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NAME

       PCLANSY - return the value of the one norm, or the Frobenius norm,

SYNOPSIS

       REAL FUNCTION PCLANSY( NORM, UPLO, N, A, IA, JA, DESCA, WORK )

           CHARACTER NORM, UPLO

           INTEGER   IA, JA, N

           INTEGER   DESCA( * )

           REAL      WORK( * )

           COMPLEX   A( * )

PURPOSE

       PCLANSY   returns  the value of the one norm, or the Frobenius norm, or
       the infinity norm, or the element of largest absolute value of  a  real
       symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1).

       PCLANSY returns the value

          ( max(abs(A(i,j))),  NORM = ’M’ or ’m’ with IA <= i <= IA+N-1,
          (                                      and  JA <= j <= JA+N-1,
          (
          ( norm1( sub( A ) ), NORM = ’1’, ’O’ or ’o’
          (
          ( normI( sub( A ) ), NORM = ’I’ or ’i’
          (
          ( normF( sub( A ) ), NORM = ’F’, ’f’, ’E’ or ’e’

       where  norm1   denotes  the  one norm of a matrix (maximum column sum),
       normI denotes the  infinity norm  of a matrix  (maximum  row  sum)  and
       normF  denotes  the   Frobenius norm of a matrix (square root of sum of
       squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.

       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

       NORM    (global input) CHARACTER
               Specifies  the  value  to  be  returned in PCLANSY as described
               above.

       UPLO    (global input) CHARACTER
               Specifies whether the upper or lower  triangular  part  of  the
               symmetric  matrix  sub( A ) is to be referenced.  = ’U’:  Upper
               triangular part of sub( A ) is referenced,
               = ’L’:  Lower triangular part of sub( A ) is referenced.

       N       (global input) INTEGER
               The number of rows and columns to be operated on i.e the number
               of rows and columns of the distributed submatrix sub( A ). When
               N = 0, PCLANSY is set to zero. N >= 0.

       A       (local input) COMPLEX pointer into the local memory
               to an array of dimension (LLD_A, LOCc(JA+N-1))  containing  the
               local  pieces of the symmetric distributed matrix sub( A ).  If
               UPLO = ’U’, the leading N-by-N upper triangular part of sub(  A
               )  contains  the  upper  triangular  matrix which norm is to be
               computed, and the strictly lower triangular part of this matrix
               is  not  referenced.   If  UPLO = ’L’, the leading N-by-N lower
               triangular part of sub(  A  )  contains  the  lower  triangular
               matrix  which  norm  is  to be computed, and the strictly upper
               triangular part of sub( A ) is not referenced.

       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.

       WORK    (local workspace) REAL array dimension (LWORK)
               LWORK >= 0 if NORM = ’M’ or ’m’ (not referenced), 2*Nq0+Np0+LDW
               if NORM = ’1’, ’O’, ’o’, ’I’ or ’i’, where LDW is given by: IF(
               NPROW.NE.NPCOL          )          THEN          LDW          =
               MB_A*CEIL(CEIL(Np0/MB_A)/(LCM/NPROW))  ELSE LDW = 0 END IF 0 if
               NORM = ’F’, ’f’, ’E’ or ’e’ (not referenced),

               where LCM is the least common multiple of NPROW and NPCOL LCM =
               ILCM(  NPROW,  NPCOL  )  and CEIL denotes the ceiling operation
               (ICEIL).

               IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), IAROW =
               INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), IACOL = INDXG2P( JA,
               NB_A, MYCOL, CSRC_A, NPCOL ), Np0  =  NUMROC(  N+IROFFA,  MB_A,
               MYROW,  IAROW,  NPROW  ),  Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
               IACOL, NPCOL ),

               ICEIL, ILCM, INDXG2P and NUMROC are ScaLAPACK  tool  functions;
               MYROW,  MYCOL, NPROW and NPCOL can be determined by calling the
               subroutine BLACS_GRIDINFO.