SRC/ssyevx_2stage.f(3)

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🎀 SRC/ssyevx_2stage.f 🎀

okay so bestie, this is the manual page for SRC/ssyevx_2stage.f from LAPACK — like, the real deal linear algebra library. sit down, hydrate, and let's get into it 💖

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ssyevx_2stage (jobz, range, uplo, n, a, lda, vl, vu, il, iu,
    abstol, m, w, z, ldz, work, lwork, iwork, ifail, info)

SSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 🔥

🌸 Function/Subroutine Documentation 🌸

subroutine ssyevx_2stage (character jobz, character range, character uplo,
    integer n, real, dimension( lda, * ) a, integer lda, real vl, real vu,
    integer il, integer iu, real abstol, integer m, real, dimension( * ) w,
    real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work,
    integer lwork, integer, dimension( * ) iwork, integer, dimension( * )
    ifail, integer info)

SSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices 👑

Purpose 🦋

!>
!> SSYEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
!> of a real symmetric 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.
!>

like, the whole vibe is: give it a real symmetric matrix A, tell it which eigenvalues you want, and it does the 2stage reduction-to-tridiagonal thing. iconic behavior honestly 💅

⭐ Parameters ⭐

okay this is the part where every single argument matters, so pay attention bestie, no cap 🙈

JOBZ — JOBZ is CHARACTER*1
- = 'N': Compute eigenvalues only;
- = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
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.
A — A is REAL array, dimension (LDA, N) On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed.

💀 yeah bestie, it gets destroyed. your input A does NOT survive this. that's just how it is.

LDA — LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
VL — VL is REAL 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 REAL 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 REAL 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 A to tridiagonal form.

Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('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 REAL array, dimension (N) On normal exit, the first M elements contain the selected eigenvalues in ascending order. ⭐
Z — Z is REAL 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. 👀 (yes, you have to figure that bound out, the routine isn't gonna do it for you)
LDZ — LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
WORK — WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal 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, 8*N, dimension) where
            dimension = max(stage1,stage2) + (KD+1)*N + 3*N
                      = N*KD + N*max(KD+1,FACTOPTNB)
                        + max(2*KD*KD, KD*NTHREADS)
                        + (KD+1)*N + 3*N

where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice 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.

like, the whole squad collaborated on this one 🫶

💜 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
!>
!>

literally reading material for the girlies who want to understand 2stage techniques 📚✨

Definition at line 297 of file ssyevx_2stage.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

aaaand that's the whole page bestie 🎀 no gatekeeping here. this was SRC/ssyevx_2stage.f(3) from LAPACK, Version 3.12.0 — she's giving serious main character energy in the eigenvalue world, fr fr 💖✨🌸

📦 where this page comes from

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