Source code for dmdd.dmdd

    import rate_NR 
    import rate_genNR  
    import rate_UV 
    import dmdd_efficiencies as eff
except ImportError:
import os,os.path,shutil
import pickle
import logging
import time

on_rtd = False

    import numpy.random as random
    import numpy as np
    from scipy.stats import poisson
    from scipy.interpolate import UnivariateSpline as interpolate
    from scipy.optimize import fsolve
except ImportError:
    on_rtd = True
    np = None

  import pymultinest
except ImportError:
  logging.warning('pymultinest not imported!')

if not on_rtd:
    from constants import *
    from globals import *

    MAIN_PATH = os.environ['DMDD_MAIN_PATH']
except KeyError:
    logging.warning('DMDD_MAIN_PATH environment variable not defined, defaulting to:   ~/.dmdd')
    MAIN_PATH = os.path.expanduser('~/.dmdd') #os.getcwd()

SIM_PATH = MAIN_PATH + '/simulations_uv/'
CHAINS_PATH = MAIN_PATH + '/chains_uv/'
RESULTS_PATH = MAIN_PATH + '/results_uv'

if not os.path.exists(SIM_PATH):
if not os.path.exists(CHAINS_PATH):
if not os.path.exists(RESULTS_PATH):

Example usage of the objects here defined:

model1 = UV_Model('SI_Higgs', ['mass', 'sigma_si'], fixed_params={'fnfp_si': 1})
model2 = UV_Model('SD_fu', ['mass','sigma_sd'], fixed_params={'fnfp_sd': -1.1})

xe = Experiment('Xe', 'xenon', 5, 40, 1000, eff.efficiency_Xe)

run = MultinestRun('sim', [xe,ge], model1,{'mass':50.,'sigma_si':70.},
                   model2, prior_ranges={'mass':(1,1000), 'sigma_sd':(0.001,1000)})

[docs]class MultinestRun(object): """This object controls a single simulated data set and its MultiNest analysis. This is a "master" class of ``dmdd`` that makes use of all other objects. It takes in experimental parameters, particle-physics parameters, and astrophysical parameters, and then generates a simulation (if it doesn't already exist), and prepares to perform ``MultiNest`` analysis of simulated data. It has methods to do a ``MultiNest`` run (:meth:``) and to visualize outputs (:meth:`.visualize()`). :class:`Model` used for simulation does not have to be the same as the :class:`Model` used for fitting. Simulated spectra from multiple experiments will be analyzed jointly if ``MultiNest`` run is initialized with a list of appropriate :class:`Experiment` objects. The likelihod function is an argument of the fitting model (:class:`Model` object); for UV models it is set to :func:`dmdd.rate_UV.loglikelihood`, and for models that would correspond to ``rate_genNR``, :func:`dmdd.rate_genNR.loglikelihood` should be used. Both likelihood functions include the Poisson factor, and (if ``energy_resolution=True`` of the :class:`Experiment` at hand) the factors that evaluate probability of each individual event (i.e. each recoil-energy measurement), given the fitting scattering model. MultiNest-related files produced by this object will go to a directory, under ``$DMDD_MAIN_PATH``, with the name defined by the parameters passed. This directory name will be accessible via ``self.chainspath`` after the object is initialized. :param sim_name: The name of the simulation (e.g. 'sim1') :type sim_name: ``str`` :param experiments: A list of :class:`Experiment` objects, or a single such object. :type experiments: ``list`` :param sim_model: The true underlying model for the simulations (name cannot have spaces). :type sim_model: :class:`Model` :param param_values: The values of the parameters for ``sim_model``. :type param_values: ``dict`` :param fit_model: The model for MultiNest to fit to the data. Does not have to be the same as ``sim_model``, but can be. Its name cannot have spaces. :type fit_model: :class:`Model` :param prior_ranges: Dictionary of prior ranges for parameters of fit_model. e.g. {'mass':(1,1000), 'sigma_si':(0.1,1e4), etc....