linear_par.cpp

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdarg.h>
#include <locale.h>
#include "linear.h"
#include "tron.h"
#include <list>
#include <thread>
#include <mutex>
#include <vector>
#include <functional>
#include <iostream>
#include "ThreadPool/ThreadWorkers.h"

typedef signed char schar;
template <class T> static inline void swap(T& x, T& y) { T t=x; x=y; y=t; }
#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
template <class S, class T> static inline void clone(T*& dst, S* src, int n)
{
	dst = new T[n];
	memcpy((void *)dst,(void *)src,sizeof(T)*n);
}
#define Malloc(type,n) (type *)malloc((n)*sizeof(type))
#define INF HUGE_VAL

static void print_string_stdout(const char *s)
{
	fputs(s,stdout);
	fflush(stdout);
}

static void (*liblinear_print_string) (const char *) = &print_string_stdout;

#if 1
static void info(const char *fmt,...)
{
	char buf[BUFSIZ];
	va_list ap;
	va_start(ap,fmt);
	vsprintf(buf,fmt,ap);
	va_end(ap);
	(*liblinear_print_string)(buf);
}
#else
static void info(const char *fmt,...) {}
#endif

class l2r_lr_fun: public function
{
public:
	l2r_lr_fun(const problem *prob, double *C);
	~l2r_lr_fun();

	double fun(double *w);
	void grad(double *w, double *g);
	void Hv(double *s, double *Hs);

	int get_nr_variable(void);

private:
	void Xv(double *v, double *Xv);
	void XTv(double *v, double *XTv);

	double *C;
	double *z;
	double *D;

	const problem *prob;

	double *local_store;
	ThreadWorkers *threads;
};

l2r_lr_fun::l2r_lr_fun(const problem *prob, double *C)
{
	int l=prob->l;

	this->prob = prob;

	z = new double[l];
	D = new double[l];
	this->C = C;

	int w_size = get_nr_variable();

	threads = ThreadWorkers::getInstance();
	int num_cpus = threads->get_num_cpus();

	local_store = new double [w_size * num_cpus];
}

l2r_lr_fun::~l2r_lr_fun()
{
	delete[] z;
	delete[] D;

	delete [] local_store;
}


double l2r_lr_fun::fun(double *w)
{
	double total_f=0;
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();

	Xv(w, z);

	std::mutex lk;
	auto func = [&] (int tid) {

		double f = 0;

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			f += w[i]*w[i];

		f /= 2.0;

		start = threads->start(tid, l);
		end = threads->end(tid, l);

		for(int i=start;i<end;i++)
		{
			double yz = y[i]*z[i];
			if (yz >= 0)
				f += C[i]*log(1 + exp(-yz));
			else
				f += C[i]*(-yz+log(1 + exp(yz)));
		}

		{
			std::lock_guard<std::mutex> grd(lk);
			total_f += f;
		}
	};

	threads->run_workers(func);

	return (total_f);
}

void l2r_lr_fun::grad(double *w, double *g)
{
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();

	auto func1 = [&] (int tid) {

		int start = threads->start(tid, l); 
		int end = threads->end(tid, l);

		for(int i=start;i<end;i++)
		{
			z[i] = 1/(1 + exp(-y[i]*z[i]));
			D[i] = z[i]*(1-z[i]);
			z[i] = C[i]*(z[i]-1)*y[i];
		}
	};

	threads->run_workers(func1);

	XTv(z, g);

	auto func2 = [&] (int tid) {

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			g[i] = w[i] + g[i];
	};

	threads->run_workers(func2);
}

int l2r_lr_fun::get_nr_variable(void)
{
	return prob->n;
}

void l2r_lr_fun::Hv(double *s, double *Hs)
{
	int l=prob->l;
	int w_size=get_nr_variable();
	double *wa = new double[l];

	Xv(s, wa);

	auto func1 = [&] (int tid) {

		int start = threads->start(tid, l);
		int end = threads->end(tid, l);

		for(int i=start;i<end;i++)
			wa[i] = C[i]*D[i]*wa[i];
	};

	threads->run_workers(func1);

	XTv(wa, Hs);

	auto func2 = [&] (int tid) {

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			Hs[i] = s[i] + Hs[i];
	};

	threads->run_workers(func2);

	delete[] wa;
}

void l2r_lr_fun::Xv(double *v, double *Xv)
{
	int l=prob->l;
	feature_node **x=prob->x;

	auto func = [&](int tid) {

		int start = threads->start(tid, l);
		int end = threads->end(tid, l);

		for(int i=start;i<end;i++)
		{
			feature_node *s=x[i];
			Xv[i]=0;
			while(s->index!=-1)
			{
				Xv[i]+=v[s->index-1]*s->value;
				s++;
			}
		}
	};

	threads->run_workers(func);
}

void l2r_lr_fun::XTv(double *v, double *XTv)
{
	int l=prob->l;
	int w_size=get_nr_variable();
	feature_node **x=prob->x;

	memset(XTv, 0, sizeof(double) * w_size);

	std::mutex lk;
	auto func = [&] (int tid) {

		int start = threads->start(tid, l);
		int end = threads->end(tid, l);

		double *tmp_XTv = & local_store[tid*w_size];
		memset(tmp_XTv, 0, sizeof(double) * w_size);

		for(int i=start;i<end;i++)
		{
			feature_node *s=x[i];
			while(s->index!=-1)
			{
				tmp_XTv[s->index-1]+=v[i]*s->value;
				s++;
			}
		}

		{
			std::lock_guard<std::mutex> grd(lk);
			for(int i=0;i<w_size;i++)
				XTv[i] += tmp_XTv[i];
			
		}
	};

	threads->run_workers(func);
}

class l2r_l2_svc_fun: public function
{
public:
	l2r_l2_svc_fun(const problem *prob, double *C);
	~l2r_l2_svc_fun();

	double fun(double *w);
	void grad(double *w, double *g);
	void Hv(double *s, double *Hs);

	int get_nr_variable(void);

protected:
	void Xv(double *v, double *Xv);
	void subXv(double *v, double *Xv);
	void subXTv(double *v, double *XTv);

	double *C;
	double *z;
	double *D;
	int *I;
	int sizeI;
	const problem *prob;

	int *local_sizeI;
	double *local_store;
	ThreadWorkers *threads;
};

l2r_l2_svc_fun::l2r_l2_svc_fun(const problem *prob, double *C)
{
	int l=prob->l;

	this->prob = prob;

	z = new double[l];
	D = new double[l];
	I = new int[l];
	this->C = C;

	threads = ThreadWorkers::getInstance();
	int num_cpus = threads->get_num_cpus();
	int w_size = get_nr_variable();
	local_store = new double [w_size * num_cpus];
	local_sizeI = new int [num_cpus];
}

l2r_l2_svc_fun::~l2r_l2_svc_fun()
{
	delete[] z;
	delete[] D;
	delete[] I;

	delete [] local_store;
	delete [] local_sizeI;
}

double l2r_l2_svc_fun::fun(double *w)
{
	double total_f=0;
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();

	Xv(w, z);

	std::mutex lk;
	auto func = [&] (int tid) {
	
		double f = 0;

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			f += w[i]*w[i];
		f /= 2.0;

		start = threads->start(tid, l);
		end = threads->end(tid, l);

		for(int i=start;i<end;i++)
		{
			z[i] = y[i]*z[i];
			double d = 1-z[i];
			if (d > 0)
				f += C[i]*d*d;
		}

		{
			std::lock_guard<std::mutex> grd(lk);
			total_f += f;	
		}
	};

	threads->run_workers(func);

	return (total_f);
}

void l2r_l2_svc_fun::grad(double *w, double *g)
{
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();

	sizeI = 0;

	auto func1 = [&] (int tid) {

		int start = threads->start(tid, l);
		int end = threads->end(tid, l);

		int t_sizeI = start;

		for (int i=start;i<end;i++) {
			if (z[i] < 1)
			{
				z[t_sizeI] = C[i]*y[i]*(z[i]-1);
				I[t_sizeI] = i;
				t_sizeI++;
			}
		}

		local_sizeI[tid] = t_sizeI;
	};

	threads->run_workers(func1);

	int num_cpus = threads->get_num_cpus();
	sizeI = local_sizeI[0];
	for (int tid = 1; tid < num_cpus; ++tid) {
		int start = threads->start(tid, l);
		for (int j = start; j < local_sizeI[tid]; ++j) {
			z[sizeI] = z[j];
			I[sizeI] = I[j];
			sizeI++;
		}	
	}

	subXTv(z, g);

	auto func2 = [&] (int tid) {

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			g[i] = w[i] + 2*g[i];
	};

	threads->run_workers(func2);
}

int l2r_l2_svc_fun::get_nr_variable(void)
{
	return prob->n;
}

void l2r_l2_svc_fun::Hv(double *s, double *Hs)
{
	int w_size=get_nr_variable();
	double *wa = new double[sizeI];

	subXv(s, wa);

	auto func1 = [&] (int tid) {

		int start = threads->start(tid, sizeI);
		int end = threads->end(tid, sizeI);

		for(int i=start;i<end;i++)
			wa[i] = C[I[i]]*wa[i];
	};

	threads->run_workers(func1);


	subXTv(wa, Hs);

	auto func2 = [&] (int tid) {

		int start = threads->start(tid, w_size);
		int end = threads->end(tid, w_size);

		for(int i=start;i<end;i++)
			Hs[i] = s[i] + 2*Hs[i];
	};

	threads->run_workers(func2);

	delete[] wa;
}

void l2r_l2_svc_fun::Xv(double *v, double *Xv)
{
	int l=prob->l;
	feature_node **x=prob->x;

	auto func = [&] (int tid) {

		int start = threads->start(tid, l);
		int end = threads->end(tid, l);

		for(int i=start;i<end;i++)
		{
			feature_node *s=x[i];
			Xv[i]=0;
			while(s->index!=-1)
			{
				Xv[i]+=v[s->index-1]*s->value;
				s++;
			}
		}
	};

	threads->run_workers(func);
}

void l2r_l2_svc_fun::subXv(double *v, double *Xv)
{
	feature_node **x=prob->x;

	auto func = [&] (int tid) {

		int start = threads->start(tid, sizeI);
		int end = threads->end(tid, sizeI);
	
		for(int i=start;i<end;i++)
		{
			feature_node *s=x[I[i]];
			Xv[i]=0;
			while(s->index!=-1)
			{
				Xv[i]+=v[s->index-1]*s->value;
				s++;
			}
		}
	};

	threads->run_workers(func);
}

void l2r_l2_svc_fun::subXTv(double *v, double *XTv)
{
	int w_size=get_nr_variable();
	feature_node **x=prob->x;

	memset(XTv, 0, sizeof(double) * w_size);

	std::mutex lk;
	auto func = [&] (int tid) {
	
		int start = threads->start(tid, sizeI);	
		int end = threads->end(tid, sizeI);	

		if (start < end) {

			double *tmp_XTv = &local_store[tid * w_size];
			memset(tmp_XTv, 0, sizeof(double) * w_size);

			for(int i=start;i<end;i++)
			{
				feature_node *s=x[I[i]];
				while(s->index!=-1)
				{
					tmp_XTv[s->index-1]+=v[i]*s->value;
					s++;
				}
			}

