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

DSYEVX(l)					)					DSYEVX(l)

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

SYNOPSIS
       SUBROUTINE DSYEVX( 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

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       DSYEVX  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) DOUBLE PRECISION 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) 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  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*DLAMCH('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) DOUBLE PRECISION array, dimension (N)
	       On normal exit, the first M elements contain the selected eigenvalues in ascending
	       order.

       Z       (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DSYTRD and DORMTR 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 				DSYEVX(l)


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