SSYGV_2STAGE(3)

💅 SSYGV_2STAGE(3) 💅

Okay so bestie, welcome to the Library Functions Manual page for SSYGV_2STAGE — this is the whole manual-name situation folded in right at the top, no cap. The facts are all here, the vibe is just way more fun. ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/ssygv_2stage.f

That's the source file path, literally character-for-character. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine SSYGV_2STAGE (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
           lwork, info)
           SSYGV_2STAGE

💖 Function/Subroutine Documentation 💖

   subroutine SSYGV_2STAGE (integer itype, character jobz, character uplo,
       integer n, real, dimension( lda, * ) a, integer lda, real, dimension(
       ldb, * ) b, integer ldb, real, dimension( * ) w, real, dimension( * )
       work, integer lwork, integer info)
       SSYGV_2STAGE

🎯 Purpose 🎯

SSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be symmetric and B is also positive definite. This routine use the 2stage technique for the reduction to tridiagonal which showed higher performance on recent architecture and for large sizes N>2000. 🔥

🧚 Parameters 🧚

• ITYPE — ITYPE is INTEGER. Specifies the problem type to be solved:
  • = 1: A*x = (lambda)*B*x
  • = 2: A*B*x = (lambda)*x
  • = 3: B*A*x = (lambda)*x
• JOBZ — JOBZ is CHARACTER*1.
  • = 'N': Compute eigenvalues only;
  • = 'V': Compute eigenvalues and eigenvectors. Not available in this release. (so don't come for that option in this release 👀)
• UPLO — UPLO is CHARACTER*1.
  • = 'U': Upper triangles of A and B are stored;
  • = 'L': Lower triangles of A and B are stored.
• N — N is INTEGER. The order of the matrices A and B. 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 matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is destroyed. Destroyed destroyed, bestie — that's a real caveat.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is REAL array, dimension (LDB, N). On entry, the symmetric positive definite matrix B. If UPLO = 'U', the leading N-by-N upper triangular part of B contains the upper triangular part of the matrix B. If UPLO = 'L', the leading N-by-N lower triangular part of B contains the lower triangular part of the matrix B. On exit, if INFO <= N, the part of B containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• W — W is REAL array, dimension (N). If INFO = 0, the eigenvalues in ascending order. 🌈
• 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, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + 2*N
          = N*KD + N*max(KD+1,FACTOPTNB)
            + max(2*KD*KD, KD*NTHREADS)
            + (KD+1)*N + 2*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.

• INFO — INFO is INTEGER.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: SPOTRF or SSYEV returned an error code:
    • <= N: if INFO = i, SSYEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero;
    • > N: if INFO = N + i, for 1 <= i <= N, then the leading principal minor of order i of B is not positive. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

👑 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 224 of file ssygv_2stage.f.

🧚 Author 🧚

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