This file contains function prototypes and constant definitions for EVSL. More...

#include <complex.h>
#include <stdio.h>
#include "struct.h"

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Functions
int	ChebLanNr (double intv, int maxit, double tol, double vinit, polparams pol, int nevOut, double lamo, double Wo, double *reso, FILE fstats)

int	ChebLanTr (int lanm, int nev, double intv, int maxit, double tol, double vinit, polparams pol, int nev2, double vals, double W, double *resW, FILE fstats)
	Chebyshev polynomial filtering Lanczos process [Thick restart version]. More...

void	set_pol_def (polparams *pol)
	set default values for polparams struct. More...

int	find_pol (double intv, polparams pol)
	Sets the values in pol. More...

void	free_pol (polparams *pol)

int	ChebSI (int nev, double intv, int maxit, double tol, double vinit, polparams pol, int nevo, double lamo, double Yo, double *reso, FILE fstats)
	Chebyshev polynomial filtering Subspace Iteration. More...

void	SetupPolRec (int n, int max_deg, double tol, double lmin, double lmax, BSolDataPol *data)

void	SetupPolSqrt (int n, int max_deg, double tol, double lmin, double lmax, BSolDataPol *data)

void	FreeBSolPolData (BSolDataPol *data)

void	BSolPol (double b, double x, void *data)

void	extrDiagCsr (csrMat B, double d)

void	diagScalCsr (csrMat A, double d)

int	LanBounds (int msteps, double v, double lmin, double *lmax)

int	LanDos (const int nvec, int msteps, const int npts, double xdos, double ydos, double neig, const double const intv)

int	LanDosG (const int nvec, int msteps, const int npts, double xdos, double ydos, double neig, const double const intv)

int	LanTrbounds (int lanm, int maxit, double tol, double vinit, int bndtype, double lammin, double lammax, FILE fstats)
	Lanczos process for eigenvalue bounds [Thick restart version]. More...

int	scalEigVec (int n, int nev, double Y, double sqrtdiag)

void	set_ratf_def (ratparams *rat)
	Sets default values for ratparams struct. More...

int	find_ratf (double intv, ratparams rat)

int	set_ratf_solfunc (ratparams rat, csrMat A, csrMat B, SolFuncC funcs, void **data)

void	free_rat (ratparams *rat)

int	RatLanNr (double intv, int maxit, double tol, double vinit, ratparams rat, int nevOut, double lamo, double Wo, double *reso, FILE fstats)
	Rational filtering Lanczos process [NON-restarted version]. More...

int	RatLanTr (int lanm, int nev, double intv, int maxit, double tol, double vinit, ratparams rat, int nev2, double vals, double W, double *resW, FILE fstats)
	RatLanTR filtering Lanczos process [Thick restart version]. More...

void	csr_copy (csrMat A, csrMat B, int allocB)
	copy a csr matrix A into B alloB: 0: will not allocate memory for B (have been alloced outside) 1: will allocate memory for B (same size as A) More...

int	cooMat_to_csrMat (int cooidx, cooMat coo, csrMat csr)
	convert coo to csr More...

void	free_csr (csrMat *csr)
	memory deallocation for csr matrix More...

void	free_coo (cooMat *coo)
	memory deallocation for coo matrix More...

int	matvec (char trans, csrMat A, double x, double *y)

int	SetAMatvec (int n, MVFunc func, void *data)
	Set the user-input matvec routine and the associated data for A. Save them in evsldata. More...

int	SetBMatvec (int n, MVFunc func, void *data)
	Set the user-input matvec routine and the associated data for B. Save them in evsldata. More...

int	UnsetAMatvec ()

int	UnsetBMatvec ()

int	SetAMatrix (csrMat *A)
	Set the matrix A. More...

int	SetBMatrix (csrMat *B)
	Set the B matrix. More...

int	SetBSol (SolFuncR func, void *data)
	Set the solve routine and the associated data for B. More...

int	SetLTSol (SolFuncR func, void *data)
	Set the solve routine for LT. More...

int	SetASigmaBSol (ratparams rat, SolFuncC func, SolFuncC allf, void **data)
	Set the solve routine and the associated data for A-SIGMA*B if func == NULL, set all functions to be allf. More...

int	SetStdEig ()
	Set the problem to standard eigenvalue problem. More...

