矩阵的 Doolittle LU 分解

Question

我正在尝试使用 python 实现一个原始的（不导入库，如 scipy 或 numpy）用于方阵的 Doolittle LU 分解。到目前为止，这是我的代码。

def luDecomposition(mat, n):
 
    lower = [[0 for x in range(n)]
             for y in range(n)]
    upper = [[0 for x in range(n)]
             for y in range(n)]
 
    # Decomposing matrix into Upper
    # and Lower triangular matrix
    for i in range(n):
 
        # Upper Triangular
        for k in range(i, n):
 
            # Summation of L(i, j) * U(j, k)
            soma = 0
            for j in range(i):
                soma += (lower[i][j] * upper[j][k])
 
            # Evaluating U(i, k)
            upper[i][k] = mat[i][k] - soma
 
        # Lower Triangular
        for k in range(i, n):
            if (i == k):
                lower[i][i] = 1  # Diagonal as 1
            else:
 
                # Summation of L(k, j) * U(j, i)
                soma = 0
                for j in range(i):
                    soma += (lower[k][j] * upper[j][i])
 
                # Evaluating L(k, i)
                lower[k][i] = int((mat[k][i] - soma) /
                                  upper[i][i])
 
    # setw is for displaying nicely
    print("     L    \t\t          U    ")
 
    # Displaying the result :
    for i in range(n):
 
        # Lower
        for j in range(n):
            print(lower[i][j], end="\t")
        print("", end="\t")
 
        # Upper
        for j in range(n):
            print(upper[i][j], end="\t")
        print("")
 
 
# Driver code
mat = [[4, 2, -1, 1],
       [8, 4, 2, -2],
       [1, 4, 2, -2],
       [2, 1, -2, 6]]
 
luDecomposition(mat, 4)

但是，我收到以下错误：

lower[k][i] = int((mat[k][i] - soma) / ZeroDivisionError：除以零。

直到现在我都无法解决这个问题。我的代码有任何理论上的错误吗？

Answer 1

if (upper[i][i]!=0):
    lower[k][i] = (mat[k][i] - soma) /(upper[i][i])