PSLASSQ - return the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2
+...+ x( n )**2 + ( scale**2 )*sumsq,
- SUBROUTINE PSLASSQ(
- N, X, IX, JX, DESCX, INCX, SCALE, SUMSQ )
INTEGER IX, INCX, JX, N REAL SCALE, SUMSQ INTEGER DESCX( * ) REAL X( * )
PSLASSQ 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 ) = 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.
- 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.