heevd_2stage(3)

📦

version 3.12.1 · 9 versions

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🦋 heevd_2stage(3) — Library Functions Manual 🦋

okay so bestie, welcome to heevd_2stage — yes that's the manual name, it lives in Library Functions Manual, and honestly the whole thing is a vibe. we're doing eig, and it's giving divide and conquer energy. grab a snack, this one's a baddie with a LOT of options 💅✨

✨ NAME ✨

heevd_2stage — {he,sy}evd_2stage: eig, divide and conquer

like… the whole point. you hand it a matrix, it hands you back eigenvalues (and maybe eigenvectors, we'll get into it), and it does the reduction to tridiagonal with the 2stage technique. iconic behavior, no cap 🎀

🌈 SYNOPSIS 🌈

🫶 Functions

💜 `cheevd_2stage`

subroutine cheevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork,
    lrwork, iwork, liwork, info)

CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

🌸 `dsyevd_2stage`

subroutine dsyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork,
    liwork, info)

DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

🦋 `ssyevd_2stage`

subroutine ssyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork,
    liwork, info)

SSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

🎀 `zheevd_2stage`

subroutine zheevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork,
    lrwork, iwork, liwork, info)

ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

💖 Detailed Description 💖

so the Detailed Description is where the real tea is, and the Function Documentation has the receipts for every single subroutine, one by one. we're going in order, no skipping, because bestie you deserve every parameter 💜

🔥 Function Documentation 🔥

⭐ subroutine `cheevd_2stage`

subroutine cheevd_2stage (character jobz, character uplo, integer n,
    complex, dimension( lda, * ) a, integer lda, real, dimension( * ) w,
    complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork,
    integer lrwork, integer, dimension( * ) iwork, integer liwork, integer
    info)

CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 👑

🎯 Purpose

CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm.

fr fr it's doing a lot for you and it's not even charging rent 🫶

🌟 Parameters

JOBZ JOBZ is CHARACTER*1
- 'N': Compute eigenvalues only;
- 'V': Compute eigenvalues and eigenvectors. Not available in this release.

okay important: 'V' is literally listed as not available in this release — so don't come crying to me when it doesn't do the thing 🙈

UPLO UPLO is CHARACTER*1
- 'U': Upper triangle of A is stored;
- 'L': Lower triangle of A is stored.

pick your fighter, and remember — only one triangle gets read ✨

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

zero is a valid order, matrix of nothing, we love a minimalist 💅

A A is COMPLEX array, dimension (LDA, N)

On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A.

If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.

🫣 yes bestie, destroyed. the diagonal too. she's not coming back. work on a copy if you're emotionally attached.

LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
W W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.

sorted for you, no extra charge, we love an organized queen 🌸

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

If N <= 1, LWORK must be at least 1.

If JOBZ = 'N' and N > 1, LWORK must be queried.

LWORK = MAX(1, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + N+1
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + N+1

where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice, NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1.

If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2

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.

🧚 the -1 thing is the classic "ask before you commit" move — you query, it tells you how much space it wants, then you allocate and come back. very demure, very mindful.

RWORK RWORK is REAL array, dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK LRWORK is INTEGER The dimension of the array RWORK.

If N <= 1, LRWORK must be at least 1.

If JOBZ = 'N' and N > 1, LRWORK must be at least N.

If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2.

If LRWORK = -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.

IWORK IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK LIWORK is INTEGER The dimension of the array IWORK.

If N <= 1, LIWORK must be at least 1.

If JOBZ = 'N' and N > 1, LIWORK must be at least 1.

If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -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.

💀 three separate arrays to query, three separate -1 flags. yes it's a lot. yes you have to do all of them. stay strong bestie.

INFO INFO is INTEGER
- = 0: successful exit 🎉
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

😭 a positive INFO is the algorithm saying "bestie I tried, here's exactly where it went sideways". read the number, it's telling you where.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📚 Further Details:

Modified description of INFO. Sven, 16 Feb 05.

(shoutout Sven 🫶)

🧠 Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

🔬 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

📖 yes, all three papers stay. cite your sources, it's called being a scholar 💅

Definition at line 245 of file cheevd_2stage.f.

⭐ subroutine `dsyevd_2stage`

subroutine dsyevd_2stage (character jobz, character uplo, integer n, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) w, double precision, dimension( * ) work, integer lwork,
    integer, dimension( * ) iwork, integer liwork, integer info)

DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 🌸

🎯 Purpose

DSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm.

same energy as its complex sibling, just real and symmetric — and notice there's no RWORK/LRWORK situation here, she travels light ✨

🌟 Parameters

JOBZ JOBZ is CHARACTER*1
- 'N': Compute eigenvalues only;
- 'V': Compute eigenvalues and eigenvectors. Not available in this release.

🙈 same warning bestie, 'V' still says not available in this release. don't say I didn't tell you twice.

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.
A

…and that's exactly where the page cuts off, so A and everything after it for dsyevd_2stage is coming at you in the next part 🫶 hold that thought, bestie 💖

A — DOUBLE PRECISION array, dimension (LDA, N). On entry this is your symmetric matrix A, bestie. If UPLO = 'U', the leading N-by-N upper triangular part of A holds the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A holds the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then when INFO = 0, A contains the orthonormal eigenvectors of the matrix A ✨. But if JOBZ = 'N', then on exit the lower triangle (when UPLO='L') or the upper triangle (when UPLO='U') of A, including the diagonal, is straight-up destroyed 💀. Like, gone. She ate but she also emptied the fridge.
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). No cap, no notes, it's giving very simple rules 💅.
W — DOUBLE PRECISION array, dimension (N). If INFO = 0, this is where the eigenvalues live, in ascending order 🎀. Sorted, tidy, iconic.
WORK — DOUBLE PRECISION array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal LWORK 👑. She's a workspace girlie and she's telling you how much room she actually wanted.
LWORK — INTEGER. The dimension of the array WORK. Here's the whole ruleset, no skipping 🫶:
- If N <= 1, LWORK must be at least 1.
- If JOBZ = 'N' and N > 1, LWORK must be queried (yes, queried, don't guess ngl):

LWORK = MAX(1, dimension) where
        dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1
                  = N*KD + N*max(KD+1,FACTOPTNB)
                    + max(2*KD*KD, KD*NTHREADS)
                    + (KD+1)*N + 2*N+1

where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm — usually FACTOPTNB=128 is a good choice — and NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1 🔥.

If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2.

And the plot twist: if LWORK = -1, then a workspace query is assumed 🕵️‍♀️. The routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. It's giving "just asking, not committing" energy.

IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK 💜.
LIWORK — INTEGER. The dimension of the array IWORK.
- If N <= 1, LIWORK must be at least 1.
- If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
- If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

And same deal as before: if LIWORK = -1, then a workspace query is assumed — the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA 🌈.

INFO — INTEGER. The vibe check at the end 😭:
- = 0: successful exit 🎉 iconic, no notes.
- < 0: if INFO = -i, the i-th argument had an illegal value 🙈.
- > 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge — i off-diagonal elements of an intermediate tridiagonal form did not converge to zero 💀. If INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1) 🔥. Like bestie, those exact coordinates, write them down.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

🫶 Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee Modified description of INFO. Sven, 16 Feb 05.

🧚 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 219 of file dsyevd_2stage.f 📖.

🌸 subroutine ssyevd_2stage

subroutine ssyevd_2stage (character jobz, character uplo, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

SSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 💖

Purpose:

SSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm 🦋.

Parameters

JOBZ — CHARACTER*1.
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 😭 (I know. heartbreaking. not in this release, bestie.)
UPLO — CHARACTER*1.
- = 'U': Upper triangle of A is stored;
- = 'L': Lower triangle of A is stored.
N — INTEGER. The order of the matrix A. N >= 0. 🎀
A — REAL array, dimension (LDA, N). On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A ✨. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed 💀.
LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💅
W — REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order 🌸.
WORK — REAL array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal LWORK 👑.
LWORK — INTEGER. The dimension of the array WORK. Same energy as before, here we go:
- If N <= 1, LWORK must be at least 1.
- If JOBZ = 'N' and N > 1, LWORK must be queried:

LWORK = MAX(1, dimension) where
        dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1
                  = N*KD + N*max(KD+1,FACTOPTNB)
                    + max(2*KD*KD, KD*NTHREADS)
                    + (KD+1)*N + 2*N+1

where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice, and NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1 🔥.

If JOBZ = 'V' and N > 1, LWORK must be at least 1 + 6*N + 2*N**2.

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

IWORK — INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK 💜.
LIWORK — 💫

okay so LIWORK is INTEGER, bestie, and it's literally the dimension of the IWORK array 💖

If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK 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 and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Contributors

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee
Modified description of INFO. Sven, 16 Feb 05.

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 219 of file ssyevd_2stage.f.

subroutine zheevd_2stage

subroutine zheevd_2stage (character jobz, character uplo, integer n,
    complex*16, dimension( lda, * ) a, integer lda, double precision,
    dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double
    precision, dimension( * ) rwork, integer lrwork, integer, dimension( * )
    iwork, integer liwork, integer info)

ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 👑

Purpose

ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm ✨

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.

A — A is COMPLEX*16 array, dimension (LDA, N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.

LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

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

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

LWORK — LWORK is INTEGER The dimension of the array WORK.

If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be queried.

LWORK = MAX(1, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + N+1
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + N+1
where KD is the blocking size of the reduction,
FACTOPTNB is the blocking used by the QR or LQ
algorithm, usually FACTOPTNB=128 is a good choice
NTHREADS is the number of threads used when
openMP compilation is enabled, otherwise =1.

If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2

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 (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK — LRWORK is INTEGER The dimension of the array RWORK.

If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N.
If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2.

If LRWORK = -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.

IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK — LIWORK is INTEGER The dimension of the array IWORK.

If N <= 1, LIWORK must be at least 1.
If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

If LIWORK = -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.

INFO — INFO is INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

Author

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Further Details

Modified description of INFO. Sven, 16 Feb 05.

Contributors

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Further Details

okay so, if you want the full 2stage lore, bestie, it's literally all right here — no gatekeeping:

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. iconic, honestly. 💅

Also, for the record: Definition at line 245 of file zheevd_2stage.f. keep that receipt, iykyk. 🧾✨

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heevd_2stage(3)

🦋 heevd_2stage(3) — Library Functions Manual 🦋

✨ NAME ✨

🌈 SYNOPSIS 🌈

🫶 Functions

💜 cheevd_2stage

🌸 dsyevd_2stage

🦋 ssyevd_2stage

🎀 zheevd_2stage

💖 Detailed Description 💖

🔥 Function Documentation 🔥

⭐ subroutine cheevd_2stage

🎯 Purpose

🌟 Parameters

👑 Author

📚 Further Details:

🧠 Contributors:

🔬 Further Details:

⭐ subroutine dsyevd_2stage

🎯 Purpose

🌟 Parameters

👑 Author

🫶 Contributors:

🧚 Further Details:

🌸 subroutine ssyevd_2stage

Purpose:

Parameters

Author

Contributors

Further Details

subroutine zheevd_2stage

Purpose

Parameters

Author

Further Details

Contributors

Further Details

👑 Author 👑

💜 `cheevd_2stage`

🌸 `dsyevd_2stage`

🦋 `ssyevd_2stage`

🎀 `zheevd_2stage`

⭐ subroutine `cheevd_2stage`

⭐ subroutine `dsyevd_2stage`