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 )
- CHARACTER
- SIDE, TRANS, VECT
- INTEGER
- IA, IC, INFO, JA, JC, K, LWORK, M, N
- INTEGER
- DESCA( * ), DESCC( * )
- DOUBLE
- PRECISION A( * ), C( * ), TAU( * ), WORK( * )
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**T
If VECT = 'P', PDORMBR overwrites sub( C ) with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * sub( C ) sub( C ) * P
TRANS = 'T': P**T * sub( C ) sub( C ) * P**T
Here Q and P**T are the orthogonal distributed matrices determined by PDGEBRD
when reducing a real distributed matrix A(IA:*,JA:*) to bidiagonal form:
A(IA:*,JA:*) = Q * B * P**T. Q and P**T are defined as products of elementary
reflectors H(i) and G(i) respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the
orthogonal matrix Q or P**T that is applied.
If VECT = 'Q', A(IA:*,JA:*) is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = 'P', A(IA:*,JA:*) is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
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
ARGUMENTS¶
- VECT (global input) CHARACTER
- = 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
- SIDE (global input) CHARACTER
-
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
- TRANS (global input) CHARACTER
-
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**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
- If VECT = 'Q', the number of columns in the original
distributed 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)) if
VECT='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 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(JA+MIN(NQ,K)-1) if VECT = 'Q', LOCr(IA+MIN(NQ,K)-1) if
VECT = '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 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', 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
< 0: If the i-th argument is an array and the j-entry had an illegal
value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an
illegal value, then INFO = -i.
Alignment requirements ======================
The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1) must
verify some alignment properties, namely the following expressions should
be true:
If VECT = 'Q', If SIDE = 'L', ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND.
IAROW.EQ.ICROW ) If SIDE = 'R', ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC )
else If SIDE = 'L', ( MB_A.EQ.MB_C .AND. ICOFFA.EQ.IROFFC ) If SIDE = 'R',
( NB_A.EQ.NB_C .AND. ICOFFA.EQ.ICOFFC .AND. IACOL.EQ.ICCOL ) end if