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



NAME
       PZLAUUM  -  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 PZLAUUM( UPLO, N, A, IA, JA, DESCA )

           CHARACTER       UPLO

           INTEGER         IA, JA, N

           INTEGER         DESCA( * )

           COMPLEX*16      A( * )

PURPOSE
       PZLAUUM  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  dis-
               tributed 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*16 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 routine               31 October 2017                     PZLAUUM(3)