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]);
		}
		System.out.print("nu = "+sum_alpha/(param.C*l)+"\n");
	}

	private static void solve_nu_svr(svm_problem prob, svm_parameter param,
					double[] alpha, Solver.SolutionInfo si)
	{
		if(param.nu < 0 || param.nu > 1)
		{
			System.err.print("specified nu is out of range\n");
			System.exit(1);
		}

		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);

		System.out.print("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;
		}

		System.out.print("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;
				}
			}
		}

		System.out.print("nSV = "+nSV+", nBSV = "+nBSV+"\n");

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

	//
	// 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.sv_coef = new double[1][];
			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];
			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];
					++j;
				}
		}
		else
		{
			// classification
			// find out the number of classes
			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[] index = 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;
					}
				index[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;
				}
			}

			// group training data of the same class

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

			svm_node[][] x = new svm_node[l][];

			for(i=0;i<l;i++)
			{
				x[start[index[i]]] = prob.x[i];
				++start[index[i]];
			}

			start[0] = 0;
			for(i=1;i<nr_class;i++)
				start[i] = start[i-1]+count[i-1];

			// 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 n*(n-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];

			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;
					}

					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;

			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;
			}

			System.out.print("Total nSV = "+nnz+"\n");

			model.l = nnz;
			model.SV = new svm_node[nnz][];
			p = 0;
			for(i=0;i<l;i++)
				if(nonzero[i]) model.SV[p++] = x[i];

			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;
	}

	public static double svm_predict(svm_model model, svm_node[] x)
	{
		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(int i=0;i<model.l;i++)
				sum += sv_coef[i] * Kernel.k_function(x,model.SV[i],model.param);
			sum -= model.rho[0];
			if(model.param.svm_type == svm_parameter.ONE_CLASS)
				return (sum>0)?1:-1;
			else
				return sum;
		}
		else
		{
			int i;
			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++];
					if(sum > 0)
						++vote[i];
					else
						++vote[j];
				}

			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];
		}
	}
	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",
	};

	public static void svm_save_model(String model_file_name, svm_model model) throws IOException
	{
		DataOutputStream fp = new DataOutputStream(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.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];
			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);
	}

	public static svm_model svm_load_model(String model_file_name) throws IOException
	{
		BufferedReader fp = new BufferedReader(new FileReader(model_file_name));

		// read parameters

		svm_model model = new svm_model();
		svm_parameter param = new svm_parameter();
		model.param = param;
		model.label = null;
		model.nSV = null;

		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");
					System.exit(1);
				}
			}
			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");
					System.exit(1);
				}
			}
			else if(cmd.startsWith("degree"))
				param.degree = atof(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("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\n");
				System.exit(1);
			}
		}

		// 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;
	}
}