Scroll to navigation

hb2st_kernels(3) LAPACK 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

Generated automatically by Doxygen for LAPACK from the source code.

Wed Feb 7 2024 11:30:40 Version 3.12.0