cstegr.f(3)

NAME
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)

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 exceptiona 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.

Author

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