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## cstegr()

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

Download CSTEGR + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  JOBZ

      !>          JOBZ is CHARACTER*1
      !>          = 'N':  Compute eigenvalues only;
      !>          = 'V':  Compute eigenvalues and eigenvectors.
      !>

  [in]

  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.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix.  N >= 0.
      !>

  [in,out]

  D

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

  [in,out]

  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.
      !>

  [in]

  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'.
      !>

  [in]

  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'.
      !>

  [in]

  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'.
      !>

  [in]

  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'.
      !>

  [in]

  ABSTOL

      !>          ABSTOL is REAL
      !>          Unused.  Was the absolute error tolerance for the
      !>          eigenvalues/eigenvectors in previous versions.
      !>

  [out]

  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.
      !>

  [out]

  W

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

  [out]

  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.
      !>

  [in]

  LDZ

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

  [out]

  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.
      !>

  [out]

  WORK

      !>          WORK is REAL array, dimension (LWORK)
      !>          On exit, if INFO = 0, WORK(1) returns the optimal
      !>          (and minimal) LWORK.
      !>

  [in]

  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.
      !>

  [out]

  IWORK

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

  [in]

  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.
      !>

  [out]

  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