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
|
SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
INTEGER INCC, INCX, INCY, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION C( * )
COMPLEX*16 X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* ZLARGV generates a vector of complex plane rotations with real
* cosines, determined by elements of the complex vectors x and y.
* For i = 1,2,...,n
*
* ( c(i) s(i) ) ( x(i) ) = ( a(i) )
* ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 )
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of plane rotations to be generated.
*
* X (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
* On entry, the vector x.
* On exit, x(i) is overwritten by a(i), for i = 1,...,n.
*
* INCX (input) INTEGER
* The increment between elements of X. INCX > 0.
*
* Y (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY)
* On entry, the vector y.
* On exit, the sines of the plane rotations.
*
* INCY (input) INTEGER
* The increment between elements of Y. INCY > 0.
*
* C (output) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
* The cosines of the plane rotations.
*
* INCC (input) INTEGER
* The increment between elements of C. INCC > 0.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IC, IX, IY
DOUBLE PRECISION ABSX, ABSY, TT, W
COMPLEX*16 T, XI, YI
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCONJG, MAX, SQRT
* ..
* .. Executable Statements ..
*
IX = 1
IY = 1
IC = 1
DO 10 I = 1, N
XI = X( IX )
YI = Y( IY )
ABSX = ABS( XI )
IF( ABSX.EQ.ZERO ) THEN
C( IC ) = ZERO
Y( IY ) = ONE
X( IX ) = YI
ELSE
ABSY = ABS( YI )
W = MAX( ABSX, ABSY )
T = XI / ABSX
ABSX = ABSX / W
ABSY = ABSY / W
TT = SQRT( ABSX*ABSX+ABSY*ABSY )
C( IC ) = ABSX / TT
Y( IY ) = ( T*DCONJG( YI ) ) / ( W*TT )
X( IX ) = T*( W*TT )
END IF
IX = IX + INCX
IY = IY + INCY
IC = IC + INCC
10 CONTINUE
RETURN
*
* End of ZLARGV
*
END
|
