Provided by: scalapack-doc_1.5-11_all 
NAME
PZLARZ - applie a complex elementary reflector Q to a complex M-by-N distributed matrix sub( C ) =
C(IC:IC+M-1,JC:JC+N-1), from either the left or the right
SYNOPSIS
SUBROUTINE PZLARZ( SIDE, M, N, L, V, IV, JV, DESCV, INCV, TAU, C, IC, JC, DESCC, WORK )
CHARACTER SIDE
INTEGER IC, INCV, IV, JC, JV, L, M, N
INTEGER DESCC( * ), DESCV( * )
COMPLEX*16 C( * ), TAU( * ), V( * ), WORK( * )
PURPOSE
PZLARZ applies a complex elementary reflector Q to a complex M-by-N distributed matrix sub( C ) =
C(IC:IC+M-1,JC:JC+N-1), from either the left or the right. Q is represented in the form
Q = I - tau * v * v'
where tau is a complex scalar and v is a complex vector.
If tau = 0, then Q is taken to be the unit matrix.
Q is a product of k elementary reflectors as returned by PZTZRZF.
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
Because vectors may be viewed as a subclass of matrices, a distributed vector is considered to be a
distributed matrix.
Restrictions
============
If SIDE = 'Left' and INCV = 1, then the row process having the first entry V(IV,JV) must also own C(IC+M-
L,JC:JC+N-1). Moreover, MOD(IV-1,MB_V) must be equal to MOD(IC+N-L-1,MB_C), if INCV=M_V, only the last
equality must be satisfied.
If SIDE = 'Right' and INCV = M_V then the column process having the first entry V(IV,JV) must also own
C(IC:IC+M-1,JC+N-L) and MOD(JV-1,NB_V) must be equal to MOD(JC+N-L-1,NB_C), if INCV = 1 only the last
equality must be satisfied.
ARGUMENTS
SIDE (global input) CHARACTER
= 'L': form Q * sub( C ),
= 'R': form sub( C ) * Q.
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.
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,*) containing the local pieces of the distributed vectors V
representing the Householder transformation Q, V(IV:IV+L-1,JV) if SIDE = 'L' and INCV = 1,
V(IV,JV:JV+L-1) if SIDE = 'L' and INCV = M_V,
V(IV:IV+L-1,JV) if SIDE = 'R' and INCV = 1,
V(IV,JV:JV+L-1) if SIDE = 'R' and INCV = M_V,
The vector v in the representation of Q. V is not used if TAU = 0.
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.
INCV (global input) INTEGER
The global increment for the elements of V. Only two values of INCV are supported in this
version, namely 1 and M_V. INCV must not be zero.
TAU (local input) COMPLEX*16, array, dimension LOCc(JV) if
INCV = 1, and LOCr(IV) otherwise. This array contains the Householder scalars related to the
Householder vectors. TAU is tied to the distributed matrix V.
C (local input/local output) COMPLEX*16 pointer into the
local memory to an array of dimension (LLD_C, LOCc(JC+N-1) ), containing the local pieces of sub(
C ). On exit, sub( C ) is overwritten by the Q * sub( C ) if SIDE = 'L', or sub( C ) * Q if SIDE
= 'R'.
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 INCV = 1, if SIDE = 'L', if IVCOL = ICCOL, LWORK >= NqC0 else LWORK >= MpC0 + MAX( 1, NqC0 )
end if else if SIDE = 'R', LWORK >= NqC0 + MAX( MAX( 1, MpC0 ), NUMROC( NUMROC(
N+ICOFFC,NB_V,0,0,NPCOL ),NB_V,0,0,LCMQ ) ) end if else if INCV = M_V, if SIDE = 'L', LWORK >=
MpC0 + MAX( MAX( 1, NqC0 ), NUMROC( NUMROC( M+IROFFC,MB_V,0,0,NPROW ),MB_V,0,0,LCMP ) ) else if
SIDE = 'R', if IVROW = ICROW, LWORK >= MpC0 else LWORK >= NqC0 + MAX( 1, MpC0 ) end if end if end
if
where LCM is the least common multiple of NPROW and NPCOL and LCM = ILCM( NPROW, NPCOL ), LCMP =
LCM / NPROW, LCMQ = LCM / 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.
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:
MB_V = NB_V,
If INCV = 1, If SIDE = 'Left', ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW ) If
SIDE = 'Right', ( MB_V.EQ.NB_A .AND. MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC ) else if INCV = M_V, If
SIDE = 'Left', ( MB_V.EQ.NB_V .AND. MB_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