NAME
PCLAPV2 - 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 PCLAPV2( 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 A( * )
PURPOSE
PCLAPV2 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) COMPLEX 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.