nbestperiods':None,
                    'lspvals':None,
                    'periods':None,
                    'durations':None,
                    'method':'bls',
                    'blsresult':None,
                    'blsmodel':None,
                    'kwargs':{'startp':startp,
                              'endp':endp,
                              'stepsize':stepsize,
                              'mintransitduration':mintransitduration,
                              'maxtransitduration':maxtransitduration,
                              'ndurations':ndurations,
                              'blsobjective':blsobjective,
                              'blsmethod':blsmethod,
                              'blsoversample':blsoversample,
                              'autofreq':autofreq,
                              'periodepsilon':periodepsilon,
                              'nbestpeaks':nbestpeaks,
                              'sigclip':sigclip,
                              'magsarefluxes':magsarefluxes}}

        sortedlspind = npargsort(finlsp)[::-1]
        sortedlspperiods = finperiods[sortedlspind]
        sortedlspvals = finlsp[sortedlspind]

        # now get the nbestpeaks
        nbestperiods, nbestlspvals, nbestinds, peakcount = (
            [finperiods[bestperiodind]],
            [finlsp[bestperiodind]],
            [bestperiodind],
            1
        )
        prevperiod = sortedlspperiods[0]

        # find the best nbestpeaks in the lsp and their periods
        for period, lspval, ind in zip(sortedlspperiods,
                                       sortedlspvals,
                                       sortedlspind):

            if peakcount == nbestpeaks:
                break
            perioddiff = abs(period - prevperiod)
            bestperiodsdiff = [abs(period - x) for x in nbestperiods]

            # this ensures that this period is different from the last
            # period and from all the other existing best periods by
            # periodepsilon to make sure we jump to an entire different
            # peak in the periodogram
            if (perioddiff > (periodepsilon*prevperiod) and
                all(x > (periodepsilon*period)
                    for x in bestperiodsdiff)):
                nbestperiods.append(period)
                nbestlspvals.append(lspval)
                nbestinds.append(ind)
                peakcount = peakcount + 1

            prevperiod = period


        # generate the return dict
        resultdict = {
            'bestperiod':finperiods[bestperiodind],
            'bestlspval':finlsp[bestperiodind],
            'nbestpeaks':nbestpeaks,
            'nbestinds':nbestinds,
            'nbestlspvals':nbestlspvals,
            'nbestperiods':nbestperiods,
            'lspvals':lsp,
            'frequencies':frequencies,
            'periods':periods,
            'durations':[x['durations'] for x in results],
            'blsresult':[x['blsresult'] for x in results],
            'blsmodel':[x['blsmodel'] for x in results],
            'stepsize':stepsize,
            'nfreq':nfreq,
            'mintransitduration':mintransitduration,
            'maxtransitduration':maxtransitduration,
            'method':'bls',
            'kwargs':{'startp':startp,
                      'endp':endp,
                      'stepsize':stepsize,
                      'mintransitduration':mintransitduration,
                      'maxtransitduration':maxtransitduration,
                      'ndurations':ndurations,
                      'blsobjective':blsobjective,
                      'blsmethod':blsmethod,
                      'blsoversample':blsoversample,
                      'autofreq':autofreq,
                      'periodepsilon':periodepsilon,
                      'nbestpeaks':nbestpeaks,
                      'sigclip':sigclip,
                      'magsarefluxes':magsarefluxes}
        }

        return resultdict


    else:

