Question about Jacobian of NavState::Expmap

[Wuqiqi123]

gtsam/gtsam/navigation/NavState.cpp

Lines 133 to 146 in 0d44d3a

	const Vector3 t = local.applyLeftJacobian(rho, Hxi ? &H_t_w : nullptr);
	const Vector3 v = local.applyLeftJacobian(nu, Hxi ? &H_v_w : nullptr);
	if (Hxi) {
	const Matrix3 Jr = local.rightJacobian();
	// We are creating a NavState, so we still need to chain H_t_w and H_v_w
	// with R^T, the Jacobian of Navstate::Create with respect to both t and v.
	const Matrix3 M = R.matrix();
	*Hxi << Jr, Z_3x3, Z_3x3, // Jr here *is* the Jacobian of expmap
	M.transpose() * H_t_w, Jr, Z_3x3, //
	M.transpose() * H_v_w, Z_3x3, Jr;
	// In the last two rows, Jr = R^T * J_l, see Barfoot eq. (8.83).
	// J_l is the Jacobian of applyLeftJacobian in the second argument.
	}

And this class has a function named
NavState NavState::retract(const Vector9& xi, OptionalJacobian<9, 9> H1, OptionalJacobian<9, 9> H2) const;

What's the difference between this two function.

[dellaert]

They have the same function: retract back to the manifold. But retract does not have to be the exponential map.