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#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
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, int max_iter, BlasFunctions *blas)
{
this->fun_obj=const_cast<function *>(fun_obj);
this->eps=eps;
this->max_iter=max_iter;
this->blas=blas;
tron_print_string = default_print;
}
TRON::~TRON()
{
}
int 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;
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 *w_new = new double[n];
double *g = new double[n];
for (i=0; i<n; i++)
w[i] = 0;
f = fun_obj->fun(w);
fun_obj->grad(w, g);
delta = blas->nrm2(n, g, inc);
double gnorm1 = delta;
double gnorm = gnorm1;
if (gnorm <= eps*gnorm1)
search = 0;
iter = 1;
while (iter <= max_iter && search)
{
cg_iter = trcg(delta, g, s, r);
memcpy(w_new, w, sizeof(double)*n);
blas->axpy(n, 1.0, s, inc, w_new, inc);
gs = blas->dot(n, g, inc, s, inc);
prered = -0.5*(gs - blas->dot(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 = blas->nrm2(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
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 = blas->nrm2(n, g, inc);
if (gnorm <= eps*gnorm1)
break;
}
if (f < -1.0e+32)
{
info("WARNING: f < -1.0e+32\n");
break;
}
if (fabs(actred) <= 0 && prered <= 0)
{
info("WARNING: actred and 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;
return --iter;
}
int TRON::trcg(double delta, double *g, double *s, double *r)
{
int i, inc = 1;
int n = fun_obj->get_nr_variable();
double *d = new double[n];
double *Hd = new double[n];
double rTr, rnewTrnew, alpha, beta, cgtol;
for (i=0; i<n; i++)
{
s[i] = 0;
r[i] = -g[i];
d[i] = r[i];
}
cgtol = 0.1 * blas->nrm2(n, g, inc);
int cg_iter = 0;
rTr = blas->dot(n, r, inc, r, inc);
while (1)
{
if (blas->nrm2(n, r, inc) <= cgtol)
break;
cg_iter++;
fun_obj->Hv(d, Hd);
alpha = rTr / blas->dot(n, d, inc, Hd, inc);
blas->axpy(n, alpha, d, inc, s, inc);
if (blas->nrm2(n, s, inc) > delta)
{
info("cg reaches trust region boundary\n");
alpha = -alpha;
blas->axpy(n, alpha, d, inc, s, inc);
double std = blas->dot(n, s, inc, d, inc);
double sts = blas->dot(n, s, inc, s, inc);
double dtd = blas->dot(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;
blas->axpy(n, alpha, d, inc, s, inc);
alpha = -alpha;
blas->axpy(n, alpha, Hd, inc, r, inc);
break;
}
alpha = -alpha;
blas->axpy(n, alpha, Hd, inc, r, inc);
rnewTrnew = blas->dot(n, r, inc, r, inc);
beta = rnewTrnew/rTr;
blas->scal(n, beta, d, inc);
blas->axpy(n, 1.0, 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;
}
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