        LOGERROR('no good detections for these times and mags, skipping...')
        return {'bestperiod':npnan,
                'bestlspval':npnan,
                'nbestinds':None,
                'nbestpeaks':nbestpeaks,
                'nbestlspvals':None,
                'nbestperiods':None,
                'lspvals':None,
                'periods':None,
                'durations':None,
                'blsresult':None,
                'blsmodel':None,
                'stepsize':stepsize,
                'nfreq':None,
                'nphasebins':None,
                'mintransitduration':mintransitduration,
                'maxtransitduration':maxtransitduration,
                'method':'bls',
                'kwargs':{'startp':startp,
                          'endp':endp,
                          'stepsize':stepsize,
                          'mintransitduration':mintransitduration,
                          'maxtransitduration':maxtransitduration,
                          'ndurations':ndurations,
                          'blsobjective':blsobjective,
                          'blsmethod':blsmethod,
                          'blsoversample':blsoversample,
                          'autofreq':autofreq,
                          'periodepsilon':periodepsilon,
                          'nbestpeaks':nbestpeaks,
                          'sigclip':sigclip,
                          'magsarefluxes':magsarefluxes}}
def bls_parallel_pfind ( times , mags , errs , magsarefluxes = False , startp = 0.1 , # by default, search from 0.1 d to... endp = 100.0 , # ... 100.0 d -- don't search full timebase stepsize = 1.0e-4 , mintransitduration = 0.01 , # minimum transit length in phase maxtransitduration = 0.4 , # maximum transit length in phase ndurations = 100 , autofreq = True , # figure out f0, nf, and df automatically blsobjective = 'likelihood' , blsmethod = 'fast' , blsoversample = 5 , blsmintransits = 3 , blsfreqfactor = 10.0 , nbestpeaks = 5 , periodepsilon = 0.1 , # 0.1 sigclip = 10.0 , verbose = True , nworkers = None , ) : # get rid of nans first and sigclip stimes , smags , serrs = sigclip_magseries ( times , mags , errs , magsarefluxes = magsarefluxes , sigclip = sigclip ) # make sure there are enough points to calculate a spectrum if len ( stimes ) > 9 and len ( smags ) > 9 and len ( serrs ) > 9 : # if we're setting up everything automatically if isinstance ( autofreq , bool ) and autofreq : # use heuristic to figure out best timestep stepsize = 0.25 * mintransitduration / ( stimes . max ( ) - stimes . min ( ) ) # now figure out the frequencies to use minfreq = 1.0 / endp maxfreq = 1.0 / startp nfreq = int ( npceil ( ( maxfreq - minfreq ) / stepsize ) ) # say what we're using if verbose : LOGINFO ( 'min P: %s, max P: %s, nfreq: %s, ' 'minfreq: %s, maxfreq: %s' % ( startp , endp , nfreq , minfreq , maxfreq ) ) LOGINFO ( 'autofreq = True: using AUTOMATIC values for ' 'freq stepsize: %s, ndurations: %s, ' 'min transit duration: %s, max transit duration: %s' % ( stepsize , ndurations , mintransitduration , maxtransitduration ) ) use_autoperiod = False elif isinstance ( autofreq , bool ) and not autofreq : minfreq = 1.0 / endp maxfreq = 1.0 / startp nfreq = int ( npceil ( ( maxfreq - minfreq ) / stepsize ) ) # say what we're using if verbose : LOGINFO ( 'min P: %s, max P: %s, nfreq: %s, ' 'minfreq: %s, maxfreq: %s' % ( startp , endp , nfreq , minfreq , maxfreq ) ) LOGINFO ( 'autofreq = False: using PROVIDED values for ' 'freq stepsize: %s, ndurations: %s, ' 'min transit duration: %s, max transit duration: %s' % ( stepsize , ndurations , mintransitduration , maxtransitduration ) ) use_autoperiod = False elif isinstance ( autofreq , str ) and autofreq == 'astropy' : use_autoperiod = True minfreq = 1.0 / endp maxfreq = 1.0 / startp else : LOGERROR ( "unknown autofreq kwarg encountered. can't continue..." ) return None # check the minimum frequency if minfreq < ( 1.0 / ( stimes . max ( ) - stimes . min ( ) ) ) : minfreq = 2.0 / ( stimes . max ( ) - stimes . min ( ) ) if verbose : LOGWARNING ( 'the requested max P = %.3f is larger than ' 'the time base of the observations = %.3f, ' ' will make minfreq = 2 x 1/timebase' % ( endp , stimes . max ( ) - stimes . min ( ) ) ) LOGINFO ( 'new minfreq: %s, maxfreq: %s' % ( minfreq , maxfreq ) ) ############################# ## NOW RUN BLS IN PARALLEL ## ############################# # fix number of CPUs if needed if not nworkers or nworkers > NCPUS : nworkers = NCPUS if verbose : LOGINFO ( 'using %s workers...' % nworkers ) # check if autoperiod is True and get the correct period-grid if use_autoperiod : # astropy's BLS requires durations in units of time durations = nplinspace ( mintransitduration * startp , maxtransitduration * startp , ndurations ) # set up the correct units for the BLS model if magsarefluxes : blsmodel = BoxLeastSquares ( stimes * u . day , smags * u . dimensionless_unscaled , dy = serrs * u . dimensionless_unscaled ) else : blsmodel = BoxLeastSquares ( stimes * u . day , smags * u . mag , dy = serrs * u . mag ) periods = nparray ( blsmodel . autoperiod ( durations * u . day , minimum_period = startp , maximum_period = endp , minimum_n_transit = blsmintransits , frequency_factor = blsfreqfactor ) ) frequencies = 1.0 / periods nfreq = frequencies . size if verbose : LOGINFO ( "autofreq = 'astropy', used .autoperiod() with " "minimum_n_transit = %s, freq_factor = %s " "to generate the frequency grid" % ( blsmintransits , blsfreqfactor ) ) LOGINFO ( 'stepsize = %s, nfreq = %s, minfreq = %.5f, ' 'maxfreq = %.5f, ndurations = %s' % ( abs ( frequencies [ 1 ] - frequencies [ 0 ] ) , nfreq , 1.0 / periods . max ( ) , 1.0 / periods . min ( ) , durations . size ) ) del blsmodel del durations # otherwise, use kbls method else : frequencies = minfreq + nparange ( nfreq ) * stepsize # break up the tasks into chunks csrem = int ( fmod ( nfreq , nworkers ) ) csint = int ( float ( nfreq / nworkers ) ) chunk_minfreqs , chunk_nfreqs = [ ] , [ ] for x in range ( nworkers ) : this_minfreqs = frequencies [ x * csint ] # handle usual nfreqs if x < ( nworkers - 1 ) : this_nfreqs = frequencies [ x * csint : x * csint + csint ] . size else : this_nfreqs = frequencies [ x * csint : x * csint + csint + csrem ] . size chunk_minfreqs . append ( this_minfreqs ) chunk_nfreqs . append ( this_nfreqs ) # populate the tasks list # # task[0] = times # task[1] = mags # task[2] = errs # task[3] = magsarefluxes # task[4] = minfreq # task[5] = nfreq # task[6] = stepsize # task[7] = nphasebins # task[8] = mintransitduration # task[9] = maxtransitduration # task[10] = blsobjective # task[11] = blsmethod # task[12] = blsoversample # populate the tasks list tasks = [ ( stimes , smags , serrs , magsarefluxes , chunk_minf , chunk_nf , stepsize , ndurations , mintransitduration , maxtransitduration , blsobjective , blsmethod , blsoversample ) for ( chunk_minf , chunk_nf ) in zip ( chunk_minfreqs , chunk_nfreqs ) ] if verbose : for ind , task in enumerate ( tasks ) : LOGINFO ( 'worker %s: minfreq = %.6f, nfreqs = %s' % ( ind + 1 , task [ 4 ] , task [ 5 ] ) ) LOGINFO ( 'running...' ) # return tasks # start the pool pool = Pool ( nworkers ) results = pool . map ( _parallel_bls_worker , tasks ) pool . close ( ) pool . join ( ) del pool # now concatenate the output lsp arrays lsp = npconcatenate ( [ x [ 'power' ] for x in results ] ) periods = 1.0 / frequencies # find the nbestpeaks for the periodogram: 1. sort the lsp array # by highest value first 2. go down the values until we find # five values that are separated by at least periodepsilon in # period # make sure to get only the finite peaks in the periodogram # this is needed because BLS may produce infs for some peaks finitepeakind = npisfinite ( lsp ) finlsp = lsp [ finitepeakind ] finperiods = periods [ finitepeakind ] # make sure that finlsp has finite values before we work on it try : bestperiodind = npargmax ( finlsp ) except ValueError : LOGERROR ( 'no finite periodogram values ' 'for this mag series, skipping...' ) return { 'bestperiod' : npnan , 'bestlspval' : npnan , 'nbestpeaks' : nbestpeaks , 'nbestinds' : None , 'nbestlspvals' : None , 'nbestperiods' : None , 'lspvals' : None , 'periods' : None , 'durations' : None , 'method' : 'bls' , 'blsresult' : None , 'blsmodel' : None , 'kwargs' : { 'startp' : startp , 'endp' : endp , 'stepsize' : stepsize , 'mintransitduration' : mintransitduration , 'maxtransitduration' : maxtransitduration , 'ndurations' : ndurations , 'blsobjective' : blsobjective , 'blsmethod' : blsmethod , 'blsoversample' : blsoversample , 'autofreq' : autofreq , 'periodepsilon' : periodepsilon , 'nbestpeaks' : nbestpeaks , 'sigclip' : sigclip , 'magsarefluxes' : magsarefluxes } } sortedlspind = npargsort ( finlsp ) [ : : - 1 ] sortedlspperiods = finperiods [ sortedlspind ] sortedlspvals = finlsp [ sortedlspind ] # now get the nbestpeaks nbestperiods , nbestlspvals , nbestinds , peakcount = ( [ finperiods [ bestperiodind ] ] , [ finlsp [ bestperiodind ] ] , [ bestperiodind ] , 1 ) prevperiod = sortedlspperiods [ 0 ] # find the best nbestpeaks in the lsp and their periods for period , lspval , ind in zip ( sortedlspperiods , sortedlspvals , sortedlspind ) : if peakcount == nbestpeaks : break perioddiff = abs ( period - prevperiod ) bestperiodsdiff = [ abs ( period - x ) for x in nbestperiods ] # this ensures that this period is different from the last # period and from all the other existing best periods by # periodepsilon to make sure we jump to an entire different # peak in the periodogram if ( perioddiff > ( periodepsilon * prevperiod ) and all ( x > ( periodepsilon * period ) for x in bestperiodsdiff ) ) : nbestperiods . append ( period ) nbestlspvals . append ( lspval ) nbestinds . append ( ind ) peakcount = peakcount + 1 prevperiod = period # generate the return dict resultdict = { 'bestperiod' : finperiods [ bestperiodind ] , 'bestlspval' : finlsp [ bestperiodind ] , 'nbestpeaks' : nbestpeaks , 'nbestinds' : nbestinds , 'nbestlspvals' : nbestlspvals , 'nbestperiods' : nbestperiods , 'lspvals' : lsp , 'frequencies' : frequencies , 'periods' : periods , 'durations' : [ x [ 'durations' ] for x in results ] , 'blsresult' : [ x [ 'blsresult' ] for x in results ] , 'blsmodel' : [ x [ 'blsmodel' ] for x in results ] , 'stepsize' : stepsize , 'nfreq' : nfreq , 'mintransitduration' : mintransitduration , 'maxtransitduration' : maxtransitduration , 'method' : 'bls' , 'kwargs' : { 'startp' : startp , 'endp' : endp , 'stepsize' : stepsize , 'mintransitduration' : mintransitduration , 'maxtransitduration' : maxtransitduration , 'ndurations' : ndurations , 'blsobjective' : blsobjective , 'blsmethod' : blsmethod , 'blsoversample' : blsoversample , 'autofreq' : autofreq , 'periodepsilon' : periodepsilon , 'nbestpeaks' : nbestpeaks , 'sigclip' : sigclip , 'magsarefluxes' : magsarefluxes } } return resultdict else : LOGERROR ( 'no good detections for these times and mags, skipping...' ) return { 'bestperiod' : npnan , 'bestlspval' : npnan , 'nbestinds' : None , 'nbestpeaks' : nbestpeaks , 'nbestlspvals' : None , 'nbestperiods' : None , 'lspvals' : None , 'periods' : None , 'durations' : None , 'blsresult' : None , 'blsmodel' : None , 'stepsize' : stepsize , 'nfreq' : None , 'nphasebins' : None , 'mintransitduration' : mintransitduration , 'maxtransitduration' : maxtransitduration , 'method' : 'bls' , 'kwargs' : { 'startp' : startp , 'endp' : endp , 'stepsize' : stepsize , 'mintransitduration' : mintransitduration , 'maxtransitduration' : maxtransitduration , 'ndurations' : ndurations , 'blsobjective' : blsobjective , 'blsmethod' : blsmethod , 'blsoversample' : blsoversample , 'autofreq' : autofreq , 'periodepsilon' : periodepsilon , 'nbestpeaks' : nbestpeaks , 'sigclip' : sigclip , 'magsarefluxes' : magsarefluxes } }
Runs the Box Least Squares Fitting Search for transit-shaped signals.

