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, 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) con
tain 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).
Man(1) output converted with
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