Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.1.1.1
1.1 bertrand 1: SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: DOUBLE PRECISION CS1, RT1, RT2
10: COMPLEX*16 A, B, C, SN1
11: * ..
12: *
13: * Purpose
14: * =======
15: *
16: * ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
17: * [ A B ]
18: * [ CONJG(B) C ].
19: * On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
20: * eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
21: * eigenvector for RT1, giving the decomposition
22: *
23: * [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
24: * [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
25: *
26: * Arguments
27: * =========
28: *
29: * A (input) COMPLEX*16
30: * The (1,1) element of the 2-by-2 matrix.
31: *
32: * B (input) COMPLEX*16
33: * The (1,2) element and the conjugate of the (2,1) element of
34: * the 2-by-2 matrix.
35: *
36: * C (input) COMPLEX*16
37: * The (2,2) element of the 2-by-2 matrix.
38: *
39: * RT1 (output) DOUBLE PRECISION
40: * The eigenvalue of larger absolute value.
41: *
42: * RT2 (output) DOUBLE PRECISION
43: * The eigenvalue of smaller absolute value.
44: *
45: * CS1 (output) DOUBLE PRECISION
46: * SN1 (output) COMPLEX*16
47: * The vector (CS1, SN1) is a unit right eigenvector for RT1.
48: *
49: * Further Details
50: * ===============
51: *
52: * RT1 is accurate to a few ulps barring over/underflow.
53: *
54: * RT2 may be inaccurate if there is massive cancellation in the
55: * determinant A*C-B*B; higher precision or correctly rounded or
56: * correctly truncated arithmetic would be needed to compute RT2
57: * accurately in all cases.
58: *
59: * CS1 and SN1 are accurate to a few ulps barring over/underflow.
60: *
61: * Overflow is possible only if RT1 is within a factor of 5 of overflow.
62: * Underflow is harmless if the input data is 0 or exceeds
63: * underflow_threshold / macheps.
64: *
65: * =====================================================================
66: *
67: * .. Parameters ..
68: DOUBLE PRECISION ZERO
69: PARAMETER ( ZERO = 0.0D0 )
70: DOUBLE PRECISION ONE
71: PARAMETER ( ONE = 1.0D0 )
72: * ..
73: * .. Local Scalars ..
74: DOUBLE PRECISION T
75: COMPLEX*16 W
76: * ..
77: * .. External Subroutines ..
78: EXTERNAL DLAEV2
79: * ..
80: * .. Intrinsic Functions ..
81: INTRINSIC ABS, DBLE, DCONJG
82: * ..
83: * .. Executable Statements ..
84: *
85: IF( ABS( B ).EQ.ZERO ) THEN
86: W = ONE
87: ELSE
88: W = DCONJG( B ) / ABS( B )
89: END IF
90: CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
91: SN1 = W*T
92: RETURN
93: *
94: * End of ZLAEV2
95: *
96: END
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