

SUBROUTINE PDORMRQ(  SIDE, TRANS, M, N, K, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO ) 
CHARACTER SIDE, TRANS  
INTEGER IA, IC, INFO, JA, JC, K, LWORK, M, N  
INTEGER DESCA( * ), DESCC( * )  
DOUBLE PRECISION A( * ), C( * ), TAU( * ), WORK( * )  
PDORMRQ overwrites the general real MbyN distributed matrix sub( C ) = C(IC:IC+M1,JC:JC+N1) with SIDE = ’L’ SIDE = ’R’ TRANS = ’N’: Q * sub( C ) sub( C ) * Q TRANS = ’T’: Q**T * sub( C ) sub( C ) * Q**Twhere Q is a real orthogonal distributed matrix defined as the product of K elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by PDGERQF. Q is of order M if SIDE = ’L’ and of order N if SIDE = ’R’.
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
SIDE (global input) CHARACTER = ’L’: apply Q or Q**T from the Left;
= ’R’: apply Q or Q**T from the Right.TRANS (global input) CHARACTER = ’N’: No transpose, apply Q;
= ’T’: Transpose, apply Q**T.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 number of elementary reflectors whose product defines the matrix Q. If SIDE = ’L’, M >= K >= 0, if SIDE = ’R’, N >= K >= 0. A (local input) DOUBLE PRECISION pointer into the local memory to an array of dimension (LLD_A,LOCc(JA+M1)) if SIDE=’L’, and (LLD_A,LOCc(JA+N1)) if SIDE=’R’, where LLD_A >= MAX(1,LOCr(IA+K1)); On entry, the ith row must contain the vector which defines the elementary reflector H(i), IA <= i <= IA+K1, as returned by PDGERQF in the K rows of its distributed matrix argument A(IA:IA+K1,JA:*).
A(IA:IA+K1,JA:*) is modified by the routine but restored on exit.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. TAU (local input) DOUBLE PRECISION array, dimension LOCc(IA+K1). This array contains the scalar factors TAU(i) of the elementary reflectors H(i) as returned by PDGERQF. 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+N1)). On entry, the local pieces of the 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/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 least if SIDE = ’L’, LWORK >= MAX( (MB_A*(MB_A1))/2, ( MpC0 + MAX( MqA0 + NUMROC( NUMROC( M+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_A1))/2, (MpC0 + NqC0)*MB_A ) + MB_A * MB_A end if where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
IROFFA = MOD( IA1, MB_A ), ICOFFA = MOD( JA1, NB_A ), IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
IROFFC = MOD( IC1, MB_C ), ICOFFC = MOD( JC1, 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 ), 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.
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
< 0: If the ith argument is an array and the jentry had an illegal value, then INFO = (i*100+j), if the ith argument is a scalar and had an illegal value, then INFO = i.Alignment requirements ======================
The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M1,JC:JC+N1) must verify some alignment properties, namely the following expressions should be true:
If SIDE = ’L’, ( NB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC ) If SIDE = ’R’, ( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL )
ScaLAPACK version 1.7  PDORMRQ (l)  13 August 2001 
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