PDROT(3) ScaLAPACK routine of NEC Numeric Library Collection PDROT(3)
NAME
PDROT - applies a planar rotation defined by CS and SN to the two dis-
tributed vectors sub(X) and sub(Y)
SYNOPSIS
SUBROUTINE PDROT( N, X, IX, JX, DESCX, INCX, Y, IY, JY, DESCY, INCY,
CS, SN, WORK, LWORK, INFO )
INTEGER N, IX, JX, INCX, IY, JY, INCY, LWORK, INFO
DOUBLE PRECISION CS, SN
INTEGER DESCX( * ), DESCY( * )
DOUBLE PRECISION X( * ), Y( * ), WORK( * )
PURPOSE
PDROT applies a planar rotation defined by CS and SN to the two dis-
tributed vectors sub(X) and sub(Y).
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
ARGUMENTS
N (global input) INTEGER
The number of elements to operate on when applying the planar
rotation to X and Y. N>=0.
X (local input/local output) DOUBLE PRECSION array of dimension
( (JX-1)*M_X + IX + ( N - 1 )*abs( INCX ) )
This array contains the entries of the distributed vector sub(
X ).
IX (global input) INTEGER
The global row index of the submatrix of the distributed matrix
X to operate on. If INCX = 1, then it is required that IX = IY.
1 <= IX <= M_X.
JX (global input) INTEGER
The global column index of the submatrix of the distributed
matrix X to operate on. If INCX = M_X, then it is required that
JX = JY. 1 <= IX <= N_X.
DESCX (global and local input) INTEGER array of dimension 9
The array descriptor of 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.
Moreover, it must hold that INCX = M_X if INCY = M_Y and that
INCX = 1 if INCY = 1.
Y (local input/local output) DOUBLE PRECSION array of dimension
( (JY-1)*M_Y + IY + ( N - 1 )*abs( INCY ) ) This array contains
the entries of the distributed vector sub( Y ).
IY (global input) INTEGER
The global row index of the submatrix of the distributed matrix
Y to operate on. If INCY = 1, then it is required that IY = IX.
1 <= IY <= M_Y.
JY (global input) INTEGER
The global column index of the submatrix of the distributed
matrix Y to operate on. If INCY = M_X, then it is required that
JY = JX. 1 <= JY <= N_Y.
DESCY (global and local input) INTEGER array of dimension 9
The array descriptor of the distributed matrix Y.
INCY (global input) INTEGER
The global increment for the elements of Y. Only two values of
INCY are supported in this version, namely 1 and M_Y.
Moreover, it must hold that INCY = M_Y if INCX = M_X and that
INCY = 1 if INCX = 1.
CS (global input) DOUBLE PRECISION
SN (global input) DOUBLE PRECISION
The parameters defining the properties of the planar rotation.
It must hold that 0 <= CS,SN <= 1 and that SN**2 + CS**2 = 1.
The latter is hardly checked in finite precision arithmetics.
WORK (local input) DOUBLE PRECISION array of dimension LWORK
Local workspace area.
LWORK (local input) INTEGER
The length of the workspace array WORK.
If INCX = 1 and INCY = 1, then LWORK = 2*MB_X
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the IWORK array, and no error
message related to LIWORK is issued by PXERBLA.
INFO (global output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
If the i-th argument is an array and the j-entry had an illegal
value, then INFO = -(i*100+j), if the i-th argument is a scalar
and had an illegal value, then INFO = -i.
Additional requirements
=======================
The following alignment requirements must hold:
(a) DESCX( MB_ ) = DESCY( MB_ ) and DESCX( NB_ ) = DESCY( NB_ )
(b) DESCX( RSRC_ ) = DESCY( RSRC_ )
(c) DESCX( CSRC_ ) = DESCY( CSRC_ )
ScaLAPACK routine 31 October 2017 PDROT(3)