# FreeBSD Manual Pages

PCLAPIV(l) ) PCLAPIV(l)NAMEPCLAPIV - 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 pivotingSYNOPSISSUBROUTINE PCLAPIV( 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 A( * )PURPOSEPCLAPIV 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 as- sume that its process grid has dimension p x q. LOCr( K ) denotes the number of elements of K that a process would re- ceive 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( 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 IFARGUMENTSDIREC (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 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 distrib- uted submatrix sub( A ) to which the row or column interchanges will be applied. On exit, the local pieces of the permuted dis- tributed 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 version 1.7 13 August 2001 PCLAPIV(l)

NAME | SYNOPSIS | PURPOSE | ARGUMENTS

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