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PDLAQGE(l)			       )			    PDLAQGE(l)

NAME
       PDLAQGE	-  equilibrate	a general M-by-N distributed matrix sub( A ) =
       A(IA:IA+M-1,JA:JA+N-1) using the	row and	scaling	factors	in the vectors
       R and C

SYNOPSIS
       SUBROUTINE PDLAQGE( M, N, A, IA,	JA, DESCA, R, C, ROWCND, COLCND, AMAX,
			   EQUED )

	   CHARACTER	   EQUED

	   INTEGER	   IA, JA, M, N

	   DOUBLE	   PRECISION AMAX, COLCND, ROWCND

	   INTEGER	   DESCA( * )

	   DOUBLE	   PRECISION A(	* ), C(	* ), R(	* )

PURPOSE
       PDLAQGE equilibrates a general M-by-N distributed matrix	 sub(  A  )  =
       A(IA:IA+M-1,JA:JA+N-1) using the	row and	scaling	factors	in the vectors
       R and C.	 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
       M       (global input) INTEGER
	       The number of rows to be	operated on i.e	the number of rows  of
	       the distributed submatrix sub( A	). 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( A	). N >=	0.

       A       (local input/local output) DOUBLE PRECISION pointer into	the
	       local memory to an array	of dimension (LLD_A,LOCc(JA+N-1)) con-
	       taining on entry	the M-by-N matrix sub( A ). On exit, the equi-
	       librated	distributed matrix.  See EQUED for  the	 form  of  the
	       equilibrated distributed	submatrix.

       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.

       R       (local input) DOUBLE PRECISION array, dimension LOCr(M_A)
	       The  row	scale factors for sub( A ). R is aligned with the dis-
	       tributed	matrix A, and replicated across	every process  column.
	       R is tied to the	distributed matrix A.

       C       (local input) DOUBLE PRECISION array, dimension LOCc(N_A)
	       The  column  scale  factors  of sub( A ). C is aligned with the
	       distributed matrix A, and replicated down every process row.  C
	       is tied to the distributed matrix A.

       ROWCND  (global input) DOUBLE PRECISION
	       The  global  ratio of the smallest R(i) to the largest R(i), IA
	       <= i <= IA+M-1.

       COLCND  (global input) DOUBLE PRECISION
	       The global ratio	of the smallest	C(i) to	the largest  C(i),  JA
	       <= j <= JA+N-1.

       AMAX    (global input) DOUBLE PRECISION
	       Absolute	value of largest distributed submatrix entry.

       EQUED   (global output) CHARACTER
	       Specifies  the form of equilibration that was done.  = 'N':  No
	       equilibration
	       = 'R':  Row equilibration, i.e.,	sub( A ) has been pre-
	       multiplied by diag(R(IA:IA+M-1)),
	       = 'C':  Column equilibration, i.e., sub(	A ) has	been post-
	       multiplied by diag(C(JA:JA+N-1)),
	       = 'B':  Both row	and column equilibration, i.e.,	sub( A	)  has
	       been   replaced	 by   diag(R(IA:IA+M-1))   *   sub(   A	  )  *
	       diag(C(JA:JA+N-1)).

PARAMETERS
       THRESH is a threshold value used	to decide if  row  or  column  scaling
       should be done based on the ratio of the	row or column scaling factors.
       If ROWCND < THRESH, row scaling is done,	and if COLCND <	THRESH,	column
       scaling is done.

       LARGE  and  SMALL  are  threshold  values used to decide	if row scaling
       should be done based on the absolute size of the	 largest  matrix  ele-
       ment.  If AMAX >	LARGE or AMAX <	SMALL, row scaling is done.

ScaLAPACK version 1.7		13 August 2001			    PDLAQGE(l)

NAME | SYNOPSIS | PURPOSE | ARGUMENTS | PARAMETERS

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