dlaev2.f (3) - Linux Man Pages
subroutine dlaev2 (double precisionA, double precisionB, double precisionC, double precisionRT1, double precisionRT2, double precisionCS1, double precisionSN1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
DLAEV2 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 ].
A is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
B is DOUBLE PRECISION The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
C is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.
RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value.
CS1 is DOUBLE PRECISION
SN1 is DOUBLE PRECISION 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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