PSLARFG(l)

NAME
PSLARFG - generate a real elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I

SYNOPSIS

SUBROUTINE PSLARFG(
    N, ALPHA, IAX, JAX, X, IX, JX, DESCX, INCX, TAU )

INTEGER
    IAX, INCX, IX, JAX, JX, N

REAL
    ALPHA

INTEGER
    DESCX( * )

REAL
    TAU( * ), X( * )

PURPOSE
PSLARFG generates a real elementary reflector H of order n, such that
                      ( x ) ( 0 )

where alpha is a scalar, and sub( X ) is an (N-1)-element real 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 real scalar and v is a real (N-1)-element
vector.

If the elements of sub( X ) are all zero, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= tau <= 2.

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) REAL
    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) REAL, 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) REAL, 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.