mcmc_based_searches.py 87.8 KB
Newer Older
Gregory Ashton's avatar
Gregory Ashton committed
1
2
""" Searches using MCMC-based methods """

3
import sys
Gregory Ashton's avatar
Gregory Ashton committed
4
import os
5
import copy
Gregory Ashton's avatar
Gregory Ashton committed
6
import logging
7
from collections import OrderedDict
8
9
10
11
12
13
14
15

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

16
import core
Gregory Ashton's avatar
Gregory Ashton committed
17
from core import tqdm, args, earth_ephem, sun_ephem
18
from optimal_setup_functions import get_V_estimate
Gregory Ashton's avatar
Gregory Ashton committed
19
20
from optimal_setup_functions import get_optimal_setup
import helper_functions
21
22


23
class MCMCSearch(core.BaseSearchClass):
Gregory Ashton's avatar
Gregory Ashton committed
24
    """ MCMC search using ComputeFstat"""
25
26

    symbol_dictionary = dict(
27
28
        F0='$f$', F1='$\dot{f}$', F2='$\ddot{f}$', Alpha=r'$\alpha$',
        Delta='$\delta$')
29
    unit_dictionary = dict(
30
        F0='Hz', F1='Hz/s', F2='Hz/s$^2$', Alpha=r'rad', Delta='rad')
31
32
33
    rescale_dictionary = {}


Gregory Ashton's avatar
Gregory Ashton committed
34
    @helper_functions.initializer
Gregory Ashton's avatar
Gregory Ashton committed
35
36
    def __init__(self, label, outdir, theta_prior, tref, minStartTime,
                 maxStartTime, sftfilepath=None, nsteps=[100, 100],
37
38
                 nwalkers=100, ntemps=1, log10temperature_min=-5,
                 theta_initial=None, scatter_val=1e-10,
39
                 binary=False, BSGL=False, minCoverFreq=None,
40
                 maxCoverFreq=None, detectors=None, earth_ephem=None,
41
                 sun_ephem=None, injectSources=None, assumeSqrtSX=None):
42
43
44
45
        """
        Parameters
        label, outdir: str
            A label and directory to read/write data from/to
46
        sftfilepath: str
47
48
            Pattern to match SFTs using wildcards (*?) and ranges [0-9];
            mutiple patterns can be given separated by colons.
49
        theta_prior: dict
50
51
52
53
            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.
54
55
56
57
        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.
58
        tref, minStartTime, maxStartTime: int
59
60
61
62
63
64
            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].
65
66
67
68
69
70
71
72
        nwalkers, ntemps: int,
            The number of walkers and temperates to use in the parallel
            tempered PTSampler.
        log10temperature_min float < 0
            The  log_10(tmin) value, the set of betas passed to PTSampler are
            generated from np.logspace(0, log10temperature_min, ntemps).
        binary: Bool
            If true, search over binary parameters
73
        detectors: str
74
75
            Two character reference to the data to use, specify None for no
            contraint.
76
77
78
79
80
81
82
83
84
85
        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
86
87
        if os.path.isdir(outdir) is False:
            os.mkdir(outdir)
88
        self._add_log_file()
Gregory Ashton's avatar
Gregory Ashton committed
89
90
        logging.info(
            'Set-up MCMC search for model {} on data {}'.format(
91
                self.label, self.sftfilepath))
92
        self.pickle_path = '{}/{}_saved_data.p'.format(self.outdir, self.label)
93
        self._unpack_input_theta()
94
        self.ndim = len(self.theta_keys)
95
96
97
98
        if self.log10temperature_min:
            self.betas = np.logspace(0, self.log10temperature_min, self.ntemps)
        else:
            self.betas = None
99

100
101
102
103
104
105
106
107
        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")

108
        self._log_input()
109

110
    def _log_input(self):
111
        logging.info('theta_prior = {}'.format(self.theta_prior))
112
        logging.info('nwalkers={}'.format(self.nwalkers))
113
114
115
116
        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(
117
            self.log10temperature_min))
118

119
    def _initiate_search_object(self):
120
        logging.info('Setting up search object')
121
        self.search = core.ComputeFstat(
122
123
124
            tref=self.tref, sftfilepath=self.sftfilepath,
            minCoverFreq=self.minCoverFreq, maxCoverFreq=self.maxCoverFreq,
            earth_ephem=self.earth_ephem, sun_ephem=self.sun_ephem,
125
            detectors=self.detectors, BSGL=self.BSGL, transient=False,
126
            minStartTime=self.minStartTime, maxStartTime=self.maxStartTime,
127
128
            binary=self.binary, injectSources=self.injectSources,
            assumeSqrtSX=self.assumeSqrtSX)
129
130

    def logp(self, theta_vals, theta_prior, theta_keys, search):
131
        H = [self._generic_lnprior(**theta_prior[key])(p) for p, key in
132
133
134
135
136
137
             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]
138
139
        FS = search.compute_fullycoherent_det_stat_single_point(
            *self.fixed_theta)
140
141
        return FS

