SRC/chbev_2stage.f(3)

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version 3.12.1 · 4 versions
, in arch rolling

SRC/chbev_2stage.f 💅

okay so bestie, quick vibe check: this is a page from the Library Functions Manual (LAPACK edition, fr fr), and it's all about one iconic little subroutine. let's get into it 🎀

✨ NAME ✨

SRC/chbev_2stage.f — that's the file, that's the whole name section, no notes 💀

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine chbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info) — CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

🦋 Function/Subroutine Documentation 🦋

subroutine chbev_2stage (character jobz, character uplo, integer n, integer
    kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
    w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )
    work, integer lwork, real, dimension( * ) rwork, integer info)

CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 💖

Purpose

CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal.

no cap, that's the whole purpose. it's giving "i do one thing and i do it well" 👑

🌈 Parameters 🌈

buckle up bestie, there's a lot of them, but they all slay in their own way ✨

  • JOBZ — JOBZ is CHARACTER*1. it's your "what do you actually want from me" switch:
    • = 'N': Compute eigenvalues only;
    • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. (so don't come for me when it doesn't work 🙈)
  • UPLO — UPLO is CHARACTER*1. which triangle of A is stored:
    • = '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. that's it, that's the whole vibe 🫶
  • 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 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. 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. she gets a whole glow-up on exit, obsessed ✨

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1. non-negotiable.
  • W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. sorted and everything, we love a tidy queen 💅
  • Z — Z is COMPLEX 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 not even invited to the party, it's fine 😭
  • 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 array, dimension LWORK. On exit, if INFO = 0, WORK(1) returns the optimal LWORK. she's a little snitch and that's a compliment 💜
  • 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. the -1 is the "just tell me the size, don't actually do anything" button, iykyk 🧚
  • RWORK — RWORK is REAL array, dimension (max(1,3*N-2)). that's the whole description, she's lowkey mysterious 🌸
  • INFO — INFO is INTEGER, the final verdict:
    • = 0: successful exit. we cheered 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value. somebody did NOT read the docs 💀
    • > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. it tried its best, fr fr 😭

👑 Author 👑

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

the whole squad, credited and everything 🫶

🔥 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

like, the receipts are RIGHT THERE. read the papers, bestie, they ate 📚✨

⭐ Definition ⭐

Definition at line 209 of file chbev_2stage.f. that's where she lives 🏠

💖 Author (the meta one) 💖

Generated automatically by Doxygen for LAPACK from the source code. a bot wrote this part, not me, don't @ me 🤖

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