PZLAPIV(3) ScaLAPACK routine of NEC Numeric Library Collection PZLAPIV(3)
NAME
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
SYNOPSIS
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( * )
PURPOSE
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 vec-
tor. This vector stores the information required to establish the map-
ping 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 col-
umn.
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( ROW-
PIV.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
ARGUMENTS
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 bot-
tom 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 dis-
tributed 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 infor-
mation. 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 transposi-
tion, 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( ROW-
COL.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
ScaLAPACK routine 31 October 2017 PZLAPIV(3)