algebra_solver_newton()

template<typename F , typename T1 , typename T2 , require_all_eigen_vector_t< T1, T2 > * = nullptr>

Eigen::Matrix< scalar_type_t< T2 >, Eigen::Dynamic, 1 > stan::math::algebra_solver_newton	(	const F &	f,
		const T1 &	x,
		const T2 &	y,
		const std::vector< double > &	dat,
		const std::vector< int > &	dat_int,
		std::ostream *const	msgs = nullptr,
		const double	scaling_step_size = 1e-3,
		const double	function_tolerance = 1e-6,
		const long int	max_num_steps = 200
	)

Return the solution to the specified system of algebraic equations given an initial guess, and parameters and data, which get passed into the algebraic system.

Use the KINSOL solver from the SUNDIALS suite.

The user can also specify the scaled step size, the function tolerance, and the maximum number of steps.

Signature to maintain backward compatibility, will be removed in the future.

Template Parameters

F	type of equation system function.
T	type of initial guess vector.

Parameters

[in]	f	Functor that evaluated the system of equations.
[in]	x	Vector of starting values.
[in]	y	Parameter vector for the equation system.
[in]	dat	Continuous data vector for the equation system.
[in]	dat_int	Integer data vector for the equation system.
[in,out]	msgs	The print stream for warning messages.
[in]	scaling_step_size	Scaled-step stopping tolerance. If a Newton step is smaller than the scaling step tolerance, the code breaks, assuming the solver is no longer making significant progress (i.e. is stuck)
[in]	function_tolerance	determines whether roots are acceptable.
[in]	max_num_steps	maximum number of function evaluations.

Returns

theta Vector of solutions to the system of equations.

Exceptions

<code>std::invalid_argument</code>	if x has size zero.
<code>std::invalid_argument</code>	if x has non-finite elements.
<code>std::invalid_argument</code>	if y has non-finite elements.
<code>std::invalid_argument</code>	if dat has non-finite elements.
<code>std::invalid_argument</code>	if dat_int has non-finite elements.
<code>std::invalid_argument</code>	if scaled_step_size is strictly negative.
<code>std::invalid_argument</code>	if function_tolerance is strictly negative.
<code>std::invalid_argument</code>	if max_num_steps is not positive.
<code>std::domain_error	if solver exceeds max_num_steps.

Definition at line 295 of file solve_newton.hpp.