GRASS GIS 8 Programmer's Manual 8.3.2(2024)-exported
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sv2u1v.c
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1/* sv2u1v.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 sv2u1v(double *d, double *a, int m, double *v, int n)
11{
12 double *p, *p1, *q, *pp, *w, *e;
13
14 double s, t, h, r, 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, p = a; i < n; ++i, --mm, 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 = 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) = w[j++] * t;
46 }
47 *p = sv;
48 d[i] = -h;
49 }
50 if (mm == 1)
51 d[i] = *p;
52 }
53 for (i = 0, q = v, p = a; i < n; ++i) {
54 for (j = 0; j < n; ++j, ++q, ++p) {
55 if (j < i)
56 *q = 0.;
57 else if (j == i)
58 *q = d[i];
59 else
60 *q = *p;
61 }
62 }
63 atou1(a, m, n);
64 for (i = 0, mm = n, nm = n - 1, p = v; i < n; ++i, --mm, --nm, p += n + 1) {
65 if (i && mm > 1) {
66 sv = h = 0.;
67 for (j = 0, q = p, s = 0.; j < mm; ++j, q += n) {
68 w[j] = *q;
69 s += *q * *q;
70 }
71 if (s > 0.) {
72 h = sqrt(s);
73 if (*p < 0.)
74 h = -h;
75 s += *p * h;
76 s = 1. / s;
77 t = 1. / (w[0] += h);
78 sv = 1. + fabs(*p / h);
79 for (k = 1, ms = n - i; k < ms; ++k) {
80 for (j = 0, q = p + k, r = 0.; j < mm; q += n)
81 r += w[j++] * *q;
82 for (j = 0, q = p + k, r *= s; j < mm; q += n)
83 *q -= r * w[j++];
84 }
85 for (k = 0, p1 = a + i; k < m; ++k, p1 += n) {
86 for (j = 0, q = p1, r = 0.; j < mm;)
87 r += w[j++] * *q++;
88 for (j = 0, q = p1, r *= s; j < mm;)
89 *q++ -= r * w[j++];
90 }
91 }
92 *p = sv;
93 d[i] = -h;
94 }
95 if (mm == 1)
96 d[i] = *p;
97 p1 = p + 1;
98 if (nm > 1) {
99 sv = h = 0.;
100 for (j = 0, q = p1, s = 0.; j < nm; ++j, ++q)
101 s += *q * *q;
102 if (s > 0.) {
103 h = sqrt(s);
104 if (*p1 < 0.)
105 h = -h;
106 sv = 1. + fabs(*p1 / h);
107 s += *p1 * h;
108 s = 1. / s;
109 t = 1. / (*p1 += h);
110 for (k = n, ms = n * (n - i); k < ms; k += n) {
111 for (j = 0, q = p1, pp = p1 + k, r = 0.; j < nm; ++j)
112 r += *q++ * *pp++;
113 for (j = 0, q = p1, pp = p1 + k, r *= s; j < nm; ++j)
114 *pp++ -= r * *q++;
115 }
116 for (j = 1, q = p1 + 1; j < nm; ++j)
117 *q++ *= t;
118 }
119 *p1 = sv;
120 e[i] = -h;
121 }
122 if (nm == 1)
123 e[i] = *p1;
124 }
125 atovm(v, n);
126 qrbdu1(d, e, a, m, v, n);
127 for (i = 0; i < n; ++i) {
128 if (d[i] < 0.) {
129 d[i] = -d[i];
130 for (j = 0, p = v + i; j < n; ++j, p += n)
131 *p = -*p;
132 }
133 }
134 free(w);
135 return 0;
136}
void atou1(double *a, int m, int n)
Definition atou1.c:9
void atovm(double *v, int n)
Definition atovm.c:8
int qrbdu1(double *d, double *e, double *u, int m, double *v, int n)
Definition qrbdu1.c:9
double t
double r
int sv2u1v(double *d, double *a, int m, double *v, int n)
Definition sv2u1v.c:10