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 compatability wrapper around the improved ZSTEMR 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 : 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 exceptiona 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

VU

          VU is DOUBLE PRECISION


          If RANGE='V', the lower and upper bounds of the interval to


          be searched for eigenvalues. VL < VU.


          Not referenced if RANGE = 'A' or 'I'.

IL

          IL is INTEGER

IU

          IU is INTEGER


          If RANGE='I', the indices (in ascending order) of the


          smallest and largest eigenvalues 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.

November 2011

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