NAME

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

SYNOPSIS

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

           INTEGER         IX, INCX, JX, N

           REAL            SCALE, SUMSQ

           INTEGER         DESCX( * )

           REAL            X( * )

PURPOSE

       PSLASSQ  returns the values  scl  and  smsq  such that

       where  x( i ) = sub( X ) = X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ).  The value of sumsq is assumed to be non-
       negative and scl returns the value

          scl = max( scale, abs( x( 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  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

       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 available in this process row of the grid. Similarly if  sub(  X  )  is
       distributed  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) REAL
               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.