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NAME

       PDLACON - estimate the 1-norm of a square, real distributed matrix A

SYNOPSIS

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

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

           DOUBLE          PRECISION EST

           INTEGER         DESCV( * ), DESCX( * ), ISGN( * )

           DOUBLE          PRECISION V( * ), X( * )

PURPOSE

       PDLACON estimates the 1-norm of a square, real  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) DOUBLE PRECISION 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) DOUBLE PRECISION 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, PDLACON 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.

       ISGN    (local workspace) INTEGER array, dimension
               LOCr(N+MOD(IX-1,MB_X)). ISGN is aligned with X and V.

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

       KASE    (local input/local output) INTEGER
               On  the  initial  call  to  PDLACON,  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 PDLACON, KASE will again be 0.

FURTHER DETAILS

       The  serial  version  DLACON  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.