nmpc_cgmres::Gmres Class Reference

GMRES method to solve a linear equation. More...

#include <Gmres.h>

Public Types
using	AmulFunc = std::function< Eigen::VectorXd(const Eigen::Ref< const Eigen::VectorXd > &)>
	Type of function that returns x multiplied by A. More...

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	Gmres ()
	Constructor. More...
void	solve (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b, Eigen::Ref< Eigen::VectorXd > x, int k_max=100, double eps=1e-10)
	Solve. More...
void	solve (const AmulFunc &Amul_func, const Eigen::Ref< const Eigen::VectorXd > &b, Eigen::Ref< Eigen::VectorXd > x, int k_max=100, double eps=1e-10)
	Solve. More...

Public Attributes
bool	make_triangular_ = true
bool	apply_reorth_ = true
Eigen::MatrixXd	H_
Eigen::VectorXd	g_
std::vector< double >	err_list_
std::vector< Eigen::VectorXd >	basis_

Detailed Description

GMRES method to solve a linear equation.

See the following articles about the GMRES method:

• C T Kelley. Iterative methods for linear and nonlinear equations. 1995.
• https://www.coronasha.co.jp/np/isbn/9784339032109/

Definition at line 21 of file Gmres.h.

Member Typedef Documentation

AmulFunc

using nmpc_cgmres::Gmres::AmulFunc = std::function<Eigen::VectorXd(const Eigen::Ref<const Eigen::VectorXd> &)>

Type of function that returns x multiplied by A.

Definition at line 25 of file Gmres.h.

Constructor & Destructor Documentation

Gmres()

EIGEN_MAKE_ALIGNED_OPERATOR_NEW nmpc_cgmres::Gmres::Gmres ( )

inline

Constructor.

Definition at line 31 of file Gmres.h.

Member Function Documentation

solve() [1/2]

void nmpc_cgmres::Gmres::solve ( const AmulFunc &  Amul_func, const Eigen::Ref< const Eigen::VectorXd > &  b, Eigen::Ref< Eigen::VectorXd >  x, int  k_max = 100, double  eps = 1e-10  )

inline

Solve.

Parameters

Amul_func	the function to return where is given
b	the vector of linear equation
x	the initial guess of solution, which is overwritten by the final solution
k_max	the maximum number of GMRES iteration
eps	the required solution tolerance

Solve the linear equation: .

Refer to the Algorithm 3.5.1. in [1] for the case that make_triangular_ is true. Refer to the Algorithm 3.4.2. in [1] for the case that make_triangular_ is false. [1] Kelley, Carl T. Iterative methods for linear and nonlinear equations. Society for Industrial and Applied Mathematics, 1995.

Definition at line 67 of file Gmres.h.

solve() [2/2]

void nmpc_cgmres::Gmres::solve ( const Eigen::Ref< const Eigen::MatrixXd > &  A, const Eigen::Ref< const Eigen::VectorXd > &  b, Eigen::Ref< Eigen::VectorXd >  x, int  k_max = 100, double  eps = 1e-10  )

inline

Solve.

Parameters

A	the matrix of linear equation
b	the vector of linear equation
x	the initial guess of solution, which is overwritten by the final solution
k_max	the maximum number of GMRES iteration
eps	the required solution tolerance

Solve the linear equation: .

Definition at line 42 of file Gmres.h.

Member Data Documentation

apply_reorth_

bool nmpc_cgmres::Gmres::apply_reorth_ = true

Definition at line 196 of file Gmres.h.

basis_

std::vector<Eigen::VectorXd> nmpc_cgmres::Gmres::basis_

Definition at line 203 of file Gmres.h.

err_list_

std::vector<double> nmpc_cgmres::Gmres::err_list_

Definition at line 201 of file Gmres.h.

g_

Eigen::VectorXd nmpc_cgmres::Gmres::g_

Definition at line 199 of file Gmres.h.

H_

Eigen::MatrixXd nmpc_cgmres::Gmres::H_

Definition at line 198 of file Gmres.h.

make_triangular_

bool nmpc_cgmres::Gmres::make_triangular_ = true

Definition at line 195 of file Gmres.h.

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The documentation for this class was generated from the following file:

• /home/runner/work/NMPC/NMPC/catkin_ws/src/NMPC/nmpc_cgmres/include/nmpc_cgmres/Gmres.h