A Lanczos method allowing spectral transformation by Chebycheff polynomials and premature termination. More...

#include <LanczMaxEig.hxx>

Inheritance diagram for CH_Matrix_Classes::LanczMaxEig:

Public Member Functions
	LanczMaxEig ()
	intialize all to default values

	~LanczMaxEig ()
	destructor, nothing particular

int	compute (const Lanczosmatrix *bigmat, Matrix &eigval, Matrix &eigvec, Integer nreig, Integer in_blocksz=0, Integer maxcol=0)
	the main routine: compute the nreig maximum eigenvalues of the matrix specified by bigmat More...

Set and Get Parameters
There should be no need to set any parameters, default values should be available and reasonable.
void	set_mineig (Real ie)
	set a guess on the value of the smallest

void	set_maxmult (Integer mop)
	set an upper bound on the number of matrix vector multiplications

void	set_maxiter (Integer mi)
	set an upper bpound on the number of restarts

void	set_relprec (Real relprec)
	set relative precision requirement for termination

void	set_nchebit (Integer cheb)
	set the degree of the Chebycheff polynomial for the spectral transformation

void	set_nblockmult (Integer nb)
	set maximum number of block multiplications within one restart

void	enable_stop_above (Real ub)
	allow the algorithm to stop as soon as the maximum Ritz value exceeds the value ub

void	disable_stop_above ()
	do not allow premature termination as in enable_stop_above()

void	set_retlanvecs (Integer nl)
	set an upper bound on the number of vectors returned in get_lanczosvecs()

int	get_lanczosvecs (Matrix &val, Matrix &vecs) const
	returns the Lanczos vectors of the last call with their Ritz values

Real	get_relprec (void)
	returns current relative precision requirement

int	get_err () const
	returns the error code of the last call

Integer	get_iter () const
	returns the number of restarts of the last call

Integer	get_nmult () const
	returns the number of matrix-vector multiplications of the last call

Input/Output
void	set_out (std::ostream *o=0, int pril=1)
	set output stream and level of detail of log output (for debugging)

std::ostream &	save (std::ostream &out) const
	save all data in out so that the current state can be recovered completely by restore()

std::istream &	restore (std::istream &in)
	restore the data from in where it was stored by save()

Set and Get Parameters
There should be no need to set any parameters, default values should be available and reasonable.
Input/Output

Private Member Functions
void	error (const char *s)
	output of error messages

int	guess_extremes (Integer nproposed)
	compute a guess for minimum and maximum eigenvalue

int	dhua (Integer nreig, Integer nproposed, Integer maxmult)
	main routine performing the Lancozs iterations

int	bklanc (Integer neigfound, Integer blocksz, Integer s, const Matrix &d, Matrix &C, Matrix &X, Matrix &e, Matrix &u, Matrix &v)
	block lanzos multiplication without Chebycheff spectral transformation

int	bkqrlanc (Integer neigfound, Integer blocksz, Integer s, const Matrix &d, Matrix &C, Matrix &X, Matrix &e, Matrix &u, Matrix &v)
	block lanzos multiplication, with complete QR orthogonalization, without Chebycheff spectral transformation

int	bklanccheb (Integer neigfound, Integer blocksz, Integer s, Matrix &C, Matrix &X, Matrix &e, Matrix &v)
	block lanzos multiplication with Chebycheff spectral transformation

int	bkqrlanccheb (Integer neigfound, Integer blocksz, Integer s, Matrix &C, Matrix &X, Matrix &e, Matrix &v)
	block lanzos multiplication with complete QR orthogonalization and Chebycheff spectral transformation

int	err (Integer neigfound, Integer blocksz, const Matrix &X, Matrix &e)
	compute norms of deviations of the Ritz vectors from being eigenvectors

int	cnvtst (Integer neigfound, Integer blocksz, Real &errc, Real eps, const Matrix &d, const Matrix &e, Indexmatrix &newconv)
	check convergence of maximum Ritz value/vector

int	eigen (Integer neigfound, Integer blocksz, Integer sbsz, Matrix &C, Matrix &d, Matrix &u, Matrix &v, Real &af)
	compute eigenvalues of current (block) tridiagonalization

int	sectn (Matrix &X, Integer neigfound, Integer blocksz, Matrix &C, Matrix &d, Matrix &u, Matrix &v, Real &af)
	compute matrix for eigenvalue computation into C

int	rotate_extremes (Integer neigfound, Integer sbs, Matrix &d, const Matrix &C, Matrix &X, Matrix &v)
	rotate the eigenvectors of the largest and smallest eigenvalues of the tridiagonal matrix.

int	rotate (Integer neigfound, Integer sbs, Integer l, const Matrix &C, Matrix &X, Matrix &v)
	rotate the lanzos vectors to Ritz vectors

int	resort (Integer neigfound, const Indexmatrix &newconv, Matrix &X, Matrix &d, Matrix &e, Matrix &v)
	rotate the lanzos vectors to Ritz vectors

int	random (Matrix &X, Integer j)
	assign a random vector to column j of X

Integer	orthog (Integer offset, Integer blocksz, Matrix &X, Matrix &B)
	orthonormalize columns X(:,offset:offset+l_blocksz-1) to all previous columns

int	blockcheby (Integer col_offset, const Matrix &X, Matrix &v)
	apply spectral transformation by using a Chebycheff polynomial on the block multiplications

