Purpose
=======
DLASR applies a sequence of plane rotations to a real 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.
Namespace: DotNumerics.LinearAlgebra.CSLapackAssembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax public void Run(
string SIDE,
string PIVOT,
string DIRECT,
int M,
int N,
double[] C,
int offset_c,
double[] S,
int offset_s,
ref double[] A,
int offset_a,
int LDA
)
Public Sub Run (
SIDE As String,
PIVOT As String,
DIRECT As String,
M As Integer,
N As Integer,
C As Double(),
offset_c As Integer,
S As Double(),
offset_s As Integer,
ByRef A As Double(),
offset_a As Integer,
LDA As Integer
)
Request Example
View SourceParameters
- SIDE String
-
(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**T
- PIVOT String
-
(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)
- DIRECT String
-
(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)
- M Int32
-
(input) INTEGER
The number of rows of the matrix A. If m .LE. 1, an immediate
return is effected.
- N Int32
-
(input) INTEGER
The number of columns of the matrix A. If n .LE. 1, an
immediate return is effected.
- C Double
-
(input) DOUBLE PRECISION array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
The cosines c(k) of the plane rotations.
- offset_c Int32
-
- S Double
-
(input) DOUBLE PRECISION 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) ).
- offset_s Int32
-
- A Double
-
:= P*A
- offset_a Int32
-
- LDA Int32
-
(input) INTEGER
The leading dimension of the array A. LDA .GE. max(1,M).
See Also