types.trajectories.StateTrajectory

types.trajectories.StateTrajectory

State trajectory over time.

Time series of state vectors representing system evolution.

Shapes: - Single trajectory: (n_steps, nx) Each row is x[k] or x(t_k)

• Batched trajectories: (n_steps, batch, nx) Multiple trajectories simulated in parallel

• Multiple trials: (n_trials, n_steps, nx) Independent simulation runs

Indexing: - trajectory[k] -> state at step k (nx,) - trajectory[:, i] -> i-th state component over time (n_steps,) - trajectory[k, b] -> state at step k, batch b (nx,)

Examples

>>> # Single trajectory from simulation
>>> x0 = np.array([1.0, 0.0])
>>> trajectory: StateTrajectory = system.simulate(x0, u_seq, steps=100)
>>> print(trajectory.shape)  # (101, 2) - includes initial state
>>> 
>>> # Extract position and velocity
>>> position = trajectory[:, 0]  # First state component
>>> velocity = trajectory[:, 1]  # Second state component
>>> 
>>> # Batched simulation (Monte Carlo)
>>> x0_batch = np.random.randn(1000, 2)  # 1000 initial conditions
>>> trajectories: StateTrajectory = system.simulate_batch(x0_batch, u_seq)
>>> print(trajectories.shape)  # (101, 1000, 2)
>>> 
>>> # Multiple independent trials
>>> trials: StateTrajectory = np.array([
...     system.simulate(x0, u_seq, steps=100)
...     for _ in range(10)
... ])
>>> print(trials.shape)  # (10, 101, 2)