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  • Python最小二乘法拟合直线,采用了2种不同的方式,一种是直接计算,另一种是调用numpy.linalg.solve()
  • 主要给大家介绍了关于python中matplotlib实现最小二乘法拟合的相关资料,文中通过示例代码详细介绍了关于最小二乘法拟合直线和最小二乘法拟合曲线的实现过程,需要的朋友可以参考借鉴,下面来一起看看吧。
  • 最小二乘Python 二次拟合 随机生成数据,并且加上噪声干扰构造需要拟合的函数形式,使用最小二乘法进行拟合输出拟合后的参数将拟合后的函数与原始数据绘图后进行对比import numpy as npimport matplotlib.pyplot as ...

    最小二乘

    Python 二次拟合

    随机生成数据,并且加上噪声干扰

    构造需要拟合的函数形式,使用最小二乘法进行拟合

    输出拟合后的参数

    将拟合后的函数与原始数据绘图后进行对比

    import numpy as np

    import matplotlib.pyplot as plt

    from scipy.optimize import leastsq

    # X = np.array(xx)

    # Y = np.array(yy)

    X = np.linspace(0, 10, 100)

    Y = 4 * X ** 2 - 9 * X + 3 + np.random.randn(100) * 3

    # 二次函数的标准形式

    def func(params, x):

    a, b, c = params

    return a * x * x + b * x + c

    # 误差函数,即拟合曲线所求的值与实际值的差

    def error(params, x, y):

    return func(params, x) - y

    # 对参数求解

    def slovePara():

    p0 = [1, 1, 1]

    Para = leastsq(error, p0, args=(X, Y))

    return Para

    # 输出最后的结果

    def solution():

    Para = slovePara()

    a, b, c = Para[0]

    print("a=", a, " b=", b, " c=", c)

    print("cost:" + str(Para[1]))

    plt.scatter(X, Y, color="green", label="sample data", linewidth=2)

    # 画拟合直线

    x = np.linspace(0, 10, 100)

    y = a * x * x + b * x + c

    plt.plot(x, y, color="red", label="solution line", linewidth=2)

    plt.legend() # 绘制图例

    plt.show()

    solution()

    样0本点很杂乱的情况下

    将异常点去除后进行拟合

    拟合的函数需要大致符合函数图像的趋势

    def func(params, x):

    a, b, c = params

    return 1 / (a + b * np.exp(-c * x))

    拟合结果

    展开全文
  • 多元函数拟合。如 电视机和收音机价格多销售额的影响,此时自变量有两个。 python 解法: import numpy as np import pandas as pd #import statsmodels.api as sm #方法一 import statsmodels.formula.api as smf ...
  • Python最小二乘法矩阵

    2020-09-19 18:45:05
    今天小编就为大家分享一篇关于Python最小二乘法矩阵,小编觉得内容挺不错的,现在分享给大家,具有很好的参考价值,需要的朋友一起跟随小编来看看吧
  • python最小二乘法拟合直线

    万次阅读 2017-07-22 09:48:02
    最小二乘法的推导可参考下面这个博客,推导非常详细. https://my.oschina.net/keyven/blog/526010 首先画一个加入了噪声的散点图,函数是y=0.2x,加入噪声后如下图所示: 代码如下:# -*- coding: utf-8 -* import ...

    最小二乘法的推导可参考下面这个博客,推导非常详细.
    https://my.oschina.net/keyven/blog/526010
    首先画一个加入了噪声的散点图,函数是y=0.2x,加入噪声后如下图所示:


    代码如下:

    # -*- coding: utf-8 -*
    import numpy as np
    import matplotlib.pyplot as plt
    x = np.linspace(0, 30, num=50)
    y = 0.2*x+[np.random.random() for _ in range(50)]
    if __name__ == '__main__':
        plt.figure(figsize=(10, 5), facecolor='w')
        plt.plot(x, y, 'ro', lw=2, markersize=6)
        plt.grid(b=True, ls=':')
        plt.xlabel(u'X', fontsize=16)
        plt.ylabel(u'Y', fontsize=16)
        plt.show()

