LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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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*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f">
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