SciPy LeastSq Fit Fit of Fit Estimator

Question

我有一个数据表面，我正在使用SciPy的leastsq函数。

我希望在leastsq返回后对拟合的质量有一些估计。我希望这可以作为函数的返回包含在内，但是，如果是这样的话，它似乎没有明确记录。

是否有这样的回报，或者除非，我可以传递我的数据和返回的参数值和拟合函数的某些函数将给出我对拟合质量的估计（R ^ 2或其他一些）？

谢谢！

Answer 1

如果你这样打leastsq：

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

其中

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

然后，使用给定here的R^2定义，

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

---

你问的infodict['fvec']是什么？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()