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- *> \brief \b DSTEGR
- *
- * =========== DOCUMENTATION ===========
- *
- * Online html documentation available at
- * http://www.netlib.org/lapack/explore-html/
- *
- *> \htmlonly
- *> Download DSTEGR + dependencies
- *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstegr.f">
- *> [TGZ]</a>
- *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstegr.f">
- *> [ZIP]</a>
- *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstegr.f">
- *> [TXT]</a>
- *> \endhtmlonly
- *
- * Definition:
- * ===========
- *
- * SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
- * ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
- * LIWORK, INFO )
- *
- * .. Scalar Arguments ..
- * CHARACTER JOBZ, RANGE
- * INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
- * DOUBLE PRECISION ABSTOL, VL, VU
- * ..
- * .. Array Arguments ..
- * INTEGER ISUPPZ( * ), IWORK( * )
- * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
- * DOUBLE PRECISION Z( LDZ, * )
- * ..
- *
- *
- *> \par Purpose:
- * =============
- *>
- *> \verbatim
- *>
- *> 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 compatibility 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 exceptional values and hence
- *> may abort due to a floating point exception in environments which
- *> do not conform to the IEEE-754 standard.
- *> \endverbatim
- *
- * Arguments:
- * ==========
- *
- *> \param[in] JOBZ
- *> \verbatim
- *> JOBZ is CHARACTER*1
- *> = 'N': Compute eigenvalues only;
- *> = 'V': Compute eigenvalues and eigenvectors.
- *> \endverbatim
- *>
- *> \param[in] RANGE
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[in] N
- *> \verbatim
- *> N is INTEGER
- *> The order of the matrix. N >= 0.
- *> \endverbatim
- *>
- *> \param[in,out] D
- *> \verbatim
- *> D is DOUBLE PRECISION array, dimension (N)
- *> On entry, the N diagonal elements of the tridiagonal matrix
- *> T. On exit, D is overwritten.
- *> \endverbatim
- *>
- *> \param[in,out] E
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[in] VL
- *> \verbatim
- *> VL is DOUBLE PRECISION
- *>
- *> If RANGE='V', the lower bound of the interval to
- *> be searched for eigenvalues. VL < VU.
- *> Not referenced if RANGE = 'A' or 'I'.
- *> \endverbatim
- *>
- *> \param[in] VU
- *> \verbatim
- *> VU is DOUBLE PRECISION
- *>
- *> If RANGE='V', the upper bound of the interval to
- *> be searched for eigenvalues. VL < VU.
- *> Not referenced if RANGE = 'A' or 'I'.
- *> \endverbatim
- *>
- *> \param[in] IL
- *> \verbatim
- *> IL is INTEGER
- *>
- *> If RANGE='I', the index of the
- *> smallest eigenvalue to be returned.
- *> 1 <= IL <= IU <= N, if N > 0.
- *> Not referenced if RANGE = 'A' or 'V'.
- *> \endverbatim
- *>
- *> \param[in] IU
- *> \verbatim
- *> IU is INTEGER
- *>
- *> If RANGE='I', the index of the
- *> largest eigenvalue to be returned.
- *> 1 <= IL <= IU <= N, if N > 0.
- *> Not referenced if RANGE = 'A' or 'V'.
- *> \endverbatim
- *>
- *> \param[in] ABSTOL
- *> \verbatim
- *> ABSTOL is DOUBLE PRECISION
- *> Unused. Was the absolute error tolerance for the
- *> eigenvalues/eigenvectors in previous versions.
- *> \endverbatim
- *>
- *> \param[out] M
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[out] W
- *> \verbatim
- *> W is DOUBLE PRECISION array, dimension (N)
- *> The first M elements contain the selected eigenvalues in
- *> ascending order.
- *> \endverbatim
- *>
- *> \param[out] Z
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[in] LDZ
- *> \verbatim
- *> LDZ is INTEGER
- *> The leading dimension of the array Z. LDZ >= 1, and if
- *> JOBZ = 'V', then LDZ >= max(1,N).
- *> \endverbatim
- *>
- *> \param[out] ISUPPZ
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[out] WORK
- *> \verbatim
- *> WORK is DOUBLE PRECISION array, dimension (LWORK)
- *> On exit, if INFO = 0, WORK(1) returns the optimal
- *> (and minimal) LWORK.
- *> \endverbatim
- *>
- *> \param[in] LWORK
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[out] IWORK
- *> \verbatim
- *> IWORK is INTEGER array, dimension (LIWORK)
- *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
- *> \endverbatim
- *>
- *> \param[in] LIWORK
- *> \verbatim
- *> 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.
- *> \endverbatim
- *>
- *> \param[out] INFO
- *> \verbatim
- *> 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.
- *> \endverbatim
- *
- * Authors:
- * ========
- *
- *> \author Univ. of Tennessee
- *> \author Univ. of California Berkeley
- *> \author Univ. of Colorado Denver
- *> \author NAG Ltd.
- *
- *> \ingroup doubleOTHERcomputational
- *
- *> \par Contributors:
- * ==================
- *>
- *> Inderjit Dhillon, IBM Almaden, USA \n
- *> Osni Marques, LBNL/NERSC, USA \n
- *> Christof Voemel, LBNL/NERSC, USA \n
- *
- * =====================================================================
- SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
- $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
- $ LIWORK, INFO )
- *
- * -- LAPACK computational routine --
- * -- LAPACK is a software package provided by Univ. of Tennessee, --
- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
- *
- * .. Scalar Arguments ..
- CHARACTER JOBZ, RANGE
- INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
- DOUBLE PRECISION ABSTOL, VL, VU
- * ..
- * .. Array Arguments ..
- INTEGER ISUPPZ( * ), IWORK( * )
- DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
- DOUBLE PRECISION Z( LDZ, * )
- * ..
- *
- * =====================================================================
- *
- * .. Local Scalars ..
- LOGICAL TRYRAC
- * ..
- * .. External Subroutines ..
- EXTERNAL DSTEMR
- * ..
- * .. Executable Statements ..
- INFO = 0
- TRYRAC = .FALSE.
-
- CALL DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
- $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
- $ IWORK, LIWORK, INFO )
- *
- * End of DSTEGR
- *
- END
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