!>
!> ZSTEGR 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.
!>
!> ZSTEGR is a compatibility wrapper around the improved ZSTEMR routine.
!> See ZSTEMR for further details.
!>
!> One important change is that the ABSTOL parameter no longer provides any
!> benefit and hence is no longer used.
!>
!> Note : ZSTEGR and ZSTEMR 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.
!> 

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 DOUBLE PRECISION array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal matrix
!>          T. On exit, D is overwritten.
!> 

E

!>          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.
!> 

VL

!>          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'.
!> 

VU

!>          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'.
!> 

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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order.
!> 

Z

!>          Z is COMPLEX*16 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 DOUBLE PRECISION 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 DLARRE,
!>                if INFO = 2X, internal error in ZLARRV.
!>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
!>                the nonzero error code returned by DLARRE or
!>                ZLARRV, respectively.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Christof Voemel, LBNL/NERSC, USA