具有约束的scipy.optimize.leastsq [英] scipy.optimize.leastsq with bound constraints

问题描述

我正在寻找scipy/numpy中的优化例程，该例程可以解决非线性最小二乘类型的问题(例如，将参数函数拟合到大型数据集)，但包括范围和约束(例如，最小和最大值).要优化的参数).目前，我正在使用mpfit的python版本(从idl转换而来):尽管效果很好，但这显然不是最佳选择.

I am looking for an optimisation routine within scipy/numpy which could solve a non-linear least-squares type problem (e.g., fitting a parametric function to a large dataset) but including bounds and constraints (e.g. minima and maxima for the parameters to be optimised). At the moment I am using the python version of mpfit (translated from idl...): this is clearly not optimal although it works very well.

在python/scipy/etc中有一个高效的例程可能很棒！ 任何输入都非常欢迎:-)

An efficient routine in python/scipy/etc could be great to have ! Any input is very welcome here :-)

谢谢！

推荐答案

scipy 0.17中的scipy.optimize.least_squares (2016年1月) 处理界限；使用它，而不是这个hack.

scipy.optimize.least_squares in scipy 0.17 (January 2016) handles bounds; use that, not this hack.

约束可以很容易地设为二次约束， 并通过最小平方和其他最小化.
假设您要最小化10平方和的总和； f_i(p)^ 2， 所以您的func(p)是10个向量[f0(p)... f9(p)]，
并且还希望3个参数的0< = p_i< =1.
考虑"tub函数" max(-p，0，p-1)， 在0 .. 1内部为0，在外部为正，例如\ _____/浴盆.
如果我们给leastsq 13个长度的向量

Bound constraints can easily be made quadratic, and minimized by leastsq along with the rest.
Say you want to minimize a sum of 10 squares Σ f_i(p)^2, so your func(p) is a 10-vector [f0(p) ... f9(p)],
and also want 0 <= p_i <= 1 for 3 parameters.
Consider the "tub function" max( - p, 0, p - 1 ), which is 0 inside 0 .. 1 and positive outside, like a \_____/ tub.
If we give leastsq the 13-long vector

[ f0(p), f1(p), ... f9(p), w*tub(p0), w*tub(p1), w*tub(p2) ]

如果w = 100，它将最小化手数的平方和: 浴盆将限制0 <= p <= 1. 一般lo< = p< = hi相似.
以下代码只是运行leastsq的包装器 与这样的13长度向量可将其最小化.

with w = say 100, it will minimize the sum of squares of the lot: the tubs will constrain 0 <= p <= 1. General lo <= p <= hi is similar.
The following code is just a wrapper that runs leastsq with e.g. such a 13-long vector to minimize.

# 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

这篇关于具有约束的scipy.optimize.leastsq的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！