/home/abui...d_2stage.f(3)

🎀 /home/abui...d_2stage.f(3) 🎀

okay so this is a page from the Library Functions Manual bestie, and it's literally about one file: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsbevd_2stage.f 💅 like that's the whole NAME section, no notes, iconic behavior honestly.

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine DSBEVD_2STAGE (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work,
    lwork, iwork, liwork, info)

DSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 🦋

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💖 Function/Subroutine Documentation 💖

subroutine DSBEVD_2STAGE (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 lwork,
    integer, dimension( * ) iwork, integer liwork, integer info)

DSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. no cap, that's the description, twice, and honestly? slay. 💅

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Purpose 🫶

!>
!> DSBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
!> a real symmetric band matrix A using the 2stage technique for
!> the reduction to tridiagonal. If eigenvectors are desired, it uses
!> a divide and conquer algorithm.
!>
!>

so bestie, it gets all the eigenvalues, and optionally the eigenvectors too, of a real symmetric band matrix A, using the ✨2stage technique✨ for the reduction to tridiagonal. and if you do want eigenvectors, it hits them with a divide and conquer algorithm. main character energy fr fr 👑

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🌈 Parameters 🌈

• JOBZ — JOBZ is CHARACTER*1
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. 😭 (yes really, don't come for me)
• 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. 💀 your input array is GONE, that's just how it is

• LDAB — LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1.
• W — W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. 🍓
• 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. (ghosted entirely 🙈)
• 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 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, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS + 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 sizes of the WORK and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK or LIWORK is issued by XERBLA. (extremely polite of it ngl 🫶)

• 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 the array IWORK. If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. If JOBZ = 'V' and N > 2, 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 and IWORK arrays, returns these values as the first entries of the WORK and IWORK arrays, and no error message related to LWORK 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. 💀 that's the bad one bestie

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👑 Author 👑

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

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🧚 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
!>
!>

like, all the receipts, all three papers, links and page counts included. the way they cited everything — obsessed. 📚🔥

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🦋 Definition 🦋

Definition at line 226 of file dsbevd_2stage.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (not me writing this by hand, the robots did it, iykyk 🤖✨)

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and that's the whole page bestie!! shoutout to LAPACK, Version 3.12.0, for /home/abui...d_2stage.f(3) — literally the blueprint, no notes, periodt. 💖🎀🦋🌸💅🫶