基于python的数学建模---最小二乘拟合

import numpy as np

import matplotlib.pyplot as plt

from scipy.optimize import leastsq

from matplotlib.pylab import mpl

mpl.rcParams['font.sans-serif'] = ['Microsoft YaHei']  # 指定默认字体

mpl.rcParams['axes.unicode_minus'] = False  # 解决保存图像是负号'-'显示为方块的问题

# 计算以p为参数的直线与原始数据之间误差

def f(p):

    k, b = p

    return Y - (k * X + b)

if __name__ == '__main__':

    X = np.array([8.19, 2.72, 6.39, 8.71, 4.7, 2.66, 3.78])

    Y = np.array([7.01, 2.78, 6.47, 6.71, 4.1, 4.23, 4.05])

    # leastsq使得f的输出数组的平方和最小，参数初始值为[1,0]

    r = leastsq(f, [1, 0])  # 数初始值可以随便设个合理的

    k, b = r[0]

    x = np.linspace(0, 10, 1000)

    y = k * x + b

    # 画散点图，s是点的大小

    plt.scatter(X, Y, s=100, alpha=1.0, marker='o', label=u'数据点')

    # 话拟合曲线，linewidth是线宽

    plt.plot(x, y, color='r', linewidth=2, linestyle="-", markersize=20, label=u'拟合曲线')

    plt.xlabel('安培/A')

    plt.ylabel('伏特/V')

    plt.legend(loc=0, numpoints=1)  # 显示点和线的说明

    # plt.plot(X, Y)

    plt.show()

    print('k = ', k)

    print('b = ', b)

k = 0.6134953491930442
b = 1.794092543259387

下面是用anaconda写的

import numpy as np

import matplotlib.pyplot as plt

np.set_printoptions(suppress=True) # 取消科学计数法

x = np.array([8.19,2.72,6.39,8.71,4.7,2.66,3.78])

y = np.array([7.01,2.78,6.47,6.71,4.1,4.23,4.05])

plt.figure()

plt.scatter(x,y)
plt.show()

from scipy.optimize import leastsq

def error(p,x,y):

    return p[0]*x + p[1] - y

p0 = [2,2] #设置初始值

res = leastsq(error,p0,args=(x,y))

k,b = res[0]

print(k)

print(b)

0.6134953485739788

1.7940925393506084

x1 = np.linspace(0,9,1000)

y1 = k*x1+b

plt.scatter(x,y,color= 'orange',label = 'Sample Point')

plt.plot(x1,y1,color= 'red',label = 'Fitting Line')

plt.legend()

plt.show()

基于python的数学建模---最小二乘拟合的相关教程结束。