GRASS GIS 8 Programmer's Manual  8.4.0dev(2024)-2653d7b383
svduv.c
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1 /* svduv.c CCMATH mathematics library source code.
2  *
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"
10 int 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
Definition: r_raster.c:39
double r
Definition: r_raster.c:39
void free(void *)
int svduv(double *d, double *a, double *u, int m, double *v, int n)
Definition: svduv.c:10