Computes the partial derivative of a constrained residual function with respect to parameters. Uses central difference method while keeping states fixed. Returns a Jacobian matrix of size (residualCount × parameterCount).
Formula: ∂r/∂p_ij ≈ (r_i(p+h·e_j, x) - r_i(p-h·e_j, x)) / (2h)
Parameter vector p
State vector x (kept fixed)
Constrained residual function r(p, x)
Optional numerical differentiation settings
Jacobian matrix ∂r/∂p
Computes the partial derivative of a constrained residual function with respect to parameters. Uses central difference method while keeping states fixed. Returns a Jacobian matrix of size (residualCount × parameterCount).
Formula: ∂r/∂p_ij ≈ (r_i(p+h·e_j, x) - r_i(p-h·e_j, x)) / (2h)