SSTEVX(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 halfopen interval (VL,VU]
will be found.
= 'I': the ILth through IUth 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,N1))

On entry, the (n1) subdiagonal elements of the tridiagonal
matrix A in elements 1 to N1 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 1norm 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 = IUIL+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 ith
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 ith argument had an illegal value
> 0: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in array IFAIL.