    Breaks up the full frequency space into chunks and passes them to parallel
    BLS workers.

    Based on the version of BLS in Astropy 3.1:
    `astropy.stats.BoxLeastSquares`. If you don't have Astropy 3.1, this module
    will fail to import. Note that by default, this implementation of
    `bls_parallel_pfind` doesn't use the `.autoperiod()` function from
    `BoxLeastSquares` but uses the same auto frequency-grid generation as the
    functions in `periodbase.kbls`. If you want to use Astropy's implementation,
    set the value of `autofreq` kwarg to 'astropy'. The generated period array
    will then be broken up into chunks and sent to the individual workers.

    NOTE: the combined BLS spectrum produced by this function is not identical
    to that produced by running BLS in one shot for the entire frequency
    space. There are differences on the order of 1.0e-3 or so in the respective
    peak values, but peaks appear at the same frequencies for both methods. This
    is likely due to different aliasing caused by smaller chunks of the
    frequency space used by the parallel workers in this function. When in
    doubt, confirm results for this parallel implementation by comparing to
    those from the serial implementation above.

    In particular, when you want to get reliable estimates of the SNR, transit
    depth, duration, etc. that Astropy's BLS gives you, rerun `bls_serial_pfind`
    with `startp`, and `endp` close to the best period you want to characterize
    the transit at. The dict returned from that function contains a `blsmodel`
    key, which is the generated model from Astropy's BLS. Use the
    `.compute_stats()` method to calculate the required stats.

