PZHEEVD(3) ScaLAPACK routine of NEC Numeric Library Collection PZHEEVD(3)
NAME
PZHEEVD - compute all the eigenvalues and eigenvectors of a Hermitian
matrix A by using a divide and conquer algorithm
SYNOPSIS
SUBROUTINE PZHEEVD( JOBZ, UPLO, N, A, IA, JA, DESCA, W, Z, IZ, JZ,
DESCZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK,
INFO )
CHARACTER JOBZ, UPLO
INTEGER IA, INFO, IZ, JA, JZ, LIWORK, LRWORK, LWORK, N
INTEGER DESCA( * ), DESCZ( * ), IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 A( * ), WORK( * ), Z( * )
PURPOSE
PZHEEVD computes all the eigenvalues and eigenvectors of a Hermitian
matrix A by using a divide and conquer algorithm.
ARGUMENTS
NP = the number of rows local to a given process. NQ = the number of
columns local to a given process.
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only; (NOT IMPLEMENTED YET)
= 'V': Compute eigenvalues and eigenvectors.
UPLO (global input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (global input) INTEGER
The number of rows and columns of the matrix A. N >= 0.
A (local input/workspace) block cyclic COMPLEX*16 array,
global dimension (N, N), local dimension ( LLD_A, LOCc(JA+N-1)
)
On entry, the symmetric matrix A. If UPLO = 'U', only the
upper triangular part of A is used to define the elements of
the symmetric matrix. If UPLO = 'L', only the lower triangular
part of A is used to define the elements of the symmetric
matrix.
On exit, the lower triangle (if UPLO='L') or the upper triangle
(if UPLO='U') of A, including the diagonal, is destroyed.
IA (global input) INTEGER
A's global row index, which points to the beginning of the sub-
matrix which is to be operated on.
JA (global input) INTEGER
A's global column index, which points to the beginning of the
submatrix which is to be operated on.
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A. If DESCA(
CTXT_ ) is incorrect, PZHEEV cannot guarantee correct error
reporting.
W (global output) DOUBLE PRECISION array, dimension (N)
If INFO=0, the eigenvalues in ascending order.
Z (local output) COMPLEX*16 array,
global dimension (N, N), local dimension ( LLD_Z, LOCc(JZ+N-1)
) Z contains the orthonormal eigenvectors of the matrix A.
IZ (global input) INTEGER
Z's global row index, which points to the beginning of the sub-
matrix which is to be operated on.
JZ (global input) INTEGER
Z's global column index, which points to the beginning of the
submatrix which is to be operated on.
DESCZ (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix Z. DESCZ(
CTXT_ ) must equal DESCA( CTXT_ )
WORK (local workspace/output) COMPLEX*16 array,
dimension (LWORK) On output, WORK(1) returns the workspace
needed for the computation.
LWORK (local input) INTEGER
If eigenvectors are requested: LWORK = N + ( NP0 + MQ0 + NB ) *
NB, with NP0 = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPROW ) MQ0
= NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL )
If LWORK = -1, then LWORK is global input and a workspace query
is assumed; the routine calculates the size for all work
arrays. Each of these values is returned in the first entry of
the corresponding work array, and no error message is issued by
PXERBLA.
RWORK (local workspace/output) DOUBLE PRECISION array,
dimension (LRWORK) On output RWORK(1) returns the real
workspace needed to guarantee completion. If the input parame-
ters are incorrect, RWORK(1) may also be incorrect.
LRWORK (local input) INTEGER
Size of RWORK array. RWORK >= 1 + 8*N + 2*NP*NQ, NP = NUMROC(
N, NB, MYROW, IAROW, NPROW ) NQ = NUMROC( N, NB, MYCOL, IACOL,
NPCOL )
IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
On output IWORK(1) returns the integer workspace needed.
LIWORK (input) INTEGER
The dimension of the array IWORK. LIWORK = 7*N + 8*NPCOL + 2
INFO (global output) INTEGER
= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had an
illegal value, then INFO = -(i*100+j), if the i-th argument is
a scalar and had an illegal value, then INFO = -i. > 0: If
INFO = 1 through N, the i(th) eigenvalue did not converge in
PDLAED3.
ALIGNMENT REQUIREMENTS
The distributed submatrices sub( A ), sub( Z ) must verify some align-
ment properties, namely the following expression should be true: (
MB_A.EQ.NB_A.EQ.MB_Z.EQ.NB_Z .AND. IROFFA.EQ.ICOFFA .AND. IROFFA.EQ.0
.AND.IROFFA.EQ.IROFFZ. AND. IAROW.EQ.IZROW) with IROFFA = MOD( IA-1,
MB_A ) and ICOFFA = MOD( JA-1, NB_A ).
FURTHER DETAILS
Contributed by Francoise Tisseur, University of Manchester.
Reference: F. Tisseur and J. Dongarra, "A Parallel Divide and
Conquer Algorithm for the Symmetric Eigenvalue Problem
on Distributed Memory Architectures",
SIAM J. Sci. Comput., 6:20 (1999), pp. 2223--2236.
(see also LAPACK Working Note 132)
http://www.netlib.org/lapack/lawns/lawn132.ps
ScaLAPACK routine 31 October 2017 PZHEEVD(3)