SUBROUTINE PDRSCL( N, SA, SX, IX, JX, DESCX, INCX )
*
* -- 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 SA
* ..
* .. Array Arguments ..
INTEGER DESCX( * )
DOUBLE PRECISION SX( * )
* ..
*
* Purpose
* =======
*
* PDRSCL multiplies an N-element real distributed vector sub( X ) by
* the real scalar 1/a. This is done without overflow or underflow as
* long as the final result sub( X )/a does not overflow or underflow.
*
* where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1,
* X(IX:IX,JX:JX+N-1), if INCX = M_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
* --------------- -------------- --------------------------------------
* DT_A (global) descA[ DT_ ] The descriptor type. In this case,
* DT_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 distribu-
* te the rows of the array.
* NB_A (global) descA[ NB_ ] The blocking factor used to distribu-
* te 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 seen as particular matrices, a distributed
* vector is considered to be a distributed matrix.
*
* Arguments
* =========
*
* N (global input) pointer to INTEGER
* The number of components of the distributed vector sub( X ).
* N >= 0.
*
* SA (global input) DOUBLE PRECISION
* The scalar a which is used to divide each component of
* sub( X ). SA must be >= 0, or the subroutine will divide by
* zero.
*
* SX (local input/local output) DOUBLE PRECISION array
* containing the local pieces of a distributed matrix of
* dimension of at least
* ( (JX-1)*M_X + IX + ( N - 1 )*abs( INCX ) )
* This array contains the entries of the distributed vector
* sub( X ).
*
* IX (global input) pointer to INTEGER
* The global row index of the submatrix of the distributed
* matrix X to operate on.
*
* JX (global input) pointer to INTEGER
* The global column index of the submatrix of the distributed
* matrix X to operate on.
*
* DESCX (global and local input) INTEGER array of dimension 8.
* The array descriptor of the distributed matrix X.
*
* INCX (global input) pointer to INTEGER
* The global increment for the elements of X. Only two values
* of INCX are supported in this version, namely 1 and M_X.
*
* =====================================================================
*
* .. 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 ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL DONE
INTEGER ICTXT, MYCOL, MYROW, NPCOL, NPROW
DOUBLE PRECISION BIGNUM, CDEN, CDEN1, CNUM, CNUM1, MUL, SMLNUM
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, PDLABAD, PDSCAL
* ..
* .. External Functions ..
DOUBLE PRECISION PDLAMCH
EXTERNAL PDLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCX( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Quick return if possible
*
IF( N.LE.0 )
$ RETURN
*
* Get machine parameters
*
SMLNUM = PDLAMCH( ICTXT, 'S' )
BIGNUM = ONE / SMLNUM
CALL PDLABAD( ICTXT, SMLNUM, BIGNUM )
*
* Initialize the denominator to SA and the numerator to 1.
*
CDEN = SA
CNUM = ONE
*
10 CONTINUE
CDEN1 = CDEN*SMLNUM
CNUM1 = CNUM / BIGNUM
IF( ABS( CDEN1 ).GT.ABS( CNUM ) .AND. CNUM.NE.ZERO ) THEN
*
* Pre-multiply sub( X ) by SMLNUM if CDEN is large compared to
* CNUM.
*
MUL = SMLNUM
DONE = .FALSE.
CDEN = CDEN1
ELSE IF( ABS( CNUM1 ).GT.ABS( CDEN ) ) THEN
*
* Pre-multiply sub( X ) by BIGNUM if CDEN is small compared to
* CNUM.
*
MUL = BIGNUM
DONE = .FALSE.
CNUM = CNUM1
ELSE
*
* Multiply sub( X ) by CNUM / CDEN and return.
*
MUL = CNUM / CDEN
DONE = .TRUE.
END IF
*
* Scale the vector sub( X ) by MUL
*
CALL PDSCAL( N, MUL, SX, IX, JX, DESCX, INCX )
*
IF( .NOT.DONE )
$ GO TO 10
*
RETURN
*
* End of PDRSCL
*
END