Annotation of rpl/lapack/lapack/zlaev2.f, revision 1.15
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: *
1.15 ! bertrand 98: *> \date December 2016
1.8 bertrand 99: *
100: *> \ingroup complex16OTHERauxiliary
101: *
102: *> \par Further Details:
103: * =====================
104: *>
105: *> \verbatim
106: *>
107: *> RT1 is accurate to a few ulps barring over/underflow.
108: *>
109: *> RT2 may be inaccurate if there is massive cancellation in the
110: *> determinant A*C-B*B; higher precision or correctly rounded or
111: *> correctly truncated arithmetic would be needed to compute RT2
112: *> accurately in all cases.
113: *>
114: *> CS1 and SN1 are accurate to a few ulps barring over/underflow.
115: *>
116: *> Overflow is possible only if RT1 is within a factor of 5 of overflow.
117: *> Underflow is harmless if the input data is 0 or exceeds
118: *> underflow_threshold / macheps.
119: *> \endverbatim
120: *>
121: * =====================================================================
1.1 bertrand 122: SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
123: *
1.15 ! bertrand 124: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 ! bertrand 127: * December 2016
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: DOUBLE PRECISION CS1, RT1, RT2
131: COMPLEX*16 A, B, C, SN1
132: * ..
133: *
134: * =====================================================================
135: *
136: * .. Parameters ..
137: DOUBLE PRECISION ZERO
138: PARAMETER ( ZERO = 0.0D0 )
139: DOUBLE PRECISION ONE
140: PARAMETER ( ONE = 1.0D0 )
141: * ..
142: * .. Local Scalars ..
143: DOUBLE PRECISION T
144: COMPLEX*16 W
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL DLAEV2
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC ABS, DBLE, DCONJG
151: * ..
152: * .. Executable Statements ..
153: *
154: IF( ABS( B ).EQ.ZERO ) THEN
155: W = ONE
156: ELSE
157: W = DCONJG( B ) / ABS( B )
158: END IF
159: CALL DLAEV2( DBLE( A ), ABS( B ), DBLE( C ), RT1, RT2, CS1, T )
160: SN1 = W*T
161: RETURN
162: *
163: * End of ZLAEV2
164: *
165: END
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