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

SSYEVX(l)					)					SSYEVX(l)

NAME
       SSYEVX  -  compute  selected eigenvalues and, optionally, eigenvectors of a real symmetric
       matrix A

SYNOPSIS
       SUBROUTINE SSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,  M,  W,  Z,  LDZ,
			  WORK, LWORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE, UPLO

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

	   REAL 	  ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

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

PURPOSE
       SSYEVX  computes  selected  eigenvalues	and, optionally, eigenvectors of a real symmetric
       matrix A. Eigenvalues and eigenvectors can be selected by specifying  either  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 triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrix A.  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 tri-
	       angle (if UPLO='U') of A, including the diagonal, is destroyed.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= 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*SLAMCH('S'), not zero.  If this routine returns with INFO>0,
	       indicating  that  some  eigenvectors  did  not  converge,  try  setting	ABSTOL to
	       2*SLAMCH('S').

	       See "Computing Small Singular Values of Bidiagonal Matrices with  Guaranteed  High
	       Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.

       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 = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal
	       eigenvectors of the matrix A corresponding to the selected eigenvalues,	with  the
	       i-th  column of Z holding the eigenvector associated with W(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.	If JOBZ =
	       'N', then Z is not referenced.  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 max of the blocksize for SSYTRD and  SORMTR  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:   if  INFO  =  i, then i eigenvectors failed to converge.	Their indices are
	       stored in array IFAIL.

LAPACK version 3.0			   15 June 2000 				SSYEVX(l)


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