142
    def _unpack_input_theta(self):
143
        full_theta_keys = ['F0', 'F1', 'F2', 'Alpha', 'Delta']
144
145
146
        if self.binary:
            full_theta_keys += [
                'asini', 'period', 'ecc', 'tp', 'argp']
147
148
        full_theta_keys_copy = copy.copy(full_theta_keys)

149
150
        full_theta_symbols = ['$f$', '$\dot{f}$', '$\ddot{f}$', r'$\alpha$',
                              r'$\delta$']
151
152
153
154
        if self.binary:
            full_theta_symbols += [
                'asini', 'period', 'period', 'ecc', 'tp', 'argp']

155
156
        self.theta_keys = []
        fixed_theta_dict = {}
157
        for key, val in self.theta_prior.iteritems():
158
159
            if type(val) is dict:
                fixed_theta_dict[key] = 0
Gregory Ashton's avatar
Gregory Ashton committed
160
                self.theta_keys.append(key)
161
162
163
164
165
166
            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
167
            full_theta_keys_copy.pop(full_theta_keys_copy.index(key))
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182

        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]

183
    def _check_initial_points(self, p0):
184
185
186
187
188
189
190
191
192
193
194
195
196
        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))

197
                p0 = self._generate_new_p0_to_fix_initial_points(
198
199
                    p0, nt, initial_priors)

200
    def _generate_new_p0_to_fix_initial_points(self, p0, nt, initial_priors):
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
        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
220

221
    def _OLD_run_sampler_with_progress_bar(self, sampler, ns, p0):
222
223
        for result in tqdm(sampler.sample(p0, iterations=ns), total=ns):
            pass
Gregory Ashton's avatar
Gregory Ashton committed
224
225
        return sampler

226
227
    def setup_convergence_testing(
            self, convergence_period=10, convergence_length=10,
228
            convergence_burnin_fraction=0.25, convergence_threshold_number=10,
229
230
            convergence_threshold=1.2, convergence_prod_threshold=2,
            convergence_plot_upper_lim=2):
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
        """
        If called, convergence testing is used during the MCMC simulation

        This uses the Gelmanr-Rubin statistic based on the ratio of between and
        within walkers variance. The original statistic was developed for
        multiple (independent) MCMC simulations, in this context we simply use
        the walkers

        Parameters
        ----------
        convergence_period: int
            period (in number of steps) at which to test convergence
        convergence_length: int
            number of steps to use in testing convergence - this should be
            large enough to measure the variance, but if it is too long
            this will result in incorect early convergence tests
        convergence_burnin_fraction: float [0, 1]
            the fraction of the burn-in period after which to start testing
        convergence_threshold_number: int
            the number of consecutive times where the test passes after which
            to break the burn-in and go to production
        convergence_threshold: float
            the threshold to use in diagnosing convergence. Gelman & Rubin
            recomend a value of 1.2, 1.1 for strict convergence
        convergence_prod_threshold: float
            the threshold to test the production values with
257
258
        convergence_plot_upper_lim: float
            the upper limit to use in the diagnostic plot
259
        """
260
261
262
263
264
265
266

        if convergence_length > convergence_period:
            raise ValueError('convergence_length must be < convergence_period')
        logging.info('Setting up convergence testing')
        self.convergence_length = convergence_length
        self.convergence_period = convergence_period
        self.convergence_burnin_fraction = convergence_burnin_fraction
267
        self.convergence_prod_threshold = convergence_prod_threshold
268
269
270
271
272
        self.convergence_diagnostic = []
        self.convergence_diagnosticx = []
        self.convergence_threshold_number = convergence_threshold_number
        self.convergence_threshold = convergence_threshold
        self.convergence_number = 0
273
        self.convergence_plot_upper_lim = convergence_plot_upper_lim
274

275
    def _get_convergence_statistic(self, i, sampler):
276
277
278
279
280
281
282
283
284
        s = sampler.chain[0, :, i-self.convergence_length+1:i+1, :]
        within_std = np.mean(np.var(s, axis=1), axis=0)
        per_walker_mean = np.mean(s, axis=1)
        mean = np.mean(per_walker_mean, axis=0)
        between_std = np.sqrt(np.mean((per_walker_mean-mean)**2, axis=0))
        W = within_std
        B_over_n = between_std**2 / self.convergence_period
        Vhat = ((self.convergence_period-1.)/self.convergence_period * W
                + B_over_n + B_over_n / float(self.nwalkers))
285
        c = np.sqrt(Vhat/W)
286
        self.convergence_diagnostic.append(c)
287
        self.convergence_diagnosticx.append(i - self.convergence_length/2)
288
289
        return c

