pssyev(3)

NAME

PSSYEV - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines

SYNOPSIS

SUBROUTINE PSSYEV( 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( * )
    REAL           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 )
    REAL           ZERO, ONE
    PARAMETER      ( ZERO = 0.0E+0, ONE = 1.0E+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
    REAL           ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM
    INTEGER        DESCQR( 10 ), IDUM1( 3 ), IDUM2( 3 )
    LOGICAL        LSAME
    INTEGER        ILCM, INDXG2P, NUMROC, SL_GRIDRESHAPE
    REAL           PSLAMCH, PSLANSY
    EXTERNAL       LSAME,  ILCM,   INDXG2P,   NUMROC,   SL_GRIDRESHAPE,
                   PSLAMCH, PSLANSY
    EXTERNAL       BLACS_GRIDEXIT,  BLACS_GRIDINFO,  CHK1MAT, DESCINIT,
                   PCHK2MAT,  PSELGET,  PSGEMR2D,   PSLASCL,   PSLASET,
                   PSORMTR,  PSSYTRD, PXERBLA, SCOPY, SGAMN2D, SGAMX2D,
                   SSCAL, SSTEQR2
    INTRINSIC      ICHAR, MAX, MIN, MOD, REAL, SQRT

PURPOSE

PSSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines.

In its present form, PSSYEV 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 distributed 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 distributed over. The context itself is global, 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.S 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, PSSYEV cannot guarantee
correct error reporting.
W (global output) REAL array, dimension (N): On normal exit, the first M entries contain the selected
eigenvalues in ascending order.
Z (local output) REAL 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) REAL 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 PSSYTRD
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 PSORMTR

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 SSTEQR2 after a total of 30*N iterations.
If INFO = N+1, then PSSYEV has detected heterogeneity
by finding that eigenvalues were not identical across
the process grid. In this case, the accuracy of
the results from PSSYEV cannot be guaranteed.

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