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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PZLACGV(l) LAPACK auxiliary routine (version 1.5) PZLACGV(l) NAME
PZLACGV - conjugate a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and Notes ===== Each global data object is described by an associated description vector SYNOPSIS
SUBROUTINE PZLACGV( N, X, IX, JX, DESCX, INCX ) INTEGER INCX, IX, JX, N INTEGER DESCX( * ) COMPLEX*16 X( * ) PURPOSE
PZLACGV conjugates a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and 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 Because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a distributed matrix. ARGUMENTS
N (global input) INTEGER The length of the distributed vector sub( X ). X (local input/local output) COMPLEX*16 pointer into the local memory to an array of dimension (LLD_X,*). On entry the vector to be conjugated x( i ) = X(IX+(JX-1)*M_X +(i-1)*INCX ), 1 <= i <= N. On exit the conjugated vector. IX (global input) INTEGER The row index in the global array X indicating the first row of sub( X ). JX (global input) INTEGER The column index in the global array X indicating the first column of sub( X ). DESCX (global and local input) INTEGER array of dimension DLEN_. The array descriptor for the distributed matrix X. INCX (global input) INTEGER The global increment for the elements of X. Only two values of INCX are supported in this version, namely 1 and M_X. INCX must not be zero. LAPACK version 1.5 12 May 1997 PZLACGV(l)