函数

算法

这个算法不算难。甚至可以说是非常简陋。但是在代码实现上却比之前的稍微麻烦点。主要体现在分段上。

图像效果

代码

import numpy as np
from sympy import *
import matplotlib.pyplot as plt


def f(x):
    return 1 / (1 + x ** 2)


def cal(begin, end):
    by = f(begin)
    ey = f(end)
    I = (n - end) / (begin - end) * by + (n - begin) / (end - begin) * ey
    return I


def calnf(x):
    nf = []
    for i in range(len(x) - 1):
        nf.append(cal(x[i], x[i + 1]))
    return nf


def calf(f, x):
    y = []
    for i in x:
        y.append(f.subs(n, i))
    return y


def nfSub(x, nf):
    tempx = np.array(range(11)) - 5
    dx = []
    for i in range(10):
        labelx = []
        for j in range(len(x)):
            if x[j] >= tempx[i] and x[j] < tempx[i + 1]:
                labelx.append(x[j])
            elif i == 9 and x[j] >= tempx[i] and x[j] <= tempx[i + 1]:
                labelx.append(x[j])
        dx = dx + calf(nf[i], labelx)
    return np.array(dx)


def draw(nf):
    plt.rcParams['font.sans-serif'] = ['SimHei']
    plt.rcParams['axes.unicode_minus'] = False
    x = np.linspace(-5, 5, 101)
    y = f(x)
    Ly = nfSub(x, nf)
    plt.plot(x, y, label='原函数')
    plt.plot(x, Ly, label='分段线性插值函数')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()

    plt.savefig('1.png')
    plt.show()


def lossCal(nf):
    x = np.linspace(-5, 5, 101)
    y = f(x)
    Ly = nfSub(x, nf)
    Ly = np.array(Ly)
    temp = Ly - y
    temp = abs(temp)
    print(temp.mean())


if __name__ == '__main__':
    x = np.array(range(11)) - 5
    y = f(x)

    n, m = symbols('n m')
    init_printing(use_unicode=True)

    nf = calnf(x)
    draw(nf)
    lossCal(nf)