```01:       SUBROUTINE ZROT( N, CX, INCX, CY, INCY, C, S )
02: *
03: *  -- LAPACK auxiliary routine (version 3.2) --
04: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
05: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
06: *     November 2006
07: *
08: *     .. Scalar Arguments ..
09:       INTEGER            INCX, INCY, N
10:       DOUBLE PRECISION   C
11:       COMPLEX*16         S
12: *     ..
13: *     .. Array Arguments ..
14:       COMPLEX*16         CX( * ), CY( * )
15: *     ..
16: *
17: *  Purpose
18: *  =======
19: *
20: *  ZROT   applies a plane rotation, where the cos (C) is real and the
21: *  sin (S) is complex, and the vectors CX and CY are complex.
22: *
23: *  Arguments
24: *  =========
25: *
26: *  N       (input) INTEGER
27: *          The number of elements in the vectors CX and CY.
28: *
29: *  CX      (input/output) COMPLEX*16 array, dimension (N)
30: *          On input, the vector X.
31: *          On output, CX is overwritten with C*X + S*Y.
32: *
33: *  INCX    (input) INTEGER
34: *          The increment between successive values of CY.  INCX <> 0.
35: *
36: *  CY      (input/output) COMPLEX*16 array, dimension (N)
37: *          On input, the vector Y.
38: *          On output, CY is overwritten with -CONJG(S)*X + C*Y.
39: *
40: *  INCY    (input) INTEGER
41: *          The increment between successive values of CY.  INCX <> 0.
42: *
43: *  C       (input) DOUBLE PRECISION
44: *  S       (input) COMPLEX*16
45: *          C and S define a rotation
46: *             [  C          S  ]
47: *             [ -conjg(S)   C  ]
48: *          where C*C + S*CONJG(S) = 1.0.
49: *
50: * =====================================================================
51: *
52: *     .. Local Scalars ..
53:       INTEGER            I, IX, IY
54:       COMPLEX*16         STEMP
55: *     ..
56: *     .. Intrinsic Functions ..
57:       INTRINSIC          DCONJG
58: *     ..
59: *     .. Executable Statements ..
60: *
61:       IF( N.LE.0 )
62:      \$   RETURN
63:       IF( INCX.EQ.1 .AND. INCY.EQ.1 )
64:      \$   GO TO 20
65: *
66: *     Code for unequal increments or equal increments not equal to 1
67: *
68:       IX = 1
69:       IY = 1
70:       IF( INCX.LT.0 )
71:      \$   IX = ( -N+1 )*INCX + 1
72:       IF( INCY.LT.0 )
73:      \$   IY = ( -N+1 )*INCY + 1
74:       DO 10 I = 1, N
75:          STEMP = C*CX( IX ) + S*CY( IY )
76:          CY( IY ) = C*CY( IY ) - DCONJG( S )*CX( IX )
77:          CX( IX ) = STEMP
78:          IX = IX + INCX
79:          IY = IY + INCY
80:    10 CONTINUE
81:       RETURN
82: *
83: *     Code for both increments equal to 1
84: *
85:    20 CONTINUE
86:       DO 30 I = 1, N
87:          STEMP = C*CX( I ) + S*CY( I )
88:          CY( I ) = C*CY( I ) - DCONJG( S )*CX( I )
89:          CX( I ) = STEMP
90:    30 CONTINUE
91:       RETURN
92:       END
93: ```