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,

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, * )

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, 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 ) )

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).