subspace.py 文件源码

def principal_angles(X, Y, n):
    '''
    compute the principal angles between two subspaces
    return: np.array of principal angles, orthogonal matrics U and V
    '''
    QX, RX = la.qr(X)
    QY, RY = la.qr(Y)

    if X.shape[1] >= Y.shape[1]:

        C = QX.conjugate().T.dot(QY)
        M, cos, Nh = la.svd(C)

        U = QX.dot(M)
        V = QY.dot(Nh.conjugate().T)

        angles = np.arccos(cos)

        return angles, U, V

    else:

        C = QY.conjugate().T.dot(QX)
        M, cos, Nh = la.svd(C)

        U = QX.dot(M)
        V = QY.dot(Nh.conjugate().T)

        angles = np.arccos(cos)

        return angles, U, V

# Similarity between subspaces by Yamaguchi's definition