Solve a M*psi=chi linear system by FGMRESDR. More...

#include <syssolver_linop_fgmres_dr.h>

Inheritance diagram for Chroma::LinOpSysSolverFGMRESDR:

Public Types
using	T = LatticeFermion

using	U = LatticeColorMatrix

using	Q = multi1d< U >

Public Member Functions
	LinOpSysSolverFGMRESDR (Handle< LinearOperator< T > > A, Handle< FermState< T, Q, Q > > state, const SysSolverFGMRESDRParams &invParam)
	Constructor. More...

void	InitMatrices ()
	Initialize the internal matrices. More...

	~LinOpSysSolverFGMRESDR ()
	Destructor is automatic. More...

const Subset &	subset () const
	Return the subset on which the operator acts. More...

SystemSolverResults_t	operator() (T &psi, const T &chi) const
	Solver the linear system. More...

void	FlexibleArnoldi (int n_krylov, int n_deflate, const Real &rsd_target, multi1d< T > &V, multi1d< T > &Z, multi2d< DComplex > &H, multi2d< DComplex > &R, multi1d< Handle< Givens > > &givens_rots, multi1d< DComplex > &g, multi2d< DComplex > &Qk, multi1d< DComplex > &Qk_tau, int &ndim_cycle) const

void	LeastSquaresSolve (const multi2d< DComplex > &R, const multi1d< DComplex > &rhs, multi1d< DComplex > &eta, int dim) const

void	GetEigenvectors (int total_dim, const multi2d< DComplex > &H, multi1d< DComplex > &f_m, multi2d< DComplex > &evecs, multi1d< DComplex > &evals, multi1d< int > &order_array) const

Public Member Functions inherited from Chroma::SystemSolver< LatticeFermion >
virtual	~SystemSolver ()
	Virtual destructor to help with cleanup;. More...

Private Member Functions
	LinOpSysSolverFGMRESDR ()

Private Attributes
Handle< LinearOperator< T > >	A_

Handle< FermState< T, Q, Q > >	state_

SysSolverFGMRESDRParams	invParam_

Handle< LinOpSystemSolver< T > >	preconditioner_

multi2d< DComplex >	H_

multi2d< DComplex >	R_

multi1d< T >	V_

multi1d< T >	Z_

multi1d< Handle< Givens > >	givens_rots_

multi1d< DComplex >	c_

multi1d< DComplex >	eta_

multi1d< DComplex >	g_

multi2d< DComplex >	Hk_QR_

multi1d< DComplex >	Hk_QR_taus_

Detailed Description

Solve a M*psi=chi linear system by FGMRESDR.

Definition at line 155 of file syssolver_linop_fgmres_dr.h.

Member Typedef Documentation

◆ Q

using Chroma::LinOpSysSolverFGMRESDR::Q = multi1d<U>

Definition at line 160 of file syssolver_linop_fgmres_dr.h.

◆ T

using Chroma::LinOpSysSolverFGMRESDR::T = LatticeFermion

Definition at line 158 of file syssolver_linop_fgmres_dr.h.

◆ U

using Chroma::LinOpSysSolverFGMRESDR::U = LatticeColorMatrix

Definition at line 159 of file syssolver_linop_fgmres_dr.h.

Constructor & Destructor Documentation

◆ LinOpSysSolverFGMRESDR() [1/2]

Chroma::LinOpSysSolverFGMRESDR::LinOpSysSolverFGMRESDR	(	Handle< LinearOperator< T > >	A,
		Handle< FermState< T, Q, Q > >	state,
		const SysSolverFGMRESDRParams &	invParam
	)

inline

Constructor.

Parameters

A_	Linear operator ( Read )
invParam	inverter parameters ( Read )

Definition at line 167 of file syssolver_linop_fgmres_dr.h.

References A_, Chroma::GroupXML_t::id, InitMatrices(), Chroma::SingletonHolder< T, CreationPolicy, LifetimePolicy, ThreadingModel >::Instance(), invParam_, Chroma::SysSolverFGMRESDRParams::NDefl, Chroma::GroupXML_t::path, preconditioner_, Chroma::SysSolverFGMRESDRParams::PrecondParams, state_, and Chroma::GroupXML_t::xml.

