Dstegr.f -
subroutine dstegr (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO)
DSTEGR
DSTEGR
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 corresponding real eigenvectors are pairwise orthogonal. The spectrum may be computed either completely or partially by specifying 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. Normal 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.
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
T. On exit, D is overwritten.
E
E is 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
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.
Not referenced if RANGE = 'A' or 'V'.
ABSTOL
ABSTOL is DOUBLE PRECISION
Unused. Was the absolute error tolerance for the
eigenvalues/eigenvectors in previous versions.
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', and if INFO = 0, then the first M columns of Z
contain the orthonormal eigenvectors of the matrix T
corresponding 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
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', then LDZ >= max(1,N).
ISUPPZ
ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
The support of the eigenvectors in Z, i.e., the indices
indicating 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
WORK is DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
(and minimal) LWORK.
LWORK
LWORK is 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
IWORK is INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK
LIWORK is 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
INFO is 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Contributors:
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, LBNL/NERSC, USA
Definition at line 255 of file dstegr.f.
Generated automatically by Doxygen for LAPACK from the source code.