dspevd.f

          SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, 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, UPLO
          INTEGER            INFO, LDZ, LIWORK, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          DOUBLE PRECISION   AP( * ), W( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DSPEVD computes all the eigenvalues and, optionally, eigenvectors
    *  of a real symmetric matrix A in packed storage. 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.
    *
    *  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.
    *
    *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
    *          On entry, the upper or lower triangle of the symmetric matrix
    *          A, packed columnwise in a linear array.  The j-th column of A
    *          is stored in the array AP as follows:
    *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    *          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    *
    *          On exit, AP is overwritten by values generated during the
    *          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    *          and first superdiagonal of the tridiagonal matrix T overwrite
    *          the corresponding elements of A, and if UPLO = 'L', the
    *          diagonal and first subdiagonal of T overwrite the
    *          corresponding elements of A.
    *
    *  W       (output) DOUBLE PRECISION array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  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 W(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 required 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.
    *          If JOBZ = 'V' and N > 1, LWORK must be at least
    *                                                 1 + 6*N + N**2.
    *
    *          If LWORK = -1, then a workspace query is assumed; the routine
    *          only calculates the required 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 required LIWORK.
    *
    *  LIWORK  (input) INTEGER
    *          The dimension of the array IWORK.
    *          If JOBZ  = 'N' or 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 required 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 an intermediate tridiagonal
    *                form did not converge to zero.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ZERO, ONE
          PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY, WANTZ
          INTEGER            IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
         $                   LLWORK, LWMIN
          DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
         $                   SMLNUM
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   DLAMCH, DLANSP
          EXTERNAL           LSAME, DLAMCH, DLANSP
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DOPMTR, DSCAL, DSPTRD, 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
          IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
             INFO = -1
          ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
         $          THEN
             INFO = -2
          ELSE IF( N.LT.0 ) THEN
             INFO = -3
          ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
             INFO = -7
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( N.LE.1 ) THEN
                LIWMIN = 1
                LWMIN = 1
             ELSE
                IF( WANTZ ) THEN
                   LIWMIN = 3 + 5*N
                   LWMIN = 1 + 6*N + N**2
                ELSE
                   LIWMIN = 1
                   LWMIN = 2*N
                END IF
             END IF
             IWORK( 1 ) = LIWMIN
             WORK( 1 ) = LWMIN
    *
             IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -9
             ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -11
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DSPEVD', -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 ) = AP( 1 )
             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.
    *
          ANRM = DLANSP( 'M', UPLO, N, AP, 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 ) THEN
             CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
          END IF
    *
    *     Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
    *
          INDE = 1
          INDTAU = INDE + N
          CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
    *
    *     For eigenvalues only, call DSTERF.  For eigenvectors, first call
    *     DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
    *     tridiagonal matrix, then call DOPMTR to multiply it by the
    *     Householder transformations represented in AP.
    *
          IF( .NOT.WANTZ ) THEN
             CALL DSTERF( N, W, WORK( INDE ), INFO )
          ELSE
             INDWRK = INDTAU + N
             LLWORK = LWORK - INDWRK + 1
             CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
         $                LLWORK, IWORK, LIWORK, INFO )
             CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
         $                WORK( INDWRK ), IINFO )
          END IF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
          IF( ISCALE.EQ.1 )
         $   CALL DSCAL( N, ONE / SIGMA, W, 1 )
    *
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
          RETURN
    *
    *     End of DSPEVD
    *
          END