#
# Copyright (C) 2009, 2015, 2016, 2018, 2019, 2020, 2021, 2022
# Smithsonian Astrophysical Observatory
#
#
# 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.
#
import logging
import os
import signal
from functools import wraps
import numpy as np
from numpy import arange, array, abs, iterable, sqrt, where, \
ones_like, isnan, isinf, any
from sherpa.utils import NoNewAttributesAfterInit, print_fields, erf, \
bool_cast, is_in, is_iterable, list_to_open_interval, sao_fcmp
from sherpa.utils.err import FitErr, EstErr, SherpaErr
from sherpa.utils import formatting
from sherpa.data import DataSimulFit
from sherpa.estmethods import Covariance, EstNewMin
from sherpa.models import SimulFitModel
from sherpa.optmethods import LevMar, NelderMead
from sherpa.stats import Chi2, Chi2Gehrels, Cash, Chi2ModVar, \
LeastSq, Likelihood
warning = logging.getLogger(__name__).warning
info = logging.getLogger(__name__).info
__all__ = ('FitResults', 'ErrorEstResults', 'Fit')
def evaluates_model(func):
"""Fit object decorator that runs model startup() and teardown()
"""
@wraps(func)
def run(fit, *args, **kwargs):
cache = kwargs.pop('cache', True)
fit.model.startup(cache=cache)
result = func(fit, *args, **kwargs)
fit.model.teardown()
return result
return run
[docs]class StatInfoResults(NoNewAttributesAfterInit):
"""A summary of the current statistic value for one or more data sets.
Attributes
----------
name : str
The name of the data set, or sets.
ids : sequence of int or str
The data set ids (it may be a tuple or array) included in the
results.
bkg_ids: sequence of int or str, or None
The background data set ids (it may be a tuple or array)
included in the results, if any.
statname : str
The name of the statistic function.
statval : number
The statistic value.
numpoints : int
The number of bins used in the fits.
dof: int
The number of degrees of freedom in the fit (the number of
bins minus the number of free parameters).
qval: number or None
The Q-value (probability) that one would observe the reduced
statistic value, or a larger value, if the assumed model is
true and the current model parameters are the true parameter
values. This will be `None` if the value can not be calculated
with the current statistic (e.g. the Cash statistic).
rstat: number or None
The reduced statistic value (the `statval` field divided by
`dof`). This is not calculated for all statistics.
"""
# The fields to include in the __str__ output.
_fields = ('name', 'ids', 'bkg_ids', 'statname', 'statval',
'numpoints', 'dof', 'qval', 'rstat')
def __init__(self, statname, statval, numpoints, model, dof,
qval=None, rstat=None):
self.name = ''
self.ids = None
self.bkg_ids = None
self.statname = statname
self.statval = statval
self.numpoints = numpoints
self.model = model
self.dof = dof
self.qval = qval
self.rstat = rstat
def __repr__(self):
return '<Statistic information results instance>'
def __str__(self):
return print_fields(self._fields, vars(self))
def _repr_html_(self):
"""Return a HTML (string) representation of the statistics."""
return html_statinfo(self)
def _cleanup_chi2_name(stat, data):
"""Simplify the chi-square name if possible.
Returns the statistic name for reporting fit results, simplifying
the chi-square name (e.g. chi2gehrels) when possible.
Parameters
----------
stat : `sherpa.stats.Stat`
data : `sherpa.data.Data` or `sherpa.data.DataSimulFit`
Returns
-------
name : str
The statistic name (will be 'chi2' if possible)
"""
if isinstance(stat, LeastSq) or not isinstance(stat, Chi2):
return stat.name
if isinstance(data, DataSimulFit):
is_error_set = [d.staterror is not None
for d in data.datasets]
if all(is_error_set):
return 'chi2'
elif data.staterror is not None:
return 'chi2'
return stat.name
[docs]class FitResults(NoNewAttributesAfterInit):
"""The results of a fit.
This object contains the parameter values, information on the
statistic and optimisation-method used, and other relevant
information.
.. versionchanged:: 4.10.1
The ``covarerr`` attribute has been renamed to ``covar``
and now contains the covariance matrix estimated at the
best-fit location, if provided by the optimiser.
Attributes
----------
datasets : sequence of int or str, or None
A sequence of the data set ids included in the results.
itermethodname : str or None
What iterated-fit scheme was used, if any.
methodname : str
The name of the optimisation method used (in lower case).
statname : str
The name of the statistic function.
succeeded : bool
Was the fit successful (did it converge)?
parnames : tuple of str
the parameter names that were varied in the fit
(the thawed parameters in the model expression).
parvals : tuple of number
The parameter values, in the same order as `parnames`.
statval : number
The statistic value after the fit.
istatval : number
The statistic value at the start of the fit.
dstatval : number
The change in the statistic value (``istatval - statval``).
numpoints : int
The number of bins used in the fits.
dof : int
The number of degrees of freedom in the fit (the number of
bins minus the number of free parameters).
qval : number or None
The Q-value (probability) that one would observe the reduced
statistic value, or a larger value, if the assumed model is
true and the current model parameters are the true parameter
values. This will be `None` if the value can not be calculated
with the current statistic (e.g. the Cash statistic).
rstat : number or None
The reduced statistic value (the `statval` field divided by
`dof`). This is not calculated for all statistics.
message : str
A message about the results of the fit (e.g. if the fit was
unable to converge). The format and contents depend on the
optimisation method.
nfev : int
The number of model evaluations made during the fit.
extra_output
The ``extra_output`` field from the fit.
covar : tuple or None
The covariance matrix from the best-fit location, if provided
by the optimiser.
modelvals : `array`
The values of the best-fit model evaluated for the data.
"""
# The fields to include in the __str__ output.
_fields = ('datasets', 'itermethodname', 'methodname', 'statname',
'succeeded', 'parnames', 'parvals', 'statval', 'istatval',
'dstatval', 'numpoints', 'dof', 'qval', 'rstat', 'message',
'nfev')
def __init__(self, fit, results, init_stat, param_warnings):
_vals = fit.data.eval_model_to_fit(fit.model)
_dof = len(_vals) - len(tuple(results[1]))
_covar = results[4].get('covar')
_rstat, _qval = fit.stat.goodness_of_fit(results[2], _dof)
self.succeeded = results[0]
self.parnames = tuple(p.fullname for p in fit.model.pars
if not p.frozen)
self.parvals = tuple(results[1])
self.istatval = init_stat
self.statval = results[2]
self.dstatval = abs(results[2] - init_stat)
self.numpoints = len(_vals)
self.dof = _dof
self.qval = _qval
self.rstat = _rstat
self.message = results[3]
self.covar = _covar
self.nfev = results[4].get('nfev')
self.extra_output = results[4]
self.modelvals = _vals
self.methodname = type(fit.method).__name__.lower()
self.itermethodname = fit._iterfit.itermethod_opts['name']
statname = _cleanup_chi2_name(fit.stat, fit.data)
self.statname = statname
self.datasets = None # To be filled by calling function
self.param_warnings = param_warnings
NoNewAttributesAfterInit.__init__(self)
def __setstate__(self, state):
self.__dict__.update(state)
if 'itermethodname' not in state:
self.__dict__['itermethodname'] = 'none'
def __nonzero__(self):
return self.succeeded
def __repr__(self):
return '<Fit results instance>'
def __str__(self):
return print_fields(self._fields, vars(self))
def _repr_html_(self):
"""Return a HTML (string) representation of the fit results."""
return html_fitresults(self)
[docs]class ErrorEstResults(NoNewAttributesAfterInit):
"""The results of an error estimation run.
This object contains the parameter ranges, information on the
statistic and optimisation-method used, and other relevant
information.
Attributes
----------
datasets : sequence of int or str, or `None`
A sequence of the data set ids included in the results.
methodname : str
The name of the optimisation method used (in lower case).
itermethodname : str or `None`
What iterated-fit scheme was used, if any.
fitname : str
The name of the method used to fit the data, in lower case.
statname : str
The name of the statistic used to fit the data, in lower case.
sigma : number
The error values represent this number of sigma (assuming a
Gaussian distribution).
percent : number
The percentage value for the errors (calculated from the
``sigma`` value assuming Gaussian errors).
parnames : tuple of str
the parameter names that were varied in the fit
(the thawed parameters in the model expression).
parvals : tuple of number
The parameter values, in the same order as `parnames`.
parmins : tuple of number
The parameter minimum values, in the same order as `parnames`.
parmaxes : tuple of number
The parameter maximum values, in the same order as `parnames`.
nfits : int
The number of fits performed during the error analysis.
extra_output
The ``extra_output`` field from the fit.
"""
# The fields to include in the __str__ output.
_fields = ('datasets', 'methodname', 'iterfitname', 'fitname', 'statname',
'sigma', 'percent', 'parnames', 'parvals', 'parmins',
'parmaxes', 'nfits')
def __init__(self, fit, results, parlist=None):
if parlist is None:
parlist = [p for p in fit.model.pars if not p.frozen]
from sherpa.estmethods import est_hardmin, est_hardmax, \
est_hardminmax
warning_hmin = "hard minimum hit for parameter "
warning_hmax = "hard maximum hit for parameter "
self.datasets = None # To be set by calling function
self.methodname = type(fit.estmethod).__name__.lower()
self.iterfitname = fit._iterfit.itermethod_opts['name']
self.fitname = type(fit.method).__name__.lower()
self.statname = type(fit.stat).__name__.lower()
self.sigma = fit.estmethod.sigma
self.percent = erf(self.sigma / sqrt(2.0)) * 100.0
self.parnames = tuple(p.fullname for p in parlist if not p.frozen)
self.parvals = tuple(p.val for p in parlist if not p.frozen)
self.parmins = ()
self.parmaxes = ()
self.nfits = 0
for i in range(len(parlist)):
if (results[2][i] == est_hardmin or
results[2][i] == est_hardminmax):
self.parmins = self.parmins + (None,)
warning(warning_hmin + self.parnames[i])
else:
self.parmins = self.parmins + (results[0][i],)
if (results[2][i] == est_hardmax or
results[2][i] == est_hardminmax):
self.parmaxes = self.parmaxes + (None,)
warning(warning_hmax + self.parnames[i])
else:
self.parmaxes = self.parmaxes + (results[1][i],)
self.nfits = results[3]
self.extra_output = results[4]
NoNewAttributesAfterInit.__init__(self)
def __setstate__(self, state):
self.__dict__.update(state)
if 'iterfitname' not in state:
self.__dict__['iterfitname'] = 'none'
def __repr__(self):
return '<%s results instance>' % self.methodname
def __str__(self):
return print_fields(self._fields, vars(self))
def _repr_html_(self):
"""Return a HTML (string) representation of the error estimates."""
