SRC/cheev_2stage.f(3)

Okay bestie, this is the SRC/cheev_2stage.f(3) page from the Library Functions Manual — and it’s literally all about cheev_2stage, no cap. 💅

💖 NAME

SRC/cheev_2stage.f

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

   subroutine cheev_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork,
       info)

CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices. 👑

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🫶 Function/Subroutine Documentation

   subroutine cheev_2stage (character jobz, character uplo, integer n, complex,
       dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex,
       dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer
       info)

CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices. 🌸

Purpose:

!>
!> CHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A using the 2stage technique for
!> the reduction to tridiagonal.
!>

Parameters

• JOBZ — JOBZ is CHARACTER*1. Bestie, it’s giving choice:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.
    • Not available in this release. 😭
• UPLO — UPLO is CHARACTER*1. Which triangle are we storing, hmm?
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER. It’s the order of the matrix A. N >= 0. 🫶
• A — A is COMPLEX array, dimension (LDA, N).
  • On entry, it’s 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.
  • 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. 💀
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 🌟
• W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🎀
• 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. 🔥

• 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: 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.

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 187 of file cheev_2stage.f.

Author

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