NAME

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

SYNOPSIS

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

           INTEGER         IX, INCX, JX, N

           DOUBLE          PRECISION SCALE, SUMSQ

           INTEGER         DESCX( * )

           COMPLEX*16      X( * )

PURPOSE

       PZLASSQ  returns the values  scl  and  smsq  such that

       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  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) COMPLEX*16
               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) DOUBLE PRECISION
               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) DOUBLE PRECISION
               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.