# Licensed under a 3-clause BSD style license - see LICENSE.rst
import html
import itertools
import logging
import numpy as np
from astropy.table import Table
from gammapy.utils.pbar import progress_bar
from .covariance import Covariance
from .iminuit import (
confidence_iminuit,
contour_iminuit,
covariance_iminuit,
optimize_iminuit,
)
from .scipy import confidence_scipy, optimize_scipy
from .sherpa import optimize_sherpa
__all__ = ["Fit", "FitResult", "OptimizeResult", "CovarianceResult"]
log = logging.getLogger(__name__)
class Registry:
"""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(f"Unknown task {task!r}")
backend_options = cls.register[task]
if backend not in backend_options:
raise ValueError(f"Unknown backend {backend!r} for task {task!r}")
return backend_options[backend]
registry = Registry()
[docs]
class Fit:
"""Fit class.
The fit class provides a uniform interface to multiple fitting backends.
Currently available: "minuit", "sherpa" and "scipy".
Parameters
----------
backend : {"minuit", "scipy" "sherpa"}
Global backend used for fitting. Default is "minuit".
optimize_opts : dict
Keyword arguments passed to the optimizer. For the `"minuit"` backend
see https://iminuit.readthedocs.io/en/stable/reference.html#iminuit.Minuit
for a detailed description of the available options. If there is an entry
'migrad_opts', those options will be passed to `iminuit.Minuit.migrad()`.
For the `"sherpa"` backend you can from the options:
* `"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
For the `"scipy"` backend the available options are described in detail here:
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html
covariance_opts : dict
Covariance options passed to the given backend.
confidence_opts : dict
Extra arguments passed to the backend. E.g. `iminuit.Minuit.minos` supports
a ``maxcall`` option. For the scipy backend ``confidence_opts`` are forwarded
to `~scipy.optimize.brentq`. If the confidence estimation fails, the bracketing
interval can be adapted by modifying the upper bound of the interval (``b``) value.
store_trace : bool
Whether to store the trace of the fit.
"""
def __init__(
self,
backend="minuit",
optimize_opts=None,
covariance_opts=None,
confidence_opts=None,
store_trace=False,
):
self.store_trace = store_trace
self.backend = backend
if optimize_opts is None:
optimize_opts = {"backend": backend}
if covariance_opts is None:
covariance_opts = {"backend": backend}
if confidence_opts is None:
confidence_opts = {"backend": backend}
self.optimize_opts = optimize_opts
self.covariance_opts = covariance_opts
self.confidence_opts = confidence_opts
self._minuit = None
def _repr_html_(self):
try:
return self.to_html()
except AttributeError:
return f"<pre>{html.escape(str(self))}</pre>"
@staticmethod
def _parse_datasets(datasets):
from gammapy.datasets import Dataset, Datasets
if isinstance(datasets, (list, Dataset)):
datasets = Datasets(datasets)
return datasets, datasets.parameters
[docs]
def run(self, datasets):
"""Run all fitting steps.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
Returns
-------
fit_result : `FitResult`
Fit result.
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
optimize_result = self.optimize(datasets=datasets)
if self.backend not in registry.register["covariance"]:
log.warning("No covariance estimate - not supported by this backend.")
return FitResult(optimize_result=optimize_result)
covariance_result = self.covariance(
datasets=datasets, optimize_result=optimize_result
)
optimize_result.models.covariance = Covariance(
optimize_result.models.parameters, covariance_result.matrix
)
datasets._covariance = Covariance(parameters, covariance_result.matrix)
return FitResult(
optimize_result=optimize_result,
covariance_result=covariance_result,
)
[docs]
def optimize(self, datasets):
"""Run the optimization.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
Returns
-------
optimize_result : `OptimizeResult`
Optimization result.
