Crate phyz_diff 

Differentiation utilities for phyz: Jacobians of the equations of motion.

Three routines compute the same object — the Jacobians of one semi-implicit Euler step — by different means, trading accuracy against cost:

Function	Method	Exact?
finite_diff_jacobians	central differences over the whole step	no
semi_implicit_step_jacobians	chain rule through the integrator, central differences on ABA	no (ABA block is FD)
symbolic::symbolic_step_jacobians	symbolic differentiation of the dynamics	yes

Only the symbolic path is derivative-exact. The other two are finite differences and inherit the usual step-size/round-off tradeoff. For exact parameter and contact-surface gradients over a whole trajectory, see the dual-number adjoint in phyz::diff instead.

Example

use phyz_diff::semi_implicit_step_jacobians;
use phyz_math::{GRAVITY, Mat3, SpatialInertia, SpatialTransform, Vec3};
use phyz_model::ModelBuilder;

let model = ModelBuilder::new()
    .gravity(Vec3::new(0.0, -GRAVITY, 0.0))
    .dt(0.002)
    .add_revolute_body(
        "pendulum",
        -1,
        SpatialTransform::identity(),
        SpatialInertia::new(
            1.0,
            Vec3::new(0.0, -0.5, 0.0),
            Mat3::from_diagonal(&Vec3::new(0.083, 0.0, 0.083)),
        ),
    )
    .build();

let mut state = model.default_state();
state.q[0] = 0.3;

let jac = semi_implicit_step_jacobians(&model, &state);
assert_eq!(jac.dvnext_dq.nrows(), model.nv);

Re-exports

pub use rollout::AdjointGradients;

pub use rollout::AdjointRollout;

pub use rollout::CollisionMesh;

pub use rollout::ContactSetup;

pub use rollout::FinalStateObjective;

pub use rollout::GroundContact;

pub use rollout::N_INERTIA_PARAMS;

pub use rollout::adjoint_rollout_gradient;

pub use rollout::inertia_params;

pub use rollout::rollout_objective;

pub use contact_adjoint::ConvexAdjointError;

pub use contact_adjoint::ConvexAdjointGradients;

pub use contact_adjoint::ConvexContactRollout;

pub use contact_adjoint::convex_adjoint_gradient;

pub use contact_adjoint::convex_rollout_objective;

Modules

contact_adjoint

Trajectory adjoint through the convex contact solve — the same contact model the forward simulator runs.

multidual

Vector-mode forward AD: one pass through the dynamics, N derivatives out.

rollout

Differentiable rollouts: exact parameter and contact-surface adjoints.

symbolic

Symbolic Jacobian computation via tang-expr.

Structs

StepJacobians

Jacobians of a single simulation step.

Functions

analytical_step_jacobiansDeprecated

Deprecated alias for semi_implicit_step_jacobians.

finite_diff_jacobians

Compute step Jacobians via finite differences.

semi_implicit_step_jacobians

Compute step Jacobians for semi-implicit Euler by chain rule through the integrator.