pslawil(3) [debian man page]
PSLAWIL(l) LAPACK routine (version 1.5 ) PSLAWIL(l) NAME
PSLAWIL - get the transform given by H44,H33, & H43H34 into V starting at row M SYNOPSIS
SUBROUTINE PSLAWIL( II, JJ, M, A, DESCA, H44, H33, H43H34, V ) INTEGER II, JJ, M REAL H33, H43H34, H44 INTEGER DESCA( * ) REAL A( * ), V( * ) PURPOSE
PSLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M. 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
II (global input) INTEGER Row owner of H(M+2,M+2) JJ (global input) INTEGER Column owner of H(M+2,M+2) M (global input) INTEGER On entry, this is where the transform starts (row M.) Unchanged on exit. A (global input) REAL array, dimension (DESCA(LLD_),*) On entry, the Hessenberg matrix. Unchanged on exit. DESCA (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix A. Unchanged on exit. H44 H33 H43H34 (global input) REAL These three values are for the double shift QR iteration. Unchanged on exit. V (global output) REAL array of size 3. Contains the transform on output. Implemented by: G. Henry, November 17, 1996 LAPACK version 1.5 12 May 1997 PSLAWIL(l)
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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)