GRASS GIS 8 Programmer's Manual 8.4.1(2025)-45ca3179ab
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svduv.c
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1/* svduv.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"
10int svduv(double *d, double *a, double *u, int m, double *v, int n)
11{
12 double *p, *p1, *q, *pp, *w, *e;
13
14 double s, h, r, t, sv;
15
16 int i, j, k, mm, nm, ms;
17
18 if (m < n)
19 return -1;
20 w = (double *)calloc(m + n, sizeof(double));
21 e = w + m;
22 for (i = 0, mm = m, nm = n - 1, p = a; i < n; ++i, --mm, --nm, p += n + 1) {
23 if (mm > 1) {
24 sv = h = 0.;
25 for (j = 0, q = p, s = 0.; j < mm; ++j, q += n) {
26 w[j] = *q;
27 s += *q * *q;
28 }
29 if (s > 0.) {
30 h = sqrt(s);
31 if (*p < 0.)
32 h = -h;
33 s += *p * h;
34 s = 1. / s;
35 t = 1. / (w[0] += h);
36 sv = 1. + fabs(*p / h);
37 for (k = 1, ms = n - i; k < ms; ++k) {
38 for (j = 0, q = p + k, r = 0.; j < mm; q += n)
39 r += w[j++] * *q;
40 r *= s;
41 for (j = 0, q = p + k; j < mm; q += n)
42 *q -= r * w[j++];
43 }
44 for (j = 1, q = p; j < mm;)
45 *(q += n) = t * w[j++];
46 }
47 *p = sv;
48 d[i] = -h;
49 }
50 if (mm == 1)
51 d[i] = *p;
52 p1 = p + 1;
53 sv = h = 0.;
54 if (nm > 1) {
55 for (j = 0, q = p1, s = 0.; j < nm; ++j, ++q)
56 s += *q * *q;
57 if (s > 0.) {
58 h = sqrt(s);
59 if (*p1 < 0.)
60 h = -h;
61 sv = 1. + fabs(*p1 / h);
62 s += *p1 * h;
63 s = 1. / s;
64 t = 1. / (*p1 += h);
65 for (k = n, ms = n * (m - i); k < ms; k += n) {
66 for (j = 0, q = p1, pp = p1 + k, r = 0.; j < nm; ++j)
67 r += *q++ * *pp++;
68 r *= s;
69 for (j = 0, q = p1, pp = p1 + k; j < nm; ++j)
70 *pp++ -= r * *q++;
71 }
72 for (j = 1, q = p1 + 1; j < nm; ++j)
73 *q++ *= t;
74 }
75 *p1 = sv;
76 e[i] = -h;
77 }
78 if (nm == 1)
79 e[i] = *p1;
80 }
81 ldvmat(a, v, n);
82 ldumat(a, u, m, n);
83 qrbdv(d, e, u, m, v, n);
84 for (i = 0; i < n; ++i) {
85 if (d[i] < 0.) {
86 d[i] = -d[i];
87 for (j = 0, p = v + i; j < n; ++j, p += n)
88 *p = -*p;
89 }
90 }
91 free(w);
92 return 0;
93}
void ldumat(double *a, double *u, int m, int n)
Definition ldumat.c:9
int qrbdv(double *d, double *e, double *u, int m, double *v, int n)
Definition qrbdv.c:9
void ldvmat(double *a, double *v, int n)
Definition ldvmat.c:8
double t
double r
int svduv(double *d, double *a, double *u, int m, double *v, int n)
Definition svduv.c:10