PSLANGE(3)    ScaLAPACK routine of NEC Numeric Library Collection   PSLANGE(3)



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  dis-
       tributed 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  vec-
       tor.  This vector stores the information required to establish the map-
       ping 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 col-
       umn.
       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.



ScaLAPACK routine               31 October 2017                     PSLANGE(3)