GRASS GIS 8 Programmer's Manual 8.2.1RC1(2022)-exported
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#include <stdlib.h>
9#include "ccmath.h"
10void chousv(Cpx * a, double *d, double *dp, int n)
11{
12 double sc, x, y;
13
14 Cpx cc, u, *qs;
15
16 int i, j, k, m, e;
17
18 Cpx *qw, *pc, *p, *q;
19
20 qs = (Cpx *) calloc(2 * n, sizeof(Cpx));
21 q = qs + n;
22 for (j = 0, pc = a; j < n - 2; ++j, pc += n + 1, ++q) {
23 m = n - j - 1;
24 for (i = 1, sc = 0.; i <= m; ++i)
25 sc += pc[i].re * pc[i].re + pc[i].im * pc[i].im;
26 if (sc > 0.) {
27 sc = sqrt(sc);
28 p = pc + 1;
29 y = sc + (x = sqrt(p->re * p->re + p->im * p->im));
30 if (x > 0.) {
31 cc.re = p->re / x;
32 cc.im = p->im / x;
33 }
34 else {
35 cc.re = 1.;
36 cc.im = 0.;
37 }
38 q->re = -cc.re;
39 q->im = -cc.im;
40 x = 1. / sqrt(2. * sc * y);
41 y *= x;
42 for (i = 0, qw = pc + 1; i < m; ++i) {
43 qs[i].re = qs[i].im = 0.;
44 if (i) {
45 qw[i].re *= x;
46 qw[i].im *= -x;
47 }
48 else {
49 qw[0].re = y * cc.re;
50 qw[0].im = -y * cc.im;
51 }
52 }
53 for (i = 0, e = j + 2, p = pc + n + 1, y = 0.; i < m;
54 ++i, p += e++) {
55 qs[i].re += (u.re = qw[i].re) * p->re - (u.im =
56 qw[i].im) * p->im;
57 qs[i].im += u.re * p->im + u.im * p->re;
58 ++p;
59 for (k = i + 1; k < m; ++k, ++p) {
60 qs[i].re += qw[k].re * p->re - qw[k].im * p->im;
61 qs[i].im += qw[k].im * p->re + qw[k].re * p->im;
62 qs[k].re += u.re * p->re + u.im * p->im;
63 qs[k].im += u.im * p->re - u.re * p->im;
64 }
65 y += u.re * qs[i].re + u.im * qs[i].im;
66 }
67 for (i = 0; i < m; ++i) {
68 qs[i].re -= y * qw[i].re;
69 qs[i].re += qs[i].re;
70 qs[i].im -= y * qw[i].im;
71 qs[i].im += qs[i].im;
72 }
73 for (i = 0, e = j + 2, p = pc + n + 1; i < m; ++i, p += e++) {
74 for (k = i; k < m; ++k, ++p) {
75 p->re -= qw[i].re * qs[k].re + qw[i].im * qs[k].im
76 + qs[i].re * qw[k].re + qs[i].im * qw[k].im;
77 p->im -= qw[i].im * qs[k].re - qw[i].re * qs[k].im
78 + qs[i].im * qw[k].re - qs[i].re * qw[k].im;
79 }
80 }
81 }
82 d[j] = pc->re;
83 dp[j] = sc;
84 }
85 d[j] = pc->re;
86 cc = *(pc + 1);
87 d[j + 1] = (pc += n + 1)->re;
88 dp[j] = sc = sqrt(cc.re * cc.re + cc.im * cc.im);
89 q->re = cc.re /= sc;
90 q->im = cc.im /= sc;
91 for (i = 0, m = n + n, p = pc; i < m; ++i, --p)
92 p->re = p->im = 0.;
93 pc->re = 1.;
94 (pc -= n + 1)->re = 1.;
95 qw = pc - n;
96 for (m = 2; m < n; ++m, qw -= n + 1) {
97 for (j = 0, p = pc, pc->re = 1.; j < m; ++j, p += n) {
98 for (i = 0, q = p, u.re = u.im = 0.; i < m; ++i, ++q) {
99 u.re += qw[i].re * q->re - qw[i].im * q->im;
100 u.im += qw[i].re * q->im + qw[i].im * q->re;
101 }
102 for (i = 0, q = p, u.re += u.re, u.im += u.im; i < m; ++i, ++q) {
103 q->re -= u.re * qw[i].re + u.im * qw[i].im;
104 q->im -= u.im * qw[i].re - u.re * qw[i].im;
105 }
106 }
107 for (i = 0, p = qw + m - 1; i < n; ++i, --p)
108 p->re = p->im = 0.;
109 (pc -= n + 1)->re = 1.;
110 }
111 for (j = 1, p = a + n + 1, q = qs + n, u.re = 1., u.im = 0.; j < n;
112 ++j, ++p, ++q) {
113 sc = u.re * q->re - u.im * q->im;
114 u.im = u.im * q->re + u.re * q->im;
115 u.re = sc;
116 for (i = 1; i < n; ++i, ++p) {
117 sc = u.re * p->re - u.im * p->im;
118 p->im = u.re * p->im + u.im * p->re;
119 p->re = sc;
120 }
121 }
122 free(qs);
123}
void chousv(Cpx *a, double *d, double *dp, int n)
Definition: chousv.c:10
Definition: ccmath.h:38
double re
Definition: ccmath.h:38
double im
Definition: ccmath.h:38
#define x