
SLASR(l) ) SLASR(l)
NAME
SLASR  perform the transformation A := P*A, when SIDE = 'L' or 'l' ( Lefthand side ) A
:= A*P', when SIDE = 'R' or 'r' ( Righthand side ) where A is an m by n real matrix and
P is an orthogonal matrix,
SYNOPSIS
SUBROUTINE SLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
CHARACTER DIRECT, PIVOT, SIDE
INTEGER LDA, M, N
REAL A( LDA, * ), C( * ), S( * )
PURPOSE
SLASR performs the transformation A := P*A, when SIDE = 'L' or 'l' ( Lefthand side ) A :=
A*P', when SIDE = 'R' or 'r' ( Righthand side ) where A is an m by n real matrix and P is
an orthogonal matrix, consisting of a sequence of plane rotations determined by the param
eters 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 ) )
This version vectorises across rows of the array A when SIDE = 'L'.
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 (M1) if SIDE = 'L' (N1) 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) REAL 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 SLASR(l) 
