Previous: dspev Up: ../lapack-d.html Next: dspgst

# dspevx

```
NAME
DSPEVX - compute selected eigenvalues and, optionally,
eigenvectors of a real symmetric matrix A in packed storage

SYNOPSIS
SUBROUTINE DSPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
INFO )

CHARACTER      JOBZ, RANGE, UPLO

INTEGER        IL, INFO, IU, LDZ, M, N

DOUBLE         PRECISION ABSTOL, VL, VU

INTEGER        IFAIL( * ), IWORK( * )

DOUBLE         PRECISION AP( * ), W( * ), WORK( * ), Z(
LDZ, * )

PURPOSE
DSPEVX computes selected eigenvalues and, optionally, eigen-
vectors of a real symmetric matrix A in packed storage.
Eigenvalues/vectors can be selected by specifying either a
range of values or a range of indices for the desired eigen-
values.

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.

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

(N*(N+1)/2)
AP      (input/output) DOUBLE PRECISION array, dimension
On entry, the upper or lower triangle of the sym-
metric matrix A, packed columnwise in a linear
array.  The j-th column of A is stored in the array
AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =

A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-
1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated dur-
ing the reduction to tridiagonal form.  If UPLO =
'U', the diagonal and first superdiagonal of the
tridiagonal matrix T overwrite the corresponding
elements of A, and if UPLO = 'L', the diagonal and
first subdiagonal of T overwrite the corresponding
elements of A.

VL      (input) DOUBLE PRECISION
If RANGE='V', the lower bound of the interval to be
searched for eigenvalues.  Not referenced if RANGE =
'A' or 'I'.

VU      (input) DOUBLE PRECISION
If RANGE='V', the upper bound of the interval to be
searched for eigenvalues.  Not referenced if RANGE =
'A' or 'I'.

IL      (input) INTEGER
If RANGE='I', the index (from smallest to largest)
of the smallest eigenvalue to be returned.  IL >= 1.
Not referenced if RANGE = 'A' or 'V'.

IU      (input) INTEGER
If RANGE='I', the index (from smallest to largest)
of the largest eigenvalue to be returned.  min(IL,N)
<= IU <= N.  Not referenced if RANGE = 'A' or 'V'.

ABSTOL  (input) 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 obtained by reducing AP to tridi-
agonal form.

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) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the selected eigenvalues in ascending
order.

max(1,M))
Z       (output) DOUBLE PRECISION array, dimension (LDZ,
If JOBZ = 'V', then if INFO = 0, the first M columns
of Z contain the orthonormal eigenvectors of the
matrix corresponding to the selected eigenvalues.
If an eigenvector fails to converge, 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) DOUBLE PRECISION array, dimension (8*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 illegal
value
> 0:  if INFO = i, then i eigenvectors failed to
converge.  Their indices are stored in array IFAIL.
```