LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
zlaev2.f
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1 *> \brief \b ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
22 *
23 * .. Scalar Arguments ..
24 * DOUBLE PRECISION CS1, RT1, RT2
25 * COMPLEX*16 A, B, C, SN1
26 * ..
27 *
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 *
93 *> \author Univ. of Tennessee
94 *> \author Univ. of California Berkeley
95 *> \author Univ. of Colorado Denver
96 *> \author NAG Ltd.
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 * =====================================================================
120  SUBROUTINE zlaev2( A, B, C, RT1, RT2, CS1, SN1 )
121 *
122 * -- LAPACK auxiliary routine --
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
subroutine dlaev2(A, B, C, RT1, RT2, CS1, SN1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Definition: dlaev2.f:120
subroutine zlaev2(A, B, C, RT1, RT2, CS1, SN1)
ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Definition: zlaev2.f:121