mcmc_based_searches.py 92.6 KB
Newer Older
Gregory Ashton's avatar
Gregory Ashton committed
1
""" Searches using MCMC-based methods """
2
from __future__ import division, absolute_import, print_function
Gregory Ashton's avatar
Gregory Ashton committed
3

4
import sys
Gregory Ashton's avatar
Gregory Ashton committed
5
import os
6
import copy
Gregory Ashton's avatar
Gregory Ashton committed
7
import logging
8
from collections import OrderedDict
9
import subprocess
10
11
12
13
14
15
16
17

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

18
19
20
21
import pyfstat.core as core
from pyfstat.core import tqdm, args, earth_ephem, sun_ephem, read_par
from pyfstat.optimal_setup_functions import get_V_estimate, get_optimal_setup
import pyfstat.helper_functions as helper_functions
22
23


24
class MCMCSearch(core.BaseSearchClass):
Gregory Ashton's avatar
Gregory Ashton committed
25
    """ MCMC search using ComputeFstat"""
26
27

    symbol_dictionary = dict(
28
        F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$',
29
30
        Delta='$\delta$', asini='asini', period='P', ecc='ecc', tp='tp',
        argp='argp')
31
    unit_dictionary = dict(
32
33
        F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad',
        asini='', period='s', ecc='', tp='', argp='')
34
35
36
    rescale_dictionary = {}


Gregory Ashton's avatar
Gregory Ashton committed
37
    @helper_functions.initializer
Gregory Ashton's avatar
Gregory Ashton committed
38
    def __init__(self, label, outdir, theta_prior, tref, minStartTime,
39
                 maxStartTime, sftfilepattern=None, nsteps=[100, 100],
40
                 nwalkers=100, ntemps=1, log10temperature_min=-5,
41
                 theta_initial=None, scatter_val=1e-10, rhohatmax=1000,
42
                 binary=False, BSGL=False, minCoverFreq=None, SSBprec=None,
43
                 maxCoverFreq=None, detectors=None, earth_ephem=None,
44
                 sun_ephem=None, injectSources=None, assumeSqrtSX=None):
45
46
47
48
        """
        Parameters
        label, outdir: str
            A label and directory to read/write data from/to
49
        sftfilepattern: str
50
51
            Pattern to match SFTs using wildcards (*?) and ranges [0-9];
            mutiple patterns can be given separated by colons.
52
        theta_prior: dict
53
54
55
56
            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.
57
58
59
60
        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.
61
        tref, minStartTime, maxStartTime: int
62
63
64
65
66
67
            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].
68
69
70
71
72
73
        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).
74
75
76
77
        rhohatmax: float
            Upper bound for the SNR scale parameter (required to normalise the
            Bayes factor) - this needs to be carefully set when using the
            evidence.
78
79
        binary: Bool
            If true, search over binary parameters
80
        detectors: str
81
82
            Two character reference to the data to use, specify None for no
            contraint.
83
84
85
86
87
88
89
90
91
92
        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

        """

Gregory Ashton's avatar
Gregory Ashton committed
93
94
        if os.path.isdir(outdir) is False:
            os.mkdir(outdir)
95
        self._add_log_file()
96
        logging.info('Set-up MCMC search for model {}'.format(self.label))
97
98
        if sftfilepattern:
            logging.info('Using data {}'.format(self.sftfilepattern))
99
        else:
100
            logging.info('No sftfilepattern given')
101
102
        if injectSources:
            logging.info('Inject sources: {}'.format(injectSources))
103
        self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label)
104
        self._unpack_input_theta()
105
        self.ndim = len(self.theta_keys)
106
107
108
109
        if self.log10temperature_min:
            self.betas = np.logspace(0, self.log10temperature_min, self.ntemps)
        else:
            self.betas = None
110

111
112
113
114
115
116
117
118
        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")

119
120
121
122
        self._set_likelihoodcoef()

    def _set_likelihoodcoef(self):
        self.likelihoodcoef = np.log(70./self.rhohatmax**4)
123

124
        self._log_input()
125

126
    def _log_input(self):
127
        logging.info('theta_prior = {}'.format(self.theta_prior))
128
        logging.info('nwalkers={}'.format(self.nwalkers))
129
130
131
132
        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(
133
            self.log10temperature_min))
134

