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