    我将上面这个代码保存为paint_scatter_plot.py这个名字,方便其他地方调用.
    接下来画出拟合直线:

    代码如下:

    from  paint_scatter_plot import x,y
    import numpy as np 
    import matplotlib.pyplot as plt
    def Least_squares(x,y):
        x_ = x.mean()
        y_ = y.mean()
        m = np.zeros(1)
        n = np.zeros(1)
        k = np.zeros(1)
        p = np.zeros(1)
        for i in np.arange(50):
            k = (x[i]-x_)* (y[i]-y_)
            m += k
            p = np.square( x[i]-x_ )
            n = n + p
        a = m/n
        b = y_ - a* x_
        return a,b
    if __name__ == '__main__':
        a,b = Least_squares(x,y)
        print a,b
        y1 = a * x + b
        plt.figure(figsize=(10, 5), facecolor='w')
        plt.plot(x, y, 'ro', lw=2, markersize=6)
        plt.plot(x, y1, 'r-', lw=2, markersize=6)
        plt.grid(b=True, ls=':')
        plt.xlabel(u'X', fontsize=16)
        plt.ylabel(u'Y', fontsize=16)
        plt.show()

    代码运算结果: a = 0.19784577, b = 0.48503344 ,还是非常接近正确结果的.

    展开全文
  • python最小二乘法拟合实例

    千次阅读 2019-11-05 14:50:04
    1)曲线拟合最小二乘法 ⑴两种逼近概念: ①插值:在节点处函数值相同; ②拟合:在数值上误差最小; ⑵最小二乘法主要解决的是插值中出现的三个问题: ① 高多项式会龙格现象; ② 定函数关系不合理(数据误差); ...

    1)曲线拟合的最小二乘法
    ⑴两种逼近概念:
    ①插值:在节点处函数值相同;
    ②拟合:在数值上误差最小;
    ⑵最小二乘法主要解决的是插值中出现的三个问题:
    ① 高多项式会龙格现象;
    ② 定函数关系不合理(数据误差);
    ⑶评估逼近效果:
    假设“逼近”规律的近似函数为y=f(x), 即有yi﹡= f(xi)(i=1,2,…,m).它与观测值yi之差 δi = yi﹡ - yi = f(xi) – yi,i = 1, 2, …,m。这称为残差。残差大大小可以作为衡量近似函数好坏的标准。按照使残差的平方和∑δi²最小的规则求得近似函数y=f(x)的方法称为最佳平方逼近,也称为曲线拟合的最小二乘法。
    举例:
    1)假定某天的气温变化记录如下,使用最小二乘法找出这一天的气温变化规律.
    t/h 0 1 2 3 4 5 6 7 8 9 10 11 12
    T/℃ 15 14 14 14 14 15 16 18 20 22 23 25 28
    t/h 13 14 15 16 17 18 19 20 21 22 23 24
    T/℃ 31 32 31 29 27 25 24 22 20 18 17 16
    要求:编程实现考虑下列类型的拟合函数,计算误差平方和,并作图比较效果.
    (1)二次、三次、四次多项式拟合函数;
    (2)形如 在这里插入图片描述
    计算各个多项式的二范数的平方、残差的方差和残差绝对值的均值如表1-1所示.
    在这里插入图片描述
    残差的方差的意义在于评估各个偏差的离散程度,避免只是部分拟合的效果比较好,而部分偏差又非常大。残差绝对值的均值的意义在于评估总体水平上残差的大小。通过比较我们可以发现总体上是四次多项式的拟合效果比较好。

