Annotation of rpl/lapack/lapack/zlar2v.f, revision 1.17
1.11 bertrand 1: *> \brief \b ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
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 ZLAR2V + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlar2v.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlar2v.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlar2v.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INCC, INCX, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION C( * )
28: * COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
29: * ..
1.15 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZLAR2V applies a vector of complex plane rotations with real cosines
38: *> from both sides to a sequence of 2-by-2 complex Hermitian matrices,
39: *> defined by the elements of the vectors x, y and z. For i = 1,2,...,n
40: *>
41: *> ( x(i) z(i) ) :=
42: *> ( conjg(z(i)) y(i) )
43: *>
44: *> ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
45: *> ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
46: *> \endverbatim
47: *
48: * Arguments:
49: * ==========
50: *
51: *> \param[in] N
52: *> \verbatim
53: *> N is INTEGER
54: *> The number of plane rotations to be applied.
55: *> \endverbatim
56: *>
57: *> \param[in,out] X
58: *> \verbatim
59: *> X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
60: *> The vector x; the elements of x are assumed to be real.
61: *> \endverbatim
62: *>
63: *> \param[in,out] Y
64: *> \verbatim
65: *> Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
66: *> The vector y; the elements of y are assumed to be real.
67: *> \endverbatim
68: *>
69: *> \param[in,out] Z
70: *> \verbatim
71: *> Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
72: *> The vector z.
73: *> \endverbatim
74: *>
75: *> \param[in] INCX
76: *> \verbatim
77: *> INCX is INTEGER
78: *> The increment between elements of X, Y and Z. INCX > 0.
79: *> \endverbatim
80: *>
81: *> \param[in] C
82: *> \verbatim
83: *> C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
84: *> The cosines of the plane rotations.
85: *> \endverbatim
86: *>
87: *> \param[in] S
88: *> \verbatim
89: *> S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
90: *> The sines of the plane rotations.
91: *> \endverbatim
92: *>
93: *> \param[in] INCC
94: *> \verbatim
95: *> INCC is INTEGER
96: *> The increment between elements of C and S. INCC > 0.
97: *> \endverbatim
98: *
99: * Authors:
100: * ========
101: *
1.15 bertrand 102: *> \author Univ. of Tennessee
103: *> \author Univ. of California Berkeley
104: *> \author Univ. of Colorado Denver
105: *> \author NAG Ltd.
1.8 bertrand 106: *
1.15 bertrand 107: *> \date December 2016
1.8 bertrand 108: *
109: *> \ingroup complex16OTHERauxiliary
110: *
111: * =====================================================================
1.1 bertrand 112: SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
113: *
1.15 bertrand 114: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 115: * -- LAPACK is a software package provided by Univ. of Tennessee, --
116: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 117: * December 2016
1.1 bertrand 118: *
119: * .. Scalar Arguments ..
120: INTEGER INCC, INCX, N
121: * ..
122: * .. Array Arguments ..
123: DOUBLE PRECISION C( * )
124: COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
125: * ..
126: *
127: * =====================================================================
128: *
129: * .. Local Scalars ..
130: INTEGER I, IC, IX
131: DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
132: $ ZIR
133: COMPLEX*16 SI, T2, T3, T4, ZI
134: * ..
135: * .. Intrinsic Functions ..
136: INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG
137: * ..
138: * .. Executable Statements ..
139: *
140: IX = 1
141: IC = 1
142: DO 10 I = 1, N
143: XI = DBLE( X( IX ) )
144: YI = DBLE( Y( IX ) )
145: ZI = Z( IX )
146: ZIR = DBLE( ZI )
147: ZII = DIMAG( ZI )
148: CI = C( IC )
149: SI = S( IC )
150: SIR = DBLE( SI )
151: SII = DIMAG( SI )
152: T1R = SIR*ZIR - SII*ZII
153: T1I = SIR*ZII + SII*ZIR
154: T2 = CI*ZI
155: T3 = T2 - DCONJG( SI )*XI
156: T4 = DCONJG( T2 ) + SI*YI
157: T5 = CI*XI + T1R
158: T6 = CI*YI - T1R
159: X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
160: Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
161: Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
162: IX = IX + INCX
163: IC = IC + INCC
164: 10 CONTINUE
165: RETURN
166: *
167: * End of ZLAR2V
168: *
169: END
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