1 SUBROUTINE ZLAR2V( N, X, Y, Z, INCX, C, S, INCC )
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INCC, INCX, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION C( * )
13 COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZLAR2V applies a vector of complex plane rotations with real cosines
20 * from both sides to a sequence of 2-by-2 complex Hermitian matrices,
21 * defined by the elements of the vectors x, y and z. For i = 1,2,...,n
22 *
23 * ( x(i) z(i) ) :=
24 * ( conjg(z(i)) y(i) )
25 *
26 * ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
27 * ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
28 *
29 * Arguments
30 * =========
31 *
32 * N (input) INTEGER
33 * The number of plane rotations to be applied.
34 *
35 * X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
36 * The vector x; the elements of x are assumed to be real.
37 *
38 * Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
39 * The vector y; the elements of y are assumed to be real.
40 *
41 * Z (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
42 * The vector z.
43 *
44 * INCX (input) INTEGER
45 * The increment between elements of X, Y and Z. INCX > 0.
46 *
47 * C (input) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
48 * The cosines of the plane rotations.
49 *
50 * S (input) COMPLEX*16 array, dimension (1+(N-1)*INCC)
51 * The sines of the plane rotations.
52 *
53 * INCC (input) INTEGER
54 * The increment between elements of C and S. INCC > 0.
55 *
56 * =====================================================================
57 *
58 * .. Local Scalars ..
59 INTEGER I, IC, IX
60 DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
61 $ ZIR
62 COMPLEX*16 SI, T2, T3, T4, ZI
63 * ..
64 * .. Intrinsic Functions ..
65 INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG
66 * ..
67 * .. Executable Statements ..
68 *
69 IX = 1
70 IC = 1
71 DO 10 I = 1, N
72 XI = DBLE( X( IX ) )
73 YI = DBLE( Y( IX ) )
74 ZI = Z( IX )
75 ZIR = DBLE( ZI )
76 ZII = DIMAG( ZI )
77 CI = C( IC )
78 SI = S( IC )
79 SIR = DBLE( SI )
80 SII = DIMAG( SI )
81 T1R = SIR*ZIR - SII*ZII
82 T1I = SIR*ZII + SII*ZIR
83 T2 = CI*ZI
84 T3 = T2 - DCONJG( SI )*XI
85 T4 = DCONJG( T2 ) + SI*YI
86 T5 = CI*XI + T1R
87 T6 = CI*YI - T1R
88 X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
89 Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
90 Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
91 IX = IX + INCX
92 IC = IC + INCC
93 10 CONTINUE
94 RETURN
95 *
96 * End of ZLAR2V
97 *
98 END
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 INTEGER INCC, INCX, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION C( * )
13 COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZLAR2V applies a vector of complex plane rotations with real cosines
20 * from both sides to a sequence of 2-by-2 complex Hermitian matrices,
21 * defined by the elements of the vectors x, y and z. For i = 1,2,...,n
22 *
23 * ( x(i) z(i) ) :=
24 * ( conjg(z(i)) y(i) )
25 *
26 * ( c(i) conjg(s(i)) ) ( x(i) z(i) ) ( c(i) -conjg(s(i)) )
27 * ( -s(i) c(i) ) ( conjg(z(i)) y(i) ) ( s(i) c(i) )
28 *
29 * Arguments
30 * =========
31 *
32 * N (input) INTEGER
33 * The number of plane rotations to be applied.
34 *
35 * X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
36 * The vector x; the elements of x are assumed to be real.
37 *
38 * Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
39 * The vector y; the elements of y are assumed to be real.
40 *
41 * Z (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
42 * The vector z.
43 *
44 * INCX (input) INTEGER
45 * The increment between elements of X, Y and Z. INCX > 0.
46 *
47 * C (input) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
48 * The cosines of the plane rotations.
49 *
50 * S (input) COMPLEX*16 array, dimension (1+(N-1)*INCC)
51 * The sines of the plane rotations.
52 *
53 * INCC (input) INTEGER
54 * The increment between elements of C and S. INCC > 0.
55 *
56 * =====================================================================
57 *
58 * .. Local Scalars ..
59 INTEGER I, IC, IX
60 DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
61 $ ZIR
62 COMPLEX*16 SI, T2, T3, T4, ZI
63 * ..
64 * .. Intrinsic Functions ..
65 INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG
66 * ..
67 * .. Executable Statements ..
68 *
69 IX = 1
70 IC = 1
71 DO 10 I = 1, N
72 XI = DBLE( X( IX ) )
73 YI = DBLE( Y( IX ) )
74 ZI = Z( IX )
75 ZIR = DBLE( ZI )
76 ZII = DIMAG( ZI )
77 CI = C( IC )
78 SI = S( IC )
79 SIR = DBLE( SI )
80 SII = DIMAG( SI )
81 T1R = SIR*ZIR - SII*ZII
82 T1I = SIR*ZII + SII*ZIR
83 T2 = CI*ZI
84 T3 = T2 - DCONJG( SI )*XI
85 T4 = DCONJG( T2 ) + SI*YI
86 T5 = CI*XI + T1R
87 T6 = CI*YI - T1R
88 X( IX ) = CI*T5 + ( SIR*DBLE( T4 )+SII*DIMAG( T4 ) )
89 Y( IX ) = CI*T6 - ( SIR*DBLE( T3 )-SII*DIMAG( T3 ) )
90 Z( IX ) = CI*T3 + DCONJG( SI )*DCMPLX( T6, T1I )
91 IX = IX + INCX
92 IC = IC + INCC
93 10 CONTINUE
94 RETURN
95 *
96 * End of ZLAR2V
97 *
98 END