#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
BXA (Bayesian X-ray Analysis) for Xspec
Copyright: Johannes Buchner (C) 2013-2020
"""
from __future__ import print_function
from ultranest.integrator import ReactiveNestedSampler, resume_from_similar_file
from ultranest.plot import PredictionBand
import ultranest.stepsampler
import os
from math import isnan, isinf
import warnings
import numpy
from . import qq
from .sinning import binning
from xspec import Xset, AllModels, Fit, Plot
import xspec
import matplotlib.pyplot as plt
from tqdm import tqdm # if this fails --> pip install tqdm
from .priors import *
[docs]class XSilence(object):
"""Context for temporarily making xspec quiet."""
def __enter__(self):
self.oldchatter = Xset.chatter, Xset.logChatter
Xset.chatter, Xset.logChatter = 0, 0
def __exit__(self, *args):
Xset.chatter, Xset.logChatter = self.oldchatter
[docs]def create_prior_function(transformations):
"""
Create a single prior transformation function from a list of
transformations for each parameter. This assumes the priors factorize.
"""
def prior(cube):
params = cube.copy()
for i, t in enumerate(transformations):
transform = t['transform']
params[i] = transform(cube[i])
return params
return prior
[docs]def store_chain(chainfilename, transformations, posterior, fit_statistic):
"""Writes a MCMC chain file in the same format as the Xspec chain command."""
import astropy.io.fits as pyfits
group_index = 1
old_model = transformations[0]['model']
names = []
for t in transformations:
if t['model'] != old_model:
group_index += 1
old_model = t['model']
names.append('%s__%d' % (t['name'], t['index'] + (group_index - 1) * old_model.nParameters))
columns = [pyfits.Column(
name=name, format='D', array=t['aftertransform'](posterior[:, i]))
for i, name in enumerate(names)]
columns.append(pyfits.Column(name='FIT_STATISTIC', format='D', array=fit_statistic))
table = pyfits.ColDefs(columns)
header = pyfits.Header()
header.add_comment("""Created by BXA (Bayesian X-ray spectal Analysis) for Xspec""")
header.add_comment("""refer to https://github.com/JohannesBuchner/""")
header['TEMPR001'] = 1.
header['STROW001'] = 1
header['EXTNAME'] = 'CHAIN'
tbhdu = pyfits.BinTableHDU.from_columns(table, header=header)
tbhdu.writeto(chainfilename, overwrite=True)
[docs]def set_parameters(transformations, values):
"""Set current parameters."""
assert len(values) == len(transformations)
pars = []
for i, t in enumerate(transformations):
v = t['aftertransform'](values[i])
assert not isnan(v) and not isinf(v), 'ERROR: parameter %d (index %d, %s) to be set to %f' % (
i, t['index'], t['name'], v)
pars += [t['model'], {t['index']:v}]
AllModels.setPars(*pars)
[docs]class BXASolver(object):
"""
Run the Bayesian analysis.
The nested sampling package `UltraNest <https://johannesbuchner.github.io/UltraNest/>`_ is used under the hood.
If prior is None, uniform priors are used on the passed parameters.
If parameters is also None, all thawed parameters are used.
:param transformations: List of parameter transformation definitions
:param prior_function: set only if you want to specify a custom, non-separable prior
:param outputfiles_basename: prefix for output filenames.
:param resume_from: prefix for output filenames of a previous run with similar posterior from which to resume
More information on the concept of prior transformations is available at
https://johannesbuchner.github.io/UltraNest/priors.html
"""
allowed_stats = ['cstat', 'cash', 'pstat']
def __init__(
self, transformations, prior_function=None, outputfiles_basename='chains/',
resume_from=None
):
if prior_function is None:
prior_function = create_prior_function(transformations)
self.prior_function = prior_function
self.transformations = transformations
self.set_paramnames()
self.vectorized = False
# for convenience. Has to be a directory anyway for ultranest
if not outputfiles_basename.endswith('/'):
outputfiles_basename = outputfiles_basename + '/'
if not os.path.exists(outputfiles_basename):
os.mkdir(outputfiles_basename)
self.outputfiles_basename = outputfiles_basename
if resume_from is not None:
self.paramnames, self.log_likelihood, self.prior_function, self.vectorized = resume_from_similar_file(
os.path.join(resume_from, 'chains', 'weighted_post_untransformed.txt'),
self.paramnames, loglike=self.log_likelihood, transform=self.prior_function,
vectorized=False,
)
[docs] def set_paramnames(self, paramnames=None):
if paramnames is None:
self.paramnames = [str(t['name']) for t in self.transformations]
else:
self.paramnames = paramnames
[docs] def set_best_fit(self):
"""Sets model to the best fit values."""
