ZHBGVD(3)

💅 NAME 💅

okay so bestie, this page is zhbgvd.f(3) from the Library Functions Manual, and the NAME section is literally the whole source path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhbgvd.f. No cap, that's the name. It's giving "I am a Fortran file and I'm proud." 💖

✨ SYNOPSIS ✨

📚 Functions/Subroutines

The star of the show is ZHBGVD, and here's the short synopsis, exactly:

subroutine ZHBGVD (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz,
    work, lwork, rwork, lrwork, iwork, liwork, info)

ZHBGVD — that's the function, periodt. 👑

🦋 Function/Subroutine Documentation 🦋

🌸 subroutine ZHBGVD 🌸

Detailed signature, character for character:

subroutine ZHBGVD (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, integer lwork, double precision,
    dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

ZHBGVD again, because it's the main character. 💫

💖 Purpose 💖

ZHBGVD 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. If eigenvectors are desired, it uses a divide and conquer algorithm. Slay. 🔥

🎀 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 side. 💅
• 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. 😭 dramatic but true.

• 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. Cute. 🌸
• 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. So if you're not using it, it's giving ghost. 🫥
• 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 (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 >= 1. If JOBZ = 'N' and N > 1, LWORK >= N. If JOBZ = 'V' and N > 1, LWORK >= 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. Big "trust me, it's a query" energy. ✨

• RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,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 >= 1. If JOBZ = 'N' and N > 1, LRWORK >= N. If JOBZ = 'V' and N > 1, LRWORK >= 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 >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 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.

= 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.

So yeah: INFO = 0 is the slay, negative is "bad argument," and positive is "convergence or ZPBSTF said B is not positive definite." No cap. 💀

🫶 Author 🫶

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

🌟 Contributors 🌟

Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA.

🔥 Definition at line 243 of file zhbgvd.f. 🔥

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

---

Cute sign-off, bestie: this page is LAPACK, Version 3.12.0, and the source/version/date footer points at /home/abui...RC/zhbgvd.f(3) — that's the whole footer vibe. 💖✨👑