dspgvx man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

DSPGVX(l)			       )			     DSPGVX(l)

NAME
       DSPGVX  - compute selected eigenvalues, and optionally, eigenvectors of
       a  real	generalized  symmetric-definite	 eigenproblem,	of  the	  form
       A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x

SYNOPSIS
       SUBROUTINE DSPGVX( ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU,
			  ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, ITYPE, IU, LDZ, M, N

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION AP( * ), BP( * ), W( * ), WORK(  *	),  Z(
			  LDZ, * )

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

ARGUMENTS
       ITYPE   (input) INTEGER
	       Specifies the problem type to be solved:
	       = 1:  A*x = (lambda)*B*x
	       = 2:  A*B*x = (lambda)*x
	       = 3:  B*A*x = (lambda)*x

       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 triangle of A and B are stored;
	       = 'L':  Lower triangle of A and B are stored.

       N       (input) INTEGER
	       The order of the matrix pencil (A,B).  N >= 0.

       AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	       On  entry,  the upper or lower triangle of the symmetric matrix
	       A, packed columnwise in a linear array.	The j-th column	 of  A
	       is  stored  in  the  array AP as follows: if UPLO = 'U', AP(i +
	       (j-1)*j/2) =  A(i,j)  for  1<=i<=j;  if	UPLO  =	 'L',  AP(i  +
	       (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

	       On exit, the contents of AP are destroyed.

       BP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	       On  entry,  the upper or lower triangle of the symmetric matrix
	       B, packed columnwise in a linear array.	The j-th column	 of  B
	       is  stored  in  the  array BP as follows: if UPLO = 'U', BP(i +
	       (j-1)*j/2) =  B(i,j)  for  1<=i<=j;  if	UPLO  =	 'L',  BP(i  +
	       (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.

	       On exit, the triangular factor U or L from the Cholesky factor‐
	       ization B = U**T*U or B = L*L**T, in the same storage format as
	       B.

       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 precision.  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	reduc‐
	       ing 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)
	       On  normal  exit, the first M elements contain the selected ei‐
	       genvalues in ascending order.

       Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
	       If JOBZ = 'N', then Z is not referenced.	 If JOBZ =  'V',  then
	       if  INFO	 = 0, the first M columns of Z contain the orthonormal
	       eigenvectors of the matrix A corresponding to the selected  ei‐
	       genvalues,  with	 the  i-th column of Z holding the eigenvector
	       associated with W(i).  The eigenvectors are normalized as  fol‐
	       lows:  if  ITYPE	 =  1  or  2,  Z**T*B*Z	 =  I;	if  ITYPE = 3,
	       Z**T*inv(B)*Z = I.

	       If an eigenvector fails to converge, then that column of Z con‐
	       tains  the  latest  approximation  to  the eigenvector, and the
	       index of the eigenvector is returned in IFAIL.  Note: the  user
	       must  ensure that at least max(1,M) columns are supplied in the
	       array Z; if RANGE = 'V', the exact value of M is not  known  in
	       advance and an upper bound must be used.

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

       WORK    (workspace) DOUBLE PRECISION array, dimension (8*N)

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

       IFAIL   (output) INTEGER array, dimension (N)
	       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
	       eigenvectors 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
	       > 0:  DPPTRF or DSPEVX returned an error code:
	       <=  N:	if INFO = i, DSPEVX failed to converge; i eigenvectors
	       failed to converge.  Their indices are stored in	 array	IFAIL.
	       > N:   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 version 3.0		 15 June 2000			     DSPGVX(l)
[top]

List of man pages available for YellowDog

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