pdlapv2: Applie either p (permutation matrix indicated by ipiv) or inv( p ) to a m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting

SYNOPSIS

SUBROUTINE PDLAPV2(: DIREC, ROWCOL, M, N, A, IA, JA, DESCA, IPIV, IP, JP, DESCIP )
CHARACTER: DIREC, ROWCOL
INTEGER: IA, IP, JA, JP, M, N
INTEGER: DESCA( * ), DESCIP( * ), IPIV( * )
DOUBLE: PRECISION A( * )

PURPOSE

PDLAPV2 applies either P (permutation matrix indicated by IPIV) or inv( P ) to a M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector should be aligned with the distributed matrix A. For pivoting the rows of sub( A ), IPIV should be distributed along a process column and replicated over all process rows. Similarly, IPIV should be distributed along a process row and replicated over all process columns for column pivoting.

Notes

=====

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

ARGUMENTS

DIREC (global input) CHARACTER: Specifies in which order the permutation is applied: = 'F' (Forward) Applies pivots Forward from top of matrix. Computes P * sub( A ); = 'B' (Backward) Applies pivots Backward from bottom of matrix. Computes inv( P ) * sub( A ).
ROWCOL (global input) CHARACTER: Specifies if the rows or columns are to be permuted: = 'R' Rows will be permuted, = 'C' Columns will be permuted.
M (global input) INTEGER: The number of rows to be operated on, i.e. the number of rows of the distributed submatrix sub( A ). M >= 0.
N (global input) INTEGER: The number of columns to be operated on, i.e. the number of columns of the distributed submatrix sub( A ). N >= 0.
A (local input/local output) DOUBLE PRECISION pointer into the: local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). On entry, this local array contains the local pieces of the distributed matrix sub( A ) to which the row or columns interchanges will be applied. On exit, this array contains the local pieces of the permuted distributed matrix.
IA (global input) INTEGER: The row index in the global array A indicating the first row of sub( A ).
JA (global input) INTEGER: The column index in the global array A indicating the first column of sub( A ).
DESCA (global and local input) INTEGER array of dimension DLEN_.: The array descriptor for the distributed matrix A.
IPIV (input) INTEGER array, dimension >= LOCr(M_A)+MB_A if: ROWCOL = 'R', LOCc(N_A)+NB_A otherwise. It contains the pivoting information. IPIV(i) is the global row (column), local row (column) i was swapped with. The last piece of the array of size MB_A (resp. NB_A) is used as workspace. IPIV is tied to the distributed matrix A.
IP (global input) INTEGER: IPIV's global row index, which points to the beginning of the submatrix which is to be operated on.
JP (global input) INTEGER: IPIV's global column index, which points to the beginning of the submatrix which is to be operated on.
DESCIP (global and local input) INTEGER array of dimension 8: The array descriptor for the distributed matrix IPIV.

pdlapv2 (3)

SYNOPSIS

PURPOSE

ARGUMENTS