    接下我们分别作出各个多项式在样本数据上的拟合效果,结果如图1-1所示。
    图1-1
    通过图1-1我们也可以看出四次项的拟合效果比较好。
    但通过增加多项式的最高次数之后,测试发现随着次数增加拟合的效果越好,出现了过拟合的现象,所以目前的评价体系还有问题。参考机器学习中的常见防止过拟合的方法是加入L1或者L2正则化项。
    《目前还在学习阶段有些问题还请谅解》

    代码如下:

    import matplotlib.pyplot as plt
    from matplotlib.font_manager import FontProperties
    import numpy as np
    from scipy.optimize import leastsq
    
    x = np.arange(0,25,1,dtype='float')
    y = np.array([15,14,14,14,14,15,16,18,20,22,23,25,
         28,31,32,31,29,27,25,24,22,20,18,17,16], dtype='float')
    
    # param:最小化的目标| *_fun:拟合函数
    # 二次
    param0 = [0, 0, 0]
    def quadratic_fun(a, x):
        k1, k2, b = a
        return k1 * x **2 + k2 * x + b
    # 三次
    param1 = [0, 0, 0, 0]
    def cubic_fun(a, x):
        k1, k2, k3, b = a
        return k1 * x ** 3 + k2 * x**2 + k3 * x + b
    # 四次
    param2 = [0, 0, 0, 0, 0]
    def fpower_fun(a, x):
        k1, k2, k3, k4, b = a
        return k1 * x ** 4 + k2 * x**3 + k3 * x**2 + k4 * x + b
    # 自定义函数
    param3 = [0, 0, 0]
    def myfuns(s, x):
        a, b, c = s
        return a * np.exp(-b*(x-c))
    param4 = [0, 0, 0, 0, 0, 0, 0, 0]
    def testfun(a, x):
        k1, k2, k3, k4, k5, k6, k7, b = a
        return  k7 * x ** 7 + k6 * x ** 6 + k1 * x ** 5 + k2 * x**4 + k3 * x**3 + k4 * x ** 2 + k5 * x + b
    # 偏差
    def dist(a, fun, x, y):
        return fun(a, x) - y
    # 作图
    myfont = FontProperties(fname="C:\Windows\Fonts\msyh.ttc")
    plt.figure()
    plt.title(u'某天的气温变化', fontproperties=myfont)
    plt.xlabel(u't/h')
    plt.ylabel(u'T/摄氏度', fontproperties=myfont)
    # 坐标轴的范围xmin, xmax, ymin, ymax
    plt.axis([0, 24, 10, 35])
    plt.grid(True)
    plt.plot(x, y, 'k.')
    
    
    funs = [quadratic_fun, cubic_fun, fpower_fun, myfuns, testfun]
    params = [param0, param1, param2, param3, param4]
    colors = ['blue', 'red', 'black', 'green', 'yellow']
    fun_name = ['quadratic_fun', 'cubic_fun', '4power_fun', 'a*exp(-b*(t-c))', 'testfun']
    
    for i, (func, param, color, name) in enumerate(zip(funs, params, colors, fun_name)):
        var = leastsq(dist, param, args=(func, x, y))
        plt.plot(x, func(var[0], x), color)
        print('[%s] 二范数: %.4f, abs(bias): %.4f, bias-std: %.4f' % (name,
              ((y-func(var[0], x))**2).sum(),
              (abs(y-func(var[0], x))).mean(), 
              (y-func(var[0], x)).std())
        )
    plt.legend(['sample data', 'quadratic_fun', 'cubic_fun', '4power_fun', 'a*exp(-b*(t-c))', 'fivpower_fun'], loc='upper left') 
    plt.show()
    

    参考书目:
    [M] 郑继明,朱伟,刘勇等 数值分析

    展开全文
  • python最小二乘法拟合

    2020-09-14 16:48:44
    import numpy as np import matplotlib.pyplot as plt from numpy import polyval # ...wfr=spider&for=pc # 多项式拟合代码如下 from scipy.optimize import curve_fit def ax_bfi

    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]
        dataList = [1476917.5, 1476800.0, 1476697.0, 1476697.0, 1476289.0, 1476118.0, 1475955.5, 1475810.5, 1475727.5,
                    1475671.0, 1475576.0, 1475497.0, 1475428.5, 1475340.0, 1475263.5, 1475153.5, 1474983.0, 1474947.5,
                    1474852.0, 1474789.0, 1474661.5, 1474608.5, 1474484.0, 1474468.5, 1476153.0, 1476049.0, 1475947.0,
                    1475870.0, 1475792.0, 1475713.5, 1474991.5, 1474777.0, 1474334.5, 1474266.0, 1474210.0, 1473672.5,
                    1473571.0, 1473155.5, 1473116.0, 1473042.0, 1472923.5, 1472857.5, 1472750.0, 1472635.5, 1472530.0,
                    1471566.0, 1471491.0, 1471464.0, 1471423.5, 1471363.5, 1471306.5, 1471252.5, 1471207.5, 1471146.0,
                    1471103.5, 1471077.0, 1471002.5, 1470933.5, 1470875.5, 1470764.0, 1470718.0, 1470661.0, 1470623.5,
                    1470623.5, 1470564.0, 1470526.5, 1470409.5, 1470478.5, 1469858.0, 1469804.5, 1469825.5, 1470201.0,
                    1470186.5, 1470138.5, 1470057.0, 1469579.0, 1469501.5, 1469425.0, 1469412.0, 1469402.0, 1469393.0,
                    1469358.5, 1469324.5, 1469288.0, 1469255.5, 1469265.5, 1469198.5, 1469132.5, 1469180.5, 1469205.5,
                    1469269.0, 1469289.5, 1469278.5, 1469234.5, 1469240.0, 1469223.0, 1469208.0, 1469186.5, 1469154.5,
                    1469172.5, 1469140.5, 1469115.5, 1469116.5, 1469121.5, 1469068.0, 1468998.5, 1468944.0, 1468903.0,
                    1468889.0, 1468843.5, 1468831.0, 1468818.0, 1468816.0, 1469257.0, 1469318.5, 1469402.5, 1469398.0,
                    1469511.5, 1469490.5, 1469432.5, 1469439.5, 1469427.0, 1469468.0, 1469468.0, 1469442.5, 1469436.0,
                    1469455.5, 1469381.5, 1469243.0, 1469238.0, 1468692.5, 1469425.0, 1469478.0, 1469455.0, 1469472.0,
                    1469405.0, 1469411.5, 1469393.5, 1469395.0, 1469438.0, 1469421.0, 1469428.5, 1469433.5, 1469322.5,
                    1469204.5, 1469086.0, 1469113.0, 1469185.5, 1469269.5, 1469396.0, 1469477.5, 1469490.0, 1469577.5,
                    1469624.5, 1469657.5, 1469701.5, 1469756.5, 1469763.5, 1469765.5, 1469814.0, 1469823.5, 1469859.5,
                    1469866.0, 1469866.0, 1469865.0, 1469909.5, 1469925.5, 1469918.5, 1469904.0, 1469558.5, 1469665.5,
                    1469665.0, 1469822.5, 1468417.0, 1468393.0, 1468376.5, 1468283.5, 1468269.0, 1468260.5, 1468244.0,
                    1468189.0, 1468245.5, 1468296.5, 1468296.5, 1468327.0, 1468230.5, 1468289.0, 1468280.0, 1468273.0,
                    1468263.5, 1469467.0, 1469288.5, 1469322.5, 1469333.0, 1469343.5, 1469339.5, 1469299.0, 1469297.5,
                    1469291.5, 1469236.0, 1469206.5, 1469167.5, 1469177.5, 1469157.0, 1469145.5, 1469128.0, 1469125.5,
                    1469092.0, 1468073.5, 1468045.0, 1467927.0, 1468056.5, 1468033.0, 1468018.5, 1468022.0, 1468008.5,
