autopdex.dae.newton_solver

autopdex.dae.newton_solver(func, x0, *, atol=1e-10, rtol=1e-08, max_iter=20, damping_factor=1.0, tangent_fun=None, lin_solve_fun=None, constrained_dofs=None, constrained_values=None, verbose=0, settings=None, static_settings=None, termination_mode='residual', _pre_iteration_update=None)

Newton-Raphson solver to find a root of F(x)=0.

Parameters:

• func – Function F(x, settings (auxiliary data)) whose zero is sought.

• x0 – Initial guess.

• atol – Absolute tolerance.

• rtol – Relative tolerance.

• max_iter – Maximum number of iterations.

• damping_factor – Constant damping factor for the Newton update (0 < damping_factor <= 1; 1 -> no damping).

• tangent_fun – Function to compute the Jacobian. (Default: jax.jacfwd(func)), same signature as func.

• lin_solve_fun – Function to solve the linear system. (Default: jnp.linalg.solve)

• constrained_dofs – Boolean mask for fixed degrees of freedom.

• constrained_values – Fixed values for constrained DOFs.

• verbose – If >=1, prints the residual norm each iteration.

• termination_mode – ‘residual’ uses the residual norm; ‘update’ uses the update size.

Returns:

• .root: the computed solution,

• .num_iterations: number of updates performed,

• .converged: convergence flag.

Return type:

A RootSolverResult dataclass with fields