无法使用lmfit进行拟合

Question

我想用lmfit做一个fit，但我遇到了一些问题。下面是我的代码：

from lmfit import Model
import numpy as np

def fit_func(x,a,b,c):
    return a*(b-x)**(5/8)+c

x = np.array([ 131.871     ,  218.825     ,  305.046     ,  390.533     ,
        475.128     ,  558.959     ,  642.001     ,  724.307     ,
        805.794     ,  886.422     ,  966.20900001, 1045.19300001,
       1123.39300001, 1200.75800001, 1277.23700001, 1352.83300001,
       1427.57800001, 1501.49800001, 1574.55300001, 1646.69500001,
       1717.90800001, 1788.22100001, 1857.65100001, 1926.18300001,
       1993.76400001, 2060.37000001, 2126.00900001, 2190.70600001,
       2254.44800001, 2317.20000001, 2378.92000001, 2439.60300001,
       2499.25800001, 2557.89000001, 2615.46600001, 2671.95000001,
       2727.30900001, 2781.54300001, 2834.64700001, 2886.60600001,
       2937.38000001, 2986.92900001])

y = np.array([  0.        ,   3.14159265,   6.28318531,   9.42477796,
        12.56637061,  15.70796327,  18.84955592,  21.99114858,
        25.13274123,  28.27433388,  31.41592654,  34.55751919,
        37.69911184,  40.8407045 ,  43.98229715,  47.1238898 ,
        50.26548246,  53.40707511,  56.54866776,  59.69026042,
        62.83185307,  65.97344573,  69.11503838,  72.25663103,
        75.39822369,  78.53981634,  81.68140899,  84.82300165,
        87.9645943 ,  91.10618695,  94.24777961,  97.38937226,
       100.53096491, 103.67255757, 106.81415022, 109.95574288,
       113.09733553, 116.23892818, 119.38052084, 122.52211349,
       125.66370614, 128.8052988 ])


fit_model = Model(fit_func)
params = fit_model.make_params()
params['b'].set(5000, min=3500)

result = fit_model.fit(y, x=x)

但是我得到了这个错误：

ValueError: The model function generated NaN values and the fit aborted! Please check your model function and/or set boundaries on parameters where applicable. In cases like this, using "nan_policy='omit'" will probably not work.

我做错了什么？我试着手动调整a，b，c参数，a=-1.2，b=3600，c=196给出了一个很好的拟合，所以程序应该能够找到类似的东西。

Answer 1

缺少两件事：

a)您需要像下面这样将params传递给fit_model.fit()

result = fit_model.fit(y, params, x=x)

b)您需要给出所有参数的初始值。未初始化的参数将有一个值-np.inf，这是故意选择的，因为它会抛出这样的错误。

您说您知道a、b和c的合理值。使用这些知识！就像这样

fit_model = Model(fit_func)
params = fit_model.make_params(a=-1, b=4000, c=200)
params['b'].min = x.max() * (1.000001) # prevent (negative number)**fraction

result = fit_model.fit(y, params, x=x)
print(result.fit_report())

应该行得通。