			{
				std::lock_guard<std::mutex> grd(lk);
				for (int i = 0; i < w_size; ++i)
					XTv[i] += tmp_XTv[i];
			}

		}
	};

	threads->run_workers(func);

}

class l2r_l2_svr_fun: public l2r_l2_svc_fun
{
public:
	l2r_l2_svr_fun(const problem *prob, double *C, double p);

	double fun(double *w);
	void grad(double *w, double *g);

private:
	double p;
};

l2r_l2_svr_fun::l2r_l2_svr_fun(const problem *prob, double *C, double p):
	l2r_l2_svc_fun(prob, C)
{
	this->p = p;
}

double l2r_l2_svr_fun::fun(double *w)
{
	int i;
	double f=0;
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();
	double d;

	Xv(w, z);

	for(i=0;i<w_size;i++)
		f += w[i]*w[i];
	f /= 2;
	for(i=0;i<l;i++)
	{
		d = z[i] - y[i];
		if(d < -p)
			f += C[i]*(d+p)*(d+p);
		else if(d > p)
			f += C[i]*(d-p)*(d-p);
	}

	return(f);
}

void l2r_l2_svr_fun::grad(double *w, double *g)
{
	int i;
	double *y=prob->y;
	int l=prob->l;
	int w_size=get_nr_variable();
	double d;

	sizeI = 0;
	for(i=0;i<l;i++)
	{
		d = z[i] - y[i];

		// generate index set I
		if(d < -p)
		{
			z[sizeI] = C[i]*(d+p);
			I[sizeI] = i;
			sizeI++;
		}
		else if(d > p)
		{
			z[sizeI] = C[i]*(d-p);
			I[sizeI] = i;
			sizeI++;
		}

	}
	subXTv(z, g);

	for(i=0;i<w_size;i++)
		g[i] = w[i] + 2*g[i];
}

// A coordinate descent algorithm for 
// multi-class support vector machines by Crammer and Singer
//
//  min_{\alpha}  0.5 \sum_m ||w_m(\alpha)||^2 + \sum_i \sum_m e^m_i alpha^m_i
//    s.t.     \alpha^m_i <= C^m_i \forall m,i , \sum_m \alpha^m_i=0 \forall i
// 
//  where e^m_i = 0 if y_i  = m,
//        e^m_i = 1 if y_i != m,
//  C^m_i = C if m  = y_i, 
//  C^m_i = 0 if m != y_i, 
//  and w_m(\alpha) = \sum_i \alpha^m_i x_i 
//
// Given: 
// x, y, C
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Appendix of LIBLINEAR paper, Fan et al. (2008)

#define GETI(i) ((int) prob->y[i])
// To support weights for instances, use GETI(i) (i)

class Solver_MCSVM_CS
{
	public:
		Solver_MCSVM_CS(const problem *prob, int nr_class, double *C, double eps=0.1, int max_iter=100000);
		~Solver_MCSVM_CS();
		void Solve(double *w);
	private:
		void solve_sub_problem(double A_i, int yi, double C_yi, int active_i, double *alpha_new);
		bool be_shrunk(int i, int m, int yi, double alpha_i, double minG);
		double *B, *C, *G;
		int w_size, l;
		int nr_class;
		int max_iter;
		double eps;
		const problem *prob;
};

Solver_MCSVM_CS::Solver_MCSVM_CS(const problem *prob, int nr_class, double *weighted_C, double eps, int max_iter)
{
	this->w_size = prob->n;
	this->l = prob->l;
	this->nr_class = nr_class;
	this->eps = eps;
	this->max_iter = max_iter;
	this->prob = prob;
	this->B = new double[nr_class];
	this->G = new double[nr_class];
	this->C = weighted_C;
}

Solver_MCSVM_CS::~Solver_MCSVM_CS()
{
	delete[] B;
	delete[] G;
}

int compare_double(const void *a, const void *b)
{
	if(*(double *)a > *(double *)b)
		return -1;
	if(*(double *)a < *(double *)b)
		return 1;
	return 0;
}

void Solver_MCSVM_CS::solve_sub_problem(double A_i, int yi, double C_yi, int active_i, double *alpha_new)
{
	int r;
	double *D;

	clone(D, B, active_i);
	if(yi < active_i)
		D[yi] += A_i*C_yi;
	qsort(D, active_i, sizeof(double), compare_double);

	double beta = D[0] - A_i*C_yi;
	for(r=1;r<active_i && beta<r*D[r];r++)
		beta += D[r];
	beta /= r;

	for(r=0;r<active_i;r++)
	{
		if(r == yi)
			alpha_new[r] = min(C_yi, (beta-B[r])/A_i);
		else
			alpha_new[r] = min((double)0, (beta - B[r])/A_i);
	}
	delete[] D;
}

bool Solver_MCSVM_CS::be_shrunk(int i, int m, int yi, double alpha_i, double minG)
{
	double bound = 0;
	if(m == yi)
		bound = C[GETI(i)];
	if(alpha_i == bound && G[m] < minG)
		return true;
	return false;
}

void Solver_MCSVM_CS::Solve(double *w)
{
	int i, m, s;
	int iter = 0;
	double *alpha =  new double[l*nr_class];
	double *alpha_new = new double[nr_class];
	int *index = new int[l];
	double *QD = new double[l];
	int *d_ind = new int[nr_class];
	double *d_val = new double[nr_class];
	int *alpha_index = new int[nr_class*l];
	int *y_index = new int[l];
	int active_size = l;
	int *active_size_i = new int[l];
	double eps_shrink = max(10.0*eps, 1.0); // stopping tolerance for shrinking
	bool start_from_all = true;

	// Initial alpha can be set here. Note that 
	// sum_m alpha[i*nr_class+m] = 0, for all i=1,...,l-1
	// alpha[i*nr_class+m] <= C[GETI(i)] if prob->y[i] == m
	// alpha[i*nr_class+m] <= 0 if prob->y[i] != m
	// If initial alpha isn't zero, uncomment the for loop below to initialize w
	for(i=0;i<l*nr_class;i++)
		alpha[i] = 0;

	for(i=0;i<w_size*nr_class;i++)
		w[i] = 0;
	for(i=0;i<l;i++)
	{
		for(m=0;m<nr_class;m++)
			alpha_index[i*nr_class+m] = m;
		feature_node *xi = prob->x[i];
		QD[i] = 0;
		while(xi->index != -1)
		{
			double val = xi->value;
			QD[i] += val*val;

			// Uncomment the for loop if initial alpha isn't zero
			// for(m=0; m<nr_class; m++)
			//	w[(xi->index-1)*nr_class+m] += alpha[i*nr_class+m]*val;
			xi++;
		}
		active_size_i[i] = nr_class;
		y_index[i] = (int)prob->y[i];
		index[i] = i;
	}

	while(iter < max_iter)
	{
		double stopping = -INF;
		for(i=0;i<active_size;i++)
		{
			int j = i+rand()%(active_size-i);
			swap(index[i], index[j]);
		}
		for(s=0;s<active_size;s++)
		{
			i = index[s];
			double Ai = QD[i];
			double *alpha_i = &alpha[i*nr_class];
			int *alpha_index_i = &alpha_index[i*nr_class];

			if(Ai > 0)
			{
				for(m=0;m<active_size_i[i];m++)
					G[m] = 1;
				if(y_index[i] < active_size_i[i])
					G[y_index[i]] = 0;

				feature_node *xi = prob->x[i];
				while(xi->index!= -1)
				{
					double *w_i = &w[(xi->index-1)*nr_class];
					for(m=0;m<active_size_i[i];m++)
						G[m] += w_i[alpha_index_i[m]]*(xi->value);
					xi++;
				}

				double minG = INF;
				double maxG = -INF;
				for(m=0;m<active_size_i[i];m++)
				{
					if(alpha_i[alpha_index_i[m]] < 0 && G[m] < minG)
						minG = G[m];
					if(G[m] > maxG)
						maxG = G[m];
				}
				if(y_index[i] < active_size_i[i])
					if(alpha_i[(int) prob->y[i]] < C[GETI(i)] && G[y_index[i]] < minG)
						minG = G[y_index[i]];

				for(m=0;m<active_size_i[i];m++)
				{
					if(be_shrunk(i, m, y_index[i], alpha_i[alpha_index_i[m]], minG))
					{
						active_size_i[i]--;
						while(active_size_i[i]>m)
						{
							if(!be_shrunk(i, active_size_i[i], y_index[i],
											alpha_i[alpha_index_i[active_size_i[i]]], minG))
							{
								swap(alpha_index_i[m], alpha_index_i[active_size_i[i]]);
								swap(G[m], G[active_size_i[i]]);
								if(y_index[i] == active_size_i[i])
									y_index[i] = m;
								else if(y_index[i] == m)
									y_index[i] = active_size_i[i];
								break;
							}
							active_size_i[i]--;
						}
					}
				}

				if(active_size_i[i] <= 1)
				{
					active_size--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}

				if(maxG-minG <= 1e-12)
					continue;
				else
					stopping = max(maxG - minG, stopping);

				for(m=0;m<active_size_i[i];m++)
					B[m] = G[m] - Ai*alpha_i[alpha_index_i[m]] ;

				solve_sub_problem(Ai, y_index[i], C[GETI(i)], active_size_i[i], alpha_new);
				int nz_d = 0;
				for(m=0;m<active_size_i[i];m++)
				{
					double d = alpha_new[m] - alpha_i[alpha_index_i[m]];
					alpha_i[alpha_index_i[m]] = alpha_new[m];
					if(fabs(d) >= 1e-12)
					{
						d_ind[nz_d] = alpha_index_i[m];
						d_val[nz_d] = d;
						nz_d++;
					}
				}

				xi = prob->x[i];
				while(xi->index != -1)
				{
					double *w_i = &w[(xi->index-1)*nr_class];
					for(m=0;m<nz_d;m++)
						w_i[d_ind[m]] += d_val[m]*xi->value;
					xi++;
				}
			}
		}

		iter++;
		if(iter % 10 == 0)
		{
			info(".");
		}

		if(stopping < eps_shrink)
		{
			if(stopping < eps && start_from_all == true)
				break;
			else
			{
				active_size = l;
				for(i=0;i<l;i++)
					active_size_i[i] = nr_class;
				info("*");
				eps_shrink = max(eps_shrink/2, eps);
				start_from_all = true;
			}
		}
		else
			start_from_all = false;
	}

	info("\noptimization finished, #iter = %d\n",iter);
	if (iter >= max_iter)
		info("\nWARNING: reaching max number of iterations\n");

