SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. REAL CS1, RT1, RT2 COMPLEX A, B, C, SN1 * .. * * Purpose * ======= * * CLAEV2 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 ]. * * Arguments * ========= * * A (input) COMPLEX * The (1,1) element of the 2-by-2 matrix. * * B (input) COMPLEX * The (1,2) element and the conjugate of the (2,1) element of * the 2-by-2 matrix. * * C (input) COMPLEX * The (2,2) element 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) COMPLEX * 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. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) REAL ONE PARAMETER ( ONE = 1.0E0 ) * .. * .. Local Scalars .. REAL T COMPLEX W * .. * .. External Subroutines .. EXTERNAL SLAEV2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, REAL * .. * .. Executable Statements .. * IF( ABS( B ).EQ.ZERO ) THEN W = ONE ELSE W = CONJG( B ) / ABS( B ) END IF CALL SLAEV2( REAL( A ), ABS( B ), REAL( C ), RT1, RT2, CS1, T ) SN1 = W*T RETURN * * End of CLAEV2 * END