00001 SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) 00002 * 00003 * -- LAPACK auxiliary routine (version 3.2) -- 00004 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00005 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00006 * November 2006 00007 * 00008 * .. Scalar Arguments .. 00009 DOUBLE PRECISION CS1, RT1, RT2 00010 COMPLEX*16 A, B, C, SN1 00011 * .. 00012 * 00013 * Purpose 00014 * ======= 00015 * 00016 * ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix 00017 * [ A B ] 00018 * [ CONJG(B) C ]. 00019 * On return, RT1 is the eigenvalue of larger absolute value, RT2 is the 00020 * eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right 00021 * eigenvector for RT1, giving the decomposition 00022 * 00023 * [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ] 00024 * [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ]. 00025 * 00026 * Arguments 00027 * ========= 00028 * 00029 * A (input) COMPLEX*16 00030 * The (1,1) element of the 2-by-2 matrix. 00031 * 00032 * B (input) COMPLEX*16 00033 * The (1,2) element and the conjugate of the (2,1) element of 00034 * the 2-by-2 matrix. 00035 * 00036 * C (input) COMPLEX*16 00037 * The (2,2) element of the 2-by-2 matrix. 00038 * 00039 * RT1 (output) DOUBLE PRECISION 00040 * The eigenvalue of larger absolute value. 00041 * 00042 * RT2 (output) DOUBLE PRECISION 00043 * The eigenvalue of smaller absolute value. 00044 * 00045 * CS1 (output) DOUBLE PRECISION 00046 * SN1 (output) COMPLEX*16 00047 * The vector (CS1, SN1) is a unit right eigenvector for RT1. 00048 * 00049 * Further Details 00050 * =============== 00051 * 00052 * RT1 is accurate to a few ulps barring over/underflow. 00053 * 00054 * RT2 may be inaccurate if there is massive cancellation in the 00055 * determinant A*C-B*B; higher precision or correctly rounded or 00056 * correctly truncated arithmetic would be needed to compute RT2 00057 * accurately in all cases. 00058 * 00059 * CS1 and SN1 are accurate to a few ulps barring over/underflow. 00060 * 00061 * Overflow is possible only if RT1 is within a factor of 5 of overflow. 00062 * Underflow is harmless if the input data is 0 or exceeds 00063 * underflow_threshold / macheps. 00064 * 00065 * ===================================================================== 00066 * 00067 * .. Parameters .. 00068 DOUBLE PRECISION ZERO 00069 PARAMETER ( ZERO = 0.0D0 ) 00070 DOUBLE PRECISION ONE 00071 PARAMETER ( ONE = 1.0D0 ) 00072 * .. 00073 * .. Local Scalars .. 00074 DOUBLE PRECISION T 00075 COMPLEX*16 W 00076 * .. 00077 * .. External Subroutines .. 00078 EXTERNAL DLAEV2 00079 * .. 00080 * .. Intrinsic Functions .. 00081 INTRINSIC ABS, DBLE, DCONJG 00082 * .. 00083 * .. Executable Statements .. 00084 * 00085 IF( ABS( B ).EQ.ZERO ) THEN 00086 W = ONE 00087 ELSE 00088 W = DCONJG( B ) / ABS( B ) 00089 END IF 00090 CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T ) 00091 SN1 = W*T 00092 RETURN 00093 * 00094 * End of ZLAEV2 00095 * 00096 END
1.7.2