randomizedEigensolver.py 文件源码

def AorthogonalityCheck(A, U, d):
    """
    Test the frobenious norm of  D^{-1}(U^TAU) - I_k
    """
    V = np.zeros(U.shape)
    AV = np.zeros(U.shape)
    Av = Vector()
    v = Vector()
    A.init_vector(Av,0)
    A.init_vector(v,1)

    nvec  = U.shape[1]
    for i in range(0,nvec):
        v.set_local(U[:,i])
        v *= 1./math.sqrt(d[i])
        A.mult(v,Av)
        AV[:,i] = Av.get_local()
        V[:,i] = v.get_local()

    VtAV = np.dot(V.T, AV)    
    err = VtAV - np.eye(nvec, dtype=VtAV.dtype)

#    plt.imshow(np.abs(err))
#    plt.colorbar()
#    plt.show()

    print("i, ||Vt(i,:)AV(:,i) - I_i||_F, V[:,i] = 1/sqrt(lambda_i) U[:,i]")
    for i in range(1,nvec+1):
        print(i, np.linalg.norm(err[0:i,0:i], 'fro') )