} :type prior_ranges: ``dict`` :param prior: either 'logflat' or 'flat' :type prior: ``str`` :param sim_root: The path under which to store the simulations. :type sim_root: ``str`` :param chains_root: The path under which to store the Multinest chains. :type chains_root: ``str`` :param force_sim: If `True`, then redo the simulations no matter what. If `False`, then the simulations will be redone if and only if the given simulation parameters don't match what has already been simulated for this sim_name. :type force_sim: ``bool`` :param asimov: Do asimov simulations. Not currently implemented. :param nbins_asimov: Number of asimov bins. :param n_live_points,evidence_tolerance,sampling_efficiency,resume,basename: Parameters to pass to MultiNest, defined in the `PyMultiNest documentation <>`_. :param silent: If ``True``, then print messages will be suppressed. :param empty_run: if ``True``, then simulations are not initialized. """ def __init__(self, sim_name, experiments, sim_model, param_values, fit_model, prior_ranges, prior='logflat', sim_root=SIM_PATH, chains_root=CHAINS_PATH, force_sim=False, asimov=False, nbins_asimov=20, n_live_points=2000, evidence_tolerance=0.1, sampling_efficiency=0.3, resume=False, basename='1-', silent=False, empty_run=False): if type(experiments) == Experiment: experiments = [experiments] self.silent = silent self.sim_name = sim_name self.experiments = experiments self.sim_model = sim_model self.fit_model = fit_model self.param_values = param_values self.prior_ranges = prior_ranges self.prior = prior self.simulations = [] self.mn_params = {} self.mn_params['n_live_points'] = n_live_points self.mn_params['evidence_tolerance'] = evidence_tolerance self.mn_params['sampling_efficiency'] = sampling_efficiency self.mn_params['resume'] = resume self.mn_params['outputfiles_basename'] = basename self.asimov = asimov self.nbins_asimov = nbins_asimov #build folder names where chains are stored self.foldername = sim_name experiment_names = [ for ex in experiments] experiment_names.sort() for experiment in experiment_names: self.foldername += '_{}'.format(experiment) all_params = dict(param_values) for k in self.sim_model.fixed_params: all_params[k] = self.sim_model.fixed_params[k] all_param_names = self.sim_model.param_names + self.sim_model.fixed_params.keys() inds = np.argsort(all_param_names) sorted_param_names = np.array(all_param_names)[inds] sorted_param_values = [all_params[par] for par in sorted_param_names] for parname, parval in zip(sorted_param_names, sorted_param_values): self.foldername += '_{}_{:.2f}'.format(parname, parval) self.foldername += '_fitfor' inds = np.argsort(fit_model.param_names) sorted_fitparam_names = np.array(fit_model.param_names)[inds] for par in sorted_fitparam_names: self.foldername += '_{}'.format(par) if len(self.fit_model.fixed_params) > 0: self.foldername += '_fixed' keys = self.fit_model.fixed_params.keys() inds = np.argsort(keys) sorted_fixedparam_names = np.array(keys)[inds] sorted_fixedparam_values = [self.fit_model.fixed_params[par] for par in sorted_fixedparam_names] for parname, parval in zip(sorted_fixedparam_names, sorted_fixedparam_values): self.foldername += '_{}_{:.2f}'.format(parname, parval) self.foldername += '_{}_nlive{}'.format(prior,self.mn_params['n_live_points']) self.chainspath = '{}/{}/'.format(chains_root,self.foldername) self.chainsfile = self.chainspath + '/' + self.mn_params['outputfiles_basename'] + 'post_equal_weights.dat' if not empty_run: #make simulations, one for each experiment for experiment in experiments: self.simulations.append(Simulation(sim_name, experiment, sim_model, param_values, path=sim_root, force_sim=force_sim, asimov=asimov, nbins_asimov=nbins_asimov, silent=self.silent))
[docs] def return_chains_loglike(self): """ Returns MultiNest chains and equal-weighted posteriors. """ data = np.loadtxt(self.chainspath + '/' + self.mn_params['outputfiles_basename'] + 'post_equal_weights.dat') return data[:,:-1], data[:,-1]
[docs] def global_bestfit(self): """ Returns maximum a posteriori values for parameters. """ samples = np.loadtxt(self.chainsfile) posterior = samples[:,-1] max_index = posterior.argmax() return samples[max_index,:-1]
[docs] def loglikelihood_total(self,cube,ndim,nparams): """ Log-likelihood function used by MultiNest. :param cube, ndim, nparams: Params required by MulitNest. """ res = 0 fit_paramvals = {} for i in xrange(ndim): par = self.fit_model.param_names[i] fit_paramvals[par] = cube[i] for sim in self.simulations: kwargs = self.fit_model.default_rate_parameters.copy() for kw,val in fit_paramvals.iteritems(): kwargs[kw] = val for kw,val in sim.experiment.parameters.iteritems(): kwargs[kw] = val kwargs['energy_resolution'] = sim.experiment.energy_resolution res += self.fit_model.loglikelihood(sim.Q, sim.experiment.efficiency, **kwargs) return res
