pclatra(3) [debian man page]
PCLATRA(l) LAPACK auxiliary routine (version 1.5) PCLATRA(l) NAME
PCLATRA - compute the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ) SYNOPSIS
COMPLEX FUNCTION PCLATRA( N, A, IA, JA, DESCA ) INTEGER IA, JA, N INTEGER DESCA( * ) COMPLEX A( * ) PURPOSE
PCLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process of the grid. 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 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 ARGUMENTS
N (global input) INTEGER The number of rows and columns to be operated on i.e the order of the distributed submatrix sub( A ). N >= 0. A (local input) COMPLEX pointer into the local memory to an array of dimension ( LLD_A, LOCc(JA+N-1) ). This array contains the local pieces of the distributed matrix the trace is to be computed. 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. LAPACK version 1.5 12 May 1997 PCLATRA(l)
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PZLACP2(l) LAPACK auxiliary routine (version 1.5) PZLACP2(l) NAME
PZLACP2 - copie all or part of a distributed matrix A to another distributed matrix B SYNOPSIS
SUBROUTINE PZLACP2( UPLO, M, N, A, IA, JA, DESCA, B, IB, JB, DESCB ) CHARACTER UPLO INTEGER IA, IB, JA, JB, M, N INTEGER DESCA( * ), DESCB( * ) COMPLEX*16 A( * ), B( * ) PURPOSE
PZLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PZLACP2 performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). PZLACP2 requires that only dimension of the matrix operands is distributed. 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 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 ARGUMENTS
UPLO (global input) CHARACTER Specifies the part of the distributed matrix sub( A ) to be copied: = 'U': Upper triangular part is copied; the strictly lower triangular part of sub( A ) is not referenced; = 'L': Lower triangu- lar part is copied; the strictly upper triangular part of sub( A ) is not referenced; Otherwise: All of the matrix sub( A ) is copied. 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) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_A, LOCc(JA+N-1) ). This array contains the local pieces of the distributed matrix sub( A ) to be copied from. 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. B (local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_B, LOCc(JB+N-1) ). This array contains on exit the local pieces of the distributed matrix sub( B ) set as follows: if UPLO = 'U', B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), 1<=i<=j, 1<=j<=N; if UPLO = 'L', B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), j<=i<=M, 1<=j<=N; otherwise, B(IB+i-1,JB+j-1) = A(IA+i-1,JA+j-1), 1<=i<=M, 1<=j<=N. IB (global input) INTEGER The row index in the global array B indicating the first row of sub( B ). JB (global input) INTEGER The column index in the global array B indicating the first column of sub( B ). DESCB (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix B. LAPACK version 1.5 12 May 1997 PZLACP2(l)