hbev_2stage(3)

📦

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💅 `hbev_2stage(3)` — Library Functions Manual

Okay so bestie, welcome to hbev_2stage(3), straight out of the Library Functions Manual ✨. This is the group chat for the {hb,sb}ev_2stage family — eigenvalues, QR iteration, the whole vibe. Buckle up, it's a long one, so it's coming at you in three parts 🎀.

🌸 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

🎀 `chbev_2stage`

subroutine chbev_2stage (character jobz, character uplo, integer n, integer
    kd, 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
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
UPLO — UPLO is CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', or the number of subdiagonals if UPLO = 'L'. 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', 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 = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', 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 = 'V', 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 = 'N', then Z is not referenced.
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', 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 = 'N' 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 = 'V' 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 '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 209 of file chbev_2stage.f.

💖 `dsbev_2stage`

subroutine dsbev_2stage (character jobz, character uplo, integer n, integer
    kd, double precision, dimension( ldab, * ) ab, integer ldab, double
    precision, 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
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
UPLO — UPLO is CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', or the number of subdiagonals if UPLO = 'L'. 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

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 = 'V', 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 = 'N', then Z is not referenced.
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', 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 — LWORK is INTEGER. The length of the array WORK. LWORK >= 1, when N <= 1; otherwise:
- If JOBZ = 'N' 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 = 'V' 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 '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 202 of file dsbev_2stage.f.

🦋 `ssbev_2stage`

subroutine ssbev_2stage (character jobz, character uplo, integer n, integer
    kd, 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

Okay bestie, here's the vibe: 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. Iconic.

🎀 Parameters

JOBZ — JOBZ is CHARACTER*1
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
UPLO — UPLO is CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', or the number of subdiagonals if UPLO = 'L'. 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', 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 = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', 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 = 'V', 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 = 'N', then Z is not referenced.
LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', 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 = 'N' 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 = 'V' 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 '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 202 of file ssbev_2stage.f.

🧚 `zhbev_2stage`

subroutine zhbev_2stage (character jobz, character uplo, integer n, integer
    kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision,
    dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,
    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. Periodt. 💅

🎀 Parameters

JOBZ — JOBZ is CHARACTER*1
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
UPLO — UPLO is CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB — AB

Okay, picking up at AB — the actual band-matrix bestie 💅. AB is a 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

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 = 'V', 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 = 'N', then Z is not referenced.

LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', 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 = 'N' 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 = 'V' and N > 1, LWORK must be queried. Not yet available.

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 '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 209 of file zhbev_2stage.f.

🤖 Author

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hbev_2stage(3)

💅 hbev_2stage(3) — Library Functions Manual

🌸 NAME

🦋 SYNOPSIS

✨ Functions

💜 Detailed Description

🫶 Function Documentation

🎀 chbev_2stage

⭐ Purpose:

🌈 Parameters

👑 Author

🧚 Further Details:

💖 dsbev_2stage

⭐ Purpose:

🌈 Parameters

👑 Author

🔥 Further Details

🦋 ssbev_2stage

✨ Purpose

🎀 Parameters

👑 Author

🔥 Further Details

🧚 zhbev_2stage

✨ Purpose

🎀 Parameters

👑 Author

🔬 Further Details:

🤖 Author

💅 `hbev_2stage(3)` — Library Functions Manual

🎀 `chbev_2stage`

💖 `dsbev_2stage`

🦋 `ssbev_2stage`

🧚 `zhbev_2stage`