# dstevx.f (3) - Linux Man Pages

dstevx.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dstevx (characterJOBZ, characterRANGE, integerN, double precision, dimension( * )D, double precision, dimension( * )E, double precisionVL, double precisionVU, integerIL, integerIU, double precisionABSTOL, integerM, double precision, dimension( * )W, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

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

Purpose:

``` DSTEVX 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
```

VU

```          VU is DOUBLE PRECISION
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

```          IL is INTEGER
```

IU

```          IU is 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

```          ABSTOL is DOUBLE PRECISION
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*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('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 DOUBLE PRECISION array, dimension (N)
The first M elements contain the selected eigenvalues in
ascending order.
```

Z

```          Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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