SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) * * -- LAPACK auxiliary routine (version 3.2) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. DOUBLE PRECISION CS1, RT1, RT2 COMPLEX*16 A, B, C, SN1 * .. * * Purpose * ======= * * ZLAEV2 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*16 * The (1,1) element of the 2-by-2 matrix. * * B (input) COMPLEX*16 * The (1,2) element and the conjugate of the (2,1) element of * the 2-by-2 matrix. * * C (input) COMPLEX*16 * 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) COMPLEX*16 * 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 .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) * .. * .. Local Scalars .. DOUBLE PRECISION T COMPLEX*16 W * .. * .. External Subroutines .. EXTERNAL DLAEV2 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCONJG * .. * .. Executable Statements .. * IF( ABS( B ).EQ.ZERO ) THEN W = ONE ELSE W = DCONJG( B ) / ABS( B ) END IF CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T ) SN1 = W*T RETURN * * End of ZLAEV2 * END