135
    def _initiate_search_object(self):
136
        logging.info('Setting up search object')
137
        self.search = core.ComputeFstat(
138
            tref=self.tref, sftfilepattern=self.sftfilepattern,
139
140
            minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq,
            earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem,
141
            detectors=self.detectors, BSGL=self.BSGL, transient=False,
142
            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
143
            binary=self.binary, injectSources=self.injectSources,
144
            assumeSqrtSX=self.assumeSqrtSX, SSBprec=self.SSBprec)
145
146

    def logp(self, theta_vals, theta_prior, theta_keys, search):
147
        H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in
148
149
150
151
152
153
             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]
154
155
        FS = search.compute_fullycoherent_det_stat_single_point(
            *self.fixed_theta)
156
        return FS + self.likelihoodcoef
157

158
    def _unpack_input_theta(self):
159
        full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta']
160
161
162
        if self.binary:
            full_theta_keys += [
                'asini', 'period', 'ecc', 'tp', 'argp']
163
164
        full_theta_keys_copy = copy.copy(full_theta_keys)

165
166
        full_theta_symbols = ['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$',
                              r'$\delta$']
167
168
        if self.binary:
            full_theta_symbols += [
169
                'asini', 'period', 'ecc', 'tp', 'argp']
170

171
172
        self.theta_keys = []
        fixed_theta_dict = {}
173
        for key, val in self.theta_prior.iteritems():
174
175
            if type(val) is dict:
                fixed_theta_dict[key] = 0
Gregory Ashton's avatar
Gregory Ashton committed
176
                self.theta_keys.append(key)
177
178
179
180
181
182
            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))
Gregory Ashton's avatar
Gregory Ashton committed
183
            full_theta_keys_copy.pop(full_theta_keys_copy.index(key))
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198

        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]

199
    def _check_initial_points(self, p0):
200
201
202
203
204
205
206
207
208
209
210
211
212
        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))

213
                p0 = self._generate_new_p0_to_fix_initial_points(
214
215
                    p0, nt, initial_priors)

216
    def _generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors):
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
        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
236

237
    def _OLD_run_sampler_with_progress_bar(self, sampler, ns, p0):
238
239
        for result in tqdm(sampler.sample(p0, iterations=ns), total=ns):
            pass
Gregory Ashton's avatar
Gregory Ashton committed
240
241
        return sampler

242
243
    def setup_burnin_convergence_testing(
            self, n=10, test_type='autocorr', windowed=False, **kwargs):
244
245
246
247
248
        """
        If called, convergence testing is used during the MCMC simulation

        Parameters
        ----------
249
250
251
252
253
254
255
256
257
        n: int
            Number of steps after which to test convergence
        test_type: str ['autocorr', 'GR']
            If 'autocorr' use the exponential autocorrelation time (kwargs
            passed to `get_autocorr_convergence`). If 'GR' use the Gelman-Rubin
            statistic (kwargs passed to `get_GR_convergence`)
        windowed: bool
            If True, only calculate the convergence test in a window of length
            `n`
258
        """
259
        logging.info('Setting up convergence testing')
260
261
262
263
        self.convergence_n = n
        self.convergence_windowed = windowed
        self.convergence_test_type = test_type
        self.convergence_kwargs = kwargs
264
265
        self.convergence_diagnostic = []
        self.convergence_diagnosticx = []
266
267
268
        if test_type in ['autocorr']:
            self._get_convergence_test = self.test_autocorr_convergence
        elif test_type in ['GR']:
Gregory Ashton's avatar
Gregory Ashton committed
269
            self._get_convergence_test = self.test_GR_convergence
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
        else:
            raise ValueError('test_type {} not understood'.format(test_type))

    def test_autocorr_convergence(self, i, sampler, test=True, n_cut=5):
        try:
            acors = np.zeros((self.ntemps, self.ndim))
            for temp in range(self.ntemps):
                if self.convergence_windowed:
                    j = i-self.convergence_n
                else:
                    j = 0
                x = np.mean(sampler.chain[temp, :, j:i, :], axis=0)
                acors[temp, :] = emcee.autocorr.exponential_time(x)
            c = np.max(acors, axis=0)
        except emcee.autocorr.AutocorrError:
Gregory Ashton's avatar
Gregory Ashton committed
285
286
287
288
            logging.info('Failed to calculate exponential autocorrelation')
            c = np.zeros(self.ndim) + np.nan
        except AttributeError:
            logging.info('Unable to calculate exponential autocorrelation')
289
290
291
292
293
294
295
296
297
298
299
300
301
302
            c = np.zeros(self.ndim) + np.nan

