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299 lines
9.7 KiB
299 lines
9.7 KiB
*> \brief \b SSTEGR
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SSTEGR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstegr.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstegr.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstegr.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
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* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
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* LIWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER JOBZ, RANGE
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* INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
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* REAL ABSTOL, VL, VU
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* ..
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* .. Array Arguments ..
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* INTEGER ISUPPZ( * ), IWORK( * )
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* REAL D( * ), E( * ), W( * ), WORK( * )
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* REAL Z( LDZ, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SSTEGR computes selected eigenvalues and, optionally, eigenvectors
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*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
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*> a well defined set of pairwise different real eigenvalues, the corresponding
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*> real eigenvectors are pairwise orthogonal.
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*>
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*> The spectrum may be computed either completely or partially by specifying
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*> either an interval (VL,VU] or a range of indices IL:IU for the desired
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*> eigenvalues.
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*>
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*> SSTEGR is a compatibility wrapper around the improved SSTEMR routine.
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*> See SSTEMR for further details.
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*>
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*> One important change is that the ABSTOL parameter no longer provides any
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*> benefit and hence is no longer used.
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*>
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*> Note : SSTEGR and SSTEMR work only on machines which follow
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*> IEEE-754 floating-point standard in their handling of infinities and
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*> NaNs. Normal execution may create these exceptional values and hence
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*> may abort due to a floating point exception in environments which
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*> do not conform to the IEEE-754 standard.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] JOBZ
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*> \verbatim
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*> JOBZ is CHARACTER*1
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*> = 'N': Compute eigenvalues only;
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*> = 'V': Compute eigenvalues and eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] RANGE
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*> \verbatim
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*> RANGE is CHARACTER*1
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*> = 'A': all eigenvalues will be found.
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*> = 'V': all eigenvalues in the half-open interval (VL,VU]
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*> will be found.
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*> = 'I': the IL-th through IU-th eigenvalues will be found.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> On entry, the N diagonal elements of the tridiagonal matrix
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*> T. On exit, D is overwritten.
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*> \endverbatim
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*>
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*> \param[in,out] E
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*> \verbatim
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*> E is REAL array, dimension (N)
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*> On entry, the (N-1) subdiagonal elements of the tridiagonal
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*> matrix T in elements 1 to N-1 of E. E(N) need not be set on
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*> input, but is used internally as workspace.
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*> On exit, E is overwritten.
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*> \endverbatim
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*>
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*> \param[in] VL
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*> \verbatim
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*> VL is REAL
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*>
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*> If RANGE='V', the lower bound of the interval to
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*> be searched for eigenvalues. VL < VU.
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*> Not referenced if RANGE = 'A' or 'I'.
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*> \endverbatim
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*>
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*> \param[in] VU
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*> \verbatim
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*> VU is REAL
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*>
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*> If RANGE='V', the upper bound of the interval to
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*> be searched for eigenvalues. VL < VU.
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*> Not referenced if RANGE = 'A' or 'I'.
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*> \endverbatim
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*>
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*> \param[in] IL
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*> \verbatim
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*> IL is INTEGER
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*>
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*> If RANGE='I', the index of the
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*> smallest eigenvalue to be returned.
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*> 1 <= IL <= IU <= N, if N > 0.
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*> Not referenced if RANGE = 'A' or 'V'.
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*> \endverbatim
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*>
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*> \param[in] IU
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*> \verbatim
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*> IU is INTEGER
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*>
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*> If RANGE='I', the index of the
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*> largest eigenvalue to be returned.
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*> 1 <= IL <= IU <= N, if N > 0.
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*> Not referenced if RANGE = 'A' or 'V'.
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*> \endverbatim
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*>
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*> \param[in] ABSTOL
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*> \verbatim
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*> ABSTOL is REAL
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*> Unused. Was the absolute error tolerance for the
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*> eigenvalues/eigenvectors in previous versions.
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*> \endverbatim
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*>
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*> \param[out] M
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*> \verbatim
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*> M is INTEGER
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*> The total number of eigenvalues found. 0 <= M <= N.
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*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
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*> \endverbatim
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*>
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*> \param[out] W
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*> \verbatim
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*> W is REAL array, dimension (N)
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*> The first M elements contain the selected eigenvalues in
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*> ascending order.
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*> \endverbatim
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*>
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*> \param[out] Z
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*> \verbatim
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*> Z is REAL array, dimension (LDZ, max(1,M) )
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*> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
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*> contain the orthonormal eigenvectors of the matrix T
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*> corresponding to the selected eigenvalues, with the i-th
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*> column of Z holding the eigenvector associated with W(i).
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*> If JOBZ = 'N', then Z is not referenced.
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*> Note: the user must ensure that at least max(1,M) columns are
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*> supplied in the array Z; if RANGE = 'V', the exact value of M
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*> is not known in advance and an upper bound must be used.
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*> Supplying N columns is always safe.
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*> \endverbatim
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*>
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*> \param[in] LDZ
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*> \verbatim
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*> LDZ is INTEGER
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*> The leading dimension of the array Z. LDZ >= 1, and if
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*> JOBZ = 'V', then LDZ >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] ISUPPZ
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*> \verbatim
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*> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
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*> The support of the eigenvectors in Z, i.e., the indices
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*> indicating the nonzero elements in Z. The i-th computed eigenvector
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*> is nonzero only in elements ISUPPZ( 2*i-1 ) through
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*> ISUPPZ( 2*i ). This is relevant in the case when the matrix
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*> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> On exit, if INFO = 0, WORK(1) returns the optimal
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*> (and minimal) LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= max(1,18*N)
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*> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (LIWORK)
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*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
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*> \endverbatim
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*>
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*> \param[in] LIWORK
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*> \verbatim
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*> LIWORK is INTEGER
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*> The dimension of the array IWORK. LIWORK >= max(1,10*N)
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*> if the eigenvectors are desired, and LIWORK >= max(1,8*N)
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*> if only the eigenvalues are to be computed.
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*> If LIWORK = -1, then a workspace query is assumed; the
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*> routine only calculates the optimal size of the IWORK array,
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*> returns this value as the first entry of the IWORK array, and
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*> no error message related to LIWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> On exit, INFO
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> > 0: if INFO = 1X, internal error in SLARRE,
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*> if INFO = 2X, internal error in SLARRV.
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*> Here, the digit X = ABS( IINFO ) < 10, where IINFO is
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*> the nonzero error code returned by SLARRE or
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*> SLARRV, respectively.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup realOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> Inderjit Dhillon, IBM Almaden, USA \n
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*> Osni Marques, LBNL/NERSC, USA \n
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*> Christof Voemel, LBNL/NERSC, USA \n
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*
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* =====================================================================
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SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
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$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
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$ LIWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER JOBZ, RANGE
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INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
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REAL ABSTOL, VL, VU
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* ..
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* .. Array Arguments ..
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INTEGER ISUPPZ( * ), IWORK( * )
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REAL D( * ), E( * ), W( * ), WORK( * )
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REAL Z( LDZ, * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL TRYRAC
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* ..
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* .. External Subroutines ..
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EXTERNAL SSTEMR
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* ..
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* .. Executable Statements ..
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INFO = 0
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TRYRAC = .FALSE.
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CALL SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
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$ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
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$ IWORK, LIWORK, INFO )
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*
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* End of SSTEGR
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*
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END
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