# astropy.modeling.optimizers 源代码

```# Licensed under a 3-clause BSD style license - see LICENSE.rst
# pylint: disable=invalid-name

"""
Optimization algorithms used in `~astropy.modeling.fitting`.
"""

import warnings
import abc
import numpy as np
from astropy.utils.exceptions import AstropyUserWarning

__all__ = ["Optimization", "SLSQP", "Simplex"]

# Maximum number of iterations
DEFAULT_MAXITER = 100

# Step for the forward difference approximation of the Jacobian
DEFAULT_EPS = np.sqrt(np.finfo(float).eps)

# Default requested accuracy
DEFAULT_ACC = 1e-07

DEFAULT_BOUNDS = (-10 ** 12, 10 ** 12)

[文档]class Optimization(metaclass=abc.ABCMeta):
"""
Base class for optimizers.

Parameters
----------
opt_method : callable
Implements optimization method

Notes
-----
The base Optimizer does not support any constraints by default; individual
optimizers should explicitly set this list to the specific constraints
it supports.

"""

supported_constraints = []

def __init__(self, opt_method):
self._opt_method = opt_method
self._maxiter = DEFAULT_MAXITER
self._eps = DEFAULT_EPS
self._acc = DEFAULT_ACC

@property
def maxiter(self):
"""Maximum number of iterations"""
return self._maxiter

@maxiter.setter
def maxiter(self, val):
"""Set maxiter"""
self._maxiter = val

@property
def eps(self):
"""Step for the forward difference approximation of the Jacobian"""
return self._eps

@eps.setter
def eps(self, val):
"""Set eps value"""
self._eps = val

@property
def acc(self):
"""Requested accuracy"""
return self._acc

@acc.setter
def acc(self, val):
"""Set accuracy"""
self._acc = val

def __repr__(self):
fmt = f"{self.__class__.__name__}()"
return fmt

@property
def opt_method(self):
""" Return the optimization method."""
return self._opt_method

[文档]    @abc.abstractmethod
def __call__(self):
raise NotImplementedError("Subclasses should implement this method")

[文档]class SLSQP(Optimization):
"""
Sequential Least Squares Programming optimization algorithm.

The algorithm is described in [1]_. It supports tied and fixed
parameters, as well as bounded constraints. Uses
`scipy.optimize.fmin_slsqp`.

References
----------
.. [1] http://www.netlib.org/toms/733
"""
supported_constraints = ['bounds', 'eqcons', 'ineqcons', 'fixed', 'tied']

def __init__(self):
from scipy.optimize import fmin_slsqp
super().__init__(fmin_slsqp)
self.fit_info = {
'final_func_val': None,
'numiter': None,
'exit_mode': None,
'message': None
}

[文档]    def __call__(self, objfunc, initval, fargs, **kwargs):
"""
Run the solver.

Parameters
----------
objfunc : callable
objection function
initval : iterable
initial guess for the parameter values
fargs : tuple
other arguments to be passed to the statistic function
kwargs : dict
other keyword arguments to be passed to the solver

"""
kwargs['iter'] = kwargs.pop('maxiter', self._maxiter)

if 'epsilon' not in kwargs:
kwargs['epsilon'] = self._eps
if 'acc' not in kwargs:
kwargs['acc'] = self._acc
# Get the verbosity level
disp = kwargs.pop('verblevel', None)

# set the values of constraints to match the requirements of fmin_slsqp
model = fargs[0]
pars = [getattr(model, name) for name in model.param_names]
bounds = [par.bounds for par in pars if not (par.fixed or par.tied)]
bounds = np.asarray(bounds)
for i in bounds:
if i[0] is None:
i[0] = DEFAULT_BOUNDS[0]
if i[1] is None:
i[1] = DEFAULT_BOUNDS[1]
# older versions of scipy require this array to be float
bounds = np.asarray(bounds, dtype=float)
eqcons = np.array(model.eqcons)
ineqcons = np.array(model.ineqcons)
fitparams, final_func_val, numiter, exit_mode, mess = self.opt_method(
objfunc, initval, args=fargs, full_output=True, disp=disp,
bounds=bounds, eqcons=eqcons, ieqcons=ineqcons,
**kwargs)

self.fit_info['final_func_val'] = final_func_val
self.fit_info['numiter'] = numiter
self.fit_info['exit_mode'] = exit_mode
self.fit_info['message'] = mess

if exit_mode != 0:
warnings.warn("The fit may be unsuccessful; check "
AstropyUserWarning)

return fitparams, self.fit_info

[文档]class Simplex(Optimization):
"""

This algorithm [1]_ only uses function values, not derivatives.
Uses `scipy.optimize.fmin`.

References
----------
.. [1] Nelder, J.A. and Mead, R. (1965), "A simplex method for function
minimization", The Computer Journal, 7, pp. 308-313
"""

supported_constraints = ['bounds', 'fixed', 'tied']

def __init__(self):
from scipy.optimize import fmin as simplex
super().__init__(simplex)
self.fit_info = {
'final_func_val': None,
'numiter': None,
'exit_mode': None,
'num_function_calls': None
}

[文档]    def __call__(self, objfunc, initval, fargs, **kwargs):
"""
Run the solver.

Parameters
----------
objfunc : callable
objection function
initval : iterable
initial guess for the parameter values
fargs : tuple
other arguments to be passed to the statistic function
kwargs : dict
other keyword arguments to be passed to the solver

"""
if 'maxiter' not in kwargs:
kwargs['maxiter'] = self._maxiter
if 'acc' in kwargs:
self._acc = kwargs['acc']
kwargs.pop('acc')
if 'xtol' in kwargs:
self._acc = kwargs['xtol']
kwargs.pop('xtol')
# Get the verbosity level
disp = kwargs.pop('verblevel', None)

fitparams, final_func_val, numiter, funcalls, exit_mode = self.opt_method(
objfunc, initval, args=fargs, xtol=self._acc, disp=disp,
full_output=True, **kwargs)
self.fit_info['final_func_val'] = final_func_val
self.fit_info['numiter'] = numiter
self.fit_info['exit_mode'] = exit_mode
self.fit_info['num_function_calls'] = funcalls
if self.fit_info['exit_mode'] == 1:
warnings.warn("The fit may be unsuccessful; "
"Maximum number of function evaluations reached.",
AstropyUserWarning)
if self.fit_info['exit_mode'] == 2:
warnings.warn("The fit may be unsuccessful; "
"Maximum number of iterations reached.",
AstropyUserWarning)
return fitparams, self.fit_info
```