content: 
  
  
  
  
  package org.machinelearning.svm.libsvm;
  import java.io.*;
  import java.util.*;
  
  //
  // Kernel Cache
  //
  // l is the number of total data items
  // size is the cache size limit in bytes
  //
  class Cache {
  	private final int l;
  	private long size;
  	private final class head_t
  	{
  		head_t prev, next;	// a cicular list
  		float[] data;
  		int len;		// data[0,len) is cached in this entry
  	}
  	private final head_t[] head;
  	private head_t lru_head;
  
  	Cache(int l_, long size_)
  	{
  		l = l_;
  		size = size_;
  		head = new head_t[l];
  		for(int i=0;i<l;i++) head[i] = new head_t();
  		size /= 4;
  		size -= l * (16/4);	// sizeof(head_t) == 16
  		size = Math.max(size, 2* (long) l);  // cache must be large enough for two columns
  		lru_head = new head_t();
  		lru_head.next = lru_head.prev = lru_head;
  	}
  
  	private void lru_delete(head_t h)
  	{
  		// delete from current location
  		h.prev.next = h.next;
  		h.next.prev = h.prev;
  	}
  
  	private void lru_insert(head_t h)
  	{
  		// insert to last position
  		h.next = lru_head;
  		h.prev = lru_head.prev;
  		h.prev.next = h;
  		h.next.prev = h;
  	}
  
  	// request data [0,len)
  	// return some position p where [p,len) need to be filled
  	// (p >= len if nothing needs to be filled)
  	// java: simulate pointer using single-element array
  	int get_data(int index, float[][] data, int len)
  	{
  		head_t h = head[index];
  		if(h.len > 0) lru_delete(h);
  		int more = len - h.len;
  
  		if(more > 0)
  		{
  			// free old space
  			while(size < more)
  			{
  				head_t old = lru_head.next;
  				lru_delete(old);
  				size += old.len;
  				old.data = null;
  				old.len = 0;
  			}
  
  			// allocate new space
  			float[] new_data = new float[len];
  			if(h.data != null) System.arraycopy(h.data,0,new_data,0,h.len);
  			h.data = new_data;
  			size -= more;
  			do {int tmp=h.len; h.len=len; len=tmp;} while(false);
  		}
  
  		lru_insert(h);
  		data[0] = h.data;
  		return len;
  	}
  
  	void swap_index(int i, int j)
  	{
  		if(i==j) return;
  
  		if(head[i].len > 0) lru_delete(head[i]);
  		if(head[j].len > 0) lru_delete(head[j]);
  		do {float[] tmp=head[i].data; head[i].data=head[j].data; head[j].data=tmp;} while(false);
  		do {int tmp=head[i].len; head[i].len=head[j].len; head[j].len=tmp;} while(false);
  		if(head[i].len > 0) lru_insert(head[i]);
  		if(head[j].len > 0) lru_insert(head[j]);
  
  		if(i>j) do {int tmp=i; i=j; j=tmp;} while(false);
  		for(head_t h = lru_head.next; h!=lru_head; h=h.next)
  		{
  			if(h.len > i)
  			{
  				if(h.len > j)
  					do {float tmp=h.data[i]; h.data[i]=h.data[j]; h.data[j]=tmp;} while(false);
  				else
  				{
  					// give up
  					lru_delete(h);
  					size += h.len;
  					h.data = null;
  					h.len = 0;
  				}
  			}
  		}
  	}
  }
  
  //
  // Kernel evaluation
  //
  // the static method k_function is for doing single kernel evaluation
  // the constructor of Kernel prepares to calculate the l*l kernel matrix
  // the member function get_Q is for getting one column from the Q Matrix
  //
  abstract class QMatrix {
  	abstract float[] get_Q(int column, int len);
  	abstract double[] get_QD();
  	abstract void swap_index(int i, int j);
  };
  
  abstract class Kernel extends QMatrix {
  	private svm_node[][] x;
  	private final double[] x_square;
  
