SRC/ssyevd_2stage.f(3)

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💖 NAME 💖

SRC/ssyevd_2stage.f

🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

subroutine ssyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork,
    liwork, info)

SSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices ✨

🌀 FUNCTION/SUBROUTINE DOCUMENTATION 🌀

subroutine ssyevd_2stage (character jobz, character uplo, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( * ) w, real,
    dimension( * ) work, integer lwork, integer, dimension( * ) iwork,
    integer liwork, integer info)

This icon computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices. 💅

🎯 PURPOSE 🎯

Okay so SSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a real symmetric 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 plot 🫶

🎀 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.

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, if JOBZ = 'V', then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A.

If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the diagonal, is destroyed. 💀

LDA

LDA is INTEGER

The leading dimension of the array A. LDA >= max(1,N).

W

W is REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

WORK

WORK is REAL array, dimension (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER

The dimension of the array WORK.

• If N <= 1, LWORK must be at least 1.
• If JOBZ = 'N' and N > 1, LWORK must be queried.

LWORK = MAX(1, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + 2*N+1
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 at least 1 + 6*N + 2*N**2.

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.

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 N <= 1, LIWORK must be at least 1.
• If JOBZ = 'N' and 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 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 and JOBZ = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; if INFO = i and JOBZ = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1).

🧚 AUTHOR 🧚

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

🌟 CONTRIBUTORS: 🌟

• Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
• Modified by Francoise Tisseur, University of Tennessee
• Modified description of INFO. Sven, 16 Feb 05.

📚 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 219 of file ssyevd_2stage.f.

👑 AUTHOR 👑

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