DLAE2(1) LAPACK auxiliary routine (version 3.2) DLAE2(1)NAME
DLAE2 - computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ]
[ B C ]
SYNOPSIS
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 determi‐
nant A*C-B*B; higher precision or correctly rounded or correctly trun‐
cated 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.
LAPACK auxiliary routine (versioNovember 2008 DLAE2(1)
