CHBEVD(3)

💖 NAME 💖

okay so bestie, this whole page is about the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chbevd.f — that’s the literal path, not a command, and yes it’s giving very “I live in a build directory” energy. 💅

We’re in the Library Functions Manual, on the chbevd.f(3) page, and it’s all about CHBEVD, the LAPACK subroutine that computes eigenvalues and, if you want them, eigenvectors for OTHER matrices. Slay.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine CHBEVD (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork,
    rwork, lrwork, iwork, liwork, info)
     CHBEVD computes the eigenvalues and, optionally, the left and/or
    right eigenvectors for OTHER matrices

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🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, bestie — every type, every dimension, no skips:

subroutine CHBEVD (character jobz, character uplo, integer n, integer kd,
    complex, dimension( ldab, * ) ab, integer ldab, 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)
     CHBEVD computes the eigenvalues and, optionally, the left and/or right
    eigenvectors for OTHER matrices

🌟 Purpose 🌟

So the actual purpose, no cap:

CHBEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A. If eigenvectors are desired, it uses a divide and conquer algorithm.

That’s literally the whole vibe. 💖

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💅 Parameters 💅

💖 JOBZ

JOBZ is CHARACTER*1

• = 'N': Compute eigenvalues only;
• = 'V': Compute eigenvalues and eigenvectors.

💖 UPLO

UPLO is CHARACTER*1

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

💖 N

N is INTEGER

The order of the matrix A. N >= 0.

💖 KD

KD is INTEGER

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On exit, AB is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows KD and KD+1 of AB, and if UPLO = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of AB.

💖 LDAB

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KD + 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 orthonormal eigenvectors of the matrix A, with the i-th column of Z holding the eigenvector associated with W(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 >= max(1,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 must be at least 1.
• If JOBZ = 'N' and N > 1, LWORK must be at least N.
• If JOBZ = 'V' and N > 1, LWORK must be at least 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.

bestie, that workspace-query mode is real: set LWORK = -1 and it’s just sizing things up, not doing the whole computation vibe. 💅

💖 RWORK

RWORK is REAL array, dimension (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 must be at least 1.
• If JOBZ = 'N' and N > 1, LRWORK must be at least N.
• If JOBZ = 'V' and N > 1, LRWORK must be at least 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 must be at least 1.
• If JOBZ = 'V' and N > 1, LIWORK must be at least 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, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

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👑 Author 👑

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

Definition at line 207 of file chbevd.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page 💖 the footer info was giving LAPACK — Version 3.12.0 — with /home/abui...RC/chbevd.f(3) at the end. Mwah, slay, periodt. 🎀