Python 实现顺序高斯消元法示例
我就废话不多说，直接上代码吧！
# coding: utf8
import numpy as np
# 设置矩阵
def getInput():
matrix_a = np.mat([[2, 3, 11, 5],
[1, 1, 5, 2],
[2, 1, 3, 2],
[1, 1, 3, 4]],dtype=float)
matrix_b = np.mat([2,1,-3,-3])
#答案：-2 0 1 1
return matrix_a, matrix_b
def SequentialGauss(mat_a):
for i in range(0, (mat_a.shape[0])-1):
if mat_a[i, i] == 0:
print("终断运算：")
print(mat_a)
break
else:
for j in range(i+1, mat_a.shape[0]):
mat_a[j:j+1 , :] = mat_a[j:j+1,:] - \
(mat_a[j,i]/mat_a[i,i])*mat_a[i, :]
return mat_a
def revert(new_mat):
#创建矩阵存放答案 初始化为0
x = np.mat(np.zeros(new_mat.shape[0], dtype=float))
number = x.shape[1]-1
# print(number)
b = number+1
x[0,number] = new_mat[number,b]/new_mat[number, number]
for i in range(number-1,-1,-1):
try:
x[0,i] = (new_mat[i,b]-np.sum(np.multiply(new_mat[i,i+1:b],x[0,i+1:b])))/(new_mat[i,i])
except:print("错误")
print(x)
if __name__ == "__main__":
mat_a, mat_b = getInput()
# 合并两个矩阵
print("原矩阵")
print(np.hstack((mat_a, mat_b.T)))
new_mat = SequentialGauss(np.hstack((mat_a, mat_b.T)))
print("三角矩阵")
print(new_mat)
print("方程的解")
revert(new_mat)
运行结果如下
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