                    1468030.5, 1468005.0, 1467998.5, 1467988.5, 1467956.5, 1467953.5, 1467972.0, 1467983.0, 1467983.0,
                    1467958.5, 1467941.0, 1467921.0, 1467886.0, 1467857.5, 1467865.5, 1467843.0, 1467785.5, 1467776.5,
                    1467803.0, 1467783.5, 1467806.5, 1467792.5, 1467801.0, 1467801.0, 1467826.0, 1467884.5, 1467883.0,
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                    1468650.5, 1468638.5, 1468615.0, 1468652.5, 1468641.5, 1468608.0, 1468615.0, 1468598.0, 1468612.0,
                    1468571.5, 1468608.0, 1468585.0, 1468574.5, 1468591.0, 1468543.5, 1468541.5, 1468555.0, 1468546.5,
                    1468607.5, 1467933.0, 1467954.5, 1467930.0, 1467931.5, 1467896.0, 1467869.0, 1467899.5, 1467950.5,
                    1467977.0, 1467952.0, 1467892.0, 1467910.5, 1467994.0, 1468006.5, 1468025.0, 1468111.5, 1468158.0,
                    1468163.5, 1468117.0, 1468162.5, 1468194.5, 1468239.0, 1468239.0, 1468197.5, 1468199.0, 1468277.5,
                    1468296.0, 1468303.0, 1468319.5, 1468423.0, 1468489.0, 1468583.5, 1468583.5, 1468758.5, 1468825.5,
                    1468879.5, 1468886.0, 1470219.0, 1470278.0, 1470260.0, 1470340.5, 1470402.0, 1470391.0, 1470428.5,
                    1470478.0, 1470443.5, 1470350.0, 1470350.5, 1470390.5, 1470476.0, 1470528.5, 1470554.0, 1470626.0,
                    1470636.0, 1470676.0, 1470733.0, 1470773.0, 1470834.5, 1470888.5, 1471054.0, 1471146.5, 1471184.5,
                    1471240.5, 1471302.5, 1471362.0, 1471398.5, 1471466.5, 1471554.0, 1471623.0, 1471654.5, 1471726.5,
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                    1474786.5, 1474667.5, 1474551.5, 1474484.0, 1474392.0, 1474248.5, 1474240.0, 1474394.5, 1474321.5,
                    1474321.5, 1474202.5, 1474108.5, 1473993.5, 1473860.0, 1473726.0, 1473625.0, 1473501.0, 1473332.0,
                    1473181.0, 1472973.0, 1472783.5, 1472589.0, 1472272.0, 1472070.0, 1471827.0, 1471555.0, 1471299.5,
                    1471119.0, 1470935.5, 1470758.0, 1470563.0, 1470338.0, 1470123.0, 1469909.5, 1469735.0, 1469547.5,
                    1469321.5, 1469194.5, 1469032.5, 1468788.0, 1468565.0, 1468322.0, 1468082.5, 1467861.0, 1467626.5,
                    1467437.0, 1467128.0, 1466877.0, 1466694.0, 1466500.5, 1466240.0, 1466045.0, 1465709.5, 1465471.5,
                    1465246.0, 1465042.0, 1464852.0, 1464631.5, 1464430.0, 1464236.5, 1464049.0, 1463877.5, 1463685.0,
                    1463523.0, 1463351.0, 1463208.5, 1462966.5, 1462883.5, 1462773.0, 1462773.0, 1462488.0, 1462345.0,
                    1462229.5, 1462082.0, 1461974.0, 1461881.0, 1461793.5, 1461679.0, 1461588.0, 1461480.0, 1461369.0,
                    1461280.0, 1461145.0, 1461032.5, 1460926.0, 1460855.5, 1460603.5, 1460636.5, 1460542.0, 1460417.5,
                    1460376.0, 1460298.5, 1460216.5, 1460043.0, 1459977.5, 1459966.0, 1459885.0, 1459871.0, 1459934.5,
