PZLAPV2 - 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

SUBROUTINE PZLAPV2(

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( * )

COMPLEX*16 A( * )

PZLAPV2 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

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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

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) COMPLEX*16 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.