PDORMBR(l) | LAPACK routine (version 1.5) | PDORMBR(l) |
NAME¶
PDORMBR - VECT = 'Q', PDORMBR overwrites the general real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N'SYNOPSIS¶
- SUBROUTINE PDORMBR(
- VECT, SIDE, TRANS, M, N, K, A, IA, JA, DESCA,TAU, C, IC, JC, DESCC, WORK, LWORK, INFO )
PURPOSE¶
If VECT = 'Q', PDORMBR overwrites the general real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**TSIDE = 'L' SIDE = 'R'
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¶
- VECT (global input) CHARACTER
- = 'Q': apply Q or Q**T;
- SIDE (global input) CHARACTER
-
- TRANS (global input) CHARACTER
-
- M (global input) INTEGER
- The number of rows to be operated on i.e the number of rowsof the distributed submatrix sub( C ). M >= 0.
- N (global input) INTEGER
- The number of columns to be operated on i.e the number ofcolumns of the distributed submatrix sub( C ). N >= 0.
- K (global input) INTEGER
- If VECT = 'Q', the number of columns in the originaldistributed matrix reduced by PDGEBRD. If VECT = 'P', the number of rows in the original distributed matrix reduced by PDGEBRD. K >= 0.
- A (local input) DOUBLE PRECISION pointer into the local memory
- to an array of dimension (LLD_A,LOCc(JA+MIN(NQ,K)-1)) ifVECT='Q', and (LLD_A,LOCc(JA+NQ-1)) if VECT = 'P'. NQ = M if SIDE = 'L', and NQ = N otherwise. The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by PDGEBRD. If VECT = 'Q', LLD_A >= max(1,LOCr(IA+NQ-1)); if VECT = 'P', LLD_A >= max(1,LOCr(IA+MIN(NQ,K)-1)).
- IA (global input) INTEGER
- The row index in the global array A indicating the firstrow of sub( A ).
- JA (global input) INTEGER
- The column index in the global array A indicating thefirst column of sub( A ).
- DESCA (global and local input) INTEGER array of dimension DLEN_.
- The array descriptor for the distributed matrix A.
- TAU (local input) DOUBLE PRECISION array, dimension
- LOCc(JA+MIN(NQ,K)-1) if VECT = 'Q', LOCr(IA+MIN(NQ,K)-1) ifVECT = 'P', TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i), which determines Q or P, as returned by PDGEBRD in its array argument TAUQ or TAUP. TAU is tied to the distributed matrix A.
- 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 local pieces of the distributed matrix sub(C). On exit, if VECT='Q', sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C ) or sub( C )*Q' or sub( C )*Q; if VECT='P, sub( C ) is overwritten by P*sub( C ) or P'*sub( C ) or sub( C )*P or sub( C )*P'.
- IC (global input) INTEGER
- The row index in the global array C indicating the firstrow of sub( C ).
- JC (global input) INTEGER
- The column index in the global array C indicating thefirst 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/local output) DOUBLE PRECISION array,
- dimension (LWORK)On exit, WORK(1) returns the minimal and optimal LWORK.
- LWORK (local or global input) INTEGER
- The dimension of the array WORK.LWORK is local input and must be at leastIf SIDE = 'L', NQ = M; if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; else IAA=IA+1; JAA=JA; MI=M-1; NI=N; ICC=IC+1; JCC=JC; end if else if SIDE = 'R', NQ = N; if( (VECT = 'Q' and NQ >= K) or (VECT <> 'Q' and NQ > K) ), IAA=IA; JAA=JA; MI=M; NI=N; ICC=IC; JCC=JC; else IAA=IA; JAA=JA+1; MI=M; NI=N-1; ICC=IC; JCC=JC+1; end if end if If VECT = 'Q', If SIDE = 'L', LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + NB_A * NB_A else if SIDE = 'R', LWORK >= MAX( (NB_A*(NB_A-1))/2, ( NqC0 + MAX( NpA0 + NUMROC( NUMROC( NI+ICOFFC, NB_A, 0, 0, NPCOL ), NB_A, 0, 0, LCMQ ), MpC0 ) )*NB_A ) + NB_A * NB_A end if else if VECT <> 'Q', if SIDE = 'L', LWORK >= MAX( (MB_A*(MB_A-1))/2, ( MpC0 + MAX( MqA0 + NUMROC( NUMROC( MI+IROFFC, MB_A, 0, 0, NPROW ), MB_A, 0, 0, LCMP ), NqC0 ) )*MB_A ) + MB_A * MB_A else if SIDE = 'R', LWORK >= MAX( (MB_A*(MB_A-1))/2, (MpC0 + NqC0)*MB_A ) + MB_A * MB_A end if end if where LCMP = LCM / NPROW, LCMQ = LCM / NPCOL, with LCM = ICLM( NPROW, NPCOL ), IROFFA = MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), IAROW = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JAA, NB_A, MYCOL, CSRC_A, NPCOL ), MqA0 = NUMROC( MI+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW, IAROW, NPROW ), IROFFC = MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), ICROW = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL = INDXG2P( JCC, NB_C, MYCOL, CSRC_C, NPCOL ), MpC0 = NUMROC( MI+IROFFC, MB_C, MYROW, ICROW, NPROW ), NqC0 = NUMROC( NI+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ), INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine BLACS_GRIDINFO. If LWORK = -1, then LWORK is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by PXERBLA.
- INFO (global output) INTEGER
- = 0: successful exit
12 May 1997 | LAPACK version 1.5 |