CHBEV_2STAGE(3)

💅 CHBEV_2STAGE(3) ✨

okay so bestie, we're in the LAPACK Library Functions Manual, and this page is serving source-file realness from /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chbev_2stage.f. It's giving "complex Hermitian band matrix goes to tridiagonal" main character energy, and honestly? Obsessed.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chbev_2stage.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CHBEV_2STAGE (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work,
    lwork, rwork, info)

CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. That's the synopsis tea. 🫖

🎀 Function/Subroutine Documentation 🎀

subroutine CHBEV_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 info)

CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices. Iconic behavior, no cap. 👑

🦋 Purpose: 🦋

CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal. That's the whole assignment, and she ate. 💅

💖 Parameters 💖

• JOBZ — is CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release.
• UPLO — is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• 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 — is a COMPLEX array, dimension (LDAB, N). On entry, the upper or lower triangle of the Hermitian 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. She's not just storing — she's transforming. 🔥

• LDAB — is INTEGER. The leading dimension of the array AB. LDAB >= KD + 1.
• W — is a REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• Z — is a 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 — is INTEGER. The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
• WORK — is a COMPLEX array, dimension LWORK. On exit, if INFO = 0, WORK(1) returns the optimal 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 — is a REAL array, dimension (max(1,3*N-2)).
• 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:

• 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 209 of file chbev_2stage.f.

👑 Author 👑

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