  	// svm_parameter
  	private final int kernel_type;
  	private final int degree;
  	private final double gamma;
  	private final double coef0;
  
  	abstract float[] get_Q(int column, int len);
  	abstract double[] get_QD();
  
  	void swap_index(int i, int j)
  	{
  		do {svm_node[] tmp=x[i]; x[i]=x[j]; x[j]=tmp;} while(false);
  		if(x_square != null) do {double tmp=x_square[i]; x_square[i]=x_square[j]; x_square[j]=tmp;} while(false);
  	}
  
  	private static double powi(double base, int times)
  	{
  		double tmp = base, ret = 1.0;
  
  		for(int t=times; t>0; t/=2)
  		{
  			if(t%2==1) ret*=tmp;
  			tmp = tmp * tmp;
  		}
  		return ret;
  	}
  
  	double kernel_function(int i, int j)
  	{
  		switch(kernel_type)
  		{
  			case svm_parameter.LINEAR:
  				return dot(x[i],x[j]);
  			case svm_parameter.POLY:
  				return powi(gamma*dot(x[i],x[j])+coef0,degree);
  			case svm_parameter.RBF:
  				return Math.exp(-gamma*(x_square[i]+x_square[j]-2*dot(x[i],x[j])));
  			case svm_parameter.SIGMOID:
  				return Math.tanh(gamma*dot(x[i],x[j])+coef0);
  			case svm_parameter.PRECOMPUTED:
  				return x[i][(int)(x[j][0].value)].value;
  			default:
  				return 0;	// java
  		}
  	}
  
  	Kernel(int l, svm_node[][] x_, svm_parameter param)
  	{
  		this.kernel_type = param.kernel_type;
  		this.degree = param.degree;
  		this.gamma = param.gamma;
  		this.coef0 = param.coef0;
  
  		x = (svm_node[][])x_.clone();
  
  		if(kernel_type == svm_parameter.RBF)
  		{
  			x_square = new double[l];
  			for(int i=0;i<l;i++)
  				x_square[i] = dot(x[i],x[i]);
  		}
  		else x_square = null;
  	}
  
  	static double dot(svm_node[] x, svm_node[] y)
  	{
  		double sum = 0;
  		int xlen = x.length;
  		int ylen = y.length;
  		int i = 0;
  		int j = 0;
  		while(i < xlen && j < ylen)
  		{
  			if(x[i].index == y[j].index)
  				sum += x[i++].value * y[j++].value;
  			else
  			{
  				if(x[i].index > y[j].index)
  					++j;
  				else
  					++i;
  			}
  		}
  		return sum;
  	}
  
  	static double k_function(svm_node[] x, svm_node[] y,
  					svm_parameter param)
  	{
  		switch(param.kernel_type)
  		{
  			case svm_parameter.LINEAR:
  				return dot(x,y);
  			case svm_parameter.POLY:
  				return powi(param.gamma*dot(x,y)+param.coef0,param.degree);
  			case svm_parameter.RBF:
  			{
  				double sum = 0;
  				int xlen = x.length;
  				int ylen = y.length;
  				int i = 0;
  				int j = 0;
  				while(i < xlen && j < ylen)
  				{
  					if(x[i].index == y[j].index)
  					{
  						double d = x[i++].value - y[j++].value;
  						sum += d*d;
  					}
  					else if(x[i].index > y[j].index)
  					{
  						sum += y[j].value * y[j].value;
  						++j;
  					}
  					else
  					{
  						sum += x[i].value * x[i].value;
  						++i;
  					}
  				}
  
  				while(i < xlen)
  				{
  					sum += x[i].value * x[i].value;
  					++i;
  				}
  
  				while(j < ylen)
  				{
  					sum += y[j].value * y[j].value;
  					++j;
  				}
  
  				return Math.exp(-param.gamma*sum);
  			}
  			case svm_parameter.SIGMOID:
  				return Math.tanh(param.gamma*dot(x,y)+param.coef0);
  			case svm_parameter.PRECOMPUTED:
  				return	x[(int)(y[0].value)].value;
  			default:
  				return 0;	// java
  		}
  	}
  }
  
  // An SMO algorithm in Fan et al., JMLR 6(2005), p. 1889--1918
  // Solves:
  //
  //	min 0.5(\alpha^T Q \alpha) + p^T \alpha
  //
  //		y^T \alpha = \delta
  //		y_i = +1 or -1
  //		0 <= alpha_i <= Cp for y_i = 1
  //		0 <= alpha_i <= Cn for y_i = -1
  //
  // Given:
  //
  //	Q, p, y, Cp, Cn, and an initial feasible point \alpha
  //	l is the size of vectors and matrices
  //	eps is the stopping tolerance
  //
  // solution will be put in \alpha, objective value will be put in obj
  //
  class Solver {
  	int active_size;
  	byte[] y;
  	double[] G;		// gradient of objective function
  	static final byte LOWER_BOUND = 0;
  	static final byte UPPER_BOUND = 1;
  	static final byte FREE = 2;
  	byte[] alpha_status;	// LOWER_BOUND, UPPER_BOUND, FREE
  	double[] alpha;
  	QMatrix Q;
  	double[] QD;
  	double eps;
  	double Cp,Cn;
  	double[] p;
  	int[] active_set;
  	double[] G_bar;		// gradient, if we treat free variables as 0
  	int l;
  	boolean unshrink;	// XXX
  