return html_errresults(self)
[docs]class IterFit(NoNewAttributesAfterInit):
def __init__(self, data, model, stat, method, itermethod_opts=None):
if itermethod_opts is None:
itermethod_opts = {'name': 'none'}
# Even if there is only a single data set, I will
# want to treat the data and models I am given as
# collections of data and models -- so, put data and
# models into the objects needed for simultaneous fitting,
# if they are not already in such objects.
self.data = data
if type(data) is not DataSimulFit:
self.data = DataSimulFit('simulfit data', (data,))
self.model = model
if type(model) is not SimulFitModel:
self.model = SimulFitModel('simulfit model', (model,))
self.stat = stat
self.method = method
# Data set attributes needed to store fitting values between
# calls to fit
self._dep = None
# self.extra_args = None
self._staterror = None
self._syserror = None
self._nfev = 0
self._file = None
# Options to send to iterative fitting method
self.itermethod_opts = itermethod_opts
self.iterate = False
self.funcs = {'sigmarej': self.sigmarej}
self.current_func = None
if itermethod_opts['name'] != 'none':
self.current_func = self.funcs[itermethod_opts['name']]
self.iterate = True
# SIGINT (i.e., typing ctrl-C) can dump the user to the Unix prompt,
# when signal is sent from G95 compiled code. What we want is to
# get to the Sherpa prompt instead. Typically the user only thinks
# to interrupt during long fits or projection, so look for SIGINT
# here, and if it happens, raise the KeyboardInterrupt exception
# instead of aborting.
def _sig_handler(self, signum, frame):
raise KeyboardInterrupt()
def _get_callback(self, outfile=None, clobber=False):
if len(self.model.thawedpars) == 0:
raise FitErr('nothawedpar')
# support Sherpa use with SAMP
try:
signal.signal(signal.SIGINT, self._sig_handler)
except ValueError as e:
warning(e)
self._dep, self._staterror, self._syserror = self.data.to_fit(
self.stat.calc_staterror)
# self.extra_args = self.get_extra_args(self._dep)
self._nfev = 0
if outfile is not None:
if not clobber and os.path.isfile(outfile):
raise FitErr('noclobererr', outfile)
self._file = open(outfile, 'w')
names = ['# nfev statistic']
names.extend(['%s' % par.fullname for par in self.model.pars
if not par.frozen])
print(' '.join(names), file=self._file)
def cb(pars):
# We need to store the new parameter values in order to support
# linked parameters
self.model.thawedpars = pars
stat = self.stat.calc_stat(self.data, self.model)
if self._file is not None:
vals = ['%5e %5e' % (self._nfev, stat[0])]
vals.extend(['%5e' % val for val in self.model.thawedpars])
print(' '.join(vals), file=self._file)
self._nfev += 1
return stat
return cb
[docs] def sigmarej(self, statfunc, pars, parmins, parmaxes, statargs=(),
statkwargs=None, cache=True):
"""Exclude points that are significately far away from the best fit.
The `sigmarej` scheme is based on the IRAF ``sfit`` function
[3]_, where after a fit data points are excluded if the value
of ``(data-model) / error`` exceeds a threshold, and the data
re-fit. This removal of data points continues until the fit
has converged or a maximum number of iterations has been reached.
The error removal can be asymmetric, since there are separate
options for the lower and upper limits.
Raises
------
`sherpa.utils.err.FitErr`
This exception is raised if the statistic is not
supported. This method can only be used with
Chi-Square statistics with errors.
Notes
-----
The following keys are looked for in the `itermethod_opts`
dictionary:
======== ========== ===========
Key Type Description
======== ========== ===========
maxiters int > 0 The maximum number of iterations.
lrej number > 0 The number of sigma below the model to reject.
hrej number > 0 The number of sigma above the model to reject.
grow int >= 0 If greater than zero, also remove this many data
points to either side of the identified element.
======== ========== ===========
References
----------
.. [3] http://iraf.net/irafhelp.php?val=sfit
"""
if statkwargs is None:
statkwargs = {}
# Sigma-rejection can only be used with chi-squared;
# raise exception if it is attempted with least-squares,
# or maximum likelihood
if (isinstance(self.stat, Chi2) and
type(self.stat) is not LeastSq):
pass
else:
raise FitErr('needchi2', 'Sigma-rejection')
# Get maximum number of allowed iterations, high and low
# sigma thresholds for rejection of data points, and
# "grow" factor (i.e., how many surrounding data points
# to include with rejected data point).
maxiters = self.itermethod_opts['maxiters']
if type(maxiters) != int:
raise SherpaErr(
"'maxiters' value for sigma rejection method must be an integer")
if maxiters < 1:
raise SherpaErr("'maxiters' must be one or greater")
hrej = self.itermethod_opts['hrej']
if type(hrej) != int and type(hrej) != float:
raise SherpaErr(
"'hrej' value for sigma rejection method must be a number")
if hrej <= 0:
raise SherpaErr("'hrej' must be greater than zero")
lrej = self.itermethod_opts['lrej']
# FIXME: [OL] There are more reliable ways of checking if an object
# is (not) a number.
if type(lrej) != int and type(lrej) != float:
raise SherpaErr(
"'lrej' value for sigma rejection method must be a number")
if lrej <= 0:
raise SherpaErr("'lrej' must be greater than zero")
grow = self.itermethod_opts['grow']
if type(grow) != int:
raise SherpaErr(
"'grow' value for sigma rejection method must be an integer")
if grow < 0:
raise SherpaErr("'grow' factor must be zero or greater")
nfev = 0
iters = 0
# Store original masks (filters) for each data set.
mask_original = []
for d in self.data.datasets:
# If there's no filter, create a filter that is
# all True
if not iterable(d.mask):
mask_original.append(d.mask)
d.mask = ones_like(array(d.get_dep(False), dtype=bool))
else:
mask_original.append(array(d.mask))
# QUS: why is teardown being called now when the model can be
# evaluated multiple times in the following loop?
# Note that after the loop self.model.startup
# is called, so either I [DJB] or the code has them the
# wrong way around
self.model.teardown()
final_fit_results = None
rejected = True
try:
while rejected and iters < maxiters:
# Update stored y, staterror and syserror values
# from data, so callback function will work properly
self._dep, self._staterror, self._syserror = self.data.to_fit(
self.stat.calc_staterror)
self.model.startup(cache)
final_fit_results = self.method.fit(statfunc,
self.model.thawedpars,
parmins, parmaxes,
statargs, statkwargs)
model_iterator = iter(self.model())
rejected = False
for d in self.data.datasets:
# For each data set, compute
# (data - model) / staterror
# over filtered data space
residuals = (d.get_dep(True) - d.eval_model_to_fit(
next(model_iterator))) / d.get_staterror(True, self.stat.calc_staterror)
# For each modeled value that exceeds
# sigma thresholds, set the corresponding
# filter value from True to False
ressize = len(residuals)
filsize = len(d.mask)
newmask = d.mask
j = 0
kmin = 0
for i in range(0, ressize):
while not(newmask[j]) and j < filsize:
j = j + 1
if j >= filsize:
break
if residuals[i] <= -lrej or residuals[i] >= hrej:
rejected = True
kmin = j - grow
if kmin < 0:
kmin = 0
kmax = j + grow
if kmax >= filsize:
kmax = filsize - 1
for k in range(kmin, kmax + 1):
newmask[k] = False
j = j + 1
# If we've masked out *all* data,
# immediately raise fit error, clean up
# on way out.
if not(any(newmask)):
raise FitErr('nobins')
d.mask = newmask
# For data sets with backgrounds, correct that
# backgrounds have masks that match their sources
for d in self.data.datasets:
if (hasattr(d, "background_ids") and
hasattr(d, "get_background")):
for bid in d.background_ids:
b = d.get_background(bid)
if iterable(b.mask) and iterable(d.mask):
if len(b.mask) == len(d.mask):
b.mask = d.mask
# teardown model, get ready for next iteration
self.model.teardown()
iters = iters + 1
nfev += final_fit_results[4].get('nfev')
final_fit_results[4]['nfev'] = nfev
except:
# Clean up if exception occurred
mask_original.reverse()
for d in self.data.datasets:
d.mask = mask_original.pop()
# Update stored y, staterror and syserror values
# from data, so callback function will work properly
self._dep, self._staterror, self._syserror = self.data.to_fit(
self.stat.calc_staterror)
self.model.startup(cache)
raise
self._dep, self._staterror, self._syserror = self.data.to_fit(
self.stat.calc_staterror)
# QUS: shouldn't this be teardown, not startup?
self.model.startup(cache)
# N.B. -- If sigma-rejection in Sherpa 3.4 succeeded,
# it did *not* restore the filter to its state before
# sigma-rejection was called. If points are filtered
# out, they stay out. So we emulate the same behavior
# if our version of sigma-rejection succeeds.
# Mind you, if sigma-rejection *fails*, then we *do*
# restore the filter, and re-raise the exception in
# the above exception block.
# Return results from sigma rejection
return final_fit_results
[docs] def fit(self, statfunc, pars, parmins, parmaxes,
statargs=(), statkwargs=None):
if statkwargs is None:
statkwargs = {}
if not self.iterate:
return self.method.fit(statfunc, pars, parmins, parmaxes,
statargs, statkwargs)
else:
return self.current_func(statfunc, pars, parmins, parmaxes,
statargs, statkwargs)
[docs]class Fit(NoNewAttributesAfterInit):
"""Fit a model to a data set.
Parameters
----------
data : `sherpa.data.Data` or `sherpa.data.DataSimulFit`
The data to be fit.
model : `sherpa.models.model.Model` or `sherpa.models.model.SimulFitModel`
The model to fit to the data. It should match the ``data`` parameter
(i.e. be a `SimulFitModel` object when data is a `DataSimulFit`).
stat : `sherpa.stats.Stat` or `None`, optional
The statistic object to use. If not given then
`Chi2Gehrels` is used.
method : `sherpa.optmethods.OptMethod` instance or None, optional
The optimiser to use. If not given then `sherpa.optmethods.LevMar`
is used.
estmethod : `sherpa.estmethods.EstMethod` or None, optional
The class used to calculate errors. If not given then
`sherpa.estmethods.Covariance` is used.
itermethod_opts : dict or None, optional
If set, defines the iterated-fit method and options to use.
It is passed through to `IterFit`.