290
    def _burnin_convergence_test(self, i, sampler, nburn):
291
292
        if i < self.convergence_burnin_fraction*nburn:
            return False
293
        if np.mod(i+1, self.convergence_period) != 0:
294
            return False
295
        c = self._get_convergence_statistic(i, sampler)
296
297
        if np.all(c < self.convergence_threshold):
            self.convergence_number += 1
298
299
        else:
            self.convergence_number = 0
300
301
        return self.convergence_number > self.convergence_threshold_number

302
    def _prod_convergence_test(self, i, sampler, nburn):
303
304
305
        testA = i > nburn + self.convergence_length
        testB = np.mod(i+1, self.convergence_period) == 0
        if testA and testB:
306
            self._get_convergence_statistic(i, sampler)
307

308
    def _check_production_convergence(self, k):
309
310
311
312
313
314
315
316
        bools = np.any(
            np.array(self.convergence_diagnostic)[k:, :]
            > self.convergence_prod_threshold, axis=1)
        if np.any(bools):
            logging.warning(
                '{} convergence tests in the production run of {} failed'
                .format(np.sum(bools), len(bools)))

317
    def _run_sampler(self, sampler, p0, nprod=0, nburn=0):
318
        if hasattr(self, 'convergence_period'):
319
320
321
322
            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):
323
                if self._burnin_convergence_test(i, sampler, nburn):
324
325
326
327
328
329
330
331
332
333
334
                    logging.info(
                        'Converged at {} before max number {} of steps reached'
                        .format(i, nburn))
                    self.convergence_idx = i
                    break
            iterator.close()
            logging.info('Running {} production steps'.format(nprod))
            j = nburn
            k = len(self.convergence_diagnostic)
            for result in tqdm(sampler.sample(output[0], iterations=nprod),
                               total=nprod):
335
                self._prod_convergence_test(j, sampler, nburn)
336
                j += 1
337
            self._check_production_convergence(k)
338
339
340
341
342
343
            return sampler
        else:
            for result in tqdm(sampler.sample(p0, iterations=nburn+nprod),
                               total=nburn+nprod):
                pass
            return sampler
344

345
    def run(self, proposal_scale_factor=2, create_plots=True, **kwargs):
346
        """ Run the MCMC simulatation """
347

348
        self.old_data_is_okay_to_use = self._check_old_data_is_okay_to_use()
349
350
351
        if self.old_data_is_okay_to_use is True:
            logging.warning('Using saved data from {}'.format(
                self.pickle_path))
352
            d = self.get_saved_data_dictionary()
353
354
355
356
357
            self.samples = d['samples']
            self.lnprobs = d['lnprobs']
            self.lnlikes = d['lnlikes']
            return

358
        self._initiate_search_object()
359
360
361
362

        sampler = emcee.PTSampler(
            self.ntemps, self.nwalkers, self.ndim, self.logl, self.logp,
            logpargs=(self.theta_prior, self.theta_keys, self.search),
363
            loglargs=(self.search,), betas=self.betas, a=proposal_scale_factor)
364

365
366
367
        p0 = self._generate_initial_p0()
        p0 = self._apply_corrections_to_p0(p0)
        self._check_initial_points(p0)
368
369
370
371

        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
372
                j, ninit_steps, n))
373
            sampler = self._run_sampler(sampler, p0, nburn=n)
374
375
            logging.info("Mean acceptance fraction: {}"
                         .format(np.mean(sampler.acceptance_fraction, axis=1)))
376
377
378
            if self.ntemps > 1:
                logging.info("Tswap acceptance fraction: {}"
                             .format(sampler.tswap_acceptance_fraction))
379
            if create_plots:
380
                fig, axes = self._plot_walkers(sampler,
381
382
383
384
                                              symbols=self.theta_symbols,
                                              **kwargs)
                fig.tight_layout()
                fig.savefig('{}/{}_init_{}_walkers.png'.format(
385
                    self.outdir, self.label, j), dpi=400)
386

387
388
389
            p0 = self._get_new_p0(sampler)
            p0 = self._apply_corrections_to_p0(p0)
            self._check_initial_points(p0)
390
391
            sampler.reset()

