!>
!> DLASR 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.
!> 

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
!> 

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)
!> 

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)
!> 

M

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

N

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

C

!>          C is DOUBLE PRECISION array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The cosines c(k) of the plane rotations.
!> 

S

!>          S is DOUBLE PRECISION 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) ).
!> 

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The M-by-N matrix A.  On exit, A is overwritten by P*A if
!>          SIDE = 'L' or by A*P**T if SIDE = 'R'.
!> 

LDA

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

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