hb2st_kernels(3)

NAME
hb2st_kernels - {hb,sb}2st_kernels: band to tridiagonal (2nd stage)

SYNOPSIS

  Functions

subroutine chb2st_kernels (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)
CHB2ST_KERNELS
subroutine dsb2st_kernels (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)
DSB2ST_KERNELS
subroutine ssb2st_kernels (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)
SSB2ST_KERNELS
subroutine zhb2st_kernels (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)
ZHB2ST_KERNELS

Detailed Description

Function Documentation

  subroutine chb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) v, complex, dimension( * ) tau, integer ldvt, complex, dimension( * ) work)

CHB2ST_KERNELS

Purpose:

    !>
    !> CHB2ST_KERNELS is an internal routine used by the CHETRD_HB2ST
    !> subroutine.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>

    WANTZ

    !>          WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
    !>          Eigenvalue/Eigenvectors.
    !>

    TTYPE

    !>          TTYPE is INTEGER
    !>

    ST

    !>          ST is INTEGER
    !>          internal parameter for indices.
    !>

    ED

    !>          ED is INTEGER
    !>          internal parameter for indices.
    !>

    SWEEP

    !>          SWEEP is INTEGER
    !>          internal parameter for indices.
    !>

    N

    !>          N is INTEGER. The order of the matrix A.
    !>

    NB

    !>          NB is INTEGER. The size of the band.
    !>

    IB

    !>          IB is INTEGER.
    !>

    A

    !>          A is COMPLEX array. A pointer to the matrix A.
    !>

    LDA

    !>          LDA is INTEGER. The leading dimension of the matrix A.
    !>

    V

    !>          V is COMPLEX array, dimension 2*n if eigenvalues only are
    !>          requested or to be queried for vectors.
    !>

    TAU

    !>          TAU is COMPLEX array, dimension (2*n).
    !>          The scalar factors of the Householder reflectors are stored
    !>          in this array.
    !>

    LDVT

    !>          LDVT is INTEGER.
    !>

    WORK

    !>          WORK is COMPLEX array. Workspace of size nb.
    !>

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
    !>
    !>

  subroutine dsb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) v, double precision, dimension( * ) tau, integer ldvt, double precision, dimension( * ) work)

DSB2ST_KERNELS

Purpose:

    !>
    !> DSB2ST_KERNELS is an internal routine used by the DSYTRD_SB2ST
    !> subroutine.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>

    WANTZ

    !>          WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
    !>          Eigenvalue/Eigenvectors.
    !>

    TTYPE

    !>          TTYPE is INTEGER
    !>

    ST

    !>          ST is INTEGER
    !>          internal parameter for indices.
    !>

    ED

    !>          ED is INTEGER
    !>          internal parameter for indices.
    !>

    SWEEP

    !>          SWEEP is INTEGER
    !>          internal parameter for indices.
    !>

    N

    !>          N is INTEGER. The order of the matrix A.
    !>

    NB

    !>          NB is INTEGER. The size of the band.
    !>

    IB

    !>          IB is INTEGER.
    !>

    A

    !>          A is DOUBLE PRECISION array. A pointer to the matrix A.
    !>

    LDA

    !>          LDA is INTEGER. The leading dimension of the matrix A.
    !>

    V

    !>          V is DOUBLE PRECISION array, dimension 2*n if eigenvalues only are
    !>          requested or to be queried for vectors.
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (2*n).
    !>          The scalar factors of the Householder reflectors are stored
    !>          in this array.
    !>

    LDVT

    !>          LDVT is INTEGER.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array. Workspace of size nb.
    !>

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
    !>
    !>

  subroutine ssb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, real, dimension( lda, * ) a, integer lda, real, dimension( * ) v, real, dimension( * ) tau, integer ldvt, real, dimension( * ) work)

SSB2ST_KERNELS

Purpose:

    !>
    !> SSB2ST_KERNELS is an internal routine used by the SSYTRD_SB2ST
    !> subroutine.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>

    WANTZ

    !>          WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
    !>          Eigenvalue/Eigenvectors.
    !>

    TTYPE

    !>          TTYPE is INTEGER
    !>

    ST

    !>          ST is INTEGER
    !>          internal parameter for indices.
    !>

    ED

    !>          ED is INTEGER
    !>          internal parameter for indices.
    !>

    SWEEP

    !>          SWEEP is INTEGER
    !>          internal parameter for indices.
    !>

    N

    !>          N is INTEGER. The order of the matrix A.
    !>

    NB

    !>          NB is INTEGER. The size of the band.
    !>

    IB

    !>          IB is INTEGER.
    !>

    A

    !>          A is REAL array. A pointer to the matrix A.
    !>

    LDA

    !>          LDA is INTEGER. The leading dimension of the matrix A.
    !>

    V

    !>          V is REAL array, dimension 2*n if eigenvalues only are
    !>          requested or to be queried for vectors.
    !>

    TAU

    !>          TAU is REAL array, dimension (2*n).
    !>          The scalar factors of the Householder reflectors are stored
    !>          in this array.
    !>

    LDVT

    !>          LDVT is INTEGER.
    !>

    WORK

    !>          WORK is REAL array. Workspace of size nb.
    !>

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
    !>
    !>

  subroutine zhb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) v, complex*16, dimension( * ) tau, integer ldvt, complex*16, dimension( * ) work)

ZHB2ST_KERNELS

Purpose:

    !>
    !> ZHB2ST_KERNELS is an internal routine used by the ZHETRD_HB2ST
    !> subroutine.
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>

    WANTZ

    !>          WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
    !>          Eigenvalue/Eigenvectors.
    !>

    TTYPE

    !>          TTYPE is INTEGER
    !>

    ST

    !>          ST is INTEGER
    !>          internal parameter for indices.
    !>

    ED

    !>          ED is INTEGER
    !>          internal parameter for indices.
    !>

    SWEEP

    !>          SWEEP is INTEGER
    !>          internal parameter for indices.
    !>

    N

    !>          N is INTEGER. The order of the matrix A.
    !>

    NB

    !>          NB is INTEGER. The size of the band.
    !>

    IB

    !>          IB is INTEGER.
    !>

    A

    !>          A is COMPLEX*16 array. A pointer to the matrix A.
    !>

    LDA

    !>          LDA is INTEGER. The leading dimension of the matrix A.
    !>

    V

    !>          V is COMPLEX*16 array, dimension 2*n if eigenvalues only are
    !>          requested or to be queried for vectors.
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (2*n).
    !>          The scalar factors of the Householder reflectors are stored
    !>          in this array.
    !>

    LDVT

    !>          LDVT is INTEGER.
    !>

    WORK

    !>          WORK is COMPLEX*16 array. Workspace of size nb.
    !>

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
    !>
    !>

Author

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