        self.convergence_diagnosticx.append(i - self.convergence_n/2.)
        self.convergence_diagnostic.append(list(c))

        if test:
            return i > n_cut * np.max(c)

    def test_GR_convergence(self, i, sampler, test=True, R=1.1):
        if self.convergence_windowed:
            s = sampler.chain[0, :, i-self.convergence_n+1:i+1, :]
        else:
            s = sampler.chain[0, :, :i+1, :]
        N = float(self.convergence_n)
303
304
        M = float(self.nwalkers)
        W = np.mean(np.var(s, axis=1), axis=0)
305
306
        per_walker_mean = np.mean(s, axis=1)
        mean = np.mean(per_walker_mean, axis=0)
307
308
        B = N / (M-1.) * np.sum((per_walker_mean-mean)**2, axis=0)
        Vhat = (N-1)/N * W + (M+1)/(M*N) * B
309
        c = np.sqrt(Vhat/W)
310
        self.convergence_diagnostic.append(c)
311
        self.convergence_diagnosticx.append(i - self.convergence_n/2.)
312

313
314
315
        if test and np.max(c) < R:
            return True
        else:
316
            return False
317
318
319
320

    def _test_convergence(self, i, sampler, **kwargs):
        if np.mod(i+1, self.convergence_n) == 0:
            return self._get_convergence_test(i, sampler, **kwargs)
321
        else:
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
            return False

    def _run_sampler_with_conv_test(self, sampler, p0, nprod=0, nburn=0):
        logging.info('Running {} burn-in steps with convergence testing'
                     .format(nburn))
        iterator = tqdm(sampler.sample(p0, iterations=nburn), total=nburn)
        for i, output in enumerate(iterator):
            if self._test_convergence(i, sampler, test=True,
                                      **self.convergence_kwargs):
                logging.info(
                    'Converged at {} before max number {} of steps reached'
                    .format(i, nburn))
                self.convergence_idx = i
                break
        iterator.close()
        logging.info('Running {} production steps'.format(nprod))
        j = nburn
        iterator = tqdm(sampler.sample(output[0], iterations=nprod),
                        total=nprod)
        for result in iterator:
            self._test_convergence(j, sampler, test=False,
                                   **self.convergence_kwargs)
            j += 1
        return sampler
346

347
    def _run_sampler(self, sampler, p0, nprod=0, nburn=0):
348
349
        if hasattr(self, 'convergence_n'):
            self._run_sampler_with_conv_test(sampler, p0, nprod, nburn)
350
351
352
353
        else:
            for result in tqdm(sampler.sample(p0, iterations=nburn+nprod),
                               total=nburn+nprod):
                pass
354

355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
        logging.info("Mean acceptance fraction: {}"
                     .format(np.mean(sampler.acceptance_fraction, axis=1)))
        if self.ntemps > 1:
            logging.info("Tswap acceptance fraction: {}"
                         .format(sampler.tswap_acceptance_fraction))
        try:
            logging.info("Autocorrelation length: {}".format(
                sampler.get_autocorr_time(c=5)))
        except emcee.autocorr.AutocorrError as e:
            logging.warning(
                'Autocorrelation calculation failed with message {}'.format(e))

        return sampler

    def run(self, proposal_scale_factor=2, create_plots=True, c=5, **kwargs):
        """ Run the MCMC simulatation

        Parameters
        ----------
        proposal_scale_factor: float
            The proposal scale factor used by the sampler, see Goodman & Weare
            (2010). If the acceptance fraction is too low, you can raise it by
            decreasing the a parameter; and if it is too high, you can reduce
            it by increasing the a parameter [Foreman-Mackay (2013)].
        create_plots: bool
            If true, save trace plots of the walkers
        c: int
            The minimum number of autocorrelation times needed to trust the
            result when estimating the autocorrelation time (see
            emcee.autocorr.integrated_time for further details. Default is 5
        **kwargs:
            Passed to _plot_walkers to control the figures