int	SetGenEig ()
	Set the problem to generalized eigenvalue problem. More...

int	EVSLStart ()
	Initialize evslData. More...

int	EVSLFinish ()
	Finish EVSL. More...

void	SetDiagScal (double *ds)
	Set diagonal scaling matrix D. More...

int	spslicer (double sli, double mu, int Mdeg, double *intv, int n_int, int npts)
	given the dos function defined by mu find a partitioning of sub-interval [a,b] of the spectrum so each subinterval has about the same number of eigenvalues Mdeg = degree.. mu is of length Mdeg+1 [0—> Mdeg] on return [ sli[i],sli[i+1] ] is a subinterval (slice). More...

int	kpmdos (int Mdeg, int damping, int nvec, double ab, double mu, double *ecnt)
	This function computes the coefficients of the density of states in the chebyshev basis. It also returns the estimated number of eigenvalues in the interval given by intv. More...

void	spslicer2 (double xi, double yi, int n_int, int npts, double *sli)

double	evsl_timer ()
	evsl timer for mac More...

void	rand_double (int n, double *v)

void	randn_double (int n, double *v)

void	sort_double (int n, double v, int ind)

void	linspace (double a, double b, int num, double *arr)

void	StatsPrint (FILE *fstats)

void	StatsReset ()

Detailed Description

This file contains function prototypes and constant definitions for EVSL.

Definition in file evsl.h.

Function Documentation

void BSolPol	(	double *	b,
		double *	x,
		void *	data
	)

Definition at line 61 of file dos_utils.c.

References _BSolDataPol::cc, _BSolDataPol::dd, _BSolDataPol::deg, _BSolDataPol::mu, pnav(), and _BSolDataPol::wk.

Referenced by main().

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int ChebLanNr	(	double *	intv,
		int	maxit,
		double	tol,
		double *	vinit,
		polparams *	pol,
		int *	nevOut,
		double **	lamo,
		double **	Wo,
		double **	reso,
		FILE *	fstats
	)

Definition at line 60 of file cheblanNr.c.

References _polparams::bar, CGS_DGKS(), CGS_DGKS2(), ChebAv(), DAXPY(), DCOPY(), DDOT(), _polparams::deg, DGEMV(), DNRM2(), DSCAL(), evsl_timer(), evsldata, evslstat, _polparams::gam, _evsldata::ifGenEv, Malloc, min, _evsldata::n, NGS_MAX, orthTol, rand_double(), Realloc, SymmTridEig(), SymmTridEigS(), _evslstat::t_iter, and _evslstat::t_ritz.

Referenced by evsl_cheblannr(), and main().

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int ChebLanTr	(	int	lanm,
		int	nev,
		double *	intv,
		int	maxit,
		double	tol,
		double *	vinit,
		polparams *	pol,
		int *	nev2,
		double **	vals,
		double **	W,
		double **	resW,
		FILE *	fstats
	)

Chebyshev polynomial filtering Lanczos process [Thick restart version].

Parameters

[in]	lanm	Dimension of Krylov subspace [restart dimension]
[in]	nev	Estimate of number of eigenvalues in the interval – ideally nev == exact number or a little larger. This is not used for testing convergence but it helps make decisions as to when to test convergence ChebLanTr attempts to compute all eigenvalues in the interval and stops only when no more eigenvalyes are left. The convergenve test is a very simple one based on the residual norm for the filtered matrix
[in]	intv	an array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A
[in]	maxit	max Num of outer Lanczos iterations (restarts) allowed – Each restart may or use the full lanm lanczos steps or fewer.
[in]	tol	tolerance for convergence. stop when \|\|res\|\|< tol
[in]	vinit	initial vector for Lanczos – [optional]
[in]	pol	a struct containing the parameters of the polynomial. This is set up by a call to find_deg prior to calling chenlanTr
[out]	nev2	Number of eigenvalues/vectors computed
[out]	W	A set of eigenvectors [n x nev2 matrix] of unit 2-norm for standard eig prob of unit B-norm for generalized eig prob
[out]	vals	Associated eigenvalues [nev2 x 1 vector]
[out]	resW	Associated residual norms [nev x 1 vector] 2-norm for standard eig prob B-norm for generalized eig prob
[out]	fstats	File stream which stats are printed to

Returns: Returns 0 on success (or if check_intv() is non-positive), -1 if gamB is outside [-1, 1], and 2 if there are no eigenvalues found.

