Source code for bxa.xspec.solver

#!/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.solvecompat import pymultinest_solve_compat as solve
from ultranest.plot import PredictionBand
import os
from math import isnan, isinf
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. 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/' ): if prior_function is None: prior_function = create_prior_function(transformations) self.prior_function = prior_function self.transformations = transformations self.set_paramnames() # 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
[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): 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, evidence_tolerance=0.5, n_live_points=400, wrapped_params=None, **kwargs ): """ Run nested sampling with ultranest. :param n_live_points: number of live points (400 to 1000 is recommended). :param evidence_tolerance: uncertainty on the evidence to achieve :param resume: uncertainty on the evidence to achieve :param Lepsilon: numerical model inaccuracies in the statistic (default: 0.1). Increase if run is not finishing because it is trying too hard to resolve unimportant details caused e.g., by atable interpolations. :param frac_remain: fraction of the integration remainder allowed in the live points. Setting to 0.5 in mono-modal problems can be acceptable and faster. The default is 0.01 (safer). These are ultranest parameters (see ultranest.solve documentation!) """ # 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) n_dims = len(self.paramnames) resume = kwargs.pop('resume', False) Lepsilon = kwargs.pop('Lepsilon', 0.1) with XSilence(): self.results = solve( self.log_likelihood, self.prior_function, n_dims, paramnames=self.paramnames, outputfiles_basename=self.outputfiles_basename, resume=resume, Lepsilon=Lepsilon, n_live_points=n_live_points, evidence_tolerance=evidence_tolerance, seed=-1, max_iter=0, wrapped_params=wrapped_params, **kwargs ) 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. component_names: labels to use. Set to 'ignore' to skip plotting a component plot_args: matplotlib.pyplot.plot arguments for each component """ # 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 """ 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 ): """ Default analysis which produces nice plots: * 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