PDRSCL - multiplie an N-element real distributed vector sub( X ) by the real scalar 1/a

SUBROUTINE PDRSCL(

N, SA, SX, IX, JX, DESCX, INCX )

INTEGER IX, INCX, JX, N

DOUBLE PRECISION SA

INTEGER DESCX( * )

DOUBLE PRECISION SX( * )

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.

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.