GRASS GIS 8 Programmer's Manual 8.4.1(2025)-45ca3179ab
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matrix.c
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1/*!
2 * \author
3 * Lubos Mitas (original program and various modifications)
4 *
5 * \author
6 * H. Mitasova,
7 * I. Kosinovsky, D. Gerdes,
8 * D. McCauley
9 * (GRASS4.1 version of the program and GRASS4.2 modifications)
10 *
11 * \author
12 * L. Mitas,
13 * H. Mitasova,
14 * I. Kosinovsky,
15 * D.Gerdes,
16 * D. McCauley
17 * (1993, 1995)
18 *
19 * \author modified by McCauley in August 1995
20 * \author modified by Mitasova in August 1995, Nov. 1996
21 *
22 * \copyright
23 * (C) 1993-1996 by Lubos Mitas and the GRASS Development Team
24 *
25 * \copyright
26 * This program is free software under the GNU General Public License (>=v2).
27 * Read the file COPYING that comes with GRASS for details.
28 */
29
30#include <stdio.h>
31#include <math.h>
32#include <unistd.h>
33#include <grass/gis.h>
34#include <grass/interpf.h>
35#include <grass/gmath.h>
36
38 struct triple *points, /* points for interpolation */
39 int n_points, /* number of points */
40 double **matrix, /* matrix */
41 int *indx)
42{
43 static double *A = NULL;
44
45 if (!A) {
46 if (!(A = G_alloc_vector((params->KMAX2 + 2) * (params->KMAX2 + 2) +
47 1))) {
48 fprintf(stderr, "Cannot allocate memory for A\n");
49 return -1;
50 }
51 }
52 return IL_matrix_create_alloc(params, points, n_points, matrix, indx, A);
53}
54
55/*!
56 * \brief Creates system of linear equations from interpolated points
57 *
58 * Creates system of linear equations represented by matrix using given
59 * points and interpolating function interp()
60 *
61 * \param params struct interp_params *
62 * \param points points for interpolation as struct triple
63 * \param n_points number of points
64 * \param[out] matrix the matrix
65 * \param indx
66 *
67 * \return -1 on failure, 1 on success
68 */
70 struct triple *points, /* points for interpolation */
71 int n_points, /* number of points */
72 double **matrix, /* matrix */
73 int *indx, double *A
74 /* temporary matrix unique for all threads */)
75{
76 double xx, yy;
77 double rfsta2, r;
78 double d;
79 int n1, k1, k2, k, i1, l, m, i, j;
80 double fstar2 = params->fi * params->fi / 4.;
81 double RO, amaxa;
82 double rsin = 0, rcos = 0, teta,
83 scale = 0; /*anisotropy parameters - added by JH 2002 */
84 double xxr, yyr;
85
86 if (params->theta) {
87 teta = params->theta * (M_PI / 180); /* deg to rad */
88 rsin = sin(teta);
89 rcos = cos(teta);
90 }
91 if (params->scalex)
92 scale = params->scalex;
93
94 n1 = n_points + 1;
95
96 /*
97 C GENERATION OF MATRIX
98 C FIRST COLUMN
99 */
100 A[1] = 0.;
101 for (k = 1; k <= n_points; k++) {
102 i1 = k + 1;
103 A[i1] = 1.;
104 }
105 /*
106 C OTHER COLUMNS
107 */
108 RO = -params->rsm;
109 /* fprintf (stderr, "sm[%d] = %f, ro=%f\n", 1, points[1].smooth, RO); */
110 for (k = 1; k <= n_points; k++) {
111 k1 = k * n1 + 1;
112 k2 = k + 1;
113 i1 = k1 + k;
114 if (params->rsm < 0.) { /*indicates variable smoothing */
115 A[i1] = -points[k - 1].sm; /* added by Mitasova nov. 96 */
116 /* G_debug(5, "sm[%d]=%f, a=%f", k, points[k-1].sm, A[i1]); */
117 }
118 else {
119 A[i1] = RO; /* constant smoothing */
120 }
121 /* if (i1 == 100) fprintf (stderr,i "A[%d] = %f\n", i1, A[i1]); */
122
123 /* A[i1] = RO; */
124 for (l = k2; l <= n_points; l++) {
125 xx = points[k - 1].x - points[l - 1].x;
126 yy = points[k - 1].y - points[l - 1].y;
127
128 if ((params->theta) && (params->scalex)) {
129 /* re run anisotropy */
130 xxr = xx * rcos + yy * rsin;
131 yyr = yy * rcos - xx * rsin;
132 xx = xxr;
133 yy = yyr;
134 r = scale * xx * xx + yy * yy;
135 rfsta2 = fstar2 * (scale * xx * xx + yy * yy);
136 }
137 else {
138 r = xx * xx + yy * yy;
139 rfsta2 = fstar2 * (xx * xx + yy * yy);
140 }
141
142 if (rfsta2 == 0.) {
143 fprintf(stderr, "ident. points in segm.\n");
144 fprintf(stderr, "x[%d]=%f, x[%d]=%f, y[%d]=%f, y[%d]=%f\n",
145 k - 1, points[k - 1].x, l - 1, points[l - 1].x, k - 1,
146 points[k - 1].y, l - 1, points[l - 1].y);
147 return -1;
148 }
149 i1 = k1 + l;
150 A[i1] = params->interp(r, params->fi);
151 }
152 }
153
154 /* C SYMMETRISATION */
155 amaxa = 1.;
156 for (k = 1; k <= n1; k++) {
157 k1 = (k - 1) * n1;
158 k2 = k + 1;
159 for (l = k2; l <= n1; l++) {
160 m = (l - 1) * n1 + k;
161 A[m] = A[k1 + l];
162 amaxa = amax1(A[m], amaxa);
163 }
164 }
165 m = 0;
166 for (i = 0; i <= n_points; i++) {
167 for (j = 0; j <= n_points; j++) {
168 m++;
169 matrix[i][j] = A[m];
170 }
171 }
172
173 G_debug(3, "calling G_ludcmp() n=%d indx=%d", n_points, *indx);
174 if (G_ludcmp(matrix, n_points + 1, indx, &d) <= 0) {
175 /* find the inverse of the matrix */
176 fprintf(stderr, "G_ludcmp() failed! n=%d d=%.2f\n", n_points, d);
177 return -1;
178 }
179
180 /* G_free_vector(A); */
181 return 1;
182}
#define NULL
Definition ccmath.h:32
double * G_alloc_vector(size_t n)
Vector matrix memory allocation.
Definition dalloc.c:39
int G_debug(int level, const char *msg,...)
Print debugging message.
Definition debug.c:66
double l
double r
double amax1(double, double)
Definition minmax.c:52
int G_ludcmp(double **a, int n, int *indx, double *d)
LU decomposition.
Definition lu.c:17
int IL_matrix_create_alloc(struct interp_params *params, struct triple *points, int n_points, double **matrix, int *indx, double *A)
Creates system of linear equations from interpolated points.
Definition matrix.c:69
int IL_matrix_create(struct interp_params *params, struct triple *points, int n_points, double **matrix, int *indx)
Definition matrix.c:37
interp_fn * interp
Definition interpf.h:124
double fi
Definition interpf.h:88
double theta
Definition interpf.h:105
double rsm
Definition interpf.h:94
double scalex
Definition interpf.h:107
double sm
Definition dataquad.h:42
double x
Definition dataquad.h:39
double y
Definition dataquad.h:40
#define x