Gregory Ashton's avatar
Gregory Ashton committed
392
393
394
395
        if len(self.nsteps) > 1:
            nburn = self.nsteps[-2]
        else:
            nburn = 0
396
397
398
        nprod = self.nsteps[-1]
        logging.info('Running final burn and prod with {} steps'.format(
            nburn+nprod))
399
        sampler = self._run_sampler(sampler, p0, nburn=nburn, nprod=nprod)
400
401
        logging.info("Mean acceptance fraction: {}"
                     .format(np.mean(sampler.acceptance_fraction, axis=1)))
402
403
404
        if self.ntemps > 1:
            logging.info("Tswap acceptance fraction: {}"
                         .format(sampler.tswap_acceptance_fraction))
405

406
        if create_plots:
407
            fig, axes = self._plot_walkers(sampler, symbols=self.theta_symbols,
408
                                          nprod=nprod, **kwargs)
409
410
411
            fig.tight_layout()
            fig.savefig('{}/{}_walkers.png'.format(self.outdir, self.label),
                        dpi=200)
412
413
414
415

        samples = sampler.chain[0, :, nburn:, :].reshape((-1, self.ndim))
        lnprobs = sampler.lnprobability[0, :, nburn:].reshape((-1))
        lnlikes = sampler.lnlikelihood[0, :, nburn:].reshape((-1))
416
        all_lnlikelihood = sampler.lnlikelihood
417
418
419
        self.samples = samples
        self.lnprobs = lnprobs
        self.lnlikes = lnlikes
420
421
        self.all_lnlikelihood = all_lnlikelihood
        self._save_data(sampler, samples, lnprobs, lnlikes, all_lnlikelihood)
422

423
    def _get_rescale_multiplier_for_key(self, key):
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
        """ 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

448
    def _get_rescale_subtractor_for_key(self, key):
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
        """ 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

473
    def _scale_samples(self, samples, theta_keys):
474
        """ Scale the samples using the rescale_dictionary """
475
476
477
478
        for key in theta_keys:
            if key in self.rescale_dictionary:
                idx = theta_keys.index(key)
                s = samples[:, idx]
479
                subtractor = self._get_rescale_subtractor_for_key(key)
480
                s = s - subtractor
481
                multiplier = self._get_rescale_multiplier_for_key(key)
482
                s *= multiplier
483
484
                samples[:, idx] = s

485
486
        return samples

487
    def _get_labels(self):
488
        """ Combine the units, symbols and rescaling to give labels """
489

490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
        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
507

508
509
    def plot_corner(self, figsize=(7, 7), add_prior=False, nstds=None,
                    label_offset=0.4, dpi=300, rc_context={},
510
                    tglitch_ratio=False, fig_and_axes=None, save_fig=True,
511
                    **kwargs):
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
        """ Generate a corner plot of the posterior

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

        Parameters
        ----------
        figsize: tuple (7, 7)
            Figure size in inches (passed to plt.subplots)
        add_prior: bool
            If true, plot the prior as a red line
        nstds: float
            The number of standard deviations to plot centered on the mean
        label_offset: float
            Offset the labels from the plot: useful to precent overlapping the
            tick labels with the axis labels
        dpi: int
            Passed to plt.savefig
        rc_context: dict
            Dictionary of rc values to set while generating the figure (see
            matplotlib rc for more details)
        tglitch_ratio: bool
            If true, and tglitch is a parameter, plot posteriors as the
            fractional time at which the glitch occurs instead of the actual
            time
537
538
539
540
541
        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
542
543
544
545

        Note: kwargs are passed on to corner.coner

        """
546

547
548
549
550
        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
551
552
        if self.ndim < 2:
            with plt.rc_context(rc_context):
553
554
555
556
                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
557
558
559
560
561
562
563
                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

564
        with plt.rc_context(rc_context):
565
566
567
568
569
            if fig_and_axes is None:
                fig, axes = plt.subplots(self.ndim, self.ndim,
                                         figsize=figsize)
            else:
                fig, axes = fig_and_axes
570
571

            samples_plt = copy.copy(self.samples)
572
            labels = self._get_labels()
573

574
            samples_plt = self._scale_samples(samples_plt, self.theta_keys)
575
576
577
578
579

            if tglitch_ratio:
                for j, k in enumerate(self.theta_keys):
                    if k == 'tglitch':
                        s = samples_plt[:, j]
580
581
582
                        samples_plt[:, j] = (
                            s - self.minStartTime)/(
                                self.maxStartTime - self.minStartTime)
583
                        labels[j] = r'$R_{\textrm{glitch}}$'
584
585
586
587
588
589
590

            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))
591
592
            elif 'range' in kwargs:
                _range = kwargs.pop('range')
593
594
595
596
            else:
                _range = None

            fig_triangle = corner.corner(samples_plt,
597
                                         labels=labels,
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
                                         fig=fig,
                                         bins=50,
                                         max_n_ticks=4,
                                         plot_contours=True,
                                         plot_datapoints=True,
                                         label_kwargs={'fontsize': 8},
                                         data_kwargs={'alpha': 0.1,
                                                      'ms': 0.5},
                                         range=_range,
                                         **kwargs)

