double[] get_QD()
	{
		return QD;
	}
}

public class svm {
	//
	// construct and solve various formulations
	//
	public static final int LIBSVM_VERSION=319; 
	public static final Random rand = new Random();

	private static svm_print_interface svm_print_stdout = new svm_print_interface()
	{
		public void print(String s)
		{
			System.out.print(s);
			System.out.flush();
		}
	};

	private static svm_print_interface svm_print_string = svm_print_stdout;

	static void info(String s) 
	{
		svm_print_string.print(s);
	}

	private static void solve_c_svc(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si,
					double Cp, double Cn)
	{
		int l = prob.l;
		double[] minus_ones = new double[l];
		byte[] y = new byte[l];

		int i;

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

		Solver s = new Solver();
		s.Solve(l, new SVC_Q(prob,param,y), minus_ones, y,
			alpha, Cp, Cn, param.eps, si, param.shrinking);

		double sum_alpha=0;
		for(i=0;i<l;i++)
			sum_alpha += alpha[i];

		if (Cp==Cn)
			svm.info("nu = "+sum_alpha/(Cp*prob.l)+"\n");

		for(i=0;i<l;i++)
			alpha[i] *= y[i];
	}

	private static void solve_nu_svc(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si)
	{
		int i;
		int l = prob.l;
		double nu = param.nu;

		byte[] y = new byte[l];

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

		double sum_pos = nu*l/2;
		double sum_neg = nu*l/2;

		for(i=0;i<l;i++)
			if(y[i] == +1)
			{
				alpha[i] = Math.min(1.0,sum_pos);
				sum_pos -= alpha[i];
			}
			else
			{
				alpha[i] = Math.min(1.0,sum_neg);
				sum_neg -= alpha[i];
			}

		double[] zeros = new double[l];

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

		Solver_NU s = new Solver_NU();
		s.Solve(l, new SVC_Q(prob,param,y), zeros, y,
			alpha, 1.0, 1.0, param.eps, si, param.shrinking);
		double r = si.r;

		svm.info("C = "+1/r+"\n");

		for(i=0;i<l;i++)
			alpha[i] *= y[i]/r;

		si.rho /= r;
		si.obj /= (r*r);
		si.upper_bound_p = 1/r;
		si.upper_bound_n = 1/r;
	}

	private static void solve_one_class(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si)
	{
		int l = prob.l;
		double[] zeros = new double[l];
		byte[] ones = new byte[l];
		int i;

		int n = (int)(param.nu*prob.l);	// # of alpha's at upper bound

		for(i=0;i<n;i++)
			alpha[i] = 1;
		if(n<prob.l)
			alpha[n] = param.nu * prob.l - n;
		for(i=n+1;i<l;i++)
			alpha[i] = 0;

		for(i=0;i<l;i++)
		{
			zeros[i] = 0;
			ones[i] = 1;
		}

		Solver s = new Solver();
		s.Solve(l, new ONE_CLASS_Q(prob,param), zeros, ones,
			alpha, 1.0, 1.0, param.eps, si, param.shrinking);
	}

	private static void solve_epsilon_svr(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si)
	{
		int l = prob.l;
		double[] alpha2 = new double[2*l];
		double[] linear_term = new double[2*l];
		byte[] y = new byte[2*l];
		int i;

		for(i=0;i<l;i++)
		{
			alpha2[i] = 0;
			linear_term[i] = param.p - prob.y[i];
			y[i] = 1;

			alpha2[i+l] = 0;
			linear_term[i+l] = param.p + prob.y[i];
			y[i+l] = -1;
		}

		Solver s = new Solver();
		s.Solve(2*l, new SVR_Q(prob,param), linear_term, y,
			alpha2, param.C, param.C, param.eps, si, param.shrinking);

		double sum_alpha = 0;
		for(i=0;i<l;i++)
		{
			alpha[i] = alpha2[i] - alpha2[i+l];
			sum_alpha += Math.abs(alpha[i]);
		}
		svm.info("nu = "+sum_alpha/(param.C*l)+"\n");
	}

	private static void solve_nu_svr(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si)
	{
		int l = prob.l;
		double C = param.C;
		double[] alpha2 = new double[2*l];
		double[] linear_term = new double[2*l];
		byte[] y = new byte[2*l];
		int i;

		double sum = C * param.nu * l / 2;
		for(i=0;i<l;i++)
		{
			alpha2[i] = alpha2[i+l] = Math.min(sum,C);
			sum -= alpha2[i];
			
			linear_term[i] = - prob.y[i];
			y[i] = 1;

			linear_term[i+l] = prob.y[i];
			y[i+l] = -1;
		}

		Solver_NU s = new Solver_NU();
		s.Solve(2*l, new SVR_Q(prob,param), linear_term, y,
			alpha2, C, C, param.eps, si, param.shrinking);

		svm.info("epsilon = "+(-si.r)+"\n");
		
		for(i=0;i<l;i++)
			alpha[i] = alpha2[i] - alpha2[i+l];
	}

	//
	// decision_function
	//
	static class decision_function
	{
		double[] alpha;
		double rho;	
	};

	static decision_function svm_train_one(
		svm_problem prob, svm_parameter param,
		double Cp, double Cn)
	{
		double[] alpha = new double[prob.l];
		Solver.SolutionInfo si = new Solver.SolutionInfo();
		switch(param.svm_type)
		{
			case svm_parameter.C_SVC:
				solve_c_svc(prob,param,alpha,si,Cp,Cn);
				break;
			case svm_parameter.NU_SVC:
				solve_nu_svc(prob,param,alpha,si);
				break;
			case svm_parameter.ONE_CLASS:
				solve_one_class(prob,param,alpha,si);
				break;
			case svm_parameter.EPSILON_SVR:
				solve_epsilon_svr(prob,param,alpha,si);
				break;
			case svm_parameter.NU_SVR:
				solve_nu_svr(prob,param,alpha,si);
				break;
		}

		svm.info("obj = "+si.obj+", rho = "+si.rho+"\n");

