nlinalg.py 文件源码

def grad(self, inputs, g_outputs):
        r"""The gradient function should return

           .. math:: \sum_n\left(W_n\frac{\partial\,w_n}
                           {\partial a_{ij}} +
                     \sum_k V_{nk}\frac{\partial\,v_{nk}}
                           {\partial a_{ij}}\right),

        where [:math:`W`, :math:`V`] corresponds to ``g_outputs``,
        :math:`a` to ``inputs``, and  :math:`(w, v)=\mbox{eig}(a)`.

        Analytic formulae for eigensystem gradients are well-known in
        perturbation theory:

           .. math:: \frac{\partial\,w_n}
                          {\partial a_{ij}} = v_{in}\,v_{jn}


           .. math:: \frac{\partial\,v_{kn}}
                          {\partial a_{ij}} =
                \sum_{m\ne n}\frac{v_{km}v_{jn}}{w_n-w_m}

        """
        x, = inputs
        w, v = self(x)
        # Replace gradients wrt disconnected variables with
        # zeros. This is a work-around for issue #1063.
        gw, gv = _zero_disconnected([w, v], g_outputs)
        return [EighGrad(self.UPLO)(x, w, v, gw, gv)]