1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
|
.TH SLANV2 l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
SLANV2 - compute the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form
.SH SYNOPSIS
.TP 19
SUBROUTINE SLANV2(
A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
.TP 19
.ti +4
REAL
A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
.SH PURPOSE
SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form:
[ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ]
.br
[ C D ] [ SN CS ] [ CC DD ] [-SN CS ]
.br
where either
.br
1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
conjugate eigenvalues.
.br
.SH ARGUMENTS
.TP 8
A (input/output) REAL
B (input/output) REAL
C (input/output) REAL
D (input/output) REAL
On entry, the elements of the input matrix.
On exit, they are overwritten by the elements of the
standardised Schur form.
.TP 8
RT1R (output) REAL
RT1I (output) REAL
RT2R (output) REAL
RT2I (output) REAL
The real and imaginary parts of the eigenvalues. If the
eigenvalues are a complex conjugate pair, RT1I > 0.
.TP 8
CS (output) REAL
SN (output) REAL
Parameters of the rotation matrix.
.SH FURTHER DETAILS
Modified by V. Sima, Research Institute for Informatics, Bucharest,
Romania, to reduce the risk of cancellation errors,
.br
when computing real eigenvalues, and to ensure, if possible, that
abs(RT1R) >= abs(RT2R).
.br
|