		// output SVs

		int nSV = 0;
		int nBSV = 0;
		for(int i=0;i<prob.l;i++)
		{
			if(Math.abs(alpha[i]) > 0)
			{
				++nSV;
				if(prob.y[i] > 0)
				{
					if(Math.abs(alpha[i]) >= si.upper_bound_p)
					++nBSV;
				}
				else
				{
					if(Math.abs(alpha[i]) >= si.upper_bound_n)
						++nBSV;
				}
			}
		}

		svm.info("nSV = "+nSV+", nBSV = "+nBSV+"\n");

		decision_function f = new decision_function();
		f.alpha = alpha;
		f.rho = si.rho;
		return f;
	}

	// Platt's binary SVM Probablistic Output: an improvement from Lin et al.
	private static void sigmoid_train(int l, double[] dec_values, double[] labels, 
				  double[] probAB)
	{
		double A, B;
		double prior1=0, prior0 = 0;
		int i;

		for (i=0;i<l;i++)
			if (labels[i] > 0) prior1+=1;
			else prior0+=1;
	
		int max_iter=100;	// Maximal number of iterations
		double min_step=1e-10;	// Minimal step taken in line search
		double sigma=1e-12;	// For numerically strict PD of Hessian
		double eps=1e-5;
		double hiTarget=(prior1+1.0)/(prior1+2.0);
		double loTarget=1/(prior0+2.0);
		double[] t= new double[l];
		double fApB,p,q,h11,h22,h21,g1,g2,det,dA,dB,gd,stepsize;
		double newA,newB,newf,d1,d2;
		int iter; 
	
		// Initial Point and Initial Fun Value
		A=0.0; B=Math.log((prior0+1.0)/(prior1+1.0));
		double fval = 0.0;

		for (i=0;i<l;i++)
		{
			if (labels[i]>0) t[i]=hiTarget;
			else t[i]=loTarget;
			fApB = dec_values[i]*A+B;
			if (fApB>=0)
				fval += t[i]*fApB + Math.log(1+Math.exp(-fApB));
			else
				fval += (t[i] - 1)*fApB +Math.log(1+Math.exp(fApB));
		}
		for (iter=0;iter<max_iter;iter++)
		{
			// Update Gradient and Hessian (use H' = H + sigma I)
			h11=sigma; // numerically ensures strict PD
			h22=sigma;
			h21=0.0;g1=0.0;g2=0.0;
			for (i=0;i<l;i++)
			{
				fApB = dec_values[i]*A+B;
				if (fApB >= 0)
				{
					p=Math.exp(-fApB)/(1.0+Math.exp(-fApB));
					q=1.0/(1.0+Math.exp(-fApB));
				}
				else
				{
					p=1.0/(1.0+Math.exp(fApB));
					q=Math.exp(fApB)/(1.0+Math.exp(fApB));
				}
				d2=p*q;
				h11+=dec_values[i]*dec_values[i]*d2;
				h22+=d2;
				h21+=dec_values[i]*d2;
				d1=t[i]-p;
				g1+=dec_values[i]*d1;
				g2+=d1;
			}

			// Stopping Criteria
			if (Math.abs(g1)<eps && Math.abs(g2)<eps)
				break;
			
			// Finding Newton direction: -inv(H') * g
			det=h11*h22-h21*h21;
			dA=-(h22*g1 - h21 * g2) / det;
			dB=-(-h21*g1+ h11 * g2) / det;
			gd=g1*dA+g2*dB;


			stepsize = 1;		// Line Search
			while (stepsize >= min_step)
			{
				newA = A + stepsize * dA;
				newB = B + stepsize * dB;

				// New function value
				newf = 0.0;
				for (i=0;i<l;i++)
				{
					fApB = dec_values[i]*newA+newB;
					if (fApB >= 0)
						newf += t[i]*fApB + Math.log(1+Math.exp(-fApB));
					else
						newf += (t[i] - 1)*fApB +Math.log(1+Math.exp(fApB));
				}
				// Check sufficient decrease
				if (newf<fval+0.0001*stepsize*gd)
				{
					A=newA;B=newB;fval=newf;
					break;
				}
				else
					stepsize = stepsize / 2.0;
			}
			
			if (stepsize < min_step)
			{
				svm.info("Line search fails in two-class probability estimates\n");
				break;
			}
		}
		
		if (iter>=max_iter)
			svm.info("Reaching maximal iterations in two-class probability estimates\n");
		probAB[0]=A;probAB[1]=B;
	}

	private static double sigmoid_predict(double decision_value, double A, double B)
	{
		double fApB = decision_value*A+B;
		if (fApB >= 0)
			return Math.exp(-fApB)/(1.0+Math.exp(-fApB));
		else
			return 1.0/(1+Math.exp(fApB)) ;
	}

	// Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
	private static void multiclass_probability(int k, double[][] r, double[] p)
	{
		int t,j;
		int iter = 0, max_iter=Math.max(100,k);
		double[][] Q=new double[k][k];
		double[] Qp=new double[k];
		double pQp, eps=0.005/k;
	
		for (t=0;t<k;t++)
		{
			p[t]=1.0/k;  // Valid if k = 1
			Q[t][t]=0;
			for (j=0;j<t;j++)
			{
				Q[t][t]+=r[j][t]*r[j][t];
				Q[t][j]=Q[j][t];
			}
			for (j=t+1;j<k;j++)
			{
				Q[t][t]+=r[j][t]*r[j][t];
				Q[t][j]=-r[j][t]*r[t][j];
			}
		}
		for (iter=0;iter<max_iter;iter++)
		{
			// stopping condition, recalculate QP,pQP for numerical accuracy
			pQp=0;
			for (t=0;t<k;t++)
			{
				Qp[t]=0;
				for (j=0;j<k;j++)
					Qp[t]+=Q[t][j]*p[j];
				pQp+=p[t]*Qp[t];
			}
			double max_error=0;
			for (t=0;t<k;t++)
			{
				double error=Math.abs(Qp[t]-pQp);
				if (error>max_error)
					max_error=error;
			}
			if (max_error<eps) break;
		
			for (t=0;t<k;t++)
			{
				double diff=(-Qp[t]+pQp)/Q[t][t];
				p[t]+=diff;
				pQp=(pQp+diff*(diff*Q[t][t]+2*Qp[t]))/(1+diff)/(1+diff);
				for (j=0;j<k;j++)
				{
					Qp[j]=(Qp[j]+diff*Q[t][j])/(1+diff);
					p[j]/=(1+diff);
				}
			}
		}
		if (iter>=max_iter)
			svm.info("Exceeds max_iter in multiclass_prob\n");
	}

	// Cross-validation decision values for probability estimates
	private static void svm_binary_svc_probability(svm_problem prob, svm_parameter param, double Cp, double Cn, double[] probAB)
	{
		int i;
		int nr_fold = 5;
		int[] perm = new int[prob.l];
		double[] dec_values = new double[prob.l];

		// random shuffle
		for(i=0;i<prob.l;i++) perm[i]=i;
		for(i=0;i<prob.l;i++)
		{
			int j = i+rand.nextInt(prob.l-i);
			do {int _=perm[i]; perm[i]=perm[j]; perm[j]=_;} while(false);
		}
		for(i=0;i<nr_fold;i++)
		{
			int begin = i*prob.l/nr_fold;
			int end = (i+1)*prob.l/nr_fold;
			int j,k;
			svm_problem subprob = new svm_problem();

			subprob.l = prob.l-(end-begin);
			subprob.x = new svm_node[subprob.l][];
			subprob.y = new 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<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(j=0;j<k;j++)
				if(subprob.y[j]>0)
					p_count++;
				else
					n_count++;
			
			if(p_count==0 && n_count==0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = 0;
			else if(p_count > 0 && n_count == 0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = 1;
			else if(p_count == 0 && n_count > 0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = -1;
			else
			{
				svm_parameter subparam = (svm_parameter)param.clone();
				subparam.probability=0;
				subparam.C=1.0;
				subparam.nr_weight=2;
				subparam.weight_label = new int[2];
				subparam.weight = new double[2];
				subparam.weight_label[0]=+1;
				subparam.weight_label[1]=-1;
				subparam.weight[0]=Cp;
				subparam.weight[1]=Cn;
				svm_model submodel = svm_train(subprob,subparam);
				for(j=begin;j<end;j++)
				{
					double[] dec_value=new double[1];
					svm_predict_values(submodel,prob.x[perm[j]],dec_value);
					dec_values[perm[j]]=dec_value[0];
					// ensure +1 -1 order; reason not using CV subroutine
					dec_values[perm[j]] *= submodel.label[0];
				}		
			}
		}		
		sigmoid_train(prob.l,dec_values,prob.y,probAB);
	}

	// Return parameter of a Laplace distribution 
	private static double svm_svr_probability(svm_problem prob, svm_parameter param)
	{
		int i;
		int nr_fold = 5;
		double[] ymv = new double[prob.l];
		double mae = 0;

		svm_parameter newparam = (svm_parameter)param.clone();
		newparam.probability = 0;
		svm_cross_validation(prob,newparam,nr_fold,ymv);
		for(i=0;i<prob.l;i++)
		{
			ymv[i]=prob.y[i]-ymv[i];
			mae += Math.abs(ymv[i]);
		}		
		mae /= prob.l;
		double std=Math.sqrt(2*mae*mae);
		int count=0;
		mae=0;
		for(i=0;i<prob.l;i++)
			if (Math.abs(ymv[i]) > 5*std) 
				count=count+1;
			else 
				mae+=Math.abs(ymv[i]);
		mae /= (prob.l-count);
		svm.info("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma="+mae+"\n");
		return mae;
	}

	// 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
	private static void svm_group_classes(svm_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 = new int[max_nr_class];
		int[] count = new int[max_nr_class];
		int[] data_label = new 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;
					int[] new_data = new int[max_nr_class];
					System.arraycopy(label,0,new_data,0,label.length);
					label = new_data;
					new_data = new int[max_nr_class];
					System.arraycopy(count,0,new_data,0,count.length);
					count = new_data;					
				}
				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)
		{
			do {int _=label[0]; label[0]=label[1]; label[1]=_;} while(false);
			do {int _=count[0]; count[0]=count[1]; count[1]=_;} while(false);
			for(i=0;i<l;i++)
			{
				if(data_label[i] == 0)
					data_label[i] = 1;
				else
					data_label[i] = 0;
			}
		}

		int[] start = new 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[0] = nr_class;
		label_ret[0] = label;
		start_ret[0] = start;
		count_ret[0] = count;
	}

