Provided by: scalapack-doc_1.5-11_all 
NAME
PDORMTR - overwrite the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
SIDE = 'L' SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE PDORMTR( SIDE, UPLO, TRANS, M, N, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO )
CHARACTER SIDE, TRANS, UPLO
INTEGER IA, IC, INFO, JA, JC, LWORK, M, N
INTEGER DESCA( * ), DESCC( * )
DOUBLE PRECISION A( * ), C( * ), TAU( * ), WORK( * )
PURPOSE
PDORMTR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T
where Q is a real orthogonal distributed matrix of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE
= 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by PDSYTRD:
if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(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
SIDE (global input) CHARACTER
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
UPLO (global input) CHARACTER
= 'U': Upper triangle of A(IA:*,JA:*) contains elementary reflectors from PDSYTRD; = 'L': Lower
triangle of A(IA:*,JA:*) contains elementary reflectors from PDSYTRD.
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.
A (local input) DOUBLE PRECISION pointer into the local memory
to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', or (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'.
The vectors which define the elementary reflectors, as returned by PDSYTRD. If SIDE = 'L', LLD_A
>= max(1,LOCr(IA+M-1)); if SIDE = 'R', LLD_A >= max(1,LOCr(IA+N-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 LTAU, where
if SIDE = 'L' and UPLO = 'U', LTAU = LOCc(M_A), if SIDE = 'L' and UPLO = 'L', LTAU =
LOCc(JA+M-2), if SIDE = 'R' and UPLO = 'U', LTAU = LOCc(N_A), if SIDE = 'R' and UPLO = 'L', LTAU
= LOCc(JA+N-2). TAU(i) must contain the scalar factor of the elementary reflector H(i), as
returned by PDSYTRD. 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, 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 UPLO = 'U', IAA = IA, JAA = JA+1, ICC = IC, JCC = JC; else UPLO = 'L', IAA = IA+1, JAA = JA;
if SIDE = 'L', ICC = IC+1; JCC = JC; else ICC = IC; JCC = JC+1; end if end if
If SIDE = 'L', MI = M-1; NI = N; LWORK >= MAX( (NB_A*(NB_A-1))/2, (NqC0 + MpC0)*NB_A ) + NB_A *
NB_A else if SIDE = 'R', MI = M; MI = N-1; 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
where 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 ), 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 ),
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 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 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 )
LAPACK version 1.5 12 May 1997 PDORMTR(l)