[docs] def logflat_prior(self, cube, ndim, nparams): """ Logflat prior, passed to MultiNest. Converts unit cube into correct parameter values based on log-flat prior within range defined by ``self.prior_ranges``. """ params = self.fit_model.param_names for i in xrange(ndim): # if the i-th param is fnfp, then the range # might go to negative values, must force flat prior: if params[i] in FNFP_PARAM_NAMES: cube_min,cube_max = self.prior_ranges[params[i]] cube[i] = cube[i] * (cube_max - cube_min) + cube_min else: cube_min,cube_max = self.prior_ranges[params[i]] pow = (np.log10(cube_max) - np.log10(cube_min))*cube[i] + np.log10(cube_min) cube[i] = 10**pow
[docs] def flat_prior(self, cube, ndim, nparams): """ Flat prior, passed to MultiNest. Converts unit cube into correct parameter values based on flat prior within range defined by ``self.prior_ranges``. """ params = self.fit_model.param_names for i in xrange(ndim): cube_min,cube_max = self.prior_ranges[params[i]] cube[i] = cube[i] * (cube_max - cube_min) + cube_min
[docs] def get_evidence(self): """ Returns evidence from stats file produced by MultiNest. """ filename = self.chainspath + self.mn_params['outputfiles_basename'] + 'stats.dat' try: fev = open(filename,'r') except IOError,e: print e return 0 line = fev.readline() line2 = fev.readline() line = line.split() line2 = line2.split() ln_evidence = float(line[5]) fev.close() return ln_evidence
[docs] def fit(self, force_run=False): """ Runs MultiNest; parameters set by object initialization. :param force_run: If ``True``, then fit will re-run; by default, it will not, unless the simulation data has changed, or chains don't exist. """ start = time.time() # make dictionary of things to be compared: # data for each simulation, multinest, and fitting parameters pickle_content = {} pickle_content['mn_params'] = self.mn_params del pickle_content['mn_params']['resume'] inds = np.argsort(self.fit_model.param_names) sorted_fitparam_names = np.array(self.fit_model.param_names)[inds] pickle_content['fit_param_names'] = sorted_fitparam_names pickle_content['fixed_params'] = self.fit_model.fixed_params pickle_content['prior'] = self.prior pickle_content['prior_ranges'] = {kw:self.prior_ranges[kw] for kw in self.fit_model.param_names} pickle_content['data'] = {} pickle_content['sim_folders'] = {} for sim in self.simulations: pickle_content['data'][] = sim.Q pickle_content['sim_folders'][] = sim.file_basename #define filename of pickle file: pickle_file = self.chainspath + 'run_parameters.pkl' stats_file = self.chainspath + self.mn_params['outputfiles_basename'] + 'stats.dat' chains_file = self.chainspath + self.mn_params['outputfiles_basename'] + 'post_equal_weights.dat' self.pickle_file = pickle_file self.stats_file = stats_file self.chains_file = chains_file if (not os.path.exists(chains_file)) or (not os.path.exists(pickle_file)) or (not os.path.exists(stats_file)): force_run = True print 'Chains, pickle, or stats file(s) not found. Forcing run.\n\n' else: fin = open(pickle_file,'rb') pickle_old = pickle.load(fin) fin.close() try: if not compare_dictionaries(pickle_old, pickle_content): force_run = True print 'Run pickle file not a match. Forcing run.\n\n' except: raise # if not all run params are as they need to be, force run. # if force_run is True, run MultiNest: if force_run: if os.path.exists(self.chainspath): shutil.rmtree(self.chainspath) os.makedirs(self.chainspath) cwd = os.getcwd() os.chdir(self.chainspath) #go where multinest chains will be; do this because that's how multinest works if self.prior == 'logflat': prior_function = self.logflat_prior elif self.prior == 'flat': prior_function = self.flat_prior else: raise ValueError('Unknown prior: {}'.format(self.prior)) nparams = len(self.fit_model.param_names), prior_function, nparams, **self.mn_params) #create pickle file with all info defining this run. fout = open(pickle_file,'wb') pickle.dump(pickle_content, fout) fout.close() os.chdir(cwd) # go back to whatever directory you were in before #check at the end that everything for created that was supposed to: #(this might not be the case, if you ran out of storage space, or if the run was interrupted in the middle.) if (not os.path.exists(chains_file)) or (not os.path.exists(pickle_file)) or (not os.path.exists(stats_file)): raise RuntimeError('for {}: chains file, or Multinest pickle file, or stats file still does not exist!\n\n'.format(self.chainspath)) end = time.time() if not self.silent: print '\n Fit took {:.12f} minutes.\n'.format((end - start) / 60.)