	//
	// Interface functions
	//
	public static svm_model svm_train(svm_problem prob, svm_parameter param)
	{
		svm_model model = new svm_model();
		model.param = param;

		if(param.svm_type == svm_parameter.ONE_CLASS ||
		   param.svm_type == svm_parameter.EPSILON_SVR ||
		   param.svm_type == svm_parameter.NU_SVR)
		{
			// regression or one-class-svm
			model.nr_class = 2;
			model.label = null;
			model.nSV = null;
			model.probA = null; model.probB = null;
			model.sv_coef = new double[1][];

			if(param.probability == 1 &&
			   (param.svm_type == svm_parameter.EPSILON_SVR ||
			    param.svm_type == svm_parameter.NU_SVR))
			{
				model.probA = new double[1];
				model.probA[0] = svm_svr_probability(prob,param);
			}

			decision_function f = svm_train_one(prob,param,0,0);
			model.rho = new double[1];
			model.rho[0] = f.rho;

			int nSV = 0;
			int i;
			for(i=0;i<prob.l;i++)
				if(Math.abs(f.alpha[i]) > 0) ++nSV;
			model.l = nSV;
			model.SV = new svm_node[nSV][];
			model.sv_coef[0] = new double[nSV];
			model.sv_indices = new int[nSV];
			int j = 0;
			for(i=0;i<prob.l;i++)
				if(Math.abs(f.alpha[i]) > 0)
				{
					model.SV[j] = prob.x[i];
					model.sv_coef[0][j] = f.alpha[i];
					model.sv_indices[j] = i+1;
					++j;
				}
		}
		else
		{
			// classification
			int l = prob.l;
			int[] tmp_nr_class = new int[1];
			int[][] tmp_label = new int[1][];
			int[][] tmp_start = new int[1][];
			int[][] tmp_count = new int[1][];			
			int[] perm = new int[l];

			// group training data of the same class
			svm_group_classes(prob,tmp_nr_class,tmp_label,tmp_start,tmp_count,perm);
			int nr_class = tmp_nr_class[0];			
			int[] label = tmp_label[0];
			int[] start = tmp_start[0];
			int[] count = tmp_count[0];
 			
			if(nr_class == 1) 
				svm.info("WARNING: training data in only one class. See README for details.\n");
			
			svm_node[][] x = new svm_node[l][];
			int i;
			for(i=0;i<l;i++)
				x[i] = prob.x[perm[i]];

			// calculate weighted C

			double[] weighted_C = new double[nr_class];
			for(i=0;i<nr_class;i++)
				weighted_C[i] = param.C;
			for(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)
					System.err.print("WARNING: class label "+param.weight_label[i]+" specified in weight is not found\n");
				else
					weighted_C[j] *= param.weight[i];
			}

			// train k*(k-1)/2 models

			boolean[] nonzero = new boolean[l];
			for(i=0;i<l;i++)
				nonzero[i] = false;
			decision_function[] f = new decision_function[nr_class*(nr_class-1)/2];

			double[] probA=null,probB=null;
			if (param.probability == 1)
			{
				probA=new double[nr_class*(nr_class-1)/2];
				probB=new double[nr_class*(nr_class-1)/2];
			}

			int p = 0;
			for(i=0;i<nr_class;i++)
				for(int j=i+1;j<nr_class;j++)
				{
					svm_problem sub_prob = new svm_problem();
					int si = start[i], sj = start[j];
					int ci = count[i], cj = count[j];
					sub_prob.l = ci+cj;
					sub_prob.x = new svm_node[sub_prob.l][];
					sub_prob.y = new double[sub_prob.l];
					int k;
					for(k=0;k<ci;k++)
					{
						sub_prob.x[k] = x[si+k];
						sub_prob.y[k] = +1;
					}
					for(k=0;k<cj;k++)
					{
						sub_prob.x[ci+k] = x[sj+k];
						sub_prob.y[ci+k] = -1;
					}

					if(param.probability == 1)
					{
						double[] probAB=new double[2];
						svm_binary_svc_probability(sub_prob,param,weighted_C[i],weighted_C[j],probAB);
						probA[p]=probAB[0];
						probB[p]=probAB[1];
					}

					f[p] = svm_train_one(sub_prob,param,weighted_C[i],weighted_C[j]);
					for(k=0;k<ci;k++)
						if(!nonzero[si+k] && Math.abs(f[p].alpha[k]) > 0)
							nonzero[si+k] = true;
					for(k=0;k<cj;k++)
						if(!nonzero[sj+k] && Math.abs(f[p].alpha[ci+k]) > 0)
							nonzero[sj+k] = true;
					++p;
				}

