kernels.py 文件源码

def psi1compDer(dL_dpsi1, _psi1, variance, lengthscale, Z, mu, S):
    # here are the "statistics" for psi1
    # Produced intermediate results: dL_dparams w.r.t. psi1
    # _dL_dvariance     1
    # _dL_dlengthscale  Q
    # _dL_dZ            MxQ
    # _dL_dgamma        NxQ
    # _dL_dmu           NxQ
    # _dL_dS            NxQ

    lengthscale2 = np.square(lengthscale)

    Lpsi1 = dL_dpsi1 * _psi1
    Zmu = Z[None, :, :] - mu[:, None, :]  # NxMxQ
    denom = 1. / (S + lengthscale2)
    Zmu2_denom = np.square(Zmu) * denom[:, None, :]  # NxMxQ
    _dL_dvar = Lpsi1.sum() / variance
    _dL_dmu = np.einsum('nm,nmq,nq->nq', Lpsi1, Zmu, denom)
    _dL_dS = np.einsum('nm,nmq,nq->nq', Lpsi1, (Zmu2_denom - 1.), denom) / 2.
    _dL_dZ = -np.einsum('nm,nmq,nq->mq', Lpsi1, Zmu, denom)
    _dL_dl = np.einsum('nm,nmq,nq->q', Lpsi1, (Zmu2_denom +
                                               (S / lengthscale2)[:, None, :]), denom * lengthscale)

    return _dL_dvar, _dL_dl, _dL_dZ, _dL_dmu, _dL_dS