"""
def __init__(self, data, model, stat=None, method=None, estmethod=None,
itermethod_opts=None):
if itermethod_opts is None:
itermethod_opts = {'name': 'none'}
self.data = data
self.model = model
if stat is None:
stat = Chi2Gehrels()
if method is None:
method = LevMar()
if estmethod is None:
estmethod = Covariance()
self.stat = stat
self.method = method
self.estmethod = estmethod
# Confidence limit code freezes one parameter
# at a time. Keep a record here of which one
# that is, in case an exception is raised and
# this parameter needs to be thawed in the
# exception handler.
self.calc_thaw_indices()
self.current_frozen = -1
# The number of times that reminimization has occurred
# during an attempt to compute confidence limits. If
# that number equals self.estmethod.maxfits, cease all
# further attempt to reminimize.
self.refits = 0
# Set up an IterFit object, so that the user can select
# an iterative fitting option.
self._iterfit = IterFit(self.data, self.model, self.stat, self.method,
itermethod_opts)
NoNewAttributesAfterInit.__init__(self)
[docs] def calc_thaw_indices(self):
self.thaw_indices = \
tuple([i for i, par in enumerate(self.model.pars)
if not par.frozen])
def __setstate__(self, state):
self.__dict__.update(state)
if '_iterfit' not in state:
self.__dict__['_iterfit'] = IterFit(self.data, self.model,
self.stat, self.method,
{'name': 'none'})
def __str__(self):
return (('data = %s\n' +
'model = %s\n' +
'stat = %s\n' +
'method = %s\n' +
'estmethod = %s') %
(self.data.name,
self.model.name,
type(self.stat).__name__,
type(self.method).__name__,
type(self.estmethod).__name__))
[docs] def guess(self, **kwargs):
"""Guess parameter values and limits.
The model's `sherpa.models.model.Model.guess` method
is called with the data values (the dependent axis of the
data set) and the ``kwargs`` arguments.
"""
self.model.guess(*self.data.to_guess(), **kwargs)
# QUS: should this have an @evaluates_model decorator?
def _calc_stat(self):
"""Calculate the current statistic value.
Returns
-------
statval, fvec : number, array of numbers
The overall statistic value and the "per-bin" value.
"""
# TODO: is there anything missing here that
# self._iterfit.get_extra_args calculates?
return self.stat.calc_stat(self.data, self.model)
[docs] def calc_stat(self):
"""Calculate the statistic value.
Evaluate the statistic for the current model and data
settings (e.g. parameter values and data filters).
Returns
-------
stat : number
The current statistic value.
See Also
--------
calc_chisqr, calc_stat_info
"""
return self._calc_stat()[0]
[docs] def calc_chisqr(self):
"""Calculate the per-bin chi-squared statistic.
Evaluate the per-bin statistic for the current model and data
settings (e.g. parameter values and data filters).
Returns
-------
chisq : array or None
The chi-square value for each bin of the data, using the
current statistic.
A value of `None` is returned if the statistic is not a chi-square
distribution.
See Also
--------
calc_stat, calc_stat_info
"""
# Since there is some setup work needed before calling
# this routine, and to avoid catching any AttributeErrors
# thrown by the routine, use this un-pythonic check.
#
if not hasattr(self.stat, 'calc_chisqr'):
return None
return self.stat.calc_chisqr(self.data, self.model)
[docs] def calc_stat_info(self):
"""Calculate the statistic value and related information.
Evaluate the statistic for the current model and data
settings (e.g. parameter values and data filters).
Returns
-------
statinfo : `StatInfoResults` instance
The current statistic value.
See Also
--------
calc_chisqr, calc_stat
"""
# TODO: This logic would be better in the stat class than here
#
statval, fvec = self._calc_stat()
model = self.data.eval_model_to_fit(self.model)
numpoints = len(model)
dof = numpoints - len(self.model.thawedpars)
rstat, qval = self.stat.goodness_of_fit(statval, dof)
name = _cleanup_chi2_name(self.stat, self.data)
return StatInfoResults(name, statval, numpoints, model,
dof, qval, rstat)
[docs] @evaluates_model
def fit(self, outfile=None, clobber=False, numcores=1):
"""Fit the model to the data.
Parameters
----------
outfile : str or None, optional
If not `None` then information on the fit is written to
this file.
clobber : bool, optional
Determines if the output file can be overwritten.
numcores : int or None, optional
The number of cores to use in fitting simultaneous data.
Returns
-------
fitres : `FitResults`
Raises
------
`sherpa.utils.err.FitErr`
This is raised if ``clobber`` is ``False`` and ``outfile`` already
exists or if all the bins have been masked out of the fit.
See Also
--------
est_errors, simulfit
Notes
-----
The file created when ``outfile`` is set is a simple ASCII
file with a header line containing the text
"# nfev statistic" and then a list of the thawed parameters,
and then one line for each iteration, with the values separated
by spaces.
"""
dep, staterror, syserror = self.data.to_fit(self.stat.calc_staterror)
# TODO: This test may already be handled by data.to_fit(),
# which raises DataErr('notmask'), although I have not
# investigated if it is possible to pass that check
# but fail the following.
#
if not iterable(dep) or len(dep) == 0:
raise FitErr('nobins')
if ((iterable(staterror) and 0.0 in staterror) and
isinstance(self.stat, Chi2) and
type(self.stat) != Chi2 and
type(self.stat) != Chi2ModVar):
raise FitErr('binhas0')
init_stat = self.calc_stat()
# output = self.method.fit ...
tmp = self._iterfit._get_callback(outfile, clobber)
output = self._iterfit.fit(tmp,
self.model.thawedpars,
self.model.thawedparmins,
self.model.thawedparmaxes)
# LevMar always calculate chisquare, so call calc_stat
# just in case statistics is something other then chisquare
self.model.thawedpars = output[1]
tmp = list(output)
tmp[2] = self.calc_stat()
output = tuple(tmp)
# end of the gymnastics 'cause one cannot write to a tuple
# check if any parameter values are at boundaries,
# and warn user.
tol = np.finfo(np.float32).eps
param_warnings = ""
for par in self.model.pars:
if not par.frozen:
if sao_fcmp(par.val, par.min, tol) == 0:
param_warnings += ("WARNING: parameter value %s is at its minimum boundary %s\n" %
(par.fullname, str(par.min)))
if sao_fcmp(par.val, par.max, tol) == 0:
param_warnings += ("WARNING: parameter value %s is at its maximum boundary %s\n" %
(par.fullname, str(par.max)))
if self._iterfit._file is not None:
vals = ['%5e %5e' % (self._iterfit._nfev, tmp[2])]
vals.extend(['%5e' % val for val in self.model.thawedpars])
print(' '.join(vals), file=self._iterfit._file)
self._iterfit._file.close()
self._iterfit._file = None
# if a re-fit was performed with more/less thawed pars then
# self.thaw_indices must be re-calculated otherwise Confidence
# will get IndexError, see issue #342 for details
self.calc_thaw_indices()
return FitResults(self, output, init_stat, param_warnings.strip("\n"))
[docs] @evaluates_model
def simulfit(self, *others):
"""Fit multiple data sets and models simultaneously.
The current fit object is combined with the other fit
objects and a simultaneous fit is made, using the object's
statistic and optimisation method.
Parameters
----------
*others : `sherpa.fit.Fit` instances
The ``data`` and ``model`` attributes of these arguments
are used, along with those from the object.
Returns
-------
fitres : `FitResults`
See Also
--------
fit
"""
if len(others) == 0:
return self.fit()
fits = (self,) + others
d = DataSimulFit('simulfit data', tuple(f.data for f in fits))
m = SimulFitModel('simulfit model', tuple(f.model for f in fits))
f = Fit(d, m, self.stat, self.method)
return f.fit()
[docs] @evaluates_model
def est_errors(self, methoddict=None, parlist=None):
"""Estimate errors.
Calculate the low and high errors for one or more of the
thawed parameters in the fit.
Parameters
----------
methoddict : dict or None, optional
A dictionary mapping from lower-cased method name to
the associated optimisation method instance to use. This
is only used if the method is changed, as described in
the Notes section below.
parlist : sequence of `sherpa.models.parameter.Parameter` or None, optional
The names of the parameters for which the errors should
be calculated. If set to `None` then all the thawed
parameters are used.
Returns
-------
res : ErrorEstResults
Raises
------
`sherpa.utils.err.EstErr`
If any parameter in parlist is not valid (i.e. is not
thawed or is not a member of the model expression being
fit), or if the statistic is `~sherpa.stats.LeastSq`,
or if the reduced chi-square value of the current parameter
values is larger than the ``max_rstat`` option (for
chi-square statistics).
See Also
--------
fit
Notes
-----
If a new minimum is found for any parameter then the calculation
is automatically started for all the parameters using this
new best-fit location. This can repeat until the ``maxfits``
option is reached.
Unless the `~sherpa.estmethods.Covariance` estimator
is being used, or the ``fast`` option is unset, then the method
will be changed to `~sherpa.optmethods.NelderMead` (for
likelihood-based statistics) or `~sherpa.optmethods.LevMar`
(for chi-square based statistics) whilst calculating the
errors.
"""
# Define functions to freeze and thaw a parameter before
# we call fit function -- projection can call fit several
# times, for each parameter -- that parameter must be frozen
# while the others freely vary.
def freeze_par(pars, parmins, parmaxes, i):
# Freeze the indicated parameter; return
# its place in the list of all parameters,
# and the current values of the parameters,
# and the hard mins amd maxs of the parameters
self.model.pars[self.thaw_indices[i]].val = pars[i]
self.model.pars[self.thaw_indices[i]].frozen = True
self.current_frozen = self.thaw_indices[i]
keep_pars = ones_like(pars)
keep_pars[i] = 0
current_pars = pars[where(keep_pars)]
current_parmins = parmins[where(keep_pars)]
current_parmaxes = parmaxes[where(keep_pars)]
return (current_pars, current_parmins, current_parmaxes)
def thaw_par(i):
if i < 0:
pass
else:
self.model.pars[self.thaw_indices[i]].frozen = False
self.current_frozen = -1
# confidence needs to know which parameter it is working on.
def get_par_name(ii):
return self.model.pars[self.thaw_indices[ii]].fullname
# Call from a parameter estimation method, to report
# that limits for a given parameter have been found
def report_progress(i, lower, upper):
if i < 0:
pass
else:
name = self.model.pars[self.thaw_indices[i]].fullname
if isnan(lower) or isinf(lower):
info("%s \tlower bound: -----" % name)
else:
info("%s \tlower bound: %g" % (name, lower))
if isnan(upper) or isinf(upper):
info("%s \tupper bound: -----" % name)
else:
info("%s \tupper bound: %g" % (name, upper))
# If starting fit statistic is chi-squared or C-stat,
# can calculate reduced fit statistic -- if it is
# more than 3, don't bother calling method to estimate
# parameter limits.
if type(self.stat) is LeastSq:
raise EstErr('noerr4least2', type(self.stat).__name__)
if type(self.stat) is not Cash:
dep, staterror, syserror = self.data.to_fit(
self.stat.calc_staterror)
if not iterable(dep) or len(dep) == 0:
raise FitErr('nobins')