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

            if add_prior:
623
                self._add_prior_to_corner(axes, self.samples)
624

625
626
627
628
629
            if save_fig:
                fig_triangle.savefig('{}/{}_corner.png'.format(
                    self.outdir, self.label), dpi=dpi)
            else:
                return fig, axes
630

631
    def _add_prior_to_corner(self, axes, samples):
632
633
634
635
        for i, key in enumerate(self.theta_keys):
            ax = axes[i][i]
            xlim = ax.get_xlim()
            s = samples[:, i]
636
            prior = self._generic_lnprior(**self.theta_prior[key])
637
            x = np.linspace(s.min(), s.max(), 100)
638
639
            multiplier = self._get_rescale_multiplier_for_key(key)
            subtractor = self._get_rescale_subtractor_for_key(key)
640
641
            ax2 = ax.twinx()
            ax2.get_yaxis().set_visible(False)
642
643
            ax2.plot((x-subtractor)*multiplier, [prior(xi) for xi in x], '-r')
            ax2.set_xlim(xlim)
644

645
646
647
648
649
650
651
652
    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]
653
            prior_func = self._generic_lnprior(**prior_dict)
654
655
656
657
658
659
660
661
662
663
            if prior_dict['type'] == 'unif':
                x = np.linspace(prior_dict['lower'], prior_dict['upper'], N)
                prior = prior_func(x)
                prior[0] = 0
                prior[-1] = 0
            elif prior_dict['type'] == 'norm':
                lower = prior_dict['loc'] - normal_stds * prior_dict['scale']
                upper = prior_dict['loc'] + normal_stds * prior_dict['scale']
                x = np.linspace(lower, upper, N)
                prior = prior_func(x)
664
665
666
667
668
            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
669
670
671
672
673
            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]
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
            else:
                raise ValueError('Not implemented for prior type {}'.format(
                    prior_dict['type']))
            priorln = ax.plot(x, prior, 'r', label='prior')
            ax.set_xlabel(self.theta_symbols[i])

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

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

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

697
    def plot_cumulative_max(self, **kwargs):
698
699
700
701
        """ 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
702
703
704
705
        d, maxtwoF = self.get_max_twoF()
        for key, val in self.theta_prior.iteritems():
            if key not in d:
                d[key] = val
706
707

        if hasattr(self, 'search') is False:
708
            self._initiate_search_object()
709
710
711
        if self.binary is False:
            self.search.plot_twoF_cumulative(
                self.label, self.outdir, F0=d['F0'], F1=d['F1'], F2=d['F2'],
712
                Alpha=d['Alpha'], Delta=d['Delta'],
713
                tstart=self.minStartTime, tend=self.maxStartTime,
714
                **kwargs)
715
716
717
718
719
        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'],
720
                tstart=self.minStartTime, tend=self.maxStartTime, **kwargs)
Gregory Ashton's avatar
Gregory Ashton committed
721

722
    def _generic_lnprior(self, **kwargs):
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
        """ Return a lambda function of the pdf

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

        """

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

        def halfnorm(x, loc, scale):
747
            if x < loc:
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
                return -np.inf
            else:
                return -0.5*((x-loc)**2/scale**2+np.log(0.5*np.pi*scale**2))

        def cauchy(x, x0, gamma):
            return 1.0/(np.pi*gamma*(1+((x-x0)/gamma)**2))

        def exp(x, x0, gamma):
            if x > x0:
                return np.log(gamma) - gamma*(x - x0)
            else:
                return -np.inf

        if kwargs['type'] == 'unif':
            return lambda x: logunif(x, kwargs['lower'], kwargs['upper'])
        elif kwargs['type'] == 'halfnorm':
            return lambda x: halfnorm(x, kwargs['loc'], kwargs['scale'])
765
766
        elif kwargs['type'] == 'neghalfnorm':
            return lambda x: halfnorm(-x, kwargs['loc'], kwargs['scale'])
767
768
769
770
771
772
773
        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")

774
    def _generate_rv(self, **kwargs):
775
776
777
778
779
780
781
782
        dist_type = kwargs.pop('type')
        if dist_type == "unif":
            return np.random.uniform(low=kwargs['lower'], high=kwargs['upper'])
        if dist_type == "norm":
            return np.random.normal(loc=kwargs['loc'], scale=kwargs['scale'])
        if dist_type == "halfnorm":
            return np.abs(np.random.normal(loc=kwargs['loc'],
                                           scale=kwargs['scale']))
783
784
785
        if dist_type == "neghalfnorm":
            return -1 * np.abs(np.random.normal(loc=kwargs['loc'],
                                                scale=kwargs['scale']))
786
787
788
789
790
791
        if dist_type == "lognorm":
            return np.random.lognormal(
                mean=kwargs['loc'], sigma=kwargs['scale'])
        else:
            raise ValueError("dist_type {} unknown".format(dist_type))