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
datasets.parameters.check_limits()
if len(parameters.free_parameters.names) == 0:
raise ValueError("No free parameters for fitting")
parameters.autoscale()
kwargs = self.optimize_opts.copy()
backend = kwargs.pop("backend", self.backend)
compute = registry.get("optimize", backend)
# TODO: change this calling interface!
# probably should pass a fit statistic, which has a model, which has parameters
# and return something simpler, not a tuple of three things
factors, info, optimizer = compute(
parameters=parameters,
function=datasets.stat_sum,
store_trace=self.store_trace,
**kwargs,
)
if backend == "minuit":
self._minuit = optimizer
kwargs["method"] = "migrad"
trace = Table(info.pop("trace"))
if self.store_trace:
idx = [
parameters.index(par)
for par in parameters.unique_parameters.free_parameters
]
unique_names = np.array(datasets.models.parameters_unique_names)[idx]
trace.rename_columns(trace.colnames[1:], list(unique_names))
# Copy final results into the parameters object
parameters.set_parameter_factors(factors)
parameters.check_limits()
return OptimizeResult(
models=datasets.models.copy(),
total_stat=datasets.stat_sum(),
backend=backend,
method=kwargs.get("method", backend),
trace=trace,
minuit=optimizer,
**info,
)
[docs]
def covariance(self, datasets, optimize_result=None):
"""Estimate the covariance matrix.
Assumes that the model parameters are already optimised.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
optimize_result : `OptimizeResult`, optional
Optimization result. Can be optionally used to pass the state of the IMinuit object
to the covariance estimation. This might save computation time in certain cases.
Default is None.
Returns
-------
result : `CovarianceResult`
Results.
"""
datasets, unique_pars = self._parse_datasets(datasets=datasets)
parameters = datasets.models.parameters
kwargs = self.covariance_opts.copy()
if optimize_result is not None and optimize_result.backend == "minuit":
kwargs["minuit"] = optimize_result.minuit
backend = kwargs.pop("backend", self.backend)
compute = registry.get("covariance", backend)
with unique_pars.restore_status():
if self.backend == "minuit":
method = "hesse"
else:
method = ""
factor_matrix, info = compute(
parameters=unique_pars, function=datasets.stat_sum, **kwargs
)
matrix = Covariance.from_factor_matrix(
parameters=parameters, matrix=factor_matrix
)
datasets.models.covariance = matrix
if optimize_result:
optimize_result.models.covariance = matrix.data.copy()
return CovarianceResult(
backend=backend,
method=method,
success=info["success"],
message=info["message"],
matrix=matrix.data,
)
[docs]
def confidence(self, datasets, parameter, sigma=1, reoptimize=True):
"""Estimate confidence interval.
Extra ``kwargs`` are passed to the backend.
E.g. `iminuit.Minuit.minos` supports a ``maxcall`` option.
For the scipy backend ``kwargs`` are forwarded to `~scipy.optimize.brentq`. If the
confidence estimation fails, the bracketing interval can be adapted by modifying the
upper bound of the interval (``b``) value.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
parameter : `~gammapy.modeling.Parameter`
Parameter of interest.
sigma : float, optional
Number of standard deviations for the confidence level. Default is 1.
reoptimize : bool, optional
Re-optimize other parameters, when computing the confidence region.
Default is True.
Returns
-------
result : dict
Dictionary with keys "errp", 'errn", "success" and "nfev".
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
kwargs = self.confidence_opts.copy()
backend = kwargs.pop("backend", self.backend)
compute = registry.get("confidence", backend)
parameter = parameters[parameter]
with parameters.restore_status():
result = compute(
parameters=parameters,
parameter=parameter,
function=datasets.stat_sum,
sigma=sigma,
reoptimize=reoptimize,
**kwargs,
)
result["errp"] *= parameter.scale
result["errn"] *= parameter.scale
return result
[docs]
def stat_profile(self, datasets, parameter, reoptimize=False):
"""Compute fit statistic profile.
The method used is to vary one parameter, keeping all others fixed.
So this is taking a "slice" or "scan" of the fit statistic.
Notes
-----
The progress bar can be displayed for this function.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
parameter : `~gammapy.modeling.Parameter`
Parameter of interest. The specification for the scan, such as bounds
and number of values is taken from the parameter object.
reoptimize : bool, optional
Re-optimize other parameters, when computing the confidence region. Default is False.
