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OpenBLAS/lapack-netlib/SRC/dstegr.f

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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 exceptiona 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.
*
*> \date June 2016
*
*> \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 (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2016
*
* .. 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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