dlae23lapack
Computes the eigenvalues of a 2-by-2 symmetric matrix [ a b ] [ b c ]
Usage
- SUBROUTINE DLAE2(
-
A, B, C, RT1, RT2 )
- DOUBLE
-
PRECISION A, B, C, RT1, RT2
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.
Arguments
A (input) DOUBLE PRECISION
|
The (1,1) element of the 2-by-2 matrix. |
|---|---|
B (input) DOUBLE PRECISION
|
The (1,2) and (2,1) elements of the 2-by-2 matrix. |
C (input) DOUBLE PRECISION
|
The (2,2) element of the 2-by-2 matrix. |
RT1 (output) DOUBLE PRECISION
|
The eigenvalue of larger absolute value. |
RT2 (output) DOUBLE PRECISION
|
The eigenvalue of smaller absolute value. |
Further details
RT1 is accurate to a few ulps barring over/underflow.
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.
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
underflow_threshold / macheps.