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
=====
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.