PDLARFB(l) | LAPACK auxiliary routine (version 1.5) | PDLARFB(l) |
NAME¶
PDLARFB - 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)SYNOPSIS¶
- SUBROUTINE PDLARFB(
- SIDE, TRANS, DIRECT, STOREV, M, N, K, V, IV, JV, DESCV, T, C, IC, JC, DESCC, WORK )
PURPOSE¶
PDLARFB 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.DTYPE_A = 1.
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
array A.
array A.
the rows of the array.
the columns of the array.
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.
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( 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¶
- SIDE (global input) CHARACTER
- = 'L': apply Q or Q**T from the Left;
- TRANS (global input) CHARACTER
-
- DIRECT (global input) CHARACTER
- Indicates how Q is formed from a product of elementary reflectors = 'F': Q
= H(1) H(2) . . . H(k) (Forward)
- STOREV (global input) CHARACTER
- Indicates how the vectors which define the elementary reflectors are
stored:
- M (global input) INTEGER
- The number of rows to be operated on i.e the number of rows of the distributed submatrix sub( C ). 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( C ). N >= 0.
- K (global input) INTEGER
- The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
- V (local input) DOUBLE PRECISION pointer into the local memory
- to an array of dimension ( LLD_V, LOCc(JV+K-1) ) if STOREV = 'C', ( LLD_V, LOCc(JV+M-1)) if STOREV = 'R' and SIDE = 'L', ( LLD_V, LOCc(JV+N-1) ) if STOREV = 'R' and SIDE = 'R'. It contains the local pieces of the distributed vectors V representing the Householder transformation. See further details. If STOREV = 'C' and SIDE = 'L', LLD_V >= MAX(1,LOCr(IV+M-1)); if STOREV = 'C' and SIDE = 'R', LLD_V >= MAX(1,LOCr(IV+N-1)); if STOREV = 'R', LLD_V >= LOCr(IV+K-1).
- IV (global input) INTEGER
- The row index in the global array V indicating the first row of sub( V ).
- JV (global input) INTEGER
- The column index in the global array V indicating the first column of sub( V ).
- DESCV (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix V.
- T (local input) DOUBLE PRECISION array, dimension MB_V by MB_V
- if STOREV = 'R' and NB_V by NB_V if STOREV = 'C'. The trian- gular matrix T in the representation of the block reflector.
- C (local input/local output) DOUBLE PRECISION pointer into the
- 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'.
- IC (global input) INTEGER
- The row index in the global array C indicating the first row of sub( C ).
- JC (global input) INTEGER
- The column index in the global array C indicating the first column of sub( C ).
- DESCC (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix C.
- WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK)
- 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 |