linalg.py 文件源码

def groupInverse(M):
    """
    Computes the group inverse of stochastic matrix using the algorithm
    given by Golub and Meyer in:
    G. H. Golub and C. D. Meyer, Jr, SIAM J. Alg. Disc. Meth. 7, 273-
    281 (1986)

    Parameters
    ----------
        M : ndarray
            A square matrix with index 1.

    Returns
    -------
        grpInvM : ndarray
            The group inverse of M.
    """
    L=np.shape(M)[1]
    q,r=qr(M)
    piDist=q[:,L-1]
    piDist=(1/np.sum(piDist))*piDist
    specProjector=np.identity(L)-np.outer(np.ones(L),piDist)
    u=r[0:(L-1),0:(L-1)]#remember 0:(L-1) actually means 0 to L-2!
    uInv= inv(u)#REPLACE W. lapack, invert triangular matrix ROUTINE
    uInv = np.real(uInv)
    grpInvM=np.zeros((L,L))
    grpInvM[0:(L-1),0:(L-1)]=uInv
    grpInvM=np.dot(specProjector,np.dot(grpInvM,np.dot(q.transpose(),specProjector)))
    return grpInvM