Source code for gammapy.utils.fitting.fit

# Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import absolute_import, division, print_function, unicode_literals
import logging
import abc
import numpy as np
from astropy.utils.misc import InheritDocstrings
from ...extern import six
from .iminuit import optimize_iminuit, covariance_iminuit, confidence_iminuit, mncontour
from .sherpa import optimize_sherpa, covariance_sherpa
from .scipy import optimize_scipy, covariance_scipy

__all__ = ["Fit"]

log = logging.getLogger(__name__)


class FitMeta(InheritDocstrings, abc.ABCMeta):
    pass


class Registry(object):
    """Registry of available backends for given tasks.

    Gives users the power to extend from their scripts.
    Used by `Fit` below.

    Not sure if we should call it "backend" or "method" or something else.
    Probably we will code up some methods, e.g. for profile analysis ourselves,
    using scipy or even just Python / Numpy?
    """

    register = {
        "optimize": {
            "minuit": optimize_iminuit,
            "sherpa": optimize_sherpa,
            "scipy": optimize_scipy,
        },
        "covariance": {
            "minuit": covariance_iminuit,
            "sherpa": covariance_sherpa,
            "scipy": covariance_scipy,
        },
        "confidence": {
            "minuit": confidence_iminuit,
            # "sherpa": confidence_sherpa,
            # "scipy": confidence_scipy,
        },
    }

    @classmethod
    def get(cls, task, backend):
        if task not in cls.register:
            raise ValueError("Unknown task {!r}".format(task))

        task = cls.register[task]

        if backend not in task:
            raise ValueError("Unknown method {!r} for task {!r}".format(task, backend))

        return task[backend]


registry = Registry()


