python - SciPy LeastSq 拟合优度估计器

Question

我有一个数据表面，我正在使用 SciPy 的 leastsq 函数进行拟合。

我想在 leastsq 返回后对拟合质量进行一些估计。我原以为这会作为函数的返回值包含在内，但如果是这样，似乎没有明确记录。

是否有这样的返回，或者，除此之外，我可以传递我的数据和返回的参数值和拟合函数的一些函数会给我一个拟合质量的估计(R^2 或类似的)？

谢谢!

Answer 1

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)

在哪里

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

然后，使用 R^2 的定义给定 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()