Returns
-------
results : dict
Dictionary with keys "parameter_name_scan", "stat_scan" and "fit_results". The latter contains an
empty list, if `reoptimize` is set to False.
Examples
--------
>>> from gammapy.datasets import Datasets, SpectrumDatasetOnOff
>>> from gammapy.modeling.models import SkyModel, LogParabolaSpectralModel
>>> from gammapy.modeling import Fit
>>> datasets = Datasets()
>>> for obs_id in [23523, 23526]:
... dataset = SpectrumDatasetOnOff.read(
... f"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits"
... )
... datasets.append(dataset)
>>> datasets = datasets.stack_reduce(name="HESS")
>>> model = SkyModel(spectral_model=LogParabolaSpectralModel(), name="crab")
>>> datasets.models = model
>>> fit = Fit()
>>> result = fit.run(datasets)
>>> parameter = datasets.models.parameters['amplitude']
>>> stat_profile = fit.stat_profile(datasets=datasets, parameter=parameter)
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
parameter = parameters[parameter]
values = parameter.scan_values
stats = []
fit_results = []
with parameters.restore_status():
for value in progress_bar(values, desc="Scan values"):
parameter.value = value
if reoptimize:
parameter.frozen = True
result = self.optimize(datasets=datasets)
stat = result.total_stat
fit_results.append(result)
else:
stat = datasets.stat_sum()
stats.append(stat)
idx = datasets.parameters.index(parameter)
name = datasets.models.parameters_unique_names[idx]
return {
f"{name}_scan": values,
"stat_scan": np.array(stats),
"fit_results": fit_results,
}
[docs]
def stat_surface(self, datasets, x, y, reoptimize=False):
"""Compute fit statistic surface.
The method used is to vary two parameters, keeping all others fixed.
So this is taking a "slice" or "scan" of the fit statistic.
Caveat: This method can be very computationally intensive and slow
See also: `Fit.stat_contour`.
Notes
-----
The progress bar can be displayed for this function.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
x, y : `~gammapy.modeling.Parameter`
Parameters of interest.
reoptimize : bool, optional
Re-optimize other parameters, when computing the confidence region. Default is False.
Returns
-------
results : dict
Dictionary with keys "x_values", "y_values", "stat" and "fit_results".
The latter contains an empty list, if `reoptimize` is set to False.
Examples
--------
>>> from gammapy.datasets import Datasets, SpectrumDatasetOnOff
>>> from gammapy.modeling.models import SkyModel, LogParabolaSpectralModel
>>> from gammapy.modeling import Fit
>>> import numpy as np
>>> datasets = Datasets()
>>> for obs_id in [23523, 23526]:
... dataset = SpectrumDatasetOnOff.read(
... f"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits"
... )
... datasets.append(dataset)
>>> datasets = datasets.stack_reduce(name="HESS")
>>> model = SkyModel(spectral_model=LogParabolaSpectralModel(), name="crab")
>>> datasets.models = model
>>> par_alpha = datasets.models.parameters["alpha"]
>>> par_beta = datasets.models.parameters["beta"]
>>> par_alpha.scan_values = np.linspace(1.55, 2.7, 20)
>>> par_beta.scan_values = np.linspace(-0.05, 0.55, 20)
>>> fit = Fit()
>>> stat_surface = fit.stat_surface(
... datasets=datasets,
... x=par_alpha,
... y=par_beta,
... reoptimize=False,
... )
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
x = parameters[x]
y = parameters[y]
stats = []
fit_results = []
with parameters.restore_status():
for x_value, y_value in progress_bar(
itertools.product(x.scan_values, y.scan_values), desc="Trial values"
):
x.value, y.value = x_value, y_value
if reoptimize:
x.frozen, y.frozen = True, True
result = self.optimize(datasets=datasets)
stat = result.total_stat
fit_results.append(result)
else:
stat = datasets.stat_sum()
stats.append(stat)
shape = (len(x.scan_values), len(y.scan_values))
stats = np.array(stats).reshape(shape)
if reoptimize:
fit_results = np.array(fit_results).reshape(shape)
i1, i2 = datasets.parameters.index(x), datasets.parameters.index(y)
name_x = datasets.models.parameters_unique_names[i1]
name_y = datasets.models.parameters_unique_names[i2]
return {
f"{name_x}_scan": x.scan_values,
f"{name_y}_scan": y.scan_values,
"stat_scan": stats,
"fit_results": fit_results,
}
[docs]
def stat_contour(self, datasets, x, y, numpoints=10, sigma=1):
"""Compute stat contour.