[docs] def visualize(self, **kwargs): """ Makes plots of data for each experiment with theoretical and best-fit models. Also makes 2-d posteriors for each fitted parameter vs. every other. These plots get saved to ``self.chainspath``. :param **kwargs: Keyword arguments passed to :func:`dmdd.dmdd_plot.plot_2d_posterior`. """ #make theory, data, and fit plots for each experiment: import dmdd_plot as dp fitmodel_dRdQ_params = self.fit_model.default_rate_parameters param_values = self.global_bestfit() if len(self.fit_model.fixed_params) > 0: for k,v in self.fit_model.fixed_params.iteritems(): fitmodel_dRdQ_params[k] = v for i,k in enumerate(self.fit_model.param_names): fitmodel_dRdQ_params[k] = param_values[i] for sim in self.simulations: filename = self.chainspath + '/{}_theoryfitdata_{}.pdf'.format(self.sim_name, Qbins, Qhist, xerr, yerr, Qbins_theory, Qhist_theory, binsize = sim.plot_data(make_plot=False, return_plot_items=True) fitmodel_dRdQ_params['element'] = sim.experiment.element fitmodel_dRdQ = sim.model.dRdQ(Qbins_theory,**fitmodel_dRdQ_params) Ntot = sim.N Qhist_fit = fitmodel_dRdQ*binsize*sim.experiment.exposure*YEAR_IN_S*sim.experiment.efficiency(Qbins_theory) if self.fit_model.modelname_tex is None: if in MODELNAME_TEX: fitmodel_title = MODELNAME_TEX[] else: fitmodel_title = if self.sim_model.modelname_tex is None: if in MODELNAME_TEX: simmodel_title = MODELNAME_TEX[] else: simmodel_title = dp.plot_theoryfitdata(Qbins, Qhist, xerr, yerr, Qbins_theory, Qhist_theory, Qhist_fit, filename=filename, save_file=True, Ntot=Ntot, fitmodel=fitmodel_title, simmodel=simmodel_title,, labelfont=18, legendfont=17,titlefont=20, mass=self.param_values['mass']) #make 2d posterior plots: samples = np.loadtxt(self.chainspath + self.mn_params['outputfiles_basename'] + 'post_equal_weights.dat') nparams = len(self.fit_model.param_names) if nparams > 1: for i,par in enumerate(self.fit_model.param_names): for j in np.arange(i+1,nparams): xlabel = PARAM_TEX[self.fit_model.param_names[i]] ylabel = PARAM_TEX[self.fit_model.param_names[j]] savefile = self.chainspath + '2d_posterior_{}_vs_{}.pdf'.format(self.fit_model.param_names[i], self.fit_model.param_names[j]) if (self.fit_model.param_names[i] in self.sim_model.param_names): input_x = self.param_values[self.fit_model.param_names[i]] elif (self.fit_model.param_names[i] in self.sim_model.fixed_params.keys()): input_x = self.sim_model.fixed_params[self.fit_model.param_names[i]] else: input_x = 0. if (self.fit_model.param_names[j] in self.sim_model.param_names): input_y = self.param_values[self.fit_model.param_names[j]] elif (self.fit_model.param_names[j] in self.sim_model.fixed_params.keys()): input_y = self.sim_model.fixed_params[self.fit_model.param_names[j]] else: input_y = 0. dp.plot_2d_posterior(samples[:,i], samples[:,j], input_x=input_x, input_y=input_y, savefile=savefile, xlabel=xlabel, ylabel=ylabel, **kwargs)
[docs]class Simulation(object): """ A simulation of dark-matter direct-detection data under a given experiment and scattering model. This object handles a single simulated data set (nuclear recoil energy spectrum). It is generaly initialized and used by the :class:`MultinestRun` object, but can be used stand-alone. Simulation data will only be generated if a simulation with the right parameters and name does not already exist, or if ``force_sim=True`` is provided upon :class:`Simulation` initialization; if the data exist, it will just be read in. (Data is a list of nuclear recoil energies of "observed" events.) Initializing :class:`Simulation` with given parameters for the first time will produce 3 files, located by default at ``$DMDD_PATH/simulations`` (or ``./simulations`` if ``$DMDD_PATH`` not defined): - .dat file with a list of nuclear-recoil energies (keV), drawn from a Poisson distribution with an expected number of events given by the underlying scattering model. - .pkl file with all relevant initialization parameters for record - .pdf plot of the simulated recoil-energy spectrum with simulated data points (with Poisson error bars) on top of the underlying model :param name: Identifier for simulation (e.g. 