Module jacobian 

Jacobian builders for inverse profile reconstruction.

The forward model used in this crate-level inverse module maps probe-space normalized flux samples to synthetic measurements: m_i = p(psi_i) + ff(psi_i) where p and ff are mTanh profiles with independent parameter sets.

Functions

compute_analytical_jacobian

Build analytical Jacobian with 8 columns: [p_ped_height, p_ped_top, p_ped_width, p_core_alpha, ff_ped_height, ff_ped_top, ff_ped_width, ff_core_alpha].

compute_fd_jacobian

Finite-difference Jacobian using forward difference.

forward_model_response

Forward model used by inverse reconstruction.

mtanh_profile_derivatives

Re-export profile derivatives for callers expecting this symbol in jacobian.