Calls ``iminuit.Minuit.mncontour``.
This is a contouring algorithm for a 2D function
which is not simply the fit statistic function.
That 2D function is given at each point ``(par_1, par_2)``
by re-optimising all other free parameters,
and taking the fit statistic at that point.
Very compute-intensive and slow.
Parameters
----------
datasets : `Datasets` or list of `Dataset`
Datasets to optimize.
x, y : `~gammapy.modeling.Parameter`
Parameters of interest.
numpoints : int, optional
Number of contour points. Default is 10.
sigma : float, optional
Number of standard deviations for the confidence level. Default is 1.
Returns
-------
result : dict
Dictionary containing the parameter values defining the contour, with the
boolean flag "success" and the information objects from ``mncontour``.
Examples
--------
>>> from gammapy.datasets import Datasets, SpectrumDatasetOnOff
>>> from gammapy.modeling.models import SkyModel, LogParabolaSpectralModel
>>> from gammapy.modeling import Fit
>>> datasets = Datasets()
>>> for obs_id in [23523, 23526]:
... dataset = SpectrumDatasetOnOff.read(
... f"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits"
... )
... datasets.append(dataset)
>>> datasets = datasets.stack_reduce(name="HESS")
>>> model = SkyModel(spectral_model=LogParabolaSpectralModel(), name="crab")
>>> datasets.models = model
>>> fit = Fit(backend='minuit')
>>> optimize = fit.optimize(datasets)
>>> stat_contour = fit.stat_contour(
... datasets=datasets,
... x=model.spectral_model.alpha,
... y=model.spectral_model.amplitude,
... )
"""
datasets, parameters = self._parse_datasets(datasets=datasets)
x = parameters[x]
y = parameters[y]
i1, i2 = datasets.parameters.index(x), datasets.parameters.index(y)
name_x = datasets.models.parameters_unique_names[i1]
name_y = datasets.models.parameters_unique_names[i2]
with parameters.restore_status():
result = contour_iminuit(
parameters=parameters,
function=datasets.stat_sum,
x=x,
y=y,
numpoints=numpoints,
sigma=sigma,
)
x = result["x"] * x.scale
y = result["y"] * y.scale
return {
name_x: x,
name_y: y,
"success": result["success"],
}
class FitStepResult:
"""Fit result base class."""
def __init__(self, backend, method, success, message):
self._success = success
self._message = message
self._backend = backend
self._method = method
@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
@property
def success(self):
"""Fit success status flag."""
return self._success
@property
def message(self):
"""Optimizer status message."""
return self._message
def __str__(self):
return (
f"{self.__class__.__name__}\n\n"
f"\tbackend : {self.backend}\n"
f"\tmethod : {self.method}\n"
f"\tsuccess : {self.success}\n"
f"\tmessage : {self.message}\n"
)
def _repr_html_(self):
try:
return self.to_html()
except AttributeError:
return f"<pre>{html.escape(str(self))}</pre>"
def to_dict(self):
"""Convert to dictionary."""
return {
self.__class__.__name__: {
"backend": self.backend,
"method": self.method,
"success": self.success,
"message": self.message,
}
}
[docs]
class CovarianceResult(FitStepResult):
"""Covariance result object.
Parameters
----------
matrix : `~numpy.ndarray`, optional
The covariance matrix. Default is None.
kwargs : dict
Extra ``kwargs`` are passed to the backend.
"""
def __init__(self, matrix=None, **kwargs):
self._matrix = matrix
super().__init__(**kwargs)
@property
def matrix(self):
"""Covariance matrix as a `~numpy.ndarray`."""
return self._matrix
[docs]
class OptimizeResult(FitStepResult):
"""Optimize result object.
