LASR - 5.2 English - 68552

 LASR 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.