subroutine clasr (SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)
CLASR applies a sequence of plane rotations to a general rectangular matrix.
CLASR applies a sequence of plane rotations to a general rectangular matrix.
Purpose:
CLASR applies a sequence of real plane rotations to a complex matrix
A, from either the left or the right.
When SIDE = 'L', the transformation takes the form
A := P*A
and when SIDE = 'R', the transformation takes the form
A := A*P**T
where P is an orthogonal matrix consisting of a sequence of z plane
rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
and P**T is the transpose of P.
When DIRECT = 'F' (Forward sequence), then
P = P(z-1) * ... * P(2) * P(1)
and when DIRECT = 'B' (Backward sequence), then
P = P(1) * P(2) * ... * P(z-1)
where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
R(k) = ( c(k) s(k) )
= ( -s(k) c(k) ).
When PIVOT = 'V' (Variable pivot), the rotation is performed
for the plane (k,k+1), i.e., P(k) has the form
P(k) = ( 1 )
( ... )
( 1 )
( c(k) s(k) )
( -s(k) c(k) )
( 1 )
( ... )
( 1 )
where R(k) appears as a rank-2 modification to the identity matrix in
rows and columns k and k+1.
When PIVOT = 'T' (Top pivot), the rotation is performed for the
plane (1,k+1), so P(k) has the form
P(k) = ( c(k) s(k) )
( 1 )
( ... )
( 1 )
( -s(k) c(k) )
( 1 )
( ... )
( 1 )
where R(k) appears in rows and columns 1 and k+1.
Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
performed for the plane (k,z), giving P(k) the form
P(k) = ( 1 )
( ... )
( 1 )
( c(k) s(k) )
( 1 )
( ... )
( 1 )
( -s(k) c(k) )
where R(k) appears in rows and columns k and z. The rotations are
performed without ever forming P(k) explicitly.
Parameters:
SIDE is 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**T
PIVOT
PIVOT is 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)
DIRECT
DIRECT is 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)
M
M is INTEGER
The number of rows of the matrix A. If m <= 1, an immediate
return is effected.
N
N is INTEGER
The number of columns of the matrix A. If n <= 1, an
immediate return is effected.
C
C is REAL array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
The cosines c(k) of the plane rotations.
S
S is REAL array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
The sines s(k) of the plane rotations. The 2-by-2 plane
rotation part of the matrix P(k), R(k), has the form
R(k) = ( c(k) s(k) )
( -s(k) c(k) ).
A
A is 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**T if SIDE = 'L'.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 202 of file clasr.f.
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