/home/abui...x_2stage.f(3)

🦋 dsbevx_2stage.f(3) 🦋

okay so bestie, real talk — this is a page from the Library Functions Manual, and it's literally the manpage for the file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsbevx_2stage.f. That path is giving "I live deep in a build tree and I know it" energy. 🫶

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsbevx_2stage.f

like... that's the whole name. yes, the entire full path is the name. no notes, it's iconic, it's committed to the bit. 👑

🎀 SYNOPSIS 🎀

💅 Functions/Subroutines

so under here we've got exactly one (1) entry and she is the main character:

subroutine DSBEVX_2STAGE (jobz, range, uplo, n, kd, ab, ldab, q, ldq,
    vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, iwork, ifail,
    info)

that's a lot of arguments and every single one of them is listed above, character for character, no cap. 🧚

🌸 what she does

DSBEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 😭✨

like yes, that's literally the description — "OTHER matrices", capital O-T-H-E-R, she said what she said. 🔥

ngl this part is short and sweet, but don't you dare think that's all — the real lore is still coming, so stay tuned bestie 💖

💫 Function/Subroutine Documentation

okay bestie, buckle up, because this is where the actual function lives 💖

subroutine DSBEVX_2STAGE (character jobz, character range, character uplo,
    integer n, integer kd, double precision, dimension( ldab, * ) ab,
    integer ldab, double precision, dimension( ldq, * ) q, integer ldq,
    double precision vl, double precision vu, integer il, integer iu, double
    precision abstol, integer m, double precision, dimension( * ) w, double
    precision, dimension( ldz, * ) z, integer ldz, double precision,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer, dimension( * ) ifail, integer info)

DSBEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices ✨ no cap, that's the whole elevator pitch.

🎯 Purpose

DSBEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A using the 2stage technique for the reduction to tridiagonal 🔥

Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues — so you get to pick, like, exactly which ones you want 💅

🧚 Parameters

JOBZ — CHARACTER*1 👑
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 💀
RANGE — CHARACTER*1 🌈
- = 'A': all eigenvalues will be found;
- = 'V': all eigenvalues in the half-open interval (VL,VU] will be found;
- = 'I': the IL-th through IU-th eigenvalues will be found.
UPLO — CHARACTER*1 🦋
- = 'U': Upper triangle of A is stored;
- = 'L': Lower triangle of A is stored.
N — INTEGER 🌸 The order of the matrix A. N >= 0.
KD — INTEGER 🎀 The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
AB — 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 🔥 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. (so like, your input array is gone — she ate and left no crumbs, plan accordingly 🙈)

LDAB — INTEGER ⭐ The leading dimension of the array AB. LDAB >= KD + 1.
Q — DOUBLE PRECISION array, dimension (LDQ, N) 🫶
- If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction to tridiagonal form.
- If JOBZ = 'N', the array Q is not referenced.
LDQ — INTEGER 🌟 The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N).
VL — DOUBLE PRECISION 💜 If RANGE='V', the lower bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
VU — DOUBLE PRECISION 💜 If RANGE='V', the upper bound of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
IL — INTEGER 🍓 If RANGE='I', the index of the smallest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
IU — INTEGER 🍓 If RANGE='I', the index of the largest eigenvalue to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
ABSTOL — DOUBLE PRECISION 🎯 The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to

ABSTOL + EPS *   max( |a|,|b| ) ,

where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AB to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*DLAMCH('S'), not zero ⚠️ If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S').

See the work by Demmel and Kahan, LAPACK Working Note #3.

M — INTEGER ✨ The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W — DOUBLE PRECISION array, dimension (N) 🌸 The first M elements contain the selected eigenvalues in ascending order ⬆️ (yes bestie, ascending, always).
Z — DOUBLE PRECISION array, dimension (LDZ, max(1,M)) 🦋 If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced.

⚠️ Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used. fr fr, do not skimp on the columns 😭

LDZ — INTEGER ⭐ The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
WORK — DOUBLE PRECISION array, dimension (LWORK) 🧰
LWORK — INTEGER 🔥 The length of the array WORK. LWORK >= 1, when N <= 1; otherwise

If JOBZ = 'N' and N > 1, LWORK must be queried.
                         LWORK = MAX(1, 7*N, dimension) where
                         dimension = (2KD+1)*N + KD*NTHREADS + 2*N
                         where KD is the size of the band.
                         NTHREADS is the number of threads used when
                         openMP compilation is enabled, otherwise =1.
If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA 💅

IWORK — INTEGER array, dimension (5*N) 🎀
IFAIL — INTEGER array, dimension (N) 🫶 If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.
INFO — INTEGER 👑
- = 0: successful exit 🎉
- < 0: if INFO = -i, the i-th argument had an illegal value 💀
- > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.

and that's the whole parameter lineup — still got credits and the deep-cut research refs coming, don't scroll away 💜

🫶 Author 🫶

Okay so nobody wrote this one by hand, bestie — not even a little. It was generated automatically by Doxygen for LAPACK from the source code. That's the whole vibe: the docs are literally extracted straight out of the code itself, so if something looks a bit stiff and mechanical, that's because it is mechanical. A robot did the typing, we just gave it a glow-up. 💅

Which honestly? Iconic. The source code is the main character, Doxygen is just the hype friend taking notes, and LAPACK is the whole friend group. No cap. 🔥

Lowkey important: since this page was auto-generated from source, treat it as the mirror of the code, not as extra lore. The code is the source of truth, always. 🎀

And that's a wrap on the /home/abui...x_2stage.f(3) page, bestie — go forth and call your subroutines with confidence. 💖

✨ Generated automatically by Doxygen for LAPACK from the source code, this whole page is brought to you by LAPACK, Version 3.12.0, living at /home/abui...x_2stage.f(3). Bye bestie, slay your linear algebra! 🦋💜

📦 where this page comes from

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opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
opensuse-leap 16.0: lapack-man 3.12.0-160000.2.2 · BSD-3-Clause
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms