PZLARZB(3) ScaLAPACK routine of NEC Numeric Library Collection PZLARZB(3)
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 vec-
tor. This vector stores the information required to establish the map-
ping 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 col-
umn.
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 reflec-
tors = '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 reflec-
tors 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 reflec-
tors 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 House-
holder 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( NUM-
ROC( 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 subrou-
tine 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
ScaLAPACK routine 31 October 2017 PZLARZB(3)