python最小二乘法拟合

https://www.jianshu.com/p/354b1f2a5fd0
https://www.cnblogs.com/qi-yuan-008/p/12323535.html

import numpy as np
import matplotlib.pyplot as plt
from numpy import polyval
# https://baijiahao.baidu.com/s?id=1643468349140251072&wfr=spider&for=pc
# 多项式拟合代码如下
from scipy.optimize import curve_fit
def ax_bfit(x,y,calculate_x,n):
    x=np.array(x)
    y=np.array(y)
    calculate_x=np.array(calculate_x)
    fit_coef=np.polyfit(x,y,n)
    calculate_y=np.polyval(fit_coef,calculate_x)
    fit_coef=[round(i,3) for i in fit_coef]
    plt.plot(x,y,'^')
    plt.plot(calculate_x,calculate_y)
    plt.show()
    return fit_coef,calculate_y
def func(x,a,b,c):
    return  a*np.exp(b*x)*c
# 幂函数拟合
def a_xfit(x,y,calculate_x):
    plt.plot(x,y,'.')
    popt,pcov=curve_fit(func,x,y)
    calculate_y = [func(i,popt[0],popt[1],popt[2]) for i in calculate_x]
    plt.plot(calculate_x,calculate_y,'r--')
    plt.show()
    return popt,calculate_y
def fund(x,a,b):
    return x**a+b
# 指数拟合
def x_afit(x,y,calculate_x):
    plt.plot(x,y,'.')
    popt,pcov= curve_fit(fund,x,y)
    calculate_y=[fund(i,popt[0],popt[1]) for i in calculate_x]
    popt=[round(i,3) for i in popt]
    plt.plot(calculate_x,calculate_y,'r__')
    plt.show()
    return  popt,calculate_y

