PZLAPIV - applie either P (permutation matrix indicated by IPIV) or inv( P ) to
a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1),
resulting in row or column pivoting
- SUBROUTINE PZLAPIV(
- DIREC, ROWCOL, PIVROC, M, N, A, IA, JA, DESCA, IPIV, IP, JP, DESCIP, IWORK
)
CHARACTER*1 DIREC, PIVROC, ROWCOL INTEGER IA, IP, JA, JP, M, N INTEGER DESCA( *
), DESCIP( * ), IPIV( * ), IWORK( * ) COMPLEX*16 A( * )
PZLAPIV applies either P (permutation matrix indicated by IPIV) or inv( P ) to a
general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1), resulting
in row or column pivoting. The pivot vector may be distributed across a
process row or a column. The pivot vector should be aligned with the
distributed matrix A. This routine will transpose the pivot vector if
necessary. For example if the row pivots should be applied to the columns of
sub( A ), pass ROWCOL='C' and PIVROC='C'.
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
Restrictions
============
IPIV must always be a distributed vector (not a matrix). Thus: IF( ROWPIV .EQ.
'C' ) THEN
JP must be 1
ELSE
IP must be 1
END IF
The following restrictions apply when IPIV must be transposed: IF( ROWPIV.EQ.'C'
.AND. PIVROC.EQ.'C') THEN
DESCIP(MB_) must equal DESCA(NB_)
ELSE IF( ROWPIV.EQ.'R" .AND. PIVROC.EQ.'R') THEN
DESCIP(NB_) must equal DESCA(MB_)
END IF
- DIREC (global input) CHARACTER*1
- 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*1
- Specifies if the rows or columns are to be permuted: = 'R' Rows will be
permuted, = 'C' Columns will be permuted.
- PIVROC (global input) CHARACTER*1
- Specifies whether IPIV is distributed over a process row or column: = 'R'
IPIV distributed over a process row = 'C' IPIV distributed over a process
column
- 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 array contains the local pieces of the distributed submatrix sub( A )
to which the row or column interchanges will be applied. On exit, the
local pieces of the permuted distributed submatrix.
- 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 (local input) INTEGER array, dimension (LIPIV) where LIPIV is
- when ROWCOL='R' or 'r': >= LOCr( IA+M-1 ) + MB_A if PIVROC='C' or 'c',
>= LOCc( M + MOD(JP-1,NB_P) ) if PIVROC='R' or 'r', and, when
ROWCOL='C' or 'c': >= LOCr( N + MOD(IP-1,MB_P) ) if PIVROC='C' or 'c',
>= LOCc( JA+N-1 ) + NB_A if PIVROC='R' or 'r'. This array contains the
pivoting information. IPIV(i) is the global row (column), local row
(column) i was swapped with. When ROWCOL='R' or 'r' and PIVROC='C' or 'c',
or ROWCOL='C' or 'c' and PIVROC='R' or 'r', the last piece of this array
of size MB_A (resp. NB_A) is used as workspace. In those cases, this array
is tied to the distributed matrix A.
- IP (global input) INTEGER
- The row index in the global array P indicating the first row of sub( P
).
- JP (global input) INTEGER
- The column index in the global array P indicating the first column of sub(
P ).
- DESCIP (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed vector IPIV.
- IWORK (local workspace) INTEGER array, dimension (LDW)
- where LDW is equal to the workspace necessary for transposition, and the
storage of the tranposed IPIV:
Let LCM be the least common multiple of NPROW and NPCOL. IF( ROWCOL.EQ.'R'
.AND. PIVROC.EQ.'R' ) THEN IF( NPROW.EQ.NPCOL ) THEN LDW = LOCr( N_P +
MOD(JP-1, NB_P) ) + NB_P ELSE LDW = LOCr( N_P + MOD(JP-1, NB_P) ) + NB_P *
CEIL( CEIL(LOCc(N_P)/NB_P) / (LCM/NPCOL) ) END IF ELSE IF( ROWCOL.EQ.'C'
.AND. PIVROC.EQ.'C' ) THEN IF( NPROW.EQ.NPCOL ) THEN LDW = LOCc( M_P +
MOD(IP-1, MB_P) ) + MB_P ELSE LDW = LOCc( M_P + MOD(IP-1, MB_P) ) + MB_P *
CEIL( CEIL(LOCr(M_P)/MB_P) / (LCM/NPROW) ) END IF ELSE IWORK is not
referenced. END IF