Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  applies a sequence of real plane rotations to a complex matrix A, from either
       the left or the right

SYNOPSIS

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

           CHARACTER     DIRECT, PIVOT, SIDE

           INTEGER       LDA, M, N

           DOUBLE        PRECISION C( * ), S( * )

           COMPLEX*16    A( LDA, * )

PURPOSE

       ZLASR applies a sequence of real plane rotations to a complex 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) 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) 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) 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) INTEGER
                The number of rows of the matrix A.  If m <= 1, an immediate
                return is effected.

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

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

        S       (input) 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       (input/output) COMPLEX*16 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) INTEGER
                The leading dimension of the array A.  LDA >= max(1,M).

 LAPACK auxiliary routine (version 3.2)     April 2011                             ZLASR(3lapack)