import numpy as np

import matplotlib.pyplot as plt

A = np.array([[8, -3, 2], [4, 11, -1], [6, 3, 12]])

b = np.array([[20, 33, 36]])

# 方法一：消元法求解方程组的解

result = np.linalg.solve(A, b.T)

# print('Result:\n', result)

# 方法二：迭代法求解方程组的解

B = np.array([[0, 3/8, -2/8], [-4/11, 0, 1/11], [-6/12, -3/12, 0]])

f = np.array([[20/8, 33/11, 36/12]])

error = 1.0e-6

steps = 100

xk = np.zeros((3, 1))  # initialize parameter setting

errorlist = []

for k in range(steps):

    xk_1 = xk

    xk = np.matmul(B, xk) + f.T

    print('xk:\n', xk)

    errorlist.append(np.linalg.norm(xk-xk_1))

    if errorlist[-1] < error:

        print('iteration: ', k+1)

        break

# 把误差画出来

x_axis = [i for i in range(len(errorlist))]

plt.figure()

plt.plot(x_axis, errorlist)