GRASS GIS 8 Programmer's Manual 8.3.2(2024)-exported
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brent.c
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1/* min/brent.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
4 *
5 * Taken from 'GSL - The GNU Scientific Library':
6 * "One dimensional Minimization"
7 * http://sources.redhat.com/gsl/
8 * modified by Stefano Menegon 2004
9 *
10 * This program is free software; you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation; either version 2 of the License, or (at
13 * your option) any later version.
14 *
15 * This program is distributed in the hope that it will be useful, but
16 * WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
18 * General Public License for more details.
19 *
20 * You should have received a copy of the GNU General Public License
21 * along with this program; if not, write to the Free Software
22 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 */
24
25#include <stdlib.h>
26#include <stdio.h>
27#include <math.h>
28#include <float.h>
29
30#define GSL_SQRT_DBL_EPSILON 1.e-4
31#define GSL_DBL_EPSILON 1.e-8
32
33/*
34 #define SAFE_FUNC_CALL(f, x, yp) \
35 do { \
36 *yp = GSL_FN_EVAL(f,x); \
37 if (!finite(*yp)) \
38 fprintf(stderr,"function not continuous\n");\
39 } while (0)
40 */
41
42typedef struct {
43 double d, e, v, w;
44 double f_v, f_w;
45} brent_state_t;
46
47static int brent(void *vstate, double (*f)(double), double *x_minimum,
48 double *f_minimum, double *x_lower, double *f_lower,
49 double *x_upper, double *f_upper)
50{
51 brent_state_t *state = (brent_state_t *)vstate;
52
53 const double x_left = *x_lower;
54 const double x_right = *x_upper;
55
56 const double z = *x_minimum;
57 double d = state->e;
58 double e = state->d;
59 double u, f_u;
60 const double v = state->v;
61 const double w = state->w;
62 const double f_v = state->f_v;
63 const double f_w = state->f_w;
64 const double f_z = *f_minimum;
65
66 const double golden = 0.3819660; /* golden = (3 - sqrt(5))/2 */
67
68 const double w_lower = (z - x_left);
69 const double w_upper = (x_right - z);
70
71 const double tolerance = GSL_SQRT_DBL_EPSILON * fabs(z);
72
73 double p = 0, q = 0, r = 0;
74
75 const double midpoint = 0.5 * (x_left + x_right);
76
77 if (fabs(e) > tolerance) {
78 /* fit parabola */
79
80 r = (z - w) * (f_z - f_v);
81 q = (z - v) * (f_z - f_w);
82 p = (z - v) * q - (z - w) * r;
83 q = 2 * (q - r);
84
85 if (q > 0) {
86 p = -p;
87 }
88 else {
89 q = -q;
90 }
91
92 r = e;
93 e = d;
94 }
95
96 if (fabs(p) < fabs(0.5 * q * r) && p < q * w_lower && p < q * w_upper) {
97 double t2 = 2 * tolerance;
98
99 d = p / q;
100 u = z + d;
101
102 if ((u - x_left) < t2 || (x_right - z) < t2) {
103 d = (z < midpoint) ? tolerance : -tolerance;
104 }
105 }
106 else {
107 e = (z < midpoint) ? x_right - z : -(z - x_left);
108 d = golden * e;
109 }
110
111 if (fabs(d) >= tolerance) {
112 u = z + d;
113 }
114 else {
115 u = z + ((d > 0) ? tolerance : -tolerance);
116 }
117
118 state->e = e;
119 state->d = d;
120
121 /* SAFE_FUNC_CALL(f, u, &f_u); */
122 f_u = (*f)(u);
123
124 if (f_u > f_z) {
125 if (u < z) {
126 *x_lower = u;
127 *f_lower = f_u;
128 return 0;
129 }
130 else {
131 *x_upper = u;
132 *f_upper = f_u;
133 return 0;
134 }
135 }
136 else if (f_u < f_z) {
137 if (u < z) {
138 *x_upper = z;
139 *f_upper = f_z;
140 }
141 else {
142 *x_lower = z;
143 *f_lower = f_z;
144 }
145
146 state->v = w;
147 state->f_v = f_w;
148 state->w = z;
149 state->f_w = f_z;
150 *x_minimum = u;
151 *f_minimum = f_u;
152 return 0;
153 }
154 else if (f_u <= f_w || w == z) {
155 state->v = w;
156 state->f_v = f_w;
157 state->w = u;
158 state->f_w = f_u;
159 return 0;
160 }
161 else if (f_u <= f_v || v == z || v == w) {
162 state->v = u;
163 state->f_v = f_u;
164 return 0;
165 }
166 else {
167 return -1;
168 }
169}
170
171/* Code modified by Stefano Menegon 1st of February 2004 */
172
173double brent_iterate(double (*f)(double), double x_lower, double x_upper,
174 int maxiter)
175{
176 int i;
177 double x_minimum = (x_upper + x_lower) / 2.;
178 double f_minimum;
179 double f_lower;
180 double f_upper;
181
182 /* stato iterazione */
183 brent_state_t itstate;
184 const double golden = 0.3819660; /* golden = (3 - sqrt(5))/2 */
185 double v = x_lower + golden * (x_upper - x_lower);
186 double w = v;
187 double f_vw;
188
189 f_lower = (*f)(x_lower);
190 f_upper = (*f)(x_upper);
191 f_minimum = (*f)(x_minimum);
192
193 itstate.v = v;
194 itstate.w = w;
195
196 itstate.d = 0.;
197 itstate.e = 0.;
198
199 /* SAFE_FUNC_CALL (f, v, &f_vw); */
200
201 f_vw = (*f)(v);
202
203 itstate.f_v = f_vw;
204 itstate.f_w = f_vw;
205
206 for (i = 0; i < maxiter; i++) {
207 brent(&itstate, f, &x_minimum, &f_minimum, &x_lower, &f_lower, &x_upper,
208 &f_upper);
209 if (fabs(f_upper - f_lower) < GSL_DBL_EPSILON * fabs(f_minimum)) {
210 return x_minimum;
211 }
212 }
213
214 return x_minimum;
215}
#define GSL_SQRT_DBL_EPSILON
Definition brent.c:30
#define GSL_DBL_EPSILON
Definition brent.c:31
double brent_iterate(double(*f)(double), double x_lower, double x_upper, int maxiter)
Definition brent.c:173
double r
struct state state
Definition parser.c:103