ssyevd.f

          SUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
         $                   LIWORK, 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, LIWORK, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          REAL               A( LDA, * ), W( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
    *  real symmetric matrix A. If eigenvectors are desired, it uses a
    *  divide and conquer algorithm.
    *
    *  The divide and conquer algorithm makes very mild assumptions about
    *  floating point arithmetic. It will work on machines with a guard
    *  digit in add/subtract, or on those binary machines without guard
    *  digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
    *  Cray-2. It could conceivably fail on hexadecimal or decimal machines
    *  without guard digits, but we know of none.
    *
    *  Because of large use of BLAS of level 3, SSYEVD needs N**2 more
    *  workspace than SSYEVX.
    *
    *  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 (LWORK)
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          If N <= 1,               LWORK must be at least 1.
    *          If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
    *          If JOBZ = 'V' and N > 1, LWORK must be at least
    *                                                1 + 6*N + 2*N**2.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the optimal sizes of the WORK and IWORK
    *          arrays, returns these values as the first entries of the WORK
    *          and IWORK arrays, and no error message related to LWORK or
    *          LIWORK is issued by XERBLA.
    *
    *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
    *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    *
    *  LIWORK  (input) INTEGER
    *          The dimension of the array IWORK.
    *          If N <= 1,                LIWORK must be at least 1.
    *          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
    *          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    *
    *          If LIWORK = -1, then a workspace query is assumed; the
    *          routine only calculates the optimal sizes of the WORK and
    *          IWORK arrays, returns these values as the first entries of
    *          the WORK and IWORK arrays, and no error message related to
    *          LWORK or LIWORK 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 and JOBZ = 'N', then the algorithm failed
    *                to converge; i off-diagonal elements of an intermediate
    *                tridiagonal form did not converge to zero;
    *                if INFO = i and JOBZ = 'V', then the algorithm failed
    *                to compute an eigenvalue while working on the submatrix
    *                lying in rows and columns INFO/(N+1) through
    *                mod(INFO,N+1).
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *     Jeff Rutter, Computer Science Division, University of California
    *     at Berkeley, USA
    *  Modified by Francoise Tisseur, University of Tennessee.
    *
    *  Modified description of INFO. Sven, 16 Feb 05.
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
    *
          LOGICAL            LOWER, LQUERY, WANTZ
          INTEGER            IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
         $                   LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN
          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           SLACPY, SLASCL, SORMTR, SSCAL, SSTEDC, 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 .OR. LIWORK.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
             IF( N.LE.1 ) THEN
                LIWMIN = 1
                LWMIN = 1
                LOPT = LWMIN
                LIOPT = LIWMIN
             ELSE
                IF( WANTZ ) THEN
                   LIWMIN = 3 + 5*N
                   LWMIN = 1 + 6*N + 2*N**2
                ELSE
                   LIWMIN = 1
                   LWMIN = 2*N + 1
                END IF
                LOPT = MAX( LWMIN, 2*N +
         $                  ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) )
                LIOPT = LIWMIN
             END IF
             WORK( 1 ) = LOPT
             IWORK( 1 ) = LIOPT
    *
             IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -8
             ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -10
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SSYEVD', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          IF( N.EQ.1 ) THEN
             W( 1 ) = A( 1, 1 )
             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
          INDWK2 = INDWRK + N*N
          LLWRK2 = LWORK - INDWK2 + 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
    *     SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
    *     tridiagonal matrix, then call SORMTR to multiply it by the
    *     Householder transformations stored in A.
    *
          IF( .NOT.WANTZ ) THEN
             CALL SSTERF( N, W, WORK( INDE ), INFO )
          ELSE
             CALL SSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
         $                WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
             CALL SORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
         $                WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
             CALL SLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
          END IF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
          IF( ISCALE.EQ.1 )
         $   CALL SSCAL( N, ONE / SIGMA, W, 1 )
    *
          WORK( 1 ) = LOPT
          IWORK( 1 ) = LIOPT
    *
          RETURN
    *
    *     End of SSYEVD
    *
          END