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



NAME
       PCLASSQ  -  return the values scl and smsq such that  ( scl**2 )*smsq =
       x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,

SYNOPSIS
       SUBROUTINE PCLASSQ( N, X, IX, JX, DESCX, INCX, SCALE, SUMSQ )

           INTEGER         IX, INCX, JX, N

           REAL            SCALE, SUMSQ

           INTEGER         DESCX( * )

           COMPLEX         X( * )

PURPOSE
       PCLASSQ returns the values scl and smsq such that ( scl**2 )*smsq =  x(
       1  )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, where x( i ) = sub( X ) =
       abs( X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ) ).   The  value  of  sumsq  is
       assumed to be at least unity and the value of ssq will then satisfy

          1.0 .le. ssq .le. ( sumsq + 2*n ).

       scale is assumed to be non-negative and scl returns the value

          scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
                 i

       scale  and  sumsq  must  be  supplied  in SCALE and SUMSQ respectively.
       SCALE and SUMSQ are overwritten by scl and ssq respectively.

       The routine makes only one pass through the vector sub( X ).


       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

       Because vectors may be viewed as a subclass of matrices, a  distributed
       vector is considered to be a distributed matrix.

       The result are only available in the scope of sub( X ), i.e if sub( X )
       is distributed along a process row, the correct results are only avail-
       able  in  this  process  row of the grid. Similarly if sub( X ) is dis-
       tributed along a process column, the correct results are only available
       in this process column of the grid.


ARGUMENTS
       N       (global input) INTEGER
               The length of the distributed vector sub( X ).

       X       (input) COMPLEX
               The vector for which a scaled sum of squares is computed.  x( i
               )  = X(IX+(JX-1)*M_X +(i-1)*INCX ), 1 <= i <= n.

       IX      (global input) INTEGER
               The row index in the global array X indicating the first row of
               sub( X ).

       JX      (global input) INTEGER
               The  column  index  in  the global array X indicating the first
               column of sub( X ).

       DESCX   (global and local input) INTEGER array of dimension DLEN_.
               The array descriptor for the distributed matrix X.

       INCX    (global input) INTEGER
               The global increment for the elements of X. Only two values  of
               INCX  are  supported  in  this version, namely 1 and M_X.  INCX
               must not be zero.

       SCALE   (local input/local output) REAL
               On entry, the value  scale  in the equation  above.   On  exit,
               SCALE is overwritten with  scl , the scaling factor for the sum
               of squares.

       SUMSQ   (local input/local output) REAL
               On entry, the value  sumsq  in the equation  above.   On  exit,
               SUMSQ is overwritten with  smsq , the basic sum of squares from
               which  scl  has been factored out.



ScaLAPACK routine               31 October 2017                     PCLASSQ(3)