[docs]@six.add_metaclass(FitMeta) class Fit(object): """Abstract Fit base class. """
[docs] @abc.abstractmethod def total_stat(self, parameters): """Total likelihood given the current model parameters""" pass
# TODO: probably we should change the `Fit` class to be coupled # to a likelihood object, not a model object # To facilitate this evolution, we centralise the coupling # in this property in a single place, # and only use `parameters` from `Fit`, not `model`. @property def _parameters(self): return self._model.parameters
[docs] def run(self, optimize_opts=None, covariance_opts=None): """ Run all fitting steps. Parameters ---------- optimize_opts : dict Options passed to `Fit.optimize`. covariance_opts : dict Options passed to `Fit.covariance`. Returns ------- fit_result : `FitResult` Results """ if optimize_opts is None: optimize_opts = {} optimize_result = self.optimize(**optimize_opts) if covariance_opts is None: covariance_opts = {} covariance_opts.setdefault("backend", "minuit") if covariance_opts["backend"] not in registry.register["covariance"]: log.warning("No covariance estimate - not supported by this backend.") return optimize_result covariance_result = self.covariance(**covariance_opts) # TODO: not sure how best to report the results # back or how to form the FitResult object. optimize_result._model = covariance_result.model optimize_result._success = optimize_result.success and covariance_result.success optimize_result._nfev += covariance_result.nfev return optimize_result
[docs] def optimize(self, backend="minuit", **kwargs): """Run the optimization. Parameters ---------- backend : str Which backend to use (see ``gammapy.utils.fitting.registry``) **kwargs : dict Keyword arguments passed to the optimizer. For the `"minuit"` backend see https://iminuit.readthedocs.io/en/latest/api.html#iminuit.Minuit for a detailed description of the available options. For the `"sherpa"` backend you can from the options `method = {"simplex", "levmar", "moncar", "gridsearch"}` Those methods are described and compared in detail on http://cxc.cfa.harvard.edu/sherpa/methods/index.html. The available options of the optimization methods are described on the following pages in detail: * http://cxc.cfa.harvard.edu/sherpa/ahelp/neldermead.html * http://cxc.cfa.harvard.edu/sherpa/ahelp/montecarlo.html * http://cxc.cfa.harvard.edu/sherpa/ahelp/gridsearch.html * http://cxc.cfa.harvard.edu/sherpa/ahelp/levmar.html Returns ------- fit_result : `FitResult` Results """ parameters = self._parameters if parameters.apply_autoscale: parameters.autoscale() compute = registry.get("optimize", backend) # TODO: change this calling interface! # probably should pass a likelihood, which has a model, which has parameters # and return something simpler, not a tuple of three things factors, info, optimizer = compute( parameters=parameters, function=self.total_stat, **kwargs ) # TODO: Change to a stateless interface for minuit also, or if we must support # stateful backends, put a proper, backend-agnostic solution for this. # As preliminary solution would like to provide a possibility that the user # can access the Minuit object, because it features a lot useful functionality if backend == "minuit": self.minuit = optimizer # Copy final results into the parameters object parameters.set_parameter_factors(factors) return FitResult( model=self._model, total_stat=self.total_stat(self._model.parameters), backend=backend, method=kwargs.get("method", backend), **info )
[docs] def covariance(self, backend="minuit"): """Estimate the covariance matrix. Assumes that the model parameters are already optimised. Parameters ---------- backend : str Which backend to use (see ``gammapy.utils.fitting.registry``) Returns ------- result : `CovarianceResult` Results """ compute = registry.get("covariance", backend) parameters = self._parameters # TODO: wrap MINUIT in a stateless backend with parameters.restore_values: if backend == "minuit": if hasattr(self, "minuit"): covariance_factors, info = compute(self.minuit) else: raise RuntimeError("To use minuit, you must first optimize.") else: function = self.total_stat covariance_factors, info = compute(parameters, function) parameters.set_covariance_factors(covariance_factors) # TODO: decide what to return, and fill the info correctly! return CovarianceResult(model=self._model, success=info["success"], nfev=0)
[docs] def confidence(self, parameter, backend="minuit", sigma=1, **kwargs): """Estimate confidence interval. Extra ``kwargs`` are passed to the backend. E.g. `iminuit.Minuit.minos` supports a ``maxcall`` option. Parameters ---------- backend : str Which backend to use (see ``gammapy.utils.fitting.registry``) parameter : `~gammapy.utils.fitting.Parameter` Parameter of interest sigma : float Number of standard deviations for the confidence level Returns ------- result : dict Dictionary with keys "errp", 'errn", "success" and "nfev". """ compute = registry.get("confidence", backend) parameters = self._parameters parameter = parameters[parameter] # TODO: wrap MINUIT in a stateless backend with parameters.restore_values: if backend == "minuit": if hasattr(self, "minuit"): # This is ugly. We will access parameters and make a copy # from the backend, to avoid modifying the state result = compute( self.minuit, parameters, parameter, sigma, **kwargs ) else: raise RuntimeError("To use minuit, you must first optimize.") else: raise NotImplementedError() errp = parameter.scale * result["errp"] errn = parameter.scale * result["errn"] return { "errp": errp, "errn": errn, "success": result["success"], "nfev": result["nfev"], }
[docs] def likelihood_profile(self, parameter, values=None, bounds=2, nvalues=11): """Compute likelihood profile. The method used is to vary one parameter, keeping all others fixed. So this is taking a "slice" or "scan" of the likelihood. See also: `Fit.minos_profile`. Parameters ---------- parameter : `~gammapy.utils.fitting.Parameter` Parameter of interest values : `~astropy.units.Quantity` (optional) Parameter values to evaluate the likelihood for. bounds : int or tuple of float When an `int` is passed the bounds are computed from `bounds * sigma` from the best fit value of the parameter, where `sigma` corresponds to the one sigma error on the parameter. If a tuple of floats is given those are taken as the min and max values and `nvalues` are linearly spaced between those. nvalues : int Number of parameter grid points to use. Returns ------- results : dict Dictionary with keys "values" and "likelihood". """ parameters = self._parameters parameter = parameters[parameter] if values is None: if isinstance(bounds, tuple): parmin, parmax = bounds else: parerr = parameters.error(parameter) parval = parameter.value parmin, parmax = parval - bounds * parerr, parval + bounds * parerr values = np.linspace(parmin, parmax, nvalues) likelihood = [] with parameters.restore_values: for value in values: parameter.value = value stat = self.total_stat(parameters) likelihood.append(stat) return {"values": values, "likelihood": np.array(likelihood)}
[docs] def minos_profile(self): """Compute MINOS profile. The method used is to vary one parameter, then re-optimise all other free parameters and to take the likelihood at that point. See also: `Fit.likelihood_profile` Calls ``iminuit.Minuit.mnprofile`` """ raise NotImplementedError
[docs] def likelihood_contour(self): """Compute likelihood contour. The method used is to vary two parameters, keeping all others fixed. So this is taking a "slice" or "scan" of the likelihood. See also: `Fit.minos_contour` Parameters ---------- TODO Returns ------- TODO """ raise NotImplementedError
[docs] def minos_contour(self, x, y, numpoints=10, sigma=1.0): """Compute MINOS contour. Calls ``iminuit.Minuit.mncontour``. This is a contouring algorithm for a 2D function which is not simply the likelihood function. That 2D function is given at each point ``(par_1, par_2)`` by re-optimising all other free parameters, and taking the likelihood at that point. Very compute-intensive and slow. Parameters ---------- x, y : `~gammapy.utils.fitting.Parameter` Parameters of interest numpoints : int Number of contour points sigma : float Number of standard deviations for the confidence level Returns ------- result : dict Dictionary with keys "x", "y" (Numpy arrays with contour points) and a boolean flag "success". The result objects from ``mncontour`` are in the additional keys "x_info" and "y_info". """ parameters = self._parameters x = parameters[x] y = parameters[y] with parameters.restore_values: result = mncontour(self.minuit, parameters, x, y, numpoints, sigma) x = result["x"] * x.scale y = result["y"] * y.scale return { "x": x, "y": y, "success": result["success"], "x_info": result["x_info"], "y_info": result["y_info"], }
class CovarianceResult(object): """Covariance result object.""" def __init__(self, model, success, nfev): self._model = model self._success = success self._nfev = nfev @property def model(self): """Best fit model.""" return self._model @property def success(self): """Fit success status flag.""" return self._success @property def nfev(self): """Number of function evaluations.""" return self._nfev class FitResult(object): """Fit result object.""" def __init__(self, model, success, nfev, total_stat, message, backend, method): self._model = model self._success = success self._nfev = nfev self._total_stat = total_stat self._message = message self._backend = backend self._method = method @property def model(self): """Best fit model.""" return self._model @property def success(self): """Fit success status flag.""" return self._success @property def nfev(self): """Number of function evaluations.""" return self._nfev @property def total_stat(self): """Value of the fit statistic at minimum.""" return self._total_stat @property def message(self): """Optimizer status message.""" return self._message @property def backend(self): """Optimizer backend used for the fit.""" return self._backend @property def method(self): """Optimizer method used for the fit.""" return self._method def __repr__(self): str_ = self.__class__.__name__ str_ += "\n\n" str_ += "\tbackend : {}\n".format(self.backend) str_ += "\tmethod : {}\n".format(self.method) str_ += "\tsuccess : {}\n".format(self.success) str_ += "\tnfev : {}\n".format(self.nfev) str_ += "\ttotal stat : {:.2f}\n".format(self.total_stat) str_ += "\tmessage : {}\n".format(self.message) return str_