SUBROUTINE PDLASSQ( N, X, IX, JX, DESCX, INCX, SCALE, SUMSQ )
*
* -- ScaLAPACK auxiliary routine (version 1.5) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IX, INCX, JX, N
DOUBLE PRECISION SCALE, SUMSQ
* ..
* .. Array Arguments ..
INTEGER DESCX( * )
DOUBLE PRECISION X( * )
* ..
*
* Purpose
* =======
*
* PDLASSQ 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.
*
* Arguments
* =========
*
* N (global input) INTEGER
* The length of the distributed vector sub( X ).
*
* X (input) DOUBLE PRECISION
* 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.
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, ICOFF, ICTXT, IIX, IOFF, IROFF, IXCOL,
$ IXROW, JJX, LDX, MYCOL, MYROW, NP, NPCOL,
$ NPROW, NQ
DOUBLE PRECISION TEMP1
* ..
* .. Local Arrays ..
DOUBLE PRECISION WORK( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DCOMBSSQ, INFOG2L, PDTREECOMB
* ..
* .. External Functions ..
INTEGER NUMROC
EXTERNAL NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters.
*
ICTXT = DESCX( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Figure local indexes
*
CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, IIX, JJX,
$ IXROW, IXCOL )
*
LDX = DESCX( LLD_ )
IF( INCX.EQ.DESCX( M_ ) ) THEN
*
* X is rowwise distributed.
*
IF( MYROW.NE.IXROW )
$ RETURN
ICOFF = MOD( JX, DESCX( NB_ ) )
NQ = NUMROC( N+ICOFF, DESCX( NB_ ), MYCOL, IXCOL, NPCOL )
IF( MYCOL.EQ.IXCOL )
$ NQ = NQ - ICOFF
*
* Code direct from LAPACK's DLASSQ, (save subroutine call)
*
IF( NQ.GT.0 ) THEN
IOFF = IIX + ( JJX - 1 ) * LDX
DO 10 I = 1, NQ
IF( X( IOFF ).NE.ZERO ) THEN
TEMP1 = ABS( X( IOFF ) )
IF( SCALE.LT.TEMP1 ) THEN
SUMSQ = 1 + SUMSQ * ( SCALE / TEMP1 )**2
SCALE = TEMP1
ELSE
SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2
END IF
END IF
IOFF = IOFF + LDX
10 CONTINUE
END IF
*
* Take local result and find global
*
WORK( 1 ) = SCALE
WORK( 2 ) = SUMSQ
*
CALL PDTREECOMB( ICTXT, 'Rowwise', 2, WORK, -1, IXCOL,
$ DCOMBSSQ )
*
SCALE = WORK( 1 )
SUMSQ = WORK( 2 )
*
ELSE IF( INCX.EQ.1 ) THEN
*
* X is columnwise distributed.
*
IF( MYCOL.NE.IXCOL )
$ RETURN
IROFF = MOD( IX, DESCX( MB_ ) )
NP = NUMROC( N+IROFF, DESCX( MB_ ), MYROW, IXROW, NPROW )
IF( MYROW.EQ.IXROW )
$ NP = NP - IROFF
*
* Code direct from LAPACK's DLASSQ, (save subroutine call)
*
IF( NP.GT.0 ) THEN
IOFF = IIX + ( JJX - 1 ) * LDX
DO 20 I = 1, NP
IF( X( IOFF ).NE.ZERO ) THEN
TEMP1 = ABS( X( IOFF ) )
IF( SCALE.LT.TEMP1 ) THEN
SUMSQ = 1 + SUMSQ*( SCALE / TEMP1 )**2
SCALE = TEMP1
ELSE
SUMSQ = SUMSQ + ( TEMP1 / SCALE )**2
END IF
END IF
IOFF = IOFF + 1
20 CONTINUE
END IF
*
* Take local result and find global
*
WORK( 1 ) = SCALE
WORK( 2 ) = SUMSQ
*
CALL PDTREECOMB( ICTXT, 'Columnwise', 2, WORK, -1, IXCOL,
$ DCOMBSSQ )
*
SCALE = WORK( 1 )
SUMSQ = WORK( 2 )
*
END IF
*
RETURN
*
* End of PDLASSQ
*
END