NAME
PDSYEV - compute all eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A by calling the recommended sequence of
ScaLAPACK routines.
SYNOPSIS
SUBROUTINE PDSYEV( JOBZ, UPLO, N, A, IA, JA, DESCA, W, Z, IZ, JZ,
DESCZ, WORK, LWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER IA, INFO, IZ, JA, JZ, LWORK, N
INTEGER DESCA( * ), DESCZ( * )
DOUBLE PRECISION A( * ), W( * ), WORK( * ), Z( * )
INTEGER BLOCK_CYCLIC_2D, DLEN_, DTYPE_, CTXT_, M_, N_, MB_,
NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, CTXT_
= 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, RSRC_ = 7,
CSRC_ = 8, LLD_ = 9 )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
INTEGER ITHVAL
PARAMETER ( ITHVAL = 10 )
LOGICAL LOWER, WANTZ
INTEGER CONTEXTC, CSRC_A, I, IACOL, IAROW, ICOFFA, IINFO,
INDD, INDD2, INDE, INDE2, INDTAU, INDWORK, INDWORK2,
IROFFA, IROFFZ, ISCALE, IZROW, J, K, LCM, LCMQ, LDC,
LLWORK, LWMIN, MB_A, MB_Z, MYCOL, MYPCOLC, MYPROWC,
MYROW, NB, NB_A, NB_Z, NN, NP, NPCOL, NPCOLC,
NPROCS, NPROW, NPROWC, NQ, NRC, QRMEM, RSRC_A,
RSRC_Z, SIZEMQRLEFT, SIZEMQRRIGHT
DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
SIGMA, SMLNUM
INTEGER DESCQR( 10 ), IDUM1( 3 ), IDUM2( 3 )
LOGICAL LSAME
INTEGER ILCM, INDXG2P, NUMROC, SL_GRIDRESHAPE
DOUBLE PRECISION PDLAMCH, PDLANSY
EXTERNAL LSAME, ILCM, INDXG2P, NUMROC, SL_GRIDRESHAPE,
PDLAMCH, PDLANSY
EXTERNAL BLACS_GRIDEXIT, BLACS_GRIDINFO, CHK1MAT, DCOPY,
DESCINIT, DGAMN2D, DGAMX2D, DSCAL, DSTEQR2,
PCHK2MAT, PDELGET, PDGEMR2D, PDLASCL, PDLASET,
PDORMTR, PDSYTRD, PXERBLA
INTRINSIC DBLE, ICHAR, MAX, MIN, MOD, SQRT
PURPOSE
PDSYEV computes all eigenvalues and, optionally, eigenvectors of a real
symmetric matrix A by calling the recommended sequence of ScaLAPACK
routines.
In its present form, PDSYEV 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.
NOTES
A description vector is associated with each 2D block-cyclicly dis-
tributed matrix. This vector stores the information required to
establish the mapping between a matrix entry and its corresponding
process and memory location.
In the following comments, the character _ should be read as "of the
distributed matrix". Let A be a generic term for any 2D block cyclicly
distributed matrix. Its description vector is DESCA:
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_) The descriptor type.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the distributed
matrix A.
N_A (global) DESCA( N_ ) The number of columns in the distri-
buted matrix A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of A.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of A.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the matrix A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of A is distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array storing the local blocks of the
distributed matrix A.
LLD_A >= MAX(1,LOCr(M_A)).
Let K be the number of rows or columns of a distributed matrix, and
assume that its process grid has dimension p x q. LOCr( K ) denotes
the number of elements of K that a process would receive if K were
distributed over the p processes of its process column.
Similarly, LOCc( K ) denotes the number of elements of K that a process
would receive if K were distributed over the q processes of its process
row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
ARGUMENTS
NP = the number of rows local to a given process.
NQ = the number of columns local to a given process.
JOBZ (global input) CHARACTER*1
Specifies whether or not to compute the eigenvectors:
= ’N’: Compute eigenvalues only.
= ’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 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
submatrix 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, PDSYEV cannot guarantee
correct error reporting.
W (global output) DOUBLE PRECISION array, dimension (N)
On normal exit, the first M entries contain the selected
eigenvalues in ascending order.
Z (local output) DOUBLE PRECISION array,
global dimension (N, N),
local dimension ( LLD_Z, LOCc(JZ+N-1) )
If JOBZ = ’V’, then on normal exit the first M columns of Z
contain the orthonormal eigenvectors of the matrix
corresponding to the selected eigenvalues.
If JOBZ = ’N’, then Z is not referenced.
IZ (global input) INTEGER
Z’s global row index, which points to the beginning of the
submatrix 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)
Version 1.0: on output, WORK(1) returns the workspace
needed to guarantee completion.
If the input parameters are incorrect, WORK(1) may also be
incorrect.
If JOBZ=’N’ WORK(1) = minimal=optimal amount of workspace
If JOBZ=’V’ WORK(1) = minimal workspace required to
generate all the eigenvectors.
LWORK (local input) INTEGER
See below for definitions of variables used to define LWORK.
If no eigenvectors are requested (JOBZ = ’N’) then
LWORK >= 5*N + SIZESYTRD + 1
where
SIZESYTRD = The workspace requirement for PDSYTRD
and is MAX( NB * ( NP +1 ), 3 * NB )
If eigenvectors are requested (JOBZ = ’V’ ) then
the amount of workspace required to guarantee that all
eigenvectors are computed is:
QRMEM = 2*N-2
LWMIN = 5*N + N*LDC + MAX( SIZEMQRLEFT, QRMEM ) + 1
Variable definitions:
NB = DESCA( MB_ ) = DESCA( NB_ ) =
DESCZ( MB_ ) = DESCZ( NB_ )
NN = MAX( N, NB, 2 )
DESCA( RSRC_ ) = DESCA( RSRC_ ) = DESCZ( RSRC_ ) =
DESCZ( CSRC_ ) = 0
NP = NUMROC( NN, NB, 0, 0, NPROW )
NQ = NUMROC( MAX( N, NB, 2 ), NB, 0, 0, NPCOL )
NRC = NUMROC( N, NB, MYPROWC, 0, NPROCS)
LDC = MAX( 1, NRC )
SIZEMQRLEFT = The workspace requirement for PDORMTR
when it’s SIDE argument is ’L’.
With MYPROWC defined when a new context is created as:
CALL BLACS_GET( DESCA( CTXT_ ), 0, CONTEXTC )
CALL BLACS_GRIDINIT( CONTEXTC, ’R’, NPROCS, 1 )
CALL BLACS_GRIDINFO( CONTEXTC, NPROWC, NPCOLC, MYPROWC,
MYPCOLC )
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.
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 DSTEQR2 after a total of 30*N iterations.
If INFO = N+1, then PDSYEV has detected heterogeneity
by finding that eigenvalues were not identical across
the process grid. In this case, the accuracy of
the results from PDSYEV cannot be guaranteed.