PDLAEVSWP - move the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted

SUBROUTINE PDLAEVSWP(

N, ZIN, LDZI, Z, IZ, JZ, DESCZ, NVS, KEY, WORK, LWORK )

INTEGER IZ, JZ, LDZI, LWORK, N

INTEGER DESCZ( * ), KEY( * ), NVS( * )

DOUBLE PRECISION WORK( * ), Z( * ), ZIN( LDZI, * )

PDLAEVSWP moves the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted.

Notes

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Each global data object is described by an associated description vector. This vector stores the information required to establish the mapping between an object element and its corresponding process and memory location.

Let A be a generic term for any 2D block cyclicly distributed array. Such a global array has an associated description vector DESCA. In the following comments, the character _ should be read as "of the global array".

NOTATION STORED IN EXPLANATION

--------------- -------------- -------------------------------------- DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, DTYPE_A = 1.

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 global array A.

N_A (global) DESCA( N_ ) The number of columns in the global array A.

MB_A (global) DESCA( MB_ ) The blocking factor used to distribute the rows of the array.

NB_A (global) DESCA( NB_ ) The blocking factor used to distribute the columns of the array.

RSRC_A (global) DESCA( RSRC_ ) The process row over which the first row of the array A is distributed. CSRC_A (global) DESCA( CSRC_ ) The process column over which the first column of the array A is distributed.

LLD_A (local) DESCA( LLD_ ) The leading dimension of the local array. 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 ). An upper bound for these quantities may be computed by:

LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A

LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

NP = the number of rows local to a given process. NQ = the number of columns local to a given process.

N (global input) INTEGER

The order of the matrix A. N >= 0.

ZIN (local input) DOUBLE PRECISION array,

dimension ( LDZI, NVS(iam) ) The eigenvectors on input. Each eigenvector resides entirely in one process. Each process holds a contiguous set of NVS(iam) eigenvectors. The first eigenvector which the process holds is: sum for i=[0,iam-1) of NVS(i)

LDZI (locl input) INTEGER

leading dimension of the ZIN array

Z (local output) DOUBLE PRECISION array

global dimension (N, N), local dimension (DESCZ(DLEN_), NQ) The eigenvectors on output. The eigenvectors are distributed in a block cyclic manner in both dimensions, with a block size of NB.

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.

NVS (global input) INTEGER array, dimension( nprocs+1 )

nvs(i) = number of processes number of eigenvectors held by processes [0,i-1) nvs(1) = number of eigen vectors held by [0,1-1) == 0 nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) == total number of eigenvectors

KEY (global input) INTEGER array, dimension( N )

Indicates the actual index (after sorting) for each of the eigenvectors.

WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK)

LWORK (local input) INTEGER dimension of WORK