PZLASSQ(3) ScaLAPACK routine of NEC Numeric Library Collection PZLASSQ(3)
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 ( 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*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.
ScaLAPACK routine 31 October 2017 PZLASSQ(3)