sstev.f

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*> \brief <b> SSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          JOBZ
*       INTEGER            INFO, LDZ, N
*       ..
*       .. Array Arguments ..
*       REAL               D( * ), E( * ), WORK( * ), Z( LDZ, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SSTEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric tridiagonal matrix A.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] JOBZ
*> \verbatim
*>          JOBZ is CHARACTER*1
*>          = 'N':  Compute eigenvalues only;
*>          = 'V':  Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          On entry, the n diagonal elements of the tridiagonal matrix
*>          A.
*>          On exit, if INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*>          E is REAL array, dimension (N-1)
*>          On entry, the (n-1) subdiagonal elements of the tridiagonal
*>          matrix A, stored in elements 1 to N-1 of E.
*>          On exit, the contents of E are destroyed.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*>          Z is REAL array, dimension (LDZ, N)
*>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
*>          eigenvectors of the matrix A, with the i-th column of Z
*>          holding the eigenvector associated with D(i).
*>          If JOBZ = 'N', then Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*>          LDZ is INTEGER
*>          The leading dimension of the array Z.  LDZ >= 1, and if
*>          JOBZ = 'V', LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (max(1,2*N-2))
*>          If JOBZ = 'N', WORK is not referenced.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  if INFO = i, the algorithm failed to converge; i
*>                off-diagonal elements of E did not converge to zero.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realOTHEReigen
*
*  =====================================================================
      SUBROUTINE sstev( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ
      INTEGER            INFO, LDZ, N
*     ..
*     .. Array Arguments ..
      REAL               D( * ), E( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e0, one = 1.0e0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            WANTZ
      INTEGER            IMAX, ISCALE
      REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
     $                   TNRM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH, SLANST
      EXTERNAL           lsame, slamch, slanst
*     ..
*     .. External Subroutines ..
      EXTERNAL           sscal, ssteqr, ssterf, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      wantz = lsame( jobz, 'V' )
*
      info = 0
      IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
         info = -6
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SSTEV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( n.EQ.1 ) THEN
         IF( wantz )
     $      z( 1, 1 ) = one
         RETURN
      END IF
*
*     Get machine constants.
*
      safmin = slamch( 'Safe minimum' )
      eps = slamch( 'Precision' )
      smlnum = safmin / eps
      bignum = one / smlnum
      rmin = sqrt( smlnum )
      rmax = sqrt( bignum )
*
*     Scale matrix to allowable range, if necessary.
*
      iscale = 0
      tnrm = slanst( 'M', n, d, e )
      IF( tnrm.GT.zero .AND. tnrm.LT.rmin ) THEN
         iscale = 1
         sigma = rmin / tnrm
      ELSE IF( tnrm.GT.rmax ) THEN
         iscale = 1
         sigma = rmax / tnrm
      END IF
      IF( iscale.EQ.1 ) THEN
         CALL sscal( n, sigma, d, 1 )
         CALL sscal( n-1, sigma, e( 1 ), 1 )
      END IF
*
*     For eigenvalues only, call SSTERF.  For eigenvalues and
*     eigenvectors, call SSTEQR.
*
      IF( .NOT.wantz ) THEN
         CALL ssterf( n, d, e, info )
      ELSE
         CALL ssteqr( 'I', n, d, e, z, ldz, work, info )
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
      IF( iscale.EQ.1 ) THEN
         IF( info.EQ.0 ) THEN
            imax = n
         ELSE
            imax = info - 1
         END IF
         CALL sscal( imax, one / sigma, d, 1 )
      END IF
*
      RETURN
*
*     End of SSTEV
*
      END