SSYEV_2STAGE(3)

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssyev_2stage.f

okay so bestie, this is the file itself — that whole long path is literally the source file this page is documenting (LAPACK's ssyev_2stage.f, if you wanna say it out loud 💅). It lives in the LAPACK manual, Library Functions Manual energy, and the header up top is /home/abui...ev_2stage.f(3) — yes the path is truncated with ... in the header, that's just how it is, no cap. 🫶

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SSYEV_2STAGE (jobz, uplo, n, a, lda, w, work, lwork, info)

SSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices ✨

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💅 Function/Subroutine Documentation 💅

🎀 the actual signature 🎀

subroutine SSYEV_2STAGE (character jobz, character uplo, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,
    dimension( * ) work, integer lwork, integer info)

SSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 🔥 (yes, the synopsis says it twice — iconic of it, honestly, we love a routine that knows its brand 💅)

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✨ Purpose ✨

SSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A using the 2stage technique for the reduction to tridiagonal.

so like — eigenvalues, optionally eigenvectors, real symmetric matrix A, and the whole flex is that 2stage technique for the reduction to tridiagonal. that's the main character move here 👑💜

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🎀 Parameters 🎀

• JOBZ — JOBZ is CHARACTER*1. The vibe selector, basically:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 😭 (crying, but documented — don't come for me)
• UPLO — UPLO is CHARACTER*1. Which triangle of A is the moment:
  • = '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. (zero is allowed bestie, don't worry 🫶)
• A — A is 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. 💀 yeah. that part of A is GONE. reading is fundamental, so pls don't be surprised when it happens.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). literally just respect the leading dimension bestie, it's not a suggestion 🌸
• W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. sorted and serving ✨
• WORK — WORK is REAL array, dimension LWORK. On exit, if INFO = 0, WORK(1) returns the optimal LWORK. (it's always the first entry spilling the tea about the optimal size 💅)
• 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 + 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. (the -1 is the lil "just checking, don't actually run anything" hack, and XERBLA stays quiet about it — cute of them 🎀)

• INFO — INFO is INTEGER. The receipts:
  • = 0: successful exit ✅ slay
  • < 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. 😭 it tried its best, but those off-diagonals refused to go to zero.

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🌈 Author 🌈

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

the whole squad 🫶👑

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🔥 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, read the papers if you want the full 2stage lore, they're literally right there 📚💜

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Definition at line 181 of file ssyev_2stage.f. 📍

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and that's the whole page!! 🎀 made for LAPACK, Version 3.12.0, path-in-the-footer /home/abui...ev_2stage.f(3) and all — generated automatically by Doxygen for LAPACK straight from the source code, so no human hand prettied it up before I did 💅✨ bye bestie, go query your LWORK 💜🦋