quda::IRAM Class Reference

Implicitly Restarted Arnoldi Method. More...

#include <eigensolve_quda.h>

Inheritance diagram for quda::IRAM:

Public Member Functions
	IRAM (const DiracMatrix &mat, QudaEigParam *eig_param, TimeProfile &profile)
	Constructor for Thick Restarted Eigensolver class. More...
virtual bool	hermitian ()
virtual	~IRAM ()
	Destructor for Thick Restarted Eigensolver class. More...
void	operator() (std::vector< ColorSpinorField * > &kSpace, std::vector< Complex > &evals)
	Compute eigenpairs. More...
void	arnoldiStep (std::vector< ColorSpinorField * > &v, std::vector< ColorSpinorField * > &r, double &beta, int j)
	Arnoldi step: extends the Krylov space by one vector. More...
void	eigensolveFromUpperHess (std::vector< Complex > &evals, const double beta)
	Get the eigendecomposition from the upper Hessenberg matrix via QR. More...
void	rotateBasis (std::vector< ColorSpinorField * > &v, int keep)
	Rotate the Krylov space. More...
void	qrShifts (const std::vector< Complex > evals, const int num_shifts)
	Apply shifts to the upper Hessenberg matrix via QR decomposition. More...
void	qrIteration (Complex **Q, Complex **R)
	Apply One step of the the QR algorithm. More...
void	reorder (std::vector< ColorSpinorField * > &kSpace, std::vector< Complex > &evals, const QudaEigSpectrumType spec_type)
	Reorder the Krylov space and eigenvalues. More...
Public Member Functions inherited from quda::EigenSolver
	EigenSolver (const DiracMatrix &mat, QudaEigParam *eig_param, TimeProfile &profile)
	Constructor for base Eigensolver class. More...
virtual	~EigenSolver ()
void	prepareInitialGuess (std::vector< ColorSpinorField * > &kSpace)
	Check for an initial guess. If none present, populate with rands, then orthonormalise. More...
void	checkChebyOpMax (const DiracMatrix &mat, std::vector< ColorSpinorField * > &kSpace)
	Check for a maximum of the Chebyshev operator. More...
void	prepareKrylovSpace (std::vector< ColorSpinorField * > &kSpace, std::vector< Complex > &evals)
	Extend the Krylov space. More...
double	setEpsilon (const QudaPrecision prec)
	Set the epsilon parameter. More...
void	queryPrec (const QudaPrecision prec)
	Query the eigensolver precision to stdout. More...
void	printEigensolverSetup ()
	Dump the eigensolver parameters to stdout. More...
void	cleanUpEigensolver (std::vector< ColorSpinorField * > &kSpace, std::vector< Complex > &evals)
	Release memory, save eigenvectors, resize the Krylov space to its original dimension. More...
void	matVec (const DiracMatrix &mat, ColorSpinorField &out, const ColorSpinorField &in)
	Applies the specified matVec operation: M, Mdag, MMdag, MdagM. More...
void	chebyOp (const DiracMatrix &mat, ColorSpinorField &out, const ColorSpinorField &in)
	Promoted the specified matVec operation: M, Mdag, MMdag, MdagM to a Chebyshev polynomial. More...
double	estimateChebyOpMax (const DiracMatrix &mat, ColorSpinorField &out, ColorSpinorField &in)
	Estimate the spectral radius of the operator for the max value of the Chebyshev polynomial. More...
void	blockOrthogonalize (std::vector< ColorSpinorField * > v, std::vector< ColorSpinorField * > &r, int j)
	Orthogonalise input vectors r against vector space v using block-BLAS. More...
void	orthonormalizeMGS (std::vector< ColorSpinorField * > &v, int j)
	Orthonormalise input vector space v using Modified Gram-Schmidt. More...
bool	orthoCheck (std::vector< ColorSpinorField * > v, int j)
	Check orthonormality of input vector space v. More...
void	rotateVecs (std::vector< ColorSpinorField * > &kSpace, const double *rot_array, const int offset, const int dim, const int keep, const int locked, TimeProfile &profile)
	Rotate the Krylov space. More...
