LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
clargv.f
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1 *> \brief \b CLARGV generates a vector of plane rotations with real cosines and complex sines.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CLARGV + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clargv.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clargv.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLARGV( N, X, INCX, Y, INCY, C, INCC )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER INCC, INCX, INCY, N
25 * ..
26 * .. Array Arguments ..
27 * REAL C( * )
28 * COMPLEX X( * ), Y( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CLARGV generates a vector of complex plane rotations with real
38 *> cosines, determined by elements of the complex vectors x and y.
39 *> For i = 1,2,...,n
40 *>
41 *> ( c(i) s(i) ) ( x(i) ) = ( r(i) )
42 *> ( -conjg(s(i)) c(i) ) ( y(i) ) = ( 0 )
43 *>
44 *> where c(i)**2 + ABS(s(i))**2 = 1
45 *>
46 *> The following conventions are used (these are the same as in CLARTG,
47 *> but differ from the BLAS1 routine CROTG):
48 *> If y(i)=0, then c(i)=1 and s(i)=0.
49 *> If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
50 *> \endverbatim
51 *
52 * Arguments:
53 * ==========
54 *
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The number of plane rotations to be generated.
59 *> \endverbatim
60 *>
61 *> \param[in,out] X
62 *> \verbatim
63 *> X is COMPLEX array, dimension (1+(N-1)*INCX)
64 *> On entry, the vector x.
65 *> On exit, x(i) is overwritten by r(i), for i = 1,...,n.
66 *> \endverbatim
67 *>
68 *> \param[in] INCX
69 *> \verbatim
70 *> INCX is INTEGER
71 *> The increment between elements of X. INCX > 0.
72 *> \endverbatim
73 *>
74 *> \param[in,out] Y
75 *> \verbatim
76 *> Y is COMPLEX array, dimension (1+(N-1)*INCY)
77 *> On entry, the vector y.
78 *> On exit, the sines of the plane rotations.
79 *> \endverbatim
80 *>
81 *> \param[in] INCY
82 *> \verbatim
83 *> INCY is INTEGER
84 *> The increment between elements of Y. INCY > 0.
85 *> \endverbatim
86 *>
87 *> \param[out] C
88 *> \verbatim
89 *> C is REAL array, dimension (1+(N-1)*INCC)
90 *> The cosines of the plane rotations.
91 *> \endverbatim
92 *>
93 *> \param[in] INCC
94 *> \verbatim
95 *> INCC is INTEGER
96 *> The increment between elements of C. INCC > 0.
97 *> \endverbatim
98 *
99 * Authors:
100 * ========
101 *
102 *> \author Univ. of Tennessee
103 *> \author Univ. of California Berkeley
104 *> \author Univ. of Colorado Denver
105 *> \author NAG Ltd.
106 *
107 *> \date September 2012
108 *
109 *> \ingroup complexOTHERauxiliary
110 *
111 *> \par Further Details:
112 * =====================
113 *>
114 *> \verbatim
115 *>
116 *> 6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
117 *>
118 *> This version has a few statements commented out for thread safety
119 *> (machine parameters are computed on each entry). 10 feb 03, SJH.
120 *> \endverbatim
121 *>
122 * =====================================================================
123  SUBROUTINE clargv( N, X, INCX, Y, INCY, C, INCC )
124 *
125 * -- LAPACK auxiliary routine (version 3.4.2) --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 * September 2012
129 *
130 * .. Scalar Arguments ..
131  INTEGER INCC, INCX, INCY, N
132 * ..
133 * .. Array Arguments ..
134  REAL C( * )
135  COMPLEX X( * ), Y( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL TWO, ONE, ZERO
142  parameter ( two = 2.0e+0, one = 1.0e+0, zero = 0.0e+0 )
143  COMPLEX CZERO
144  parameter ( czero = ( 0.0e+0, 0.0e+0 ) )
145 * ..
146 * .. Local Scalars ..
147 * LOGICAL FIRST
148  INTEGER COUNT, I, IC, IX, IY, J
149  REAL CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
150  $ safmn2, safmx2, scale
151  COMPLEX F, FF, FS, G, GS, R, SN
152 * ..
153 * .. External Functions ..
154  REAL SLAMCH, SLAPY2
155  EXTERNAL slamch, slapy2
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, aimag, cmplx, conjg, int, log, max, REAL,
159  $ sqrt
160 * ..
161 * .. Statement Functions ..
162  REAL ABS1, ABSSQ
163 * ..
164 * .. Save statement ..
165 * SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
166 * ..
167 * .. Data statements ..
168 * DATA FIRST / .TRUE. /
169 * ..
170 * .. Statement Function definitions ..
