ssyev.f

          SUBROUTINE SSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, UPLO
          INTEGER            INFO, LDA, LWORK, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * ), W( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SSYEV computes all eigenvalues and, optionally, eigenvectors of a
    *  real symmetric matrix A.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) REAL 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.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  W       (output) REAL array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) 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 SSYTRD 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.
    *
    *  INFO    (output) 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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LOWER, LQUERY, WANTZ
          INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
         $                   LLWORK, LWKOPT, NB
          REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
         $                   SMLNUM
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          INTEGER            ILAENV
          REAL               SLAMCH, SLANSY
          EXTERNAL           ILAENV, LSAME, SLAMCH, SLANSY
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SLASCL, SORGTR, SSCAL, SSTEQR, SSTERF, SSYTRD,
         $                   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, 'SSYTRD', 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( 'SSYEV ', -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 = 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.
    *
          ANRM = SLANSY( '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 SLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
    *
    *     Call SSYTRD to reduce symmetric matrix to tridiagonal form.
    *
          INDE = 1
          INDTAU = INDE + N
          INDWRK = INDTAU + N
          LLWORK = LWORK - INDWRK + 1
          CALL SSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
         $             WORK( INDWRK ), LLWORK, IINFO )
    *
    *     For eigenvalues only, call SSTERF.  For eigenvectors, first call
    *     SORGTR to generate the orthogonal matrix, then call SSTEQR.
    *
          IF( .NOT.WANTZ ) THEN
             CALL SSTERF( N, W, WORK( INDE ), INFO )
          ELSE
             CALL SORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
         $                LLWORK, IINFO )
             CALL SSTEQR( 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 SSCAL( IMAX, ONE / SIGMA, W, 1 )
          END IF
    *
    *     Set WORK(1) to optimal workspace size.
    *
          WORK( 1 ) = LWKOPT
    *
          RETURN
    *
    *     End of SSYEV
    *
          END