NAME

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

SYNOPSIS

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

           CHARACTER NORM

           INTEGER   IA, JA, N

           INTEGER   DESCA( * )

           REAL      A( * ), WORK( * )

PURPOSE

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

       PSLANHS 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 PSLANHS as described above.

       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, PSLANHS 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
               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 ),  Np0  =
               NUMROC(  N+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.