zhetrd_hb2st()

subroutine zhetrd_hb2st	(	character	stage1,
		character	vect,
		character	uplo,
		integer	n,
		integer	kd,
		complex*16, dimension( ldab, * )	ab,
		integer	ldab,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e,
		complex*16, dimension( * )	hous,
		integer	lhous,
		complex*16, dimension( * )	work,
		integer	lwork,
		integer	info )

ZHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T

Download ZHETRD_HB2ST + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric
!> tridiagonal form T by a unitary similarity transformation:
!> Q**H * A * Q = T.
!> 

Parameters

[in]	STAGE1	!> STAGE1 is CHARACTER*1 !> = 'N': : to mention that the stage 1 of the reduction !> from dense to band using the zhetrd_he2hb routine !> was not called before this routine to reproduce AB. !> In other term this routine is called as standalone. !> = 'Y': : to mention that the stage 1 of the !> reduction from dense to band using the zhetrd_he2hb !> routine has been called to produce AB (e.g., AB is !> the output of zhetrd_he2hb. !>
[in]	VECT	!> VECT is CHARACTER*1 !> = 'N': No need for the Housholder representation, !> and thus LHOUS is of size max(1, 4*N); !> = 'V': the Householder representation is needed to !> either generate or to apply Q later on, !> then LHOUS is to be queried and computed. !> (NOT AVAILABLE IN THIS RELEASE). !>
[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	KD	!> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !>
[in,out]	AB	!> AB is COMPLEX*16 array, dimension (LDAB,N) !> On entry, the upper or lower triangle of the Hermitian band !> matrix A, stored in the first KD+1 rows of the array. The !> j-th column of A is stored in the j-th column of the array AB !> as follows: !> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; !> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). !> On exit, the diagonal elements of AB are overwritten by the !> diagonal elements of the tridiagonal matrix T; if KD > 0, the !> elements on the first superdiagonal (if UPLO = 'U') or the !> first subdiagonal (if UPLO = 'L') are overwritten by the !> off-diagonal elements of T; the rest of AB is overwritten by !> values generated during the reduction. !>
[in]	LDAB	!> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !>
[out]	D	!> D is DOUBLE PRECISION array, dimension (N) !> The diagonal elements of the tridiagonal matrix T. !>
[out]	E	!> E is DOUBLE PRECISION array, dimension (N-1) !> The off-diagonal elements of the tridiagonal matrix T: !> E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. !>
[out]	HOUS	!> HOUS is COMPLEX*16 array, dimension (MAX(1,LHOUS)) !> Stores the Householder representation. !>
[in]	LHOUS	!> LHOUS is INTEGER !> The dimension of the array HOUS. !> If N = 0 or KD <= 1, LHOUS >= 1, else LHOUS = MAX(1, dimension). !> !> If LWORK = -1, or LHOUS = -1, !> then a query is assumed; the routine !> only calculates the optimal size of the HOUS array, returns !> this value as the first entry of the HOUS array, and no error !> message related to LHOUS is issued by XERBLA. !> LHOUS = MAX(1, dimension) where !> dimension = 4*N if VECT='N' !> not available now if VECT='H' !>
[out]	WORK	!> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> If N = 0 or KD <= 1, LWORK >= 1, else LWORK = MAX(1, dimension). !> !> If LWORK = -1, or LHOUS = -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 = (2KD+1)*N + KD*NTHREADS !> 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. !>
[out]	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
!>
!>