DLASR(l)								 )								  DLASR(l)

NAME

       DLASR  -  perform  the  transformation  A := P*A, when SIDE = 'L' or 'l' ( Left-hand side )  A := A*P', when SIDE = 'R' or 'r' ( Right-hand
       side )  where A is an m by n real matrix and P is an orthogonal matrix,

SYNOPSIS

       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )

	   CHARACTER	 DIRECT, PIVOT, SIDE

	   INTEGER	 LDA, M, N

	   DOUBLE	 PRECISION A( LDA, * ), C( * ), S( * )

PURPOSE

       DLASR performs the transformation A := P*A, when SIDE = 'L' or 'l' ( Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
       where  A  is  an m by n real matrix and P is an orthogonal matrix, consisting of a sequence of plane rotations determined by the parameters
       PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' and z = n when SIDE = 'R' or 'r' ):

       When  DIRECT = 'F' or 'f'  ( Forward sequence ) then

	  P = P( z - 1 )*...*P( 2 )*P( 1 ),

       and when DIRECT = 'B' or 'b'  ( Backward sequence ) then

	  P = P( 1 )*P( 2 )*...*P( z - 1 ),

       where  P( k ) is a plane rotation matrix for the following planes:

	  when	PIVOT = 'V' or 'v'  ( Variable pivot ),
	     the plane ( k, k + 1 )

	  when	PIVOT = 'T' or 't'  ( Top pivot ),
	     the plane ( 1, k + 1 )

	  when	PIVOT = 'B' or 'b'  ( Bottom pivot ),
	     the plane ( k, z )

       c( k ) and s( k )  must contain the  cosine and sine that define the matrix  P( k ).  The two by two plane rotation part of the matrix P( k
       ), R( k ), is assumed to be of the form

	  R( k ) = (  c( k )  s( k ) ).
		   ( -s( k )  c( k ) )

       This version vectorises across rows of the array A when SIDE = 'L'.

ARGUMENTS

       SIDE    (input) CHARACTER*1
	       Specifies whether the plane rotation matrix P is applied to A on the left or the right.	= 'L':	Left, compute A := P*A
	       = 'R':  Right, compute A:= A*P'

       DIRECT  (input) CHARACTER*1
	       Specifies whether P is a forward or backward sequence of plane rotations.  = 'F':  Forward, P = P( z - 1 )*...*P( 2 )*P( 1 )
	       = 'B':  Backward, P = P( 1 )*P( 2 )*...*P( z - 1 )

       PIVOT   (input) CHARACTER*1
	       Specifies the plane for which P(k) is a plane rotation matrix.  = 'V':  Variable pivot, the plane (k,k+1)
	       = 'T':  Top pivot, the plane (1,k+1)
	       = 'B':  Bottom pivot, the plane (k,z)

       M       (input) INTEGER
	       The number of rows of the matrix A.  If m <= 1, an immediate return is effected.

       N       (input) INTEGER
	       The number of columns of the matrix A.  If n <= 1, an immediate return is effected.

	       C,  S	 (input)  DOUBLE  PRECISION arrays, dimension (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' c(k) and s(k) contain the cosine and
	       sine that define the matrix P(k).  The two by two plane rotation part of the matrix P(k), R(k), is assumed to be of the form R( k )
	       = (  c( k )  s( k ) ).  ( -s( k )  c( k ) )

       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	       The m by n matrix A.  On exit, A is overwritten by P*A if SIDE = 'R' or by A*P' if SIDE = 'L'.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,M).

LAPACK version 3.0						   15 June 2000 							  DLASR(l)