Skip site navigation (1)Skip section navigation (2)

FreeBSD Manual Pages

  
 
  

home | help
PCUNMHR(l)			       )			    PCUNMHR(l)

NAME
       PCUNMHR	- overwrite the	general	complex	M-by-N distributed matrix sub(
       C ) = C(IC:IC+M-1,JC:JC+N-1) with  SIDE = 'L' SIDE = 'R'	TRANS =	'N'

SYNOPSIS
       SUBROUTINE PCUNMHR( SIDE, TRANS,	M, N, ILO, IHI,	A, IA, JA, DESCA, TAU,
			   C, IC, JC, DESCC, WORK, LWORK, INFO )

	   CHARACTER	   SIDE, TRANS

	   INTEGER	   IA, IC, IHI,	ILO, INFO, JA, JC, LWORK, M, N

	   INTEGER	   DESCA( * ), DESCC( *	)

	   COMPLEX	   A( *	), C( *	), TAU(	* ), WORK( * )

PURPOSE
       PCUNMHR overwrites the general complex M-by-N distributed matrix	sub( C
       ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q  *
       sub(  C ) sub( C	) * Q TRANS = 'C':	Q**H * sub( C )	      sub( C )
       * Q**H

       where Q is a complex unitary distributed	matrix of order	nq, with nq  =
       m  if  SIDE = 'L' and nq	= n if SIDE = 'R'. Q is	defined	as the product
       of IHI-ILO elementary reflectors, as returned by	PCGEHRD:

       Q = H(ilo) H(ilo+1) . . . H(ihi-1).

       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.

       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.

       ILO     (global input) INTEGER
	       IHI     (global input) INTEGER ILO and IHI must have  the  same
	       values  as  in  the previous call of PCGEHRD. Q is equal	to the
	       unit   matrix   except	 in    the    distributed    submatrix
	       Q(ia+ilo:ia+ihi-1,ia+ilo:ja+ihi-1).  If SIDE = 'L', 1 <=	ILO <=
	       IHI <= max(1,M);	if SIDE	= 'R', 1 <= ILO	<=  IHI	 <=  max(1,N);
	       ILO and IHI are relative	indexes.

       A       (local input) COMPLEX pointer into the local memory
	       to  an array of dimension (LLD_A,LOCc(JA+M-1)) if SIDE='L', and
	       (LLD_A,LOCc(JA+N-1)) if SIDE = 'R'. The	vectors	 which	define
	       the elementary reflectors, as returned by PCGEHRD.

       IA      (global input) INTEGER
	       The row index in	the global array A indicating the first	row of
	       sub( A ).

       JA      (global input) INTEGER
	       The column index	in the global array  A	indicating  the	 first
	       column of sub( A	).

       DESCA   (global and local input)	INTEGER	array of dimension DLEN_.
	       The array descriptor for	the distributed	matrix A.

       TAU     (local input) COMPLEX, array, dimension LOCc(JA+M-2)
	       if  SIDE	= 'L', and LOCc(JA+N-2)	if SIDE	= 'R'. This array con-
	       tains the scalar	factors	TAU(j) of  the	elementary  reflectors
	       H(j) as returned	by PCGEHRD. TAU	is tied	to the distributed ma-
	       trix A.

       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  local pieces of the	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/local output) COMPLEX array,
	       dimension  (LWORK) On exit, WORK(1) returns the minimal and op-
	       timal LWORK.

       LWORK   (local or global	input) INTEGER
	       The dimension of	the array WORK.	 LWORK is local	input and must
	       be at least

	       IAA = IA	+ ILO; JAA = JA+ILO-1; If SIDE = 'L', MI = IHI-ILO; NI
	       = N; ICC	= IC + ILO; JCC	= JC; LWORK >= MAX( (NB_A*(NB_A-1))/2,
	       (NqC0  +	MpC0)*NB_A ) + NB_A * NB_A else	if SIDE	= 'R', MI = M;
	       NI = IHI-ILO; ICC  =  IC;  JCC  =  JC  +	 ILO;  LWORK  >=  MAX(
	       (NB_A*(NB_A-1))/2,  (  NqC0  +  MAX(  NpA0  +  NUMROC(  NUMROC(
	       NI+ICOFFC, NB_A,	0, 0, NPCOL ), NB_A, 0,	 0,  LCMQ  ),  MpC0  )
	       )*NB_A )	+ NB_A * NB_A end if

	       where LCMQ = LCM	/ NPCOL	with LCM = ICLM( NPROW,	NPCOL ),

	       IROFFA =	MOD( IAA-1, MB_A ), ICOFFA = MOD( JAA-1, NB_A ), IAROW
	       = INDXG2P( IAA, MB_A, MYROW, RSRC_A, NPROW ),  NpA0  =  NUMROC(
	       NI+IROFFA, MB_A,	MYROW, IAROW, NPROW ),

	       IROFFC =	MOD( ICC-1, MB_C ), ICOFFC = MOD( JCC-1, NB_C ), ICROW
	       = INDXG2P( ICC, MB_C, MYROW, RSRC_C, NPROW ), ICCOL =  INDXG2P(
	       JCC,  NB_C,  MYCOL,  CSRC_C, NPCOL ), MpC0 = NUMROC( MI+IROFFC,
	       MB_C, MYROW, ICROW, NPROW ), NqC0 =  NUMROC(  NI+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.

	       If LWORK	= -1, then LWORK is global input and a workspace query
	       is assumed; the routine only calculates the minimum and optimal
	       size  for  all work arrays. Each	of these values	is returned in
	       the first entry of the corresponding work array,	and  no	 error
	       message is issued by PXERBLA.

       INFO    (global output) INTEGER
	       = 0:  successful	exit
	       <  0:   If the i-th argument is an array	and the	j-entry	had an
	       illegal value, then INFO	= -(i*100+j), if the i-th argument  is
	       a scalar	and had	an illegal value, then INFO = -i.

	       Alignment requirements ======================

	       The     distributed     submatrices     A(IA:*,	  JA:*)	   and
	       C(IC:IC+M-1,JC:JC+N-1) must verify some	alignment  properties,
	       namely the following expressions	should be true:

	       If  SIDE	 =  'L',  (  MB_A.EQ.MB_C .AND.	IROFFA.EQ.IROFFC .AND.
	       IAROW.EQ.ICROW  )  If  SIDE  =  'R',   (	  MB_A.EQ.NB_C	 .AND.
	       IROFFA.EQ.ICOFFC	)

ScaLAPACK version 1.7		13 August 2001			    PCUNMHR(l)

NAME | SYNOPSIS | PURPOSE | ARGUMENTS

Want to link to this manual page? Use this URL:
<https://www.freebsd.org/cgi/man.cgi?query=pcunmhr&manpath=FreeBSD+12.0-RELEASE+and+Ports>

home | help