00001 #include <math.h>
00002 #include <stdio.h>
00003 #include <string.h>
00004 #include <stdarg.h>
00005
00006 #include "lib/config.h"
00007
00008 #ifdef HAVE_LAPACK
00009 #include "lib/Mathematics.h"
00010 #include "classifier/svm/Tron.h"
00011
00012 CTron::CTron(const function *f, float64_t e, int32_t it)
00013 : CSGObject()
00014 {
00015 this->fun_obj=const_cast<function *>(f);
00016 this->eps=e;
00017 this->max_iter=it;
00018 }
00019
00020 CTron::~CTron()
00021 {
00022 }
00023
00024 void CTron::tron(float64_t *w)
00025 {
00026
00027 float64_t eta0 = 1e-4, eta1 = 0.25, eta2 = 0.75;
00028
00029
00030 float64_t sigma1 = 0.25, sigma2 = 0.5, sigma3 = 4.;
00031
00032 int32_t i, cg_iter;
00033 float64_t delta, snorm, one=1.0;
00034 float64_t alpha, f, fnew, prered, actred, gs;
00035
00036
00037 int n = (int) fun_obj->get_nr_variable();
00038 int search = 1, iter = 1, inc = 1;
00039 double *s = new double[n];
00040 double *r = new double[n];
00041 double *w_new = new double[n];
00042 double *g = new double[n];
00043
00044 for (i=0; i<n; i++)
00045 w[i] = 0;
00046
00047 f = fun_obj->fun(w);
00048 fun_obj->grad(w, g);
00049 delta = cblas_dnrm2(n, g, inc);
00050 float64_t gnorm1 = delta;
00051 float64_t gnorm = gnorm1;
00052
00053 if (gnorm <= eps*gnorm1)
00054 search = 0;
00055
00056 iter = 1;
00057
00058 while (iter <= max_iter && search)
00059 {
00060 cg_iter = trcg(delta, g, s, r);
00061
00062 memcpy(w_new, w, sizeof(float64_t)*n);
00063 cblas_daxpy(n, one, s, inc, w_new, inc);
00064
00065 gs = cblas_ddot(n, g, inc, s, inc);
00066 prered = -0.5*(gs-cblas_ddot(n, s, inc, r, inc));
00067 fnew = fun_obj->fun(w_new);
00068
00069
00070 actred = f - fnew;
00071
00072
00073 snorm = cblas_dnrm2(n, s, inc);
00074 if (iter == 1)
00075 delta = CMath::min(delta, snorm);
00076
00077
00078 if (fnew - f - gs <= 0)
00079 alpha = sigma3;
00080 else
00081 alpha = CMath::max(sigma1, -0.5*(gs/(fnew - f - gs)));
00082
00083
00084 if (actred < eta0*prered)
00085 delta = CMath::min(CMath::max(alpha, sigma1)*snorm, sigma2*delta);
00086 else if (actred < eta1*prered)
00087 delta = CMath::max(sigma1*delta, CMath::min(alpha*snorm, sigma2*delta));
00088 else if (actred < eta2*prered)
00089 delta = CMath::max(sigma1*delta, CMath::min(alpha*snorm, sigma3*delta));
00090 else
00091 delta = CMath::max(delta, CMath::min(alpha*snorm, sigma3*delta));
00092
00093 SG_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);
00094
00095 if (actred > eta0*prered)
00096 {
00097 iter++;
00098 memcpy(w, w_new, sizeof(float64_t)*n);
00099 f = fnew;
00100 fun_obj->grad(w, g);
00101
00102 gnorm = cblas_dnrm2(n, g, inc);
00103 if (gnorm < eps*gnorm1)
00104 break;
00105 }
00106 if (f < -1.0e+32)
00107 {
00108 SG_WARNING("f < -1.0e+32\n");
00109 break;
00110 }
00111 if (CMath::abs(actred) <= 0 && CMath::abs(prered) <= 0)
00112 {
00113 SG_WARNING("actred and prered <= 0\n");
00114 break;
00115 }
00116 if (CMath::abs(actred) <= 1.0e-12*CMath::abs(f) &&
00117 CMath::abs(prered) <= 1.0e-12*CMath::abs(f))
00118 {
00119 SG_WARNING("actred and prered too small\n");
00120 break;
00121 }
00122 }
00123
00124 delete[] g;
00125 delete[] r;
00126 delete[] w_new;
00127 delete[] s;
00128 }
00129
00130 int32_t CTron::trcg(float64_t delta, double* g, double* s, double* r)
00131 {
00132
00133 int i, cg_iter;
00134 int n = (int) fun_obj->get_nr_variable();
00135 int inc = 1;
00136 double one = 1;
00137 double *Hd = new double[n];
00138 double *d = new double[n];
00139 double rTr, rnewTrnew, alpha, beta, cgtol;
00140
00141 for (i=0; i<n; i++)
00142 {
00143 s[i] = 0;
00144 r[i] = -g[i];
00145 d[i] = r[i];
00146 }
00147 cgtol = 0.1* cblas_dnrm2(n, g, inc);
00148
00149 cg_iter = 0;
00150 rTr = cblas_ddot(n, r, inc, r, inc);
00151 while (1)
00152 {
00153 if (cblas_dnrm2(n, r, inc) <= cgtol)
00154 break;
00155 cg_iter++;
00156 fun_obj->Hv(d, Hd);
00157
00158 alpha = rTr/cblas_ddot(n, d, inc, Hd, inc);
00159 cblas_daxpy(n, alpha, d, inc, s, inc);
00160 if (cblas_dnrm2(n, s, inc) > delta)
00161 {
00162 SG_INFO("cg reaches trust region boundary\n");
00163 alpha = -alpha;
00164 cblas_daxpy(n, alpha, d, inc, s, inc);
00165
00166 double std = cblas_ddot(n, s, inc, d, inc);
00167 double sts = cblas_ddot(n, s, inc, s, inc);
00168 double dtd = cblas_ddot(n, d, inc, d, inc);
00169 double dsq = delta*delta;
00170 double rad = sqrt(std*std + dtd*(dsq-sts));
00171 if (std >= 0)
00172 alpha = (dsq - sts)/(std + rad);
00173 else
00174 alpha = (rad - std)/dtd;
00175 cblas_daxpy(n, alpha, d, inc, s, inc);
00176 alpha = -alpha;
00177 cblas_daxpy(n, alpha, Hd, inc, r, inc);
00178 break;
00179 }
00180 alpha = -alpha;
00181 cblas_daxpy(n, alpha, Hd, inc, r, inc);
00182 rnewTrnew = cblas_ddot(n, r, inc, r, inc);
00183 beta = rnewTrnew/rTr;
00184 cblas_dscal(n, beta, d, inc);
00185 cblas_daxpy(n, one, r, inc, d, inc);
00186 rTr = rnewTrnew;
00187 }
00188
00189 delete[] d;
00190 delete[] Hd;
00191
00192 return(cg_iter);
00193 }
00194
00195 float64_t CTron::norm_inf(int32_t n, float64_t *x)
00196 {
00197 float64_t dmax = CMath::abs(x[0]);
00198 for (int32_t i=1; i<n; i++)
00199 if (CMath::abs(x[i]) >= dmax)
00200 dmax = CMath::abs(x[i]);
00201 return(dmax);
00202 }
00203 #endif //HAVE_LAPACK