tangentspace.py 文件源码

def untangent_space(T, Cref):
    """Project a set of Tangent space vectors in the manifold according to the given reference point Cref

    :param T: the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)
    :param Cref: The reference covariance matrix
    :returns: A set of Covariance matrix, Ntrials X Nchannels X Nchannels

    """
    Nt, Nd = T.shape
    Ne = int((numpy.sqrt(1 + 8 * Nd) - 1) / 2)
    C12 = sqrtm(Cref)

    idx = numpy.triu_indices_from(Cref)
    covmats = numpy.empty((Nt, Ne, Ne))
    covmats[:, idx[0], idx[1]] = T
    for i in range(Nt):
        covmats[i] = numpy.diag(numpy.diag(covmats[i])) + numpy.triu(
            covmats[i], 1) / numpy.sqrt(2) + numpy.triu(covmats[i], 1).T / numpy.sqrt(2)
        covmats[i] = expm(covmats[i])
        covmats[i] = numpy.dot(numpy.dot(C12, covmats[i]), C12)

    return covmats