scipy.optimize.curve_fit函数用法解析

转:https://zhuanlan.zhihu.com/p/144353126

optimize.curve_fit()函数，用于日常数据分析中的数据曲线拟合。

语法：scipy.optimize.curve_fit(f,xdata,ydata,p0=None,sigma=None,absolute_sigma=False,check_finite=True,bounds=(-inf,inf),method=None,jac=None,**kwargs)

参数解析：

（官方文档说明：https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html#scipy-optimize-curve-fit）

f 函数名
callable

The model function, f(x, …). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments.

简单来说就是需要拟合的函数y，包括自变量x，参数A,B;
而curve_fit的主要功能就是计算A，B

#要拟合的一次函数
def f_1(x, A, B):return A * x + B

xdata
array_like or object
The independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object.
简单说就是要拟合的自变量数组
ydata
array_like
The dependent data, a length M array - nominallyf(xdata,...)
简单说就是要拟合的因变量的值
p0
array_like , optional
Initial guess for the parameters (length N). If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised).
就是给你的函数的参数确定一个初始值来减少计算机的计算量
其它的参数均不再说明！

返回值解析

popt array
Optimal values for the parameters so that the sum of the squared residuals off(xdata,*popt)-ydatais minimized
即残差最小时参数的值
pcov 2d array
The estimated covariance of popt. The diagonals provide the variance of the parameter estimate. To compute one standard deviation errors on the parameters use perr=np.sqrt(np.diag(pcov)).

How the sigma parameter affects the estimated covariance depends on absolute_sigma argument, as described above.

If the Jacobian matrix at the solution doesn’t have a full rank, then ‘lm’ method returns a matrix filled with np.inf, on the other hand ‘trf’ and ‘dogbox’ methods use Moore-Penrose pseudoinverse to compute the covariance matrix.

简单例子

例子1：拟合直线

# 引用库函数
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize as op# 需要拟合的数据组
x_group = np.array([3, 6.1, 9.1, 11.9, 14.9])
y_group = np.array([0.0221, 0.0491, 0.0711, 0.0971, 0.1238])# 需要拟合的函数
def f_1(x, A, B):return A * x + B# 得到返回的A，B值
A, B = op.curve_fit(f_1, x_group, y_group)[0]
# 数据点与原先的进行画图比较
plt.scatter(x_group, y_group, marker='o',label='real')
x = np.arange(0, 15, 0.01)
y = A * x + B
plt.plot(x, y,color='red',label='curve_fit')
plt.legend()
plt.title('%.5fx%.5f=y' % (A, B))
plt.show()

例子2：官方例子[1]

import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
import numpy as np# 定义需要拟合的函数
def func(x, a, b, c):return a * np.exp(-b * x) + c# Define the data to be fit with some noise:
# 用numpy的random库生成干扰
xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5)
np.random.seed(1729)
y_noise = 0.2 * np.random.normal(size=xdata.size)
ydata = y + y_noise
plt.plot(xdata, ydata, 'b-', label='data')
# Fit for the parameters a, b, c of the function func:popt, pcov = curve_fit(func, xdata, ydata)
print(popt)plt.plot(xdata, func(xdata, *popt), 'r-',label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
# Constrain the optimization to the region of 0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5:
# 限定范围进行拟合
popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5]))
print(popt)plt.plot(xdata, func(xdata, *popt), 'g--',label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()
#结果
#[2.55423706 1.35190947 0.47450618]
#[2.43708905 1.         0.35015434]

参考

scipy.optimize官方文档 https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html#scipy-optimize-curve-fit