◆ ~LinOpSysSolverFGMRESDR()

Chroma::LinOpSysSolverFGMRESDR::~LinOpSysSolverFGMRESDR ( )

inline

Destructor is automatic.

Definition at line 212 of file syssolver_linop_fgmres_dr.h.

◆ LinOpSysSolverFGMRESDR() [2/2]

Chroma::LinOpSysSolverFGMRESDR::LinOpSysSolverFGMRESDR ( )

inlineprivate

Definition at line 253 of file syssolver_linop_fgmres_dr.h.

Member Function Documentation

◆ FlexibleArnoldi()

void Chroma::LinOpSysSolverFGMRESDR::FlexibleArnoldi	(	int	n_krylov,
		int	n_deflate,
		const Real &	rsd_target,
		multi1d< T > &	V,
		multi1d< T > &	Z,
		multi2d< DComplex > &	H,
		multi2d< DComplex > &	R,
		multi1d< Handle< Givens > > &	givens_rots,
		multi1d< DComplex > &	g,
		multi2d< DComplex > &	Qk,
		multi1d< DComplex > &	Qk_tau,
		int &	ndim_cycle
	)		const

Flexible Arnolid Process. Currently not using augmentation (n_deflate ignored)

NB: This currentl just forwards to a templated free function

Definition at line 429 of file syssolver_linop_fgmres_dr.cc.

References A_, and preconditioner_.

Referenced by operator()(), TEST_F(), and TEST_P().

◆ GetEigenvectors()

void Chroma::LinOpSysSolverFGMRESDR::GetEigenvectors	(	int	total_dim,
		const multi2d< DComplex > &	H,
		multi1d< DComplex > &	f_m,
		multi2d< DComplex > &	evecs,
		multi1d< DComplex > &	evals,
		multi1d< int > &	order_array
	)		const

Get the eigenvectors of the matrix H_tilde = H_m + f_m h^{H}_m

of which we will keep the first NDefl corresponding to the NDefl eigenvalues of smallest modulus as our matrix G. In turn the Harmonic Ritz vectors are V_m G_m.

We need a two stage process here. One: first we need to solve H_m^H f_m = h^H_m where h_m is the last row of the \hat{H}_m

second, once in posession of f_m we need to constuct H_tilde and get its eigenvalues and eigenvectors.

NB: We use lapack here, specifically the routines: zgetrf/zgetrs to solve for f_m

zgeev to get the eigenvalues/eigenvectors

Definition at line 343 of file syssolver_linop_fgmres_dr.cc.

References Chroma::i, Chroma::info, and j.

Referenced by TEST_F().

◆ InitMatrices()

void Chroma::LinOpSysSolverFGMRESDR::InitMatrices ( )

Initialize the internal matrices.

Initialize the key matrices (resize and zero)

Definition at line 199 of file syssolver_linop_fgmres_dr.cc.

References c_, eta_, g_, givens_rots_, H_, invParam_, Chroma::SysSolverFGMRESDRParams::NDefl, Chroma::SysSolverFGMRESDRParams::NKrylov, R_, V_, Z_, and Chroma::zero.

Referenced by LinOpSysSolverFGMRESDR().

◆ LeastSquaresSolve()

void Chroma::LinOpSysSolverFGMRESDR::LeastSquaresSolve	(	const multi2d< DComplex > &	R,
		const multi1d< DComplex > &	Q_rhs,
		multi1d< DComplex > &	eta,
		int	n_cols
	)		const

Solve least squares system to get the coefficients for Updating the solution at the end of an GGMRES-DR Cycle. In this instantiation the system solved is

R \eta = rhs

where R is the matrix H from GMRES, reduced to upper triangular form by Givens rotations, and rhs is the result of the Givens rotations applied to the orignal g = [ beta, 0, 0 ... ]^T vector.

Hence this operation is a straightforward back substitution NB: the matrix R has dim+1 rows and dim columns, but the dim+1-th row has All zero entries and should be deleted. d

dim is passed in instead of using matrix dimensions in case the cycle terminated early.

Definition at line 257 of file syssolver_linop_fgmres_dr.cc.

References Chroma::eta.

Referenced by operator()(), and TEST_F().