792
793
794
    def _plot_walkers(self, sampler, symbols=None, alpha=0.4, color="k",
                      temp=0, lw=0.1, nprod=0, add_det_stat_burnin=False,
                      fig=None, axes=None, xoffset=0, plot_det_stat=False,
795
                      context='ggplot', subtractions=None, labelpad=0.05):
796
797
        """ Plot all the chains from a sampler """

798
799
800
801
802
        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))

803
804
805
        if np.ndim(axes) > 1:
            axes = axes.flatten()

806
807
808
809
810
811
812
813
814
815
816
817
818
        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, :, :, :]

819
820
        if subtractions is None:
            subtractions = [0 for i in range(ndim)]
821
822
823
        else:
            if len(subtractions) != self.ndim:
                raise ValueError('subtractions must be of length ndim')
824

825
826
827
828
        if plot_det_stat:
            extra_subplots = 1
        else:
            extra_subplots = 0
829
        with plt.style.context((context)):
Gregory Ashton's avatar
Gregory Ashton committed
830
            plt.rcParams['text.usetex'] = True
Gregory Ashton's avatar
Gregory Ashton committed
831
            if fig is None and axes is None:
832
                fig = plt.figure(figsize=(4, 3.0*ndim))
833
834
                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
835
                               for i in range(2, ndim+1)]
836

Gregory Ashton's avatar
Gregory Ashton committed
837
            idxs = np.arange(chain.shape[1])
838
839
840
841
842
            burnin_idx = chain.shape[1] - nprod
            if hasattr(self, 'convergence_idx'):
                convergence_idx = self.convergence_idx
            else:
                convergence_idx = burnin_idx
843
844
            if ndim > 1:
                for i in range(ndim):
845
                    axes[i].ticklabel_format(useOffset=False, axis='y')
Gregory Ashton's avatar
Gregory Ashton committed
846
                    cs = chain[:, :, i].T
847
                    if burnin_idx > 0:
848
849
                        axes[i].plot(xoffset+idxs[:convergence_idx+1],
                                     cs[:convergence_idx+1]-subtractions[i],
850
                                     color="r", alpha=alpha,
Gregory Ashton's avatar
Gregory Ashton committed
851
                                     lw=lw)
852
                        axes[i].axvline(xoffset+convergence_idx,
853
                                        color='k', ls='--', lw=0.25)
854
855
                    axes[i].plot(xoffset+idxs[burnin_idx:],
                                 cs[burnin_idx:]-subtractions[i],
Gregory Ashton's avatar
Gregory Ashton committed
856
                                 color="k", alpha=alpha, lw=lw)
857
                    if symbols:
858
                        if subtractions[i] == 0:
859
                            axes[i].set_ylabel(symbols[i], labelpad=labelpad)
860
861
                        else:
                            axes[i].set_ylabel(
862
863
                                symbols[i]+'$-$'+symbols[i]+'$_0$',
                                labelpad=labelpad)
864

865
866
                    if hasattr(self, 'convergence_diagnostic'):
                        ax = axes[i].twinx()
867
868
                        c_x = np.array(self.convergence_diagnosticx)
                        c_y = np.array(self.convergence_diagnostic)
869
870
871
872
                        break_idx = np.argmin(np.abs(c_x - burnin_idx))
                        ax.plot(c_x[:break_idx], c_y[:break_idx, i], '-b')
                        ax.plot(c_x[break_idx:], c_y[break_idx:, i], '-b')
                        ax.set_ylabel('PSRF')
873
                        ax.ticklabel_format(useOffset=False)
874
                        ax.set_ylim(1, self.convergence_plot_upper_lim)
875
            else:
Gregory Ashton's avatar
Gregory Ashton committed
876
                axes[0].ticklabel_format(useOffset=False, axis='y')
Gregory Ashton's avatar
Gregory Ashton committed
877
                cs = chain[:, :, temp].T
Gregory Ashton's avatar
Gregory Ashton committed
878
879
880
881
882
883
                if burnin_idx:
                    axes[0].plot(idxs[:burnin_idx], cs[:burnin_idx],
                                 color="r", alpha=alpha, lw=lw)
                axes[0].plot(idxs[burnin_idx:], cs[burnin_idx:], color="k",
                             alpha=alpha, lw=lw)
                if symbols:
884
                    axes[0].set_ylabel(symbols[0], labelpad=labelpad)
885

