/home/abui...RC/zhbgv.f(3)

🌸 NAME 🌸

okay so this page is from the Library Functions Manual — manual name folded in, bestie — and it's for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhbgv.f. the manpage path is /home/abui...RC/zhbgv.f(3). we are deep in LAPACK territory 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZHBGV (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
    work, rwork, info)
    ZHBGV

💖 Function/Subroutine Documentation 💖

🌟 subroutine ZHBGV 🌟

subroutine ZHBGV (character jobz, character uplo, integer n, integer ka,
    integer kb, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldbb, * ) bb, integer ldbb, double precision,
    dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz,
    complex*16, dimension( * ) work, double precision, dimension( * ) rwork,
    integer info)

ZHBGV is the main character here: it computes all the eigenvalues, and optionally the eigenvectors, of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. here A and B are assumed to be Hermitian and banded, and B is also positive definite. periodt 💖

🎯 Purpose

ZHBGV computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. slay ✨

🎀 Parameters 🎀

• JOBZ — JOBZ is CHARACTER*1; = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. 💖
• UPLO — UPLO is CHARACTER*1; = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.
• N — N is INTEGER; the order of the matrices A and B. N >= 0.
• KA — KA is INTEGER; the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.
• KB — KB is INTEGER; the number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed. 😭
• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KA+1.
• BB — BB is COMPLEX*16 array, dimension (LDBB, N). On entry, the upper or lower triangle of the Hermitian band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**H*S, as returned by ZPBSTF.
• LDBB — LDBB is INTEGER; the leading dimension of the array BB. LDBB >= KB+1.
• W — W is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🎀
• Z — Z is COMPLEX*16 array, dimension (LDZ, N). If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**H*B*Z = I. If JOBZ = 'N', then Z is not referenced.
• LDZ — LDZ is INTEGER; the leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.
• WORK — WORK is COMPLEX*16 array, dimension (N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (3*N).
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, and i is:
  • <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
  • > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

⚠️ heads up bestie: AB gets destroyed on exit. that's not a drill. 💀

⚠️ also B has to be positive definite — if ZPBSTF can't factor it, you get INFO and no eigenvalues or eigenvectors. no cap.

👑 Author

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

📍 Definition at line 181 of file zhbgv.f. 📍

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole vibe 🫶 this page is from LAPACK Version 3.12.0, and its manpage path is /home/abui...RC/zhbgv.f(3) — bye bestie! ✨💖