PCLAUUM(l)			       )			    PCLAUUM(l)

NAME
       PCLAUUM	-  compute  the product U * U' or L' * L, where the triangular
       factor U or L is stored in the upper or lower triangular	 part  of  the
       distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1)

SYNOPSIS
       SUBROUTINE PCLAUUM( UPLO, N, A, IA, JA, DESCA )

	   CHARACTER	   UPLO

	   INTEGER	   IA, JA, N

	   INTEGER	   DESCA( * )

	   COMPLEX	   A( * )

PURPOSE
       PCLAUUM	computes  the  product	U * U' or L' * L, where the triangular
       factor U or L is stored in the upper or lower triangular	 part  of  the
       distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).  If UPLO = 'U' or
       'u' then the upper triangle of the result is  stored,  overwriting  the
       factor U in sub( A ).
       If  UPLO	 = 'L' or 'l' then the lower triangle of the result is stored,
       overwriting the factor L in sub( A ).

       This is the blocked form of the algorithm, calling Level 3 PBLAS.

       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
       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  col‐
       umn.
       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
       UPLO    (global input) CHARACTER*1
	       Specifies  whether the triangular factor stored in the distrib‐
	       uted matrix sub( A ) is upper or lower triangular:
	       = 'U':  Upper triangular
	       = 'L':  Lower triangular

       N       (global input) INTEGER
	       The number of rows and columns to  be  operated	on,  i.e.  the
	       order of the triangular factor U or L. N >= 0.

       A       (local input/local output) COMPLEX pointer into the
	       local  memory  to  an array of dimension (LLD_A, LOCc(JA+N-1)).
	       On entry, the local pieces of the triangular factor L or U.  On
	       exit,  if  UPLO	=  'U',	 the upper triangle of the distributed
	       matrix sub( A ) is overwritten with the upper triangle  of  the
	       product	U  * U'; if UPLO = 'L', the lower triangle of sub( A )
	       is overwritten with the lower triangle of the product L' * L.

       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.

ScaLAPACK version 1.7		13 August 2001			    PCLAUUM(l)

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