Warning: memory allocation for W/vals/resW within this function

Definition at line 62 of file cheblanTr.c.

References _polparams::bar, Calloc, CGS_DGKS(), CGS_DGKS2(), ChebAv(), DAXPY(), DCOPY(), DDOT(), DGEMM(), DGEMV(), DNRM2(), DSCAL(), evsl_timer(), evsldata, evslstat, _polparams::gam, _evsldata::ifGenEv, Malloc, max, min, _evsldata::n, NGS_MAX, orthTol, rand_double(), Realloc, SymEigenSolver(), and _evslstat::t_iter.

Referenced by evsl_cheblantr(), and main().

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int ChebSI	(	int	nev,
		double *	intv,
		int	maxit,
		double	tol,
		double *	vinit,
		polparams *	pol,
		int *	nevo,
		double **	lamo,
		double **	Yo,
		double **	reso,
		FILE *	fstats
	)

Chebyshev polynomial filtering Subspace Iteration.

Parameters

nev	Estimate of number of eigenvalues in the interval – ideally nev == exact number or a little larger. ChebSI stops when at least nev eigenvalues are found or when no more candidates are left in interval.
intv	An array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A
maxit	Max Num of outer subspace iterations allowed
tol	Tolerance for convergence. stop when \|\|res\|\|< tol
vinit	Nev initial vectors [to be made optional]
pol	A struct containing the parameters of the polynomial..

Modifies:

Parameters

[out]	nevo	Number of eigenvalues/vectors computed
[out]	Yo	A set of eigenvectors [n x nev2 matrix]
[out]	lamo	Associated eigenvalues [nev2 x 1 vector]
[out]	reso	Associated residual norms [nev x 1 vector]
[out]	fstats	File stream which stats are printed to

Warning: Memory allocation for Yo/lamo/reso within this function

*-----------------— memory for converged Ritz pairs (Y, Lam) */

Definition at line 42 of file chebsi.c.

References _polparams::bar, ChebAv(), DCOPY(), DDOT(), _polparams::deg, DGEMM(), evsl_timer(), evsldata, _polparams::gam, Malloc, _evsldata::n, NBUF, orth(), and SymEigenSolver().

Referenced by main().

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int cooMat_to_csrMat	(	int	cooidx,
		cooMat *	coo,
		csrMat *	csr
	)

convert coo to csr

Definition at line 135 of file spmat.c.

References _csrMat::a, csr_resize(), _csrMat::ia, _cooMat::ir, _csrMat::ja, _cooMat::jc, _cooMat::ncols, _cooMat::nnz, _cooMat::nrows, sortrow(), and _cooMat::vv.

Referenced by evsl_coo2csr(), and main().

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void csr_copy	(	csrMat *	A,
		csrMat *	B,
		int	allocB
	)

copy a csr matrix A into B alloB: 0: will not allocate memory for B (have been alloced outside) 1: will allocate memory for B (same size as A)

Definition at line 106 of file spmat.c.

References _csrMat::a, csr_resize(), _csrMat::ia, _csrMat::ja, _csrMat::ncols, and _csrMat::nrows.

Referenced by main().

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void diagScalCsr	(	csrMat *	A,
		double *	d
	)

Definition at line 390 of file spmat.c.

References _csrMat::a, _csrMat::ia, _csrMat::ja, and _csrMat::nrows.

Referenced by main().

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double evsl_timer ( )

evsl timer for mac

Definition at line 14 of file mactime.c.

Referenced by CGS_DGKS(), CGS_DGKS2(), ChebAv(), ChebLanNr(), ChebLanTr(), ChebSI(), EVSLStart(), main(), RatFiltApply(), RatLanNr(), RatLanTr(), SetupASIGMABSolDirect(), SetupBSolDirect(), SymEigenSolver(), SymmTridEig(), SymmTridEigS(), and time_seeder().

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int EVSLFinish ( )

Finish EVSL.

Definition at line 48 of file evsl.c.

References _evsldata::Amv, _evsldata::Bmv, _evsldata::Bsol, and _evsldata::LTsol.

