slasr()

subroutine slasr	(	character	side,
		character	pivot,
		character	direct,
		integer	m,
		integer	n,
		real, dimension( * )	c,
		real, dimension( * )	s,
		real, dimension( lda, * )	a,
		integer	lda )

SLASR applies a sequence of plane rotations to a general rectangular matrix.

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Purpose:

!>
!> SLASR applies a sequence of plane rotations to a real matrix A,
!> from either the left or the right.
!>
!> When SIDE = 'L', the transformation takes the form
!>
!>    A := P*A
!>
!> and when SIDE = 'R', the transformation takes the form
!>
!>    A := A*P**T
!>
!> where P is an orthogonal matrix consisting of a sequence of z plane
!> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
!> and P**T is the transpose of P.
!>
!> When DIRECT = 'F' (Forward sequence), then
!>
!>    P = P(z-1) * ... * P(2) * P(1)
!>
!> and when DIRECT = 'B' (Backward sequence), then
!>
!>    P = P(1) * P(2) * ... * P(z-1)
!>
!> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
!>
!>    R(k) = (  c(k)  s(k) )
!>         = ( -s(k)  c(k) ).
!>
!> When PIVOT = 'V' (Variable pivot), the rotation is performed
!> for the plane (k,k+1), i.e., P(k) has the form
!>
!>    P(k) = (  1                                            )
!>           (       ...                                     )
!>           (              1                                )
!>           (                   c(k)  s(k)                  )
!>           (                  -s(k)  c(k)                  )
!>           (                                1              )
!>           (                                     ...       )
!>           (                                            1  )
!>
!> where R(k) appears as a rank-2 modification to the identity matrix in
!> rows and columns k and k+1.
!>
!> When PIVOT = 'T' (Top pivot), the rotation is performed for the
!> plane (1,k+1), so P(k) has the form
!>
!>    P(k) = (  c(k)                    s(k)                 )
!>           (         1                                     )
!>           (              ...                              )
!>           (                     1                         )
!>           ( -s(k)                    c(k)                 )
!>           (                                 1             )
!>           (                                      ...      )
!>           (                                             1 )
!>
!> where R(k) appears in rows and columns 1 and k+1.
!>
!> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
!> performed for the plane (k,z), giving P(k) the form
!>
!>    P(k) = ( 1                                             )
!>           (      ...                                      )
!>           (             1                                 )
!>           (                  c(k)                    s(k) )
!>           (                         1                     )
!>           (                              ...              )
!>           (                                     1         )
!>           (                 -s(k)                    c(k) )
!>
!> where R(k) appears in rows and columns k and z.  The rotations are
!> performed without ever forming P(k) explicitly.
!> 

Parameters

[in]	SIDE	!> SIDE is 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**T !>
[in]	PIVOT	!> PIVOT is 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) !>
[in]	DIRECT	!> DIRECT is 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) !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix A. If m <= 1, an immediate !> return is effected. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix A. If n <= 1, an !> immediate return is effected. !>
[in]	C	!> C is REAL array, dimension !> (M-1) if SIDE = 'L' !> (N-1) if SIDE = 'R' !> The cosines c(k) of the plane rotations. !>
[in]	S	!> S is REAL array, dimension !> (M-1) if SIDE = 'L' !> (N-1) if SIDE = 'R' !> The sines s(k) of the plane rotations. The 2-by-2 plane !> rotation part of the matrix P(k), R(k), has the form !> R(k) = ( c(k) s(k) ) !> ( -s(k) c(k) ). !>
[in,out]	A	!> A is 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**T if SIDE = 'L'. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.