dsytrd_sb2st.F(3)

NAME
dsytrd_sb2st.F

SYNOPSIS

  Functions/Subroutines
subroutine dsytrd_sb2st (stage1, vect, uplo, n, kd, ab, ldab, d, e, hous, lhous, work, lwork, info)
DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T

Function/Subroutine Documentation

  subroutine dsytrd_sb2st (character stage1, character vect, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) hous, integer lhous, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T

Purpose:

     DSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric
     tridiagonal form T by a orthogonal similarity transformation:
     Q**T * A * Q = T.

Parameters
    STAGE1

              STAGE1 is CHARACTER*1
              = 'N':  'No': to mention that the stage 1 of the reduction
                      from dense to band using the dsytrd_sy2sb routine
                      was not called before this routine to reproduce AB.
                      In other term this routine is called as standalone.
              = 'Y':  'Yes': to mention that the stage 1 of the
                      reduction from dense to band using the dsytrd_sy2sb
                      routine has been called to produce AB (e.g., AB is
                      the output of dsytrd_sy2sb.

    VECT

              VECT is CHARACTER*1
              = 'N':  No need for the Housholder representation,
                      and thus LHOUS is of size max(1, 4*N);
              = 'V':  the Householder representation is needed to
                      either generate or to apply Q later on,
                      then LHOUS is to be queried and computed.
                      (NOT AVAILABLE IN THIS RELEASE).

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of A is stored;
              = 'L':  Lower triangle of A is stored.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    KD

              KD is INTEGER
              The number of superdiagonals of the matrix A if UPLO = 'U',
              or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

    AB

              AB is DOUBLE PRECISION 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, the diagonal elements of AB are overwritten by the
              diagonal elements of the tridiagonal matrix T; if KD > 0, the
              elements on the first superdiagonal (if UPLO = 'U') or the
              first subdiagonal (if UPLO = 'L') are overwritten by the
              off-diagonal elements of T; the rest of AB is overwritten by
              values generated during the reduction.

    LDAB

              LDAB is INTEGER
              The leading dimension of the array AB.  LDAB >= KD+1.

    D

              D is DOUBLE PRECISION array, dimension (N)
              The diagonal elements of the tridiagonal matrix T.

    E

              E is DOUBLE PRECISION array, dimension (N-1)
              The off-diagonal elements of the tridiagonal matrix T:
              E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

    HOUS

              HOUS is DOUBLE PRECISION array, dimension LHOUS, that
              store the Householder representation.

    LHOUS

              LHOUS is INTEGER
              The dimension of the array HOUS. LHOUS = MAX(1, dimension)
              If LWORK = -1, or LHOUS=-1,
              then a query is assumed; the routine
              only calculates the optimal size of the HOUS array, returns
              this value as the first entry of the HOUS array, and no error
              message related to LHOUS is issued by XERBLA.
              LHOUS = MAX(1, dimension) where
              dimension = 4*N if VECT='N'
              not available now if VECT='H'

    WORK

              WORK is DOUBLE PRECISION array, dimension LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK. LWORK = MAX(1, dimension)
              If LWORK = -1, or LHOUS=-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.
              LWORK = MAX(1, dimension) where
              dimension   = (2KD+1)*N + KD*NTHREADS
              where KD is the blocking size of the reduction,
              FACTOPTNB is the blocking used by the QR or LQ
              algorithm, usually FACTOPTNB=128 is a good choice
              NTHREADS is the number of threads used when
              openMP compilation is enabled, otherwise =1.

    INFO

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      Implemented by Azzam Haidar.
      All details are available on technical report, SC11, SC13 papers.
      Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
      Parallel reduction to condensed forms for symmetric eigenvalue problems
      using aggregated fine-grained and memory-aware kernels. In Proceedings
      of 2011 International Conference for High Performance Computing,
      Networking, Storage and Analysis (SC '11), New York, NY, USA,
      Article 8 , 11 pages.
      http://doi.acm.org/10.1145/2063384.2063394
      A. Haidar, J. Kurzak, P. Luszczek, 2013.
      An improved parallel singular value algorithm and its implementation
      for multicore hardware, In Proceedings of 2013 International Conference
      for High Performance Computing, Networking, Storage and Analysis (SC '13).
      Denver, Colorado, USA, 2013.
      Article 90, 12 pages.
      http://doi.acm.org/10.1145/2503210.2503292
      A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
      A novel hybrid CPU-GPU generalized eigensolver for electronic structure
      calculations based on fine-grained memory aware tasks.
      International Journal of High Performance Computing Applications.
      Volume 28 Issue 2, Pages 196-209, May 2014.
      http://hpc.sagepub.com/content/28/2/196

Definition at line 228 of file dsytrd_sb2st.F.

Author

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