    Parameters
    ----------

    times,mags,errs : np.array
        The magnitude/flux time-series to search for transits.

    magsarefluxes : bool
        If the input measurement values in `mags` and `errs` are in fluxes, set
        this to True.

    startp,endp : float
        The minimum and maximum periods to consider for the transit search.

    stepsize : float
        The step-size in frequency to use when constructing a frequency grid for
        the period search.

    mintransitduration,maxtransitduration : float
        The minimum and maximum transitdurations (in units of phase) to consider
        for the transit search.

    ndurations : int
        The number of transit durations to use in the period-search.

    autofreq : bool or str
        If this is True, the values of `stepsize` and `nphasebins` will be
        ignored, and these, along with a frequency-grid, will be determined
        based on the following relations::

            nphasebins = int(ceil(2.0/mintransitduration))
            if nphasebins > 3000:
                nphasebins = 3000

            stepsize = 0.25*mintransitduration/(times.max()-times.min())

            minfreq = 1.0/endp
            maxfreq = 1.0/startp
            nfreq = int(ceil((maxfreq - minfreq)/stepsize))

        If this is False, you must set `startp`, `endp`, and `stepsize` as
        appropriate.

        If this is str == 'astropy', will use the
        `astropy.stats.BoxLeastSquares.autoperiod()` function to calculate the
        frequency grid instead of the kbls method.

    blsobjective : {'likelihood','snr'}
        Sets the type of objective to optimize in the `BoxLeastSquares.power()`
        function.

    blsmethod : {'fast','slow'}
        Sets the type of method to use in the `BoxLeastSquares.power()`
        function.

    blsoversample : {'likelihood','snr'}
        Sets the `oversample` kwarg for the `BoxLeastSquares.power()` function.

    blsmintransits : int
        Sets the `min_n_transits` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    blsfreqfactor : float
        Sets the `frequency_factor` kwarg for the `BoxLeastSquares.autoperiod()`
        function.

    periodepsilon : float
        The fractional difference between successive values of 'best' periods
        when sorting by periodogram power to consider them as separate periods
        (as opposed to part of the same periodogram peak). This is used to avoid
        broad peaks in the periodogram and make sure the 'best' periods returned
        are all actually independent.

    nbestpeaks : int
        The number of 'best' peaks to return from the periodogram results,
        starting from the global maximum of the periodogram peak values.

    sigclip : float or int or sequence of two floats/ints or None
        If a single float or int, a symmetric sigma-clip will be performed using
        the number provided as the sigma-multiplier to cut out from the input
        time-series.

        If a list of two ints/floats is provided, the function will perform an
        'asymmetric' sigma-clip. The first element in this list is the sigma
        value to use for fainter flux/mag values; the second element in this
        list is the sigma value to use for brighter flux/mag values. For
        example, `sigclip=[10., 3.]`, will sigclip out greater than 10-sigma
        dimmings and greater than 3-sigma brightenings. Here the meaning of
        "dimming" and "brightening" is set by *physics* (not the magnitude
        system), which is why the `magsarefluxes` kwarg must be correctly set.

        If `sigclip` is None, no sigma-clipping will be performed, and the
        time-series (with non-finite elems removed) will be passed through to
        the output.

    verbose : bool
        If this is True, will indicate progress and details about the frequency
        grid used for the period search.

    nworkers : int or None
        The number of parallel workers to launch for period-search. If None,
        nworkers = NCPUS.

    Returns
    -------

    dict
        This function returns a dict, referred to as an `lspinfo` dict in other
        astrobase functions that operate on periodogram results. This is a
        standardized format across all astrobase period-finders, and is of the
        form below::

            {'bestperiod': the best period value in the periodogram,
             'bestlspval': the periodogram peak associated with the best period,
             'nbestpeaks': the input value of nbestpeaks,
             'nbestlspvals': nbestpeaks-size list of best period peak values,
             'nbestperiods': nbestpeaks-size list of best periods,
             'lspvals': the full array of periodogram powers,
             'frequencies': the full array of frequencies considered,
             'periods': the full array of periods considered,
             'durations': the array of durations used to run BLS,
             'blsresult': Astropy BLS result object (BoxLeastSquaresResult),
             'blsmodel': Astropy BLS BoxLeastSquares object used for work,
             'stepsize': the actual stepsize used,
             'nfreq': the actual nfreq used,
             'durations': the durations array used,
             'mintransitduration': the input mintransitduration,
             'maxtransitduration': the input maxtransitdurations,
             'method':'bls' -> the name of the period-finder method,
             'kwargs':{ dict of all of the input kwargs for record-keeping}}
Runs the Box Least Squares Fitting Search for transit - shaped signals .