        """
389

390
        self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use()
391
392
393
        if self.old_data_is_okay_to_use is True:
            logging.warning('Using saved data from {}'.format(
                self.pickle_path))
394
            d = self.get_saved_data_dictionary()
395
396
397
            self.samples = d['samples']
            self.lnprobs = d['lnprobs']
            self.lnlikes = d['lnlikes']
398
            self.all_lnlikelihood = d['all_lnlikelihood']
399
400
            return

401
        self._initiate_search_object()
402
403
404
405

        sampler = emcee.PTSampler(
            self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp,
            logpargs=(self.theta_prior, self.theta_keys, self.search),
406
            loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor)
407

408
409
410
        p0 = self._generate_initial_p0()
        p0 = self._apply_corrections_to_p0(p0)
        self._check_initial_points(p0)
411
412
413
414

        ninit_steps = len(self.nsteps) - 2
        for j, n in enumerate(self.nsteps[:-2]):
            logging.info('Running {}/{} initialisation with {} steps'.format(
Gregory Ashton's avatar
Gregory Ashton committed
415
                j, ninit_steps, n))
416
            sampler = self._run_sampler(sampler, p0, nburn=n)
417
            if create_plots:
418
                fig, axes = self._plot_walkers(sampler,
419
420
                                               symbols=self.theta_symbols,
                                               **kwargs)
421
422
                fig.tight_layout()
                fig.savefig('{}/{}_init_{}_walkers.png'.format(
423
                    self.outdir, self.label, j), dpi=400)
424

425
426
427
            p0 = self._get_new_p0(sampler)
            p0 = self._apply_corrections_to_p0(p0)
            self._check_initial_points(p0)
428
429
            sampler.reset()

Gregory Ashton's avatar
Gregory Ashton committed
430
431
432
433
        if len(self.nsteps) > 1:
            nburn = self.nsteps[-2]
        else:
            nburn = 0
434
435
436
        nprod = self.nsteps[-1]
        logging.info('Running final burn and prod with {} steps'.format(
            nburn+nprod))
437
        sampler = self._run_sampler(sampler, p0, nburn=nburn, nprod=nprod)
438
        if create_plots:
439
            fig, axes = self._plot_walkers(sampler, symbols=self.theta_symbols,
440
                                           nprod=nprod, **kwargs)
441
442
443
            fig.tight_layout()
            fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label),
                        dpi=200)
444
445
446
447

        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
        lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1))
448
        all_lnlikelihood = sampler.lnlikelihood[:, :, nburn:]
449
450
451
        self.samples = samples
        self.lnprobs = lnprobs
        self.lnlikes = lnlikes
452
453
        self.all_lnlikelihood = all_lnlikelihood
        self._save_data(sampler, samples, lnprobs, lnlikes, all_lnlikelihood)
454

455
    def _get_rescale_multiplier_for_key(self, key):
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
        """ Get the rescale multiplier from the rescale_dictionary

        Can either be a float, a string (in which case it is interpretted as
        a attribute of the MCMCSearch class, e.g. minStartTime, or non-existent
        in which case 0 is returned
        """
        if key not in self.rescale_dictionary:
            return 1

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

480
    def _get_rescale_subtractor_for_key(self, key):
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
        """ Get the rescale subtractor from the rescale_dictionary

        Can either be a float, a string (in which case it is interpretted as
        a attribute of the MCMCSearch class, e.g. minStartTime, or non-existent
        in which case 0 is returned
        """
        if key not in self.rescale_dictionary:
            return 0

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

505
    def _scale_samples(self, samples, theta_keys):
506
        """ Scale the samples using the rescale_dictionary """
507
508
509
510
        for key in theta_keys:
            if key in self.rescale_dictionary:
                idx = theta_keys.index(key)
                s = samples[:, idx]
511
                subtractor = self._get_rescale_subtractor_for_key(key)
512
                s = s - subtractor
513
                multiplier = self._get_rescale_multiplier_for_key(key)
514
                s *= multiplier
515
516
                samples[:, idx] = s

517
518
        return samples

519
    def _get_labels(self):
520
        """ Combine the units, symbols and rescaling to give labels """
521