i = numpy.argmax(self.results['weighted_samples']['logl'])
params = self.results['weighted_samples']['points'][i, :]
set_parameters(transformations=self.transformations, values=params)
[docs] def log_likelihood(self, params):
""" returns -0.5 of the fit statistic."""
set_parameters(transformations=self.transformations, values=params)
like = -0.5 * Fit.statistic
# print("like = %.1f" % like)
if not numpy.isfinite(like):
return -1e100
return like
[docs] def run(
self, sampler_kwargs={'resume': 'overwrite'}, run_kwargs={'Lepsilon': 0.1},
speed="safe", resume=None, n_live_points=None,
frac_remain=None, Lepsilon=0.1, evidence_tolerance=None
):
"""Run nested sampling with ultranest.
:sampler_kwargs: arguments passed to ReactiveNestedSampler (see ultranest documentation)
:run_kwargs: arguments passed to ReactiveNestedSampler.run() (see ultranest documentation)
The following arguments are also available directly for backward compatibility:
:param resume: sets sampler_kwargs['resume']='resume' if True, otherwise 'overwrite'
:param n_live_points: sets run_kwargs['min_num_live_points']
:param evidence_tolerance: sets run_kwargs['dlogz']
:param Lepsilon: sets run_kwargs['Lepsilon']
:param frac_remain: sets run_kwargs['frac_remain']
"""
# run nested sampling
if Fit.statMethod.lower() not in BXASolver.allowed_stats:
raise RuntimeError('ERROR: not using cash (Poisson likelihood) for Poisson data! set Fit.statMethod to cash before analysing (currently: %s)!' % Fit.statMethod)
if resume is not None:
sampler_kwargs['resume'] = 'resume' if resume else 'overwrite'
run_kwargs['Lepsilon'] = run_kwargs.pop('Lepsilon', Lepsilon)
del Lepsilon
if evidence_tolerance is not None:
run_kwargs['evidence_tolerance'] = run_kwargs.pop('dlogz', evidence_tolerance)
del evidence_tolerance
if frac_remain is not None:
run_kwargs['frac_remain'] = run_kwargs.pop('frac_remain', frac_remain)
del frac_remain
if n_live_points is not None:
run_kwargs['min_num_live_points'] = run_kwargs.pop('min_num_live_points', n_live_points)
del n_live_points
with XSilence():
self.sampler = ReactiveNestedSampler(
self.paramnames, self.log_likelihood, transform=self.prior_function,
log_dir=self.outputfiles_basename,
vectorized=self.vectorized, **sampler_kwargs)
if speed == "safe":
pass
elif speed == "auto":
region_filter = run_kwargs.pop('region_filter', True)
self.sampler.run(max_ncalls=40000, **run_kwargs)
self.sampler.stepsampler = ultranest.stepsampler.SliceSampler(
nsteps=1000,
generate_direction=ultranest.stepsampler.generate_mixture_random_direction,
adaptive_nsteps='move-distance', region_filter=region_filter
)
else:
self.sampler.stepsampler = ultranest.stepsampler.SliceSampler(
generate_direction=ultranest.stepsampler.generate_mixture_random_direction,
nsteps=speed,
adaptive_nsteps=False,
region_filter=False)
self.sampler.run(**run_kwargs)
self.sampler.print_results()
self.results = self.sampler.results
try:
self.sampler.plot()
except Exception as e:
warnings.warn("plotting failed because:", e)
pass
logls = [self.results['weighted_samples']['logl'][
numpy.where(self.results['weighted_samples']['points'] == sample)[0][0]]
for sample in self.results['samples']]
self.posterior = self.results['samples']
chainfilename = '%schain.fits' % self.outputfiles_basename
store_chain(chainfilename, self.transformations, self.posterior, -2 * logls)
xspec.AllChains.clear()
xspec.AllChains += chainfilename
# set current parameters to best fit
self.set_best_fit()
return self.results
[docs] def create_flux_chain(self, spectrum, erange="2.0 10.0", nsamples=None):
"""
For each posterior sample, computes the flux in the given energy range.
The so-created chain can be combined with redshift information to propagate
the uncertainty. This is especially important if redshift is a variable
parameter in the fit (with some prior).
Returns erg/cm^2 energy flux (first column) and photon flux (second column)
for each posterior sample.