'sim1') :type name: ``str`` :param experiment: Experiment for simulation. :type experiment: :class:`Experiment` :param model: Model under which to simulate data. :type model: :class:`Model` :param parvals: Values of model parameters. Must contain the same parameters as ``model``. :type parvals: ``dict`` :param path: The path under which to store the simulations. :type path: ``str`` :param force_sim: If ``True``, then redo the simulations no matter what. If ``False``, then the simulations will be redone if and only if the given simulation parameters don't match what has already been simulated for this simulation name. :type force_sim: ``bool`` :param asimov: Do asimov simulations. Not currently implemented. :param nbins_asimov: Number of asimov bins. :param plot_nbins: Number of bins to bin data in for rate plot. :param plot_theory: Whether to plot the "true" theoretical rate curve along with the simulated data. :param silent: If ``True``, then print messages will be suppressed. """ def __init__(self, name, experiment, model, parvals, path=SIM_PATH, force_sim=False, asimov=False, nbins_asimov=20, plot_nbins=20, plot_theory=True, silent=False): self.silent = silent if not set(parvals.keys())==set(model.param_names): raise ValueError('Must pass parameter value dictionary corresponding exactly to model.param_names') self.model = model #underlying model self.experiment = experiment #build param_values from parvals self.param_values = [parvals[par] for par in model.param_names] self.param_names = list(self.model.param_names) for k,v in self.model.fixed_params.items(): self.param_values.append(v) self.param_names.append(k) = name self.path = path self.asimov = asimov self.nbins_asimov = nbins_asimov self.file_basename = '{}_{}'.format(name, inds = np.argsort(self.param_names) sorted_parnames = np.array(self.param_names)[inds] sorted_parvals = np.array(self.param_values)[inds] for parname, parval in zip(sorted_parnames, sorted_parvals): self.file_basename += '_{}_{:.2f}'.format(parname, parval) #calculate total expected rate dRdQ_params = model.default_rate_parameters.copy() allpars = model.default_rate_parameters.copy() allpars['simname'] = for i,par in enumerate(model.param_names): #model parameters dRdQ_params[par] = self.param_values[i] allpars[par] = self.param_values[i] for kw,val in experiment.parameters.iteritems(): #add experiment parameters allpars[kw] = val dRdQ_params['element'] = experiment.element self.dRdQ_params = dRdQ_params self.model_Qgrid = np.linspace(experiment.Qmin,experiment.Qmax,1000) efficiencies = experiment.efficiency(self.model_Qgrid) self.model_dRdQ = self.model.dRdQ(self.model_Qgrid,**dRdQ_params) R_integrand = self.model_dRdQ * efficiencies self.model_R = np.trapz(R_integrand,self.model_Qgrid) self.model_N = self.model_R * experiment.exposure * YEAR_IN_S #create dictionary of all parameters relevant to simulation self.allpars = allpars self.allpars['experiment'] = #record dictionary for relevant coupling normalizations only: norm_dict = {} for kw in model.param_names: if kw in PAR_NORMS: norm_dict[kw] = PAR_NORMS[kw] self.allpars['norms'] = norm_dict self.datafile = '{}/{}.dat'.format(self.path,self.file_basename) self.plotfile = '{}/{}.pdf'.format(self.path,self.file_basename) self.picklefile = '{}/{}.pkl'.format(self.path,self.file_basename) #control to make sure simulations are forced if they need to be if os.path.exists(self.picklefile) and os.path.exists(self.datafile): fin = open(self.picklefile,'rb') allpars_old = pickle.load(fin) fin.close() if not compare_dictionaries(self.allpars,allpars_old): print('Existing simulation does not match current parameters. Forcing simulation.\n\n') force_sim = True else: print 'Simulation data and/or pickle file does not exist. Forcing simulation.\n\n' force_sim = True if force_sim: if asimov: raise ValueError('Asimov simulations not yet implemented!') else: Q = self.simulate_data() np.savetxt(self.datafile,Q) fout = open(self.picklefile,'wb') pickle.dump(self.allpars,fout) fout.close() self.Q = np.atleast_1d(Q) self.N = len(self.Q) else: if asimov: raise ValueError('Asimov simulations not yet implemented!') else: Q = np.loadtxt(self.datafile) self.Q = np.atleast_1d(Q) self.N = len(self.Q) if asimov: raise ValueError('Asimov not yet implemented!') else: self.N = len(self.Q) if force_sim or (not os.path.exists(self.plotfile)): self.plot_data(plot_nbins=plot_nbins, plot_theory=plot_theory, save_plot=True) else: if not self.silent: print "simulation had %i events (expected %.0f)." % (self.N,self.model_N)
