Man page - hbev_2stage(3)

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Manual

hbev_2stage

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chbev_2stage (character jobz, character uplo, integer n, integerkd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( *) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( *) work, integer lwork, real, dimension( * ) rwork, integer info)
subroutine dsbev_2stage (character jobz, character uplo, integer n, integerkd, double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer lwork,integer info)
subroutine ssbev_2stage (character jobz, character uplo, integer n, integerkd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * )w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer lwork, integer info)
subroutine zhbev_2stage (character jobz, character uplo, integer n, integerkd, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer info)
Author

NAME

hbev_2stage - {hb,sb}ev_2stage: eig, QR iteration

SYNOPSIS

Functions

subroutine chbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)
CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dsbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)
DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)
SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)
ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

subroutine chbev_2stage (character jobz, character uplo, integer n, integerkd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( *) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( *) work, integer lwork, real, dimension( * ) rwork, integer info)

CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A using the 2stage technique for
the reduction to tridiagonal.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.
Not available in this release.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is COMPLEX array, dimension LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be queried.
LWORK = MAX(1, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS
where KD is the size of the band.
NTHREADS is the number of threads used when
openMP compilation is enabled, otherwise =1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be queried. Not yet available.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is REAL array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

All details about the 2stage techniques are available in:

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 ā€™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 ā€™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 dsbev_2stage (character jobz, character uplo, integer n, integerkd, double precision, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, double precision, dimension( ldz, * ) z,integer ldz, double precision, dimension( * ) work, integer lwork,integer info)

DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

DSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A using the 2stage technique for
the reduction to tridiagonal.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.
Not available in this release.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is DOUBLE PRECISION array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is DOUBLE PRECISION array, dimension LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be queried.
LWORK = MAX(1, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS + N
where KD is the size of the band.
NTHREADS is the number of threads used when
openMP compilation is enabled, otherwise =1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be queried. Not yet available.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

All details about the 2stage techniques are available in:

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 ā€™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 ā€™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 ssbev_2stage (character jobz, character uplo, integer n, integerkd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * )w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,integer lwork, integer info)

SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

SSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
a real symmetric band matrix A using the 2stage technique for
the reduction to tridiagonal.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.
Not available in this release.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is REAL array, dimension (LDAB, N)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.

W

W is REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is REAL array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is REAL array, dimension LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be queried.
LWORK = MAX(1, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS + N
where KD is the size of the band.
NTHREADS is the number of threads used when
openMP compilation is enabled, otherwise =1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be queried. Not yet available.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

All details about the 2stage techniques are available in:

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 ā€™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 ā€™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 zhbev_2stage (character jobz, character uplo, integer n, integerkd, complex*16, dimension( ldab, * ) ab, integer ldab, doubleprecision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integerldz, complex*16, dimension( * ) work, integer lwork, double precision,dimension( * ) rwork, integer info)

ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

ZHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian band matrix A using the 2stage technique for
the reduction to tridiagonal.

Parameters

JOBZ

JOBZ is CHARACTER*1
= ā€™Nā€™: Compute eigenvalues only;
= ā€™Vā€™: Compute eigenvalues and eigenvectors.
Not available in this release.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB, N)
On entry, the upper or lower triangle of the Hermitian band
matrix A, stored in the first KD+1 rows of the array. The
j-th column of A is stored in the j-th column of the array AB
as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = ā€™Uā€™, the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows KD and KD+1 of AB, and if UPLO = ā€™Lā€™,
the diagonal and first subdiagonal of T are returned in the
first two rows of AB.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD + 1.

W

W is DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z

Z is COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = ā€™Vā€™, then if INFO = 0, Z contains the orthonormal
eigenvectors of the matrix A, with the i-th column of Z
holding the eigenvector associated with W(i).
If JOBZ = ā€™Nā€™, then Z is not referenced.

LDZ

LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = ā€™Vā€™, LDZ >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The length of the array WORK. LWORK >= 1, when N <= 1;
otherwise
If JOBZ = ā€™Nā€™ and N > 1, LWORK must be queried.
LWORK = MAX(1, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS
where KD is the size of the band.
NTHREADS is the number of threads used when
openMP compilation is enabled, otherwise =1.
If JOBZ = ā€™Vā€™ and N > 1, LWORK must be queried. Not yet available.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))

INFO

INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

All details about the 2stage techniques are available in:

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 ā€™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 ā€™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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