在 true_divide 中遇到 Gram_Schimdt 算法的无效值

Question

我试图使用以下函数实现 Gram-Schimdt。但是，代码中似乎有一个零分频器。但是我不知道怎么解决。

def gs(A):
    x = A.shape[0]
    y = A.shape[1]
    U = np.zeros((x,y))
    U[:,1] = A[:,1]/np.linalg.norm(A[:,1])
    for i in range(1,y):
        U[:,i] = A[:,i]
        for j in range(0,i):
            U[:,i] = U[:,i] - U[:,j].dot(U[:,i])*U[:,j]/(U[:,j].dot(U[:,j]))
        U[:,i] = U[:,i]/np.linalg.norm(U[:,i])
    return U

错误信息：

/var/folders/tr/ssszhd_x03jdz162mg0j01vm0000gn/T/ipykernel_39952/685295545.py:9: RuntimeWarning: invalid value encountered in true_divide
  U[:,i] = U[:,i] - U[:,j].dot(U[:,i])*U[:,j]/(U[:,j].dot(U[:,j]))

Answer 1

问题出在初始化

U[:,1] = A[:,1]/np.linalg.norm(A[:,1])

第一列是 U[:,0]，因为您要分配给 U[:,1]，所以 U[:,0] 将保持全零，并且循环将用 zero-divisions 填充矩阵.

修正那条线就可以了

def gs(A):
    x = A.shape[0]
    y = A.shape[1]
    U = np.zeros((x,y))
    U[:,0] = A[:,0]/np.linalg.norm(A[:,0])
    for i in range(1,y):
        U[:,i] = A[:,i]
        for j in range(0,i):
            U[:,i] = U[:,i] - U[:,j].dot(U[:,i])*U[:,j]/(U[:,j].dot(U[:,j]))
        U[:,i] = U[:,i]/np.linalg.norm(U[:,i])
    return U

# test
A = gs(np.random.rand(100, 50))
assert np.allclose(A.T @ A, np.eye(50)) # check the results

在 true_divide 中遇到 Gram_Schimdt 算法的无效值

invalid value encountered in true_divide for Gram_Schimdt algorithm

python

linear-algebra