Return the state space representation of the covariance.

def sde(self): 
        """ 
        Return the state space representation of the covariance. 
        """ 
        
        variance = float(self.variance.values)
        lengthscale = float(self.lengthscale.values)

        lamda = np.sqrt(5.0)/lengthscale
        kappa = 5.0/3.0*variance/lengthscale**2        
        
        F = np.array(((0, 1,0), (0, 0, 1), (-lamda**3, -3.0*lamda**2, -3*lamda)))
        L = np.array(((0,),(0,),(1,)))
        Qc = np.array((((variance*400.0*np.sqrt(5.0)/3.0/lengthscale**5),),))
        H = np.array(((1,0,0),))        
        
        Pinf = np.array(((variance,0,-kappa), (0, kappa, 0), (-kappa, 0, 25.0*variance/lengthscale**4)))
        P0 = Pinf.copy()
        # Allocate space for the derivatives         
        dF = np.empty((3,3,2))        
        dQc = np.empty((1,1,2))        
        dPinf = np.empty((3,3,2))
        
         # The partial derivatives 
        dFvariance = np.zeros((3,3))
        dFlengthscale = np.array(((0,0,0),(0,0,0),(15.0*np.sqrt(5.0)/lengthscale**4, 
                                   30.0/lengthscale**3, 3*np.sqrt(5.0)/lengthscale**2)))
        dQcvariance = np.array((((400*np.sqrt(5)/3/lengthscale**5,),)))
        dQclengthscale = np.array((((-variance*2000*np.sqrt(5)/3/lengthscale**6,),)))        
        
        dPinf_variance = Pinf/variance
        kappa2 = -2.0*kappa/lengthscale
        dPinf_lengthscale = np.array(((0,0,-kappa2),(0,kappa2,0),(-kappa2, 
                                    0,-100*variance/lengthscale**5)))        
        # Combine the derivatives 
        dF[:,:,0] = dFvariance
        dF[:,:,1] = dFlengthscale        
        dQc[:,:,0] = dQcvariance         
        dQc[:,:,1] = dQclengthscale        
        dPinf[:,:,0] = dPinf_variance
        dPinf[:,:,1] = dPinf_lengthscale
        dP0 = dPinf.copy()
        
        return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)