misc_la.c File Reference

Miscellaneous linear algebra functions. More...

#include <stdio.h>
#include <string.h>
#include "def.h"
#include "blaslapack.h"
#include "struct.h"
#include "internal_proto.h"

Go to the source code of this file.

Macros
#define	USE_DGEMV   1
#define	NGS_MAX   2

Functions
int	SymmTridEig (double *eigVal, double *eigVec, int n, const double *diag, const double *sdiag)
	compute all eigenvalues and eigenvectors of a symmetric tridiagonal matrix More...
int	SymmTridEigS (double *eigVal, double *eigVec, int n, double vl, double vu, int *nevO, const double *diag, const double *sdiag)
	compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix in a slice More...
void	SymEigenSolver (int n, double *A, int lda, double *Q, int ldq, double *lam)
	interface to LAPACK SYMMETRIC EIGEN-SOLVER More...
void	CGS_DGKS (int n, int k, int i_max, double *Q, double *v, double *nrmv, double *w)
	Classical GS reortho with Daniel, Gragg, Kaufman, Stewart test. More...
void	CGS_DGKS2 (int n, int k, int i_max, double *Z, double *Q, double *v, double *w)
	Classical GS reortho. No test. just do i_max times used in generalized ev problems. More...
void	orth (double *V, int n, int k, double *Vo, double *work)
	Orthogonalize columns of n-by-k matrix V. More...

Detailed Description

Miscellaneous linear algebra functions.

Definition in file misc_la.c.

Macro Definition Documentation

#define NGS_MAX   2

Definition at line 260 of file misc_la.c.

Referenced by ChebLanNr(), ChebLanTr(), LanDosG(), LanTrbounds(), orth(), RatLanNr(), and RatLanTr().

#define USE_DGEMV   1

Definition at line 14 of file misc_la.c.

Function Documentation

void CGS_DGKS	(	int	n,
		int	k,
		int	i_max,
		double *	Q,
		double *	v,
		double *	nrmv,
		double *	w
	)

Classical GS reortho with Daniel, Gragg, Kaufman, Stewart test.

Definition at line 195 of file misc_la.c.

References DAXPY(), DDOT(), DGEMV(), DNRM2(), evsl_timer(), evslstat, and _evslstat::t_reorth.

Referenced by ChebLanNr(), ChebLanTr(), LanDosG(), LanTrbounds(), orth(), RatLanNr(), and RatLanTr().

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void CGS_DGKS2	(	int	n,
		int	k,
		int	i_max,
		double *	Z,
		double *	Q,
		double *	v,
		double *	w
	)

Classical GS reortho. No test. just do i_max times used in generalized ev problems.

Definition at line 235 of file misc_la.c.

References DAXPY(), DDOT(), DGEMV(), evsl_timer(), evslstat, and _evslstat::t_reorth.

Referenced by ChebLanNr(), ChebLanTr(), LanDosG(), LanTrbounds(), RatLanNr(), and RatLanTr().

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void orth	(	double *	V,
		int	n,
		int	k,
		double *	Vo,
		double *	work
	)

Orthogonalize columns of n-by-k matrix V.

Parameters

	n	number of rows in V
	V	Matrix which columns are to be orthogonalized
	k	number of columns in V
[out]	Vo	Output matrix
	work	work

Definition at line 269 of file misc_la.c.

References CGS_DGKS(), DCOPY(), DDOT(), DSCAL(), and NGS_MAX.

Referenced by ChebSI().

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void SymEigenSolver	(	int	n,
		double *	A,
		int	lda,
		double *	Q,
		int	ldq,
		double *	lam
	)

interface to LAPACK SYMMETRIC EIGEN-SOLVER

---

---

Definition at line 156 of file misc_la.c.

References DSYEV(), evsl_timer(), evslstat, Malloc, and _evslstat::t_eig.

Referenced by ChebLanTr(), ChebSI(), LanTrbounds(), and RatLanTr().

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int SymmTridEig	(	double *	eigVal,
		double *	eigVec,
		int	n,
		const double *	diag,
		const double *	sdiag
	)

compute all eigenvalues and eigenvectors of a symmetric tridiagonal matrix

---

Parameters

	n	The dimension of the symmetric tridiagonal matrix
	diag[],sdiag[]	Define the symmetric tridiagonal matrix: the diagonal elements are diag[0,...,n-1] in order and the subdiagonal elements are sdiag[0,...,n-2] in order
[out]	eigVal	The output vector of length n containing all eigenvalues in ascending order
[out]	eigVec	The output n-by-n matrix with columns as eigenvectors, in the order as elements in eigVal. If NULL, then no eigenvector will be computed

Returns

The flag returned by the

LAPACK routine DSTEV() (if double) or stev_() (if float)

Definition at line 36 of file misc_la.c.

References DSTEV(), evsl_timer(), evslstat, Malloc, save_vec(), and _evslstat::t_eig.

Referenced by ChebLanNr(), LanBounds(), LanDos(), LanDosG(), and RatLanNr().

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int SymmTridEigS	(	double *	eigVal,
		double *	eigVec,
		int	n,
		double	vl,
		double	vu,
		int *	nevO,
		const double *	diag,
		const double *	sdiag
	)

compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix in a slice

---

Parameters

	n	The dimension of the symmetric tridiagonal matrix
	diag[],sdiag[]	define the symmetric tridiagonal matrix.
[out]	eigVal	Total number of eigenvalues found.
[out]	eigVec	The first M elements contain teh selected eigenvalues in ascending oredr
[in]	vl	If range='V', The lower bound of the interval to be searched for eigen values.
[in]	vu	If range='V', the upper bound of the interval to be searched for eigenvalues.
[in]	nevO	If range='I', the index of the smallest eigen value to be returned.

This routine computes selected eigenvalues/vectors as specified by a

range of values. This is a wrapper to the LAPACK routine DSTEMR().

Definition at line 93 of file misc_la.c.

References Calloc, DSTEMR(), evsl_timer(), evslstat, Malloc, and _evslstat::t_eig.

Referenced by ChebLanNr(), and RatLanNr().

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