SRC/zhbevd_2stage.f(3)

NAME
SRC/zhbevd_2stage.f

SYNOPSIS

  Functions/Subroutines
subroutine zhbevd_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

  subroutine zhbevd_2stage (character jobz, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

ZHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

     ZHBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
     a complex Hermitian band matrix A using the 2stage technique for
     the reduction to tridiagonal.  If eigenvectors are desired, it
     uses a divide and conquer algorithm.

Parameters
    JOBZ

              JOBZ is CHARACTER*1
              = 'N':  Compute eigenvalues only;
              = 'V':  Compute eigenvalues and eigenvectors.
                      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 COMPLEX*16 array, dimension (LDAB, N)
              On entry, the upper or lower triangle of the Hermitian 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

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

    W

              W is DOUBLE PRECISION array, dimension (N)
              If INFO = 0, the eigenvalues in ascending order.

    Z

              Z is COMPLEX*16 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

              LDZ is INTEGER
              The leading dimension of the array Z.  LDZ >= 1, and if
              JOBZ = 'V', LDZ >= max(1,N).

    WORK

              WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The length of the array WORK. LWORK >= 1, when N <= 1;
              otherwise
              If JOBZ = 'N' and N > 1, LWORK must be queried.
                                       LWORK = MAX(1, dimension) where
                                       dimension = (2KD+1)*N + KD*NTHREADS
                                       where KD is the size of the band.
                                       NTHREADS is the number of threads used when
                                       openMP compilation is enabled, otherwise =1.
              If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal sizes of the WORK, RWORK and
              IWORK arrays, returns these values as the first entries of
              the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    RWORK

              RWORK is DOUBLE PRECISION array,
                                             dimension (LRWORK)
              On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

    LRWORK

              LRWORK is INTEGER
              The dimension of array RWORK.
              If N <= 1,               LRWORK must be at least 1.
              If JOBZ = 'N' and N > 1, LRWORK must be at least N.
              If JOBZ = 'V' and N > 1, LRWORK must be at least
                            1 + 5*N + 2*N**2.
              If LRWORK = -1, then a workspace query is assumed; the
              routine only calculates the optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    IWORK

              IWORK is INTEGER array, dimension (MAX(1,LIWORK))
              On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

    LIWORK

              LIWORK is INTEGER
              The dimension of 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 optimal sizes of the WORK, RWORK
              and IWORK arrays, returns these values as the first entries
              of the WORK, RWORK and IWORK arrays, and no error message
              related to LWORK or LRWORK or LIWORK is issued by XERBLA.

    INFO

              INFO is 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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

      All details about the 2stage techniques are available in:
      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 251 of file zhbevd_2stage.f.

Author

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