                    1459899.0, 1459816.5, 1459773.5, 1459742.5, 1459720.0, 1459686.0, 1459595.0, 1459519.5, 1459492.5,
                    1459492.0, 1459435.0, 1459444.5, 1459447.5, 1459467.0, 1459479.0, 1459408.5, 1459394.0, 1459403.0,
                    1459418.5, 1459423.0, 1459144.0, 1459418.0, 1459384.0, 1459350.0, 1459356.5, 1459399.0, 1459486.5,
                    1459594.5, 1459757.0, 1459849.5, 1459849.5, 1459936.0, 1459958.5, 1460031.0, 1460105.0, 1460208.5,
                    1460265.5, 1460311.0, 1460356.5, 1460457.5, 1460511.0, 1460523.5, 1460578.0, 1460635.0, 1460644.5,
                    1460699.0, 1460725.5, 1460779.5, 1460845.0, 1460911.5, 1460967.0, 1460976.0, 1461003.5, 1461044.5,
                    1461142.5, 1461181.5, 1461220.5, 1461290.5, 1461339.5, 1461368.5, 1461402.5, 1461480.5, 1461527.0,
                    1461607.5, 1461621.0, 1461671.0, 1461708.0, 1461734.0, 1461780.0, 1461803.0, 1461833.5, 1461892.5,
                    1461922.0, 1461973.5, 1461973.0, 1462028.0, 1462082.0, 1462114.0, 1462142.0, 1462184.5, 1462243.5,
                    1462296.0, 1462334.5, 1462384.5, 1462410.0, 1462456.0, 1462499.5, 1462509.5, 1462585.5, 1462661.0,
                    1462661.0, 1462769.0, 1462796.0, 1462882.5, 1462942.0, 1462996.5, 1463025.5, 1463104.0, 1463175.0,
                    1463202.5, 1463252.5, 1463288.5, 1463382.5, 1463389.0, 1463437.5, 1463483.5, 1463571.5, 1463652.0,
                    1463664.0, 1463725.0, 1463832.0, 1463879.5, 1463883.5, 1463971.5, 1464044.5, 1464180.5, 1464227.0,
                    1464288.0, 1464340.5, 1464315.5, 1464372.0, 1464424.0, 1464501.0, 1464563.0, 1464624.0, 1464652.0,
                    1464690.5, 1464701.0, 1464739.5, 1466150.5, 1466638.1666666667, 1466833.0555555557, 1466953.0185185187,
                    1467027.3395061728, 1467106.113168724, 1467151.7043895747, 1467221.9014631917, 1467256.9671543974,
                    1467320.3223847991, 1467378.1074615996, 1467436.0358205333, 1467484.6786068445, 1467495.8928689482,
                    1467547.9642896494, 1467620.9880965499, 1467696.9960321833, 1467780.665344061, 1467860.2217813537,
                    1467884.0739271177, 1467879.3579757058, 1467877.7859919018, 1468030.2619973004, 1468132.4206657668,
                    1468235.806888589, 1468282.6022961962, 1468356.2007653986, 1466111.5, 1466212.0, 1466297.0, 1466381.5,
                    1466480.0, 1466560.0, 1466617.0, 1466696.0, 1466760.0, 1466822.5, 1466892.0, 1466952.0, 1467042.0,
                    1467158.5, 1467233.5, 1467306.5, 1467347.5, 1467422.5, 1467485.0, 1467567.5, 1467604.0, 1467668.0,
                    1467721.0, 1467792.0, 1467902.5, 1468008.0, 1468066.0, 1468121.5, 1468183.5, 1468275.5, 1468346.5,
                    1468447.5, 1468488.0, 1468549.5, 1468626.5, 1468738.5, 1468827.0, 1468899.5, 1468952.5, 1469033.0,
