ssbevd.f

          SUBROUTINE SSBEVD( JOBZ, UPLO, N, KD, AB, LDAB, 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, KD, LDAB, LDZ, LIWORK, LWORK, N
    *     ..
    *     .. Array Arguments ..
          INTEGER            IWORK( * )
          REAL               AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SSBEVD computes all the eigenvalues and, optionally, eigenvectors of
    *  a real symmetric band 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.
    *
    *  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.
    *
    *  KD      (input) INTEGER
    *          The number of superdiagonals of the matrix A if UPLO = 'U',
    *          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    *
    *  AB      (input/output) REAL array, dimension (LDAB, N)
    *          On entry, the upper or lower triangle of the symmetric band
    *          matrix A, stored in the first KD+1 rows of the array.  The
    *          j-th column of A is stored in the j-th column of the array AB
    *          as follows:
    *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    *
    *          On exit, AB is overwritten by values generated during the
    *          reduction to tridiagonal form.  If UPLO = 'U', the first
    *          superdiagonal and the diagonal of the tridiagonal matrix T
    *          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
    *          the diagonal and first subdiagonal of T are returned in the
    *          first two rows of AB.
    *
    *  LDAB    (input) INTEGER
    *          The leading dimension of the array AB.  LDAB >= KD + 1.
    *
    *  W       (output) REAL array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  Z       (output) REAL 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) 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 > 2, LWORK must be at least 2*N.
    *          If JOBZ  = 'V' and N > 2, LWORK must be at least
    *                         ( 1 + 5*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 LIWORK.
    *          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
    *          If JOBZ  = 'V' and N > 2, 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 an intermediate tridiagonal
    *                form did not converge to zero.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO, ONE
          PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LOWER, LQUERY, WANTZ
          INTEGER            IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
         $                   LLWRK2, LWMIN
          REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
         $                   SMLNUM
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          REAL               SLAMCH, SLANSB
          EXTERNAL           LSAME, SLAMCH, SLANSB
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEMM, SLACPY, SLASCL, SSBTRD, SSCAL, SSTEDC,
         $                   SSTERF, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          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( N.LE.1 ) THEN
             LIWMIN = 1
             LWMIN = 1
          ELSE
             IF( WANTZ ) THEN
                LIWMIN = 3 + 5*N
                LWMIN = 1 + 5*N + 2*N**2
             ELSE
                LIWMIN = 1
                LWMIN = 2*N
             END IF
          END IF
          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( KD.LT.0 ) THEN
             INFO = -4
          ELSE IF( LDAB.LT.KD+1 ) THEN
             INFO = -6
          ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
             INFO = -9
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             WORK( 1 ) = LWMIN
             IWORK( 1 ) = LIWMIN
    *
             IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -11
             ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
                INFO = -13
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SSBEVD', -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 ) = AB( 1, 1 )
             IF( WANTZ )
         $      Z( 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 = SLANSB( 'M', UPLO, N, KD, AB, LDAB, 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
             IF( LOWER ) THEN
                CALL SLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
             ELSE
                CALL SLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
             END IF
          END IF
    *
    *     Call SSBTRD to reduce symmetric band matrix to tridiagonal form.
    *
          INDE = 1
          INDWRK = INDE + N
          INDWK2 = INDWRK + N*N
          LLWRK2 = LWORK - INDWK2 + 1
          CALL SSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, WORK( INDE ), Z, LDZ,
         $             WORK( INDWRK ), IINFO )
    *
    *     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEDC.
    *
          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 SGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
         $               ZERO, WORK( INDWK2 ), N )
             CALL SLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
          END IF
    *
    *     If matrix was scaled, then rescale eigenvalues appropriately.
    *
          IF( ISCALE.EQ.1 )
         $   CALL SSCAL( N, ONE / SIGMA, W, 1 )
    *
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
          RETURN
    *
    *     End of SSBEVD
    *
          END