DOKK / manpages / debian 11 / scalapack-doc / pslarzb.3.en
PSLARZB(l) LAPACK auxiliary routine (version 1.5) PSLARZB(l)

PSLARZB - applie a real block reflector Q or its transpose Q**T to a real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1)

SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, IV, JV, DESCV, T, C, IC, JC, DESCC, WORK )

CHARACTER DIRECT, SIDE, STOREV, TRANS INTEGER IC, IV, JC, JV, K, L, M, N INTEGER DESCC( * ), DESCV( * ) REAL C( * ), T( * ), V( * ), WORK( * )

PSLARZB applies a real block reflector Q or its transpose Q**T to a real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) from the left or the right.

Q is a product of k elementary reflectors as returned by PSTZRZF.

Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

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 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

= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.

= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
Indicates how H is formed from a product of elementary reflectors = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
Indicates how the vectors which define the elementary reflectors are stored:
= 'C': Columnwise (not supported yet)
= 'R': Rowwise
The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( C ). M >= 0.
The number of columns to be operated on i.e the number of columns of the distributed submatrix sub( C ). N >= 0.
The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
The columns of the distributed submatrix sub( A ) containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
to an array of dimension (LLD_V, LOCc(JV+M-1)) if SIDE = 'L', (LLD_V, LOCc(JV+N-1)) if SIDE = 'R'. It contains the local pieces of the distributed vectors V representing the Householder transformation as returned by PSTZRZF. LLD_V >= LOCr(IV+K-1).
The row index in the global array V indicating the first row of sub( V ).
The column index in the global array V indicating the first column of sub( V ).
The array descriptor for the distributed matrix V.
The lower triangular matrix T in the representation of the block reflector.
local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). On entry, the M-by-N distributed matrix sub( C ). On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) or sub( C )*Q or sub( C )*Q'.
The row index in the global array C indicating the first row of sub( C ).
The column index in the global array C indicating the first column of sub( C ).
The array descriptor for the distributed matrix C.
If STOREV = 'C', if SIDE = 'L', LWORK >= ( NqC0 + MpC0 ) * K else if SIDE = 'R', LWORK >= ( NqC0 + MAX( NpV0 + NUMROC( NUMROC( N+ICOFFC, NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ), MpC0 ) ) * K end if else if STOREV = 'R', if SIDE = 'L', LWORK >= ( MpC0 + MAX( MqV0 + NUMROC( NUMROC( M+IROFFC, MB_V, 0, 0, NPROW ), MB_V, 0, 0, LCMP ), NqC0 ) ) * K else if SIDE = 'R', LWORK >= ( MpC0 + NqC0 ) * K end if end if

where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),

IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ), IVROW = INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ), IVCOL = INDXG2P( JV, NB_V, MYCOL, CSRC_V, NPCOL ), MqV0 = NUMROC( M+ICOFFV, NB_V, MYCOL, IVCOL, NPCOL ), NpV0 = NUMROC( N+IROFFV, MB_V, MYROW, IVROW, NPROW ),

IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ), ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ), MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ), NpC0 = NUMROC( N+ICOFFC, MB_C, MYROW, ICROW, NPROW ), NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),

ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO.

Alignment requirements ======================

The distributed submatrices V(IV:*, JV:*) and C(IC:IC+M-1,JC:JC+N-1) must verify some alignment properties, namely the following expressions should be true:

If STOREV = 'Columnwise' If SIDE = 'Left', ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW ) If SIDE = 'Right', ( MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC ) else if STOREV = 'Rowwise' If SIDE = 'Left', ( NB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC ) If SIDE = 'Right', ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL ) end if

12 May 1997 LAPACK version 1.5