Referenced by evsl_finish(), and main().

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int EVSLStart ( )

Initialize evslData.

Definition at line 27 of file evsl.c.

References _evsldata::Amv, _evsldata::Bmv, _evsldata::Bsol, _evsldata::ds, evsl_timer(), _evsldata::ifGenEv, _evsldata::LTsol, _evsldata::n, and StatsReset().

Referenced by evsl_start(), and main().

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void extrDiagCsr	(	csrMat *	B,
		double *	d
	)

Definition at line 406 of file spmat.c.

References _csrMat::a, _csrMat::ia, _csrMat::ja, and _csrMat::nrows.

Referenced by main().

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int find_pol	(	double *	intv,
		polparams *	pol
	)

Sets the values in pol.

Parameters

intv	An array of length 4, [intv[0, intv[1]] is the interval of desired eigenvalues. [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A.
pol	The polynomial struct to set the values of.

Warning: Set the following values of pol
mu Expansion coefficients of best polynomial found
gam Site of delta function that is expanded. accurate 'balancing' is done: if p(t) is best approximation to delta function at gam then gam is selected so that p(a)=p(b) - within the tolerance tolBal (set in this function to 1.e-10)
bar If $p(\lambda_i)) \geq$ bar, accept eignevalue as belonging to interval; else reject.
deg degree of polynomial
dd half-width and...
cc ... Center of interval containing all eigenvalues [these are used by ChebAv]

Definition at line 361 of file chebpoly.c.

References _polparams::bar, _polparams::cc, chebxPltd(), chext(), dampcf(), _polparams::damping, _polparams::dd, _polparams::deg, _polparams::gam, _polparams::intvtol, Malloc, max, _polparams::max_deg, min, _polparams::min_deg, _polparams::mu, rootchb(), _polparams::thresh_int, and _polparams::type.

Referenced by evsl_find_pol(), and main().

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int find_ratf	(	double *	intv,
		ratparams *	rat
	)

Parameters

intv	= an array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A

OUT:

Parameters

[out]

rat

these are set in rat struct:
omega : expansion coefficients of rational filter
zk : location of the poles used
aa : adjusted left endpoint
bb : adjusted right endpoint
dd : half-width and..
cc : ..center of interval

Definition at line 375 of file ratfilter.c.

References _ratparams::aa, _ratparams::ASIGBsol, _ratparams::bb, _ratparams::beta, contQuad(), Malloc, max, _ratparams::method, min, _ratparams::mulp, _ratparams::num, _ratparams::omega, _ratparams::pow, _ratparams::pw, scaleweigthts(), weights(), and _ratparams::zk.

Referenced by evsl_find_rat(), and main().

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void free_coo ( cooMat * coo )

memory deallocation for coo matrix

Definition at line 126 of file spmat.c.

References _cooMat::ir, _cooMat::jc, and _cooMat::vv.

Referenced by main().

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void free_csr ( csrMat * csr )

memory deallocation for csr matrix

Definition at line 91 of file spmat.c.

References _csrMat::a, _csrMat::ia, _csrMat::ja, and _csrMat::owndata.

Referenced by evsl_free_csr(), main(), and SetupASIGMABSolDirect().

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void free_pol ( polparams * pol )

Definition at line 488 of file chebpoly.c.

References _polparams::mu.

Referenced by evsl_free_pol(), and main().

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void free_rat ( ratparams * rat )

Definition at line 424 of file ratfilter.c.

References _ratparams::ASIGBsol, _ratparams::mulp, _ratparams::omega, and _ratparams::zk.

Referenced by evsl_free_rat(), and main().

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void FreeBSolPolData ( BSolDataPol * data )

Definition at line 53 of file dos_utils.c.

References _BSolDataPol::mu, and _BSolDataPol::wk.

Referenced by main().

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int kpmdos	(	int	Mdeg,
		int	damping,
		int	nvec,
		double *	intv,
		double *	mu,
		double *	ecnt
	)

This function computes the coefficients of the density of states in the chebyshev basis. It also returns the estimated number of eigenvalues in the interval given by intv.

