SRC/dsyevd_2stage.f(3)

💖 NAME

okay so this is the Library Functions Manual page for SRC/dsyevd_2stage.f, and it's literally the home of the dsyevd_2stage subroutine. Bestie, get into it. ✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine dsyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info) — DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices.

🫶 Function/Subroutine Documentation 🫶

       subroutine dsyevd_2stage (character jobz, character uplo, integer n, double
           precision, dimension( lda, * ) a, integer lda, double precision,
           dimension( * ) w, double precision, dimension( * ) work, integer lwork,
           integer, dimension( * ) iwork, integer liwork, integer info)

DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices.

🍓 Purpose 🍓

okay so DSYEVD_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 purpose, bestie. 🦋

🧚 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.
• A — is 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 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 — is INTEGER: the leading dimension of the array A. LDA >= max(1,N).
• W — is DOUBLE PRECISION array, dimension (N). If INFO = 0, the eigenvalues in ascending order.
• WORK — is DOUBLE PRECISION array, dimension (LWORK). On exit, if INFO = 0, WORK(1) returns the optimal 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 — is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal 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 — 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 dsyevd_2stage.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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source/version sign-off, bestie: SRC/dsyevd_2stage.f(3) — LAPACK Version 3.12.0. That's the footer energy, and it ate 💅✨