DLASR(3F)DLASR(3F)NAME
DLASR - 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 real matrix and P is an orthogonal matrix,
SYNOPSIS
SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
CHARACTER DIRECT, PIVOT, SIDE
INTEGER LDA, M, N
DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
PURPOSE
DLASR 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 ) )
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
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DLASR(3F)DLASR(3F)
= '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) DOUBLE PRECISION 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) DOUBLE PRECISION 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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