CHBGVD(3)

💅 CHBGVD(3) — the LAPACK banded generalized Hermitian-definite eigen-slay 💅

okay so bestie, welcome to CHBGVD(3) from the Library Functions Manual — this is the LAPACK routine that computes eigenvalues and optionally eigenvectors for a complex generalized Hermitian-definite banded eigenproblem, and it is lowkey iconic. 🦋

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🌸 NAME 🌸

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

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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🎀 Function/Subroutine Documentation 🎀

subroutine CHBGVD (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,
    integer lwork, real, dimension( * ) rwork, integer lrwork, integer,
    dimension( * ) iwork, integer liwork, integer info)
CHBGVD

This one is literally called CHBGVD, and she is giving major “I solve banded generalized Hermitian-definite eigenproblems” energy. 👑

🌟 Purpose 🌟

CHBGVD 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. periodt. 💅

💖 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 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 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 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, the eigenvalues in ascending order. ✨

🔹 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 (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.

🔹 RWORK

RWORK is REAL 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 CPBSTF
          returned INFO = i: B is not positive definite.
          The factorization of B could not be completed and
          no eigenvalues or eigenvectors were computed.

bestie, if B is not positive definite, the factorization cannot be completed and no eigenvalues or eigenvectors are computed. that is not a slay. 💀

🫶 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 🧚

Definition at line 243 of file chbgvd.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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