"""
# prefix = analyzer.outputfiles_basename
# modelnames = set([t['model'].name for t in transformations])
with XSilence():
# plot models
flux = []
for k, row in enumerate(tqdm(self.posterior[:nsamples], disable=None)):
set_parameters(values=row, transformations=self.transformations)
AllModels.calcFlux(erange)
f = spectrum.flux
# compute flux in current energies
flux.append([f[0], f[3]])
return numpy.array(flux)
[docs] def posterior_predictions_convolved(
self, component_names=None, plot_args=None, nsamples=400
):
"""Plot convolved model posterior predictions.
Also returns data points for plotting.
:param component_names: labels to use. Set to 'ignore' to skip plotting a component
:param plot_args: matplotlib.pyplot.plot arguments for each component
:param nsamples: number of posterior samples to use (lower is faster)
"""
# get data, binned to 10 counts
# overplot models
# can we do this component-wise?
data = [None] # bin, bin width, data and data error
models = [] #
if component_names is None:
component_names = [''] * 100
if plot_args is None:
plot_args = [{}] * 100
bands = []
Plot.background = True
def plot_convolved_components(content):
xmid = content[:, 0]
ndata_columns = 6 if Plot.background else 4
ncomponents = content.shape[1] - ndata_columns
if data[0] is None:
data[0] = content[:, 0:ndata_columns]
model_contributions = []
for component in range(ncomponents):
y = content[:, ndata_columns + component]
kwargs = dict(drawstyle='steps', alpha=0.1, color='k')
kwargs.update(plot_args[component])
label = component_names[component]
# we only label the first time we enter here
# otherwise we get lots of entries in the legend
component_names[component] = ''
if component >= len(bands):
bands.append(PredictionBand(
xmid,
shadeargs=dict(color=kwargs['color']),
lineargs=dict(color=kwargs['color'])))
if label != 'ignore':
# plt.plot(xmid, y, label=label, **kwargs)
bands[component].add(y)
model_contributions.append(y)
models.append(model_contributions)
self.posterior_predictions_plot(
plottype='counts',
callback=plot_convolved_components,
nsamples=nsamples)
for band, label in zip(bands, component_names):
band.shade(alpha=0.5, label=label)
band.shade(q=0.495, alpha=0.1)
band.line()
if Plot.background:
results = dict(list(zip('bins,width,data,error,background,backgrounderr'.split(','), data[0].transpose())))
else:
results = dict(list(zip('bins,width,data,error'.split(','), data[0].transpose())))
results['models'] = numpy.array(models)
return results
[docs] def posterior_predictions_unconvolved(
self, component_names=None, plot_args=None, nsamples=400,
plottype='model',
):
"""
Plot unconvolved model posterior predictions.
:param component_names: labels to use. Set to 'ignore' to skip plotting a component
:param plot_args: matplotlib.pyplot.plot arguments for each component
:param nsamples: number of posterior samples to use (lower is faster)
"""
if component_names is None:
component_names = [''] * 100
if plot_args is None:
plot_args = [{}] * 100
bands = []
def plot_unconvolved_components(content):
xmid = content[:, 0]
ncomponents = content.shape[1] - 2
for component in range(ncomponents):
y = content[:, 2 + component]
kwargs = dict(drawstyle='steps', alpha=0.1, color='k')
kwargs.update(plot_args[component])
label = component_names[component]
# we only label the first time we enter here
# otherwise we get lots of entries in the legend
component_names[component] = ''
if component >= len(bands):
bands.append(PredictionBand(
xmid,
shadeargs=dict(color=kwargs['color']),
lineargs=dict(color=kwargs['color'])))
if label != 'ignore':
# plt.plot(xmid, y, label=label, **kwargs)
bands[component].add(y)
self.posterior_predictions_plot(
plottype=plottype,
callback=plot_unconvolved_components,
nsamples=nsamples)
for band, label in zip(bands, component_names):
band.shade(alpha=0.5, label=label)
band.shade(q=0.495, alpha=0.1)
band.line()
[docs] def posterior_predictions_plot(self, plottype, callback, nsamples=None):
"""
Internal Routine used by posterior_predictions_unconvolved, posterior_predictions_convolved
"""
