我不断收到此错误：第 57 行列出索引超出范围

Question

import pprint

def mult_matrix(M, N):
    """Multiply square matrices of same dimension M and N"""

    # Converts N into a list of tuples of columns                                                                                                                                                                                                      
    tuple_N = zip(*N)

    # Nested list comprehension to calculate matrix multiplication                                                                                                                                                                                     
    return [[sum(el_m * el_n for el_m, el_n in zip(row_m, col_n)) for col_n in tuple_N] for row_m in M]

def pivot_matrix(M):
    """Returns the pivoting matrix for M, used in Doolittle's method."""
    m = len(M)

    # Create an identity matrix, with floating point values                                                                                                                                                                                            
    id_mat = [[float(i ==j) for i in range(m)] for j in range(m)]

    # Rearrange the identity matrix such that the largest element of                                                                                                                                                                                   
    # each column of M is placed on the diagonal of of M                                                                                                                                                                                               
    for j in range(m):
        row = max(range(j, m), key=lambda i: abs(M[i][j]))
        if j != row:
            # Swap the rows                                                                                                                                                                                                                            
            id_mat[j], id_mat[row] = id_mat[row], id_mat[j]

    return id_mat

def lu_decomposition(A):
    """Performs an LU Decomposition of A (which must be square)                                                                                                                                                                                        
    into PA = LU. The function returns P, L and U."""
    n = len(A)

    # Create zero matrices for L and U                                                                                                                                                                                                                 
    L = [[0.0] * n for i in range(0,n)]
    U = [[0.0] * n for i in range(0,n)]

    # Create the pivot matrix P and the multipled matrix PA                                                                                                                                                                                            
    P = pivot_matrix(A)
    PA = mult_matrix(P, A)

    # Perform the LU Decomposition                                                                                                                                                                                                                     
    for j in range(n):
        # All diagonal entries of L are set to unity                                                                                                                                                                                                   
        L[j][j] = 1.0

        # LaTeX: u_{ij} = a_{ij} - \sum_{k=1}^{i-1} u_{kj} l_{ik}                                                                                                                                                                                      
        for i in range(j+1):
            s1 = sum(U[k][j] * L[i][k] for k in range(i))
            U[i][j] = PA[i][j] - s1

        # LaTeX: l_{ij} = \frac{1}{u_{jj}} (a_{ij} - \sum_{k=1}^{j-1} u_{kj} l_{ik} )                                                                                                                                                                  
        for i in range(j, n):
            s2 = sum(U[k][j] * L[i][k] for k in range(j))
            L[i][j] = (PA[i][j] - s2) / U[j][j]

    return (P, L, U)


A = [[7, 3, -1, 2], [3, 8, 1, -4], [-1, 1, 4, -1], [2, -4, -1, 6]]
P, L, U = lu_decomposition(A)

print ("A:")
pprint.pprint(A)

print ("P:")
pprint.pprint(P)

print ("L:")
pprint.pprint(L)

print ("U:")
pprint.pprint(U)

Answer 1

我相信错误在以下 for 循环中

 for i in range(j+1):
    s1 = sum(U[k][j] * L[i][k] for k in range(i))
    U[i][j] = PA[i][j] - s1

当第一个循环从 ( for j in range(n): ) 开始时，当j==n第二个循环转到n+1引发异常。 希望能帮助到你