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# clasr

```
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 consisting 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 rota-
tion 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).
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