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zhegv_2stage.f(3) LAPACK zhegv_2stage.f(3)

NAME

zhegv_2stage.f

SYNOPSIS

Functions/Subroutines


subroutine zhegv_2stage (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, INFO)
ZHEGV_2STAGE

Function/Subroutine Documentation

subroutine zhegv_2stage (integer ITYPE, character JOBZ, character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) W, complex*16, dimension( * ) WORK, integer LWORK, double precision, dimension( * ) RWORK, integer INFO)

ZHEGV_2STAGE

Purpose:


ZHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
Here A and B are assumed to be Hermitian and B is also
positive definite.
This routine use the 2stage technique for the reduction to tridiagonal
which showed higher performance on recent architecture and for large
sizes N>2000.

Parameters:

ITYPE


ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x

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 triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.

N


N is INTEGER
The order of the matrices A and B. 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
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
or the lower triangle (if UPLO='L') of A, including the
diagonal, is destroyed.

LDA


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

B


B is COMPLEX*16 array, dimension (LDB, N)
On entry, the Hermitian positive definite matrix B.
If UPLO = 'U', the leading N-by-N upper triangular part of B
contains the upper triangular part of the matrix B.
If UPLO = 'L', the leading N-by-N lower triangular part of B
contains the lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= 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 length of the array WORK. LWORK >= 1, when N <= 1;
otherwise
If JOBZ = 'N' and N > 1, LWORK must be queried.
LWORK = MAX(1, dimension) where
dimension = max(stage1,stage2) + (KD+1)*N + N
= N*KD + N*max(KD+1,FACTOPTNB)
+ max(2*KD*KD, KD*NTHREADS)
+ (KD+1)*N + 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.
If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
If LWORK = -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.

RWORK


RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV failed to converge;
i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2017

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 234 of file zhegv_2stage.f.

Author

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