ZHBEVD(3)

💖 NAME 💖

okay bestie, this page is literally the file path for zhbevd.f(3) in the Library Functions Manual 🫶:

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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

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🦋 Function/Subroutine Documentation 🦋

subroutine ZHBEVD (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 computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. That’s the whole vibe of this icon, periodt 💅.

Purpose

okay so bestie, here’s the tea: ZHBEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm. That’s the purpose, no cap ✨.

Parameters

JOBZ

JOBZ is CHARACTER*1 — the “what do you actually want” switch:

• = 'N': Compute eigenvalues only;
• = 'V': Compute eigenvalues and eigenvectors.

UPLO

UPLO is CHARACTER*1 — it tells you 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. 🎀

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 is 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’s busy and she’s overwriting, bestie 😭.

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. Cute and sorted 💅.

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 literally not invited to the function, no hard feelings 🫶.

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 dimension of the array WORK.

• If N <= 1, LWORK must be at least 1.
• If JOBZ = 'N' and N > 1, LWORK must be at least N.
• If JOBZ = 'V' and N > 1, LWORK must be at least 2*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. It’s giving “just asking, not committing” energy 🌈.

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. Same workspace-query vibe, different array 💜.

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. The workspace-query trio really said “we are one” 💀.

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.

So if INFO > 0, it’s not a cute little glitch — the algorithm failed to converge, bestie 😭.

Author 💖

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

Definition at line 207 of file zhbevd.f. 📌

Author (Doxygen-generated note) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, LAPACK Version 3.12.0 — /home/abui...RC/zhbevd.f(3) 🫶✨ (the footer didn’t give a date, so no invented date, bestie 💀)