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RedHat 9 (Linux i386) - man page for ssygvx (redhat section l)

SSYGVX(l)					)					SSYGVX(l)

NAME
       SSYGVX  - 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 SSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M,
			  W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

	   INTEGER	  IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N

	   REAL 	  ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   REAL 	  A( LDA, * ), B( LDB, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       SSYGVX 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 and B is  also  positive  defi-
       nite.  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.

       A       (input/output) REAL array, dimension (LDA, N)
	       On  entry, the symmetric matrix A.  If UPLO = 'U', the leading N-by-N upper trian-
	       gular part of A contains the upper triangular part of the matrix  A.   If  UPLO	=
	       'L',  the  leading N-by-N lower triangular part of A contains the lower triangular
	       part of the matrix A.

	       On exit, the lower triangle (if UPLO='L') or the upper triangle (if  UPLO='U')  of
	       A, including the diagonal, is destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       B       (input/output) REAL array, dimension (LDA, N)
	       On  entry, the symmetric matrix B.  If UPLO = 'U', the leading N-by-N upper trian-
	       gular part of B contains the upper triangular part of the matrix  B.   If  UPLO	=
	       'L',  the  leading N-by-N lower triangular part of B contains the lower triangular
	       part of the matrix B.

	       On exit, if INFO <= N, the part of B containing the matrix is overwritten  by  the
	       triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.

       LDB     (input) INTEGER
	       The leading dimension of the array B.  LDB >= max(1,N).

       VL      (input) REAL
	       VU	(input)  REAL 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) REAL
	       The absolute error tolerance for the eigenvalues.  An  approximate  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 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  eigenvectors  did  not  converge,  try  setting  ABSTOL  to
	       2*SLAMCH('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) REAL array, dimension (N)
	       On normal exit, the first M elements contain the selected eigenvalues in ascending
	       order.

       Z       (output) REAL 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  corre-
	       sponding to the selected eigenvalues, with the i-th column of Z holding the eigen-
	       vector associated with W(i).  The eigenvectors are normalized as follows: 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 contains 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/output) REAL array, dimension (LWORK)
	       On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

       LWORK   (input) INTEGER
	       The length of the array WORK.  LWORK >= max(1,8*N).  For optimal efficiency, LWORK
	       >= (NB+3)*N, where NB is the blocksize for SSYTRD returned by ILAENV.

	       If  LWORK = -1, then a workspace query is assumed; the routine only calculates the
	       optimal size of the WORK array, returns this value as the first entry of the  WORK
	       array, and no error message related to LWORK is issued by XERBLA.

       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:  SPOTRF or SSYEVX returned an error code:
	       <=  N:  if INFO = i, SSYEVX 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 factoriza-
	       tion 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 				SSYGVX(l)


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