SRC/chbgv.f(3)

💅 NAME 💅

SRC/chbgv.f — that's the name, bestie. This is the Library Functions Manual page for it, and we're about to get into the whole subroutine vibe. 💖

---

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

CHBGV — iconic. Periodt. ✨

---

🦋 Function/Subroutine Documentation 🦋

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

CHBGV 🫶

🎀 Purpose 🎀

Okay so CHBGV 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. That's the whole main-character assignment, no cap. 👑

💖 Parameters 💖

• JOBZ — JOBZ is CHARACTER*1; = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. Choose your fighter, bestie. 💅
• UPLO — UPLO is CHARACTER*1; = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. Pick a triangle, literally. 🔺
• 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 array, dimension (LDAB, N). On entry, it holds 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. 💀 Yeah, she's gone.

• LDAB — LDAB is INTEGER; the leading dimension of the array AB. LDAB >= KA+1. 🎀
• BB — BB is COMPLEX array, dimension (LDBB, N). On entry, it holds 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, BB holds the factor S from the split Cholesky factorization B = S**H*S, as returned by CPBSTF. 🧚

• LDBB — LDBB is INTEGER; the leading dimension of the array BB. LDBB >= KB+1. 💜
• W — W is REAL array, dimension (N). If INFO = 0, this holds the eigenvalues in ascending order. Slay, sorted. ⭐
• Z — Z is COMPLEX 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 array, dimension (N). 🫶
• RWORK — RWORK is REAL array, dimension (3*N). 💖
• INFO — INFO is INTEGER; the vibe check:
  • = 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 CPBSTF 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 chbgv.f.

---

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

🫶 Okay that's the whole page, bestie. It's from the Library Functions Manual, and the footer signs off with LAPACK, Version 3.12.0, and SRC/chbgv.f(3). The footer doesn't list a date, so I'm not inventing one — periodt. 💜✨