ZHEEV_2STAGE(3)

🌸 ZHEEV_2STAGE(3) — bestie's guide to the 2stage Hermitian eigensolver 🌸

okay so first things first: this is a page from the Library Functions Manual, and the file it lives in is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zheev_2stage.f ✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zheev_2stage.f

like, that's literally it, that's the name, that's the whole vibe 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine ZHEEV_2STAGE (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)

ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 👑

🌈 Function/Subroutine Documentation 🌈

subroutine ZHEEV_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 info)

ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices 💅

✨ Purpose ✨

!> ZHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a !> complex Hermitian matrix A using the 2stage technique for !> the reduction to tridiagonal. !>

so yeah, it gets all the eigenvalues of a complex Hermitian matrix A, and if you want, the eigenvectors too — and it does the tridiagonal reduction with the 2stage technique (iykyk, that's the whole point of this one, it's the fancy two-stage version) 🔥

🎀 Parameters 🎀

JOBZ

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

'N' — eigenvalues only, minimal queen behavior 😌
'V' — eigenvalues and eigenvectors… except bestie, this one is literally not available in this release 💀 do not come for me, that's what the page says

UPLO

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

'U' — you're storing the upper triangle of A
'L' — you're storing the lower triangle of A

pick one, bestie, the matrix is Hermitian, it knows both halves anyway 🫶

N

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

the order of the matrix A. gotta be N >= 0, no negative vibes allowed 🚫

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. !>

A is COMPLEX*16, dimension (LDA, N). here's the tea:

on entry it's your Hermitian matrix A. if UPLO = 'U', the leading N-by-N upper triangular part holds the upper triangle of A. if UPLO = 'L', the leading N-by-N lower triangular part holds the lower triangle.
on exit, if JOBZ = 'V' and INFO = 0, A contains the orthonormal eigenvectors of A. iconic 💅
but 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 😭 like genuinely gone, so don't come crying to me

LDA

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

the leading dimension of the array A, and it better be LDA >= max(1,N) ⭐

W

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

DOUBLE PRECISION, dimension (N). if INFO = 0, you get the eigenvalues in ascending order — sorted, organized, main character energy 👑

WORK

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

COMPLEX*16, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK — it's literally telling you the ideal workspace size, take the hint 🎀

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 = max(stage1,stage2) + (KD+1)*N + N !> = N*KD + N*max(KD+1,FACTOPTNB) !> + max(2*KD*KD, KD*NTHREADS) !> + (KD+1)*N + N !> 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 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. !>

LWORK is INTEGER, the length of the array WORK. LWORK >= 1 when N <= 1. otherwise, buckle up:

if JOBZ = 'N' and N > 1, LWORK must be queried:

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

and the glossary, because acronyms are a whole thing:

KD — the blocking size of the reduction
FACTOPTNB — the blocking used by the QR or LQ algorithm, and usually FACTOPTNB=128 is a good choice
NTHREADS — 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 🙈

and the special case, bestie: 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. it's giving "just asking, not committing" 💅

RWORK

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

DOUBLE PRECISION, dimension (max(1, 3*N-2)). that's it, that's the whole entry 🍓

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. !>

INFO is INTEGER, the vibe check at the end:

= 0 — successful exit, we ate 🎉
< 0 — if INFO = -i, the i-th argument had an illegal value (check your args, bestie)
> 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.

the whole squad, honestly 🫶

🧚 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 !> !>

all the details about the 2stage techniques live in these three papers, so if you want the full lore, go read them 📚:

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 187 of file `zheev_2stage.f`. ⭐

that's where the source lives, if you ever wanna go look at it yourself 🦋

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. a bot wrote this, and honestly? it ate 🤖✨

and that's the whole page, bestie! 🎀 this one's from LAPACK, Version 3.12.0, dated /home/abui...ev_2stage.f(3) — going out with a <rainbow>slay</rainbow> and a reminder to always query your LWORK 💖

📦 where this page comes from

opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms