CLASR(1) LAPACK auxiliary routine (version 3.2) CLASR(1)NAME
CLASR - applies 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 per‐
formed 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).
LAPACK auxiliary routine (versioNovember 2008 CLASR(1)
