在日常数据分析中，免不了要用到数据曲线拟合，而optimize.curve_fit()函数正好满足你的需求

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好函数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 + Bxdata

array_like or objectThe 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.

ydata

array_likeThe dependent data, a length M array - nominallyf(xdata,...).

p0

array_like , optionalInitial 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).其它的参数均不再说明！

返回值解析poptarray

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

pcov2d 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

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