Parameters
----------
models : `~gammapy.modeling.models.DatasetModels`
Best fit models.
nfev : int
Number of function evaluations.
total_stat : float
Value of the fit statistic at minimum.
trace : `~astropy.table.Table`
Parameter trace from the optimisation.
minuit : `~iminuit.minuit.Minuit`, optional
Minuit object. Default is None.
kwargs : dict
Extra ``kwargs`` are passed to the backend.
"""
def __init__(self, models, nfev, total_stat, trace, minuit=None, **kwargs):
self._models = models
self._nfev = nfev
self._total_stat = total_stat
self._trace = trace
self._minuit = minuit
super().__init__(**kwargs)
@property
def minuit(self):
"""Minuit object."""
return self._minuit
@property
def parameters(self):
"""Best fit parameters."""
return self.models.parameters
@property
def models(self):
"""Best fit models."""
return self._models
@property
def trace(self):
"""Parameter trace from the optimisation."""
return self._trace
@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
def __str__(self):
string = super().__str__()
string += f"\tnfev : {self.nfev}\n"
string += f"\ttotal stat : {self.total_stat:.2f}\n\n"
return string
[docs]
def to_dict(self):
"""Convert to dictionary."""
output = super().to_dict()
output[self.__class__.__name__]["nfev"] = self.nfev
output[self.__class__.__name__]["total_stat"] = float(self._total_stat)
return output
[docs]
class FitResult:
"""Fit result class.
The fit result class provides the results from the optimisation and covariance of the fit.
Parameters
----------
optimize_result : `~OptimizeResult`
Result of the optimization step.
covariance_result : `~CovarianceResult`
Result of the covariance step.
"""
def __init__(self, optimize_result=None, covariance_result=None):
self._optimize_result = optimize_result
self._covariance_result = covariance_result
@property
def minuit(self):
"""Minuit object."""
return self.optimize_result.minuit
@property
def parameters(self):
"""Best fit parameters of the optimization step."""
return self.optimize_result.parameters
@property
def models(self):
"""Best fit parameters of the optimization step."""
return self.optimize_result.models
@property
def total_stat(self):
"""Total stat of the optimization step."""
return self.optimize_result.total_stat
@property
def trace(self):
"""Parameter trace of the optimisation step."""
return self.optimize_result.trace
@property
def nfev(self):
"""Number of function evaluations of the optimisation step."""
return self.optimize_result.nfev
@property
def backend(self):
"""Optimizer backend used for the fit."""
return self.optimize_result.backend
@property
def method(self):
"""Optimizer method used for the fit."""
return self.optimize_result.method
@property
def message(self):
"""Optimizer status message."""
return self.optimize_result.message
@property
def success(self):
"""Total success flag."""
success = self.optimize_result.success
if self.covariance_result:
success &= self.covariance_result.success
return success
@property
def optimize_result(self):
"""Optimize result."""
return self._optimize_result
@property
def covariance_result(self):
"""Optimize result."""
return self._covariance_result
[docs]
def write(
self,
path,
overwrite=False,
full_output=True,
overwrite_templates=False,
write_covariance=True,
checksum=False,
):
"""Write to file.
Parameters
----------
path : `pathlib.Path` or str
Path to write files.
overwrite : bool, optional
Overwrite existing file. Default is False.
full_output : bool, optional
Store full parameter output. Default is True.
overwrite_templates : bool, optional
Overwrite templates FITS files. Default is False.
checksum : bool, optional
When True adds a CHECKSUM entry to the file.
Default is False.
"""
from gammapy.modeling.models.core import _write_models
output = {}
if self.optimize_result is not None:
output.update(self.optimize_result.to_dict())
if self.covariance_result is not None:
output.update(self.covariance_result.to_dict())
_write_models(
self.models,
path,
overwrite,
full_output,
overwrite_templates,
write_covariance,
extra_dict=output,
)
def __str__(self):
string = ""
if self.optimize_result:
string += str(self.optimize_result)
if self.covariance_result:
string += str(self.covariance_result)
return string
def _repr_html_(self):
try:
return self.to_html()
except AttributeError:
return f"<pre>{html.escape(str(self))}</pre>"
