|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( * )|
PDSYEVD computes all the eigenvalues and eigenvectors of a real symmetric 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 heterogeneous system may return incorrect results without any error messages.
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 As global row index, which points to the beginning of the submatrix which is to be operated on. JA (global input) INTEGER As 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 Zs global row index, which points to the beginning of the submatrix which is to be operated on. JZ (global input) INTEGER Zs 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 alignment 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 ).
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)
|ScaLAPACK version 1.7||PDSYEVD (l)||13 August 2001|