PDSYEVD(3) ScaLAPACK routine of NEC Numeric Library Collection PDSYEVD(3)
NAME
PDSYEVD - compute all the eigenvalues and eigenvectors of a real sym-
metric matrix A by calling the recommended sequence of ScaLAPACK rou-
tines
SYNOPSIS
SUBROUTINE PDSYEVD( JOBZ, UPLO, N, A, IA, JA, DESCA, W, Z, IZ, JZ,
DESCZ, WORK, LWORK, IWORK, LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER IA, INFO, IZ, JA, JZ, LIWORK, LWORK, N
INTEGER DESCA( * ), DESCZ( * ), IWORK( * )
DOUBLE PRECISION A( * ), W( * ), WORK( * ), Z( * )
PURPOSE
PDSYEVD computes all the eigenvalues and eigenvectors of a real symmet-
ric matrix A by calling the recommended sequence of ScaLAPACK routines.
In its present form, PDSYEVD assumes a homogeneous system and makes no
checks for consistency of the eigenvalues or eigenvectors across the
different processes. Because of this, it is possible that a heteroge-
neous system may return incorrect results without any error messages.
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 to be operated on, i.e. the
order of the distributed submatrix sub( A ). N >= 0.
A (local input/workspace) block cyclic DOUBLE PRECISION 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.
W (global output) DOUBLE PRECISION array, dimension (N)
If INFO=0, the eigenvalues in ascending order.
Z (local output) DOUBLE PRECISION array,
global dimension (N, N), local dimension ( LLD_Z, LOCc(JZ+N-1)
) Z contains the orthonormal eigenvectors of the symmetric
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) DOUBLE PRECISION array,
dimension (LWORK) On output, WORK(1) returns the workspace
required.
LWORK (local input) INTEGER
LWORK >= MAX( 1+6*N+2*NP*NQ, TRILWMIN ) + 2*N TRILWMIN = 3*N +
MAX( NB*( NP+1 ), 3*NB ) NP = NUMROC( N, NB, MYROW, IAROW,
NPROW ) NQ = NUMROC( N, NB, MYCOL, IACOL, NPCOL )
If LWORK = -1, the LWORK is global input and a workspace query
is assumed; the routine only calculates the minimum size for
the WORK array. The required workspace is returned as the
first element of WORK and no error message is issued by
PXERBLA.
IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
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: The
algorithm failed to compute the INFO/(N+1) th eigenvalue while
working on the submatrix lying in global rows and columns
mod(INFO,N+1).
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 PDSYEVD(3)