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)