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



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  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
       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 com-
               puted, and the strictly lower triangular part of this matrix is
               not referenced.  If UPLO = 'L', the leading N-by-N lower trian-
               gular  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.



ScaLAPACK routine               31 October 2017                     PCLANSY(3)