SciPy LeastSq 拟合优度估计器

问题描述

我有一个使用 SciPy 的 leastsq 函数拟合的数据表面.

I have a data surface that I'm fitting using SciPy's leastsq function.

我想对 leastsq 返回后的拟合质量进行一些估计.我原以为这会作为函数的返回包含在内，但如果是这样，它似乎没有明确记录.

I would like to have some estimate of the quality of the fit after leastsq returns. I'd expected that this would be included as a return from the function, but, if so, it doesn't seem to be clearly documented.

是否有这样的返回，或者，除此之外，我可以将数据和返回的参数值以及拟合函数传递给某些函数，以便对拟合质量进行估计(R^2 或类似的)?

Is there such a return or, barring that, some function I can pass my data and the returned parameter values and fit function to that will give me an estimate of fit quality (R^2 or some such)?

谢谢！

推荐答案

如果你这样调用 leastsq :

import scipy.optimize
p,cov,infodict,mesg,ier = optimize.leastsq(
        residuals,a_guess,args=(x,y),full_output=True)

哪里

def residuals(a,x,y):
    return y-f(x,a)

然后，使用 R^2 的定义给定 here,

then, using the definition of R^2 given here,

ss_err=(infodict['fvec']**2).sum()
ss_tot=((y-y.mean())**2).sum()
rsquared=1-(ss_err/ss_tot)

你问什么是 infodict['fvec']?这是残差数组:

In [48]: optimize.leastsq?
...
      infodict -- a dictionary of optional outputs with the keys:
                  'fvec' : the function evaluated at the output

例如:

import scipy.optimize as optimize
import numpy as np
import collections
import matplotlib.pyplot as plt

x = np.array([821,576,473,377,326])
y = np.array([255,235,208,166,157])

def sigmoid(p,x):
    x0,y0,c,k=p
    y = c / (1 + np.exp(-k*(x-x0))) + y0
    return y

def residuals(p,x,y):
    return y - sigmoid(p,x)

Param=collections.namedtuple('Param','x0 y0 c k')
p_guess=Param(x0=600,y0=200,c=100,k=0.01)
p,cov,infodict,mesg,ier = optimize.leastsq(
    residuals,p_guess,args=(x,y),full_output=True)
p=Param(*p)
xp = np.linspace(100, 1600, 1500)
print('''\
x0 = {p.x0}
y0 = {p.y0}
c = {p.c}
k = {p.k}
'''.format(p=p))
pxp=sigmoid(p,xp)

# You could compute the residuals this way:
resid=residuals(p,x,y)
print(resid)
# [ 0.76205302 -2.010142    2.60265297 -3.02849144  1.6739274 ]

# But you don't have to compute `resid` -- `infodict['fvec']` already
# contains the info.
print(infodict['fvec'])
# [ 0.76205302 -2.010142    2.60265297 -3.02849144  1.6739274 ]

ss_err=(infodict['fvec']**2).sum()
ss_tot=((y-y.mean())**2).sum()
rsquared=1-(ss_err/ss_tot)
print(rsquared)
# 0.996768131959

plt.plot(x, y, '.', xp, pxp, '-')
plt.xlim(100,1000)
plt.ylim(130,270)
plt.xlabel('x')
plt.ylabel('y',rotation='horizontal')
plt.grid(True)
plt.show()

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