Library Functions Manual

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 is INTEGER
!>          internal parameter for indices.
!>

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

SWEEP

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

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

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

!>          IB is INTEGER.
!>

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

LDA

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

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

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

SWEEP

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

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

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

!>          IB is INTEGER.
!>

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

LDA

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

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

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

SWEEP

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

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

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

!>          IB is INTEGER.
!>

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

LDA

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

!>          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, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) v, complex16, dimension( ) tau, integer ldvt, complex16, 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 is INTEGER
!>          internal parameter for indices.
!>

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

SWEEP

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

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

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

!>          IB is INTEGER.
!>

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

LDA

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

!>          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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