使用python的scipy包做非线性回归 - Performing Nonlinear Regression Using Python's Scipy Package

可以使用python的scipy.optimize包的curve_fit来进行非线性回归。

Nonlinear regression can be conducted using the curve_fit function from Python's scipy.optimize package.

这其中最重要的是，需要定义一个函数充当要回归的方程。这里以Langmuir吸附方程举例

Crucially, you need to define a function that represents the equation to be regressed. For example, consider the Langmuir adsorption equation:

y=max*kc/(1+kc)

这个方程有2个参数：k和max。将其转化为python格式，如下所示：

This equation has two parameters: k and max. Transformed into Python format, it appears as follows:

```
def func(x, k, max):
    return max * k * x / (1 + k * x)
```

输入需要用于拟合的xdata和ydata，然后使用curve_fit函数拟合。xdata和ydata需为np.array格式。

Input the xdata and ydata to be used for fitting, then use the curve_fit function for fitting. Both xdata and ydata should be in the np.array format.

```popt, pcov = curve_fit(f=func, xdata=xdata, ydata=ydata)
```

如果需要指定参数的初始猜测值的话，需在curve_fit指定p0参数，p0的长度需与参数个数相同。

If you want to specify initial guesses for the parameters, use the p0 parameter in curve_fit. The length of p0 should match the number of parameters.

完整版代码如下：

Here's the complete code:

```
import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# the value of x and y
xdata = np.array([0.001, 0.0025, 0.005, 0.01, 0.015, 0.02])
ydata = np.array([1.77, 7.07, 11.90, 16.41, 19.02, 20.42])


# y=max*kc/(1+kc)
def func(x, k, max):
    return max * k * x / (1 + k * x)


popt, pcov = curve_fit(f=func, xdata=xdata, ydata=ydata, p0=(200, 30))

k_fit = popt[0]
max_fit = popt[1]

# adjust the range of x
x_linspace = np.linspace(0, 0.05, 50)
y_linspace = func(x_linspace, *popt)

plt.plot(x_linspace, y_linspace, label='Fit line\nk=%5.3f' % k_fit + '\nmax=%5.3f' % max_fit, color='red')
plt.title('Non-linear Curve Fitting')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

print(k_fit)
print(max_fit)
```

拟合结果如下所示。

The results of the fitting are as follows