[docs] def simulate_data(self): """ Do Poisson simulation of data according to scattering model's dR/dQ. """ Nexpected = self.model_N if Nexpected > 0: npts = 10000 Nevents = poisson.rvs(Nexpected) Qgrid = np.linspace(self.experiment.Qmin,self.experiment.Qmax,npts) efficiency = self.experiment.efficiency(Qgrid) pdf = self.model.dRdQ(Qgrid,**self.dRdQ_params) * efficiency / self.model_R cdf = pdf.cumsum() cdf /= cdf.max() u = random.rand(Nevents) Q = np.zeros(Nevents) for i in np.arange(Nevents): Q[i] = Qgrid[np.absolute(cdf - u[i]).argmin()] else: Q = np.array([]) Nevents = 0 Nexpected = 0 if not self.silent: print "simulated: %i events (expected %.0f)." % (Nevents,Nexpected) return Q
[docs] def plot_data(self, plot_nbins=20, plot_theory=True, save_plot=True, make_plot=True, return_plot_items=False): """ Plot simuated data. :param plot_nbins: Number of bins for plotting. :param plot_theory: Whether to overplot the theory rate curve on top of the data points. :param save_plot: Whether to save plot under ``self.plotfile``. :param make_plot: Whether to make the plot. No reason really to ever be false unless you only want the "plot items" returned if ``return_plot_items=True`` is passed. :param return_plot_items: If ``True``, then function will return lots of things. """ Qhist,bins = np.histogram(self.Q,plot_nbins) Qbins = (bins[1:]+bins[:-1])/2. binsize = Qbins[1]-Qbins[0] #valid only for uniform gridding. Qwidths = (bins[1:]-bins[:-1])/2. xerr = Qwidths yerr = Qhist**0.5 Qhist_theory = self.model_dRdQ*binsize*self.experiment.exposure*YEAR_IN_S*self.experiment.efficiency(self.model_Qgrid) Qbins_theory = self.model_Qgrid if make_plot: import matplotlib.pyplot as plt plt.figure() plt.title('%s (total events = %i)' % (,self.N), fontsize=18) xlabel = 'Nuclear recoil energy [keV]' ylabel = 'Number of events' ax = plt.gca() fig = plt.gcf() xlabel = ax.set_xlabel(xlabel,fontsize=18) ylabel = ax.set_ylabel(ylabel,fontsize=18) if plot_theory: if in MODELNAME_TEX.keys(): label='True model ({})'.format(MODELNAME_TEX[]) else: label='True model' plt.plot(Qbins_theory, Qhist_theory,lw=3, color='blue', label=label) plt.errorbar(Qbins, Qhist,xerr=xerr,yerr=yerr,marker='o',color='black',linestyle='None',label='Simulated data') plt.legend(prop={'size':20},numpoints=1) if save_plot: plt.savefig(self.plotfile, bbox_extra_artists=[xlabel, ylabel], bbox_inches='tight') if return_plot_items: return Qbins, Qhist, xerr, yerr, Qbins_theory, Qhist_theory, binsize
[docs]class Model(object): """ A generic class describing a dark-matter scattering model. This object facilitates handling of a "hypothesis" that describes the scattering interaction at hand (to be used either to simulate recoil spectra, or to fit them). There is an option to give any parameter a fixed value, which will not be varied if the model is used to fit data. Subclassed by :class:`UV_Model`. :param name: Name of the model, matching the operator(s) name. It cannot have spaces. :type name: ``str`` :param param_names: Names of the parameters. :type param_names: ``list`` :param dRdQ_fn: Appropriate rate function. :type dRdQ_fn: ``function`` :param loglike_fn: Function that returns the log-likelihood of an array of event energies, given experimental and astrophysical parameters. Must take ``Q, eff_fn, **kwargs`` as arguments. :type loglike_fn: ``function`` :param default_rate_parameters: Default parameters to be passed to rate function. :type default_rate_parameters: ``dict`` :param tex_names: Dictionary of LaTeX names of parameters. :type tex_names: ``dict`` :param fixed_params: Parameters of model that are not intended to be fit for. :type fixed_params: ``dict`` """ def __init__(self, name, param_names, dRdQ_fn, loglike_fn, default_rate_parameters, tex_names=None, fixed_params=None, modelname_tex=None): """ fixed_params: dictionary tex_names is dictionary """ = name self.param_names = param_names self.dRdQ = dRdQ_fn self.loglikelihood = loglike_fn self.default_rate_parameters = default_rate_parameters if fixed_params is None: fixed_params = {} self.fixed_params = fixed_params for k,v in fixed_params.items(): self.default_rate_parameters[k] = v if tex_names is None: tex_names = {p:p for p in param_names} self.tex_names = tex_names self.modelname_tex = modelname_tex
[docs]class UV_Model(Model): """ Subclass of Model implementing UV-complete scattering models. Rate function and log-likelihood function are taken from the ``rate_UV`` module. """ def __init__(self,name,param_names,**kwargs): default_rate_parameters = dict(mass=50., sigma_si=0., sigma_sd=0., sigma_anapole=0., sigma_magdip=0., sigma_elecdip=0., sigma_LS=0., sigma_f1=0., sigma_f2=0., sigma_f3=0., sigma_si_massless=0., sigma_sd_massless=0., sigma_anapole_massless=0., sigma_magdip_massless=0., sigma_elecdip_massless=0., sigma_LS_massless=0., sigma_f1_massless=0., sigma_f2_massless=0., sigma_f3_massless=0., fnfp_si=1., fnfp_sd=1., fnfp_anapole=1., fnfp_magdip=1., fnfp_elecdip=1., fnfp_LS=1., fnfp_f1=1., fnfp_f2=1., fnfp_f3=1., fnfp_si_massless=1., fnfp_sd_massless=1., fnfp_anapole_massless=1., fnfp_magdip_massless=1., fnfp_elecdip_massless=1., fnfp_LS_massless=1., fnfp_f1_massless=1., fnfp_f2_massless=1., fnfp_f3_massless=1., v_lag=220., v_rms=220., v_esc=544., rho_x=0.3) Model.__init__(self,name,param_names, rate_UV.dRdQ, rate_UV.loglikelihood, default_rate_parameters, **kwargs)
