Provided by: liblapack-doc_3.12.0-3build1_all 
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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