NAME
PZLARZB - applie a complex block reflector Q or its conjugate transpose
Q**H to a complex M-by-N distributed matrix sub( C ) denoting
C(IC:IC+M-1,JC:JC+N-1), from the left or the right
SYNOPSIS
SUBROUTINE PZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, IV, JV,
DESCV, T, C, IC, JC, DESCC, WORK )
CHARACTER DIRECT, SIDE, STOREV, TRANS
INTEGER IC, IV, JC, JV, K, L, M, N
INTEGER DESCC( * ), DESCV( * )
COMPLEX*16 C( * ), T( * ), V( * ), WORK( * )
PURPOSE
PZLARZB applies a complex block reflector Q or its conjugate transpose
Q**H to a complex M-by-N distributed matrix sub( C ) denoting
C(IC:IC+M-1,JC:JC+N-1), from the left or the right.
Q is a product of k elementary reflectors as returned by PZTZRZF.
Currently, only STOREV = ’R’ and DIRECT = ’B’ are supported.
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**H from the Left;
= ’R’: apply Q or Q**H from the Right.
TRANS (global input) CHARACTER
= ’N’: No transpose, apply Q;
= ’C’: Conjugate transpose, apply Q**H.
DIRECT (global input) CHARACTER
Indicates how H is formed from a product of elementary
reflectors = ’F’: H = H(1) H(2) . . . H(k) (Forward, not
supported yet)
= ’B’: H = H(k) . . . H(2) H(1) (Backward)
STOREV (global input) CHARACTER
Indicates how the vectors which define the elementary
reflectors are stored:
= ’C’: Columnwise (not supported yet)
= ’R’: Rowwise
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 order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
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.
V (local input) COMPLEX*16 pointer into the local memory
to an array of dimension (LLD_V, LOCc(JV+M-1)) if SIDE = ’L’,
(LLD_V, LOCc(JV+N-1)) if SIDE = ’R’. It contains the local
pieces of the distributed vectors V representing the
Householder transformation as returned by PZTZRZF. LLD_V >=
LOCr(IV+K-1).
IV (global input) INTEGER
The row index in the global array V indicating the first row of
sub( V ).
JV (global input) INTEGER
The column index in the global array V indicating the first
column of sub( V ).
DESCV (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix V.
T (local input) COMPLEX*16 array, dimension MB_V by MB_V
The lower triangular matrix T in the representation of the
block reflector.
C (local input/local output) COMPLEX*16 pointer into the
local memory to an array of dimension (LLD_C,LOCc(JC+N-1)). On
entry, the M-by-N 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) COMPLEX*16 array, dimension (LWORK)
If STOREV = ’C’, if SIDE = ’L’, LWORK >= ( NqC0 + MpC0 ) * K
else if SIDE = ’R’, LWORK >= ( NqC0 + MAX( NpV0 + NUMROC(
NUMROC( N+ICOFFC, NB_V, 0, 0, NPCOL ), NB_V, 0, 0, LCMQ ), MpC0
) ) * K end if else if STOREV = ’R’, if SIDE = ’L’, LWORK >= (
MpC0 + MAX( MqV0 + NUMROC( NUMROC( M+IROFFC, MB_V, 0, 0, NPROW
), MB_V, 0, 0, LCMP ), NqC0 ) ) * K else if SIDE = ’R’, LWORK
>= ( MpC0 + NqC0 ) * K end if end if
where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),
IROFFV = MOD( IV-1, MB_V ), ICOFFV = MOD( JV-1, NB_V ), IVROW =
INDXG2P( IV, MB_V, MYROW, RSRC_V, NPROW ), IVCOL = INDXG2P( JV,
NB_V, MYCOL, CSRC_V, NPCOL ), MqV0 = NUMROC( M+ICOFFV, NB_V,
MYCOL, IVCOL, NPCOL ), NpV0 = NUMROC( N+IROFFV, MB_V, MYROW,
IVROW, NPROW ),
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 ), NpC0 = NUMROC( N+ICOFFC, 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.
Alignment requirements ======================
The distributed submatrices V(IV:*, JV:*) and
C(IC:IC+M-1,JC:JC+N-1) must verify some alignment properties,
namely the following expressions should be true:
If STOREV = ’Columnwise’ If SIDE = ’Left’, ( MB_V.EQ.MB_C .AND.
IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW ) If SIDE = ’Right’, (
MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC ) else if STOREV =
’Rowwise’ If SIDE = ’Left’, ( NB_V.EQ.MB_C .AND.
ICOFFV.EQ.IROFFC ) If SIDE = ’Right’, ( NB_V.EQ.NB_C .AND.
ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL ) end if