PZLACON(3)    ScaLAPACK routine of NEC Numeric Library Collection   PZLACON(3)



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

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

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

           DOUBLE          PRECISION EST

           INTEGER         DESCV( * ), DESCX( * )

           COMPLEX*16      V( * ), X( * )

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

       V       (local workspace) COMPLEX*16 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*16 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 trans-
               pose of A, and PZLACON 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) DOUBLE PRECISION
               An estimate (a lower bound) for norm(A).

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

FURTHER DETAILS
       The serial version ZLACON has been contributed by Nick Higham,  Univer-
       sity  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.




ScaLAPACK routine               31 October 2017                     PZLACON(3)