[docs]class Experiment(object): """ An object representing a dark-matter direct-detection experiment. This object packages all the information that defines a single "experiment". For statistical analysis, a list of these objects is passed to initialize an instance of a :class:`MultinestRun` object, or to initialize an instance of a :class:`Simulation` object. It can also be used on its own to explore the capabilities of an experiment with given characteristics. Experiments set up here can either have perfect energy resolution in a given analysis window, or no resolution (controlled by the parameter ``energy_resolution``, default being ``True``). :param name: Name of experiment. :type name: ``str`` :param element: Detector target element. Only single-element targets currently supported. :type element: ``str`` :param Qmin,Qmax: Nuclear-recoil energy range of experiment [in keV]. :param exposure: Total exposure of experiment [kg-years]. :param efficiency_fn: Efficiency as a function of nuclear recoil energy. :type efficiency_fn: ``function`` :param tex_name: Optional; provide this if you want a specific tex name on plots. :type tex_name: ``str`` :param energy_resolution: If ``True``, then the energy of recoil events will be taken into account in likelihood analyses using this experiment; otherwise, not (e.g., for bubble-chamber experiments). :type energy_resolution: ``bool`` """ #pass the name of element instead of A, use natural isotope abundances for now. def __init__(self, name, element, Qmin, Qmax, exposure, efficiency_fn, tex_name=None, energy_resolution=True): """ Exposure in kg-yr """ #implement exps with multiple nuclei? self.energy_resolution = energy_resolution = name self.Qmin = Qmin self.Qmax = Qmax self.exposure = exposure self.element = element self.efficiency = efficiency_fn self.parameters = {'Qmin':Qmin, 'Qmax':Qmax, 'exposure':exposure, 'element':element} if tex_name is None: tex_name = name
[docs] def NminusNbg(self, sigma_val, sigma_name='sigma_si', fnfp_name='fnfp_si', fnfp_val=None, mass=50., Nbackground=4, v_esc=540., v_lag=220., v_rms=220., rho_x=0.3): """ Expected number of events minus background :param sigma_val: Scattering cross-section for interaction with proton [cm^2] :param sigma_name: Which sigma this corresponds to (i.e., which argument of :func:`rate_UV.R`) :type fnfp_name: ``str`` :param fnfp_name: Which fnfp to use. :type fnfp_name: ``str`` :param fnfp_val: Value of fnfp (optional). :param mass: Dark-matter particle mass in GeV. :param Nbackground: Number of background events expected. :param v_esc,v_lag,v_rms,rho_x: Passed to :func:`rate_UV.R`. """ kwargs = { 'mass': mass, sigma_name: sigma_val, 'v_lag': v_lag, 'v_rms': v_rms, 'v_esc': v_esc, 'rho_x': rho_x, 'element': self.element, 'Qmin': self.Qmin, 'Qmax': self.Qmax, } if fnfp_val is not None: kwargs[fnfp_name] = fnfp_val Nexpected = rate_UV.R(self.efficiency, **kwargs) * YEAR_IN_S * self.exposure return Nexpected - Nbackground
[docs] def sigma_limit(self, sigma_name='sigma_si', fnfp_name='fnfp_si', fnfp_val=None, mass=50., Nbackground=4, sigma_guess = 1.e10, mx_guess=1., v_esc=540., v_lag=220., v_rms=220., rho_x=0.3): """ Returns value of sigma at which expected number of dark-matter induced recoil events is equal to the number of expected background events, N = Nbg, in order to get a rough projected exclusion for this experiment. :param sigma_guess: Initial guess for solver. :param mx_guess: Initial guess for dark-matter particle mass in order to find the minimum mass detectable from experiment (:meth:`Experiment.find_min_mass`). For other arguments, see :meth:`Experiment.NminusNbg` """ if mass < self.find_min_mass(mx_guess = mx_guess): return np.inf res = fsolve(self.NminusNbg, sigma_guess, xtol=1e-3, args=(sigma_name, fnfp_name, fnfp_val, mass, Nbackground, v_esc, v_lag, v_rms, rho_x)) return res[0]
