<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def gradient_log_joint(self, x):
 """ The gradient of the log joint probability. For the Gaussian terms, this is d/dx [-1/2 x^T J x + h^T x] = -Jx + h. For the likelihood terms, we have for each time t d/dx log p(yt | xt) """

        T, D = self.T, self.D_latent
        assert x.shape == (T, D)

        # Collect the Gaussian LDS prior terms
        _, h_init, _ = self.info_init_params
        _, _, _, h1, h2, _ = self.info_dynamics_params
        H_diag, H_upper_diag = self.sparse_J_prior

        # Compute the gradient from the prior
        g = -1 * symm_block_tridiag_matmul(H_diag, H_upper_diag, x)
        g[0] += h_init
        g[:-1] += h1
        g[1:] += h2

        # Compute gradient from the likelihood terms
        g += self.grad_local_log_likelihood(x)

        return g