                    1469194.0, 1469267.0, 1469344.0, 1469386.5, 1469434.0, 1469504.0, 1469581.0, 1469654.5, 1469721.5,
                    1469802.0, 1469876.0, 1469941.0, 1470009.5, 1470094.0, 1470094.0, 1470194.5, 1470264.5, 1470324.0,
                    1470380.5, 1470443.0, 1470521.5, 1470564.0, 1470583.5, 1470629.5, 1470651.5, 1470240.5, 1470376.5,
                    1470552.0, 1470615.5, 1470758.5, 1470793.5, 1470804.5, 1470883.0, 1470890.5, 1470962.0, 1471016.5,
                    1471068.5, 1471106.5, 1471125.0, 1471153.0, 1471181.0, 1471238.5, 1471242.5, 1471184.5, 1471217.0,
                    1471243.0, 1471267.5, 1471284.5, 1471297.5, 1471318.5, 1471347.0, 1471375.0, 1471410.5, 1471464.0,
                    1471551.5, 1471603.0, 1471636.0, 1471657.0, 1471725.0, 1471763.5, 1471823.5, 1471960.5, 1471992.5,
                    1472016.5, 1472080.0, 1472072.0, 1472108.0, 1472156.5, 1472203.0, 1472173.5, 1472107.5, 1472110.0,
                    1472119.5, 1472083.0, 1472083.0, 1472088.0, 1472046.0, 1471980.5, 1471929.0, 1471908.5, 1471929.0,
                    1471904.5, 1471867.0, 1471842.0, 1471778.0, 1471783.0, 1471763.0, 1471698.5, 1471699.5, 1471636.0,
                    1471622.5, 1471599.5, 1471645.0, 1471648.0, 1471617.5, 1471637.5, 1471635.0, 1471642.0, 1471637.5,
                    1471566.0, 1471574.5, 1471541.5, 1471531.5, 1471511.5, 1471462.0, 1471426.0, 1471427.5, 1471416.0,
                    1471404.0, 1471352.5, 1471289.0, 1471296.5, 1471278.5, 1471292.5, 1471295.5, 1471310.0, 1471308.5,
                    1471294.5, 1471288.5, 1471270.0, 1471249.5, 1471277.5, 1471269.0, 1471282.0, 1471295.0, 1471321.5,
                    1471325.0, 1471330.0, 1471301.5, 1471317.0, 1471255.0, 1471248.0, 1471267.0, 1471172.0, 1471172.0,
                    1471231.5, 1471226.0, 1471237.0, 1471237.5, 1471209.0, 1471191.5, 1471185.5, 1471185.5, 1471199.5,
                    1471176.5, 1471211.0, 1471227.5, 1471182.5, 1471187.0, 1471223.0, 1471235.0, 1471247.5, 1471233.5,
                    1471239.0, 1471243.0, 1471254.5, 1471226.0, 1471254.0, 1471274.0, 1471286.0, 1471267.5, 1471274.5,
                    1471291.5, 1471265.5, 1471244.5, 1471280.5, 1471302.5, 1471295.0, 1471324.0, 1474501.0, 1474521.5,
                    1474580.5, 1474646.0, 1471318.0, 1471237.5, 1471249.5, 1471263.0, 1471258.0, 1471301.0, 1471349.0,
                    1471334.0, 1471343.0, 1471327.0, 1471332.5, 1474829.5, 1474848.0, 1474852.0, 1471063.5, 1471070.5,
                    1471063.0, 1471066.5, 1474777.5, 1471061.5, 1471066.5, 1471066.5, 1471213.0, 1471212.0, 1471162.5,
                    1471188.5, 1471194.5, 1471203.0, 1471113.5, 1471176.0, 1471215.0, 1471253.5, 1471251.5, 1471261.0,
                    1471258.5, 1471185.0, 1471205.0, 1471220.0, 1471241.5, 1471229.5, 1471237.0, 1471273.5, 1471291.0,
                    1471326.5, 1471343.0, 1471348.0, 1471375.0, 1471382.0, 1471391.5, 1471387.5, 1471405.5, 1471356.0,
