/home/abui...d_2stage.f(3)

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zheevd_2stage.f

Bestie, this is the manual page for that file, coming at you from the Library Functions Manual 💅. The header shortens it to /home/abui...d_2stage.f(3), and we are keeping that energy.

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🌸 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. Periodt ✨

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💅 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.

🎯 Purpose

Okay so 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. That's the whole purpose, and it ate 💅

🧾 Parameters

• 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 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 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.

🚨 Heads up, bestie: 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 a drill 💀

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

• RWORK — RWORK is 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.

• IWORK — IWORK is 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.

• 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).

👑 Author

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

🔎 Further Details

Modified description of INFO. Sven, 16 Feb 05.

🌟 Contributors

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

📚 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 at line 245 of file zheevd_2stage.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie 🫶 This page is from LAPACK Version 3.12.0, tied to /home/abui...d_2stage.f(3), and the date energy on deck is Sven, 16 Feb 05 ✨💖