	// calculate objective value
	double v = 0;
	int nSV = 0;
	for(i=0;i<w_size*nr_class;i++)
		v += w[i]*w[i];
	v = 0.5*v;
	for(i=0;i<l*nr_class;i++)
	{
		v += alpha[i];
		if(fabs(alpha[i]) > 0)
			nSV++;
	}
	for(i=0;i<l;i++)
		v -= alpha[i*nr_class+(int)prob->y[i]];
	info("Objective value = %lf\n",v);
	info("nSV = %d\n",nSV);

	delete [] alpha;
	delete [] alpha_new;
	delete [] index;
	delete [] QD;
	delete [] d_ind;
	delete [] d_val;
	delete [] alpha_index;
	delete [] y_index;
	delete [] active_size_i;
}

// 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
// 
// See Algorithm 3 of Hsieh et al., ICML 2008

#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)

static void solve_l2r_l1l2_svc(
	const problem *prob, double *w, double eps,
	double Cp, double Cn, int solver_type)
{
	int l = prob->l;
	int w_size = prob->n;
	int i, iter = 0;
	double *QD = new double[l];
	//int max_iter = 1000;
	int max_iter = 10000;
	int *index = new int[l];
	double *alpha = new double[l];
	schar *y = new schar[l];
	int active_size = l;

	// PG: projected gradient, for shrinking and stopping
	double PGmax_old = INF;
	double PGmin_old = -INF;
	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] = {INF, 0, INF};
	if(solver_type == L2R_L1LOSS_SVC_DUAL)
	{
		diag[0] = 0;
		diag[2] = 0;
		upper_bound[0] = Cn;
		upper_bound[2] = Cp;
	}

	for(i=0; i<l; i++)
	{
		if(prob->y[i] > 0)
		{
			y[i] = +1;
		}
		else
		{
			y[i] = -1;
		}
	}

	// Initial alpha can be set here. Note that
	// 0 <= alpha[i] <= upper_bound[GETI(i)]
	for(i=0; i<l; i++)
		alpha[i] = 0;

	for(i=0; i<w_size; i++)
		w[i] = 0;
	for(i=0; i<l; i++)
	{
		QD[i] = diag[GETI(i)];

		feature_node *xi = prob->x[i];
		while (xi->index != -1)
		{
			double val = xi->value;
			QD[i] += val*val;
			w[xi->index-1] += y[i]*alpha[i]*val;
			xi++;
		}
		index[i] = i;
	}

	
	// NEW: probability esitmate
	ThreadWorkers *threads = ThreadWorkers::getInstance();
	int num_cpus = threads->get_num_cpus();

	double *tmpW = new double [w_size];
	double *gW = new double [num_cpus * w_size];

	while (iter < max_iter)
	{
		PGmax_new = -INF;
		PGmin_new = INF;

		for (i=0; i<active_size; i++)
		{
			int j = i+rand()%(active_size-i);
			swap(index[i], index[j]);
		}

		// NEW: probability esitmate
		std::list<int> removal_list;
		std::mutex lk;
		memset(tmpW, 0, sizeof(double) * w_size);

		auto func = [&](int tid) {

			double local_PGmax_new = -INF;
			double local_PGmin_new = INF;
			std::list<int> local_removal_list;
			double *local_w = &gW[tid * w_size];
			memcpy(local_w, w, sizeof(double) * w_size);

			int start = threads->start(tid, active_size);
			int end = threads->end(tid, active_size);

			for (int s=start; s<end; s++)
			{
				int i = index[s];
				double G = 0; 
				schar yi = y[i];

				feature_node *xi = prob->x[i];
				while(xi->index!= -1)
				{
					G += local_w[xi->index-1]*(xi->value);
					xi++;
				}
				G = G*yi-1;

				double C = upper_bound[GETI(i)];
				G += alpha[i]*diag[GETI(i)];

				double PG = 0;
				if (alpha[i] == 0)
				{
					if (G > PGmax_old)
					{
						local_removal_list.push_back(s);
						continue;
					}
					else if (G < 0)
						PG = G;
				}
				else if (alpha[i] == C)
				{
					if (G < PGmin_old)
					{
						local_removal_list.push_back(s);
						continue;
					}
					else if (G > 0)
						PG = G;
				}
				else
					PG = G;

				local_PGmax_new = max(local_PGmax_new, PG);
				local_PGmin_new = min(local_PGmin_new, PG);

				if(fabs(PG) > 1.0e-12)
				{
					double alpha_old = alpha[i];
					alpha[i] = min(max(alpha[i] - G/QD[i], 0.0), C);
					double d = (alpha[i] - alpha_old)*yi;
					xi = prob->x[i];
					while (xi->index != -1)
					{
						local_w[xi->index-1] += d*xi->value;
						xi++;
					}
				}
			}


			{
				std::lock_guard<std::mutex> guard(lk);
				PGmax_new = max(PGmax_new, local_PGmax_new);
				PGmin_new = min(PGmin_new, local_PGmin_new);
				removal_list.splice(removal_list.end(), local_removal_list);
				for (int i = 0; i < w_size; ++i)
					tmpW[i] += local_w[i];
			}

		};

		// NEW: probability esitmate
		threads->run_workers(func);

		for (int i = 0; i < w_size; ++i) {
			w[i] = tmpW[i] / num_cpus;
		}

		for (auto s: removal_list) {
			active_size--;
			swap(index[s], index[active_size]);
		}

		iter++;
		if(iter % 10 == 0)
			info(".");

		if(PGmax_new - PGmin_new <= eps)
		{
			//std::cout << "PGmax_new " << PGmax_new << " - PGmin_new " << PGmin_new << " = ";
			//std::cout << PGmax_new - PGmin_new << std::endl;
			if(active_size == l)
				break;
			else
			{
				active_size = l;
				info("*");
				PGmax_old = INF;
				PGmin_old = -INF;
				continue;
			}
		}
		PGmax_old = PGmax_new;
		PGmin_old = PGmin_new;
		if (PGmax_old <= 0)
			PGmax_old = INF;
		if (PGmin_old >= 0)
			PGmin_old = -INF;
		//std::cout << "PGmax_old = " << PGmax_old << " PGmin_old = " << PGmin_old << std::endl;
	}

	info("\noptimization finished, #iter = %d\n",iter);
	if (iter >= max_iter)
		info("\nWARNING: reaching max number of iterations\nUsing -s 2 may be faster (also see FAQ)\n\n");

	// calculate objective value

	double v = 0;
	int nSV = 0;
	for(i=0; i<w_size; i++)
		v += w[i]*w[i];
	for(i=0; i<l; i++)
	{
		v += alpha[i]*(alpha[i]*diag[GETI(i)] - 2);
		if(alpha[i] > 0)
			++nSV;
	}
	info("Objective value = %lf\n",v/2);
	info("nSV = %d\n",nSV);

	delete [] QD;
	delete [] alpha;
	delete [] y;
	delete [] index;

	// NEW: probability esitmate
	delete [] tmpW;
	delete [] gW;
}

// A coordinate descent algorithm for 
// L1-loss and L2-loss epsilon-SVR dual problem
//
//  min_\beta  0.5\beta^T (Q + diag(lambda)) \beta - p \sum_{i=1}^l|\beta_i| + \sum_{i=1}^l yi\beta_i,
//    s.t.      -upper_bound_i <= \beta_i <= upper_bound_i,
// 
//  where Qij = xi^T xj and
//  D is a diagonal matrix 
//
// In L1-SVM case:
// 		upper_bound_i = C
// 		lambda_i = 0
// In L2-SVM case:
// 		upper_bound_i = INF
// 		lambda_i = 1/(2*C)
//
// Given: 
// x, y, p, C
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Algorithm 4 of Ho and Lin, 2012   

#undef GETI
#define GETI(i) (0)
// To support weights for instances, use GETI(i) (i)

static void solve_l2r_l1l2_svr(
	const problem *prob, double *w, const parameter *param,
	int solver_type)
{
	int l = prob->l;
	double C = param->C;
	double p = param->p;
	int w_size = prob->n;
	double eps = param->eps;
	int i, s, iter = 0;
	int max_iter = 1000;
	int active_size = l;
	int *index = new int[l];

	double d, G, H;
	double Gmax_old = INF;
	double Gmax_new, Gnorm1_new;
	double Gnorm1_init = -1.0; // Gnorm1_init is initialized at the first iteration
	double *beta = new double[l];
	double *QD = new double[l];
	double *y = prob->y;

	// L2R_L2LOSS_SVR_DUAL
	double lambda[1], upper_bound[1];
	lambda[0] = 0.5/C;
	upper_bound[0] = INF;

	if(solver_type == L2R_L1LOSS_SVR_DUAL)
	{
		lambda[0] = 0;
		upper_bound[0] = C;
	}

	// Initial beta can be set here. Note that
	// -upper_bound <= beta[i] <= upper_bound
	for(i=0; i<l; i++)
		beta[i] = 0;

	for(i=0; i<w_size; i++)
		w[i] = 0;
	for(i=0; i<l; i++)
	{
		QD[i] = 0;
		feature_node *xi = prob->x[i];
		while(xi->index != -1)
		{
			double val = xi->value;
			QD[i] += val*val;
			w[xi->index-1] += beta[i]*val;
			xi++;
		}

		index[i] = i;
	}


	while(iter < max_iter)
	{
		Gmax_new = 0;
		Gnorm1_new = 0;

		for(i=0; i<active_size; i++)
		{
			int j = i+rand()%(active_size-i);
			swap(index[i], index[j]);
		}

		for(s=0; s<active_size; s++)
		{
			i = index[s];
			G = -y[i] + lambda[GETI(i)]*beta[i];
			H = QD[i] + lambda[GETI(i)];

			feature_node *xi = prob->x[i];
			while(xi->index != -1)
			{
				int ind = xi->index-1;
				double val = xi->value;
				G += val*w[ind];
				xi++;
			}

			double Gp = G+p;
			double Gn = G-p;
			double violation = 0;
			if(beta[i] == 0)
			{
				if(Gp < 0)
					violation = -Gp;
				else if(Gn > 0)
					violation = Gn;
				else if(Gp>Gmax_old && Gn<-Gmax_old)
				{
					active_size--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}
			}
			else if(beta[i] >= upper_bound[GETI(i)])
			{
				if(Gp > 0)
					violation = Gp;
				else if(Gp < -Gmax_old)
				{
					active_size--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}
			}
			else if(beta[i] <= -upper_bound[GETI(i)])
			{
				if(Gn < 0)
					violation = -Gn;
				else if(Gn > Gmax_old)
				{
					active_size--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}
			}
			else if(beta[i] > 0)
				violation = fabs(Gp);
			else
				violation = fabs(Gn);

			Gmax_new = max(Gmax_new, violation);
			Gnorm1_new += violation;

			// obtain Newton direction d
			if(Gp < H*beta[i])
				d = -Gp/H;
			else if(Gn > H*beta[i])
				d = -Gn/H;
			else
				d = -beta[i];

			if(fabs(d) < 1.0e-12)
				continue;

			double beta_old = beta[i];
			beta[i] = min(max(beta[i]+d, -upper_bound[GETI(i)]), upper_bound[GETI(i)]);
			d = beta[i]-beta_old;

			if(d != 0)
			{
				xi = prob->x[i];
				while(xi->index != -1)
				{
					w[xi->index-1] += d*xi->value;
					xi++;
				}
			}
		}

		if(iter == 0)
			Gnorm1_init = Gnorm1_new;
		iter++;
		if(iter % 10 == 0)
			info(".");

		if(Gnorm1_new <= eps*Gnorm1_init)
		{
			if(active_size == l)
				break;
			else
			{
				active_size = l;
				info("*");
				Gmax_old = INF;
				continue;
			}
		}

		Gmax_old = Gmax_new;
	}

	info("\noptimization finished, #iter = %d\n", iter);
	if(iter >= max_iter)
		info("\nWARNING: reaching max number of iterations\nUsing -s 11 may be faster\n\n");

	// calculate objective value
	double v = 0;
	int nSV = 0;
	for(i=0; i<w_size; i++)
		v += w[i]*w[i];
	v = 0.5*v;
	for(i=0; i<l; i++)
	{
		v += p*fabs(beta[i]) - y[i]*beta[i] + 0.5*lambda[GETI(i)]*beta[i]*beta[i];
		if(beta[i] != 0)
			nSV++;
	}

	info("Objective value = %lf\n", v);
	info("nSV = %d\n",nSV);

	delete [] beta;
	delete [] QD;
	delete [] index;
}


// A coordinate descent algorithm for 
// the dual of L2-regularized logistic regression problems
//
//  min_\alpha  0.5(\alpha^T Q \alpha) + \sum \alpha_i log (\alpha_i) + (upper_bound_i - \alpha_i) log (upper_bound_i - \alpha_i),
//    s.t.      0 <= \alpha_i <= upper_bound_i,
// 
//  where Qij = yi yj xi^T xj and 
//  upper_bound_i = Cp if y_i = 1
//  upper_bound_i = Cn if y_i = -1
//
// Given: 
// x, y, Cp, Cn
// eps is the stopping tolerance
//
// solution will be put in w
//
// See Algorithm 5 of Yu et al., MLJ 2010

#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)

void solve_l2r_lr_dual(const problem *prob, double *w, double eps, double Cp, double Cn)
{
	int l = prob->l;
	int w_size = prob->n;
	int i, s, iter = 0;
	double *xTx = new double[l];
	int max_iter = 1000;
	int *index = new int[l];	
	double *alpha = new double[2*l]; // store alpha and C - alpha
	schar *y = new schar[l];
	int max_inner_iter = 100; // for inner Newton
	double innereps = 1e-2;
	double innereps_min = min(1e-8, eps);
	double upper_bound[3] = {Cn, 0, Cp};

	for(i=0; i<l; i++)
	{
		if(prob->y[i] > 0)
		{
			y[i] = +1;
		}
		else
		{
			y[i] = -1;
		}
	}
	
	// Initial alpha can be set here. Note that
	// 0 < alpha[i] < upper_bound[GETI(i)]
	// alpha[2*i] + alpha[2*i+1] = upper_bound[GETI(i)]
	for(i=0; i<l; i++)
	{
		alpha[2*i] = min(0.001*upper_bound[GETI(i)], 1e-8);
		alpha[2*i+1] = upper_bound[GETI(i)] - alpha[2*i];
	}

	for(i=0; i<w_size; i++)
		w[i] = 0;
	for(i=0; i<l; i++)
	{
		xTx[i] = 0;
		feature_node *xi = prob->x[i];
		while (xi->index != -1)
		{
			double val = xi->value;
			xTx[i] += val*val;
			w[xi->index-1] += y[i]*alpha[2*i]*val;
			xi++;
		}
		index[i] = i;
	}

	while (iter < max_iter)
	{
		for (i=0; i<l; i++)
		{
			int j = i+rand()%(l-i);
			swap(index[i], index[j]);
		}
		int newton_iter = 0;
		double Gmax = 0;
		for (s=0; s<l; s++)
		{
			i = index[s];
			schar yi = y[i];
			double C = upper_bound[GETI(i)];
			double ywTx = 0, xisq = xTx[i];
			feature_node *xi = prob->x[i];
			while (xi->index != -1)
			{
				ywTx += w[xi->index-1]*xi->value;
				xi++;
			}
			ywTx *= y[i];
			double a = xisq, b = ywTx;

			// Decide to minimize g_1(z) or g_2(z)
			int ind1 = 2*i, ind2 = 2*i+1, sign = 1;
			if(0.5*a*(alpha[ind2]-alpha[ind1])+b < 0)
			{
				ind1 = 2*i+1;
				ind2 = 2*i;
				sign = -1;
			}

			//  g_t(z) = z*log(z) + (C-z)*log(C-z) + 0.5a(z-alpha_old)^2 + sign*b(z-alpha_old)
			double alpha_old = alpha[ind1];
			double z = alpha_old;
			if(C - z < 0.5 * C)
				z = 0.1*z;
			double gp = a*(z-alpha_old)+sign*b+log(z/(C-z));
			Gmax = max(Gmax, fabs(gp));

			// Newton method on the sub-problem
			const double eta = 0.1; // xi in the paper
			int inner_iter = 0;
			while (inner_iter <= max_inner_iter)
			{
				if(fabs(gp) < innereps)
					break;
				double gpp = a + C/(C-z)/z;
				double tmpz = z - gp/gpp;
				if(tmpz <= 0)
					z *= eta;
				else // tmpz in (0, C)
					z = tmpz;
				gp = a*(z-alpha_old)+sign*b+log(z/(C-z));
				newton_iter++;
				inner_iter++;
			}

			if(inner_iter > 0) // update w
			{
				alpha[ind1] = z;
				alpha[ind2] = C-z;
				xi = prob->x[i];
				while (xi->index != -1)
				{
					w[xi->index-1] += sign*(z-alpha_old)*yi*xi->value;
					xi++;
				}
			}
		}

		iter++;
		if(iter % 10 == 0)
			info(".");

		if(Gmax < eps)
			break;

		if(newton_iter <= l/10)
			innereps = max(innereps_min, 0.1*innereps);

	}

	info("\noptimization finished, #iter = %d\n",iter);
	if (iter >= max_iter)
		info("\nWARNING: reaching max number of iterations\nUsing -s 0 may be faster (also see FAQ)\n\n");

	// calculate objective value

	double v = 0;
	for(i=0; i<w_size; i++)
		v += w[i] * w[i];
	v *= 0.5;
	for(i=0; i<l; i++)
		v += alpha[2*i] * log(alpha[2*i]) + alpha[2*i+1] * log(alpha[2*i+1])
			- upper_bound[GETI(i)] * log(upper_bound[GETI(i)]);
	info("Objective value = %lf\n", v);

	delete [] xTx;
	delete [] alpha;
	delete [] y;
	delete [] 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
//
// See Yuan et al. (2010) and appendix of LIBLINEAR paper, Fan et al. (2008)

#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)

static void solve_l1r_l2_svc(
	problem *prob_col, double *w, double eps,
	double Cp, double Cn)
{
	int l = prob_col->l;
	int w_size = prob_col->n;
	int j, s, iter = 0;
	int max_iter = 1000;
	int active_size = w_size;
	int max_num_linesearch = 20;

	double sigma = 0.01;
	double d, G_loss, G, H;
	double Gmax_old = INF;
	double Gmax_new, Gnorm1_new;
	double Gnorm1_init = -1.0; // Gnorm1_init is initialized at the first iteration
	double d_old, d_diff;
	double loss_old, loss_new;
	double appxcond, cond;

	int *index = new int[w_size];
	schar *y = new schar[l];
	double *b = new double[l]; // b = 1-ywTx
	double *xj_sq = new double[w_size];
	feature_node *x;

	double C[3] = {Cn,0,Cp};

	// Initial w can be set here.
	for(j=0; j<w_size; j++)
		w[j] = 0;

	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++)
	{
		index[j] = j;
		xj_sq[j] = 0;
		x = prob_col->x[j];
		while(x->index != -1)
		{
			int ind = x->index-1;
			x->value *= y[ind]; // x->value stores yi*xij
			double val = x->value;
			b[ind] -= w[j]*val;
			xj_sq[j] += C[GETI(ind)]*val*val;
			x++;
		}
	}

	while(iter < max_iter)
	{
		Gmax_new = 0;
		Gnorm1_new = 0;

		for(j=0; j<active_size; j++)
		{
			int i = j+rand()%(active_size-j);
			swap(index[i], index[j]);
		}

		for(s=0; s<active_size; s++)
		{
			j = index[s];
			G_loss = 0;
			H = 0;

			x = prob_col->x[j];
			while(x->index != -1)
			{
				int ind = x->index-1;
				if(b[ind] > 0)
				{
					double val = x->value;
					double tmp = C[GETI(ind)]*val;
					G_loss -= tmp*b[ind];
					H += tmp*val;
				}
				x++;
			}
			G_loss *= 2;

			G = G_loss;
			H *= 2;
			H = max(H, 1e-12);

			double Gp = G+1;
			double Gn = G-1;
			double violation = 0;
			if(w[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--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}
			}
			else if(w[j] > 0)
				violation = fabs(Gp);
			else
				violation = fabs(Gn);

			Gmax_new = max(Gmax_new, violation);
			Gnorm1_new += violation;

			// obtain Newton direction d
			if(Gp < H*w[j])
				d = -Gp/H;
			else if(Gn > H*w[j])
				d = -Gn/H;
			else
				d = -w[j];

			if(fabs(d) < 1.0e-12)
				continue;

			double delta = fabs(w[j]+d)-fabs(w[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[j]+d)-fabs(w[j]) - sigma*delta;

				appxcond = xj_sq[j]*d*d + G_loss*d + cond;
				if(appxcond <= 0)
				{
					x = prob_col->x[j];
					while(x->index != -1)
					{
						b[x->index-1] += d_diff*x->value;
						x++;
					}
					break;
				}

				if(num_linesearch == 0)
				{
					loss_old = 0;
					loss_new = 0;
					x = prob_col->x[j];
					while(x->index != -1)
					{
						int ind = x->index-1;
						if(b[ind] > 0)
							loss_old += C[GETI(ind)]*b[ind]*b[ind];
						double b_new = b[ind] + d_diff*x->value;
						b[ind] = b_new;
						if(b_new > 0)
							loss_new += C[GETI(ind)]*b_new*b_new;
						x++;
					}
				}
				else
				{
					loss_new = 0;
					x = prob_col->x[j];
					while(x->index != -1)
					{
						int ind = x->index-1;
						double b_new = b[ind] + d_diff*x->value;
						b[ind] = b_new;
						if(b_new > 0)
							loss_new += C[GETI(ind)]*b_new*b_new;
						x++;
					}
				}

				cond = cond + loss_new - loss_old;
				if(cond <= 0)
					break;
				else
				{
					d_old = d;
					d *= 0.5;
					delta *= 0.5;
				}
			}

			w[j] += d;

			// recompute b[] if line search takes too many steps
			if(num_linesearch >= max_num_linesearch)
			{
				info("#");
				for(int i=0; i<l; i++)
					b[i] = 1;

				for(int i=0; i<w_size; i++)
				{
					if(w[i]==0) continue;
					x = prob_col->x[i];
					while(x->index != -1)
					{
						b[x->index-1] -= w[i]*x->value;
						x++;
					}
				}
			}
		}

		if(iter == 0)
			Gnorm1_init = Gnorm1_new;
		iter++;
		if(iter % 10 == 0)
			info(".");

		if(Gnorm1_new <= eps*Gnorm1_init)
		{
			if(active_size == w_size)
				break;
			else
			{
				active_size = w_size;
				info("*");
				Gmax_old = INF;
				continue;
			}
		}

		Gmax_old = Gmax_new;
	}

	info("\noptimization finished, #iter = %d\n", iter);
	if(iter >= max_iter)
		info("\nWARNING: reaching max number of iterations\n");

	// calculate objective value

	double v = 0;
	int nnz = 0;
	for(j=0; j<w_size; j++)
	{
		x = prob_col->x[j];
		while(x->index != -1)
		{
			x->value *= prob_col->y[x->index-1]; // restore x->value
			x++;
		}
		if(w[j] != 0)
		{
			v += fabs(w[j]);
			nnz++;
		}
	}
	for(j=0; j<l; j++)
		if(b[j] > 0)
			v += C[GETI(j)]*b[j]*b[j];

	info("Objective value = %lf\n", v);
	info("#nonzeros/#features = %d/%d\n", nnz, w_size);

	delete [] index;
	delete [] y;
	delete [] b;
	delete [] 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
//
// See Yuan et al. (2011) and appendix of LIBLINEAR paper, Fan et al. (2008)

#undef GETI
#define GETI(i) (y[i]+1)
// To support weights for instances, use GETI(i) (i)

static void solve_l1r_lr(
	const problem *prob_col, double *w, double eps,
	double Cp, double Cn)
{
	int l = prob_col->l;
	int w_size = prob_col->n;
	int j, s, newton_iter=0, iter=0;
	int max_newton_iter = 100;
	int max_iter = 1000;
	int max_num_linesearch = 20;
	int active_size;
	int QP_active_size;

	double nu = 1e-12;
	double inner_eps = 1;
	double sigma = 0.01;
	double w_norm, w_norm_new;
	double z, G, H;
	double Gnorm1_init = -1.0; // Gnorm1_init is initialized at the first iteration
	double Gmax_old = INF;
	double Gmax_new, Gnorm1_new;
	double QP_Gmax_old = INF;
	double QP_Gmax_new, QP_Gnorm1_new;
	double delta, negsum_xTd, cond;

	int *index = new int[w_size];
	schar *y = new schar[l];
	double *Hdiag = new double[w_size];
	double *Grad = new double[w_size];
	double *wpd = new double[w_size];
	double *xjneg_sum = new double[w_size];
	double *xTd = new double[l];
	double *exp_wTx = new double[l];
	double *exp_wTx_new = new double[l];
	double *tau = new double[l];
	double *D = new double[l];
	feature_node *x;

	double C[3] = {Cn,0,Cp};

	// Initial w can be set here.
	for(j=0; j<w_size; j++)
		w[j] = 0;

	for(j=0; j<l; j++)
	{
		if(prob_col->y[j] > 0)
			y[j] = 1;
		else
			y[j] = -1;

		exp_wTx[j] = 0;
	}

	w_norm = 0;
	for(j=0; j<w_size; j++)
	{
		w_norm += fabs(w[j]);
		wpd[j] = w[j];
		index[j] = j;
		xjneg_sum[j] = 0;
		x = prob_col->x[j];
		while(x->index != -1)
		{
			int ind = x->index-1;
			double val = x->value;
			exp_wTx[ind] += w[j]*val;
			if(y[ind] == -1)
				xjneg_sum[j] += C[GETI(ind)]*val;
			x++;
		}
	}
	for(j=0; j<l; j++)
	{
		exp_wTx[j] = exp(exp_wTx[j]);
		double tau_tmp = 1/(1+exp_wTx[j]);
		tau[j] = C[GETI(j)]*tau_tmp;
		D[j] = C[GETI(j)]*exp_wTx[j]*tau_tmp*tau_tmp;
	}

	while(newton_iter < max_newton_iter)
	{
		Gmax_new = 0;
		Gnorm1_new = 0;
		active_size = w_size;

		for(s=0; s<active_size; s++)
		{
			j = index[s];
			Hdiag[j] = nu;
			Grad[j] = 0;

			double tmp = 0;
			x = prob_col->x[j];
			while(x->index != -1)
			{
				int ind = x->index-1;
				Hdiag[j] += x->value*x->value*D[ind];
				tmp += x->value*tau[ind];
				x++;
			}
			Grad[j] = -tmp + xjneg_sum[j];

			double Gp = Grad[j]+1;
			double Gn = Grad[j]-1;
			double violation = 0;
			if(w[j] == 0)
			{
				if(Gp < 0)
					violation = -Gp;
				else if(Gn > 0)
					violation = Gn;
				//outer-level shrinking
				else if(Gp>Gmax_old/l && Gn<-Gmax_old/l)
				{
					active_size--;
					swap(index[s], index[active_size]);
					s--;
					continue;
				}
			}
			else if(w[j] > 0)
				violation = fabs(Gp);
			else
				violation = fabs(Gn);

			Gmax_new = max(Gmax_new, violation);
			Gnorm1_new += violation;
		}

		if(newton_iter == 0)
			Gnorm1_init = Gnorm1_new;

		if(Gnorm1_new <= eps*Gnorm1_init)
			break;

		iter = 0;
		QP_Gmax_old = INF;
		QP_active_size = active_size;

		for(int i=0; i<l; i++)
			xTd[i] = 0;

		// optimize QP over wpd
		while(iter < max_iter)
		{
			QP_Gmax_new = 0;
			QP_Gnorm1_new = 0;

			for(j=0; j<QP_active_size; j++)
			{
				int i = j+rand()%(QP_active_size-j);
				swap(index[i], index[j]);
			}

			for(s=0; s<QP_active_size; s++)
			{
				j = index[s];
				H = Hdiag[j];

				x = prob_col->x[j];
				G = Grad[j] + (wpd[j]-w[j])*nu;
				while(x->index != -1)
				{
					int ind = x->index-1;
					G += x->value*D[ind]*xTd[ind];
					x++;
				}

				double Gp = G+1;
				double Gn = G-1;
				double violation = 0;
				if(wpd[j] == 0)
				{
					if(Gp < 0)
						violation = -Gp;
					else if(Gn > 0)
						violation = Gn;
					//inner-level shrinking
					else if(Gp>QP_Gmax_old/l && Gn<-QP_Gmax_old/l)
					{
						QP_active_size--;
						swap(index[s], index[QP_active_size]);
						s--;
						continue;
					}
				}
				else if(wpd[j] > 0)
					violation = fabs(Gp);
				else
					violation = fabs(Gn);

				QP_Gmax_new = max(QP_Gmax_new, violation);
				QP_Gnorm1_new += violation;

				// obtain solution of one-variable problem
				if(Gp < H*wpd[j])
					z = -Gp/H;
				else if(Gn > H*wpd[j])
					z = -Gn/H;
				else
					z = -wpd[j];

				if(fabs(z) < 1.0e-12)
					continue;
				z = min(max(z,-10.0),10.0);

				wpd[j] += z;

				x = prob_col->x[j];
				while(x->index != -1)
				{
					int ind = x->index-1;
					xTd[ind] += x->value*z;
					x++;
				}
			}

			iter++;

			if(QP_Gnorm1_new <= inner_eps*Gnorm1_init)
			{
				//inner stopping
				if(QP_active_size == active_size)
					break;
				//active set reactivation
				else
				{
					QP_active_size = active_size;
					QP_Gmax_old = INF;
					continue;
				}
			}

			QP_Gmax_old = QP_Gmax_new;
		}

		if(iter >= max_iter)
			info("WARNING: reaching max number of inner iterations\n");

		delta = 0;
		w_norm_new = 0;
		for(j=0; j<w_size; j++)
		{
			delta += Grad[j]*(wpd[j]-w[j]);
			if(wpd[j] != 0)
				w_norm_new += fabs(wpd[j]);
		}
		delta += (w_norm_new-w_norm);

		negsum_xTd = 0;
		for(int i=0; i<l; i++)
			if(y[i] == -1)
				negsum_xTd += C[GETI(i)]*xTd[i];

		int num_linesearch;
		for(num_linesearch=0; num_linesearch < max_num_linesearch; num_linesearch++)
		{
			cond = w_norm_new - w_norm + negsum_xTd - sigma*delta;

			for(int i=0; i<l; i++)
			{
				double exp_xTd = exp(xTd[i]);
				exp_wTx_new[i] = exp_wTx[i]*exp_xTd;
				cond += C[GETI(i)]*log((1+exp_wTx_new[i])/(exp_xTd+exp_wTx_new[i]));
			}

			if(cond <= 0)
			{
				w_norm = w_norm_new;
				for(j=0; j<w_size; j++)
					w[j] = wpd[j];
				for(int i=0; i<l; i++)
				{
					exp_wTx[i] = exp_wTx_new[i];
					double tau_tmp = 1/(1+exp_wTx[i]);
					tau[i] = C[GETI(i)]*tau_tmp;
					D[i] = C[GETI(i)]*exp_wTx[i]*tau_tmp*tau_tmp;
				}
				break;
			}
			else
			{
				w_norm_new = 0;
				for(j=0; j<w_size; j++)
				{
					wpd[j] = (w[j]+wpd[j])*0.5;
					if(wpd[j] != 0)
						w_norm_new += fabs(wpd[j]);
				}
				delta *= 0.5;
				negsum_xTd *= 0.5;
				for(int i=0; i<l; i++)
					xTd[i] *= 0.5;
			}
		}

		// Recompute some info due to too many line search steps
		if(num_linesearch >= max_num_linesearch)
		{
			for(int i=0; i<l; i++)
				exp_wTx[i] = 0;

			for(int i=0; i<w_size; i++)
			{
				if(w[i]==0) continue;
				x = prob_col->x[i];
				while(x->index != -1)
				{
					exp_wTx[x->index-1] += w[i]*x->value;
					x++;
				}
			}

			for(int i=0; i<l; i++)
				exp_wTx[i] = exp(exp_wTx[i]);
		}

		if(iter == 1)
			inner_eps *= 0.25;

		newton_iter++;
		Gmax_old = Gmax_new;

		info("iter %3d  #CD cycles %d\n", newton_iter, iter);
	}

	info("=========================\n");
	info("optimization finished, #iter = %d\n", newton_iter);
	if(newton_iter >= max_newton_iter)
		info("WARNING: reaching max number of iterations\n");

	// calculate objective value

	double v = 0;
	int nnz = 0;
	for(j=0; j<w_size; j++)
		if(w[j] != 0)
		{
			v += fabs(w[j]);
			nnz++;
		}
	for(j=0; j<l; j++)
		if(y[j] == 1)
			v += C[GETI(j)]*log(1+1/exp_wTx[j]);
		else
			v += C[GETI(j)]*log(1+exp_wTx[j]);

	info("Objective value = %lf\n", v);
	info("#nonzeros/#features = %d/%d\n", nnz, w_size);

	delete [] index;
	delete [] y;
	delete [] Hdiag;
	delete [] Grad;
	delete [] wpd;
	delete [] xjneg_sum;
	delete [] xTd;
	delete [] exp_wTx;
	delete [] exp_wTx_new;
	delete [] tau;
	delete [] D;
}

// transpose matrix X from row format to column format
static void transpose(const problem *prob, feature_node **x_space_ret, problem *prob_col)
{
	int i;
	int l = prob->l;
	int n = prob->n;
	size_t nnz = 0;
	size_t *col_ptr = new size_t [n+1];
	feature_node *x_space;
	prob_col->l = l;
	prob_col->n = n;
	prob_col->y = new double[l];
	prob_col->x = new feature_node*[n];

	for(i=0; i<l; i++)
		prob_col->y[i] = prob->y[i];

	for(i=0; i<n+1; i++)
		col_ptr[i] = 0;
	for(i=0; i<l; i++)
	{
		feature_node *x = prob->x[i];
		while(x->index != -1)
		{
			nnz++;
			col_ptr[x->index]++;
			x++;
		}
	}
	for(i=1; i<n+1; i++)
		col_ptr[i] += col_ptr[i-1] + 1;

	x_space = new feature_node[nnz+n];
	for(i=0; i<n; i++)
		prob_col->x[i] = &x_space[col_ptr[i]];

	for(i=0; i<l; i++)
	{
		feature_node *x = prob->x[i];
		while(x->index != -1)
		{
			int ind = x->index-1;
			x_space[col_ptr[ind]].index = i+1; // starts from 1
			x_space[col_ptr[ind]].value = x->value;
			col_ptr[ind]++;
			x++;
		}
	}
	for(i=0; i<n; i++)
		x_space[col_ptr[i]].index = -1;

	*x_space_ret = x_space;

	delete [] col_ptr;
}

// label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
// perm, length l, must be allocated before calling this subroutine
static void group_classes(const problem *prob, int *nr_class_ret, int **label_ret, int **start_ret, int **count_ret, int *perm)
{
	int l = prob->l;
	int max_nr_class = 16;
	int nr_class = 0;
	int *label = Malloc(int,max_nr_class);
	int *count = Malloc(int,max_nr_class);
	int *data_label = Malloc(int,l);
	int i;

	for(i=0;i<l;i++)
	{
		int this_label = (int)prob->y[i];
		int j;
		for(j=0;j<nr_class;j++)
		{
			if(this_label == label[j])
			{
				++count[j];
				break;
			}
		}
		data_label[i] = j;
		if(j == nr_class)
		{
			if(nr_class == max_nr_class)
			{
				max_nr_class *= 2;
				label = (int *)realloc(label,max_nr_class*sizeof(int));
				count = (int *)realloc(count,max_nr_class*sizeof(int));
			}
			label[nr_class] = this_label;
			count[nr_class] = 1;
			++nr_class;
		}
	}

	//
	// Labels are ordered by their first occurrence in the training set. 
	// However, for two-class sets with -1/+1 labels and -1 appears first, 
	// we swap labels to ensure that internally the binary SVM has positive data corresponding to the +1 instances.
	//
	if (nr_class == 2 && label[0] == -1 && label[1] == 1)
	{
		swap(label[0],label[1]);
		swap(count[0],count[1]);
		for(i=0;i<l;i++)
		{
			if(data_label[i] == 0)
				data_label[i] = 1;
			else
				data_label[i] = 0;
		}
	}

	int *start = Malloc(int,nr_class);
	start[0] = 0;
	for(i=1;i<nr_class;i++)
		start[i] = start[i-1]+count[i-1];
	for(i=0;i<l;i++)
	{
		perm[start[data_label[i]]] = i;
		++start[data_label[i]];
	}
	start[0] = 0;
	for(i=1;i<nr_class;i++)
		start[i] = start[i-1]+count[i-1];

	*nr_class_ret = nr_class;
	*label_ret = label;
	*start_ret = start;
	*count_ret = count;
	free(data_label);
}

static void train_one(const problem *prob, const parameter *param, double *w, double Cp, double Cn)
{
	double eps=param->eps;
	int pos = 0;
	int neg = 0;
	for(int i=0;i<prob->l;i++)
		if(prob->y[i] > 0)
			pos++;
	neg = prob->l - pos;

	double primal_solver_tol = eps*max(min(pos,neg), 1)/prob->l;

	function *fun_obj=NULL;
	switch(param->solver_type)
	{
		case L2R_LR:
		{
			double *C = new double[prob->l];
			for(int i = 0; i < prob->l; i++)
			{
				if(prob->y[i] > 0)
					C[i] = Cp;
				else
					C[i] = Cn;
			}
			fun_obj=new l2r_lr_fun(prob, C);
			TRON tron_obj(fun_obj, primal_solver_tol);
			tron_obj.set_print_string(liblinear_print_string);
			tron_obj.tron(w);
			delete fun_obj;
			delete[] C;
			break;
		}
		case L2R_L2LOSS_SVC:
		{
			double *C = new double[prob->l];
			for(int i = 0; i < prob->l; i++)
			{
				if(prob->y[i] > 0)
					C[i] = Cp;
				else
					C[i] = Cn;
			}
			fun_obj=new l2r_l2_svc_fun(prob, C);
			TRON tron_obj(fun_obj, primal_solver_tol);
			tron_obj.set_print_string(liblinear_print_string);
			tron_obj.tron(w);
			delete fun_obj;
			delete[] C;
			break;
		}
		case L2R_L2LOSS_SVC_DUAL:
			solve_l2r_l1l2_svc(prob, w, eps, Cp, Cn, L2R_L2LOSS_SVC_DUAL);
			break;
		case L2R_L1LOSS_SVC_DUAL:
			solve_l2r_l1l2_svc(prob, w, eps, Cp, Cn, L2R_L1LOSS_SVC_DUAL);
			break;
		case L1R_L2LOSS_SVC:
		{
			problem prob_col;
			feature_node *x_space = NULL;
			transpose(prob, &x_space ,&prob_col);
			solve_l1r_l2_svc(&prob_col, w, primal_solver_tol, Cp, Cn);
			delete [] prob_col.y;
			delete [] prob_col.x;
			delete [] x_space;
			break;
		}
		case L1R_LR:
		{
			problem prob_col;
			feature_node *x_space = NULL;
			transpose(prob, &x_space ,&prob_col);
			solve_l1r_lr(&prob_col, w, primal_solver_tol, Cp, Cn);
			delete [] prob_col.y;
			delete [] prob_col.x;
			delete [] x_space;
			break;
		}
		case L2R_LR_DUAL:
			solve_l2r_lr_dual(prob, w, eps, Cp, Cn);
			break;
		case L2R_L2LOSS_SVR:
		{
			double *C = new double[prob->l];
			for(int i = 0; i < prob->l; i++)
				C[i] = param->C;

			fun_obj=new l2r_l2_svr_fun(prob, C, param->p);
			TRON tron_obj(fun_obj, param->eps);
			tron_obj.set_print_string(liblinear_print_string);
			tron_obj.tron(w);
			delete fun_obj;
			delete[] C;
			break;

		}
		case L2R_L1LOSS_SVR_DUAL:
			solve_l2r_l1l2_svr(prob, w, param, L2R_L1LOSS_SVR_DUAL);
			break;
		case L2R_L2LOSS_SVR_DUAL:
			solve_l2r_l1l2_svr(prob, w, param, L2R_L2LOSS_SVR_DUAL);
			break;
		default:
			fprintf(stderr, "ERROR: unknown solver_type\n");
			break;
	}
}

/** NEW: probability esitmate */

#include "probability.h"

// Cross-validation decision values for probability estimates
static void binary_svc_probability(
		const problem *prob, const parameter *param,
		double Cp, double Cn, double& probA, double& probB)
{

	int nr_fold = 5;
	int *perm = Malloc(int,prob->l);
	double *dec_values = Malloc(double,prob->l);

	// random shuffle
	for(int i=0;i<prob->l;i++) 
		perm[i]=i;

	for(int i=0;i<prob->l;i++)
	{
		int j = i+rand()%(prob->l-i);
		swap(perm[i],perm[j]);
	}

	for(int i=0;i<nr_fold;i++)
	{
		int begin = i*prob->l/nr_fold;
		int end = (i+1)*prob->l/nr_fold;
		int k;
		struct problem subprob;

		subprob.n = prob->n;
		subprob.l = prob->l-(end-begin);
		subprob.x = Malloc(struct feature_node*,subprob.l);
		subprob.y = Malloc(double,subprob.l);

		k=0;
		for(int j=0;j<begin;j++)
		{
			subprob.x[k] = prob->x[perm[j]];
			subprob.y[k] = prob->y[perm[j]];
			++k;
		}
		for(int j=end;j<prob->l;j++)
		{
			subprob.x[k] = prob->x[perm[j]];
			subprob.y[k] = prob->y[perm[j]];
			++k;
		}

		int p_count=0,n_count=0;
		for(int j=0;j<k;j++)
			if(subprob.y[j]>0)
				p_count++;
			else
				n_count++;

		if(p_count==0 && n_count==0)
			for(int j=begin;j<end;j++)
				dec_values[perm[j]] = 0;
		else if(p_count > 0 && n_count == 0)
			for(int j=begin;j<end;j++)
				dec_values[perm[j]] = 1;
		else if(p_count == 0 && n_count > 0)
			for(int j=begin;j<end;j++)
				dec_values[perm[j]] = -1;
		else
		{
			parameter subparam = *param; // get the parameters from the original problem
			subparam.probability=0;
			subparam.nr_weight=2;
			subparam.weight_label = Malloc(int,2);
			subparam.weight = Malloc(double,2);
			subparam.weight_label[0]=+1;
			subparam.weight_label[1]=-1;
			subparam.weight[0]=Cp;
			subparam.weight[1]=Cn;
			struct model *submodel = train(&subprob,&subparam);
			for(int j=begin;j<end;j++)
			{
				predict_values(submodel,prob->x[perm[j]],&(dec_values[perm[j]]));
				// ensure +1 -1 order; reason not using CV subroutine
				dec_values[perm[j]] *= submodel->label[0];
			}
			free_and_destroy_model(&submodel);
			destroy_param(&subparam);
		}
		free(subprob.x);
        free(subprob.y);
	}
    sigmoid_train(prob->l,dec_values,prob->y,probA,probB);
    free(dec_values);
    free(perm);
}

/*****/

//
// Interface functions
//
model* train(const problem *prob, const parameter *param)
{
	int l = prob->l;
	int n = prob->n;
	int w_size = prob->n;

	model *model_ = Malloc(model,1);

	if(prob->bias>=0)
		model_->nr_feature=n-1;
	else
		model_->nr_feature=n;
	model_->param = *param;
	model_->bias = prob->bias;

	// NEW: probability estimate
	model_->probA = NULL;
	model_->probB = NULL;

	if(check_regression_model(model_))
	{
		model_->w = Malloc(double, w_size);
		model_->nr_class = 2;
		model_->label = NULL;
		train_one(prob, param, &model_->w[0], 0, 0);
	}
	else
	{
		int nr_class;
		int *label = NULL;
		int *start = NULL;
		int *count = NULL;
		int *perm = Malloc(int,l);

		// group training data of the same class
		group_classes(prob,&nr_class,&label,&start,&count,perm);

		model_->nr_class=nr_class;
		model_->label = Malloc(int,nr_class);
		for(int i=0;i<nr_class;i++)
			model_->label[i] = label[i];

		// calculate weighted C
		double *weighted_C = Malloc(double, nr_class);
		for(int i=0;i<nr_class;i++)
			weighted_C[i] = param->C;
		for(int i=0;i<param->nr_weight;i++)
		{
			int j;
			for(j=0;j<nr_class;j++)
				if(param->weight_label[i] == label[j])
					break;
			if(j == nr_class)
				fprintf(stderr,"WARNING: class label %d specified in weight is not found\n", param->weight_label[i]);
			else
				weighted_C[j] *= param->weight[i];
		}

		// constructing the subproblem
		feature_node **x = Malloc(feature_node *,l);
		for(int i=0;i<l;i++)
			x[i] = prob->x[perm[i]];

		problem sub_prob;
		sub_prob.l = l;
		sub_prob.n = n;
		sub_prob.x = Malloc(feature_node *,sub_prob.l);
		sub_prob.y = Malloc(double,sub_prob.l);

		for(int k=0; k<sub_prob.l; k++)
			sub_prob.x[k] = x[k];

		// multi-class svm by Crammer and Singer
		if(param->solver_type == MCSVM_CS)
		{
			model_->w=Malloc(double, n*nr_class);
			for(int i=0;i<nr_class;i++)
				for(int j=start[i];j<start[i]+count[i];j++)
					sub_prob.y[j] = i;
			Solver_MCSVM_CS Solver(&sub_prob, nr_class, weighted_C, param->eps);
			Solver.Solve(model_->w);
		}
		else
		{

			if(nr_class == 2)
			{
				model_->w=Malloc(double, w_size);

				int e0 = start[0]+count[0];
				int k=0;
				for(; k<e0; k++)
					sub_prob.y[k] = +1;
				for(; k<sub_prob.l; k++)
					sub_prob.y[k] = -1;

				// NEW: probability estimate
				double *probA=NULL,*probB=NULL;

				// Probability estimate for nr_class == 2 only
				if (param->probability && 
						(param->solver_type == L2R_L2LOSS_SVC_DUAL || 
						 param->solver_type == L2R_L2LOSS_SVC || 
						 param->solver_type == L2R_L1LOSS_SVC_DUAL || 
						 param->solver_type == L2R_LR)) {

					probA=Malloc(double,1);
					probB=Malloc(double,1);

					binary_svc_probability(&sub_prob,param,weighted_C[0], weighted_C[1], probA[0], probB[0]);
				}

				train_one(&sub_prob, param, &model_->w[0], weighted_C[0], weighted_C[1]);

				model_->probA = probA;
				model_->probB = probB;
			}
			else
			{
				model_->w=Malloc(double, w_size*nr_class);
				double *w=Malloc(double, w_size);
				for(int i=0;i<nr_class;i++)
				{
					int si = start[i];
					int ei = si+count[i];

					int k=0;
					for(; k<si; k++)
						sub_prob.y[k] = -1;
					for(; k<ei; k++)
						sub_prob.y[k] = +1;
					for(; k<sub_prob.l; k++)
						sub_prob.y[k] = -1;

					train_one(&sub_prob, param, w, weighted_C[i], param->C);

					for(int j=0;j<w_size;j++)
						model_->w[j*nr_class+i] = w[j];
				}
				free(w);
			}

		}

		free(x);
		free(label);
		free(start);
		free(count);
		free(perm);
		free(sub_prob.x);
		free(sub_prob.y);
		free(weighted_C);
	}
	return model_;
}

void cross_validation(const problem *prob, const parameter *param, int nr_fold, double *target)
{
	int i;
	int *fold_start;
	int l = prob->l;
	int *perm = Malloc(int,l);
	if (nr_fold > l)
	{
		nr_fold = l;
		fprintf(stderr,"WARNING: # folds > # data. Will use # folds = # data instead (i.e., leave-one-out cross validation)\n");
	}
	fold_start = Malloc(int,nr_fold+1);
	for(i=0;i<l;i++) perm[i]=i;
	for(i=0;i<l;i++)
	{
		int j = i+rand()%(l-i);
		swap(perm[i],perm[j]);
	}
	for(i=0;i<=nr_fold;i++)
		fold_start[i]=i*l/nr_fold;

	for(i=0;i<nr_fold;i++)
	{
		int begin = fold_start[i];
		int end = fold_start[i+1];
		int j,k;
		struct problem subprob;

		subprob.bias = prob->bias;
		subprob.n = prob->n;
		subprob.l = l-(end-begin);
		subprob.x = Malloc(struct feature_node*,subprob.l);
		subprob.y = Malloc(double,subprob.l);

		k=0;
		for(j=0;j<begin;j++)
		{
			subprob.x[k] = prob->x[perm[j]];
			subprob.y[k] = prob->y[perm[j]];
			++k;
		}
		for(j=end;j<l;j++)
		{
			subprob.x[k] = prob->x[perm[j]];
			subprob.y[k] = prob->y[perm[j]];
			++k;
		}
		struct model *submodel = train(&subprob,param);
		for(j=begin;j<end;j++)
			target[perm[j]] = predict(submodel,prob->x[perm[j]]);
		free_and_destroy_model(&submodel);
		free(subprob.x);
		free(subprob.y);
	}
	free(fold_start);
	free(perm);
}

double predict_values(const struct model *model_, const struct feature_node *x, double *dec_values)
{
	int idx;
	int n;
	if(model_->bias>=0)
		n=model_->nr_feature+1;
	else
		n=model_->nr_feature;
	double *w=model_->w;
	int nr_class=model_->nr_class;
	int i;
	int nr_w;
	if(nr_class==2 && model_->param.solver_type != MCSVM_CS)
		nr_w = 1;
	else
		nr_w = nr_class;

	const feature_node *lx=x;
	for(i=0;i<nr_w;i++)
		dec_values[i] = 0;
	for(; (idx=lx->index)!=-1; lx++)
	{
		// the dimension of testing data may exceed that of training
		if(idx<=n)
			for(i=0;i<nr_w;i++)
				dec_values[i] += w[(idx-1)*nr_w+i]*lx->value;
	}

	if(nr_class==2)
	{
		if(check_regression_model(model_))
			return dec_values[0];
		else
			return (dec_values[0]>0)?model_->label[0]:model_->label[1];
	}
	else
	{
		int dec_max_idx = 0;
		for(i=1;i<nr_class;i++)
		{
			if(dec_values[i] > dec_values[dec_max_idx])
				dec_max_idx = i;
		}
		return model_->label[dec_max_idx];
	}
}

double predict(const model *model_, const feature_node *x)
{
	double *dec_values = Malloc(double, model_->nr_class);
	double label=predict_values(model_, x, dec_values);
	free(dec_values);
	return label;
}

double predict_probability2(const struct model *model_, const struct feature_node *x, double* prob_estimates)
{
	if (model_->nr_class == 2 && model_->probA != NULL && model_->probB != NULL) 
	{
		int nr_class = model_->nr_class;
		double *dec_values = Malloc(double, nr_class*(nr_class-1)/2);
		predict_values(model_, x, dec_values);

		double min_prob=1e-7;
		double **pairwise_prob=Malloc(double *,nr_class);

		for(int i=0;i<nr_class;i++)
			pairwise_prob[i]=Malloc(double,nr_class);

		int k=0;
		for(int i=0;i<nr_class;i++)
		{
			for(int j=i+1;j<nr_class;j++)
			{
				pairwise_prob[i][j]=std::min(std::max(sigmoid_predict(dec_values[k],model_->probA[k],model_->probB[k]),min_prob),1-min_prob);
				pairwise_prob[j][i]=1-pairwise_prob[i][j];
				k++;
			}
		}

		multiclass_probability(nr_class,pairwise_prob,prob_estimates);

		int prob_max_idx = 0;
		for(int i=1;i<nr_class;i++)
			if(prob_estimates[i] > prob_estimates[prob_max_idx])
					prob_max_idx = i;

		for(int i=0;i<nr_class;i++)
			free(pairwise_prob[i]);

		free(dec_values);
		free(pairwise_prob);
		return model_->label[prob_max_idx];
	} else
		return 0;
}

double predict_probability(const struct model *model_, const struct feature_node *x, double* prob_estimates)
{
	if(check_probability_model(model_))
	{
		int i;
		int nr_class=model_->nr_class;
		int nr_w;
		if(nr_class==2)
			nr_w = 1;
		else
			nr_w = nr_class;

		double label=predict_values(model_, x, prob_estimates);
		for(i=0;i<nr_w;i++)
			prob_estimates[i]=1/(1+exp(-prob_estimates[i]));

		if(nr_class==2) // for binary classification
			prob_estimates[1]=1.-prob_estimates[0];
		else
		{
			double sum=0;
			for(i=0; i<nr_class; i++)
				sum+=prob_estimates[i];

			for(i=0; i<nr_class; i++)
				prob_estimates[i]=prob_estimates[i]/sum;
		}

		return label;
	}
	else
		return 0;
}

static const char *solver_type_table[]=
{
	"L2R_LR", "L2R_L2LOSS_SVC_DUAL", "L2R_L2LOSS_SVC", "L2R_L1LOSS_SVC_DUAL", "MCSVM_CS",
	"L1R_L2LOSS_SVC", "L1R_LR", "L2R_LR_DUAL",
	"", "", "",
	"L2R_L2LOSS_SVR", "L2R_L2LOSS_SVR_DUAL", "L2R_L1LOSS_SVR_DUAL", NULL
};

int save_model(const char *model_file_name, const struct model *model_)
{
	int i;
	int nr_feature=model_->nr_feature;
	int n;
	const parameter& param = model_->param;

	if(model_->bias>=0)
		n=nr_feature+1;
	else
		n=nr_feature;
	int w_size = n;
	FILE *fp = fopen(model_file_name,"w");
	if(fp==NULL) return -1;

	char *old_locale = strdup(setlocale(LC_ALL, NULL));
	setlocale(LC_ALL, "C");

	int nr_w;
	if(model_->nr_class==2 && model_->param.solver_type != MCSVM_CS)
		nr_w=1;
	else
		nr_w=model_->nr_class;

	fprintf(fp, "solver_type %s\n", solver_type_table[param.solver_type]);
	fprintf(fp, "nr_class %d\n", model_->nr_class);

	if(model_->label)
	{
		fprintf(fp, "label");
		for(i=0; i<model_->nr_class; i++)
			fprintf(fp, " %d", model_->label[i]);
		fprintf(fp, "\n");
	}

	fprintf(fp, "nr_feature %d\n", nr_feature);

	fprintf(fp, "bias %.16g\n", model_->bias);

	if (model_->probA) {
		fprintf(fp, "probA %g\n", model_->probA[0]);
	}

	if (model_->probB) {
		fprintf(fp, "probB %g\n", model_->probB[0]);
	}

	fprintf(fp, "w\n");
	for(i=0; i<w_size; i++)
	{
		int j;
		for(j=0; j<nr_w; j++)
			fprintf(fp, "%.16g ", model_->w[i*nr_w+j]);
		fprintf(fp, "\n");
	}

	setlocale(LC_ALL, old_locale);
	free(old_locale);

	if (ferror(fp) != 0 || fclose(fp) != 0) return -1;
	else return 0;
}

struct model *load_model(const char *model_file_name)
{
	FILE *fp = fopen(model_file_name,"r");
	if(fp==NULL) return NULL;

	int i;
	int nr_feature;
	int n;
	int nr_class;
	double bias;
	model *model_ = Malloc(model,1);
	parameter& param = model_->param;

	// NEW: Probability estimate
	model_->probA = NULL;
	model_->probB = NULL;

	model_->label = NULL;

	char *old_locale = strdup(setlocale(LC_ALL, NULL));
	setlocale(LC_ALL, "C");

	char cmd[81];
	while(1)
	{
		fscanf(fp,"%80s",cmd);
		if(strcmp(cmd,"solver_type")==0)
		{
			fscanf(fp,"%80s",cmd);
			int i;
			for(i=0;solver_type_table[i];i++)
			{
				if(strcmp(solver_type_table[i],cmd)==0)
				{
					param.solver_type=i;
					break;
				}
			}
			if(solver_type_table[i] == NULL)
			{
				fprintf(stderr,"unknown solver type.\n");

				setlocale(LC_ALL, old_locale);
				free(model_->label);
				free(model_);
				free(old_locale);
				return NULL;
			}
		}
		else if(strcmp(cmd,"nr_class")==0)
		{
			fscanf(fp,"%d",&nr_class);
			model_->nr_class=nr_class;
		}
		else if(strcmp(cmd,"nr_feature")==0)
		{
			fscanf(fp,"%d",&nr_feature);
			model_->nr_feature=nr_feature;
		}
		else if(strcmp(cmd,"bias")==0)
		{
			fscanf(fp,"%lf",&bias);
			model_->bias=bias;
		}
		else if(strcmp(cmd,"probA")==0)
		{
			double probA;
			fscanf(fp,"%lf",&probA);
			model_->probA= Malloc(double, 1);
			model_->probA[0] = probA;
		}
		else if(strcmp(cmd,"probB")==0)
		{
			double probB;
			fscanf(fp,"%lf",&probB);
			model_->probB= Malloc(double, 1);
			model_->probB[0] = probB;
		}
		else if(strcmp(cmd,"w")==0)
		{
			break;
		}
		else if(strcmp(cmd,"label")==0)
		{
			int nr_class = model_->nr_class;
			model_->label = Malloc(int,nr_class);
			for(int i=0;i<nr_class;i++)
				fscanf(fp,"%d",&model_->label[i]);
		}
		else
		{
			fprintf(stderr,"unknown text in model file: [%s]\n",cmd);
			setlocale(LC_ALL, old_locale);
			free(model_->label);
			free(model_);
			free(old_locale);
			return NULL;
		}
	}

	nr_feature=model_->nr_feature;
	if(model_->bias>=0)
		n=nr_feature+1;
	else
		n=nr_feature;
	int w_size = n;
	int nr_w;
	if(nr_class==2 && param.solver_type != MCSVM_CS)
		nr_w = 1;
	else
		nr_w = nr_class;

	model_->w=Malloc(double, w_size*nr_w);
	for(i=0; i<w_size; i++)
	{
		int j;
		for(j=0; j<nr_w; j++)
			fscanf(fp, "%lf ", &model_->w[i*nr_w+j]);
		fscanf(fp, "\n");
	}

	setlocale(LC_ALL, old_locale);
	free(old_locale);

	if (ferror(fp) != 0 || fclose(fp) != 0) return NULL;

	return model_;
}

int get_nr_feature(const model *model_)
{
	return model_->nr_feature;
}

int get_nr_class(const model *model_)
{
	return model_->nr_class;
}

void get_labels(const model *model_, int* label)
{
	if (model_->label != NULL)
		for(int i=0;i<model_->nr_class;i++)
			label[i] = model_->label[i];
}

// use inline here for better performance (around 20% faster than the non-inline one)
static inline double get_w_value(const struct model *model_, int idx, int label_idx) 
{
	int nr_class = model_->nr_class;
	int solver_type = model_->param.solver_type;
	const double *w = model_->w;

	if(idx < 0 || idx > model_->nr_feature)
		return 0;
	if(check_regression_model(model_))
		return w[idx];
	else 
	{
		if(label_idx < 0 || label_idx >= nr_class)
			return 0;
		if(nr_class == 2 && solver_type != MCSVM_CS)
		{
			if(label_idx == 0)
				return w[idx];
			else
				return -w[idx];
		}
		else
			return w[idx*nr_class+label_idx];
	}
}

// feat_idx: starting from 1 to nr_feature
// label_idx: starting from 0 to nr_class-1 for classification models;
//            for regression models, label_idx is ignored.
double get_decfun_coef(const struct model *model_, int feat_idx, int label_idx)
{
	if(feat_idx > model_->nr_feature)
		return 0;
	return get_w_value(model_, feat_idx-1, label_idx);
}

double get_decfun_bias(const struct model *model_, int label_idx)
{
	int bias_idx = model_->nr_feature;
	double bias = model_->bias;
	if(bias <= 0)
		return 0;
	else
		return bias*get_w_value(model_, bias_idx, label_idx);
}

void free_model_content(struct model *model_ptr)
{
	// NEW: probability estimate
	if (model_ptr->probA)
		free(model_ptr->probA);
	if (model_ptr->probB)
		free(model_ptr->probB);

	if(model_ptr->w != NULL)
		free(model_ptr->w);
	if(model_ptr->label != NULL)
		free(model_ptr->label);
}

void free_and_destroy_model(struct model **model_ptr_ptr)
{
	struct model *model_ptr = *model_ptr_ptr;
	if(model_ptr != NULL)
	{
		free_model_content(model_ptr);
		free(model_ptr);
	}
}

void destroy_param(parameter* param)
{
	if(param->weight_label != NULL)
		free(param->weight_label);
	if(param->weight != NULL)
		free(param->weight);
}

const char *check_parameter(const problem *prob, const parameter *param)
{
	if(param->eps <= 0)
		return "eps <= 0";

	if(param->C <= 0)
		return "C <= 0";

	if(param->p < 0)
		return "p < 0";

	if(param->solver_type != L2R_LR
		&& param->solver_type != L2R_L2LOSS_SVC_DUAL
		&& param->solver_type != L2R_L2LOSS_SVC
		&& param->solver_type != L2R_L1LOSS_SVC_DUAL
		&& param->solver_type != MCSVM_CS
		&& param->solver_type != L1R_L2LOSS_SVC
		&& param->solver_type != L1R_LR
		&& param->solver_type != L2R_LR_DUAL
		&& param->solver_type != L2R_L2LOSS_SVR
		&& param->solver_type != L2R_L2LOSS_SVR_DUAL
		&& param->solver_type != L2R_L1LOSS_SVR_DUAL)
		return "unknown solver type";

	return NULL;
}

int check_probability_model(const struct model *model_)
{
	// NEW: Probability estimate
	return (
			model_->param.solver_type==L2R_LR ||
			model_->param.solver_type==L2R_LR_DUAL ||
			model_->param.solver_type==L1R_LR ||

			((model_->nr_class == 2 && 
			 model_->probA != NULL && 
			 model_->probB != NULL) &&
				(model_->param.solver_type == L2R_L2LOSS_SVC_DUAL ||
				model_->param.solver_type == L2R_L2LOSS_SVC ||
				model_->param.solver_type == L2R_L1LOSS_SVC_DUAL))
			);
}

int check_regression_model(const struct model *model_)
{
	return (model_->param.solver_type==L2R_L2LOSS_SVR ||
			model_->param.solver_type==L2R_L1LOSS_SVR_DUAL ||
			model_->param.solver_type==L2R_L2LOSS_SVR_DUAL);
}

void set_print_string_function(void (*print_func)(const char*))
{
	if (print_func == NULL)
		liblinear_print_string = &print_string_stdout;
	else
		liblinear_print_string = print_func;
}