Computes the eigenvalues of a 2-by-2 symmetric matrix.
Include Files
The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).
Description
The routines sla2/dlae2 compute the eigenvalues of a 2-by-2 symmetric matrix
On return, rt1 is the eigenvalue of larger absolute value, and rt1 is the eigenvalue of smaller absolute value.
Input Parameters
- a, b, c
REAL for slae2
DOUBLE PRECISION for dlae2
The elements a, b, and c of the 2-by-2 matrix above.
Output Parameters
- rt1, rt2
REAL for slae2
DOUBLE PRECISION for dlae2
The computed eigenvalues of larger and smaller absolute value, respectively.
Application Notes
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.