522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
        labels = []
        for key in self.theta_keys:
            label = None
            s = self.symbol_dictionary[key]
            s.replace('_{glitch}', r'_\textrm{glitch}')
            u = self.unit_dictionary[key]
            if key in self.rescale_dictionary:
                if 'symbol' in self.rescale_dictionary[key]:
                    s = self.rescale_dictionary[key]['symbol']
                if 'label' in self.rescale_dictionary[key]:
                    label = self.rescale_dictionary[key]['label']
                if 'unit' in self.rescale_dictionary[key]:
                    u = self.rescale_dictionary[key]['unit']
            if label is None:
                label = '{} \n [{}]'.format(s, u)
            labels.append(label)
        return labels
539

540
541
    def plot_corner(self, figsize=(7, 7), add_prior=False, nstds=None,
                    label_offset=0.4, dpi=300, rc_context={},
542
                    tglitch_ratio=False, fig_and_axes=None, save_fig=True,
543
                    **kwargs):
544
545
546
547
548
549
550
551
552
        """ Generate a corner plot of the posterior

        Using the `corner` package (https://pypi.python.org/pypi/corner/),
        generate estimates of the posterior from the production samples.

        Parameters
        ----------
        figsize: tuple (7, 7)
            Figure size in inches (passed to plt.subplots)
553
554
555
        add_prior: bool, str
            If true, plot the prior as a red line. If 'full' then for uniform
            priors plot the full extent of the prior.
556
557
558
559
560
561
562
563
564
565
566
567
568
569
        nstds: float
            The number of standard deviations to plot centered on the mean
        label_offset: float
            Offset the labels from the plot: useful to precent overlapping the
            tick labels with the axis labels
        dpi: int
            Passed to plt.savefig
        rc_context: dict
            Dictionary of rc values to set while generating the figure (see
            matplotlib rc for more details)
        tglitch_ratio: bool
            If true, and tglitch is a parameter, plot posteriors as the
            fractional time at which the glitch occurs instead of the actual
            time
570
571
572
573
574
        fig_and_axes: tuple
            fig and axes to plot on, the axes must be of the right shape,
            namely (ndim, ndim)
        save_fig: bool
            If true, save the figure, else return the fig, axes
575

576
        Note: kwargs are passed on to corner.corner
577
578

        """
579

580
581
582
583
        if 'truths' in kwargs and len(kwargs['truths']) != self.ndim:
            logging.warning('len(Truths) != ndim, Truths will be ignored')
            kwargs['truths'] = None

Gregory Ashton's avatar
Gregory Ashton committed
584
585
        if self.ndim < 2:
            with plt.rc_context(rc_context):
586
587
588
589
                if fig_and_axes is None:
                    fig, ax = plt.subplots(figsize=figsize)
                else:
                    fig, ax = fig_and_axes
Gregory Ashton's avatar
Gregory Ashton committed
590
591
592
593
594
595
596
                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

597
        with plt.rc_context(rc_context):
598
599
600
601
602
            if fig_and_axes is None:
                fig, axes = plt.subplots(self.ndim, self.ndim,
                                         figsize=figsize)
            else:
                fig, axes = fig_and_axes
603
604

            samples_plt = copy.copy(self.samples)
605
            labels = self._get_labels()
606

607
            samples_plt = self._scale_samples(samples_plt, self.theta_keys)
608
609
610
611
612

            if tglitch_ratio:
                for j, k in enumerate(self.theta_keys):
                    if k == 'tglitch':
                        s = samples_plt[:, j]
613
614
615
                        samples_plt[:, j] = (
                            s - self.minStartTime)/(
                                self.maxStartTime - self.minStartTime)
616
                        labels[j] = r'$R_{\textrm{glitch}}$'
617
618
619
620
621
622
623

            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))
624
625
            elif 'range' in kwargs:
                _range = kwargs.pop('range')
626
627
628
            else:
                _range = None

629
630
631
632
            hist_kwargs = kwargs.pop('hist_kwargs', dict())
            if 'normed' not in hist_kwargs:
                hist_kwargs['normed'] = True

633
            fig_triangle = corner.corner(samples_plt,
634
                                         labels=labels,
635
636
637
638
639
640
641
642
643
                                         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,
644
                                         hist_kwargs=hist_kwargs,
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
                                         **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:
661
                self._add_prior_to_corner(axes, self.samples, add_prior)
662

