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## 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.

Download SLASR + dependencies [TGZ] [ZIP] [TXT]

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.