                    1471350.0, 1471369.0, 1471360.5, 1471390.5, 1471384.0, 1471410.0, 1472648.6666666667, 1473057.888888889,
                    1471338.0, 1471410.5, 1471392.5, 1471409.5, 1471390.5, 1471400.5, 1471387.0, 1471412.0, 1471438.0,
                    1474995.0, 1475017.0, 1475070.0, 1475115.0, 1475127.5, 1471778.0, 1475222.0, 1475235.0, 1475241.5,
                    1475248.0, 1475284.5, 1475298.0, 1475298.0, 1475381.5, 1471932.0, 1471925.0, 1475469.5, 1475555.0,
                    1475633.5, 1475688.0, 1472330.0, 1475786.5, 1475846.5, 1475872.0, 1475913.5, 1476028.0, 1476090.5,
                    1476149.0, 1476213.0, 1476274.0, 1476324.0, 1476391.0, 1476483.5, 1473098.0, 1473154.5, 1476726.0,
                    1476814.5, 1473398.0, 1473505.0, 1473650.0, 1473716.0, 1473736.5, 1473856.5, 1473904.0, 1473968.5,
                    1474064.5, 1474145.5, 1474215.5, 1474306.0, 1478699.1666666667, 1474300.0, 1474297.5, 1474331.0,
                    1474427.0, 1478181.7222222222, 1474636.5, 1474712.5, 1474799.5, 1474886.0, 1475007.5, 1475113.5,
                    1475136.0, 1475270.5, 1475353.5, 1478636.574074074, 1475523.0, 1475587.0, 1475667.5, 1475739.5,
                    1475804.0, 1475873.0, 1475951.5, 1475951.5, 1476124.0, 1476208.0, 1476298.5, 1476350.5, 1476412.5,
                    1476537.5, 1476645.5, 1476775.5, 1476887.5, 1476964.5, 1477084.0, 1477204.5, 1477347.5, 1477428.0,
                    1477524.5, 1477683.5, 1477778.0, 1477920.5, 1478032.0, 1478172.5, 1478302.0, 1478429.5, 1478529.0,
                    1478629.0, 1478739.0, 1478864.0, 1478935.0, 1478966.5, 1479029.5, 1479157.0, 1479261.0, 1479349.0,
                    1479461.0, 1479580.5, 1479722.5, 1479852.5, 1479711.0, 1479846.0, 1479921.5, 1480072.5, 1480199.5,
                    1480342.5, 1480480.5, 1480563.5, 1480693.0, 1480823.5, 1481095.0, 1481274.5, 1481406.0, 1481556.0,
                    1481686.0, 1481795.0, 1481944.5, 1482025.0, 1482137.0, 1482255.5, 1482348.5, 1482429.0, 1482451.5,
                    1482451.5, 1482595.5, 1482715.0, 1482842.5, 1482938.5, 1483062.5, 1483124.5, 1483226.0, 1483307.5,
                    1483406.5, 1483552.5, 1483645.5, 1483807.0, 1483945.5, 1484032.0, 1484173.0, 1484302.0, 1484396.5,
                    1484527.5, 1484637.5, 1484766.0, 1484854.0, 1484978.0, 1485081.5, 1485140.0, 1485268.5, 1485368.5,
                    1485463.5, 1485579.5, 1485656.5, 1485746.0, 1485878.0, 1485970.0, 1486095.5, 1486191.5, 1486309.5,
                    1486397.0, 1486490.5, 1486634.5, 1486720.5, 1486786.0, 1486895.0, 1486223.5, 1486632.0, 1486922.5,
                    1487017.5, 1487300.0, 1487402.5, 1487482.5, 1487555.0, 1487645.0, 1487758.5, 1487870.0, 1488010.5,
                    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:
    在这里插入图片描述

    展开全文
  • python最小二乘法代码

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