NAME
PZLARFG - generate a complex elementary reflector H of order n, such
that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H’ * H = I
SYNOPSIS
SUBROUTINE PZLARFG( N, ALPHA, IAX, JAX, X, IX, JX, DESCX, INCX, TAU )
INTEGER IAX, INCX, IX, JAX, JX, N
COMPLEX*16 ALPHA
INTEGER DESCX( * )
COMPLEX*16 TAU( * ), X( * )
PURPOSE
PZLARFG generates a complex elementary reflector H of order n, such
that
( x ) ( 0 )
where alpha is a real scalar, and sub( X ) is an (N-1)-element complex
distributed vector X(IX:IX+N-2,JX) if INCX = 1 and X(IX,JX:JX+N-2) if
INCX = DESCX(M_). H is represented in the form
H = I - tau * ( 1 ) * ( 1 v’ ) ,
( v )
where tau is a complex scalar and v is a complex (N-1)-element vector.
Note that H is not Hermitian.
If the elements of sub( X ) are all zero and X(IAX,JAX) is real, then
tau = 0 and H is taken to be the unit matrix.
Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1.
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.
ARGUMENTS
N (global input) INTEGER
The global order of the elementary reflector. N >= 0.
ALPHA (local output) COMPLEX*16
On exit, alpha is computed in the process scope having the
vector sub( X ).
IAX (global input) INTEGER
The global row index in X of X(IAX,JAX).
JAX (global input) INTEGER
The global column index in X of X(IAX,JAX).
X (local input/local output) COMPLEX*16, pointer into the
local memory to an array of dimension (LLD_X,*). This array
contains the local pieces of the distributed vector sub( X ).
Before entry, the incremented array sub( X ) must contain the
vector x. On exit, it is overwritten with the vector v.
IX (global input) INTEGER
The row index in the global array X indicating the first row of
sub( X ).
JX (global input) INTEGER
The column index in the global array X indicating the first
column of sub( X ).
DESCX (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix X.
INCX (global input) INTEGER
The global increment for the elements of X. Only two values of
INCX are supported in this version, namely 1 and M_X. INCX
must not be zero.
TAU (local output) COMPLEX*16, array, dimension LOCc(JX)
if INCX = 1, and LOCr(IX) otherwise. This array contains the
Householder scalars related to the Householder vectors. TAU is
tied to the distributed matrix X.