scipy.optimize.least_squares http://scipy.github.io/devdocs/generated/scipy.optimize.least_squares.html在 scipy 0.17 中(2016 年 1 月)
处理边界;使用那个,而不是这个黑客。
边界约束可以很容易地变成二次的,
并通过最小化与其余部分一起最小化。
假设您想要最小化 10 个平方之和 Σ f_i(p)^2,
所以你的 func(p) 是一个 10 向量 [f0(p) ... f9(p)],
并且还希望 0 考虑“tub 函数” max( - p, 0, p - 1 ),
0 .. 1 内部为 0,外部为正值,就像 \_____/ 浴缸一样。
如果我们给leastsq
13 长向量
[ f0(p), f1(p), ... f9(p), w*tub(p0), w*tub(p1), w*tub(p2) ]
当 w = 100 时,它将最小化手数的平方和:
桶将限制 0 下面的代码只是一个运行的包装器leastsq
例如这样一个 13 长的向量就最小化了。
# leastsq_bounds.py
# see also test_leastsq_bounds.py on gist.github.com/denis-bz
from __future__ import division
import numpy as np
from scipy.optimize import leastsq
__version__ = "2015-01-10 jan denis" # orig 2012
#...............................................................................
def leastsq_bounds( func, x0, bounds, boundsweight=10, **kwargs ):
""" leastsq with bound conatraints lo <= p <= hi
run leastsq with additional constraints to minimize the sum of squares of
[func(p) ...]
+ boundsweight * [max( lo_i - p_i, 0, p_i - hi_i ) ...]
Parameters
----------
func() : a list of function of parameters `p`, [err0 err1 ...]
bounds : an n x 2 list or array `[[lo_0,hi_0], [lo_1, hi_1] ...]`.
Use e.g. [0, inf]; do not use NaNs.
A bound e.g. [2,2] pins that x_j == 2.
boundsweight : weights the bounds constraints
kwargs : keyword args passed on to leastsq
Returns
-------
exactly as for leastsq,
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html
Notes
-----
The bounds may not be met if boundsweight is too small;
check that with e.g. check_bounds( p, bounds ) below.
To access `x` in `func(p)`, `def func( p, x=xouter )`
or make it global, or `self.x` in a class.
There are quite a few methods for box constraints;
you'll maybe sing a longer song ...
Comments are welcome, test cases most welcome.
"""
# Example: test_leastsq_bounds.py
if bounds is not None and boundsweight > 0:
check_bounds( x0, bounds )
if "args" in kwargs: # 8jan 2015
args = kwargs["args"]
del kwargs["args"]
else:
args = ()
#...............................................................................
funcbox = lambda p: \
np.hstack(( func( p, *args ),
_inbox( p, bounds, boundsweight )))
else:
funcbox = func
return leastsq( funcbox, x0, **kwargs )
def _inbox( X, box, weight=1 ):
""" -> [tub( Xj, loj, hij ) ... ]
all 0 <=> X in box, lo <= X <= hi
"""
assert len(X) == len(box), \
"len X %d != len box %d" % (len(X), len(box))
return weight * np.array([
np.fmax( lo - x, 0 ) + np.fmax( 0, x - hi )
for x, (lo,hi) in zip( X, box )])
# def tub( x, lo, hi ):
# """ \___/ down to lo, 0 lo .. hi, up from hi """
# return np.fmax( lo - x, 0 ) + np.fmax( 0, x - hi )
#...............................................................................
def check_bounds( X, box ):
""" print Xj not in box, loj <= Xj <= hij
return nr not in
"""
nX, nbox = len(X), len(box)
assert nX == nbox, \
"len X %d != len box %d" % (nX, nbox)
nnotin = 0
for j, x, (lo,hi) in zip( range(nX), X, box ):
if not (lo <= x <= hi):
print "check_bounds: x[%d] %g is not in box %g .. %g" % (j, x, lo, hi)
nnotin += 1
return nnotin