posterior = self.posterior
# for plotting, we don't need so many points, and especially the
# points that barely made it into the analysis are not that interesting.
# so pick a random subset of at least nsamples points
if nsamples is not None and len(posterior) > nsamples:
if hasattr(numpy.random, 'choice'):
chosen = numpy.random.choice(
numpy.arange(len(posterior)),
replace=False, size=nsamples)
else:
chosen = list(set(numpy.random.randint(
0, len(posterior), size=10 * nsamples)))[:nsamples]
posterior = posterior[chosen, :]
assert len(posterior) == nsamples
prefix = self.outputfiles_basename
tmpfilename = os.path.join(os.path.dirname(prefix), os.path.basename(prefix).replace('.', '_') + '-wdatatmp.qdp')
if os.path.exists(tmpfilename):
os.remove(tmpfilename)
with XSilence():
olddevice = Plot.device
Plot.device = '/null'
# modelnames = set([t['model'].name for t in transformations])
while len(Plot.commands) > 0:
Plot.delCommand(1)
Plot.addCommand('wdata "%s"' % tmpfilename.replace('.qdp', ''))
# plot models
for k, row in enumerate(tqdm(posterior, disable=None)):
set_parameters(values=row, transformations=self.transformations)
if os.path.exists(tmpfilename):
os.remove(tmpfilename)
xspec.Plot(plottype)
content = numpy.genfromtxt(tmpfilename, skip_header=3)
os.remove(tmpfilename)
callback(content)
xspec.Plot.device = olddevice
while len(Plot.commands) > 0:
Plot.delCommand(1)
if os.path.exists(tmpfilename):
os.remove(tmpfilename)
[docs]def standard_analysis(
transformations, outputfiles_basename,
skipsteps=[], **kwargs
):
"""
Run a default analysis which produces nice plots.
Deprecated; copy the code of this function into
your script and adjust to your needs.
* runs nested sampling analysis, creates MCMC chain file
* marginal probabilities (1d and 2d)
* model posterior predictions + data overplotted, convolved
* model posterior predictions unconvolved
* quantile-quantile plot with statistics
* prints out summary of parameters
* prints out model evidence
Look at the source of this function to figure out how to do
the individual parts.
Copy them to your scripts and adapt them to your needs.
"""
# run nested sampling
print('running analysis ...')
solver = BXASolver(
transformations=transformations,
outputfiles_basename=outputfiles_basename)
solver.run(**kwargs)
print('running analysis ... done')
# analyse results
print('analysing results...')
if 'unconvolved' not in skipsteps:
print('creating plot of posterior predictions ...')
plt.figure()
solver.posterior_predictions_unconvolved(nsamples=100)
ylim = plt.ylim()
# 3 orders of magnitude at most
plt.ylim(max(ylim[0], ylim[1] / 1000), ylim[1])
plt.gca().set_yscale('log')
if Plot.xAxis == 'keV':
plt.xlabel('Energy [keV]')
elif Plot.xAxis == 'channel':
plt.xlabel('Channel')
plt.ylabel('Counts/s/cm$^2$')
print('saving plot...')
plt.savefig(outputfiles_basename + 'unconvolved_posterior.pdf', bbox_inches='tight')
plt.close()
if 'convolved' not in skipsteps:
print('creating plot of posterior predictions against data ...')
plt.figure()
data = solver.posterior_predictions_convolved(nsamples=100)
# plot data
# plt.errorbar(x=data['bins'], xerr=data['width'], y=data['data'], yerr=data['error'],
# label='data', marker='o', color='green')
# bin data for plotting
print('binning for plot...')
binned = binning(
outputfiles_basename=outputfiles_basename,
bins=data['bins'], widths=data['width'],
data=data['data'], models=data['models'])
for point in binned['marked_binned']:
plt.errorbar(marker='o', zorder=-1, **point)
plt.xlim(binned['xlim'])
plt.ylim(binned['ylim'][0], binned['ylim'][1] * 2)
plt.gca().set_yscale('log')
if Plot.xAxis == 'keV':
plt.xlabel('Energy [keV]')
elif Plot.xAxis == 'channel':
plt.xlabel('Channel')
plt.ylabel('Counts/s/cm$^2$')
print('saving plot...')
plt.savefig(outputfiles_basename + 'convolved_posterior.pdf', bbox_inches='tight')
plt.close()
if 'qq' not in skipsteps:
print('creating quantile-quantile plot ...')
solver.set_best_fit()
plt.figure(figsize=(7, 7))
qq.qq(outputfiles_basename, markers=5, annotate=True)
print('saving plot...')
plt.savefig(outputfiles_basename + 'qq_model_deviations.pdf', bbox_inches='tight')
plt.close()
return solver