			// build output

			model.nr_class = nr_class;

			model.label = new int[nr_class];
			for(i=0;i<nr_class;i++)
				model.label[i] = label[i];

			model.rho = new double[nr_class*(nr_class-1)/2];
			for(i=0;i<nr_class*(nr_class-1)/2;i++)
				model.rho[i] = f[i].rho;

			if(param.probability == 1)
			{
				model.probA = new double[nr_class*(nr_class-1)/2];
				model.probB = new double[nr_class*(nr_class-1)/2];
				for(i=0;i<nr_class*(nr_class-1)/2;i++)
				{
					model.probA[i] = probA[i];
					model.probB[i] = probB[i];
				}
			}
			else
			{
				model.probA=null;
				model.probB=null;
			}

			int nnz = 0;
			int[] nz_count = new int[nr_class];
			model.nSV = new int[nr_class];
			for(i=0;i<nr_class;i++)
			{
				int nSV = 0;
				for(int j=0;j<count[i];j++)
					if(nonzero[start[i]+j])
					{
						++nSV;
						++nnz;
					}
				model.nSV[i] = nSV;
				nz_count[i] = nSV;
			}

			svm.info("Total nSV = "+nnz+"\n");

			model.l = nnz;
			model.SV = new svm_node[nnz][];
			model.sv_indices = new int[nnz];
			p = 0;
			for(i=0;i<l;i++)
				if(nonzero[i])
				{
					model.SV[p] = x[i];
					model.sv_indices[p++] = perm[i] + 1;
				}

			int[] nz_start = new int[nr_class];
			nz_start[0] = 0;
			for(i=1;i<nr_class;i++)
				nz_start[i] = nz_start[i-1]+nz_count[i-1];

			model.sv_coef = new double[nr_class-1][];
			for(i=0;i<nr_class-1;i++)
				model.sv_coef[i] = new double[nnz];

			p = 0;
			for(i=0;i<nr_class;i++)
				for(int j=i+1;j<nr_class;j++)
				{
					// classifier (i,j): coefficients with
					// i are in sv_coef[j-1][nz_start[i]...],
					// j are in sv_coef[i][nz_start[j]...]

					int si = start[i];
					int sj = start[j];
					int ci = count[i];
					int cj = count[j];

					int q = nz_start[i];
					int k;
					for(k=0;k<ci;k++)
						if(nonzero[si+k])
							model.sv_coef[j-1][q++] = f[p].alpha[k];
					q = nz_start[j];
					for(k=0;k<cj;k++)
						if(nonzero[sj+k])
							model.sv_coef[i][q++] = f[p].alpha[ci+k];
					++p;
				}
		}
		return model;
	}
	
	// Stratified cross validation
	public static void svm_cross_validation(svm_problem prob, svm_parameter param, int nr_fold, double[] target)
	{
		int i;
		int[] fold_start = new int[nr_fold+1];
		int l = prob.l;
		int[] perm = new int[l];
		
		// stratified cv may not give leave-one-out rate
		// Each class to l folds -> some folds may have zero elements
		if((param.svm_type == svm_parameter.C_SVC ||
		    param.svm_type == svm_parameter.NU_SVC) && nr_fold < l)
		{
			int[] tmp_nr_class = new int[1];
			int[][] tmp_label = new int[1][];
			int[][] tmp_start = new int[1][];
			int[][] tmp_count = new int[1][];

			svm_group_classes(prob,tmp_nr_class,tmp_label,tmp_start,tmp_count,perm);

			int nr_class = tmp_nr_class[0];
			int[] start = tmp_start[0];
			int[] count = tmp_count[0];		

			// random shuffle and then data grouped by fold using the array perm
			int[] fold_count = new int[nr_fold];
			int c;
			int[] index = new int[l];
			for(i=0;i<l;i++)
				index[i]=perm[i];
			for (c=0; c<nr_class; c++)
				for(i=0;i<count[c];i++)
				{
					int j = i+rand.nextInt(count[c]-i);
					do {int _=index[start[c]+j]; index[start[c]+j]=index[start[c]+i]; index[start[c]+i]=_;} while(false);
				}
			for(i=0;i<nr_fold;i++)
			{
				fold_count[i] = 0;
				for (c=0; c<nr_class;c++)
					fold_count[i]+=(i+1)*count[c]/nr_fold-i*count[c]/nr_fold;
			}
			fold_start[0]=0;
			for (i=1;i<=nr_fold;i++)
				fold_start[i] = fold_start[i-1]+fold_count[i-1];
			for (c=0; c<nr_class;c++)
				for(i=0;i<nr_fold;i++)
				{
					int begin = start[c]+i*count[c]/nr_fold;
					int end = start[c]+(i+1)*count[c]/nr_fold;
					for(int j=begin;j<end;j++)
					{
						perm[fold_start[i]] = index[j];
						fold_start[i]++;
					}
				}
			fold_start[0]=0;
			for (i=1;i<=nr_fold;i++)
				fold_start[i] = fold_start[i-1]+fold_count[i-1];
		}
		else
		{
			for(i=0;i<l;i++) perm[i]=i;
			for(i=0;i<l;i++)
			{
				int j = i+rand.nextInt(l-i);
				do {int _=perm[i]; perm[i]=perm[j]; perm[j]=_;} while(false);
			}
			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;
			svm_problem subprob = new svm_problem();

			subprob.l = l-(end-begin);
			subprob.x = new svm_node[subprob.l][];
			subprob.y = new 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;
			}
			svm_model submodel = svm_train(subprob,param);
			if(param.probability==1 &&
			   (param.svm_type == svm_parameter.C_SVC ||
			    param.svm_type == svm_parameter.NU_SVC))
			{
				double[] prob_estimates= new double[svm_get_nr_class(submodel)];
				for(j=begin;j<end;j++)
					target[perm[j]] = svm_predict_probability(submodel,prob.x[perm[j]],prob_estimates);
			}
			else
				for(j=begin;j<end;j++)
					target[perm[j]] = svm_predict(submodel,prob.x[perm[j]]);
		}
	}

