dsbgvx man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

DSBGVX(1)	      LAPACK driver routine (version 3.2)	     DSBGVX(1)

NAME
       DSBGVX - computes selected eigenvalues, and optionally, eigenvectors of
       a real generalized symmetric-definite banded eigenproblem, of the  form
       A*x=(lambda)*B*x

SYNOPSIS
       SUBROUTINE DSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q,
			  LDQ, VL, VU, IL, IU, ABSTOL, M,  W,  Z,  LDZ,	 WORK,
			  IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, IU, KA, KB, LDAB, LDBB, LDQ, LDZ, M, N

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
			  W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       DSBGVX computes selected eigenvalues, and optionally, eigenvectors of a
       real  generalized  symmetric-definite  banded eigenproblem, of the form
       A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric and banded,
       and  B  is also positive definite.  Eigenvalues and eigenvectors can be
       selected by specifying either all eigenvalues, a range of values	 or  a
       range of indices for the desired eigenvalues.

ARGUMENTS
       JOBZ    (input) CHARACTER*1
	       = 'N':  Compute eigenvalues only;
	       = 'V':  Compute eigenvalues and eigenvectors.

       RANGE   (input) CHARACTER*1
	       = 'A': all eigenvalues will be found.
	       =  'V':	all eigenvalues in the half-open interval (VL,VU] will
	       be found.  = 'I': the IL-th through IU-th eigenvalues  will  be
	       found.

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangles of A and B are stored;
	       = 'L':  Lower triangles of A and B are stored.

       N       (input) INTEGER
	       The order of the matrices A and B.  N >= 0.

       KA      (input) INTEGER
	       The  number of superdiagonals of the matrix A if UPLO = 'U', or
	       the number of subdiagonals if UPLO = 'L'.  KA >= 0.

       KB      (input) INTEGER
	       The number of superdiagonals of the matrix B if UPLO = 'U',  or
	       the number of subdiagonals if UPLO = 'L'.  KB >= 0.

       AB      (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
	       On  entry,  the	upper  or lower triangle of the symmetric band
	       matrix A, stored in the first ka+1 rows of the array.  The j-th
	       column  of  A  is  stored in the j-th column of the array AB as
	       follows: if UPLO = 'U', AB(ka+1+i-j,j) =	 A(i,j)	 for  max(1,j-
	       ka)<=i<=j;   if	 UPLO  =  'L',	AB(1+i-j,j)	=  A(i,j)  for
	       j<=i<=min(n,j+ka).  On exit, the contents of AB are destroyed.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KA+1.

       BB      (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
	       On entry, the upper or lower triangle  of  the  symmetric  band
	       matrix B, stored in the first kb+1 rows of the array.  The j-th
	       column of B is stored in the j-th column of  the	 array	BB  as
	       follows:	 if  UPLO  = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-
	       kb)<=i<=j;  if  UPLO  =	'L',  BB(1+i-j,j)     =	  B(i,j)   for
	       j<=i<=min(n,j+kb).   On	exit,  the  factor  S  from  the split
	       Cholesky factorization B = S**T*S, as returned by DPBSTF.

       LDBB    (input) INTEGER
	       The leading dimension of the array BB.  LDBB >= KB+1.

       Q       (output) DOUBLE PRECISION array, dimension (LDQ, N)
	       If JOBZ = 'V', the n-by-n matrix used in the reduction of A*x =
	       (lambda)*B*x  to standard form, i.e. C*x = (lambda)*x, and con‐
	       sequently C to tridiagonal form.	 If JOBZ = 'N', the array Q is
	       not referenced.

       LDQ     (input) INTEGER
	       The leading dimension of the array Q.  If JOBZ = 'N', LDQ >= 1.
	       If JOBZ = 'V', LDQ >= max(1,N).

       VL      (input) DOUBLE PRECISION
	       VU      (input) DOUBLE PRECISION If RANGE='V',  the  lower  and
	       upper bounds of the interval to be searched for eigenvalues. VL
	       < VU.  Not referenced if RANGE = 'A' or 'I'.

       IL      (input) INTEGER
	       IU      (input) INTEGER If RANGE='I', the indices (in ascending
	       order)  of the smallest and largest eigenvalues to be returned.
	       1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.   Not
	       referenced if RANGE = 'A' or 'V'.

       ABSTOL  (input) DOUBLE PRECISION
	       The  absolute error tolerance for the eigenvalues.  An approxi‐
	       mate eigenvalue is accepted as converged when it is  determined
	       to  lie	in  an	interval  [a,b] of width less than or equal to
	       ABSTOL + EPS *	max( |a|,|b| ) , where EPS is the machine pre‐
	       cision.	If ABSTOL is less than or equal to zero, then  EPS*|T|
	       will be used in its place, where	 |T|  is  the  1-norm  of  the
	       tridiagonal  matrix obtained by reducing A to tridiagonal form.
	       Eigenvalues will be computed most accurately when ABSTOL is set
	       to  twice  the underflow threshold 2*DLAMCH('S'), not zero.  If
	       this routine returns with INFO>0, indicating that  some	eigen‐
	       vectors did not converge, try setting ABSTOL to 2*DLAMCH('S').

       M       (output) INTEGER
	       The  total number of eigenvalues found.	0 <= M <= N.  If RANGE
	       = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

       W       (output) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, the eigenvalues in ascending order.

       Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
	       If JOBZ = 'V', then if INFO = 0, Z contains  the	 matrix	 Z  of
	       eigenvectors, with the i-th column of Z holding the eigenvector
	       associated with	W(i).	The  eigenvectors  are	normalized  so
	       Z**T*B*Z = I.  If JOBZ = 'N', then Z is not referenced.

       LDZ     (input) INTEGER
	       The  leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	       'V', LDZ >= max(1,N).

       WORK    (workspace/output) DOUBLE PRECISION array, dimension (7*N)

       IWORK   (workspace/output) INTEGER array, dimension (5*N)

       IFAIL   (output) INTEGER array, dimension (M)
	       If JOBZ = 'V', then if INFO = 0, the first M elements of	 IFAIL
	       are  zero.  If INFO > 0, then IFAIL contains the indices of the
	       eigenvalues that failed to converge.  If JOBZ = 'N', then IFAIL
	       is not referenced.

       INFO    (output) INTEGER
	       = 0 : successful exit
	       < 0 : if INFO = -i, the i-th argument had an illegal value
	       <=  N:  if  INFO	 =  i, then i eigenvectors failed to converge.
	       Their indices are stored in IFAIL.  > N :  DPBSTF  returned  an
	       error  code;  i.e.,  if INFO = N + i, for 1 <= i <= N, then the
	       leading minor of order i of B is not  positive  definite.   The
	       factorization of B could not be completed and no eigenvalues or
	       eigenvectors were computed.

FURTHER DETAILS
       Based on contributions by
	  Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

 LAPACK driver routine (version 3November 2008			     DSBGVX(1)
[top]

List of man pages available for Scientific

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net