Man Linux: Main Page and Category List

NAME

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

SYNOPSIS

       DOUBLE PRECISION FUNCTION  PDLANSY(  NORM,  UPLO,  N, A, IA, JA, DESCA,
                        WORK )

           CHARACTER    NORM, UPLO

           INTEGER      IA, JA, N

           INTEGER      DESCA( * )

           DOUBLE       PRECISION A( * ), WORK( * )

PURPOSE

       PDLANSY  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).

       PDLANSY 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  PDLANSY  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, PDLANSY is set to zero. N >= 0.

       A       (local input) DOUBLE PRECISION 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) DOUBLE PRECISION 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.