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PCLARFB(l)			       )			    PCLARFB(l)

NAME
       PCLARFB - 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 PCLARFB( SIDE,  TRANS,  DIRECT,  STOREV, M, N, K, V, IV, JV,
			   DESCV, T, C,	IC, JC,	DESCC, WORK )

	   CHARACTER	   SIDE, TRANS,	DIRECT,	STOREV

	   INTEGER	   IC, IV, JC, JV, K, M, N

	   INTEGER	   DESCC( * ), DESCV( *	)

	   COMPLEX	   C( *	), T( *	), V( *	), WORK( * )

PURPOSE
       PCLARFB 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.  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 as-
       sume that its process grid has dimension	p x q.
       LOCr(  K	) denotes the number of	elements of K that a process would re-
       ceive 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

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 Q is formed from a	product	of elementary  reflec-
	       tors = 'F': Q = H(1) H(2) . . . H(k) (Forward)
	       = 'B': Q	= 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
	       = '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 col-
	       umns 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).

       V       (local input) COMPLEX pointer into the local memory
	       to  an  array  of dimension ( LLD_V, LOCc(JV+K-1) ) if STOREV =
	       'C', ( LLD_V, LOCc(JV+M-1)) if STOREV = 'R' and SIDE =  'L',  (
	       LLD_V,  LOCc(JV+N-1)  ) if STOREV = 'R' and SIDE	= 'R'. It con-
	       tains the local pieces of the distributed vectors V  represent-
	       ing  the	 Householder transformation.  See further details.  If
	       STOREV =	'C' and	SIDE = 'L', LLD_V >=  MAX(1,LOCr(IV+M-1));  if
	       STOREV  =  'C' and SIDE = 'R', LLD_V >= MAX(1,LOCr(IV+N-1)); if
	       STOREV =	'R', 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 array, dimension MB_V by MB_V
	       if STOREV = 'R' and NB_V	by NB_V	if STOREV =  'C'.  The	trian-
	       gular matrix T in the representation of the block reflector.

       C       (local input/local output) COMPLEX 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 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 = 'Row-
	       wise' 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 version 1.7		13 August 2001			    PCLARFB(l)

NAME | SYNOPSIS | PURPOSE | ARGUMENTS

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