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NAME
     sstevx  -  compute  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, * )



     #include <sunperf.h>

     void sstevx(char jobz, char range, int n,  float  *d,  float
               *e,  float  vl,  float  vu,  int il, int iu, float
               abstol, int *m, float *w, float *sz, int ldz,  int
               *ifail, int *info) ;

PURPOSE
     SSTEVX computes selected eigenvalues and, optionally, eigen-
     vectors  of  a  real symmetric tridiagonal matrix A.  Eigen-
     values 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 tridiago-
               nal  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 (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  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'.

     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 refer-
               enced 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.

               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)
               The first M elements contain the  selected  eigen-
               values 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 eigenvec-
               tor fails to converge (INFO > 0), 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) REAL 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  ele-
               ments  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 ille-
               gal value
               > 0:  if INFO = i, then i eigenvectors  failed  to
               converge.   Their  indices  are  stored  in  array
               IFAIL.

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