SRC/cstegr.f(3) Library Functions Manual SRC/cstegr.f(3) NAME SRC/cstegr.f SYNOPSIS Functions/Subroutines subroutine cstegr (jobz, range, n, d, e, vl, vu, il, iu, abstol, m, w, z, ldz, isuppz, work, lwork, iwork, liwork, info) CSTEGR Function/Subroutine Documentation subroutine cstegr (character jobz, character range, integer n, real, dimension( * ) d, real, dimension( * ) e, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info) CSTEGR Purpose: !> !> CSTEGR 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. !> !> CSTEGR is a compatibility wrapper around the improved CSTEMR 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 : CSTEGR and CSTEMR 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. !> 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 REAL array, dimension (N) !> On entry, the N diagonal elements of the tridiagonal matrix !> T. On exit, D is overwritten. !> E !> 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. !> VL !> 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'. !> VU !> 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'. !> IL !> 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'. !> IU !> 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'. !> ABSTOL !> ABSTOL is REAL !> 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 REAL array, dimension (N) !> The first M elements contain the selected eigenvalues in !> ascending order. !> Z !> Z is COMPLEX 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 REAL 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 SLARRE, !> if INFO = 2X, internal error in CLARRV. !> Here, the digit X = ABS( IINFO ) < 10, where IINFO is !> the nonzero error code returned by SLARRE or !> CLARRV, respectively. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: Inderjit Dhillon, IBM Almaden, USA Osni Marques, LBNL/NERSC, USA Christof Voemel, LBNL/NERSC, USA Definition at line 262 of file cstegr.f. 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