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DSTEVX(l)			       )			     DSTEVX(l)

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

SYNOPSIS
       SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M,  W,
			  Z, LDZ, WORK, IWORK, IFAIL, INFO )

	   CHARACTER	  JOBZ, RANGE

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

	   DOUBLE	  PRECISION ABSTOL, VL, VU

	   INTEGER	  IFAIL( * ), IWORK( * )

	   DOUBLE	  PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ,
			  * )

PURPOSE
       DSTEVX computes selected eigenvalues and, optionally, eigenvectors of a
       real  symmetric	tridiagonal 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.

       N       (input) INTEGER
	       The order of the matrix.	 N >= 0.

       D       (input/output) DOUBLE PRECISION array, dimension (N)
	       On  entry, the n diagonal elements of the tridiagonal matrix A.
	       On exit, D may be multiplied by a  constant  factor  chosen  to
	       avoid over/underflow in computing the eigenvalues.

       E       (input/output) DOUBLE PRECISION array, dimension (N)
	       On  entry,  the	(n-1)  subdiagonal elements of the tridiagonal
	       matrix A in elements 1 to N-1 of E; E(N) need not be  set.   On
	       exit,  E may be multiplied by a constant factor chosen to avoid
	       over/underflow in computing the eigenvalues.

       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.

	       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').

	       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)
	       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  con‐
	       tain 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 (INFO > 0), then that column of Z contains the lat‐
	       est  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) DOUBLE PRECISION array, dimension (5*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:  if INFO = i, then	i  eigenvectors	 failed	 to  converge.
	       Their indices are stored in array IFAIL.

LAPACK version 3.0		 15 June 2000			     DSTEVX(l)
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