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NAME SLAEV2 - compute the eigendecomposition of a 2-by-2 sym- metric matrix [ A B ] [ B C ] SYNOPSIS SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) REAL A, B, C, CS1, RT1, RT2, SN1 PURPOSE 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 ]. ARGUMENTS A (input) REAL The (1,1) entry of the 2-by-2 matrix. B (input) REAL The (1,2) entry and the conjugate of the (2,1) entry of the 2-by-2 matrix. C (input) REAL The (2,2) entry of the 2-by-2 matrix. RT1 (output) REAL The eigenvalue of larger absolute value. RT2 (output) REAL The eigenvalue of smaller absolute value. CS1 (output) REAL SN1 (output) REAL The vector (CS1, SN1) is a unit right eigenvector for RT1. FURTHER 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.