886
            if plot_det_stat:
887
888
889
                if len(axes) == ndim:
                    axes.append(fig.add_subplot(ndim+1, 1, ndim+1))

890
891
892
                lnl = sampler.lnlikelihood[temp, :, :]
                if burnin_idx and add_det_stat_burnin:
                    burn_in_vals = lnl[:, :burnin_idx].flatten()
893
894
895
896
897
898
899
                    try:
                        axes[-1].hist(burn_in_vals[~np.isnan(burn_in_vals)],
                                      bins=50, histtype='step', color='r')
                    except ValueError:
                        logging.info('Det. Stat. hist failed, most likely all '
                                     'values where the same')
                        pass
900
901
902
                else:
                    burn_in_vals = []
                prod_vals = lnl[:, burnin_idx:].flatten()
903
904
905
906
907
908
909
                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
910
911
912
913
914
915
916
917
918
919
920
921
                if self.BSGL:
                    axes[-1].set_xlabel(r'$\mathcal{B}_\mathrm{S/GL}$')
                else:
                    axes[-1].set_xlabel(r'$\widetilde{2\mathcal{F}}$')
                axes[-1].set_ylabel(r'$\textrm{Counts}$')
                combined_vals = np.append(burn_in_vals, prod_vals)
                if len(combined_vals) > 0:
                    minv = np.min(combined_vals)
                    maxv = np.max(combined_vals)
                    Range = abs(maxv-minv)
                    axes[-1].set_xlim(minv-0.1*Range, maxv+0.1*Range)

922
                xfmt = matplotlib.ticker.ScalarFormatter()
923
                xfmt.set_powerlimits((-4, 4))
924
925
                axes[-1].xaxis.set_major_formatter(xfmt)

926
            axes[-2].set_xlabel(r'$\textrm{Number of steps}$', labelpad=0.2)
927
928
        return fig, axes

929
    def _apply_corrections_to_p0(self, p0):
Gregory Ashton's avatar
Gregory Ashton committed
930
931
932
        """ Apply any correction to the initial p0 values """
        return p0

933
    def _generate_scattered_p0(self, p):
934
        """ Generate a set of p0s scattered about p """
Gregory Ashton's avatar
Gregory Ashton committed
935
        p0 = [[p + self.scatter_val * p * np.random.randn(self.ndim)
936
937
938
939
               for i in xrange(self.nwalkers)]
              for j in xrange(self.ntemps)]
        return p0

940
    def _generate_initial_p0(self):
941
942
943
        """ Generate a set of init vals for the walkers """

        if type(self.theta_initial) == dict:
944
            logging.info('Generate initial values from initial dictionary')
945
            if hasattr(self, 'nglitch') and self.nglitch > 1:
946
                raise ValueError('Initial dict not implemented for nglitch>1')
947
            p0 = [[[self._generate_rv(**self.theta_initial[key])
948
949
950
                    for key in self.theta_keys]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
951
952
        elif type(self.theta_initial) == list:
            logging.info('Generate initial values from list of theta_initial')
953
            p0 = [[[self._generate_rv(**val)
954
955
956
                    for val in self.theta_initial]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
957
        elif self.theta_initial is None:
958
            logging.info('Generate initial values from prior dictionary')
959
            p0 = [[[self._generate_rv(**self.theta_prior[key])
960
961
962
963
                    for key in self.theta_keys]
                   for i in range(self.nwalkers)]
                  for j in range(self.ntemps)]
        elif len(self.theta_initial) == self.ndim:
964
            p0 = self._generate_scattered_p0(self.theta_initial)
965
966
967
968
969
        else:
            raise ValueError('theta_initial not understood')

        return p0

970
    def _get_new_p0(self, sampler):
971
972
973
974
975
976
        """ Returns new initial positions for walkers are burn0 stage

        This returns new positions for all walkers by scattering points about
        the maximum posterior with scale `scatter_val`.

        """
Gregory Ashton's avatar
Gregory Ashton committed
977
978
979
980
        temp_idx = 0
        pF = sampler.chain[temp_idx, :, :, :]
        lnl = sampler.lnlikelihood[temp_idx, :, :]
        lnp = sampler.lnprobability[temp_idx, :, :]
981
982

        # General warnings about the state of lnp
Gregory Ashton's avatar
Gregory Ashton committed
983
        if np.any(np.isnan(lnp)):
984
985
            logging.warning(
                "Of {} lnprobs {} are nan".format(
Gregory Ashton's avatar
Gregory Ashton committed
986
987
                    np.shape(lnp), np.sum(np.isnan(lnp))))
        if np.any(np.isposinf(lnp)):
988
989
            logging.warning(
                "Of {} lnprobs {} are +np.inf".format(
Gregory Ashton's avatar
Gregory Ashton committed
990
991
                    np.shape(lnp), np.sum(np.isposinf(lnp))))
        if np.any(np.isneginf(lnp)):
992
993
            logging.warning(
                "Of {} lnprobs {} are -np.inf".format(
Gregory Ashton's avatar
Gregory Ashton committed
994
                    np.shape(lnp), np.sum(np.isneginf(lnp))))
995

