![]() |
LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
|
subroutine zlaev2 | ( | complex*16 | A, |
complex*16 | B, | ||
complex*16 | C, | ||
double precision | RT1, | ||
double precision | RT2, | ||
double precision | CS1, | ||
complex*16 | SN1 | ||
) |
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Download ZLAEV2 + dependencies [TGZ] [ZIP] [TXT]
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 ].
[in] | A | A is COMPLEX*16 The (1,1) element of the 2-by-2 matrix. |
[in] | B | B is COMPLEX*16 The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. |
[in] | C | C is COMPLEX*16 The (2,2) element of the 2-by-2 matrix. |
[out] | RT1 | RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value. |
[out] | RT2 | RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value. |
[out] | CS1 | CS1 is DOUBLE PRECISION |
[out] | SN1 | SN1 is COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1. |
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.
Definition at line 123 of file zlaev2.f.