Python 实现顺序高斯消元法示例

# 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)