663
664
665
666
667
            if save_fig:
                fig_triangle.savefig('{}/{}_corner.png'.format(
                    self.outdir, self.label), dpi=dpi)
            else:
                return fig, axes
668

669
    def _add_prior_to_corner(self, axes, samples, add_prior):
670
671
672
        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            s = samples[:, i]
673
674
675
676
677
678
679
680
681
682
            lnprior = self._generic_lnprior(**self.theta_prior[key])
            if add_prior == 'full' and self.theta_prior[key]['type'] == 'unif':
                lower = self.theta_prior[key]['lower']
                upper = self.theta_prior[key]['upper']
                r = upper-lower
                xlim = [lower-0.05*r, upper+0.05*r]
                x = np.linspace(xlim[0], xlim[1], 1000)
            else:
                xlim = ax.get_xlim()
                x = np.linspace(s.min(), s.max(), 1000)
683
684
            multiplier = self._get_rescale_multiplier_for_key(key)
            subtractor = self._get_rescale_subtractor_for_key(key)
685
686
687
688
689
690
691
692
            ax.plot((x-subtractor)*multiplier,
                    [np.exp(lnprior(xi)) for xi in x], '-C3',
                    label='prior')

            for j in range(i, self.ndim):
                axes[j][i].set_xlim(xlim[0], xlim[1])
            for k in range(0, i):
                axes[i][k].set_ylim(xlim[0], xlim[1])
693

694
695
696
697
698
699
700
701
    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]
702
            prior_func = self._generic_lnprior(**prior_dict)
703
704
705
706
707
            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
Gregory Ashton's avatar
Gregory Ashton committed
708
709
710
711
712
            elif prior_dict['type'] == 'log10unif':
                upper = prior_dict['log10upper']
                lower = prior_dict['log10lower']
                x = np.linspace(lower, upper, N)
                prior = [prior_func(xi) for xi in x]
713
714
715
716
717
            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)
718
719
720
721
722
            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]
Gregory Ashton's avatar
Gregory Ashton committed
723
724
725
726
727
            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]
728
729
730
            else:
                raise ValueError('Not implemented for prior type {}'.format(
                    prior_dict['type']))
731
            priorln = ax.plot(x, prior, 'C3', label='prior')
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
            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))

751
    def plot_cumulative_max(self, **kwargs):
752
753
754
755
        """ Plot the cumulative twoF for the maximum posterior estimate

        See the pyfstat.core.plot_twoF_cumulative function for further details
        """
Gregory Ashton's avatar
Gregory Ashton committed
756
757
758
759
        d, maxtwoF = self.get_max_twoF()
        for key, val in self.theta_prior.iteritems():
            if key not in d:
                d[key] = val
760
761

        if hasattr(self, 'search') is False:
762
            self._initiate_search_object()
763
764
765
        if self.binary is False:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
766
                Alpha=d['Alpha'], Delta=d['Delta'],
767
                tstart=self.minStartTime, tend=self.maxStartTime,
768
                **kwargs)
769
770
771
772
773
        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'],
774
                tstart=self.minStartTime, tend=self.maxStartTime, **kwargs)
Gregory Ashton's avatar
Gregory Ashton committed
775

776
    def _generic_lnprior(self, **kwargs):
777
778
779
780
781
782
783
784
785
        """ Return a lambda function of the pdf

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

        """

Gregory Ashton's avatar
Gregory Ashton committed
786
        def log_of_unif(x, a, b):
787
788
789
790
791
792
793
794
795
796
797
798
799
            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