996
997
        lnp_finite = copy.copy(lnp)
        lnp_finite[np.isinf(lnp)] = np.nan
Gregory Ashton's avatar
Gregory Ashton committed
998
999
        idx = np.unravel_index(np.nanargmax(lnp_finite), lnp_finite.shape)
        p = pF[idx]
1000
        p0 = self._generate_scattered_p0(p)
1001

1002
1003
1004
1005
1006
1007
1008
1009
        self.search.BSGL = False
        twoF = self.logl(p, self.search)
        self.search.BSGL = self.BSGL

        logging.info(('Gen. new p0 from pos {} which had det. stat.={:2.1f},'
                      ' twoF={:2.1f} and lnp={:2.1f}')
                     .format(idx[1], lnl[idx], twoF, lnp_finite[idx]))

1010
1011
        return p0

1012
    def _get_data_dictionary_to_save(self):
1013
1014
        d = dict(nsteps=self.nsteps, nwalkers=self.nwalkers,
                 ntemps=self.ntemps, theta_keys=self.theta_keys,
Gregory Ashton's avatar
Gregory Ashton committed
1015
                 theta_prior=self.theta_prior, scatter_val=self.scatter_val,
1016
                 log10temperature_min=self.log10temperature_min,
1017
                 BSGL=self.BSGL)
1018
1019
        return d

1020
    def _save_data(self, sampler, samples, lnprobs, lnlikes, all_lnlikelihood):
1021
        d = self._get_data_dictionary_to_save()
1022
1023
1024
        d['samples'] = samples
        d['lnprobs'] = lnprobs
        d['lnlikes'] = lnlikes
1025
        d['all_lnlikelihood'] = all_lnlikelihood
1026
1027
1028
1029
1030
1031
1032
1033

        if os.path.isfile(self.pickle_path):
            logging.info('Saving backup of {} as {}.old'.format(
                self.pickle_path, self.pickle_path))
            os.rename(self.pickle_path, self.pickle_path+".old")
        with open(self.pickle_path, "wb") as File:
            pickle.dump(d, File)

1034
1035
    def get_saved_data_dictionary(self):
        """ Returns dictionary of the data saved as pickle """
1036
1037
1038
1039
        with open(self.pickle_path, "r") as File:
            d = pickle.load(File)
        return d

1040
    def _check_old_data_is_okay_to_use(self):
1041
1042
1043
1044
        if args.use_old_data:
            logging.info("Forcing use of old data")
            return True

1045
1046
1047
1048
        if os.path.isfile(self.pickle_path) is False:
            logging.info('No pickled data found')
            return False

Gregory Ashton's avatar
Gregory Ashton committed
1049
1050
        if self.sftfilepath is not None:
            oldest_sft = min([os.path.getmtime(f) for f in
1051
                              self._get_list_of_matching_sfts()])
Gregory Ashton's avatar
Gregory Ashton committed
1052
1053
1054
            if os.path.getmtime(self.pickle_path) < oldest_sft:
                logging.info('Pickled data outdates sft files')
                return False
1055

1056
1057
        old_d = self.get_saved_data_dictionary().copy()
        new_d = self._get_data_dictionary_to_save().copy()
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068

        old_d.pop('samples')
        old_d.pop('lnprobs')
        old_d.pop('lnlikes')

        mod_keys = []
        for key in new_d.keys():
            if key in old_d:
                if new_d[key] != old_d[key]:
                    mod_keys.append((key, old_d[key], new_d[key]))
            else:
1069
                raise ValueError('Keys {} not in old dictionary'.format(key))
1070
1071
1072
1073
1074
1075
1076
1077
1078

        if len(mod_keys) == 0:
            return True
        else:
            logging.warning("Saved data differs from requested")
            logging.info("Differences found in following keys:")
            for key in mod_keys:
                if len(key) == 3:
                    if np.isscalar(key[1]) or key[0] == 'nsteps':
1079
                        logging.info("    {} : {} -> {}".format(*key))
1080
                    else:
1081
                        logging.info("    " + key[0])
1082
1083
1084
1085
1086
                else:
                    logging.info(key)
            return False

    def get_max_twoF(self, threshold=0.05):
1087
        """ Returns the max likelihood sample and the corresponding 2F value
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101

        Note: the sample is returned as a dictionary al