DSTEGR(3)      LAPACK routine of NEC Numeric Library Collection      DSTEGR(3)



NAME
       DSTEGR

SYNOPSIS
       SUBROUTINE DSTEGR (JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W,
           Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO)



PURPOSE
            DSTEGR 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.

            DSTEGR is a compatability wrapper around the improved DSTEMR 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 : DSTEGR and DSTEMR 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.




ARGUMENTS
           JOBZ      (input)
                     JOBZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only;
                     = 'V':  Compute eigenvalues and eigenvectors.

           RANGE     (input)
                     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         (input)
                     N is INTEGER
                     The order of the matrix.  N >= 0.

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

           E         (input/output)
                     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        (input)
                     VL is DOUBLE PRECISION

           VU        (input)
                     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        (input)
                     IL is INTEGER

           IU        (input)
                     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    (input)
                     ABSTOL is DOUBLE PRECISION
                     Unused.  Was the absolute error tolerance for the
                     eigenvalues/eigenvectors in previous versions.

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

           Z         (output)
                     Z is DOUBLE PRECISION 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       (input)
                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', then LDZ >= max(1,N).

           ISUPPZ    (output)
                     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      (output)
                     WORK is DOUBLE PRECISION array, dimension (LWORK)
                     On exit, if INFO = 0, WORK(1) returns the optimal
                     (and minimal) LWORK.

           LWORK     (input)
                     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     (output)
                     IWORK is INTEGER array, dimension (LIWORK)
                     On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

           LIWORK    (input)
                     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      (output)
                     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 DLARRV.
                           Here, the digit X = ABS( IINFO ) < 10, where IINFO is
                           the nonzero error code returned by DLARRE or
                           DLARRV, respectively.



LAPACK routine                  31 October 2017                      DSTEGR(3)