Parameters

	Mdeg	degree of polynomial to be used.
	damping	type of damping to be used [0=none,1=jackson,2=sigma]
	nvec	number of random vectors to use for sampling
	intv	an array of length 4 [intv[0] intv[1]] is the interval of desired eigenvalues that must be cut (sliced) into n_int sub-intervals [intv[2],intv[3]] is the global interval of eigenvalues it must contain all eigenvalues of A
[out]	mu	array of Chebyshev coefficients
[out]	ecnt	estimated num of eigenvalues in the interval of interest

Definition at line 32 of file spslice.c.

References dampcf(), DDOT(), DNRM2(), DSCAL(), evsldata, _evsldata::ifGenEv, Malloc, max, min, _evsldata::n, PI, rand_double(), and time_seeder().

Referenced by evsl_kpm_spslicer(), and main().

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int LanBounds	(	int	msteps,
		double *	v,
		double *	lmin,
		double *	lmax
	)

Parameters

	msteps	number of Lanczos steps
	*v	initial vector
[out]	lmin,lmax	[lmin lmax] is the desired interval containing all eigenvalues of matrix pair (A,B)

Definition at line 21 of file lanbounds.c.

References DAXPY(), DCOPY(), DDOT(), DNRM2(), DSCAL(), evsldata, _evsldata::ifGenEv, Malloc, min, _evsldata::n, orthTol, and SymmTridEig().

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int LanDos	(	const int	nvec,
		int	msteps,
		int	npts,
		double *	xdos,
		double *	ydos,
		double *	neig,
		const double *const	intv
	)

Computes the density of states (DOS, or spectral density)

Parameters

[in]	nvec	number of sample vectors used
[in]	msteps	number of Lanczos steps
[in]	npts	number of sample points used for the DOS curve
[in]	*intv	Stores the two intervals of interest \ intv[0:1] = [a b] = interval where DOS is to be computed intv[2:3] = [lambda_min, lambda_max]\
[out]	*xdos	Length-npts long vector, x-coordinate points for plotting the DOS. Must be preallocated before calling LanDos
[out]	*ydos	Length-npts long vector, y-coordinate points for plotting the DOS. Must be preallocated before calling LanDos
[out]	neig	estimated number of eigenvalues

Note: This only works with the standard eigenvalue problem. Use landosG.c /LanDosG for the generalized eigenvalue problem.

Definition at line 40 of file landos.c.

References Calloc, DAXPY(), DCOPY(), DDOT(), DSCAL(), evsldata, _evsldata::ifGenEv, linspace(), Malloc, max, min, _evsldata::n, orthTol, PI, randn_double(), simpson(), and SymmTridEig().

Referenced by main().

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int LanDosG	(	const int	nvec,
		const int	msteps,
		int	npts,
		double *	xdos,
		double *	ydos,
		double *	neig,
		const double *const	intv
	)

Computes the density of states (DOS, or spectral density) using Lanczos algorithm for the generalized eigenvalue problem.

Parameters

[in]	nvec	number of sample vectors used
[in]	msteps	number of Lanczos steps
[in]	npts	number of sample points used for the DOS curve
[in]	*intv	Stores the the intervals of interest intv[0:1] = [a b] = interval where DOS is to be computed intv[2:3] = [lambda_min, lambda_max] \
[out]	*xdos	Length-npts long vector, x-coordinate points for plotting the DOS. Must be preallocated before calling LanDos
[out]	*ydos	Length-npts long vector, y-coordinate points for plotting the DOS. Must be preallocated before calling LanDos
[out]	neig	estimated number of eigenvalues

Note: This works for both the standard and generalized eigenvalue problems.
landos.c/LanDos is only for the standard eigenvalue problem.

Definition at line 43 of file landosG.c.

References Calloc, CGS_DGKS(), CGS_DGKS2(), DAXPY(), DCOPY(), DDOT(), DNRM2(), DSCAL(), evsldata, _evsldata::ifGenEv, linspace(), Malloc, max, min, _evsldata::n, NGS_MAX, orthTol, PI, rand_double(), randn_double(), simpson(), and SymmTridEig().

Referenced by main().

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int LanTrbounds	(	int	lanm,
		int	maxit,
		double	tol,
		double *	vinit,
		int	bndtype,
		double *	lammin,
		double *	lammax,
		FILE *	fstats
	)

Lanczos process for eigenvalue bounds [Thick restart version].

Parameters

[in]	lanm	Dimension of Krylov subspace [restart dimension]
[in]	maxit	max Num of outer Lanczos iterations (restarts) allowed – Each restart may or use the full lanm lanczos steps or fewer.
[in]	tol	tolerance for convergence
[in]	vinit	initial vector for Lanczos – [optional]
[in]	bndtype	Type of bound >1 for kato-temple, otherwise simple
[out]	lammin	Lower bound of the spectrum
[out]	lammax	Upper bound of the spectrum
[out]	fstats	File stream which stats are printed to

Returns: Returns 0 on success

Definition at line 38 of file lanTrbounds.c.

References Calloc, CGS_DGKS(), CGS_DGKS2(), DAXPY(), DCOPY(), DDOT(), DGEMV(), DNRM2(), DSCAL(), evsldata, _evsldata::ifGenEv, Malloc, min, _evsldata::n, NGS_MAX, orthTol, rand_double(), and SymEigenSolver().

Referenced by evsl_lanbounds(), and main().

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void linspace	(	double	a,
		double	b,
		int	num,
		double *	arr
	)

Definition at line 54 of file vect.c.

int matvec	(	char	trans,
		csrMat *	A,
		double *	x,
		double *	y
	)

void rand_double	(	int	n,
		double *	v
	)

Definition at line 11 of file vect.c.

Referenced by ChebLanNr(), ChebLanTr(), evsl_cheblannr(), evsl_cheblantr(), evsl_lanbounds(), evsl_ratlannr(), evsl_ratlantr(), kpmdos(), LanDosG(), LanTrbounds(), main(), RatLanNr(), and RatLanTr().

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void randn_double	(	int	n,
		double *	v
	)

Definition at line 26 of file vect.c.

Referenced by LanDos(), and LanDosG().

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int RatLanNr	(	double *	intv,
		int	maxit,
		double	tol,
		double *	vinit,
		ratparams *	rat,
		int *	nevOut,
		double **	lamo,
		double **	Wo,
		double **	reso,
		FILE *	fstats
	)

Rational filtering Lanczos process [NON-restarted version].

Parameters

intv	an array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A
maxit	max Num of outer Lanczos steps allowed –[max dim of Krylov subspace]
tol	tolerance for convergence. The code uses a stopping criterion based on the convergence of the restricted trace. i.e., the sum of the eigenvalues of T_k that are in the desired interval. This test is rather simple since these eigenvalues are above `bar'. We want the relative error on this restricted trace to be less than tol. Note that the test performed on filtered matrix only - but the actual residual norm associated with the original matrix A is returned
vinit	initial vector for Lanczos – [optional]

Warning: RatLanNr() Modifies the following variables:

Parameters

[out]	rat	A struct containing the rational filter
[out]	nevOut	Number of eigenvalues/vectors computed
[out]	Wo	A set of eigenvectors [n x nevOut matrix]
[out]	lamo	Associated eigenvalues [nevOut x 1 vector]
[out]	reso	Associated residual norms [nev x 1 vector]
[out]	fstats	File stream which stats are printed to

Definition at line 54 of file ratlanNr.c.

References CGS_DGKS(), CGS_DGKS2(), DAXPY(), DCOPY(), DDOT(), DGEMV(), DNRM2(), _evsldata::ds, DSCAL(), evsl_timer(), evsldata, evslstat, _evsldata::ifGenEv, Malloc, min, _evsldata::n, NGS_MAX, orthTol, rand_double(), RatFiltApply(), Realloc, SymmTridEig(), SymmTridEigS(), _evslstat::t_iter, and _evslstat::t_ritz.

Referenced by evsl_ratlannr(), and main().

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int RatLanTr	(	int	lanm,
		int	nev,
		double *	intv,
		int	maxit,
		double	tol,
		double *	vinit,
		ratparams *	rat,
		int *	nev2,
		double **	vals,
		double **	W,
		double **	resW,
		FILE *	fstats
	)

RatLanTR filtering Lanczos process [Thick restart version].

