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
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
|
/* lapack/complex16/zlarfg.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static doublecomplex c_b5 = {1.,0.};
/*< SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) >*/
/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
x, integer *incx, doublecomplex *tau)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);
/* Local variables */
integer j, knt;
doublereal beta, alphi, alphr;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
doublereal xnorm;
extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *),
dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *,
ftnlen);
doublereal safmin;
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
doublereal rsafmn;
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/*< INTEGER INCX, N >*/
/*< COMPLEX*16 ALPHA, TAU >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 X( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZLARFG generates a complex elementary reflector H of order n, such */
/* that */
/* H' * ( alpha ) = ( beta ), H' * H = I. */
/* ( x ) ( 0 ) */
/* where alpha and beta are scalars, with beta real, and x is an */
/* (n-1)-element complex vector. H is represented in the form */
/* H = I - tau * ( 1 ) * ( 1 v' ) , */
/* ( v ) */
/* where tau is a complex scalar and v is a complex (n-1)-element */
/* vector. Note that H is not hermitian. */
/* If the elements of x are all zero and alpha is real, then tau = 0 */
/* and H is taken to be the unit matrix. */
/* Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the elementary reflector. */
/* ALPHA (input/output) COMPLEX*16 */
/* On entry, the value alpha. */
/* On exit, it is overwritten with the value beta. */
/* X (input/output) COMPLEX*16 array, dimension */
/* (1+(N-2)*abs(INCX)) */
/* On entry, the vector x. */
/* On exit, it is overwritten with the vector v. */
/* INCX (input) INTEGER */
/* The increment between elements of X. INCX > 0. */
/* TAU (output) COMPLEX*16 */
/* The value tau. */
/* ===================================================================== */
/* .. Parameters .. */
/*< DOUBLE PRECISION ONE, ZERO >*/
/*< PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER J, KNT >*/
/*< DOUBLE PRECISION ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH, DLAPY3, DZNRM2 >*/
/*< COMPLEX*16 ZLADIV >*/
/*< EXTERNAL DLAMCH, DLAPY3, DZNRM2, ZLADIV >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, DBLE, DCMPLX, DIMAG, SIGN >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL ZDSCAL, ZSCAL >*/
/* .. */
/* .. Executable Statements .. */
/*< IF( N.LE.0 ) THEN >*/
/* Parameter adjustments */
--x;
/* Function Body */
if (*n <= 0) {
/*< TAU = ZERO >*/
tau->r = 0., tau->i = 0.;
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< XNORM = DZNRM2( N-1, X, INCX ) >*/
i__1 = *n - 1;
xnorm = dznrm2_(&i__1, &x[1], incx);
/*< ALPHR = DBLE( ALPHA ) >*/
alphr = alpha->r;
/*< ALPHI = DIMAG( ALPHA ) >*/
alphi = d_imag(alpha);
/*< IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN >*/
if (xnorm == 0. && alphi == 0.) {
/* H = I */
/*< TAU = ZERO >*/
tau->r = 0., tau->i = 0.;
/*< ELSE >*/
} else {
/* general case */
/*< BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) >*/
d__1 = dlapy3_(&alphr, &alphi, &xnorm);
beta = -d_sign(&d__1, &alphr);
/*< SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' ) >*/
safmin = dlamch_("S", (ftnlen)1) / dlamch_("E", (ftnlen)1);
/*< RSAFMN = ONE / SAFMIN >*/
rsafmn = 1. / safmin;
/*< IF( ABS( BETA ).LT.SAFMIN ) THEN >*/
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
/*< KNT = 0 >*/
knt = 0;
/*< 10 CONTINUE >*/
L10:
/*< KNT = KNT + 1 >*/
++knt;
/*< CALL ZDSCAL( N-1, RSAFMN, X, INCX ) >*/
i__1 = *n - 1;
zdscal_(&i__1, &rsafmn, &x[1], incx);
/*< BETA = BETA*RSAFMN >*/
beta *= rsafmn;
/*< ALPHI = ALPHI*RSAFMN >*/
alphi *= rsafmn;
/*< ALPHR = ALPHR*RSAFMN >*/
alphr *= rsafmn;
/*< >*/
if (abs(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
/*< XNORM = DZNRM2( N-1, X, INCX ) >*/
i__1 = *n - 1;
xnorm = dznrm2_(&i__1, &x[1], incx);
/*< ALPHA = DCMPLX( ALPHR, ALPHI ) >*/
z__1.r = alphr, z__1.i = alphi;
alpha->r = z__1.r, alpha->i = z__1.i;
/*< BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR ) >*/
d__1 = dlapy3_(&alphr, &alphi, &xnorm);
beta = -d_sign(&d__1, &alphr);
/*< TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) >*/
d__1 = (beta - alphr) / beta;
d__2 = -alphi / beta;
z__1.r = d__1, z__1.i = d__2;
tau->r = z__1.r, tau->i = z__1.i;
/*< ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) >*/
z__2.r = alpha->r - beta, z__2.i = alpha->i;
zladiv_(&z__1, &c_b5, &z__2);
alpha->r = z__1.r, alpha->i = z__1.i;
/*< CALL ZSCAL( N-1, ALPHA, X, INCX ) >*/
i__1 = *n - 1;
zscal_(&i__1, alpha, &x[1], incx);
/* If ALPHA is subnormal, it may lose relative accuracy */
/*< ALPHA = BETA >*/
alpha->r = beta, alpha->i = 0.;
/*< DO 20 J = 1, KNT >*/
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
/*< ALPHA = ALPHA*SAFMIN >*/
z__1.r = safmin * alpha->r, z__1.i = safmin * alpha->i;
alpha->r = z__1.r, alpha->i = z__1.i;
/*< 20 CONTINUE >*/
/* L20: */
}
/*< ELSE >*/
} else {
/*< TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA ) >*/
d__1 = (beta - alphr) / beta;
d__2 = -alphi / beta;
z__1.r = d__1, z__1.i = d__2;
tau->r = z__1.r, tau->i = z__1.i;
/*< ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA ) >*/
z__2.r = alpha->r - beta, z__2.i = alpha->i;
zladiv_(&z__1, &c_b5, &z__2);
alpha->r = z__1.r, alpha->i = z__1.i;
/*< CALL ZSCAL( N-1, ALPHA, X, INCX ) >*/
i__1 = *n - 1;
zscal_(&i__1, alpha, &x[1], incx);
/*< ALPHA = BETA >*/
alpha->r = beta, alpha->i = 0.;
/*< END IF >*/
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of ZLARFG */
/*< END >*/
} /* zlarfg_ */
#ifdef __cplusplus
}
#endif
|
