SRC/zhetrd_2stage.f(3) Library Functions Manual SRC/zhetrd_2stage.f(3) NAME SRC/zhetrd_2stage.f SYNOPSIS Functions/Subroutines subroutine zhetrd_2stage (vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info) ZHETRD_2STAGE Function/Subroutine Documentation subroutine zhetrd_2stage (character vect, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( * ) tau, complex*16, dimension( * ) hous2, integer lhous2, complex*16, dimension( * ) work, integer lwork, integer info) ZHETRD_2STAGE Purpose: !> !> ZHETRD_2STAGE reduces a complex Hermitian matrix A to real symmetric !> tridiagonal form T by a unitary similarity transformation: !> Q1**H Q2**H* A * Q2 * Q1 = T. !> Parameters VECT !> VECT is CHARACTER*1 !> = 'N': No need for the Housholder representation, !> in particular for the second stage (Band to !> tridiagonal) and thus LHOUS2 is of size max(1, 4*N); !> = 'V': the Householder representation is needed to !> either generate Q1 Q2 or to apply Q1 Q2, !> then LHOUS2 is to be queried and computed. !> (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, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> On exit, if UPLO = 'U', the band superdiagonal !> of A are overwritten by the corresponding elements of the !> internal band-diagonal matrix AB, and the elements above !> the KD superdiagonal, with the array TAU, represent the unitary !> matrix Q1 as a product of elementary reflectors; if UPLO !> = 'L', the diagonal and band subdiagonal of A are over- !> written by the corresponding elements of the internal band-diagonal !> matrix AB, and the elements below the KD subdiagonal, with !> the array TAU, represent the unitary matrix Q1 as a product !> of elementary reflectors. See Further Details. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> D !> D is DOUBLE PRECISION array, dimension (N) !> The diagonal elements of the tridiagonal matrix T. !> E !> E is DOUBLE PRECISION array, dimension (N-1) !> The off-diagonal elements of the tridiagonal matrix T. !> TAU !> TAU is COMPLEX*16 array, dimension (N-KD) !> The scalar factors of the elementary reflectors of !> the first stage (see Further Details). !> HOUS2 !> HOUS2 is COMPLEX*16 array, dimension (MAX(1,LHOUS2)) !> Stores the Householder representation of the stage2 !> band to tridiagonal. !> LHOUS2 !> LHOUS2 is INTEGER !> The dimension of the array HOUS2. !> LHOUS2 >= 1. !> !> If LWORK = -1, or LHOUS2 = -1, !> then a query is assumed; the routine !> only calculates the optimal size of the HOUS2 array, returns !> this value as the first entry of the HOUS2 array, and no error !> message related to LHOUS2 is issued by XERBLA. !> If VECT='N', LHOUS2 = max(1, 4*n); !> if VECT='V', option not yet available. !> 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 = 0, LWORK >= 1, else LWORK = MAX(1, dimension). !> !> If LWORK = -1, or LHOUS2 = -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. !> LWORK = MAX(1, dimension) where !> dimension = max(stage1,stage2) + (KD+1)*N !> = N*KD + N*max(KD+1,FACTOPTNB) !> + max(2*KD*KD, KD*NTHREADS) !> + (KD+1)*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. !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Further Details: !> !> Implemented by Azzam Haidar. !> !> All details are available on technical report, SC11, SC13 papers. !> !> 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 227 of file zhetrd_2stage.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/zhetrd_2stage.f(3)