CXML
        	    
LAPACK version 3.0
slasr(3)

PURPOSE
  SLASR - 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,

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

      CHARACTER	    DIRECT, PIVOT, SIDE

      INTEGER	    LDA, M, N

      REAL	    A( LDA, * ), C( * ), S( * )

DESCRIPTION
  SLASR 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) 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) REAL 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).