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NAME

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

SYNOPSIS

       DOUBLE PRECISION FUNCTION PDLANGE( NORM, M, N, A, IA, JA, DESCA, WORK )

           CHARACTER    NORM

           INTEGER      IA, JA, M, N

           INTEGER      DESCA( * )

           DOUBLE       PRECISION A( * ), WORK( * )

PURPOSE

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

       PDLANGE returns the value

          ( max(abs(A(i,j))),  NORM = ’M’ or ’m’ with IA <= i <= IA+M-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  PDLANGE  as  described
               above.

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

       N       (global input) INTEGER
               The  number  of  columns  to  be  operated on i.e the number of
               columns of the distributed submatrix sub( A  ).  When  N  =  0,
               PDLANGE 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 distributed matrix sub( A ).

       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), Nq0 if NORM
               =  ’1’,  ’O’ or ’o’, Mp0 if NORM = ’I’ or ’i’, 0 if NORM = ’F’,
               ’f’, ’E’ or ’e’ (not referenced), where

               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 ), Mp0  =  NUMROC(  M+IROFFA,  MB_A,
               MYROW,  IAROW,  NPROW  ),  Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL,
               IACOL, NPCOL ),

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