Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.18
1.11 bertrand 1: *> \brief \b ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZLAEV2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaev2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * DOUBLE PRECISION CS1, RT1, RT2
25: * COMPLEX*16 A, B, C, SN1
26: * ..
1.15 bertrand 27: *
1.8 bertrand 28: *
29: *> \par Purpose:
30: * =============
31: *>
32: *> \verbatim
33: *>
34: *> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
35: *> [ A B ]
36: *> [ CONJG(B) C ].
37: *> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
38: *> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
39: *> eigenvector for RT1, giving the decomposition
40: *>
41: *> [ CS1 CONJG(SN1) ] [ A B ] [ CS1 -CONJG(SN1) ] = [ RT1 0 ]
42: *> [-SN1 CS1 ] [ CONJG(B) C ] [ SN1 CS1 ] [ 0 RT2 ].
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] A
49: *> \verbatim
50: *> A is COMPLEX*16
51: *> The (1,1) element of the 2-by-2 matrix.
52: *> \endverbatim
53: *>
54: *> \param[in] B
55: *> \verbatim
56: *> B is COMPLEX*16
57: *> The (1,2) element and the conjugate of the (2,1) element of
58: *> the 2-by-2 matrix.
59: *> \endverbatim
60: *>
61: *> \param[in] C
62: *> \verbatim
63: *> C is COMPLEX*16
64: *> The (2,2) element of the 2-by-2 matrix.
65: *> \endverbatim
66: *>
67: *> \param[out] RT1
68: *> \verbatim
69: *> RT1 is DOUBLE PRECISION
70: *> The eigenvalue of larger absolute value.
71: *> \endverbatim
72: *>
73: *> \param[out] RT2
74: *> \verbatim
75: *> RT2 is DOUBLE PRECISION
76: *> The eigenvalue of smaller absolute value.
77: *> \endverbatim
78: *>
79: *> \param[out] CS1
80: *> \verbatim
81: *> CS1 is DOUBLE PRECISION
82: *> \endverbatim
83: *>
84: *> \param[out] SN1
85: *> \verbatim
86: *> SN1 is COMPLEX*16
87: *> The vector (CS1, SN1) is a unit right eigenvector for RT1.
88: *> \endverbatim
89: *
90: * Authors:
91: * ========
92: *
1.15 bertrand 93: *> \author Univ. of Tennessee
94: *> \author Univ. of California Berkeley
95: *> \author Univ. of Colorado Denver
96: *> \author NAG Ltd.
1.8 bertrand 97: *
98: *> \ingroup complex16OTHERauxiliary
99: *
100: *> \par Further Details:
101: * =====================
102: *>
103: *> \verbatim
104: *>
105: *> RT1 is accurate to a few ulps barring over/underflow.
106: *>
107: *> RT2 may be inaccurate if there is massive cancellation in the
108: *> determinant A*C-B*B; higher precision or correctly rounded or
109: *> correctly truncated arithmetic would be needed to compute RT2
110: *> accurately in all cases.
111: *>
112: *> CS1 and SN1 are accurate to a few ulps barring over/underflow.
113: *>
114: *> Overflow is possible only if RT1 is within a factor of 5 of overflow.
115: *> Underflow is harmless if the input data is 0 or exceeds
116: *> underflow_threshold / macheps.
117: *> \endverbatim
118: *>
119: * =====================================================================
1.1 bertrand 120: SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
121: *
1.18 ! bertrand 122: * -- LAPACK auxiliary routine --
1.1 bertrand 123: * -- LAPACK is a software package provided by Univ. of Tennessee, --
124: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125: *
126: * .. Scalar Arguments ..
127: DOUBLE PRECISION CS1, RT1, RT2
128: COMPLEX*16 A, B, C, SN1
129: * ..
130: *
131: * =====================================================================
132: *
133: * .. Parameters ..
134: DOUBLE PRECISION ZERO
135: PARAMETER ( ZERO = 0.0D0 )
136: DOUBLE PRECISION ONE
137: PARAMETER ( ONE = 1.0D0 )
138: * ..
139: * .. Local Scalars ..
140: DOUBLE PRECISION T
141: COMPLEX*16 W
142: * ..
143: * .. External Subroutines ..
144: EXTERNAL DLAEV2
145: * ..
146: * .. Intrinsic Functions ..
147: INTRINSIC ABS, DBLE, DCONJG
148: * ..
149: * .. Executable Statements ..
150: *
151: IF( ABS( B ).EQ.ZERO ) THEN
152: W = ONE
153: ELSE
154: W = DCONJG( B ) / ABS( B )
155: END IF
156: CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
157: SN1 = W*T
158: RETURN
159: *
160: * End of ZLAEV2
161: *
162: END
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