DSTEGR(1) LAPACK computational routine (version 3.2) DSTEGR(1)NAME
DSTEGR - computes selected eigenvalues and, optionally, eigenvectors of
a real symmetric tridiagonal matrix T
SYNOPSIS
SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W,
Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO )
IMPLICIT NONE
CHARACTER JOBZ, RANGE
INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
DOUBLE PRECISION ABSTOL, VL, VU
INTEGER ISUPPZ( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
DOUBLE PRECISION Z( LDZ, * )
PURPOSE
DSTEGR computes selected eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix T. Any such unreduced matrix has a
well defined set of pairwise different real eigenvalues, the corre‐
sponding real eigenvectors are pairwise orthogonal.
The spectrum may be computed either completely or partially by specify‐
ing either an interval (VL,VU] or a range of indices IL:IU for the
desired eigenvalues.
DSTEGR is a compatability wrapper around the improved DSTEMR routine.
See DSTEMR for further details.
One important change is that the ABSTOL parameter no longer provides
any benefit and hence is no longer used.
Note : DSTEGR and DSTEMR work only on machines which follow IEEE-754
floating-point standard in their handling of infinities and NaNs. Nor‐
mal execution may create these exceptiona values and hence may abort
due to a floating point exception in environments which do not conform
to the IEEE-754 standard.
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) DOUBLE PRECISION array, dimension (N)
On entry, the N diagonal elements of the tridiagonal matrix T.
On exit, D is overwritten.
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the (N-1) subdiagonal elements of the tridiagonal
matrix T in elements 1 to N-1 of E. E(N) need not be set on
input, but is used internally as workspace. On exit, E is
overwritten.
VL (input) DOUBLE PRECISION
VU (input) 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 (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. Not referenced if RANGE = 'A' or
'V'.
ABSTOL (input) DOUBLE PRECISION
Unused. Was the absolute error tolerance for the eigenval‐
ues/eigenvectors in previous versions.
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)
The first M elements contain the selected eigenvalues in
ascending order.
Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
contain the orthonormal eigenvectors of the matrix T corre‐
sponding to the selected eigenvalues, with the i-th column of Z
holding the eigenvector associated with W(i). 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. Supplying N columns is always safe.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', then LDZ >= max(1,N).
ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
The support of the eigenvectors in Z, i.e., the indices indi‐
cating the nonzero elements in Z. The i-th computed eigenvector
is nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i
). This is relevant in the case when the matrix is split.
ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal (and minimal)
LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,18*N) if JOBZ =
'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. If LWORK = -1,
then a workspace query is assumed; the routine only calculates
the optimal size of the WORK array, returns this value as the
first entry of the WORK array, and no error message related to
LWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK. LIWORK >= max(1,10*N) if the
eigenvectors are desired, and LIWORK >= max(1,8*N) if only the
eigenvalues are to be computed. If LIWORK = -1, then a
workspace query is assumed; the routine only calculates the
optimal size of the IWORK array, returns this value as the
first entry of the IWORK array, and no error message related to
LIWORK is issued by XERBLA.
INFO (output) INTEGER
On exit, INFO = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = 1X, internal error in DLARRE, if INFO = 2X,
internal error in DLARRV. Here, the digit X = ABS( IINFO ) <
10, where IINFO is the nonzero error code returned by DLARRE or
DLARRV, respectively.
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, LBNL/NERSC, USA
LAPACK computational routine (veNovember22008 DSTEGR(1)
