OpenBLAS/lapack-netlib/SRC/dsyev.f

*> \brief <b> DSYEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          JOBZ, UPLO
*       INTEGER            INFO, LDA, LWORK, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DSYEV computes all eigenvalues and, optionally, eigenvectors of a
*> real symmetric matrix A.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] JOBZ
*> \verbatim
*>          JOBZ is CHARACTER*1
*>          = 'N':  Compute eigenvalues only;
*>          = 'V':  Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangle of A is stored;
*>          = 'L':  Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA, N)
*>          On entry, the symmetric matrix A.  If UPLO = 'U', the
*>          leading N-by-N upper triangular part of A contains the
*>          upper triangular part of the matrix A.  If UPLO = 'L',
*>          the leading N-by-N lower triangular part of A contains
*>          the lower triangular part of the matrix A.
*>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
*>          orthonormal eigenvectors of the matrix A.
*>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
*>          or the upper triangle (if UPLO='U') of A, including the
*>          diagonal, is destroyed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*>          W is DOUBLE PRECISION array, dimension (N)
*>          If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK.  LWORK >= max(1,3*N-1).
*>          For optimal efficiency, LWORK >= (NB+2)*N,
*>          where NB is the blocksize for DSYTRD returned by ILAENV.
*>
*>          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.
*> \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 an intermediate tridiagonal
*>                form did not converge to zero.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleSYeigen
*
*  =====================================================================
      SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
*
*  -- LAPACK driver routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, LDA, LWORK, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), W( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LOWER, LQUERY, WANTZ
      INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
     $                   LLWORK, LWKOPT, NB
      DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
     $                   SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      DOUBLE PRECISION   DLAMCH, DLANSY
      EXTERNAL           LSAME, ILAENV, DLAMCH, DLANSY
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD,
     $                   XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      WANTZ = LSAME( JOBZ, 'V' )
      LOWER = LSAME( UPLO, 'L' )
      LQUERY = ( LWORK.EQ.-1 )
*
      INFO = 0
      IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
         INFO = -1
      ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      END IF
*
      IF( INFO.EQ.0 ) THEN
         NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
         LWKOPT = MAX( 1, ( NB+2 )*N )
         WORK( 1 ) = LWKOPT
*
         IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY )
     $      INFO = -8
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DSYEV ', -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.0 ) THEN
         RETURN
      END IF
*
      IF( N.EQ.1 ) THEN
         W( 1 ) = A( 1, 1 )
         WORK( 1 ) = 2
         IF( WANTZ )
     $      A( 1, 1 ) = ONE
         RETURN
      END IF
*
*     Get machine constants.
*
      SAFMIN = DLAMCH( 'Safe minimum' )
      EPS = DLAMCH( 'Precision' )
      SMLNUM = SAFMIN / EPS
      BIGNUM = ONE / SMLNUM
      RMIN = SQRT( SMLNUM )
      RMAX = SQRT( BIGNUM )
*
*     Scale matrix to allowable range, if necessary.
*
      ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
      ISCALE = 0
      IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
         ISCALE = 1
         SIGMA = RMIN / ANRM
      ELSE IF( ANRM.GT.RMAX ) THEN
         ISCALE = 1
         SIGMA = RMAX / ANRM
      END IF
      IF( ISCALE.EQ.1 )
     $   CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
*
*     Call DSYTRD to reduce symmetric matrix to tridiagonal form.
*
      INDE = 1
      INDTAU = INDE + N
      INDWRK = INDTAU + N
      LLWORK = LWORK - INDWRK + 1
      CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
     $             WORK( INDWRK ), LLWORK, IINFO )
*
*     For eigenvalues only, call DSTERF.  For eigenvectors, first call
*     DORGTR to generate the orthogonal matrix, then call DSTEQR.
*
      IF( .NOT.WANTZ ) THEN
         CALL DSTERF( N, W, WORK( INDE ), INFO )
      ELSE
         CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
     $                LLWORK, IINFO )
         CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ),
     $                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 DSCAL( IMAX, ONE / SIGMA, W, 1 )
      END IF
*
*     Set WORK(1) to optimal workspace size.
*
      WORK( 1 ) = LWKOPT
*
      RETURN
*
*     End of DSYEV
*
      END