void	rotateVecsComplex (std::vector< ColorSpinorField * > &kSpace, const Complex *rot_array, const int offset, const int dim, const int keep, const int locked, TimeProfile &profile)
	Rotate the Krylov space. More...
void	permuteVecs (std::vector< ColorSpinorField * > &kSpace, int *mat, int size)
	Permute the vector space using the permutation matrix. More...
void	blockRotate (std::vector< ColorSpinorField * > &kSpace, double *array, int rank, const range &i, const range &j, blockType b_type)
	Rotate part of kSpace. More...
void	blockRotateComplex (std::vector< ColorSpinorField * > &kSpace, Complex *array, int rank, const range &i, const range &j, blockType b_type, int offset)
	Rotate part of kSpace. More...
void	blockReset (std::vector< ColorSpinorField * > &kSpace, int js, int je, int offset)
	Copy temp part of kSpace, zero out for next use. More...
void	deflate (std::vector< ColorSpinorField * > &sol, const std::vector< ColorSpinorField * > &src, const std::vector< ColorSpinorField * > &evecs, const std::vector< Complex > &evals, bool accumulate=false) const
	Deflate a set of source vectors with a given eigenspace. More...
void	deflate (ColorSpinorField &sol, const ColorSpinorField &src, const std::vector< ColorSpinorField * > &evecs, const std::vector< Complex > &evals, bool accumulate=false)
	Deflate a given source vector with a given eigenspace. This is a wrapper variant for a single source vector. More...
void	deflateSVD (std::vector< ColorSpinorField * > &sol, const std::vector< ColorSpinorField * > &vec, const std::vector< ColorSpinorField * > &evecs, const std::vector< Complex > &evals, bool accumulate=false) const
	Deflate a set of source vectors with a set of left and right singular vectors. More...
void	deflateSVD (ColorSpinorField &sol, const ColorSpinorField &src, const std::vector< ColorSpinorField * > &evecs, const std::vector< Complex > &evals, bool accumulate=false)
	Deflate a a given source vector with a given with a set of left and right singular vectors This is a wrapper variant for a single source vector. More...
void	computeSVD (const DiracMatrix &mat, std::vector< ColorSpinorField * > &evecs, std::vector< Complex > &evals)
	Computes Left/Right SVD from pre computed Right/Left. More...
void	computeEvals (const DiracMatrix &mat, std::vector< ColorSpinorField * > &evecs, std::vector< Complex > &evals, int size)
	Compute eigenvalues and their residiua. More...
void	computeEvals (const DiracMatrix &mat, std::vector< ColorSpinorField * > &evecs, std::vector< Complex > &evals)
	Compute eigenvalues and their residiua. This variant compute the number of converged eigenvalues. More...
void	loadFromFile (const DiracMatrix &mat, std::vector< ColorSpinorField * > &eig_vecs, std::vector< Complex > &evals)
	Load and check eigenpairs from file. More...
void	sortArrays (QudaEigSpectrumType spec_type, int n, std::vector< Complex > &x, std::vector< Complex > &y)
	Sort array the first n elements of x according to spec_type, y comes along for the ride. More...
void	sortArrays (QudaEigSpectrumType spec_type, int n, std::vector< double > &x, std::vector< Complex > &y)
	Sort array the first n elements of x according to spec_type, y comes along for the ride Overloaded version with real x. More...
void	sortArrays (QudaEigSpectrumType spec_type, int n, std::vector< Complex > &x, std::vector< double > &y)
	Sort array the first n elements of x according to spec_type, y comes along for the ride Overloaded version with real y. More...
void	sortArrays (QudaEigSpectrumType spec_type, int n, std::vector< double > &x, std::vector< double > &y)
	Sort array the first n elements of x according to spec_type, y comes along for the ride Overloaded version with real x and real y. More...