Gregory Ashton's avatar
Gregory Ashton committed
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
        def log_of_log10unif(x, log10lower, log10upper):
            log10x = np.log10(x)
            above = log10x < log10upper
            below = log10x > log10lower
            if type(above) is not np.ndarray:
                if above and below:
                    return -np.log(x*np.log(10)*(log10upper-log10lower))
                else:
                    return -np.inf
            else:
                idxs = np.array([all(tup) for tup in zip(above, below)])
                p = np.zeros(len(x)) - np.inf
                p[idxs] = -np.log(x*np.log(10)*(log10upper-log10lower))
                return p

        def log_of_halfnorm(x, loc, scale):
816
            if x < loc:
817
818
819
820
821
822
823
824
825
826
827
828
829
830
                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':
Gregory Ashton's avatar
Gregory Ashton committed
831
832
833
834
            return lambda x: log_of_unif(x, kwargs['lower'], kwargs['upper'])
        if kwargs['type'] == 'log10unif':
            return lambda x: log_of_log10unif(
                x, kwargs['log10lower'], kwargs['log10upper'])
835
        elif kwargs['type'] == 'halfnorm':
Gregory Ashton's avatar
Gregory Ashton committed
836
            return lambda x: log_of_halfnorm(x, kwargs['loc'], kwargs['scale'])
837
        elif kwargs['type'] == 'neghalfnorm':
Gregory Ashton's avatar
Gregory Ashton committed
838
839
            return lambda x: log_of_halfnorm(
                -x, kwargs['loc'], kwargs['scale'])
840
841
842
843
844
845
846
        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")

847
    def _generate_rv(self, **kwargs):
848
849
850
        dist_type = kwargs.pop('type')
        if dist_type == "unif":
            return np.random.uniform(low=kwargs['lower'], high=kwargs['upper'])
Gregory Ashton's avatar
Gregory Ashton committed
851
852
853
        if dist_type == "log10unif":
            return 10**(np.random.uniform(low=kwargs['log10lower'],
                                          high=kwargs['log10upper']))
854
855
856
857
858
        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']))
859
860
861
        if dist_type == "neghalfnorm":
            return -1 * np.abs(np.random.normal(loc=kwargs['loc'],
                                                scale=kwargs['scale']))
862
863
864
865
866
867
        if dist_type == "lognorm":
            return np.random.lognormal(
                mean=kwargs['loc'], sigma=kwargs['scale'])
        else:
            raise ValueError("dist_type {} unknown".format(dist_type))

868
    def _plot_walkers(self, sampler, symbols=None, alpha=0.8, color="k",
869
870
                      temp=0, lw=0.1, nprod=0, add_det_stat_burnin=False,
                      fig=None, axes=None, xoffset=0, plot_det_stat=False,
871
                      context='ggplot', subtractions=None, labelpad=0.05):
872
873
        """ Plot all the chains from a sampler """

874
875
876
877
878
        if context not in plt.style.available:
            raise ValueError((
                'The requested context {} is not available; please select a'
                ' context from `plt.style.available`').format(context))

879
880
881
        if np.ndim(axes) > 1:
            axes = axes.flatten()

882
883
884
885
886
887
888
889
890
891
892
893
894
        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, :, :, :]

895
896
        if subtractions is None:
            subtractions = [0 for i in range(ndim)]
897
898
899
        else:
            if len(subtractions) != self.ndim:
                raise ValueError('subtractions must be of length ndim')
900

901
902
903
904
        if plot_det_stat:
            extra_subplots = 1
        else:
            extra_subplots = 0
905
        with plt.style.context((context)):
Gregory Ashton's avatar
Gregory Ashton committed
906
            plt.rcParams['text.usetex'] = True
Gregory Ashton's avatar
Gregory Ashton committed
907
            if fig is None and axes is None:
908
                fig = plt.figure(figsize=(4, 3.0*ndim))
909
910
                ax = fig.add_subplot(ndim+extra_subplots, 1, 1)
                axes = [ax] + [fig.add_subplot(ndim+extra_subplots, 1, i)
Gregory Ashton's avatar
Gregory Ashton committed
911
                               for i in range(2, ndim+1)]
912