if __name__ == '__main__':
    # x=[1,2,3,4,5,6,7,8,9,10,11,12,13]
    # y = [1, 2, 4, 26, 33, 50, 58, 84, 104, 142, 170, 186, 199]
    # calculate_x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14,15,16]
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                1488090.0, 1488143.5, 1488251.0, 1488293.0, 1488364.0, 1488363.0, 1488363.0, 1488473.5, 1488482.0,
                1488503.5, 1488563.5, 1488666.5, 1488738.5, 1488774.5, 1488811.0, 1488890.0, 1488940.0, 1489021.5,
                1489114.5, 1489157.0, 1489268.5, 1489344.5, 1489417.5, 1489510.0, 1489570.5, 1489631.0, 1489741.5,
                1489869.0, 1489947.5, 1490032.5, 1490118.0, 1490211.0, 1490276.5, 1490317.5, 1490405.0, 1490471.5,
                1490591.0, 1490674.0, 1490765.5, 1490875.5, 1490954.5, 1491055.0, 1491143.5, 1491196.5, 1491286.0,
                1491380.0, 1491462.5, 1491554.0, 1491631.0, 1491758.0, 1491826.5, 1491913.0, 1491988.5, 1492089.5,
                1492211.5, 1492330.0, 1492415.5, 1492537.5, 1492654.5, 1492760.0, 1492854.0, 1492972.0, 1493093.5,
                1493184.0, 1493258.0, 1493401.0, 1493401.0, 1493608.0, 1493703.0, 1493839.0, 1493969.0, 1494080.0,
                1494183.0, 1494323.0, 1494457.0, 1494580.5, 1494729.5, 1494878.5, 1494977.5, 1495108.5, 1495255.5,
                1495373.5, 1495482.0, 1495614.0, 1495737.5, 1495858.0, 1495973.0, 1496102.5, 1496223.5, 1496355.0,
                1496425.5, 1496556.5, 1496654.5, 1496722.5, 1496824.0, 1496889.5, 1496950.5, 1497040.0, 1497132.0,
                1497196.5, 1497192.5, 1497249.0, 1497298.5, 1497425.5, 1497488.5, 1497566.5, 1497638.0, 1497752.5,
                1497862.0, 1497924.5, 1497971.0, 1498055.5, 1498158.0, 1498257.0, 1498364.5, 1498468.5, 1498540.0,
                1498578.0, 1498647.0, 1498670.5, 1498650.0, 1498684.5, 1498729.5, 1498760.0, 1498789.0, 1498770.0,
                1498770.0, 1498778.5, 1498786.5, 1498581.0, 1498605.5, 1498631.0, 1498610.5, 1498666.5, 1498701.0,
                1498742.0, 1498764.0, 1498796.0, 1498798.0, 1498803.0, 1498829.0, 1498856.0, 1498874.0, 1498915.0,
                1498950.0, 1498973.0, 1498977.5, 1498983.0, 1498970.5, 1498930.0, 1498890.5, 1498862.0, 1498835.5,
                1498800.5, 1498749.0, 1498702.0, 1498637.5, 1498560.5, 1498527.0, 1498457.5, 1498427.0, 1498457.5,
                1498454.5, 1498432.5, 1498416.5, 1498353.5, 1498286.5, 1498226.0, 1498162.0, 1498087.5, 1498088.0,
                1498030.5, 1498009.5, 1497962.5, 1497886.5, 1497829.5, 1497726.5, 1497605.0, 1497518.0, 1497484.0,
                1497384.5, 1497276.5, 1497193.0, 1497083.0, 1496884.0, 1496718.0, 1496718.0, 1496410.5, 1496202.5,
                1496051.0, 1495970.5, 1495854.0, 1499001.5, 1499018.0, 1499247.0, 1499391.0, 1499376.0, 1499307.5,
                1499193.5, 1499045.0, 1498932.0, 1498830.5, 1498795.5, 1498686.5, 1498532.5, 1498405.0, 1498260.5,
                1498140.0, 1497980.0, 1497868.0, 1497720.0, 1497591.0, 1497451.0, 1497311.0, 1497100.0, 1496890.0,
                1496650.5, 1496469.0, 1496253.0, 1496049.0, 1495931.0, 1495758.5, 1495607.0, 1495476.0, 1495300.0,
                1495164.5, 1495033.5, 1494925.0, 1494777.5, 1494630.5, 1494477.0, 1494348.0, 1494220.0, 1494068.5,
                1493902.0, 1493746.5, 1493588.0, 1493453.5, 1493296.5, 1493115.0, 1492972.0, 1492800.5, 1492632.5,
                1492323.5, 1491261.5, 1490581.5, 1490581.5, 1489472.5, 1488888.5, 1488297.5, 1487825.0, 1487398.0,
                1487264.5, 1487121.5, 1486999.5, 1486911.5, 1486786.0, 1486692.0, 1486542.5, 1486385.5, 1486271.0,
                1486136.5, 1486020.5, 1485890.5, 1485778.0, 1485665.0, 1485536.0, 1485426.5, 1485298.5, 1485120.0,
                1484999.0, 1484877.5, 1484716.0, 1484598.5, 1484437.5, 1484263.5, 1484049.0, 1483879.5, 1483654.0,
                1483405.5, 1483234.0, 1483098.5, 1482960.0, 1482846.5, 1482746.0, 1482637.0, 1482519.0, 1482396.0,
                1482205.0, 1481980.5, 1481831.5, 1481698.0, 1481591.0, 1481462.5, 1481343.5, 1481272.5, 1481175.5,
                1481076.5, 1480975.0, 1480851.5, 1480762.0, 1480686.5, 1480578.5]
    y_dataList = dataList[0:1440]
    x = []
    for i in range(1, 1441):
        # x0List=[i]
        x.append(i)

    y = []
    for i in y_dataList:
        # y0List=[i]
        y.append(i)
    n=16
    calculate_x=x
    result=ax_bfit(x,y,calculate_x,n)

    print(result[0])
    print(result[1])

多项式拟合结果：