PDORMTR  overwrite the general real MbyN distributed matrix sub( C ) =
C(IC:IC+M1,JC:JC+N1) with SIDE = 'L' SIDE = 'R' TRANS = 'N'
 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( * )
PDORMTR 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**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 nq1 elementary
reflectors, as returned by PDSYTRD:
if UPLO = 'U', Q = H(nq1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(nq1).
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.
 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+M1)) if SIDE='L', or
(LLD_A,LOCc(JA+N1)) if SIDE = 'R'. The vectors which define the
elementary reflectors, as returned by PDSYTRD. If SIDE = 'L', LLD_A >=
max(1,LOCr(IA+M1)); if SIDE = 'R', LLD_A >= max(1,LOCr(IA+N1)).
 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+M2), if SIDE = 'R' and UPLO = 'U', LTAU = LOCc(N_A),
if SIDE = 'R' and UPLO = 'L', LTAU = LOCc(JA+N2). 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+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 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 = M1; NI = N; LWORK >= MAX( (NB_A*(NB_A1))/2, (NqC0 +
MpC0)*NB_A ) + NB_A * NB_A else if SIDE = 'R', MI = M; MI = N1; LWORK
>= MAX( (NB_A*(NB_A1))/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( IAA1, MB_A ), ICOFFA = MOD( JAA1, NB_A ), IAROW = INDXG2P(
IAA, MB_A, MYROW, RSRC_A, NPROW ), NpA0 = NUMROC( NI+IROFFA, MB_A, MYROW,
IAROW, NPROW ),
IROFFC = MOD( ICC1, MB_C ), ICOFFC = MOD( JCC1, 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 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', ( 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 )