GRASS GIS 8 Programmer's Manual 8.4.1(2025)-45ca3179ab
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cminv.c
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1/* cminv.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
12int cminv(Cpx *a, int n)
13{
14 int i, j, k, m, lc, *le;
15
16 Cpx *ps, *p, *q, *pa, *pd;
17
18 Cpx z, h, *q0;
19
20 double s, t, tq = 0., zr = 1.e-15;
21
22 le = (int *)calloc(n, sizeof(int));
23 q0 = (Cpx *)calloc(n, sizeof(Cpx));
24 pa = pd = a;
25 for (j = 0; j < n; ++j, ++pa, pd += n + 1) {
26 if (j > 0) {
27 for (i = 0, p = pa, q = q0; i < n; ++i, p += n)
28 *q++ = *p;
29 for (i = 1; i < n; ++i) {
30 lc = i < j ? i : j;
31 z.re = z.im = 0.;
32 for (k = 0, p = pa + i * n - j, q = q0; k < lc; ++k, ++q, ++p) {
33 z.re += p->re * q->re - p->im * q->im;
34 z.im += p->im * q->re + p->re * q->im;
35 }
36 q0[i].re -= z.re;
37 q0[i].im -= z.im;
38 }
39 for (i = 0, p = pa, q = q0; i < n; ++i, p += n)
40 *p = *q++;
41 }
42 s = fabs(pd->re) + fabs(pd->im);
43 lc = j;
44 for (k = j + 1, ps = pd; k < n; ++k) {
45 ps += n;
46 if ((t = fabs(ps->re) + fabs(ps->im)) > s) {
47 s = t;
48 lc = k;
49 }
50 }
51 tq = tq > s ? tq : s;
52 if (s < zr * tq) {
53 free(le - j);
54 free(q0);
55 return -1;
56 }
57 *le++ = lc;
58 if (lc != j) {
59 p = a + n * j;
60 q = a + n * lc;
61 for (k = 0; k < n; ++k, ++p, ++q) {
62 h = *p;
63 *p = *q;
64 *q = h;
65 }
66 }
67 t = pd->re * pd->re + pd->im * pd->im;
68 h.re = pd->re / t;
69 h.im = -(pd->im) / t;
70 for (k = j + 1, ps = pd + n; k < n; ++k, ps += n) {
71 z.re = ps->re * h.re - ps->im * h.im;
72 z.im = ps->im * h.re + ps->re * h.im;
73 *ps = z;
74 }
75 *pd = h;
76 }
77 for (j = 1, pd = ps = a; j < n; ++j) {
78 for (k = 0, pd += n + 1, q = ++ps; k < j; ++k, q += n) {
79 z.re = q->re * pd->re - q->im * pd->im;
80 z.im = q->im * pd->re + q->re * pd->im;
81 *q = z;
82 }
83 }
84 for (j = 1, pa = a; j < n; ++j) {
85 ++pa;
86 for (i = 0, q = q0, p = pa; i < j; ++i, p += n)
87 *q++ = *p;
88 for (k = 0; k < j; ++k) {
89 h.re = h.im = 0.;
90 for (i = k, p = pa + k * n + k - j, q = q0 + k; i < j; ++i) {
91 h.re -= p->re * q->re - p->im * q->im;
92 h.im -= p->im * q->re + p->re * q->im;
93 ++p;
94 ++q;
95 }
96 q0[k] = h;
97 }
98 for (i = 0, q = q0, p = pa; i < j; ++i, p += n)
99 *p = *q++;
100 }
101 for (j = n - 2, pd = pa = a + n * n - 1; j >= 0; --j) {
102 --pa;
103 pd -= n + 1;
104 for (i = 0, m = n - j - 1, q = q0, p = pd + n; i < m; ++i, p += n)
105 *q++ = *p;
106 for (k = n - 1, ps = pa; k > j; --k, ps -= n) {
107 z.re = -ps->re;
108 z.im = -ps->im;
109 for (i = j + 1, p = ps + 1, q = q0; i < k; ++i, ++p, ++q) {
110 z.re -= p->re * q->re - p->im * q->im;
111 z.im -= p->im * q->re + p->re * q->im;
112 }
113 q0[--m] = z;
114 }
115 for (i = 0, m = n - j - 1, q = q0, p = pd + n; i < m; ++i, p += n)
116 *p = *q++;
117 }
118 for (k = 0, pa = a; k < n - 1; ++k, ++pa) {
119 for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
120 *q++ = *p;
121 for (j = 0, ps = a; j < n; ++j, ps += n) {
122 if (j > k) {
123 h.re = h.im = 0.;
124 p = ps + j;
125 i = j;
126 }
127 else {
128 h = q0[j];
129 p = ps + k + 1;
130 i = k + 1;
131 }
132 for (; i < n; ++i, ++p) {
133 h.re += p->re * q0[i].re - p->im * q0[i].im;
134 h.im += p->im * q0[i].re + p->re * q0[i].im;
135 }
136 q0[j] = h;
137 }
138 for (i = 0, q = q0, p = pa; i < n; ++i, p += n)
139 *p = *q++;
140 }
141 for (j = n - 2, le--; j >= 0; --j) {
142 for (k = 0, p = a + j, q = a + *(--le); k < n; ++k, p += n, q += n) {
143 h = *p;
144 *p = *q;
145 *q = h;
146 }
147 }
148 free(le);
149 free(q0);
150 return 0;
151}
struct complex Cpx
Definition ccmath.h:41
int cminv(Cpx *a, int n)
Definition cminv.c:12
double t
struct ps_state ps
double re
Definition ccmath.h:39
double im
Definition ccmath.h:39