claev2.f (3) - Linux Manuals
subroutine claev2 (complexA, complexB, complexC, realRT1, realRT2, realCS1, complexSN1)
CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix [ A B ] [ CONJG(B) C ]. On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
A is COMPLEX The (1,1) element of the 2-by-2 matrix.
B is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
C is COMPLEX The (2,2) element of the 2-by-2 matrix.
RT1 is REAL The eigenvalue of larger absolute value.
RT2 is REAL The eigenvalue of smaller absolute value.
CS1 is REAL
SN1 is COMPLEX The vector (CS1, SN1) is a unit right eigenvector for RT1.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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.
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