SRC/zhbev_2stage.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 NAME 💅

Okay bestie, welcome to SRC/zhbev_2stage.f — straight out of the Library Functions Manual, and no cap, this one's a whole vibe. It's a Fortran source file page documenting one very specific LAPACK subroutine, and we're gonna get into it. 🫶

✨ SYNOPSIS ✨

🔥 Functions/Subroutines

  • subroutine zhbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info) — the main character!! ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 💖

🎀 Function/Subroutine Documentation 🎀

Here's the whole signature, verbatim, because we do not mess with the facts:

subroutine zhbev_2stage (character jobz, character uplo, integer n, integer
    kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision,
    dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,
    complex*16, dimension( * ) work, integer lwork, double precision,
    dimension( * ) rwork, integer info)

ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. Slay. 👑

🌸 Purpose 🌸

ZHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal. That's the whole assignment, 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.

🌈 KD

KD is INTEGER. The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

🌈 AB

AB is COMPLEX*16 array, dimension (LDAB, N).

On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the reduction to tridiagonal form. (Lowkey important, don't come for me later. 🙈) If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.

🌈 LDAB

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.

🌈 W

W is DOUBLE PRECISION array, dimension (N).

If INFO = 0, the eigenvalues in ascending order. Chef's kiss. 🍓

🌈 Z

Z is COMPLEX*16 array, dimension (LDZ, N).

If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(i). If JOBZ = 'N', then Z is not referenced — she's off duty, don't bother her. 💅

🌈 LDZ

LDZ is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

🌈 WORK

WORK is COMPLEX*16 array, dimension LWORK.

On exit, if INFO = 0, WORK(1) returns the optimal LWORK. Iconic behaviour tbh.

🌈 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 = (2KD+1)*N + KD*NTHREADS
where KD is the size of the band.
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 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. ✨ (Yes, IWORK gets mentioned here even though it's not one of this routine's arguments — that's just what the page says, bestie, I don't make the rules.)

🌈 RWORK

RWORK is DOUBLE PRECISION 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 ⭐

Definition at line 209 of file zhbev_2stage.f.

🎀 the cute sign-off 🎀

And that's the whole page, bestie!! This was Generated automatically by Doxygen for LAPACK from the source code, which is giving "the robots wrote my biography" energy honestly. 🌈

Page footer tea: LAPACK, Version 3.12.0, and the file is SRC/zhbev_2stage.f(3). Periodt. 💖✨🎀

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