pdlatra(3) [debian man page]
PDLATRA(l) LAPACK auxiliary routine (version 1.5) PDLATRA(l) NAME
PDLATRA - compute the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ) SYNOPSIS
DOUBLE PRECISION FUNCTION PDLATRA( N, A, IA, JA, DESCA ) INTEGER IA, JA, N INTEGER DESCA( * ) DOUBLE PRECISION A( * ) PURPOSE
PDLATRA 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) DOUBLE PRECISION 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 PDLATRA(l)
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PDLARED1D(l) LAPACK routine (version 1.5) PDLARED1D(l) NAME
PDLARED1D - redistribute a 1D array It assumes that the input array, BYCOL, is distributed across rows and that all process column contain the same copy of BYCOL SYNOPSIS
SUBROUTINE PDLARED1D( N, IA, JA, DESC, BYCOL, BYALL, WORK, LWORK ) INTEGER IA, JA, LWORK, N INTEGER DESC( * ) DOUBLE PRECISION BYALL( * ), BYCOL( * ), WORK( LWORK ) PURPOSE
PDLARED1D redistributes a 1D array and will contain the entire array. 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
NP = Number of local rows in BYCOL() N (global input) INTEGER The number of elements to be redistributed. N >= 0. IA (global input) INTEGER IA must be equal to 1 JA (global input) INTEGER JA must be equal to 1 DESC (global/local input) INTEGER Array of dimension 8 A 2D array descirptor, which describes BYCOL BYCOL (local input) distributed block cyclic DOUBLE PRECISION array global dimension (N), local dimension NP BYCOL is distributed across the process rows All process columns are assumed to contain the same value BYALL (global output) DOUBLE PRECISION global dimension( N ) local dimension (N) BYALL is exactly duplicated on all processes It contains the same values as BYCOL, but it is replicated across all processes rather than being distributed BYALL(i) = BYCOL( NUMROC(i,NB,MYROW,0,NPROW ) on the procs whose MYROW == mod((i-1)/NB,NPROW) WORK (local workspace) DOUBLE PRECISION dimension (LWORK) Used to hold the buffers sent from one process to another LWORK (local input) INTEGER size of WORK array LWORK >= NUMROC(N, DESC( NB_ ), 0, 0, NPCOL) LAPACK version 1.5 12 May 1997 PDLARED1D(l)