	public static int svm_get_svm_type(svm_model model)
	{
		return model.param.svm_type;
	}

	public static int svm_get_nr_class(svm_model model)
	{
		return model.nr_class;
	}

	public static void svm_get_labels(svm_model model, int[] label)
	{
		if (model.label != null)
			for(int i=0;i<model.nr_class;i++)
				label[i] = model.label[i];
	}

	public static void svm_get_sv_indices(svm_model model, int[] indices)
	{
		if (model.sv_indices != null)
			for(int i=0;i<model.l;i++)
				indices[i] = model.sv_indices[i];
	}

	public static int svm_get_nr_sv(svm_model model)
	{
		return model.l;
	}

	public static double svm_get_svr_probability(svm_model model)
	{
		if ((model.param.svm_type == svm_parameter.EPSILON_SVR || model.param.svm_type == svm_parameter.NU_SVR) &&
		    model.probA!=null)
		return model.probA[0];
		else
		{
			System.err.print("Model doesn't contain information for SVR probability inference\n");
			return 0;
		}
	}

	public static double svm_predict_values(svm_model model, svm_node[] x, double[] dec_values)
	{
		int i;
		if(model.param.svm_type == svm_parameter.ONE_CLASS ||
		   model.param.svm_type == svm_parameter.EPSILON_SVR ||
		   model.param.svm_type == svm_parameter.NU_SVR)
		{
			double[] sv_coef = model.sv_coef[0];
			double sum = 0;
			for(i=0;i<model.l;i++)
				sum += sv_coef[i] * Kernel.k_function(x,model.SV[i],model.param);
			sum -= model.rho[0];
			dec_values[0] = sum;

			if(model.param.svm_type == svm_parameter.ONE_CLASS)
				return (sum>0)?1:-1;
			else
				return sum;
		}
		else
		{
			int nr_class = model.nr_class;
			int l = model.l;
		
			double[] kvalue = new double[l];
			for(i=0;i<l;i++)
				kvalue[i] = Kernel.k_function(x,model.SV[i],model.param);

			int[] start = new int[nr_class];
			start[0] = 0;
			for(i=1;i<nr_class;i++)
				start[i] = start[i-1]+model.nSV[i-1];

			int[] vote = new int[nr_class];
			for(i=0;i<nr_class;i++)
				vote[i] = 0;

			int p=0;
			for(i=0;i<nr_class;i++)
				for(int j=i+1;j<nr_class;j++)
				{
					double sum = 0;
					int si = start[i];
					int sj = start[j];
					int ci = model.nSV[i];
					int cj = model.nSV[j];
				
					int k;
					double[] coef1 = model.sv_coef[j-1];
					double[] coef2 = model.sv_coef[i];
					for(k=0;k<ci;k++)
						sum += coef1[si+k] * kvalue[si+k];
					for(k=0;k<cj;k++)
						sum += coef2[sj+k] * kvalue[sj+k];
					sum -= model.rho[p];
					dec_values[p] = sum;					

					if(dec_values[p] > 0)
						++vote[i];
					else
						++vote[j];
					p++;
				}

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

			return model.label[vote_max_idx];
		}
	}

	public static double svm_predict(svm_model model, svm_node[] x)
	{
		int nr_class = model.nr_class;
		double[] dec_values;
		if(model.param.svm_type == svm_parameter.ONE_CLASS ||
				model.param.svm_type == svm_parameter.EPSILON_SVR ||
				model.param.svm_type == svm_parameter.NU_SVR)
			dec_values = new double[1];
		else
			dec_values = new double[nr_class*(nr_class-1)/2];
		double pred_result = svm_predict_values(model, x, dec_values);
		return pred_result;
	}

	public static double svm_predict_probability(svm_model model, svm_node[] x, double[] prob_estimates)
	{
		if ((model.param.svm_type == svm_parameter.C_SVC || model.param.svm_type == svm_parameter.NU_SVC) &&
		    model.probA!=null && model.probB!=null)
		{
			int i;
			int nr_class = model.nr_class;
			double[] dec_values = new double[nr_class*(nr_class-1)/2];
			svm_predict_values(model, x, dec_values);

			double min_prob=1e-7;
			double[][] pairwise_prob=new double[nr_class][nr_class];
			
			int k=0;
			for(i=0;i<nr_class;i++)
				for(int j=i+1;j<nr_class;j++)
				{
					pairwise_prob[i][j]=Math.min(Math.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(i=1;i<nr_class;i++)
				if(prob_estimates[i] > prob_estimates[prob_max_idx])
					prob_max_idx = i;
			return model.label[prob_max_idx];
		}
		else 
			return svm_predict(model, x);
	}

	static final String svm_type_table[] =
	{
		"c_svc","nu_svc","one_class","epsilon_svr","nu_svr",
	};

	static final String kernel_type_table[]=
	{
		"linear","polynomial","rbf","sigmoid","precomputed"
	};

	public static void svm_save_model(String model_file_name, svm_model model) throws IOException
	{
		DataOutputStream fp = new DataOutputStream(new BufferedOutputStream(new FileOutputStream(model_file_name)));

		svm_parameter param = model.param;

		fp.writeBytes("svm_type "+svm_type_table[param.svm_type]+"\n");
		fp.writeBytes("kernel_type "+kernel_type_table[param.kernel_type]+"\n");

		if(param.kernel_type == svm_parameter.POLY)
			fp.writeBytes("degree "+param.degree+"\n");

		if(param.kernel_type == svm_parameter.POLY ||
		   param.kernel_type == svm_parameter.RBF ||
		   param.kernel_type == svm_parameter.SIGMOID)
			fp.writeBytes("gamma "+param.gamma+"\n");

		if(param.kernel_type == svm_parameter.POLY ||
		   param.kernel_type == svm_parameter.SIGMOID)
			fp.writeBytes("coef0 "+param.coef0+"\n");

		int nr_class = model.nr_class;
		int l = model.l;
		fp.writeBytes("nr_class "+nr_class+"\n");
		fp.writeBytes("total_sv "+l+"\n");
	
