Provided by: scalapack-doc_1.5-10_all 
NAME
PSORMRQ - 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 PSORMRQ( 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( * )
REAL A( * ), C( * ), TAU( * ), WORK( * )
PURPOSE
PSORMRQ 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 defined as the product of K elementary
reflectors
Q = H(1) H(2) . . . H(k)
as returned by PSGERQF. 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
ARGUMENTS
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) REAL pointer into the local memory
to an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', and
(LLD_A,LOCc(JA+N-1)) if SIDE='R', where LLD_A >= MAX(1,LOCr(IA+K-1)); On entry,
the i-th row must contain the vector which defines the elementary reflector H(i),
IA <= i <= IA+K-1, as returned by PSGERQF in the K rows of its distributed matrix
argument A(IA:IA+K-1,JA:*).
A(IA:IA+K-1,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) REAL, array, dimension LOCc(IA+K-1).
This array contains the scalar factors TAU(i) of the elementary reflectors H(i) as
returned by PSGERQF. TAU is tied to the distributed matrix A.
C (local input/local output) REAL 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) REAL 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_A-1))/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_A-1))/2, (MpC0 + NqC0)*MB_A ) + MB_A *
MB_A end if
where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IACOL = INDXG2P( JA, NB_A,
MYCOL, CSRC_A, NPCOL ), MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, 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 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', ( 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 )