


SSTEVX(3f)     LAPACK driver routine (version 3.1)     SSTEVX(3f)


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

SYNOPSIS
       SUBROUTINE SSTEVX( 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

           REAL           ABSTOL, VL, VU

           INTEGER        IFAIL( * ), IWORK( * )

           REAL           D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       SSTEVX 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) REAL 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) REAL array, dimension (max(1,N-1))
               On entry, the (n-1) subdiagonal  elements  of  the  tridiagonal
               matrix  A  in elements 1 to N-1 of E.  On exit, E may be multi-
               plied by a constant factor chosen to  avoid  over/underflow  in
               computing the eigenvalues.

       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'.



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SSTEVX(3f)     LAPACK driver routine (version 3.1)     SSTEVX(3f)


       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  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*SLAMCH('S'), not zero.  If
               this routine returns with INFO>0, indicating that  some  eigen-
               vectors  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)
               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  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) REAL array, dimension (5*N)





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SSTEVX(3f)     LAPACK driver routine (version 3.1)     SSTEVX(3f)


       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.












































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