sstegr.f

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

          IMPLICIT NONE
    *
    *
    *  -- LAPACK computational routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, RANGE
          INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
          REAL             ABSTOL, VL, VU
    *     ..
    *     .. Array Arguments ..
          INTEGER            ISUPPZ( * ), IWORK( * )
          REAL               D( * ), E( * ), W( * ), WORK( * )
          REAL               Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SSTEGR 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.
    *
    *  SSTEGR is a compatability wrapper around the improved SSTEMR 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 : SSTEGR and SSTEMR 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) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  RANGE   (input) 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) INTEGER
    *          The order of the matrix.  N >= 0.
    *
    *  D       (input/output) REAL array, dimension (N)
    *          On entry, the N diagonal elements of the tridiagonal matrix
    *          T. On exit, D is overwritten.
    *
    *  E       (input/output) 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      (input) REAL
    *  VU      (input) REAL
    *          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) INTEGER
    *  IU      (input) 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) REAL
    *          Unused.  Was the absolute error tolerance for the
    *          eigenvalues/eigenvectors in previous versions.
    *
    *  M       (output) 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) REAL array, dimension (N)
    *          The first M elements contain the selected eigenvalues in
    *          ascending order.
    *
    *  Z       (output) REAL 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) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', then LDZ >= max(1,N).
    *
    *  ISUPPZ  (output) 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    (workspace/output) REAL array, dimension (LWORK)
    *          On exit, if INFO = 0, WORK(1) returns the optimal
    *          (and minimal) LWORK.
    *
    *  LWORK   (input) 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   (workspace/output) INTEGER array, dimension (LIWORK)
    *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    *
    *  LIWORK  (input) 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) 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 SLARRV.
    *                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
    *                the nonzero error code returned by SLARRE or
    *                SLARRV, respectively.
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Inderjit Dhillon, IBM Almaden, USA
    *     Osni Marques, LBNL/NERSC, USA
    *     Christof Voemel, LBNL/NERSC, USA
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          LOGICAL TRYRAC
    *     ..
    *     .. External Subroutines ..
          EXTERNAL SSTEMR
    *     ..
    *     .. Executable Statements ..
          INFO = 0
          TRYRAC = .FALSE.

          CALL SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
         $                   M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
         $                   IWORK, LIWORK, INFO )
    *
    *     End of SSTEGR
    *
          END