DOKK / manpages / debian 11 / scalapack-doc / pdlapiv.3.en
PDLAPIV(l) LAPACK auxiliary routine (version 1.5) PDLAPIV(l)

PDLAPIV - 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

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( * ) DOUBLE PRECISION A( * )

PDLAPIV 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

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 ).
Specifies if the rows or columns are to be permuted: = 'R' Rows will be permuted, = 'C' Columns will be permuted.
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
The number of rows to be operated on, i.e. the number of rows of the distributed submatrix sub( A ). M >= 0.
The number of columns to be operated on, i.e. the number of columns of the distributed submatrix sub( A ). N >= 0.
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.
The row index in the global array A indicating the first row of sub( A ).
The column index in the global array A indicating the first column of sub( A ).
The array descriptor for the distributed matrix A.
if ROWCOL='R', otherwise LOCc(N_A)+NB_A. 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. This array is tied to the distributed matrix A.
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

12 May 1997 LAPACK version 1.5