CLASR(l) ) CLASR(l)NAME
CLASR - perform the transformation A := P*A, when SIDE = 'L' or 'l' (
Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
where A is an m by n complex matrix and P is an orthogonal matrix,
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 performs the transformation A := P*A, when SIDE = 'L' or 'l' (
Left-hand side ) A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
where A is an m by n complex matrix and P is an orthogonal matrix, con‐
sisting of a sequence of plane rotations determined by the parameters
PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l' and z = n
when SIDE = 'R' or 'r' ):
When DIRECT = 'F' or 'f' ( Forward sequence ) then
P = P( z - 1 )*...*P( 2 )*P( 1 ),
and when DIRECT = 'B' or 'b' ( Backward sequence ) then
P = P( 1 )*P( 2 )*...*P( z - 1 ),
where P( k ) is a plane rotation matrix for the following planes:
when PIVOT = 'V' or 'v' ( Variable pivot ),
the plane ( k, k + 1 )
when PIVOT = 'T' or 't' ( Top pivot ),
the plane ( 1, k + 1 )
when PIVOT = 'B' or 'b' ( Bottom pivot ),
the plane ( k, z )
c( k ) and s( k ) must contain the cosine and sine that define the
matrix P( k ). The two by two plane rotation part of the matrix P( k
), R( k ), is assumed to be of the form
R( k ) = ( c( k ) s( k ) ).
( -s( k ) c( k ) )
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'
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 )
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)
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, S (input) REAL arrays, dimension (M-1) if SIDE = 'L'
(N-1) if SIDE = 'R' c(k) and s(k) contain the cosine and sine
that define the matrix P(k). The two by two plane rotation
part of the matrix P(k), R(k), is assumed to be of 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' if SIDE = 'L'.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
LAPACK version 3.0 15 June 2000 CLASR(l)
