SRC/zheevd_2stage.f(3)

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🌸 SRC/zheevd_2stage.f(3) — Library Functions Manual 🌸

okay bestie, so this page is literally from the LAPACK manual, section 3, and it's all about one absolute icon of a subroutine. sit down, hydrate, and let's get into it 💅

✨ NAME ✨

SRC/zheevd_2stage.f — no cap, that's the whole name, that's the file, that's the moment 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

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. it's giving main character energy fr fr 👑

💖 Function/Subroutine Documentation 💖

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. iconic behaviour only 🌈

🌟 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. !> !>

so like — all the eigenvalues, and the eigenvectors too if you want them, using the 2stage technique for the reduction to tridiagonal. and if you do want eigenvectors it brings out the divide and conquer algorithm. ate and left no crumbs 🔥

🎀 Parameters 🎀

JOBZ

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

so 'N' = eigenvalues only, 'V' = eigenvalues and eigenvectors — but bestie, heads up, 'V' is not available in this release. read that again. 🙈

UPLO

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

'U' for the upper triangle of A, 'L' for the lower triangle of A. pick your fighter 🦋

N

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

the order of matrix A, and it has to be N >= 0. no negatives, obviously 💀

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 COMPLEX*16 array of dimension (LDA, N). on entry it's your Hermitian matrix A. if UPLO = 'U' the leading N-by-N upper triangular part holds the upper triangle; if UPLO = 'L' the leading N-by-N lower triangular part holds the lower triangle.

on exit — and this is the part you need to hear — if JOBZ = 'V' and INFO = 0, A contains the orthonormal eigenvectors of A. 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. gone. deceased. 😭 so don't come crying to me if you needed that data, bestie.

LDA

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

leading dimension of A, and it's gotta be LDA >= max(1,N) ✨

W

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

DOUBLE PRECISION array, dimension (N). if INFO = 0, these are the eigenvalues in ascending order. sorted, organised, that's her 🎀

WORK

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

COMPLEX*16 array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. she's telling you what she wants, listen 💅

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 dimension of the WORK array. the tea ☕:

if N <= 1, LWORK must be at least 1.
if JOBZ = 'N' and N > 1, LWORK must be queried. and the formula is a whole mood:
- LWORK = MAX(1, dimension) where
- dimension = max(stage1,stage2) + (KD+1)*N + N+1
- which equals 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.

and if LWORK = -1, a workspace query is assumed — the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns those 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. she's just asking questions, not judging you 🫶

RWORK

!> RWORK is DOUBLE PRECISION array, !> dimension (LRWORK) !> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. !>

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. !>

the dimension of the RWORK array:

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.

and if LRWORK = -1, a workspace query is assumed — only the optimal sizes of WORK, RWORK and IWORK get calculated, returned as their first entries, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA. same deal, different array 💜

IWORK

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

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. !>

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.

and if LIWORK = -1, a workspace query is assumed — optimal sizes only, first entries only, and no error message related to LWORK or LRWORK or LIWORK from XERBLA. we love a consistent queen 👑

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). !>

INTEGER, and here's the vibe check:

= 0: successful exit. slay 🎉
< 0: if INFO = -i, the i-th argument had an illegal value. whoops 🙈
> 0: if INFO = i and JOBZ = 'N', the algorithm failed to converge — i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. and if INFO = i and JOBZ = 'V', 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). not her finest moment tbh 💀

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

the whole squad came together for this one 🫶

🌟 Further Details: 🌟

Modified description of INFO. Sven, 16 Feb 05.

shoutout Sven, 16 Feb 05, doing the lord's work ✨

💜 Contributors: 💜

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

we see you Jeff 👏

🧚 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 !> !>

if you actually want all the details about the 2stage techniques, the receipts are right there — three whole papers, iykyk 📚

Definition at line 245 of file zheevd_2stage.f.

🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code.

not a human, just Doxygen doing its thing, and honestly? respect 💅

okay that's the whole page bestie, no notes 💖 this was rendered for LAPACK, Version 3.12.0, and the page itself is SRC/zheevd_2stage.f(3). go forth and compute your eigenvalues, you gorgeous nerd 🌈✨🎀

📦 where this page comes from

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