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.