Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - computes 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 multiplied 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 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.
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 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 (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 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 driver routine (version 3.2)        April 2011                            SSTEVX(3lapack)
```