NAME

       PCLACON - estimate the 1-norm of a square, complex distributed matrix A

SYNOPSIS

       SUBROUTINE PCLACON( N, V, IV, JV, DESCV, X, IX, JX, DESCX, EST, KASE )

           INTEGER         IV, IX, JV, JX, KASE, N

           REAL            EST

           INTEGER         DESCV( * ), DESCX( * )

           COMPLEX         V( * ), X( * )

PURPOSE

       PCLACON  estimates  the  1-norm  of  a  square,  complex  distributed  matrix  A.  Reverse
       communication is used for evaluating matrix-vector products. X and V are aligned with  the
       distributed  matrix  A, this information is implicitly contained within IV, IX, DESCV, and
       DESCX.

       Notes
       =====

       Each global data object is described by an associated  description  vector.   This  vector
       stores the information required to establish the mapping 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 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

       N       (global input) INTEGER
               The length of the distributed vectors V and X.  N >= 0.

       V       (local workspace) COMPLEX pointer into the local
               memory  to  an array of dimension LOCr(N+MOD(IV-1,MB_V)). On the final return, V =
               A*W, where EST = norm(V)/norm(W) (W is not returned).

       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.

       X       (local input/local output) COMPLEX pointer into the
               local memory to an array of dimension LOCr(N+MOD(IX-1,MB_X)). On  an  intermediate
               return,  X  should be overwritten by A * X,   if KASE=1, A' * X,  if KASE=2, where
               A' is the conjugate transpose of A, and PCLACON must be  re-called  with  all  the
               other parameters unchanged.

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

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

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

       EST     (global output) REAL
               An estimate (a lower bound) for norm(A).

       KASE    (local input/local output) INTEGER
               On the initial call to PCLACON, KASE should be 0.  On an intermediate return, KASE
               will be 1 or 2, indicating whether X should be overwritten by A * X  or  A'  *  X.
               On the final return from PCLACON, KASE will again be 0.

FURTHER DETAILS

       The  serial  version CLACON has been contributed by Nick Higham, University of Manchester.
       It was originally named SONEST, dated March 16, 1988.

       Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of a  real  or  complex
       matrix,  with  applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no.
       4, pp. 381-396, December 1988.