Parameters

[in]	lanm	Dimension of Krylov subspace [restart dimension]
[in]	nev	Estimate of number of eigenvalues in the interval – ideally nev == exact number or a little larger. This is not used for testing convergence but it helps make decisions as to when to test convergence RatLanTr attempts to compute all eigenvalues in the interval and stops only when no more eigenvalyes are left. The convergenve test is a very simple one based on the residual norm for the filtered matrix
[in]	intv	an array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A
[in]	maxit	max Num of outer Lanczos iterations (restarts) allowed – Each restart may or use the full lanm lanczos steps or fewer.
[in]	tol	tolerance for convergence. stop when \|\|res\|\|< tol
[in]	vinit	initial vector for Lanczos – [optional]
[in]	rat	a struct containing the parameters of the rational.
[out]	nev2	Number of eigenvalues/vectors computed
[out]	W	A set of eigenvectors [n x nev2 matrix] of unit 2-norm for standard eig prob of unit B-norm for generalized eig prob
[out]	vals	Associated eigenvalues [nev2 x 1 vector]
[out]	resW	Associated residual norms [nev x 1 vector] 2-norm for standard eig prob B-norm for generalized eig prob
[out]	fstats	File stream which stats are printed to

Returns: Returns 0 on success (or if check_intv() is non-positive), and 2 if there are no eigenvalues found.

Warning: memory allocation for W/vals/resW within this function

Definition at line 61 of file ratlanTr.c.

References Calloc, CGS_DGKS(), CGS_DGKS2(), DAXPY(), DCOPY(), DDOT(), DGEMM(), DGEMV(), DNRM2(), _evsldata::ds, DSCAL(), evsl_timer(), evsldata, evslstat, _evsldata::ifGenEv, Malloc, max, min, _evsldata::n, NGS_MAX, orthTol, rand_double(), RatFiltApply(), Realloc, SymEigenSolver(), and _evslstat::t_iter.

Referenced by evsl_ratlantr(), and main().

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int scalEigVec	(	int	n,
		int	nev,
		double *	Y,
		double *	sqrtdiag
	)

void set_pol_def ( polparams * pol )

set default values for polparams struct.

Definition at line 18 of file chebpoly.c.

References _polparams::damping, _polparams::deg, _polparams::intvtol, _polparams::max_deg, _polparams::min_deg, _polparams::mu, _polparams::thresh_ext, _polparams::thresh_int, and _polparams::tol.

Referenced by evsl_find_pol(), and main().

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void set_ratf_def ( ratparams * rat )

Sets default values for ratparams struct.

Definition at line 345 of file ratfilter.c.

References _ratparams::aa, _ratparams::bar, _ratparams::bb, _ratparams::beta, _ratparams::method, _ratparams::num, and _ratparams::pw.

Referenced by evsl_find_rat(), and main().

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int set_ratf_solfunc	(	ratparams *	rat,
		csrMat *	A,
		csrMat *	B,
		SolFuncC *	funcs,
		void **	data
	)

int SetAMatrix ( csrMat * A )

Set the matrix A.

Definition at line 68 of file evsl.c.

References _evsldata::Amv, Calloc, _EVSLMatvec::data, _EVSLMatvec::func, matvec_csr(), _evsldata::n, and _csrMat::ncols.

Referenced by evsl_seta_csr(), and main().

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int SetAMatvec	(	int	n,
		MVFunc	func,
		void *	data
	)

Set the user-input matvec routine and the associated data for A. Save them in evsldata.

Warning: Once this matvec func is set, matrix A will be ignored even it is provided

Definition at line 100 of file evsl.c.

References _evsldata::Amv, Calloc, _EVSLMatvec::data, _EVSLMatvec::func, and _evsldata::n.

Referenced by evsl_setamv(), and main().

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int SetASigmaBSol	(	ratparams *	rat,
		SolFuncC *	func,
		SolFuncC	allf,
		void **	data
	)

Set the solve routine and the associated data for A-SIGMA*B if func == NULL, set all functions to be allf.

Definition at line 168 of file evsl.c.

References _ratparams::ASIGBsol, Calloc, _EVSLASIGMABSol::data, _EVSLASIGMABSol::func, and _ratparams::num.

Referenced by main(), and set_asigmabsol_direct().

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int SetBMatrix ( csrMat * B )

Set the B matrix.

Definition at line 83 of file evsl.c.

References _evsldata::Bmv, Calloc, _EVSLMatvec::data, _EVSLMatvec::func, matvec_csr(), _evsldata::n, and _csrMat::ncols.

