SRC/dsbevx_2stage.f(3)

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💅 SRC/dsbevx_2stage.f 💅

okay so bestie, welcome to page 3 of the Library Functions Manual — yes that's the actual manual name, we're in the big-league reference docs now 🎀

this whole page is about one single file, and that file is:

SRC/dsbevx_2stage.f

that's it. that's the name. the whole NAME section is literally just the path, because Fortran source files don't get cute nicknames in the manpage index, they get file paths and honestly? iconic. 👑

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

okay this is the part you actually came for — the file has one subroutine in it and she's a whole main character 👑 so let's give her the respect she deserves:

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)

look at that argument list. count them. i'll wait. 🫶 that's 24 arguments, no cap, and they wrap across three lines because she refused to be contained. that's not a red flag that's a red carpet. 🔥

and what does she do? the one-liner says, and i quote:

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

eigenvalues ✅ optionally eigenvectors ✅ and note the drama of "OTHER matrices" — capital letters, bestie, the manpage is yelling it at us. this is the two-stage variant of the routine, and she's filed under the "OTHER" bucket because she is, in fact, not like the other girls 🦋 (the subroutine, i mean. the subroutine is not like the other subroutines. anyway.)

that's the whole synopsis — one function, twenty-four parameters, zero chill. the breakdown of what each of those arguments actually means is coming up next, so don't go anywhere 💜

💖 Function/Subroutine Documentation 💖

   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

🎯 Purpose 🎯

okay so bestie, 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. ✨

✨ Parameters ✨

`JOBZ`

JOBZ is CHARACTER*1.

= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors. Not available in this release.

🫶 heads up: JOBZ = 'V' is flagged as Not available in this release. — that's the original rule, no cap.

`RANGE`

RANGE is 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`

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 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.

`LDAB`

LDAB is INTEGER.

The leading dimension of the array AB. LDAB >= KD + 1.

`Q`

Q is 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`

LDQ is INTEGER.

The leading dimension of the array Q. If JOBZ = 'V', then LDQ >= max(1,N).

`VL`

VL is 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`

VU is 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`

IL is 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`

IU is 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`

ABSTOL is 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 by Demmel and Kahan, LAPACK Working Note #3.

`M`

M is INTEGER.

The total number of eigenvalues found. 0 <= M <= N.

If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.

`W`

W is DOUBLE PRECISION array, dimension (N).

The first M elements contain the selected eigenvalues in ascending order.

`Z`

Z is 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.

`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 (LWORK).

`LWORK`

LWORK is 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`

IWORK is INTEGER array, dimension (5*N).

`IFAIL`

IFAIL is 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`

INFO is 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.

👑 Author 👑

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

🌈 Further Details 🌈

All details about the 2stage techniques are available in:

Azzam Haidar, Hatem Ltaief, and Jack Dongarra. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages. http://doi.acm.org/10.1145/2063384.2063394
A. Haidar, J. Kurzak, P. Luszczek, 2013. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13). Denver, Colorado, USA, 2013. Article 90, 12 pages. http://doi.acm.org/10.1145/2503210.2503292
A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks. International Journal of High Performance Computing Applications. Volume 28 Issue 2, Pages 196-209, May 2014. http://hpc.sagepub.com/content/28/2/196

Definition at line 319 of file dsbevx_2stage.f.

✨ AUTHOR ✨

okay so nobody hand-wrote this bad boy — it was literally generated automatically by Doxygen for LAPACK, straight from the source code 🎀 so yeah, the robot did the typing, we just gave it the vibe ✨

and that's a wrap bestie!! 🫶 this little page is from LAPACK, Version 3.12.0, and it's covering SRC/dsbevx_2stage.f(3) — go forth and slay your eigenvalue problems, ily, bye 💅💖🦋

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms