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LibLinear.cpp
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LibLinear.cpp
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/*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or
* (at your option) any later version.
*
* Written (W) 2007-2010 Soeren Sonnenburg
* Copyright (c) 2007-2009 The LIBLINEAR Project.
* Copyright (C) 2007-2010 Fraunhofer Institute FIRST and Max-Planck-Society
*/
#include <shogun/lib/config.h>
#include <shogun/base/Parameter.h>
#include <shogun/base/progress.h>
#include <shogun/classifier/svm/LibLinear.h>
#include <shogun/features/DotFeatures.h>
#include <shogun/io/SGIO.h>
#include <shogun/labels/BinaryLabels.h>
#include <shogun/lib/Signal.h>
#include <shogun/lib/Time.h>
#include <shogun/optimization/liblinear/tron.h>
using namespace shogun;
CLibLinear::CLibLinear()
: CLinearMachine()
{
init();
}
CLibLinear::CLibLinear(LIBLINEAR_SOLVER_TYPE l)
: CLinearMachine()
{
init();
liblinear_solver_type=l;
}
CLibLinear::CLibLinear(
float64_t C, CDotFeatures* traindat, CLabels* trainlab)
: CLinearMachine()
{
init();
C1=C;
C2=C;
use_bias=true;
set_features(traindat);
set_labels(trainlab);
init_linear_term();
}
void CLibLinear::init()
{
liblinear_solver_type=L2R_L1LOSS_SVC_DUAL;
use_bias=false;
C1=1;
C2=1;
set_max_iterations();
epsilon=1e-5;
/** Prevent default bias computation*/
set_compute_bias(false);
SG_ADD(&C1, "C1", "C Cost constant 1.", MS_AVAILABLE);
SG_ADD(&C2, "C2", "C Cost constant 2.", MS_AVAILABLE);
SG_ADD(&use_bias, "use_bias", "Indicates if bias is used.",
MS_NOT_AVAILABLE);
SG_ADD(&epsilon, "epsilon", "Convergence precision.", MS_NOT_AVAILABLE);
SG_ADD(&max_iterations, "max_iterations", "Max number of iterations.",
MS_NOT_AVAILABLE);
SG_ADD(&m_linear_term, "linear_term", "Linear Term", MS_NOT_AVAILABLE);
SG_ADD((machine_int_t*) &liblinear_solver_type, "liblinear_solver_type",
"Type of LibLinear solver.", MS_NOT_AVAILABLE);
}
CLibLinear::~CLibLinear()
{
}
bool CLibLinear::train_machine(CFeatures* data)
{
ASSERT(m_labels)
ASSERT(m_labels->get_label_type() == LT_BINARY)
if (data)
{
if (!data->has_property(FP_DOT))
SG_ERROR("Specified features are not of type CDotFeatures\n")
set_features((CDotFeatures*) data);
}
ASSERT(features)
index_t num_train_labels=m_labels->get_num_labels();
index_t num_feat=features->get_dim_feature_space();
index_t num_vec=features->get_num_vectors();
if (liblinear_solver_type == L1R_L2LOSS_SVC ||
(liblinear_solver_type == L1R_LR) )
{
if (num_feat!=num_train_labels)
{
SG_ERROR("L1 methods require the data to be transposed: "
"number of features %d does not match number of "
"training labels %d\n",
num_feat, num_train_labels);
}
CMath::swap(num_feat, num_vec);
}
else
{
if (num_vec!=num_train_labels)
{
SG_ERROR("number of vectors %d does not match "
"number of training labels %d\n",
num_vec, num_train_labels);
}
}
SGVector<float64_t> w;
if (use_bias)
w=SGVector<float64_t>(SG_MALLOC(float64_t, num_feat+1), num_feat);
else
w=SGVector<float64_t>(num_feat);
liblinear_problem prob;
if (use_bias)
{
if(liblinear_solver_type!=L2R_LR_DUAL)
prob.n=w.vlen+1;
else
prob.n=w.vlen;
memset(w.vector, 0, sizeof(float64_t)*(w.vlen+1));
}
else
{
prob.n=w.vlen;
memset(w.vector, 0, sizeof(float64_t)*(w.vlen+0));
}
prob.l=num_vec;
prob.x=features;
prob.y=SG_MALLOC(double, prob.l);
float64_t* Cs=SG_MALLOC(double, prob.l);
prob.use_bias=use_bias;
double Cp=C1;
double Cn=C2;
for (index_t i=0; i<prob.l; i++)
{
prob.y[i]=((CBinaryLabels*) m_labels)->get_int_label(i);
if (prob.y[i] == +1)
Cs[i]=C1;
else if (prob.y[i] == -1)
Cs[i]=C2;
else
SG_ERROR("labels should be +1/-1 only\n")
}
int pos = 0;
int neg = 0;
for(int i=0;i<prob.l;i++)
{
if(prob.y[i]==+1)
pos++;
}
neg = prob.l - pos;
SG_INFO("%d training points %d dims\n", prob.l, prob.n)
function *fun_obj=NULL;
switch (liblinear_solver_type)
{
case L2R_LR:
{
fun_obj=new l2r_lr_fun(&prob, Cs);
CTron tron_obj(fun_obj, epsilon*CMath::min(pos,neg)/prob.l, max_iterations);
SG_DEBUG("starting L2R_LR training via tron\n")
tron_obj.tron(w.vector, m_max_train_time);
SG_DEBUG("done with tron\n")
delete fun_obj;
break;
}
case L2R_L2LOSS_SVC:
{
fun_obj=new l2r_l2_svc_fun(&prob, Cs);
CTron tron_obj(fun_obj, epsilon*CMath::min(pos,neg)/prob.l, max_iterations);
tron_obj.tron(w.vector, m_max_train_time);
delete fun_obj;
break;
}
case L2R_L2LOSS_SVC_DUAL:
solve_l2r_l1l2_svc(w, &prob, epsilon, Cp, Cn, L2R_L2LOSS_SVC_DUAL);
break;
case L2R_L1LOSS_SVC_DUAL:
solve_l2r_l1l2_svc(w, &prob, epsilon, Cp, Cn, L2R_L1LOSS_SVC_DUAL);
break;
case L1R_L2LOSS_SVC:
{
//ASSUME FEATURES ARE TRANSPOSED ALREADY
solve_l1r_l2_svc(w, &prob, epsilon*CMath::min(pos,neg)/prob.l, Cp, Cn);
break;
}
case L1R_LR:
{
//ASSUME FEATURES ARE TRANSPOSED ALREADY
solve_l1r_lr(w, &prob, epsilon*CMath::min(pos,neg)/prob.l, Cp, Cn);
break;
}
case L2R_LR_DUAL:
{
solve_l2r_lr_dual(w, &prob, epsilon, Cp, Cn);
break;
}
default:
SG_ERROR("Error: unknown solver_type\n")
break;
}
set_w(w);
if (use_bias)
set_bias(w[w.vlen]);
else
set_bias(0);
SG_FREE(prob.y);
SG_FREE(Cs);
return true;
}
// A coordinate descent algorithm for
// L1-loss and L2-loss SVM dual problems
//
// min_\alpha 0.5(\alpha^T (Q + D)\alpha) - e^T \alpha,
// s.t. 0 <= alpha_i <= upper_bound_i,
//
// where Qij = yi yj xi^T xj and
// D is a diagonal matrix
//
// In L1-SVM case:
// upper_bound_i = Cp if y_i = 1
// upper_bound_i = Cn if y_i = -1
// D_ii = 0
// In L2-SVM case:
// upper_bound_i = INF
// D_ii = 1/(2*Cp) if y_i = 1
// D_ii = 1/(2*Cn) if y_i = -1
//
// Given:
// x, y, Cp, Cn
// eps is the stopping tolerance
//
// solution will be put in w
#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)
void CLibLinear::solve_l2r_l1l2_svc(
SGVector<float64_t>& w,
const liblinear_problem *prob, double eps, double Cp, double Cn, LIBLINEAR_SOLVER_TYPE st)
{
int l = prob->l;
int w_size = prob->n;
int i, s, iter = 0;
double C, d, G;
double *QD = SG_MALLOC(double, l);
int *index = SG_MALLOC(int, l);
double *alpha = SG_MALLOC(double, l);
int32_t *y = SG_MALLOC(int32_t, l);
int active_size = l;
// PG: projected gradient, for shrinking and stopping
double PG;
double PGmax_old = CMath::INFTY;
double PGmin_old = -CMath::INFTY;
double PGmax_new, PGmin_new;
// default solver_type: L2R_L2LOSS_SVC_DUAL
double diag[3] = {0.5/Cn, 0, 0.5/Cp};
double upper_bound[3] = {CMath::INFTY, 0, CMath::INFTY};
if(st == L2R_L1LOSS_SVC_DUAL)
{
diag[0] = 0;
diag[2] = 0;
upper_bound[0] = Cn;
upper_bound[2] = Cp;
}
int n = prob->n;
if (prob->use_bias)
n--;
for(i=0; i<w_size; i++)
w[i] = 0;
for(i=0; i<l; i++)
{
alpha[i] = 0;
if(prob->y[i] > 0)
{
y[i] = +1;
}
else
{
y[i] = -1;
}
QD[i] = diag[GETI(i)];
QD[i] += prob->x->dot(i, prob->x,i);
index[i] = i;
}
auto pb = progress(range(10));
CTime start_time;
while (iter < max_iterations && !cancel_computation())
{
if (m_max_train_time > 0 && start_time.cur_time_diff() > m_max_train_time)
break;
PGmax_new = -CMath::INFTY;
PGmin_new = CMath::INFTY;
for (i=0; i<active_size; i++)
{
int j = CMath::random(i, active_size-1);
CMath::swap(index[i], index[j]);
}
for (s=0;s<active_size;s++)
{
i = index[s];
int32_t yi = y[i];
G = prob->x->dense_dot(i, w.vector, n);
if (prob->use_bias)
G+=w.vector[n];
if (m_linear_term.vector)
G = G*yi + m_linear_term.vector[i];
else
G = G*yi-1;
C = upper_bound[GETI(i)];
G += alpha[i]*diag[GETI(i)];
PG = 0;
if (alpha[i] == 0)
{
if (G > PGmax_old)
{
active_size--;
CMath::swap(index[s], index[active_size]);
s--;
continue;
}
else if (G < 0)
PG = G;
}
else if (alpha[i] == C)
{
if (G < PGmin_old)
{
active_size--;
CMath::swap(index[s], index[active_size]);
s--;
continue;
}
else if (G > 0)
PG = G;
}
else
PG = G;
PGmax_new = CMath::max(PGmax_new, PG);
PGmin_new = CMath::min(PGmin_new, PG);
if(fabs(PG) > 1.0e-12)
{
double alpha_old = alpha[i];
alpha[i] = CMath::min(CMath::max(alpha[i] - G/QD[i], 0.0), C);
d = (alpha[i] - alpha_old)*yi;
prob->x->add_to_dense_vec(d, i, w.vector, n);
if (prob->use_bias)
w.vector[n]+=d;
}
}
iter++;
float64_t gap=PGmax_new - PGmin_new;
pb.print_absolute(
gap, -CMath::log10(gap), -CMath::log10(1), -CMath::log10(eps));
if(gap <= eps)
{
if(active_size == l)
break;
else
{
active_size = l;
PGmax_old = CMath::INFTY;
PGmin_old = -CMath::INFTY;
continue;
}
}
PGmax_old = PGmax_new;
PGmin_old = PGmin_new;
if (PGmax_old <= 0)
PGmax_old = CMath::INFTY;
if (PGmin_old >= 0)
PGmin_old = -CMath::INFTY;
}
pb.complete_absolute();
SG_INFO("optimization finished, #iter = %d\n",iter)
if (iter >= max_iterations)
{
SG_WARNING("reaching max number of iterations\nUsing -s 2 may be faster"
"(also see liblinear FAQ)\n\n");
}
// calculate objective value
double v = 0;
int nSV = 0;
for(i=0; i<w_size; i++)
v += w.vector[i]*w.vector[i];
for(i=0; i<l; i++)
{
v += alpha[i]*(alpha[i]*diag[GETI(i)] - 2);
if(alpha[i] > 0)
++nSV;
}
SG_INFO("Objective value = %lf\n",v/2)
SG_INFO("nSV = %d\n",nSV)
SG_FREE(QD);
SG_FREE(alpha);
SG_FREE(y);
SG_FREE(index);
}
// A coordinate descent algorithm for
// L1-regularized L2-loss support vector classification
//
// min_w \sum |wj| + C \sum max(0, 1-yi w^T xi)^2,
//
// Given:
// x, y, Cp, Cn
// eps is the stopping tolerance
//
// solution will be put in w
#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)
void CLibLinear::solve_l1r_l2_svc(
SGVector<float64_t>& w,
liblinear_problem *prob_col, double eps, double Cp, double Cn)
{
int l = prob_col->l;
int w_size = prob_col->n;
int j, s, iter = 0;
int active_size = w_size;
int max_num_linesearch = 20;
double sigma = 0.01;
double d, G_loss, G, H;
double Gmax_old = CMath::INFTY;
double Gmax_new;
double Gmax_init=0;
double d_old, d_diff;
double loss_old=0, loss_new;
double appxcond, cond;
int *index = SG_MALLOC(int, w_size);
int32_t *y = SG_MALLOC(int32_t, l);
double *b = SG_MALLOC(double, l); // b = 1-ywTx
double *xj_sq = SG_MALLOC(double, w_size);
CDotFeatures* x = (CDotFeatures*) prob_col->x;
void* iterator;
int32_t ind;
float64_t val;
double C[3] = {Cn,0,Cp};
int n = prob_col->n;
if (prob_col->use_bias)
n--;
for(j=0; j<l; j++)
{
b[j] = 1;
if(prob_col->y[j] > 0)
y[j] = 1;
else
y[j] = -1;
}
for(j=0; j<w_size; j++)
{
w.vector[j] = 0;
index[j] = j;
xj_sq[j] = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
xj_sq[n] += C[GETI(ind)];
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
xj_sq[j] += C[GETI(ind)]*val*val;
x->free_feature_iterator(iterator);
}
}
auto pb = progress(range(10));
CTime start_time;
while (iter < max_iterations && !cancel_computation())
{
if (m_max_train_time > 0 && start_time.cur_time_diff() > m_max_train_time)
break;
Gmax_new = 0;
for(j=0; j<active_size; j++)
{
int i = CMath::random(j, active_size-1);
CMath::swap(index[i], index[j]);
}
for(s=0; s<active_size; s++)
{
j = index[s];
G_loss = 0;
H = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
{
if(b[ind] > 0)
{
double tmp = C[GETI(ind)]*y[ind];
G_loss -= tmp*b[ind];
H += tmp*y[ind];
}
}
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
{
if(b[ind] > 0)
{
double tmp = C[GETI(ind)]*val*y[ind];
G_loss -= tmp*b[ind];
H += tmp*val*y[ind];
}
}
x->free_feature_iterator(iterator);
}
G_loss *= 2;
G = G_loss;
H *= 2;
H = CMath::max(H, 1e-12);
double Gp = G+1;
double Gn = G-1;
double violation = 0;
if(w.vector[j] == 0)
{
if(Gp < 0)
violation = -Gp;
else if(Gn > 0)
violation = Gn;
else if(Gp>Gmax_old/l && Gn<-Gmax_old/l)
{
active_size--;
CMath::swap(index[s], index[active_size]);
s--;
continue;
}
}
else if(w.vector[j] > 0)
violation = fabs(Gp);
else
violation = fabs(Gn);
Gmax_new = CMath::max(Gmax_new, violation);
// obtain Newton direction d
if(Gp <= H*w.vector[j])
d = -Gp/H;
else if(Gn >= H*w.vector[j])
d = -Gn/H;
else
d = -w.vector[j];
if(fabs(d) < 1.0e-12)
continue;
double delta = fabs(w.vector[j]+d)-fabs(w.vector[j]) + G*d;
d_old = 0;
int num_linesearch;
for(num_linesearch=0; num_linesearch < max_num_linesearch; num_linesearch++)
{
d_diff = d_old - d;
cond = fabs(w.vector[j]+d)-fabs(w.vector[j]) - sigma*delta;
appxcond = xj_sq[j]*d*d + G_loss*d + cond;
if(appxcond <= 0)
{
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
b[ind] += d_diff*y[ind];
break;
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
b[ind] += d_diff*val*y[ind];
x->free_feature_iterator(iterator);
break;
}
}
if(num_linesearch == 0)
{
loss_old = 0;
loss_new = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
{
if(b[ind] > 0)
loss_old += C[GETI(ind)]*b[ind]*b[ind];
double b_new = b[ind] + d_diff*y[ind];
b[ind] = b_new;
if(b_new > 0)
loss_new += C[GETI(ind)]*b_new*b_new;
}
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
{
if(b[ind] > 0)
loss_old += C[GETI(ind)]*b[ind]*b[ind];
double b_new = b[ind] + d_diff*val*y[ind];
b[ind] = b_new;
if(b_new > 0)
loss_new += C[GETI(ind)]*b_new*b_new;
}
x->free_feature_iterator(iterator);
}
}
else
{
loss_new = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
{
double b_new = b[ind] + d_diff*y[ind];
b[ind] = b_new;
if(b_new > 0)
loss_new += C[GETI(ind)]*b_new*b_new;
}
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
{
double b_new = b[ind] + d_diff*val*y[ind];
b[ind] = b_new;
if(b_new > 0)
loss_new += C[GETI(ind)]*b_new*b_new;
}
x->free_feature_iterator(iterator);
}
}
cond = cond + loss_new - loss_old;
if(cond <= 0)
break;
else
{
d_old = d;
d *= 0.5;
delta *= 0.5;
}
}
w.vector[j] += d;
// recompute b[] if line search takes too many steps
if(num_linesearch >= max_num_linesearch)
{
SG_INFO("#")
for(int i=0; i<l; i++)
b[i] = 1;
for(int i=0; i<n; i++)
{
if(w.vector[i]==0)
continue;
iterator=x->get_feature_iterator(i);
while (x->get_next_feature(ind, val, iterator))
b[ind] -= w.vector[i]*val*y[ind];
x->free_feature_iterator(iterator);
}
if (use_bias && w.vector[n])
{
for (ind=0; ind<l; ind++)
b[ind] -= w.vector[n]*y[ind];
}
}
}
if(iter == 0)
Gmax_init = Gmax_new;
iter++;
pb.print_absolute(
Gmax_new, -CMath::log10(Gmax_new), -CMath::log10(Gmax_init),
-CMath::log10(eps * Gmax_init));
if(Gmax_new <= eps*Gmax_init)
{
if(active_size == w_size)
break;
else
{
active_size = w_size;
Gmax_old = CMath::INFTY;
continue;
}
}
Gmax_old = Gmax_new;
}
pb.complete_absolute();
SG_INFO("optimization finished, #iter = %d\n", iter)
if(iter >= max_iterations)
SG_WARNING("\nWARNING: reaching max number of iterations\n")
// calculate objective value
double v = 0;
int nnz = 0;
for(j=0; j<w_size; j++)
{
if(w.vector[j] != 0)
{
v += fabs(w.vector[j]);
nnz++;
}
}
for(j=0; j<l; j++)
if(b[j] > 0)
v += C[GETI(j)]*b[j]*b[j];
SG_INFO("Objective value = %lf\n", v)
SG_INFO("#nonzeros/#features = %d/%d\n", nnz, w_size)
SG_FREE(index);
SG_FREE(y);
SG_FREE(b);
SG_FREE(xj_sq);
}
// A coordinate descent algorithm for
// L1-regularized logistic regression problems
//
// min_w \sum |wj| + C \sum log(1+exp(-yi w^T xi)),
//
// Given:
// x, y, Cp, Cn
// eps is the stopping tolerance
//
// solution will be put in w
#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)
void CLibLinear::solve_l1r_lr(
SGVector<float64_t>& w,
const liblinear_problem *prob_col, double eps,
double Cp, double Cn)
{
int l = prob_col->l;
index_t w_size = prob_col->n;
index_t j, s, iter = 0;
index_t active_size = w_size;
index_t max_num_linesearch = 20;
double x_min = 0;
double sigma = 0.01;
double d, G, H;
double Gmax_old = CMath::INFTY;
double Gmax_new;
double Gmax_init=0;
double sum1, appxcond1;
double sum2, appxcond2;
double cond;
index_t *index = SG_MALLOC(index_t, w_size);
int32_t *y = SG_MALLOC(int32_t, l);
double *exp_wTx = SG_MALLOC(double, l);
double *exp_wTx_new = SG_MALLOC(double, l);
double *xj_max = SG_MALLOC(double, w_size);
double *C_sum = SG_MALLOC(double, w_size);
double *xjneg_sum = SG_MALLOC(double, w_size);
double *xjpos_sum = SG_MALLOC(double, w_size);
CDotFeatures* x = prob_col->x;
void* iterator;
index_t ind;
double val;
double C[3] = {Cn,0,Cp};
int n = prob_col->n;
if (prob_col->use_bias)
n--;
for(j=0; j<l; j++)
{
exp_wTx[j] = 1;
if(prob_col->y[j] > 0)
y[j] = 1;
else
y[j] = -1;
}
for(j=0; j<w_size; j++)
{
w.vector[j] = 0;
index[j] = j;
xj_max[j] = 0;
C_sum[j] = 0;
xjneg_sum[j] = 0;
xjpos_sum[j] = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
{
x_min = CMath::min(x_min, 1.0);
xj_max[j] = CMath::max(xj_max[j], 1.0);
C_sum[j] += C[GETI(ind)];
if(y[ind] == -1)
xjneg_sum[j] += C[GETI(ind)];
else
xjpos_sum[j] += C[GETI(ind)];
}
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
{
x_min = CMath::min(x_min, val);
xj_max[j] = CMath::max(xj_max[j], val);
C_sum[j] += C[GETI(ind)];
if(y[ind] == -1)
xjneg_sum[j] += C[GETI(ind)]*val;
else
xjpos_sum[j] += C[GETI(ind)]*val;
}
x->free_feature_iterator(iterator);
}
}
auto pb = progress(range(10));
CTime start_time;
while (iter < max_iterations && !cancel_computation())
{
if (m_max_train_time > 0 && start_time.cur_time_diff() > m_max_train_time)
break;
Gmax_new = 0;
for(j=0; j<active_size; j++)
{
int i = CMath::random(j, active_size-1);
CMath::swap(index[i], index[j]);
}
for(s=0; s<active_size; s++)
{
j = index[s];
sum1 = 0;
sum2 = 0;
H = 0;
if (use_bias && j==n)
{
for (ind=0; ind<l; ind++)
{
double exp_wTxind = exp_wTx[ind];
double tmp1 = 1.0/(1+exp_wTxind);
double tmp2 = C[GETI(ind)]*tmp1;
double tmp3 = tmp2*exp_wTxind;
sum2 += tmp2;
sum1 += tmp3;
H += tmp1*tmp3;
}
}
else
{
iterator=x->get_feature_iterator(j);
while (x->get_next_feature(ind, val, iterator))
{
double exp_wTxind = exp_wTx[ind];
double tmp1 = val/(1+exp_wTxind);
double tmp2 = C[GETI(ind)]*tmp1;
double tmp3 = tmp2*exp_wTxind;
sum2 += tmp2;
sum1 += tmp3;
H += tmp1*tmp3;
}
x->free_feature_iterator(iterator);
}
G = -sum2 + xjneg_sum[j];
double Gp = G+1;
double Gn = G-1;
double violation = 0;
if(w.vector[j] == 0)
{
if(Gp < 0)
violation = -Gp;
else if(Gn > 0)
violation = Gn;
else if(Gp>Gmax_old/l && Gn<-Gmax_old/l)
{
active_size--;
CMath::swap(index[s], index[active_size]);
s--;
continue;
}
}
else if(w.vector[j] > 0)
violation = fabs(Gp);
else
violation = fabs(Gn);
Gmax_new = CMath::max(Gmax_new, violation);
// obtain Newton direction d
if(Gp <= H*w.vector[j])
d = -Gp/H;
else if(Gn >= H*w.vector[j])
d = -Gn/H;
else
d = -w.vector[j];
if(fabs(d) < 1.0e-12)
continue;
d = CMath::min(CMath::max(d,-10.0),10.0);
double delta = fabs(w.vector[j]+d)-fabs(w.vector[j]) + G*d;
int num_linesearch;
for(num_linesearch=0; num_linesearch < max_num_linesearch; num_linesearch++)
{
cond = fabs(w.vector[j]+d)-fabs(w.vector[j]) - sigma*delta;
if(x_min >= 0)
{
double tmp = exp(d*xj_max[j]);
appxcond1 = log(1+sum1*(tmp-1)/xj_max[j]/C_sum[j])*C_sum[j] + cond - d*xjpos_sum[j];
appxcond2 = log(1+sum2*(1/tmp-1)/xj_max[j]/C_sum[j])*C_sum[j] + cond + d*xjneg_sum[j];
if(CMath::min(appxcond1,appxcond2) <= 0)