Real	scalarcheby (Real xval)
	compute the same polynomial as in blockcheby but for the scalar value xval

int	tred2 (Integer n, const Matrix &C, Matrix &u, Matrix &v, Matrix &Z)
	tridiagonalize a symmetric blockdiagonal matrix

int	tql2 (Integer n, Matrix &u, Matrix &v, Matrix &Z)
	compute the eigenvalues of a tridiagonal matrix

Private Attributes
int	ierr
	error return code

Integer	maxop
	upper bound on matrix vector multiplications

Integer	maxiter
	upper bound on number of restarts

Integer	maxguessiter
	upper bound on number of restarts to guess spectral interval

Integer	guessmult
	number of matrix vector multiplications to guess interval

Integer	choicencheb
	user's choice for number of block Chebychev iterations (<0 -> automatic determination)

Integer	nchebit
	number of block Chebychev iterations within one iteration

Integer	choicenbmult
	user's choice for number of block multiplications (<0 -> automatic determination, min 6)

Integer	nblockmult
	number of blockmultiplications in one restart

Integer	nlanczvecs
	number of columns of storage matrix X carrying "meaningful" Ritz vectors

Integer	retlanvecs
	user's choice for number of returend Ritz vectors (<0 -> nlanczvecs)

Integer	neigfound
	number of eigenvalues known, these are in the first neigfound columns of X

Integer	blocksz
	working block of lanczos vectors X(:,neigfound:neigfound+blocksz-1)

Integer	iter
	iteration counter for Lanczos restarts (interval guess+computation)

Integer	nmult
	number of single vector multiplications with matrix

Real	errc
	error accumulation

Real	eps
	relative precision

Real	mcheps
	machine precision (computed in constructor)

Real	maxval
	current approximation of largest eigenvalue

Real	minval
	current approximation of smallest eigenvalue

Real	polval
	the Chebychef polynomial will have this value at maxval

Matrix	X
	provides storage for the Lanczos vectors during computation

Matrix	C
	X^tAX, intermediate eigenvalue computations, orthogonalizations, etc.

Matrix	d
	diagonals (Ritz values)

Matrix	e
	error bounds

Matrix	Xqr
	for complete orthogonalization with Householder QR

Matrix	u
	temporary matrix

Matrix	v
	temporary matrix

Matrix	w
	temporary matrix

Matrix	minvec
	temporary matrix for guessing minimal eigenvalue

const Lanczosmatrix *	bigmatrix
	pointer giving the (virtual) input matrix

int	stop_above
	1 if algorithm is to stop after upper bound is exceeded

Real	upper_bound
	stop if current maximum Ritz value exceeds this value

Integer	ncalls
	counts number of calls to LanczMaxEig

Integer	mymaxj
	maximum amount of storage (columns) provided in X and C

CH_Tools::GB_rand	randgen
	local random number generator

CH_Tools::Clock	myclock
	for time measurements

CH_Tools::Microseconds	time_mult
	for each restart, the time spent in lanczosmult

CH_Tools::Microseconds	time_mult_sum
	sum over time_mult for all restarts

CH_Tools::Microseconds	time_iter
	time spent in last lanczos iteration

CH_Tools::Microseconds	time_sum
	time spent in this call to compute()

int	print_level
	level of iteration information that should be displayed

std::ostream *	myout
	everything is output to *myout, default: myout=&cout (may be 0 for no output)

Additional Inherited Members
Protected Member Functions inherited from CH_Matrix_Classes::Memarrayuser
	Memarrayuser ()
	if memarray is NULL, then a new Memarray is generated. In any case the number of users of the Memarray is incremented

virtual	~Memarrayuser ()
	the number of users is decremented and the Memarray memory manager is destructed, if the number is zero.

Static Protected Attributes inherited from CH_Matrix_Classes::Memarrayuser
static Memarray *	memarray
	pointer to common memory manager for all Memarrayusers, instantiated in memarray.cxx

Detailed Description

A Lanczos method allowing spectral transformation by Chebycheff polynomials and premature termination.

The code is a translation and adaptation of a FORTRAN code most likely written by Hua.

Member Function Documentation

◆ compute()

int CH_Matrix_Classes::LanczMaxEig::compute	(	const Lanczosmatrix *	bigmat,
		Matrix &	eigval,
		Matrix &	eigvec,
		Integer	nreig,
		Integer	in_blocksz = `0`,
		Integer	maxcol = `0`
	)

virtual

the main routine: compute the nreig maximum eigenvalues of the matrix specified by bigmat

Parameters

bigmat	the symmetric matrix
eigval	on output: converged eigenvalues
eigvec	on output: eigenvectors to eigval, on input (optional): starting vectors
nreig	number of maximal eigenvalues to be computed
in_blocksz	size of a block, if block Lanczos is used
maxcol	maximum number of columns that may be used

Implements CH_Matrix_Classes::Lanczos.

Referenced by get_nmult().

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

LanczMaxEig.hxx

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ compute()