-
Notifications
You must be signed in to change notification settings - Fork 0
/
tron.cpp
249 lines (213 loc) · 5.4 KB
/
tron.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdarg.h>
#include "tron.h"
#ifndef min
template <class T> static inline T min(T x,T y) { return (x<y)?x:y; }
#endif
#ifndef max
template <class T> static inline T max(T x,T y) { return (x>y)?x:y; }
#endif
#ifdef __cplusplus
extern "C" {
#endif
extern double dnrm2_(int *, double *, int *);
extern double ddot_(int *, double *, int *, double *, int *);
extern int daxpy_(int *, double *, double *, int *, double *, int *);
extern int dscal_(int *, double *, double *, int *);
#ifdef __cplusplus
}
#endif
static void default_print(const char *buf)
{
fputs(buf,stdout);
fflush(stdout);
}
void TRON::info(const char *fmt,...)
{
char buf[BUFSIZ];
va_list ap;
va_start(ap,fmt);
vsprintf(buf,fmt,ap);
va_end(ap);
(*tron_print_string)(buf);
}
TRON::TRON(const function *fun_obj, double eps, double eps_cg, int max_iter)
{
this->fun_obj=const_cast<function *>(fun_obj);
this->eps=eps;
this->eps_cg=eps_cg;
this->max_iter=max_iter;
tron_print_string = default_print;
}
TRON::~TRON()
{
}
void TRON::tron(double *w)
{
// Parameters for updating the iterates.
double eta0 = 1e-4, eta1 = 0.25, eta2 = 0.75;
// Parameters for updating the trust region size delta.
double sigma1 = 0.25, sigma2 = 0.5, sigma3 = 4;
int n = fun_obj->get_nr_variable();
int i, cg_iter;
double delta, snorm, one=1.0;
double alpha, f, fnew, prered, actred, gs;
int search = 1, iter = 1, inc = 1;
double *s = new double[n];
double *r = new double[n];
double *g = new double[n];
// calculate gradient norm at w=0 for stopping condition.
double *w0 = new double[n];
for (i=0; i<n; i++)
w0[i] = 0;
fun_obj->fun(w0);
fun_obj->grad(w0, g);
double gnorm0 = dnrm2_(&n, g, &inc);
delete [] w0;
f = fun_obj->fun(w);
fun_obj->grad(w, g);
delta = dnrm2_(&n, g, &inc);
double gnorm = delta;
if (gnorm <= eps*gnorm0)
search = 0;
iter = 1;
double *w_new = new double[n];
bool reach_boundary;
while (iter <= max_iter && search)
{
cg_iter = trcg(delta, g, s, r, &reach_boundary);
memcpy(w_new, w, sizeof(double)*n);
daxpy_(&n, &one, s, &inc, w_new, &inc);
gs = ddot_(&n, g, &inc, s, &inc);
prered = -0.5*(gs-ddot_(&n, s, &inc, r, &inc));
fnew = fun_obj->fun(w_new);
// Compute the actual reduction.
actred = f - fnew;
// On the first iteration, adjust the initial step bound.
snorm = dnrm2_(&n, s, &inc);
if (iter == 1)
delta = min(delta, snorm);
// Compute prediction alpha*snorm of the step.
if (fnew - f - gs <= 0)
alpha = sigma3;
else
alpha = max(sigma1, -0.5*(gs/(fnew - f - gs)));
// Update the trust region bound according to the ratio of actual to predicted reduction.
if (actred < eta0*prered)
delta = min(max(alpha, sigma1)*snorm, sigma2*delta);
else if (actred < eta1*prered)
delta = max(sigma1*delta, min(alpha*snorm, sigma2*delta));
else if (actred < eta2*prered)
delta = max(sigma1*delta, min(alpha*snorm, sigma3*delta));
else
{
if (reach_boundary)
delta = sigma3*delta;
else
delta = max(delta, min(alpha*snorm, sigma3*delta));
}
info("iter %2d act %5.3e pre %5.3e delta %5.3e f %5.3e |g| %5.3e CG %3d\n", iter, actred, prered, delta, f, gnorm, cg_iter);
if (actred > eta0*prered)
{
iter++;
memcpy(w, w_new, sizeof(double)*n);
f = fnew;
fun_obj->grad(w, g);
gnorm = dnrm2_(&n, g, &inc);
if (gnorm <= eps*gnorm0)
break;
}
if (f < -1.0e+32)
{
info("WARNING: f < -1.0e+32\n");
break;
}
if (prered <= 0)
{
info("WARNING: prered <= 0\n");
break;
}
if (fabs(actred) <= 1.0e-12*fabs(f) &&
fabs(prered) <= 1.0e-12*fabs(f))
{
info("WARNING: actred and prered too small\n");
break;
}
}
delete[] g;
delete[] r;
delete[] w_new;
delete[] s;
}
int TRON::trcg(double delta, double *g, double *s, double *r, bool *reach_boundary)
{
int i, inc = 1;
int n = fun_obj->get_nr_variable();
double one = 1;
double *d = new double[n];
double *Hd = new double[n];
double rTr, rnewTrnew, alpha, beta, cgtol;
*reach_boundary = false;
for (i=0; i<n; i++)
{
s[i] = 0;
r[i] = -g[i];
d[i] = r[i];
}
cgtol = eps_cg*dnrm2_(&n, g, &inc);
int cg_iter = 0;
rTr = ddot_(&n, r, &inc, r, &inc);
while (1)
{
if (dnrm2_(&n, r, &inc) <= cgtol)
break;
cg_iter++;
fun_obj->Hv(d, Hd);
alpha = rTr/ddot_(&n, d, &inc, Hd, &inc);
daxpy_(&n, &alpha, d, &inc, s, &inc);
if (dnrm2_(&n, s, &inc) > delta)
{
info("cg reaches trust region boundary\n");
*reach_boundary = true;
alpha = -alpha;
daxpy_(&n, &alpha, d, &inc, s, &inc);
double std = ddot_(&n, s, &inc, d, &inc);
double sts = ddot_(&n, s, &inc, s, &inc);
double dtd = ddot_(&n, d, &inc, d, &inc);
double dsq = delta*delta;
double rad = sqrt(std*std + dtd*(dsq-sts));
if (std >= 0)
alpha = (dsq - sts)/(std + rad);
else
alpha = (rad - std)/dtd;
daxpy_(&n, &alpha, d, &inc, s, &inc);
alpha = -alpha;
daxpy_(&n, &alpha, Hd, &inc, r, &inc);
break;
}
alpha = -alpha;
daxpy_(&n, &alpha, Hd, &inc, r, &inc);
rnewTrnew = ddot_(&n, r, &inc, r, &inc);
beta = rnewTrnew/rTr;
dscal_(&n, &beta, d, &inc);
daxpy_(&n, &one, r, &inc, d, &inc);
rTr = rnewTrnew;
}
delete[] d;
delete[] Hd;
return(cg_iter);
}
double TRON::norm_inf(int n, double *x)
{
double dmax = fabs(x[0]);
for (int i=1; i<n; i++)
if (fabs(x[i]) >= dmax)
dmax = fabs(x[i]);
return(dmax);
}
void TRON::set_print_string(void (*print_string) (const char *buf))
{
tron_print_string = print_string;
}