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
|
.TH DLAE2 l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
DLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
.SH SYNOPSIS
.TP 18
SUBROUTINE DLAE2(
A, B, C, RT1, RT2 )
.TP 18
.ti +4
DOUBLE
PRECISION A, B, C, RT1, RT2
.SH PURPOSE
DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]. On return, RT1 is the eigenvalue of larger absolute value, and RT2
is the eigenvalue of smaller absolute value.
.br
.SH ARGUMENTS
.TP 8
A (input) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
.TP 8
B (input) DOUBLE PRECISION
The (1,2) and (2,1) elements of the 2-by-2 matrix.
.TP 8
C (input) DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.
.TP 8
RT1 (output) DOUBLE PRECISION
The eigenvalue of larger absolute value.
.TP 8
RT2 (output) DOUBLE PRECISION
The eigenvalue of smaller absolute value.
.SH FURTHER DETAILS
RT1 is accurate to a few ulps barring over/underflow.
.br
RT2 may be inaccurate if there is massive cancellation in the
determinant A*C-B*B; higher precision or correctly rounded or
correctly truncated arithmetic would be needed to compute RT2
accurately in all cases.
.br
Overflow is possible only if RT1 is within a factor of 5 of overflow.
Underflow is harmless if the input data is 0 or exceeds
.br
underflow_threshold / macheps.
.br
|