		{
			fp.writeBytes("rho");
			for(int i=0;i<nr_class*(nr_class-1)/2;i++)
				fp.writeBytes(" "+model.rho[i]);
			fp.writeBytes("\n");
		}
	
		if(model.label != null)
		{
			fp.writeBytes("label");
			for(int i=0;i<nr_class;i++)
				fp.writeBytes(" "+model.label[i]);
			fp.writeBytes("\n");
		}

		if(model.probA != null) // regression has probA only
		{
			fp.writeBytes("probA");
			for(int i=0;i<nr_class*(nr_class-1)/2;i++)
				fp.writeBytes(" "+model.probA[i]);
			fp.writeBytes("\n");
		}
		if(model.probB != null) 
		{
			fp.writeBytes("probB");
			for(int i=0;i<nr_class*(nr_class-1)/2;i++)
				fp.writeBytes(" "+model.probB[i]);
			fp.writeBytes("\n");
		}

		if(model.nSV != null)
		{
			fp.writeBytes("nr_sv");
			for(int i=0;i<nr_class;i++)
				fp.writeBytes(" "+model.nSV[i]);
			fp.writeBytes("\n");
		}

		fp.writeBytes("SV\n");
		double[][] sv_coef = model.sv_coef;
		svm_node[][] SV = model.SV;

		for(int i=0;i<l;i++)
		{
			for(int j=0;j<nr_class-1;j++)
				fp.writeBytes(sv_coef[j][i]+" ");

			svm_node[] p = SV[i];
			if(param.kernel_type == svm_parameter.PRECOMPUTED)
				fp.writeBytes("0:"+(int)(p[0].value));
			else	
				for(int j=0;j<p.length;j++)
					fp.writeBytes(p[j].index+":"+p[j].value+" ");
			fp.writeBytes("\n");
		}

		fp.close();
	}

	private static double atof(String s)
	{
		return Double.valueOf(s).doubleValue();
	}

	private static int atoi(String s)
	{
		return Integer.parseInt(s);
	}

	private static boolean read_model_header(BufferedReader fp, svm_model model)
	{
		svm_parameter param = new svm_parameter();
		model.param = param;
		try
		{
			while(true)
			{
				String cmd = fp.readLine();
				String arg = cmd.substring(cmd.indexOf(' ')+1);

				if(cmd.startsWith("svm_type"))
				{
					int i;
					for(i=0;i<svm_type_table.length;i++)
					{
						if(arg.indexOf(svm_type_table[i])!=-1)
						{
							param.svm_type=i;
							break;
						}
					}
					if(i == svm_type_table.length)
					{
						System.err.print("unknown svm type.\n");
						return false;
					}
				}
				else if(cmd.startsWith("kernel_type"))
				{
					int i;
					for(i=0;i<kernel_type_table.length;i++)
					{
						if(arg.indexOf(kernel_type_table[i])!=-1)
						{
							param.kernel_type=i;
							break;
						}
					}
					if(i == kernel_type_table.length)
					{
						System.err.print("unknown kernel function.\n");
						return false;
					}
				}
				else if(cmd.startsWith("degree"))
					param.degree = atoi(arg);
				else if(cmd.startsWith("gamma"))
					param.gamma = atof(arg);
				else if(cmd.startsWith("coef0"))
					param.coef0 = atof(arg);
				else if(cmd.startsWith("nr_class"))
					model.nr_class = atoi(arg);
				else if(cmd.startsWith("total_sv"))
					model.l = atoi(arg);
				else if(cmd.startsWith("rho"))
				{
					int n = model.nr_class * (model.nr_class-1)/2;
					model.rho = new double[n];
					StringTokenizer st = new StringTokenizer(arg);
					for(int i=0;i<n;i++)
						model.rho[i] = atof(st.nextToken());
				}
				else if(cmd.startsWith("label"))
				{
					int n = model.nr_class;
					model.label = new int[n];
					StringTokenizer st = new StringTokenizer(arg);
					for(int i=0;i<n;i++)
						model.label[i] = atoi(st.nextToken());					
				}
				else if(cmd.startsWith("probA"))
				{
					int n = model.nr_class*(model.nr_class-1)/2;
					model.probA = new double[n];
					StringTokenizer st = new StringTokenizer(arg);
					for(int i=0;i<n;i++)
						model.probA[i] = atof(st.nextToken());					
				}
				else if(cmd.startsWith("probB"))
				{
					int n = model.nr_class*(model.nr_class-1)/2;
					model.probB = new double[n];
					StringTokenizer st = new StringTokenizer(arg);
					for(int i=0;i<n;i++)
						model.probB[i] = atof(st.nextToken());					
				}
				else if(cmd.startsWith("nr_sv"))
				{
					int n = model.nr_class;
					model.nSV = new int[n];
					StringTokenizer st = new StringTokenizer(arg);
					for(int i=0;i<n;i++)
						model.nSV[i] = atoi(st.nextToken());
				}
				else if(cmd.startsWith("SV"))
				{
					break;
				}
				else
				{
					System.err.print("unknown text in model file: ["+cmd+"]\n");
					return false;
				}
			}
		}
		catch(Exception e)
		{
			return false;
		}
		return true;
	}

	public static svm_model svm_load_model(String model_file_name) throws IOException
	{
		return svm_load_model(new BufferedReader(new FileReader(model_file_name)));
	}

	public static svm_model svm_load_model(BufferedReader fp) throws IOException
	{
		// read parameters

		svm_model model = new svm_model();
		model.rho = null;
		model.probA = null;
		model.probB = null;
		model.label = null;
		model.nSV = null;

		if (read_model_header(fp, model) == false)
		{
			System.err.print("ERROR: failed to read model\n");
			return null;
		}

