types.linearization.DiffusionJacobian

types.linearization.DiffusionJacobian

Diffusion Jacobian ∂g/∂x (stochastic systems).

For multiplicative noise: g depends on x, so linearize. For additive noise: g is constant, Jacobian is just g itself.

Shape: (nx, nw)

Examples

>>> Gc: DiffusionJacobian = sde_system.diffusion_jacobian(x_eq, u_eq)
>>> 
>>> # Additive noise (constant)
>>> Gc_additive = 0.1 * np.eye(nx)
>>> 
>>> # Multiplicative noise (state-dependent)
>>> # For dx = f(x)dt + σ*x*dW:
>>> Gc_multiplicative = σ * x_eq  # ∂(σ*x)/∂x evaluated at x_eq