GRASS GIS 8 Programmer's Manual  8.4.0dev(2024)-f4d8c62acd
chousv.c
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1 /* chousv.c CCMATH mathematics library source code.
2  *
3  * Copyright (C) 2000 Daniel A. Atkinson All rights reserved.
4  * This code may be redistributed under the terms of the GNU library
5  * public license (LGPL). ( See the lgpl.license file for details.)
6  * ------------------------------------------------------------------------
7  */
8 
9 #include <stdlib.h>
10 #include "ccmath.h"
11 
12 void chousv(Cpx *a, double *d, double *dp, int n)
13 {
14  double sc, x, y;
15 
16  Cpx cc, u, *qs;
17 
18  int i, j, k, m, e;
19 
20  Cpx *qw, *pc, *p, *q;
21 
22  qs = (Cpx *)calloc(2 * n, sizeof(Cpx));
23  q = qs + n;
24  for (j = 0, pc = a; j < n - 2; ++j, pc += n + 1, ++q) {
25  m = n - j - 1;
26  for (i = 1, sc = 0.; i <= m; ++i)
27  sc += pc[i].re * pc[i].re + pc[i].im * pc[i].im;
28  if (sc > 0.) {
29  sc = sqrt(sc);
30  p = pc + 1;
31  y = sc + (x = sqrt(p->re * p->re + p->im * p->im));
32  if (x > 0.) {
33  cc.re = p->re / x;
34  cc.im = p->im / x;
35  }
36  else {
37  cc.re = 1.;
38  cc.im = 0.;
39  }
40  q->re = -cc.re;
41  q->im = -cc.im;
42  x = 1. / sqrt(2. * sc * y);
43  y *= x;
44  for (i = 0, qw = pc + 1; i < m; ++i) {
45  qs[i].re = qs[i].im = 0.;
46  if (i) {
47  qw[i].re *= x;
48  qw[i].im *= -x;
49  }
50  else {
51  qw[0].re = y * cc.re;
52  qw[0].im = -y * cc.im;
53  }
54  }
55  for (i = 0, e = j + 2, p = pc + n + 1, y = 0.; i < m;
56  ++i, p += e++) {
57  qs[i].re +=
58  (u.re = qw[i].re) * p->re - (u.im = qw[i].im) * p->im;
59  qs[i].im += u.re * p->im + u.im * p->re;
60  ++p;
61  for (k = i + 1; k < m; ++k, ++p) {
62  qs[i].re += qw[k].re * p->re - qw[k].im * p->im;
63  qs[i].im += qw[k].im * p->re + qw[k].re * p->im;
64  qs[k].re += u.re * p->re + u.im * p->im;
65  qs[k].im += u.im * p->re - u.re * p->im;
66  }
67  y += u.re * qs[i].re + u.im * qs[i].im;
68  }
69  for (i = 0; i < m; ++i) {
70  qs[i].re -= y * qw[i].re;
71  qs[i].re += qs[i].re;
72  qs[i].im -= y * qw[i].im;
73  qs[i].im += qs[i].im;
74  }
75  for (i = 0, e = j + 2, p = pc + n + 1; i < m; ++i, p += e++) {
76  for (k = i; k < m; ++k, ++p) {
77  p->re -= qw[i].re * qs[k].re + qw[i].im * qs[k].im +
78  qs[i].re * qw[k].re + qs[i].im * qw[k].im;
79  p->im -= qw[i].im * qs[k].re - qw[i].re * qs[k].im +
80  qs[i].im * qw[k].re - qs[i].re * qw[k].im;
81  }
82  }
83  }
84  d[j] = pc->re;
85  dp[j] = sc;
86  }
87  d[j] = pc->re;
88  cc = *(pc + 1);
89  d[j + 1] = (pc += n + 1)->re;
90  dp[j] = sc = sqrt(cc.re * cc.re + cc.im * cc.im);
91  q->re = cc.re /= sc;
92  q->im = cc.im /= sc;
93  for (i = 0, m = n + n, p = pc; i < m; ++i, --p)
94  p->re = p->im = 0.;
95  pc->re = 1.;
96  (pc -= n + 1)->re = 1.;
97  qw = pc - n;
98  for (m = 2; m < n; ++m, qw -= n + 1) {
99  for (j = 0, p = pc, pc->re = 1.; j < m; ++j, p += n) {
100  for (i = 0, q = p, u.re = u.im = 0.; i < m; ++i, ++q) {
101  u.re += qw[i].re * q->re - qw[i].im * q->im;
102  u.im += qw[i].re * q->im + qw[i].im * q->re;
103  }
104  for (i = 0, q = p, u.re += u.re, u.im += u.im; i < m; ++i, ++q) {
105  q->re -= u.re * qw[i].re + u.im * qw[i].im;
106  q->im -= u.im * qw[i].re - u.re * qw[i].im;
107  }
108  }
109  for (i = 0, p = qw + m - 1; i < n; ++i, --p)
110  p->re = p->im = 0.;
111  (pc -= n + 1)->re = 1.;
112  }
113  for (j = 1, p = a + n + 1, q = qs + n, u.re = 1., u.im = 0.; j < n;
114  ++j, ++p, ++q) {
115  sc = u.re * q->re - u.im * q->im;
116  u.im = u.im * q->re + u.re * q->im;
117  u.re = sc;
118  for (i = 1; i < n; ++i, ++p) {
119  sc = u.re * p->re - u.im * p->im;
120  p->im = u.re * p->im + u.im * p->re;
121  p->re = sc;
122  }
123  }
124  free(qs);
125 }
void chousv(Cpx *a, double *d, double *dp, int n)
Definition: chousv.c:12
void free(void *)
Definition: la.h:54
double re
Definition: ccmath.h:39
double im
Definition: ccmath.h:39
#define x