		// read sv_coef and SV

		int m = model.nr_class - 1;
		int l = model.l;
		model.sv_coef = new double[m][l];
		model.SV = new svm_node[l][];

		for(int i=0;i<l;i++)
		{
			String line = fp.readLine();
			StringTokenizer st = new StringTokenizer(line," \t\n\r\f:");

			for(int k=0;k<m;k++)
				model.sv_coef[k][i] = atof(st.nextToken());
			int n = st.countTokens()/2;
			model.SV[i] = new svm_node[n];
			for(int j=0;j<n;j++)
			{
				model.SV[i][j] = new svm_node();
				model.SV[i][j].index = atoi(st.nextToken());
				model.SV[i][j].value = atof(st.nextToken());
			}
		}

		fp.close();
		return model;
	}

	public static String svm_check_parameter(svm_problem prob, svm_parameter param)
	{
		// svm_type

		int svm_type = param.svm_type;
		if(svm_type != svm_parameter.C_SVC &&
		   svm_type != svm_parameter.NU_SVC &&
		   svm_type != svm_parameter.ONE_CLASS &&
		   svm_type != svm_parameter.EPSILON_SVR &&
		   svm_type != svm_parameter.NU_SVR)
		return "unknown svm type";

		// kernel_type, degree
	
		int kernel_type = param.kernel_type;
		if(kernel_type != svm_parameter.LINEAR &&
		   kernel_type != svm_parameter.POLY &&
		   kernel_type != svm_parameter.RBF &&
		   kernel_type != svm_parameter.SIGMOID &&
		   kernel_type != svm_parameter.PRECOMPUTED)
			return "unknown kernel type";

		if(param.gamma < 0)
			return "gamma < 0";

		if(param.degree < 0)
			return "degree of polynomial kernel < 0";

		// cache_size,eps,C,nu,p,shrinking

		if(param.cache_size <= 0)
			return "cache_size <= 0";

		if(param.eps <= 0)
			return "eps <= 0";

		if(svm_type == svm_parameter.C_SVC ||
		   svm_type == svm_parameter.EPSILON_SVR ||
		   svm_type == svm_parameter.NU_SVR)
			if(param.C <= 0)
				return "C <= 0";

		if(svm_type == svm_parameter.NU_SVC ||
		   svm_type == svm_parameter.ONE_CLASS ||
		   svm_type == svm_parameter.NU_SVR)
			if(param.nu <= 0 || param.nu > 1)
				return "nu <= 0 or nu > 1";

		if(svm_type == svm_parameter.EPSILON_SVR)
			if(param.p < 0)
				return "p < 0";

		if(param.shrinking != 0 &&
		   param.shrinking != 1)
			return "shrinking != 0 and shrinking != 1";

		if(param.probability != 0 &&
		   param.probability != 1)
			return "probability != 0 and probability != 1";

		if(param.probability == 1 &&
		   svm_type == svm_parameter.ONE_CLASS)
			return "one-class SVM probability output not supported yet";
		
		// check whether nu-svc is feasible
	
		if(svm_type == svm_parameter.NU_SVC)
		{
			int l = prob.l;
			int max_nr_class = 16;
			int nr_class = 0;
			int[] label = new int[max_nr_class];
			int[] count = new int[max_nr_class];

			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;
					}

				if(j == nr_class)
				{
					if(nr_class == max_nr_class)
					{
						max_nr_class *= 2;
						int[] new_data = new int[max_nr_class];
						System.arraycopy(label,0,new_data,0,label.length);
						label = new_data;
						
						new_data = new int[max_nr_class];
						System.arraycopy(count,0,new_data,0,count.length);
						count = new_data;
					}
					label[nr_class] = this_label;
					count[nr_class] = 1;
					++nr_class;
				}
			}

			for(i=0;i<nr_class;i++)
			{
				int n1 = count[i];
				for(int j=i+1;j<nr_class;j++)
				{
					int n2 = count[j];
					if(param.nu*(n1+n2)/2 > Math.min(n1,n2))
						return "specified nu is infeasible";
				}
			}
		}

		return null;
	}

	public static int svm_check_probability_model(svm_model model)
	{
		if (((model.param.svm_type == svm_parameter.C_SVC || model.param.svm_type == svm_parameter.NU_SVC) &&
		model.probA!=null && model.probB!=null) ||
		((model.param.svm_type == svm_parameter.EPSILON_SVR || model.param.svm_type == svm_parameter.NU_SVR) &&
		 model.probA!=null))
			return 1;
		else
			return 0;
	}

	public static void svm_set_print_string_function(svm_print_interface print_func)
	{
		if (print_func == null)
			svm_print_string = svm_print_stdout;
		else 
			svm_print_string = print_func;
	}