*> \brief \b SSTEGR * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SSTEGR + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SSTEGR( 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 * REAL ABSTOL, VL, VU * .. * .. Array Arguments .. * INTEGER ISUPPZ( * ), IWORK( * ) * REAL D( * ), E( * ), W( * ), WORK( * ) * REAL Z( LDZ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSTEGR 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. *> *> SSTEGR is a compatibility wrapper around the improved SSTEMR routine. *> See SSTEMR for further details. *> *> One important change is that the ABSTOL parameter no longer provides any *> benefit and hence is no longer used. *> *> Note : SSTEGR and SSTEMR 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 REAL 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 REAL 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 REAL *> *> 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 REAL *> *> 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 REAL *> 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 REAL array, dimension (N) *> The first M elements contain the selected eigenvalues in *> ascending order. *> \endverbatim *> *> \param[out] Z *> \verbatim *> Z is REAL 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 REAL 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 SLARRE, *> if INFO = 2X, internal error in SLARRV. *> Here, the digit X = ABS( IINFO ) < 10, where IINFO is *> the nonzero error code returned by SLARRE or *> SLARRV, respectively. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date June 2016 * *> \ingroup realOTHERcomputational * *> \par Contributors: * ================== *> *> Inderjit Dhillon, IBM Almaden, USA \n *> Osni Marques, LBNL/NERSC, USA \n *> Christof Voemel, LBNL/NERSC, USA \n * * ===================================================================== SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, $ LIWORK, INFO ) * * -- LAPACK computational routine (version 3.7.1) -- * -- 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 REAL ABSTOL, VL, VU * .. * .. Array Arguments .. INTEGER ISUPPZ( * ), IWORK( * ) REAL D( * ), E( * ), W( * ), WORK( * ) REAL Z( LDZ, * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL TRYRAC * .. * .. External Subroutines .. EXTERNAL SSTEMR * .. * .. Executable Statements .. INFO = 0 TRYRAC = .FALSE. CALL SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK, $ IWORK, LIWORK, INFO ) * * End of SSTEGR * END