Solver Implementation

Solver implementation details. More...

Detailed Description

Solver implementation details.

Implementation of Newton method for solving system of non-linear equations using Eigen

• newton::newton_solver with user, e.g. SymPy, provided Jacobian

Functions
template<int N>
EIGEN_DEVICE_FUNC bool	nmodl::newton::is_converged (const Eigen::Matrix< double, N, 1 > &X, const Eigen::Matrix< double, N, N > &J, const Eigen::Matrix< double, N, 1 > &F, double eps)
template<int N, typename FUNC >
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver (Eigen::Matrix< double, N, 1 > &X, FUNC functor, double eps=EPS, int max_iter=MAX_ITER)
	Newton method with user-provided Jacobian. More...
template<typename FUNC , int N>
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver_small_N (Eigen::Matrix< double, N, 1 > &X, FUNC functor, double eps, int max_iter)
	Newton method template specializations for \(N <= 4\) Use explicit inverse of F instead of LU decomposition. More...
template<typename FUNC >
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver (Eigen::Matrix< double, 1, 1 > &X, FUNC functor, double eps=EPS, int max_iter=MAX_ITER)
template<typename FUNC >
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver (Eigen::Matrix< double, 2, 1 > &X, FUNC functor, double eps=EPS, int max_iter=MAX_ITER)
template<typename FUNC >
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver (Eigen::Matrix< double, 3, 1 > &X, FUNC functor, double eps=EPS, int max_iter=MAX_ITER)
template<typename FUNC >
EIGEN_DEVICE_FUNC int	nmodl::newton::newton_solver (Eigen::Matrix< double, 4, 1 > &X, FUNC functor, double eps=EPS, int max_iter=MAX_ITER)

Variables
static constexpr int	nmodl::newton::MAX_ITER = 50
static constexpr double	nmodl::newton::EPS = 1e-13

Function Documentation

is_converged()

template<int N>

EIGEN_DEVICE_FUNC bool nmodl::newton::is_converged	(	const Eigen::Matrix< double, N, 1 > &	X,
		const Eigen::Matrix< double, N, N > &	J,
		const Eigen::Matrix< double, N, 1 > &	F,
		double	eps
	)

Definition at line 41 of file newton.hpp.

newton_solver() [1/5]

template<typename FUNC >

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver	(	Eigen::Matrix< double, 1, 1 > &	X,
		FUNC	functor,
		double	eps = EPS,
		int	max_iter = MAX_ITER
	)

Definition at line 153 of file newton.hpp.

newton_solver() [2/5]

template<typename FUNC >

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver	(	Eigen::Matrix< double, 2, 1 > &	X,
		FUNC	functor,
		double	eps = EPS,
		int	max_iter = MAX_ITER
	)

Definition at line 161 of file newton.hpp.

newton_solver() [3/5]

template<typename FUNC >

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver	(	Eigen::Matrix< double, 3, 1 > &	X,
		FUNC	functor,
		double	eps = EPS,
		int	max_iter = MAX_ITER
	)

Definition at line 169 of file newton.hpp.

newton_solver() [4/5]

template<typename FUNC >

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver	(	Eigen::Matrix< double, 4, 1 > &	X,
		FUNC	functor,
		double	eps = EPS,
		int	max_iter = MAX_ITER
	)

Definition at line 177 of file newton.hpp.

newton_solver() [5/5]

template<int N, typename FUNC >

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver	(	Eigen::Matrix< double, N, 1 > &	X,
		FUNC	functor,
		double	eps = EPS,
		int	max_iter = MAX_ITER
	)

Newton method with user-provided Jacobian.

Newton method with user-provided Jacobian: given initial vector X and a functor that calculates F(X), J(X) where J(X) is the Jacobian of F(X), solves for \(F(X) = 0\), starting with initial value of X by iterating:

\[ X_{n+1} = X_n - J(X_n)^{-1} F(X_n) \]

when \(|F|^2 < eps^2\), solution has converged.

Returns

number of iterations (-1 if failed to converge)

Definition at line 80 of file newton.hpp.

newton_solver_small_N()

template<typename FUNC , int N>

EIGEN_DEVICE_FUNC int nmodl::newton::newton_solver_small_N	(	Eigen::Matrix< double, N, 1 > &	X,
		FUNC	functor,
		double	eps,
		int	max_iter
	)

Newton method template specializations for \(N <= 4\) Use explicit inverse of F instead of LU decomposition.

This is faster, as there is no pivoting and therefore no branches, but it is not numerically safe for \(N > 4\).

Definition at line 126 of file newton.hpp.

Variable Documentation

EPS

constexpr double nmodl::newton::EPS = 1e-13

staticconstexpr

Definition at line 38 of file newton.hpp.

MAX_ITER

constexpr int nmodl::newton::MAX_ITER = 50

staticconstexpr

Definition at line 37 of file newton.hpp.