1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
|
*> \brief \b CLAR2V
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* .. Scalar Arguments ..
* INTEGER INCC, INCX, N
* ..
* .. Array Arguments ..
* REAL C( * )
* COMPLEX S( * ), X( * ), Y( * ), Z( * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> CLAR2V applies a vector of complex plane rotations with real cosines
*> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
*> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
*>
*> ( x(i) z(i) ) :=
*> ( conjg(z(i)) y(i) )
*>
*> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
*> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of plane rotations to be applied.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*> X is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector x; the elements of x are assumed to be real.
*> \endverbatim
*>
*> \param[in,out] Y
*> \verbatim
*> Y is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector y; the elements of y are assumed to be real.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is COMPLEX array, dimension (1+(N-1)*INCX)
*> The vector z.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> The increment between elements of X, Y and Z. INCX > 0.
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is REAL array, dimension (1+(N-1)*INCC)
*> The cosines of the plane rotations.
*> \endverbatim
*>
*> \param[in] S
*> \verbatim
*> S is COMPLEX array, dimension (1+(N-1)*INCC)
*> The sines of the plane rotations.
*> \endverbatim
*>
*> \param[in] INCC
*> \verbatim
*> INCC is INTEGER
*> The increment between elements of C and S. INCC > 0.
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complexOTHERauxiliary
*
* =====================================================================
SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )
*
* -- LAPACK auxiliary routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INCC, INCX, N
* ..
* .. Array Arguments ..
REAL C( * )
COMPLEX S( * ), X( * ), Y( * ), Z( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, IC, IX
REAL CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
$ ZIR
COMPLEX SI, T2, T3, T4, ZI
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, CMPLX, CONJG, REAL
* ..
* .. Executable Statements ..
*
IX = 1
IC = 1
DO 10 I = 1, N
XI = REAL( X( IX ) )
YI = REAL( Y( IX ) )
ZI = Z( IX )
ZIR = REAL( ZI )
ZII = AIMAG( ZI )
CI = C( IC )
SI = S( IC )
SIR = REAL( SI )
SII = AIMAG( SI )
T1R = SIR*ZIR - SII*ZII
T1I = SIR*ZII + SII*ZIR
T2 = CI*ZI
T3 = T2 - CONJG( SI )*XI
T4 = CONJG( T2 ) + SI*YI
T5 = CI*XI + T1R
T6 = CI*YI - T1R
X( IX ) = CI*T5 + ( SIR*REAL( T4 )+SII*AIMAG( T4 ) )
Y( IX ) = CI*T6 - ( SIR*REAL( T3 )-SII*AIMAG( T3 ) )
Z( IX ) = CI*T3 + CONJG( SI )*CMPLX( T6, T1I )
IX = IX + INCX
IC = IC + INCC
10 CONTINUE
RETURN
*
* End of CLAR2V
*
END
|
