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

SUBROUTINE PZLASSQ(

N, X, IX, JX, DESCX, INCX, SCALE, SUMSQ )

INTEGER IX, INCX, JX, N

DOUBLE PRECISION SCALE, SUMSQ

INTEGER DESCX( * )

COMPLEX*16 X( * )

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.

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.