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

🦋 /home/abui...d_2stage.f(3) — Library Functions Manual 💅

okay so bestie, this is the Library Functions Manual page for /home/abui...d_2stage.f(3), and it's giving LAPACK main-character energy. It's literally all about the CHBEVD_2STAGE subroutine. No cap, we're keeping every flag, every array, every INFO code — all of it. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chbevd_2stage.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine CHBEVD_2STAGE (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work,
    lwork, rwork, lrwork, iwork, liwork, info)

CHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. 👑

👑 Function/Subroutine Documentation 👑

subroutine CHBEVD_2STAGE (character jobz, character uplo, integer n, integer
    kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * )
    w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * )
    work, integer lwork, real, dimension( * ) rwork, integer lrwork,
    integer, dimension( * ) iwork, integer liwork, integer info)

CHBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices.

🎯 Purpose

okay so picture this: CHBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal. If eigenvectors are desired, it uses a divide and conquer algorithm. That's the whole glow-up. ✨

🧾 Parameters

🧩 JOBZ

JOBZ is CHARACTER*1

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

🧩 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 COMPLEX array, dimension (LDAB, N)

On entry, the upper or lower triangle of the Hermitian band matrix A is 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.

🧩 W

W is REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

🧩 Z

Z is COMPLEX 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.

🧩 LDZ

LDZ is INTEGER

The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).

🧩 WORK

WORK is COMPLEX 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, dimension) where
dimension = (2KD+1)*N + KD*NTHREADS
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, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

🧩 RWORK

RWORK is REAL array, dimension (LRWORK)

On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

🧩 LRWORK

LRWORK is INTEGER

The dimension of array RWORK.

• If N <= 1, LRWORK must be at least 1.
• If JOBZ = 'N' and N > 1, LRWORK must be at least N.
• If JOBZ = 'V' and N > 1, LRWORK must be at least 1 + 5*N + 2*N**2.

If LRWORK = -1, then a workspace query is assumed; the routine only calculates the optimal sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.

🧩 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 array IWORK.

• If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
• If JOBZ = 'V' and N > 1, 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, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK 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.

👑 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:

1. 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
2. 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
3. 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 251 of file chbevd_2stage.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Sign-off: this is LAPACK Version 3.12.0, and the footer path is /home/abui...d_2stage.f(3). There's no extra date in the footer, just the version and path. Go slay your linear algebra, and remember: linear algebra is just vibes. 💖✨