# For chi-squared and C-stat, reduced statistic is
# statistic value divided by number of degrees of
# freedom.
# Degress of freedom are number of data bins included
# in fit, minus the number of thawed parameters.
dof = len(dep) - len(self.model.thawedpars)
if dof < 1:
raise EstErr('nodegfreedom')
if (hasattr(self.estmethod, "max_rstat") and
(self.calc_stat() / dof) > self.estmethod.max_rstat):
raise EstErr('rstat>max', str(self.estmethod.max_rstat))
# If statistic is chi-squared, change fitting method to
# Levenberg-Marquardt; else, switch to NelderMead. (We
# will do fitting during projection, and therefore don't
# want to use LM with a stat other than chi-squared).
# If current method is not LM or NM, warn it is not a good
# method for estimating parameter limits.
if (type(self.estmethod) is not Covariance and
type(self.method) is not NelderMead and
type(self.method) is not LevMar):
warning(self.method.name + " is inappropriate for confidence " +
"limit estimation")
oldmethod = self.method
if (hasattr(self.estmethod, "fast") and
bool_cast(self.estmethod.fast) and
methoddict is not None):
if isinstance(self.stat, Likelihood):
if type(self.method) is not NelderMead:
self.method = methoddict['neldermead']
warning("Setting optimization to " + self.method.name
+ " for confidence limit search")
else:
if type(self.method) is not LevMar:
self.method = methoddict['levmar']
warning("Setting optimization to " + self.method.name
+ " for confidence limit search")
# Now, set up before we call the confidence limit function
# Keep track of starting values, will need to set parameters
# back to starting values when we are done.
startpars = self.model.thawedpars
startsoftmins = self.model.thawedparmins
startsoftmaxs = self.model.thawedparmaxes
starthardmins = self.model.thawedparhardmins
starthardmaxs = self.model.thawedparhardmaxes
# If restricted to soft_limits, only send soft limits to
# method, and do not reset model limits
if bool_cast(self.estmethod.soft_limits):
starthardmins = self.model.thawedparmins
starthardmaxs = self.model.thawedparmaxes
else:
self.model.thawedparmins = starthardmins
self.model.thawedparmaxes = starthardmaxs
self.current_frozen = -1
# parnums is the list of indices of the thawed parameters
# we want to visit. For example, if there are three thawed
# parameters, and we want to derive limits for only the first
# and third, then parnums = [0,2]. We construct the list by
# comparing each parameter in parlist to the thawed model
# parameters. (In the default case, when parlist is None,
# that means get limits for all thawed parameters, so parnums
# is [0, ... , numpars - 1], if the number of thawed parameters
# is numpars.)
parnums = []
if parlist is not None:
allpars = [p for p in self.model.pars if not p.frozen]
for p in parlist:
count = 0
match = False
for par in allpars:
if p is par:
parnums.append(count)
match = True
count = count + 1
if not match:
raise EstErr('noparameter', p.fullname)
parnums = array(parnums)
else:
parlist = [p for p in self.model.pars if not p.frozen]
parnums = arange(len(startpars))
# If we are here, we are ready to try to derive confidence limits.
# General rule: if failure because a hard limit was hit, find
# out which parameter it was so we can tell the user.
# If a new minimum statistic was found, start over, with parameter
# values that yielded new lower statistic as the new starting point.
output = None
results = None
oldremin = -1.0
if hasattr(self.estmethod, "remin"):
oldremin = self.estmethod.remin
try:
output = self.estmethod.compute(self._iterfit._get_callback(),
self._iterfit.fit,
self.model.thawedpars,
startsoftmins,
startsoftmaxs,
starthardmins,
starthardmaxs,
parnums,
freeze_par, thaw_par,
report_progress, get_par_name)
except EstNewMin as e:
# If maximum number of refits has occurred, don't
# try to reminimize again.
if (hasattr(self.estmethod, "maxfits") and
not(self.refits < self.estmethod.maxfits - 1)):
self.refits = 0
thaw_par(self.current_frozen)
self.model.thawedpars = startpars
self.model.thawedparmins = startsoftmins
self.model.thawedparmaxes = startsoftmaxs
self.method = oldmethod
if hasattr(self.estmethod, "remin"):
self.estmethod.remin = -1.0
warning("Maximum number of reminimizations reached")
# First report results of new fit, then call
# compute limits for those new best-fit parameters
for p in parlist:
p.frozen = False
self.current_frozen = -1
if e.args != ():
self.model.thawedpars = e.args[0]
self.model.thawedparmins = startsoftmins
self.model.thawedparmaxes = startsoftmaxs
results = self.fit()
self.refits = self.refits + 1
warning("New minimum statistic found while computing " +
"confidence limits")
warning("New best-fit parameters:\n" + results.format())
# Now, recompute errors for new best-fit parameters
results = self.est_errors(methoddict, parlist)
self.model.thawedparmins = startsoftmins
self.model.thawedparmaxes = startsoftmaxs
self.method = oldmethod
if hasattr(self.estmethod, "remin"):
self.estmethod.remin = oldremin
return results
except:
for p in parlist:
p.frozen = False
self.current_frozen = -1
self.model.thawedpars = startpars
self.model.thawedparmins = startsoftmins
self.model.thawedparmaxes = startsoftmaxs
self.method = oldmethod
if hasattr(self.estmethod, "remin"):
self.estmethod.remin = oldremin
raise
for p in parlist:
p.frozen = False
self.current_frozen = -1
self.model.thawedpars = startpars
self.model.thawedparmins = startsoftmins
self.model.thawedparmaxes = startsoftmaxs
results = ErrorEstResults(self, output, parlist)
self.method = oldmethod
if hasattr(self.estmethod, "remin"):
self.estmethod.remin = oldremin
return results
# Notebook representation
#
def html_fitresults(fit):
"""Construct the HTML to display the FitResults object."""
has_covar = fit.covar is not None
ls = []
if not fit.succeeded:
out = '<p class="failed">'
out += '<strong>The fit failed:</strong> '
out += fit.message
out += '.</p>'
ls.append(out)
# The parameter values
#
header = ['Parameter', 'Best-fit value']
if has_covar:
header.append('Approximate error')
rows = []
if has_covar:
for pname, pval, perr in zip(fit.parnames, fit.parvals,
sqrt(fit.covar.diagonal())):
rows.append((pname, '{:12g}'.format(pval),
'± {:12g}'.format(perr)))
else:
for pname, pval in zip(fit.parnames, fit.parvals):
rows.append((pname, '{:12g}'.format(pval)))
out = formatting.html_table(header, rows, classname='fit',
rowcount=False,
summary='Fit parameters')
ls.append(out)
# Metadata/summary
#
meta = []
if fit.datasets is not None:
key = 'Dataset'
if len(fit.datasets) > 1:
key += 's'
meta.append((key,
','.join([str(d) for d in fit.datasets])))
rows = [('Method', 'methodname', False),
('Statistic', 'statname', False)]
if fit.itermethodname != 'none':
# TODO: what label
rows.append(('Iteration method', 'itermethodname', False))
rows.append(('Final statistic', 'statval', True))
if fit.nfev is not None:
rows.append(('Number of evaluations', 'nfev', False))
if fit.rstat is not None:
rows.append(('Reduced statistic', 'rstat', True))
if fit.qval is not None:
rows.append(('Probability (Q-value)', 'qval', True))
rows.extend([('Initial statistic', 'istatval', True),
('Δ statistic', 'dstatval', True),
('Number of data points', 'numpoints', False),
('Degrees of freedom', 'dof', False)])
for lbl, field, is_float in rows:
val = getattr(fit, field)
if is_float:
val = '{:g}'.format(val)
meta.append((lbl, val))
ls.append(formatting.html_section(meta, summary='Summary'))
return formatting.html_from_sections(fit, ls)
def html_errresults(errs):
"""Construct the HTML to display the FitResults object."""
ls = []
# The error estimates
#
header = ['Parameter', 'Best-fit value', 'Lower Bound',
'Upper Bound']
rows = []
def display(limit):
"""Display the limit
Should we try to HTML-ify the open interval?
"""
if limit is None:
return '-----'
elif is_iterable(limit):
return list_to_open_interval(limit)
else:
return '{:12g}'.format(limit)
for pname, pval, pmin, pmax in zip(errs.parnames, errs.parvals, errs.parmins, errs.parmaxes):
rows.append((pname, '{:12g}'.format(pval),
display(pmin), display(pmax)))
summary = '{} {:g}σ ({:2g}%)'.format(errs.methodname,
errs.sigma,
errs.percent)
summary += ' bounds'
out = formatting.html_table(header, rows,
rowcount=False,
summary=summary)
ls.append(out)
# Metadata/summary
#
meta = []
if errs.datasets is not None:
key = 'Dataset'
if len(errs.datasets) > 1:
key += 's'
meta.append((key,
','.join([str(d) for d in errs.datasets])))
rows = []
if errs.iterfitname is not None and errs.iterfitname != 'none':
rows.append(('Iteration method', 'iterfitname'))
rows.extend([('Fitting Method', 'fitname'),
('Statistic', 'statname')])
for lbl, field in rows:
meta.append((lbl, getattr(errs, field)))
ls.append(formatting.html_section(meta, summary='Summary'))
return formatting.html_from_sections(errs, ls)
def html_statinfo(stats):
meta = []
# This differs from the format method, both because of how the
# information is presented (a row for background separate from
# the data, which makes it easier to handle), but also because
# it doesn't assume singular source and background values (if
# both are set). It is not clear what combinations are supported.
#
if stats.ids is not None:
key = 'Dataset'
if len(stats.ids) > 1:
key += 's'
val = str(stats.ids).strip("()")
else:
val = stats.ids[0]
meta.append((key, val))
if stats.bkg_ids is not None:
# If there are multiple source datasets then the
# background ids would need to be mapped to the
# source dataset, but leave that for a later revision,
# as it isn't clear it is supported.
#
key = 'Background'
if len(stats.bkg_ids) > 1:
key += 's'
val = str(stats.bkg_ids).strip("()")
else:
val = stats.bkg_ids[0]
meta.append((key, val))
rows = [('Statistic', 'statname', False),
('Value', 'statval', True),
('Number of points', 'numpoints', False),
('Degrees of freedom', 'dof', False)]
if stats.rstat is not None:
rows.append(('Reduced statistic', 'rstat', True))
if stats.qval is not None:
rows.append(('Probability (Q-value)', 'qval', True))
for lbl, field, is_float in rows:
val = getattr(stats, field)
if is_float:
val = '{:g}'.format(val)
meta.append((lbl, val))
ls = [formatting.html_section(meta, open_block=True,
summary='Statistics summary')]
return formatting.html_from_sections(stats, ls)