PCLARFG generates a complex elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H’ * H = I. ( 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.