SLASR(3)       LAPACK routine of NEC Numeric Library Collection       SLASR(3)



NAME
       SLASR

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



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.




ARGUMENTS
           SIDE      (input)
                     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     (input)
                     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    (input)
                     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         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  If m <= 1, an immediate
                     return is effected.

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

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

           S         (input)
                     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) ).

           A         (input/output)
                     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'.

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



LAPACK routine                  31 October 2017                       SLASR(3)