DSYGV_2STAGE(3)

💅 DSYGV_2STAGE(3) — the whole entire manual, bestie 💅

Okay so, this page is from the Library Functions Manual, and it's giving serious LAPACK energy. Buckle up, we're going through it together. 🫶✨

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsygv_2stage.f

That's the name. It's a whole path. It ate. 💅

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine DSYGV_2STAGE (itype, jobz, uplo, n, a, lda, b, ldb, w, work,
    lwork, info)

DSYGV_2STAGE

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🌸 Function/Subroutine Documentation 🌸

subroutine DSYGV_2STAGE (integer itype, character jobz, character uplo,
    integer n, double precision, dimension( lda, * ) a, integer lda, double
    precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) w, double precision, dimension( * ) work, integer lwork,
    integer info)

DSYGV_2STAGE

👑 Purpose 👑

Okay so literally, DSYGV_2STAGE computes all the eigenvalues, and optionally the eigenvectors, of a real generalized symmetric-definite eigenproblem. The forms are:

• A*x=(lambda)*B*x
• A*Bx=(lambda)*x
• B*A*x=(lambda)*x

Here A and B are assumed to be symmetric, and B is also positive definite. Periodt. 💖

This routine uses the 2stage technique for the reduction to tridiagonal, which — no cap — showed higher performance on recent architecture and for large sizes N>2000. It's giving optimized. 🔥

🎀 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. 💀
• 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 a DOUBLE PRECISION 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. 😭
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is a DOUBLE PRECISION 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 a DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• WORK — WORK is a DOUBLE PRECISION 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 — and 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: DPOTRF or DSYEV returned an error code:
    • <= N: if INFO = i, DSYEV 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:

• 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

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Definition at line 224 of file dsygv_2stage.f.

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole thing, bestie! This was LAPACK Version 3.12.0, coming at you from /home/abui...gv_2stage.f(3). Bye, love you, go compute some eigenvalues responsibly 💖✨🌸🫶