GRASS GIS 8 Programmer's Manual 8.3.2(2024)-exported
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sv2uv.c
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1/* sv2uv.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 sv2uv(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, 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 ldumat(a, u, m, n);
54 for (i = 0, q = a; i < n; ++i) {
55 for (j = 0; j < n; ++j, ++q) {
56 if (j < i)
57 *q = 0.;
58 else if (j == i)
59 *q = d[i];
60 }
61 }
62 for (i = 0, mm = n, nm = n - 1, p = a; i < n; ++i, --mm, --nm, p += n + 1) {
63 if (i && mm > 1) {
64 sv = h = 0.;
65 for (j = 0, q = p, s = 0.; j < mm; ++j, q += n) {
66 w[j] = *q;
67 s += *q * *q;
68 }
69 if (s > 0.) {
70 h = sqrt(s);
71 if (*p < 0.)
72 h = -h;
73 s += *p * h;
74 s = 1. / s;
75 t = 1. / (w[0] += h);
76 sv = 1. + fabs(*p / h);
77 for (k = 1, ms = n - i; k < ms; ++k) {
78 for (j = 0, q = p + k, r = 0.; j < mm; q += n)
79 r += w[j++] * *q;
80 for (j = 0, q = p + k, r *= s; j < mm; q += n)
81 *q -= r * w[j++];
82 }
83 for (k = 0, p1 = u + i; k < m; ++k, p1 += m) {
84 for (j = 0, q = p1, r = 0.; j < mm;)
85 r += w[j++] * *q++;
86 for (j = 0, q = p1, r *= s; j < mm;)
87 *q++ -= r * w[j++];
88 }
89 }
90 *p = sv;
91 d[i] = -h;
92 }
93 if (mm == 1)
94 d[i] = *p;
95 p1 = p + 1;
96 if (nm > 1) {
97 sv = h = 0.;
98 for (j = 0, q = p1, s = 0.; j < nm; ++j, ++q)
99 s += *q * *q;
100 if (s > 0.) {
101 h = sqrt(s);
102 if (*p1 < 0.)
103 h = -h;
104 sv = 1. + fabs(*p1 / h);
105 s += *p1 * h;
106 s = 1. / s;
107 t = 1. / (*p1 += h);
108 for (k = n, ms = n * (n - i); k < ms; k += n) {
109 for (j = 0, q = p1, pp = p1 + k, r = 0.; j < nm; ++j)
110 r += *q++ * *pp++;
111 for (j = 0, q = p1, pp = p1 + k, r *= s; j < nm; ++j)
112 *pp++ -= r * *q++;
113 }
114 for (j = 1, q = p1 + 1; j < nm; ++j)
115 *q++ *= t;
116 }
117 *p1 = sv;
118 e[i] = -h;
119 }
120 if (nm == 1)
121 e[i] = *p1;
122 }
123 ldvmat(a, v, n);
124 qrbdv(d, e, u, m, v, n);
125 for (i = 0; i < n; ++i) {
126 if (d[i] < 0.) {
127 d[i] = -d[i];
128 for (j = 0, p = v + i; j < n; ++j, p += n)
129 *p = -*p;
130 }
131 }
132 free(w);
133 return 0;
134}
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 sv2uv(double *d, double *a, double *u, int m, double *v, int n)
Definition sv2uv.c:10