table of contents
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssytrd_2stage.f(3) | Library Functions Manual | /home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssytrd_2stage.f(3) |
NAME¶
/home/abuild/rpmbuild/BUILD/lapack-3.12.0/SRC/ssytrd_2stage.f
SYNOPSIS¶
Functions/Subroutines¶
subroutine SSYTRD_2STAGE (vect, uplo, n, a, lda, d, e, tau,
hous2, lhous2, work, lwork, info)
SSYTRD_2STAGE
Function/Subroutine Documentation¶
subroutine SSYTRD_2STAGE (character vect, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) tau, real, dimension( * ) hous2, integer lhous2, real, dimension( * ) work, integer lwork, integer info)¶
SSYTRD_2STAGE
Purpose:
!> !> SSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric !> tridiagonal form T by a orthogonal similarity transformation: !> Q1**T Q2**T* 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 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, 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 orthogonal !> 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 orthogonal 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 REAL array, dimension (N) !> The diagonal elements of the tridiagonal matrix T. !>
E
!> E is REAL array, dimension (N-1) !> The off-diagonal elements of the tridiagonal matrix T. !>
TAU
!> TAU is REAL array, dimension (N-KD) !> The scalar factors of the elementary reflectors of !> the first stage (see Further Details). !>
HOUS2
!> HOUS2 is REAL array, dimension (LHOUS2) !> Stores the Householder representation of the stage2 !> band to tridiagonal. !>
LHOUS2
!> LHOUS2 is INTEGER !> The dimension of the array HOUS2. !> 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 REAL array, dimension (LWORK) !>
LWORK
!> LWORK is INTEGER !> The dimension of the array WORK. 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 222 of file ssytrd_2stage.f.
Author¶
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