CLASR(l)								 )								  CLASR(l)

NAME

       CLASR  -  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 complex matrix and P is an orthogonal matrix,

SYNOPSIS

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

	   CHARACTER	 DIRECT, PIVOT, SIDE

	   INTEGER	 LDA, M, N

	   REAL 	 C( * ), S( * )

	   COMPLEX	 A( LDA, * )

PURPOSE

       CLASR 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 complex 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 ) )

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)  REAL	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) COMPLEX 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 							  CLASR(l)