CLASR(3)

NAME
CLASR - a sequence of real plane rotations to a complex matrix A, from either the left or the right

SYNOPSIS

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

CHARACTER
    DIRECT, PIVOT, SIDE

INTEGER
    LDA, M, N

REAL
    C( * ), S( * )

COMPLEX
    A( LDA, * )

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

S       (input) 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) COMPLEX 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).