dstevd.f

          SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, 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
          INTEGER            INFO, LDZ, LIWORK, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
    *  real symmetric tridiagonal matrix. 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.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  N       (input) INTEGER
    *          The order of the matrix.  N >= 0.
    *
    *  D       (input/output) DOUBLE PRECISION array, dimension (N)
    *          On entry, the n diagonal elements of the tridiagonal matrix
    *          A.
    *          On exit, if INFO = 0, the eigenvalues in ascending order.
    *
    *  E       (input/output) DOUBLE PRECISION 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.
    *
    *  Z       (output) DOUBLE PRECISION 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.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', LDZ >= max(1,N).
    *
    *  WORK    (workspace/output) DOUBLE PRECISION array,
    *                                         dimension (LWORK)
    *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    *
    *  LWORK   (input) INTEGER
    *          The dimension of the array WORK.
    *          If JOBZ  = 'N' or N <= 1 then LWORK must be at least 1.
    *          If JOBZ  = 'V' and N > 1 then LWORK must be at least
    *                         ( 1 + 4*N + 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 JOBZ  = 'N' or N <= 1 then LIWORK must be at least 1.
    *          If JOBZ  = 'V' and N > 1 then 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, the algorithm failed to converge; i
    *                off-diagonal elements of E did not converge to zero.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, WANTZ
          INTEGER            ISCALE, LIWMIN, LWMIN
          DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
         $                   TNRM
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   DLAMCH, DLANST
          EXTERNAL           LSAME, DLAMCH, DLANST
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DSCAL, DSTEDC, DSTERF, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          WANTZ = LSAME( JOBZ, 'V' )
          LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
    *
          INFO = 0
          LIWMIN = 1
          LWMIN = 1
          IF( N.GT.1 .AND. WANTZ ) THEN
             LWMIN = 1 + 4*N + N**2
             LIWMIN = 3 + 5*N
          END IF
    *
          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.EQ.0 ) THEN
             WORK( 1 ) = LWMIN
             IWORK( 1 ) = LIWMIN
    *
             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( 'DSTEVD', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             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 = 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.
    *
          ISCALE = 0
          TNRM = DLANST( '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 DSCAL( N, SIGMA, D, 1 )
             CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
          END IF
    *
    *     For eigenvalues only, call DSTERF.  For eigenvalues and
    *     eigenvectors, call DSTEDC.
    *
          IF( .NOT.WANTZ ) THEN
             CALL DSTERF( N, D, E, INFO )
          ELSE
             CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
         $                INFO )
          END IF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
          IF( ISCALE.EQ.1 )
         $   CALL DSCAL( N, ONE / SIGMA, D, 1 )
    *
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
    *
          RETURN
    *
    *     End of DSTEVD
    *
          END