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PZPOCON(l)			       )			    PZPOCON(l)

NAME
       PZPOCON	-  estimate  the  reciprocal  of  the condition number (in the
       1-norm) of a complex Hermitian  positive	 definite  distributed	matrix
       using  the  Cholesky factorization A = U**H*U or A = L*L**H computed by
       PZPOTRF

SYNOPSIS
       SUBROUTINE PZPOCON( UPLO, N, A, IA,  JA,	 DESCA,	 ANORM,	 RCOND,	 WORK,
			   LWORK, RWORK, LRWORK, INFO )

	   CHARACTER	   UPLO

	   INTEGER	   IA, INFO, JA, LRWORK, LWORK, N

	   DOUBLE	   PRECISION ANORM, RCOND

	   INTEGER	   DESCA( * )

	   DOUBLE	   PRECISION RWORK( * )

	   COMPLEX*16	   A( * ), WORK( * )

PURPOSE
       PZPOCON	estimates  the	reciprocal  of	the  condition	number (in the
       1-norm) of a complex Hermitian  positive	 definite  distributed	matrix
       using  the  Cholesky factorization A = U**H*U or A = L*L**H computed by
       PZPOTRF.	       An	 estimate	 is	   obtained	   for
       norm(inv(A(IA:IA+N-1,JA:JA+N-1))),  and the reciprocal of the condition
       number is computed as
		  RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)	  ) *
				norm( inv(A(IA:IA+N-1,JA:JA+N-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
       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
	       Specifies  whether  the factor stored in A(IA:IA+N-1,JA:JA+N-1)
	       is upper or lower triangular.
	       = 'U':  Upper triangular
	       = 'L':  Lower triangular

       N       (global input) INTEGER
	       The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1).   N
	       >= 0.

       A       (local input) COMPLEX*16 pointer into the local memory to
	       an  array  of dimension ( LLD_A, LOCc(JA+N-1) ). On entry, this
	       array contains the local pieces of the factors L or U from  the
	       Cholesky	 factorization	A(IA:IA+N-1,JA:JA+N-1) = U'*U or L*L',
	       as computed by PZPOTRF.

       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.

       ANORM   (global input) DOUBLE PRECISION
	       The 1-norm (or  infinity-norm)  of  the	hermitian  distributed
	       matrix A(IA:IA+N-1,JA:JA+N-1).

       RCOND   (global output) DOUBLE PRECISION
	       The  reciprocal	of  the	 condition  number  of the distributed
	       matrix A(IA:IA+N-1,JA:JA+N-1), computed as
	       RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1)      ) *
	       norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).

       WORK    (local workspace/local output) COMPLEX*16 array,
	       dimension (LWORK) On exit,  WORK(1)  returns  the  minimal  and
	       optimal LWORK.

       LWORK   (local or global input) INTEGER
	       The dimension of the array WORK.	 LWORK is local input and must
	       be  at  least  LWORK  >=	 2*LOCr(N+MOD(IA-1,MB_A))  +  MAX(  2,
	       MAX(NB_A*MAX(1,CEIL(P-1,Q)),LOCc(N+MOD(JA-1,NB_A))	     +
	       NB_A*MAX(1,CEIL(Q-1,P))) ).

	       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.

       RWORK   (local workspace/local output) DOUBLE PRECISION array,
	       dimension (LRWORK) On exit, RWORK(1) returns  the  minimal  and
	       optimal LRWORK.

       LRWORK  (local or global input) INTEGER
	       The  dimension  of  the array RWORK.  LRWORK is local input and
	       must be at least LRWORK >= 2*LOCc(N+MOD(JA-1,NB_A)).

	       If LRWORK = -1, then LRWORK 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.


ScaLAPACK version 1.7		13 August 2001			    PZPOCON(l)
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