Public Attributes
Complex **	upperHess
Complex **	Qmat
Complex **	Rmat

Additional Inherited Members
Static Public Member Functions inherited from quda::EigenSolver
static EigenSolver *	create (QudaEigParam *eig_param, const DiracMatrix &mat, TimeProfile &profile)
	Creates the eigensolver using the parameters given and the matrix. More...
Protected Attributes inherited from quda::EigenSolver
const DiracMatrix &	mat
QudaEigParam *	eig_param
TimeProfile &	profile
int	n_ev
int	n_kr
int	n_conv
int	n_ev_deflate
double	tol
bool	reverse
char	spectrum [3]
bool	converged
int	restart_iter
int	max_restarts
int	check_interval
int	batched_rotate
int	block_size
int	iter
int	iter_converged
int	iter_locked
int	iter_keep
int	num_converged
int	num_locked
int	num_keep
std::vector< double >	residua
std::vector< ColorSpinorField * >	r
std::vector< ColorSpinorField * >	d_vecs_tmp
ColorSpinorField *	tmp1
ColorSpinorField *	tmp2
QudaPrecision	save_prec

Detailed Description

Implicitly Restarted Arnoldi Method.

Definition at line 554 of file eigensolve_quda.h.

Constructor & Destructor Documentation

IRAM()

quda::IRAM::IRAM	(	const DiracMatrix &	mat,
		QudaEigParam *	eig_param,
		TimeProfile &	profile
	)

Constructor for Thick Restarted Eigensolver class.

Parameters

eig_param	The eigensolver parameters
mat	The operator to solve
profile	Time Profile

Definition at line 19 of file eig_iram.cpp.

~IRAM()

quda::IRAM::~IRAM ( )

virtual

Destructor for Thick Restarted Eigensolver class.

IRAM is for any linear system

Definition at line 587 of file eig_iram.cpp.

Member Function Documentation

arnoldiStep()

void quda::IRAM::arnoldiStep	(	std::vector< ColorSpinorField * > &	v,
		std::vector< ColorSpinorField * > &	r,
		double &	beta,
		int	j
	)

Arnoldi step: extends the Krylov space by one vector.

Parameters

[in]	v	Vector space
[in]	r	Residual vector
[in]	beta	Norm of residual vector
[in]	j	Index of vector being computed

Definition at line 47 of file eig_iram.cpp.

eigensolveFromUpperHess()

void quda::IRAM::eigensolveFromUpperHess	(	std::vector< Complex > &	evals,
		const double	beta
	)

Get the eigendecomposition from the upper Hessenberg matrix via QR.

Parameters

[in]	evals	Complex eigenvalues
[in]	beta	Norm of residual (used to compute errors on eigenvalues)

Definition at line 312 of file eig_iram.cpp.

hermitian()

virtual bool quda::IRAM::hermitian ( )

inlinevirtual

Returns

Whether the solver is only for Hermitian systems

Implements quda::EigenSolver.

Definition at line 573 of file eigensolve_quda.h.

operator()()

void quda::IRAM::operator() ( std::vector< ColorSpinorField * > &  kSpace, std::vector< Complex > &  evals  )

virtual

Compute eigenpairs.

Parameters

[in]	kSpace	Krylov vector space
[in]	evals	Computed eigenvalues

Implements quda::EigenSolver.

Definition at line 432 of file eig_iram.cpp.

qrIteration()

void quda::IRAM::qrIteration	(	Complex **	Q,
		Complex **	R
	)

Apply One step of the the QR algorithm.

Parameters

[in]	Q	The Q matrix
[in]	R	The R matrix

Definition at line 227 of file eig_iram.cpp.

qrShifts()

void quda::IRAM::qrShifts	(	const std::vector< Complex >	evals,
		const int	num_shifts
	)

Apply shifts to the upper Hessenberg matrix via QR decomposition.

Parameters

[in]	evals	The shifts to apply
[in]	num_shifts	The number of shifts to apply

Definition at line 197 of file eig_iram.cpp.

reorder()

void quda::IRAM::reorder	(	std::vector< ColorSpinorField * > &	kSpace,
		std::vector< Complex > &	evals,
		const QudaEigSpectrumType	spec_type
	)

Reorder the Krylov space and eigenvalues.

Parameters

[in]	kSpace	The Krylov space
[in]	evals	the eigenvalues
[in]	spec_type	The spectrum type (Largest/Smallest)(Modulus/Imaginary/Real) that determines the sorting condition

Definition at line 135 of file eig_iram.cpp.

rotateBasis()

void quda::IRAM::rotateBasis	(	std::vector< ColorSpinorField * > &	v,
		int	keep
	)

Rotate the Krylov space.

Parameters

[in]	v	Vector space
[in]	keep	The number of vectors to keep after rotation

Definition at line 125 of file eig_iram.cpp.

Member Data Documentation

Qmat

Complex** quda::IRAM::Qmat

Definition at line 559 of file eigensolve_quda.h.

Rmat

Complex** quda::IRAM::Rmat

Definition at line 560 of file eigensolve_quda.h.

upperHess

Complex** quda::IRAM::upperHess

Definition at line 558 of file eigensolve_quda.h.

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

• quda/include/eigensolve_quda.h
• quda/lib/eig_iram.cpp