DSYEV_2STAGE(3)

💅 DSYEV_2STAGE(3) — the LAPACK one, bestie

okay so this page lives in the Library Functions Manual (that's the manual name, iykyk) and it's all about DSYEV_2STAGE, a Fortran subroutine that does the absolute most. 🎀

---

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsyev_2stage.f

like... that's literally the whole name, it's a path, we love a full-glamour file path 🌸

---

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DSYEV_2STAGE (jobz, uplo, n, a, lda, w, work, lwork, info)

DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 💖

---

👑 Function/Subroutine Documentation 👑

subroutine DSYEV_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 info)

DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices ✨

🌈 Purpose 🌈

!> !> DSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a !> real symmetric matrix A using the 2stage technique for !> the reduction to tridiagonal. !>

like, two stages bestie, that's the whole vibe 🧚

💜 Parameters 💜

• JOBZ — JOBZ is CHARACTER*1 💅
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. (sorry bestie, that one's not dropping yet 😭)
• 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 DOUBLE PRECISION 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. 💀 (not me warning you twice, but like... it's gone)
• 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. (ascending! main character energy ⭐)
• WORK — WORK is DOUBLE PRECISION array, dimension LWORK
  • On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER 👑 this one's a whole paragraph, get comfy
  • 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 + 2*N
                  = N*KD + N*max(KD+1,FACTOPTNB)
                    + max(2*KD*KD, KD*NTHREADS)
                    + (KD+1)*N + 2*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. (very demure, very mindful 🌸)

• 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.

(quadruple-authoring, the collaboration of it all 🫶)

🦋 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 !> !>

like, three whole papers, they really said "cite us" and honestly? respect. 🔥

---

Definition at line 181 of file dsyev_2stage.f. ✨

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

---

and that's the page bestie 🫶 it's LAPACK, Version 3.12.0, and the whole thing is literally /home/abui...ev_2stage.f(3) — mwah, no cap, periodt. 💖🎀🦋