Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - computes the eigendecomposition of a 2-by-2 symmetric matrix [ A B ] [ B C ]

**SYNOPSIS**

SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1

**PURPOSE**

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 ].

**ARGUMENTS**

A (input) DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix. B (input) DOUBLE PRECISION The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. C (input) DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix. RT1 (output) DOUBLE PRECISION The eigenvalue of larger absolute value. RT2 (output) DOUBLE PRECISION The eigenvalue of smaller absolute value. CS1 (output) DOUBLE PRECISION SN1 (output) DOUBLE PRECISION 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. LAPACK auxiliary routine (version 3.2) April 2011 DLAEV2(3lapack)