Referenced by evsl_setb_csr(), and main().

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int SetBMatvec	(	int	n,
		MVFunc	func,
		void *	data
	)

Set the user-input matvec routine and the associated data for B. Save them in evsldata.

Warning: Once this matvec func is set, matrix B will be ignored even it is provided

Definition at line 117 of file evsl.c.

References _evsldata::Bmv, Calloc, _EVSLMatvec::data, _EVSLMatvec::func, and _evsldata::n.

Referenced by evsl_setbmv().

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int SetBSol	(	SolFuncR	func,
		void *	data
	)

Set the solve routine and the associated data for B.

Definition at line 132 of file evsl.c.

References _evsldata::Bsol, Calloc, _EVSLBSol::data, and _EVSLBSol::func.

Referenced by evsl_setbsol(), main(), and setup_bsol_direct().

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void SetDiagScal ( double * ds )

Set diagonal scaling matrix D.

Definition at line 197 of file evsl.c.

References _evsldata::ds.

int SetGenEig ( )

Set the problem to generalized eigenvalue problem.

Definition at line 158 of file evsl.c.

References _evsldata::ifGenEv.

Referenced by evsl_set_geneig(), and main().

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int SetLTSol	(	SolFuncR	func,
		void *	data
	)

Set the solve routine for LT.

Definition at line 185 of file evsl.c.

References Calloc, _EVSLLTSol::data, _EVSLLTSol::func, and _evsldata::LTsol.

Referenced by evsl_setltsol(), main(), and setup_bsol_direct().

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int SetStdEig ( )

Set the problem to standard eigenvalue problem.

Definition at line 148 of file evsl.c.

References _evsldata::ifGenEv.

Referenced by main().

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void SetupPolRec	(	int	n,
		int	max_deg,
		double	tol,
		double	lmin,
		double	lmax,
		BSolDataPol *	data
	)

Definition at line 37 of file dos_utils.c.

References rec(), and SetupBPol().

Referenced by main().

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void SetupPolSqrt	(	int	n,
		int	max_deg,
		double	tol,
		double	lmin,
		double	lmax,
		BSolDataPol *	data
	)

Definition at line 45 of file dos_utils.c.

References isqrt(), and SetupBPol().

Referenced by main().

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void sort_double	(	int	n,
		double *	v,
		int *	ind
	)

Definition at line 92 of file vect.c.

References compare1(), compare2(), _doubleint::d, _doubleint::i, and Malloc.

Referenced by exeiglap3(), and main().

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int spslicer	(	double *	sli,
		double *	mu,
		int	Mdeg,
		double *	intv,
		int	n_int,
		int	npts
	)

given the dos function defined by mu find a partitioning of sub-interval [a,b] of the spectrum so each subinterval has about the same number of eigenvalues Mdeg = degree.. mu is of length Mdeg+1 [0—> Mdeg] on return [ sli[i],sli[i+1] ] is a subinterval (slice).

Parameters

*sli	see above (output)
*mu	coeffs of polynomial (input)
Mdeg	degree of polynomial (input)
*intv	an array of length 4 [intv[0] intv[1]] is the interval of desired eigenvalues that must be cut (sliced) into n_int sub-intervals [intv[2],intv[3]] is the global interval of eigenvalues it must contain all eigenvalues of A
n_int	number of slices wanted (input)
npts	number of points to use for discretizing the interval [a b]. The more points the more accurate the intervals. it is recommended to set npts to a few times the number of eigenvalues in the interval [a b] (input).

Definition at line 204 of file spslice.c.

References intChx(), linspace(), Malloc, max, min, and save_vec().

Referenced by evsl_kpm_spslicer(), and main().

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void spslicer2	(	double *	xi,
		double *	yi,
		int	n_int,
		int	npts,
		double *	sli
	)

Interval partitioner based for Lanczos DOS output

Parameters

[in]	xi	coordinates of interval [a b]
[in]	yi	yi[k] = integral of the does from a to xi[k]
[in]	n_int	Number of desired sub-intervals
[in]	npts	number of integration points (length of xi)
[out]	sli	Array of length n_int containing the boundaries of the intervals. [sli[i], [sli[i+1]] is the i-th interval with sli[0] = xi[0] and sli[n_int] = xi[npts-1]