LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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subroutine slaev2 | ( | real | A, |
real | B, | ||
real | C, | ||
real | RT1, | ||
real | RT2, | ||
real | CS1, | ||
real | SN1 | ||
) |
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
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SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ 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 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ].
[in] | A | A is REAL The (1,1) element of the 2-by-2 matrix. |
[in] | B | B is REAL The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. |
[in] | C | C is REAL The (2,2) element of the 2-by-2 matrix. |
[out] | RT1 | RT1 is REAL The eigenvalue of larger absolute value. |
[out] | RT2 | RT2 is REAL The eigenvalue of smaller absolute value. |
[out] | CS1 | CS1 is REAL |
[out] | SN1 | SN1 is REAL 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 122 of file slaev2.f.