landmarks.py 文件源码

def dq_Kqp_a(self,q,p,a, kernels) :
        """
        Useful for the adjoint integration scheme.
        d_q (K_q p) . a  = ...
        """
        h = 1e-8
        Q0phA = q + h*a
        Q0mhA = q - h*a
        update_emp =  (  Landmarks.K(self, Q0phA, p, Landmarks.precompute_kernels(self, Q0phA))
                      -  Landmarks.K(self, Q0mhA, p, Landmarks.precompute_kernels(self, Q0mhA))) / (2*h)
        return update_emp

        """x = q.reshape((self.npoints, self.dimension))
        p = p.reshape((self.npoints, self.dimension))
        a = a.reshape((self.npoints, self.dimension))
        dists = squareform(pdist(x, 'sqeuclidean')) # dists_ij       = |x_i-x_j|^2
        # We have :
        # [K_q p]_nd = sum_j { k(|x_n - x_j|^2) * p_j^d }
        #
        # So that :
        # grad_nd = a_nd * sum_j { 2 * (x_n^d - x_j^d) * k'(|x_n - x_j|^2) * p_j^d }
        grad = zeros((self.npoints, self.dimension))
        for d in range(self.dimension) :
            diffs = atleast_2d(x[:,d]).T - x[:,d]  # diffs_ij = x_i^d - x_j^d

            # K_ij = 2 * (x_i^d - x_j^d) * k'(|x_i - x_j|^2) * p_j^d
            K = 2 * dists * kernels[1] * p[:,d]
            # grad_nd =   a_nd * sum_j { 2 * (x_n^d - x_j^d) * k'(|x_n - x_j|^2) * p_j^d }
            grad[:,d] = a[:,d] * sum( K , 1 )
        return grad.reshape((self.npoints * self.dimension,))"""