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NAME

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

SYNOPSIS

       REAL FUNCTION PSLANGE( NORM, M, N, A, IA, JA, DESCA, WORK )

           CHARACTER NORM

           INTEGER   IA, JA, M, N

           INTEGER   DESCA( * )

           REAL      A( * ), WORK( * )

PURPOSE

       PSLANGE  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).

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

       A       (local input) REAL 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) REAL 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.