# sstevx.f man page

sstevx.f

## Synopsis

### Functions/Subroutines

subroutine sstevx (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO)
SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

## Function/Subroutine Documentation

### subroutine sstevx (character JOBZ, character RANGE, integer N, real, dimension( * ) D, real, dimension( * ) E, real VL, real VU, integer IL, integer IU, real ABSTOL, integer M, real, dimension( * ) W, real, dimension( ldz, * ) Z, integer LDZ, real, dimension( * ) WORK, integer, dimension( * ) IWORK, integer, dimension( * ) IFAIL, integer INFO)

SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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.```
Parameters:

JOBZ

```          JOBZ is CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.```

RANGE

```          RANGE is 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

```          N is INTEGER
The order of the matrix.  N >= 0.```

D

```          D is 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

```          E is 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

```          VL is REAL
If RANGE='V', the lower bound of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.```

VU

```          VU is REAL
If RANGE='V', the upper bound of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = 'A' or 'I'.```

IL

```          IL is INTEGER
If RANGE='I', the index of the
smallest eigenvalue 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'.```

IU

```          IU is INTEGER
If RANGE='I', the index of the
largest eigenvalue 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

```          ABSTOL is 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

```          M is INTEGER
The total number of eigenvalues found.  0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.```

W

```          W is REAL array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.```

Z

```          Z is 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

```          LDZ is INTEGER
The leading dimension of the array Z.  LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).```

WORK

`          WORK is REAL array, dimension (5*N)`

IWORK

`          IWORK is INTEGER array, dimension (5*N)`

IFAIL

```          IFAIL is 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

```          INFO is 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.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

June 2016

Definition at line 229 of file sstevx.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sstevx(3) is an alias of sstevx.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK