SRC/dlasr.f(3)             Library Functions Manual             SRC/dlasr.f(3)

NAME
       SRC/dlasr.f

SYNOPSIS
   Functions/Subroutines
       subroutine dlasr (side, pivot, direct, m, n, c, s, a, lda)
           DLASR applies a sequence of plane rotations to a general
           rectangular matrix.

Function/Subroutine Documentation
   subroutine dlasr (character side, character pivot, character direct,
       integer m, integer n, double precision, dimension( * ) c, double
       precision, dimension( * ) s, double precision, dimension( lda, * ) a,
       integer lda)
       DLASR applies a sequence of plane rotations to a general rectangular
       matrix.

       Purpose:


            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.

       Parameters
           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).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 198 of file dlasr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                  SRC/dlasr.f(3)