SRC/zhbgv.f(3)

🌸 NAME 🌸

SRC/zhbgv.f — this is the SRC/zhbgv.f(3) page from the Library Functions Manual, bestie. 💅✨

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zhbgv (...) — ZHBGV

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

🦋 Function/Subroutine Documentation 🦋

💖 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

🎀 Purpose 🎀

Okay so here's the vibe: 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. 💅✨

🌈 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.

🌟 Author 🌟

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 181 of file zhbgv.f.

🫶 Author (page generation) 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie — LAPACK Version 3.12.0, SRC/zhbgv.f(3), and we ate. 💅🎀✨