[docs] def sigma_exclusion(self, sigma_name, fnfp_name='fnfp_si', fnfp_val=None, mass_max=5000, Nbackground=4, mx_guess=1., sigma_guess=1.e10, v_esc=540., v_lag=220., v_rms=220., rho_x=0.3, mass_spacing='log', nmass_points=100, make_plot=False,ymax=None): """ Makes exclusion curve for a chosen sigma parameter. Calculates :meth:`Experiment.sigma_limit` for a grid of masses, and interpolates. :param sigma_name: Name of cross-section to exclude. :type sigma_name: ``str`` :param mass_spacing: 'log' (logarithmic) or 'lin' (linear) spacing for mass grid. :param nmass_points: Number of points to calculate for mass grid. :param make_plot: Whether to make the plot. If ``False``, then function will return arrays of ``mass, sigma``. :param ymax: Set the y maximum of plot axis. For other parameters, see :meth:`Experiment.sigma_limit` """ mass_min = self.find_min_mass(v_esc=v_esc, v_lag=v_lag, mx_guess=mx_guess) if mass_spacing=='lin': masses = np.linspace(mass_min, mass_max, nmass_points) else: masses = np.logspace(np.log10(mass_min), np.log10(mass_max), nmass_points) sigmas = np.zeros(nmass_points) for i,m in enumerate(masses): sigmas[i] = self.sigma_limit(sigma_name=sigma_name, fnfp_name=fnfp_name, fnfp_val=fnfp_val, mass=m, Nbackground=Nbackground,sigma_guess=sigma_guess, v_esc=v_esc, v_lag=v_lag, v_rms=v_rms, rho_x=rho_x) if make_plot: import matplotlib.pyplot as plt plt.figure() plt.loglog(masses, sigmas * PAR_NORMS[sigma_name], lw=3, color='k') plt.xlabel(PARAM_TEX['mass']) plt.ylabel(PARAM_TEX[sigma_name]) figtitle = 'Limits from {}'.format( if fnfp_val is not None: figtitle += ' (for $f_n/f_p = {}$)'.format(fnfp_val) plt.title(figtitle, fontsize=18) plt.ylim(ymax=ymax) return masses, sigmas
[docs] def VminusVesc(self, mx, v_esc=540., v_lag=220.): """ This function returns the value of the minimum velocity needed to produce recoil of energy Qmin, minus escape velocity in Galactic frame. See Eq 2.3 in (Gluscevic & Peter, 2014). Zero of this function gives minimal dark-matter particle mass mx that can be detected with this Experiment. This is usually called by :meth:`Experiment.find_min_mass`. :param mx: WIMP mass [GeV] :param v_esc: escape velocity in Galactic frame [km/sec] :param v_lag: rotational velocity of the Milky Way [km/sec] :return: Vmin - Vesc """ v_esc_lab = v_esc + v_lag mT = NUCLEAR_MASSES[self.element] q = self.Qmin / GEV_IN_KEV mu = mT * mx / ( mT + mx ) res = mT * q /( 2. * mu**2 ) - (v_esc_lab / C_KMSEC)**2. return res
[docs] def find_min_mass(self, v_esc=540., v_lag=220., mx_guess=1.): """ This finds the minimum dark-matter particle mass detectable with this experiment, by finding a zero of VminusVesc. :param mx_guess: guess-value [GeV]. Other parameters documented in :meth:`Experiment.VminusVesc`. """ res = fsolve(self.VminusVesc, mx_guess, xtol=1e-3, args=(v_esc, v_lag)) return res[0] ############################################ ############################################
def compare_dictionaries(d1,d2,debug=False,rtol=1e-5): """Returns True if dictionaries are identical; false if not. It works with multi-level dicts. If elements are arrays, then numpy's array compare is used """ if not set(d1.keys())==set(d2.keys()): if debug: print 'keys not equal.' print d1.keys(),d2.keys() return False for k in d1.keys(): if type(d1[k]) != type(d2[k]): return False elif type(d1[k])==dict: if not compare_dictionaries(d1[k],d2[k],rtol=rtol): if debug: print 'dictionaries not equal for {}.'.format(k) return False elif type(d1[k])==type(np.array([1,2])): if not np.all(d1[k]==d2[k]): if debug: print 'arrays for {} not equal:'.format(k) print d1[k], d2[k] return False #make sure floats are close in value, down to rtol relative precision: elif type(d1[k])==float: if not np.isclose(d1[k], d2[k], rtol=rtol): return False else: if d1[k] != d2[k]: if debug: 'values for {} not equal: {}, {}.'.format(k,d1[k],d2[k]) return False return True ############################################ ############################################ def Nexpected(element, Qmin, Qmax, exposure, efficiency, sigma_name, sigma_val, fnfp_name=None, fnfp_val=None, mass=50., v_esc=540., v_lag=220., v_rms=220., rho_x=0.3): """ NOTE: This is only set up for models in rate_UV. """ kwargs = { 'mass': mass, sigma_name: sigma_val, 'v_lag': v_lag, 'v_rms': v_rms, 'v_esc': v_esc, 'rho_x': rho_x, 'element': element, 'Qmin': Qmin, 'Qmax': Qmax } if (fnfp_val is not None) and (fnfp_name is not None): kwargs[fnfp_name] = fnfp_val res = rate_UV.R(efficiency, **kwargs) * YEAR_IN_S * exposure return res ############################################ ############################################