hb2st_kernels - Man Page

{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

Definition at line 169 of file chb2st_kernels.f.

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

Definition at line 169 of file dsb2st_kernels.f.

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

Definition at line 170 of file ssb2st_kernels.f.

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

Definition at line 169 of file zhb2st_kernels.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK