SRC/zheevd_2stage.f(3) Library Functions Manual SRC/zheevd_2stage.f(3) NAME SRC/zheevd_2stage.f SYNOPSIS Functions/Subroutines subroutine zheevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info) ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices Function/Subroutine Documentation subroutine zheevd_2stage (character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info) ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices Purpose: !> !> ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a !> complex Hermitian matrix A using the 2stage technique for !> the reduction to tridiagonal. If eigenvectors are desired, it uses a !> divide and conquer algorithm. !> !> 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 COMPLEX*16 array, dimension (LDA, N) !> On entry, the Hermitian 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 DOUBLE PRECISION array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> WORK !> WORK is COMPLEX*16 array, dimension (MAX(1,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 + N+1 !> = N*KD + N*max(KD+1,FACTOPTNB) !> + max(2*KD*KD, KD*NTHREADS) !> + (KD+1)*N + 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 2*N + N**2 !> !> 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 !> RWORK is DOUBLE PRECISION array, !> dimension (LRWORK) !> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. !> LRWORK !> LRWORK is INTEGER !> The dimension of the array RWORK. !> If N <= 1, LRWORK must be at least 1. !> If JOBZ = 'N' and N > 1, LRWORK must be at least N. !> If JOBZ = 'V' and N > 1, LRWORK must be at least !> 1 + 5*N + 2*N**2. !> !> If LRWORK = -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. !> 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, 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. !> 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. Further Details: Modified description of INFO. Sven, 16 Feb 05. Contributors: Jeff Rutter, Computer Science Division, University of California at Berkeley, USA 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 245 of file zheevd_2stage.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/zheevd_2stage.f(3)