SRC/chegv_2stage.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 SRC/chegv_2stage.f(3)

okay bestie, welcome to the LAPACK Library Functions Manual — yes this is that SRC/chegv_2stage.f page, the one and only, and we're gonna get through it together 🫶

✨ NAME ✨

SRC/chegv_2stage.f — literally the whole file, that's the name, no notes 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine chegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, rwork, info)

CHEGV_2STAGE — say it with me, iconic 👑

🦋 Function/Subroutine Documentation 🦋

subroutine chegv_2stage (integer itype, character jobz, character uplo,
    integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, complex,
    dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer
    info)

CHEGV_2STAGE

🎀 Purpose 🎀

okay so here's the vibe: CHEGV_2STAGE computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.

Here A and B are assumed to be Hermitian and B is also positive definite. no cap.

This routine use the 2stage technique for the reduction to tridiagonal which showed higher performance on recent architecture and for large sizes N>2000. that's the whole flex, honestly 🔥

💖 Parameters 💖

  • ITYPE — ITYPE is INTEGER. Specifies the problem type to be solved:
    • = 1: A*x = (lambda)*B*x
    • = 2: A*B*x = (lambda)*x
    • = 3: B*A*x = (lambda)*x
  • 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 triangles of A and B are stored;
    • = 'L': Lower triangles of A and B are stored.
  • N — N is INTEGER. The order of the matrices A and B. N >= 0.
  • 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 matrix Z of eigenvectors. The eigenvectors are normalized as follows:

  • if ITYPE = 1 or 2, Z**H*B*Z = I;
  • if ITYPE = 3, Z**H*inv(B)*Z = I.

If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. rest in peace to your data 🪦

  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • B — B is COMPLEX array, dimension (LDB, N). On entry, the Hermitian positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B.

On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H. she gets a whole new personality ✨

  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. bestie they come pre-sorted, we love a tidy 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 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. the classic "just asking for a friend" move 💅

  • RWORK — RWORK is REAL array, dimension (max(1, 3*N-2)).
  • INFO — INFO is INTEGER
    • = 0: successful exit 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: CPOTRF or CHEEV returned an error code:
      • <= N: if INFO = i, CHEEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
      • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. 😭 that's a whole mood, but at least she tells you why

👑 Author 👑

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

🧚 Further Details: 🧚

All details about the 2stage techniques are available in — the reading list, bestie, cite your sources 📚:

  • 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 230 of file chegv_2stage.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (so don't come for her, she didn't write herself 🤖)

and that's the page!! LAPACK, Version 3.12.0, SRC/chegv_2stage.f(3) — mwah, slay, go compute some eigenvalues, ily, bye 🎀✨

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