Gregory Ashton's avatar
Gregory Ashton committed
913
            idxs = np.arange(chain.shape[1])
914
915
916
917
918
            burnin_idx = chain.shape[1] - nprod
            if hasattr(self, 'convergence_idx'):
                convergence_idx = self.convergence_idx
            else:
                convergence_idx = burnin_idx
919
920
            if ndim > 1:
                for i in range(ndim):
921
                    axes[i].ticklabel_format(useOffset=False, axis='y')
Gregory Ashton's avatar
Gregory Ashton committed
922
                    cs = chain[:, :, i].T
923
                    if burnin_idx > 0:
924
925
                        axes[i].plot(xoffset+idxs[:convergence_idx+1],
                                     cs[:convergence_idx+1]-subtractions[i],
926
                                     color="C3", alpha=alpha,
Gregory Ashton's avatar
Gregory Ashton committed
927
                                     lw=lw)
928
                        axes[i].axvline(xoffset+convergence_idx,
929
                                        color='k', ls='--', lw=0.25)
930
931
                    axes[i].plot(xoffset+idxs[burnin_idx:],
                                 cs[burnin_idx:]-subtractions[i],
Gregory Ashton's avatar
Gregory Ashton committed
932
                                 color="k", alpha=alpha, lw=lw)
933
                    if symbols:
934
                        if subtractions[i] == 0:
935
                            axes[i].set_ylabel(symbols[i], labelpad=labelpad)
936
937
                        else:
                            axes[i].set_ylabel(
938
939
                                symbols[i]+'$-$'+symbols[i]+'$_0$',
                                labelpad=labelpad)
940

941
942
                    if hasattr(self, 'convergence_diagnostic'):
                        ax = axes[i].twinx()
943
944
                        axes[i].set_zorder(ax.get_zorder()+1)
                        axes[i].patch.set_visible(False)
945
946
                        c_x = np.array(self.convergence_diagnosticx)
                        c_y = np.array(self.convergence_diagnostic)
947
                        break_idx = np.argmin(np.abs(c_x - burnin_idx))
948
949
950
951
                        ax.plot(c_x[:break_idx], c_y[:break_idx, i], '-C0',
                                zorder=-10)
                        ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-C0',
                                zorder=-10)
952
953
954
955
                        if self.convergence_test_type == 'autocorr':
                            ax.set_ylabel(r'$\tau_\mathrm{exp}$')
                        elif self.convergence_test_type == 'GR':
                            ax.set_ylabel('PSRF')
956
                        ax.ticklabel_format(useOffset=False)
957
            else:
Gregory Ashton's avatar
Gregory Ashton committed
958
                axes[0].ticklabel_format(useOffset=False, axis='y')
Gregory Ashton's avatar
Gregory Ashton committed
959
                cs = chain[:, :, temp].T
Gregory Ashton's avatar
Gregory Ashton committed
960
961
                if burnin_idx:
                    axes[0].plot(idxs[:burnin_idx], cs[:burnin_idx],
962
                                 color="C3", alpha=alpha, lw=lw)
Gregory Ashton's avatar
Gregory Ashton committed
963
964
965
                axes[0].plot(idxs[burnin_idx:], cs[burnin_idx:], color="k",
                             alpha=alpha, lw=lw)
                if symbols:
966
                    axes[0].set_ylabel(symbols[0], labelpad=labelpad)
967

Gregory Ashton's avatar
Gregory Ashton committed
968
969
            axes[-1].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)

970
            if plot_det_stat:
971
972
973
                if len(axes) == ndim:
                    axes.append(fig.add_subplot(ndim+1, 1, ndim+1))

974
975
976
                lnl = sampler.lnlikelihood[temp, :, :]
                if burnin_idx and add_det_stat_burnin:
                    burn_in_vals = lnl[:, :burnin_idx].flatten()
977
978
                    try:
                        axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)],
979
                                      bins=50, histtype='step', color='C3')
980
981
982
983
                    except ValueError:
                        logging.info('Det. Stat. hist failed, most likely all '
                                     'values where the same')
                        pass
984
985
986
                else:
                    burn_in_vals = []
                prod_vals = lnl[:, burnin_idx:].flatten()
987
988
989
990
991
992
993
                try:
                    axes[-1].hist(prod_vals[~np.isnan(prod_vals)], bins=50,
                                  histtype='step', color='k')
                except ValueError:
                    logging.info('Det. Stat. hist failed, most likely all '
                                 'values where the same')
                    pass
994
995
996
997
998
999
1000
                if self.BSGL:
                    axes[-1].set_xlabel(r'$\mathcal{B}_\mathrm{S/GL}$')
                else:
                    axes[-1].set_xlabel(r'$\widetilde{2\mathcal{F}}$')
                axes[-1].set_ylabel(r'$\textrm{Counts}$')
                combined_vals = np.append(burn_in_vals, prod_vals)
                if len(combined_vals) > 0: