SRC/zhegv_2stage.f(3)

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🌈 SRC/zhegv_2stage.f(3) — Library Functions Manual 🌈

okay bestie, welcome to the manual page for SRC/zhegv_2stage.f 💅 the manual name is Library Functions Manual, and this whole page is serving one very specific ZHEGV_2STAGE moment. Buckle up, it’s giving “big math, tiny wrapper” energy. 🎀

✨ NAME ✨

SRC/zhegv_2stage.f — that’s the page name, no cap. 💖

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

  • subroutine zhegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info) — ZHEGV_2STAGE.

🦋 Function/Subroutine Documentation 🦋

subroutine zhegv_2stage (integer itype, character jobz, character uplo,
    integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer info)

ZHEGV_2STAGE — that’s the icon. 👑

✨ Purpose ✨

Okay so ZHEGV_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. This routine uses the 2stage technique for the reduction to tridiagonal, which showed higher performance on recent architecture and for large sizes N>2000. 🔥

🎀 Parameters 🎀

  • ITYPE — 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 — CHARACTER*1.
    • = 'N': Compute eigenvalues only.
    • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 🚨
  • UPLO — CHARACTER*1.
    • = 'U': Upper triangles of A and B are stored.
    • = 'L': Lower triangles of A and B are stored.
  • N — INTEGER. The order of the matrices A and B. N >= 0.
  • A — 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 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. 💀
  • LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • B — COMPLEX*16 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.
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • W — DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
  • WORK — COMPLEX*16 array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK. ✨
  • LWORK — 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.

  • RWORK — DOUBLE PRECISION array, dimension (max(1, 3*N-2)).
  • INFO — INTEGER.
    • = 0: successful exit.
    • < 0: if INFO = -i, the i-th argument had an illegal value.
    • > 0: ZPOTRF or ZHEEV returned an error code:
      • <= N: if INFO = i, ZHEEV 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. 😭

🌟 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:

  • 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 🧚

Definition at line 230 of file zhegv_2stage.f.

💖 Author 💖

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okay that’s the whole page, bestie, mwah 💋. This footer energy is from SRC/zhegv_2stage.f(3), LAPACK Version 3.12.0. The footer didn’t give a date, so I’m not inventing one — periodt. 🎀✨

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