1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
|
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
Optimization algorithms used in `~astropy.modeling.fitting`.
"""
from __future__ import (absolute_import, unicode_literals, division,
print_function)
import warnings
import abc
import numpy as np
from ..extern import six
from ..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)
@six.add_metaclass(abc.ABCMeta)
class Optimization(object):
"""
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 = "{0}()".format(self.__class__.__name__)
return fmt
@property
def opt_method(self):
return self._opt_method
@abc.abstractmethod
def __call__(self):
raise NotImplementedError("Subclasses should implement this method")
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(SLSQP, self).__init__(fmin_slsqp)
self.fit_info = {
'final_func_val': None,
'numiter': None,
'exit_mode': None,
'message': None
}
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
# 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=np.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,
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 "
"fit_info['message'] for more information.",
AstropyUserWarning)
return fitparams, self.fit_info
class Simplex(Optimization):
"""
Neald-Mead (downhill simplex) algorithm [1].
This algorithm only uses function values, not derivatives.
Uses `scipy.optimize.fmin`.
.. [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(Simplex, self).__init__(simplex)
self.fit_info = {
'final_func_val': None,
'numiter': None,
'exit_mode': None,
'num_function_calls': None
}
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')
fitparams, final_func_val, numiter, funcalls, exit_mode = self.opt_method(
objfunc, initval, args=fargs, xtol=self._acc,
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
|
