Provided by: scalapack-doc_1.5-11_all 
NAME
PSORMRZ - 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 PSORMRZ( SIDE, TRANS, M, N, K, L, A, IA, JA, DESCA, TAU, C, IC, JC, DESCC, WORK, LWORK, INFO )
CHARACTER SIDE, TRANS
INTEGER IA, IC, INFO, JA, JC, K, L, LWORK, M, N
INTEGER DESCA( * ), DESCC( * )
REAL A( * ), C( * ), TAU( * ), WORK( * )
PURPOSE
PSORMRZ 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 PSTZRZF. 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.
L (global input) INTEGER
The columns of the distributed submatrix sub( A ) containing the meaningful part of the
Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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 PSTZRZF 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
PSTZRZF. 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 )
LAPACK version 1.5 12 May 1997 PSORMRZ(l)