# Copyright (C) 2020 Alexander Nitz, 2022 Shichao Wu # This program is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by the # Free Software Foundation; either version 3 of the License, or (at your # option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General # Public License for more details. # # You should have received a copy of the GNU General Public License along # with this program; if not, write to the Free Software Foundation, Inc., # 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. """ This modules provides classes for evaluating PDF, logPDF, CDF and inverse CDF from external arbitrary distributions, and drawing samples from them. """ import importlib import numpy as np import scipy.integrate as scipy_integrate import scipy.interpolate as scipy_interpolate from pycbc import VARARGS_DELIM class External(object): """ Distribution defined by external cdfinv and logpdf functions To add to an inference configuration file: .. code-block:: ini [prior-param1+param2] name = external module = custom_mod logpdf = custom_function_name cdfinv = custom_function_name2 Or call `DistributionFunctionFromFile` in the .ini file: .. code-block:: ini [prior-param] name = external_func_fromfile module = pycbc.distributions.external file_path = path column_index = index logpdf = _logpdf cdfinv = _cdfinv Parameters ---------- params : list list of parameter names custom_mod : module module from which logpdf and cdfinv functions can be imported logpdf : function function which returns the logpdf cdfinv : function function which applies the invcdf Examples -------- To instantate by hand and example of function format. You must provide the logpdf function, and you may either provide the rvs or cdfinv function. If the cdfinv is provided, but not the rvs, the random values will be calculated using the cdfinv function. >>> import numpy >>> params = ['x', 'y'] >>> def logpdf(x=None, y=None): ... p = numpy.ones(len(x)) ... return p >>> >>> def cdfinv(**kwds): ... return kwds >>> e = External(['x', 'y'], logpdf, cdfinv=cdfinv) >>> e.rvs(size=10) """ name = "external" def __init__(self, params=None, logpdf=None, rvs=None, cdfinv=None, **kwds): self.params = params self.logpdf = logpdf self.cdfinv = cdfinv self._rvs = rvs if not (rvs or cdfinv): raise ValueError("Must provide either rvs or cdfinv") def rvs(self, size=1, **kwds): "Draw random value" if self._rvs: return self._rvs(size=size) samples = {param: np.random.uniform(0, 1, size=size) for param in self.params} return self.cdfinv(**samples) def apply_boundary_conditions(self, **params): return params def __call__(self, **kwds): return self.logpdf(**kwds) @classmethod def from_config(cls, cp, section, variable_args): tag = variable_args params = variable_args.split(VARARGS_DELIM) modulestr = cp.get_opt_tag(section, 'module', tag) if modulestr == "pycbc.distributions.external": file_path = cp.get_opt_tag(section, 'file_path', tag) mod = DistributionFunctionFromFile( file_path=file_path, column_index=cp.get_opt_tag(section, 'column_index', tag)) else: mod = importlib.import_module(modulestr) logpdfstr = cp.get_opt_tag(section, 'logpdf', tag) logpdf = getattr(mod, logpdfstr) cdfinv = rvs = None if cp.has_option_tag(section, 'cdfinv', tag): cdfinvstr = cp.get_opt_tag(section, 'cdfinv', tag) cdfinv = getattr(mod, cdfinvstr) if cp.has_option_tag(section, 'rvs', tag): rvsstr = cp.get_opt_tag(section, 'rvs', tag) rvs = getattr(mod, rvsstr) if modulestr == "pycbc.distributions.external": return cls(params=params, file_path=file_path, column_index=mod.column_index, rvs=rvs, cdfinv=cdfinv) return cls(params=params, logpdf=logpdf, rvs=rvs, cdfinv=cdfinv) class DistributionFunctionFromFile(External): r"""Evaluating PDF, logPDF, CDF and inverse CDF from the external density function. Instances of this class can be called like a distribution in the .ini file, when used with `pycbc.distributions.external.External`. Please see the example in the `External` class. Parameters ---------- parameter : {'file_path', 'column_index'} The path of the external density function's .txt file, and the column index of the density distribution. By default, the first column should be the values of a certain parameter, such as "mass", other columns should be the corresponding density values (as a function of that parameter). If you add the name of the parameter in the first row, please add the '#' at the beginning. \**kwargs : All other keyword args are passed to `scipy.integrate.quad` to control the numerical accuracy of the inverse CDF. If not be provided, will use the default values in `self.__init__`. Notes ----- This class is different from `pycbc.distributions.arbitrary.FromFile`, which needs samples from the hdf file to construct the PDF by using KDE. This class reads in any continuous functions of the parameter. """ name = "external_func_fromfile" def __init__(self, params=None, file_path=None, column_index=None, **kwargs): if kwargs.__contains__('cdfinv'): super().__init__(cdfinv=kwargs['cdfinv']) else: super().__init__(cdfinv=not None) self.params = params self.data = np.loadtxt(fname=file_path, unpack=True, comments='#') self.column_index = int(column_index) self.epsabs = kwargs.get('epsabs', 1.49e-05) self.epsrel = kwargs.get('epsrel', 1.49e-05) self.x_list = np.linspace(self.data[0][0], self.data[0][-1], 1000) self.interp = {'pdf': callable, 'cdf': callable, 'cdfinv': callable} if not file_path: raise ValueError("Must provide the path to density function file.") def _pdf(self, x, **kwargs): """Calculate and interpolate the PDF by using the given density function, then return the corresponding value at the given x.""" if self.interp['pdf'] == callable: func_unnorm = scipy_interpolate.interp1d( self.data[0], self.data[self.column_index]) norm_const = scipy_integrate.quad( func_unnorm, self.data[0][0], self.data[0][-1], epsabs=self.epsabs, epsrel=self.epsrel, limit=500, **kwargs)[0] self.interp['pdf'] = scipy_interpolate.interp1d( self.data[0], self.data[self.column_index]/norm_const) pdf_val = np.float64(self.interp['pdf'](x)) return pdf_val def _logpdf(self, x, **kwargs): """Calculate the logPDF by calling `pdf` function.""" return np.log(self._pdf(x, **kwargs)) def _cdf(self, x, **kwargs): """Calculate and interpolate the CDF, then return the corresponding value at the given x.""" if self.interp['cdf'] == callable: cdf_list = [] for x_val in self.x_list: cdf_x = scipy_integrate.quad( self._pdf, self.data[0][0], x_val, epsabs=self.epsabs, epsrel=self.epsrel, limit=500, **kwargs)[0] cdf_list.append(cdf_x) self.interp['cdf'] = \ scipy_interpolate.interp1d(self.x_list, cdf_list) cdf_val = np.float64(self.interp['cdf'](x)) return cdf_val def _cdfinv(self, **kwargs): """Calculate and interpolate the inverse CDF, then return the corresponding parameter value at the given CDF value.""" if self.interp['cdfinv'] == callable: cdf_list = [] for x_value in self.x_list: cdf_list.append(self._cdf(x_value)) self.interp['cdfinv'] = \ scipy_interpolate.interp1d(cdf_list, self.x_list) cdfinv_val = {list(kwargs.keys())[0]: np.float64( self.interp['cdfinv'](list(kwargs.values())[0]))} return cdfinv_val __all__ = ['External', 'DistributionFunctionFromFile']