171  abs1( ff ) = max( abs( REAL( FF ) ), abs( AIMAG( ff ) ) )
172  abssq( ff ) = REAL( ff )**2 + AIMAG( ff )**2
173 * ..
174 * .. Executable Statements ..
175 *
176 * IF( FIRST ) THEN
177 * FIRST = .FALSE.
178  safmin = slamch( 'S' )
179  eps = slamch( 'E' )
180  safmn2 = slamch( 'B' )**int( log( safmin / eps ) /
181  $ log( slamch( 'B' ) ) / two )
182  safmx2 = one / safmn2
183 * END IF
184  ix = 1
185  iy = 1
186  ic = 1
187  DO 60 i = 1, n
188  f = x( ix )
189  g = y( iy )
190 *
191 * Use identical algorithm as in CLARTG
192 *
193  scale = max( abs1( f ), abs1( g ) )
194  fs = f
195  gs = g
196  count = 0
197  IF( scale.GE.safmx2 ) THEN
198  10 CONTINUE
199  count = count + 1
200  fs = fs*safmn2
201  gs = gs*safmn2
202  scale = scale*safmn2
203  IF( scale.GE.safmx2 )
204  $ GO TO 10
205  ELSE IF( scale.LE.safmn2 ) THEN
206  IF( g.EQ.czero ) THEN
207  cs = one
208  sn = czero
209  r = f
210  GO TO 50
211  END IF
212  20 CONTINUE
213  count = count - 1
214  fs = fs*safmx2
215  gs = gs*safmx2
216  scale = scale*safmx2
217  IF( scale.LE.safmn2 )
218  $ GO TO 20
219  END IF
220  f2 = abssq( fs )
221  g2 = abssq( gs )
222  IF( f2.LE.max( g2, one )*safmin ) THEN
223 *
224 * This is a rare case: F is very small.
225 *
226  IF( f.EQ.czero ) THEN
227  cs = zero
228  r = slapy2( REAL( G ), AIMAG( g ) )
229 * Do complex/real division explicitly with two real
230 * divisions
231  d = slapy2( REAL( GS ), AIMAG( gs ) )
232  sn = cmplx( REAL( GS ) / D, -AIMAG( gs ) / D )
233  GO TO 50
234  END IF
235  f2s = slapy2( REAL( FS ), AIMAG( fs ) )
236 * G2 and G2S are accurate
237 * G2 is at least SAFMIN, and G2S is at least SAFMN2
238  g2s = sqrt( g2 )
239 * Error in CS from underflow in F2S is at most
240 * UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
241 * If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
242 * and so CS .lt. sqrt(SAFMIN)
243 * If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
244 * and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
245 * Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
246  cs = f2s / g2s
247 * Make sure abs(FF) = 1
248 * Do complex/real division explicitly with 2 real divisions
249  IF( abs1( f ).GT.one ) THEN
250  d = slapy2( REAL( F ), AIMAG( f ) )
251  ff = cmplx( REAL( F ) / D, AIMAG( f ) / D )
252  ELSE
253  dr = safmx2*REAL( f )
254  di = safmx2*aimag( f )
255  d = slapy2( dr, di )
256  ff = cmplx( dr / d, di / d )
257  END IF
258  sn = ff*cmplx( REAL( GS ) / G2S, -AIMAG( gs ) / G2S )
259  r = cs*f + sn*g
260  ELSE
261 *
262 * This is the most common case.
263 * Neither F2 nor F2/G2 are less than SAFMIN
264 * F2S cannot overflow, and it is accurate
265 *
266  f2s = sqrt( one+g2 / f2 )
267 * Do the F2S(real)*FS(complex) multiply with two real
268 * multiplies
269  r = cmplx( f2s*REAL( FS ), F2S*AIMAG( fs ) )
270  cs = one / f2s
271  d = f2 + g2
272 * Do complex/real division explicitly with two real divisions
273  sn = cmplx( REAL( R ) / D, AIMAG( r ) / D )
274  sn = sn*conjg( gs )
275  IF( count.NE.0 ) THEN
276  IF( count.GT.0 ) THEN
277  DO 30 j = 1, count
278  r = r*safmx2
279  30 CONTINUE
280  ELSE
281  DO 40 j = 1, -count
282  r = r*safmn2
283  40 CONTINUE
284  END IF
285  END IF
286  END IF
287  50 CONTINUE
288  c( ic ) = cs
289  y( iy ) = sn
290  x( ix ) = r
291  ic = ic + incc
292  iy = iy + incy
293  ix = ix + incx
294  60 CONTINUE
295  RETURN
296 *
297 * End of CLARGV
298 *
299  END
subroutine clargv(N, X, INCX, Y, INCY, C, INCC)
CLARGV generates a vector of plane rotations with real cosines and complex sines. ...
Definition: clargv.f:124