subroutine zlaev2 (A, B, C, RT1, RT2, CS1, SN1)
subroutine zlaev2 (complex*16A, complex*16B, complex*16C, double precisionRT1, double precisionRT2, double precisionCS1, complex*16SN1)ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Purpose:
ZLAEV2 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*16 The (1,1) element of the 2-by-2 matrix.B
B is COMPLEX*16 The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.C
C is COMPLEX*16 The (2,2) element of the 2-by-2 matrix.RT1
RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.RT2
RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value.CS1
CS1 is DOUBLE PRECISIONSN1
SN1 is COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1.
Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.Date:
September 2012Further 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. 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.