/home/abui...RC/dsbev.f(3)

💅 dsbev.f — like, the Library Functions Manual era ✨

okay so bestie, you've stumbled into /home/abui...RC/dsbev.f(3) and honestly? iconic of you. this is dsbev.f from the LAPACK library functions manual, and it's giving very specific, very symmetric-band-matrix energy. buckle up 🎀

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🌸 NAME 🌸

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

like, that's the whole path. that's the name. it's a whole journey. no cap. 📁

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DSBEV (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, info) — DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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🦋 Function/Subroutine Documentation 🦋

subroutine DSBEV (character jobz, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)

DSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. like the "OTHER matrices" ones. bestie it's so specific and I respect it 💜

🎯 Purpose:

!>
!> DSBEV computes all the eigenvalues and, optionally, eigenvectors of
!> a real symmetric band matrix A.
!>

so it takes your real symmetric band matrix A, and it gets you the eigenvalues, and if you ask nicely it also hands over the eigenvectors. lowkey obsessed with how tidy that is. ✨

🌈 Parameters

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors.

pick your fighter, bestie. 'N' is the low-effort era, 'V' is main character energy 💅

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

which triangle of A you actually stuffed into memory. that's it, that's the choice 🫶

• N — N is INTEGER The order of the matrix A. and, and hear me out: 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. like the band width, basically. the vibe width. 🎀
• AB — AB is DOUBLE PRECISION array, dimension (LDAB, N)

On entry, the upper or lower triangle of the symmetric 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. 💀 not a drill — your input is gone, gone girl. 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. like, please. respect the bound. 🙈
• W — W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. sorted and serving. 👑
• Z — Z is DOUBLE PRECISION 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 — literally doesn't even get a text back. 😭
• LDZ — LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N). ⭐
• WORK — WORK is DOUBLE PRECISION array, dimension (max(1,3*N-2)) the workspace. the little helper. the backstage crew. 🧚
• 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.

so > 0 is the "it didn't converge" era and like… yeah. that's real. that happened. 💀

ngl, that INFO > 0 one is the one you gotta check, bestie. if it's nonzero, don't trust W. fr fr.

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💖 Author 💖

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

the whole squad 🫶

Definition at line 144 of file dsbev.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. so like, a robot wrote this and honestly? she ate. 🤖💅

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LAPACK · Version 3.12.0 · /home/abui...RC/dsbev.f(3) — mwah, that's the page, go compute your eigenvalues bestie 💖✨🎀🦋