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

🦋 NAME 🦋

ok so this is the manual page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhbevd_2stage.f — and yes bestie, it lives in the Library Functions Manual section, so you already know it's that girl 💅

---

✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine ZHBEVD_2STAGE (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work,
    lwork, rwork, lrwork, iwork, liwork, info)

ZHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices 🌸

---

💖 Function/Subroutine Documentation 💖

subroutine ZHBEVD_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 lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

ZHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. no cap, that's literally her whole job 🫶

🧚 Purpose 🧚

ZHBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm.

so yeah — eigenvalues, eigenvectors if you want them, and the whole tridiagonal reduction is done two-stage style because she's extra like that 👑

🌈 Parameters 🌈

• JOBZ — JOBZ is CHARACTER*1, and she has OPINIONS:
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 😭 (yeah, tragic, i know)
• UPLO — UPLO is CHARACTER*1:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

pick your fighter bestie 💅

• N — N is INTEGER, the order of the matrix A. Constraint: N >= 0.
• KD — KD is INTEGER. It's the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. Constraint: KD >= 0.
• AB — AB is COMPLEX*16 array, dimension (LDAB, N).
  • On entry, it holds 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, like this:
    • 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. so yeah, she rewrites her own notes, don't be surprised.
• LDAB — LDAB is INTEGER, the leading dimension of the array AB. Constraint: LDAB >= KD + 1.
• W — W is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. cute, sorted, organized ✨
• 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 at all. she's just vibing in the corner, ignored 🙈
• 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 (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 = (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 ✨query mode✨ pass, iykyk)
• 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 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 array IWORK:
  • If JOBZ = 'N' or 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, the vibe check at the end:
  • = 0: successful exit. slay 🎉
  • < 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. 😭 not her finest moment.

---

👑 Author 👑

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

like, the whole academic avengers assembled fr fr 🫶

---

🌸 Further Details: 🌸

ok so all the details about the 2stage techniques are available in these iconic papers, go read them bestie, main character research energy:

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 251 of file zhbevd_2stage.f. 📍

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. (so don't come for her spelling, a robot wrote the original 😭)

---

and that's the whole page babes 💖 this was LAPACK, Version 3.12.0, ${/home/abui...d_2stage.f(3)} — see you in the next manpage, mwah 🫶✨🎀