def mat_simp(M): n, p = M.shape for i in range(n): for j in range(p): M[i, j] = M[i, j].simplify().expand().simplify() return M def mat(u): n = len(u) M = sp.zeros(n, n) for j in range(n): cj = sp.Matrix([int(i == j) for i in range(n)]) Mcj = cj-2*cj.dot(u)/u.norm()**2*u for i in range(n): M[i, j] = Mcj[i] return M def DecompositionQR(A): n, p = A.shape if n != p or A.det() == 0: raise Exception("Les données ne sont pas correctes") AA = A.copy() O = sp.eye(n) for i in range(n): if not AA[i+1:, i].is_zero_matrix: B = AA.copy() for j in range(i): B[j, i] = 0 Ci = sp.Matrix([int(k == i) for k in range(n)]) S = mat_simp(mat(Ci-B[:, i]/B[:, i].norm())) O = S@O AA = S@AA return O.transpose(), AA修改这段代码，使她可以做QR分解

以下是修改后的代码，可以进行 QR 分解：

def mat_simp(M):
    n, p = M.shape
    for i in range(n):
        for j in range(p):
            M[i, j] = M[i, j].simplify().expand().simplify()
    return M

def mat(u):
    n = len(u)
    M = sp.zeros(n, n)
    for j in range(n):
        cj = sp.Matrix([int(i == j) for i in range(n)])
        Mcj = cj-2*cj.dot(u)/u.norm()**2*u
        for i in range(n):
            M[i, j] = Mcj[i]
    return M

def qr_decomposition(A):
    n, p = A.shape
    if n != p or A.det() == 0:
        raise Exception("Les données ne sont pas correctes")
    AA = A.copy()
    Q = sp.eye(n)
    for i in range(n):
        if not AA[i+1:, i].is_zero_matrix:
            B = AA.copy()
            for j in range(i):
                B[j, i] = 0
            Ci = sp.Matrix([int(k == i) for k in range(n)])
            S = mat_simp(mat(Ci-B[:, i]/B[:, i].norm()))
            Q = Q@S
            AA = S@AA
    R = AA
    return Q.transpose(), R

将函数名 `DecompositionQR` 改成了 `qr_decomposition`，并且修改了函数主体部分，使其能够进行 QR 分解。