  	static final double INF = Double.POSITIVE_INFINITY;
  
  	double get_C(int i)
  	{
  		return (y[i] > 0)? Cp : Cn;
  	}
  	void update_alpha_status(int i)
  	{
  		if(alpha[i] >= get_C(i))
  			alpha_status[i] = UPPER_BOUND;
  		else if(alpha[i] <= 0)
  			alpha_status[i] = LOWER_BOUND;
  		else alpha_status[i] = FREE;
  	}
  	boolean is_upper_bound(int i) { return alpha_status[i] == UPPER_BOUND; }
  	boolean is_lower_bound(int i) { return alpha_status[i] == LOWER_BOUND; }
  	boolean is_free(int i) {  return alpha_status[i] == FREE; }
  
  	// java: information about solution except alpha,
  	// because we cannot return multiple values otherwise...
  	static class SolutionInfo {
  		double obj;
  		double rho;
  		double upper_bound_p;
  		double upper_bound_n;
  		double r;	// for Solver_NU
  	}
  
  	void swap_index(int i, int j)
  	{
  		Q.swap_index(i,j);
  		do {byte tmp=y[i]; y[i]=y[j]; y[j]=tmp;} while(false);
  		do {double tmp=G[i]; G[i]=G[j]; G[j]=tmp;} while(false);
  		do {byte tmp=alpha_status[i]; alpha_status[i]=alpha_status[j]; alpha_status[j]=tmp;} while(false);
  		do {double tmp=alpha[i]; alpha[i]=alpha[j]; alpha[j]=tmp;} while(false);
  		do {double tmp=p[i]; p[i]=p[j]; p[j]=tmp;} while(false);
  		do {int tmp=active_set[i]; active_set[i]=active_set[j]; active_set[j]=tmp;} while(false);
  		do {double tmp=G_bar[i]; G_bar[i]=G_bar[j]; G_bar[j]=tmp;} while(false);
  	}
  
  	void reconstruct_gradient()
  	{
  		// reconstruct inactive elements of G from G_bar and free variables
  
  		if(active_size == l) return;
  
  		int i,j;
  		int nr_free = 0;
  
  		for(j=active_size;j<l;j++)
  			G[j] = G_bar[j] + p[j];
  
  		for(j=0;j<active_size;j++)
  			if(is_free(j))
  				nr_free++;
  
  		if(2*nr_free < active_size)
  			svm.info("\nWARNING: using -h 0 may be faster\n");
  
  		if (nr_free*l > 2*active_size*(l-active_size))
  		{
  			for(i=active_size;i<l;i++)
  			{
  				float[] Q_i = Q.get_Q(i,active_size);
  				for(j=0;j<active_size;j++)
  					if(is_free(j))
  						G[i] += alpha[j] * Q_i[j];
  			}
  		}
  		else
  		{
  			for(i=0;i<active_size;i++)
  				if(is_free(i))
  				{
  					float[] Q_i = Q.get_Q(i,l);
  					double alpha_i = alpha[i];
  					for(j=active_size;j<l;j++)
  						G[j] += alpha_i * Q_i[j];
  				}
  		}
  	}
  
  	void Solve(int l, QMatrix Q, double[] p_, byte[] y_,
  		   double[] alpha_, double Cp, double Cn, double eps, SolutionInfo si, int shrinking)
  	{
  		this.l = l;
  		this.Q = Q;
  		QD = Q.get_QD();
  		p = (double[])p_.clone();
  		y = (byte[])y_.clone();
  		alpha = (double[])alpha_.clone();
  		this.Cp = Cp;
  		this.Cn = Cn;
  		this.eps = eps;
  		this.unshrink = false;
  
  		// initialize alpha_status
  		{
  			alpha_status = new byte[l];
  			for(int i=0;i<l;i++)
  				update_alpha_status(i);
  		}
  
  		// initialize active set (for shrinking)
  		{
  			active_set = new int[l];
  			for(int i=0;i<l;i++)
  				active_set[i] = i;
  			active_size = l;
  		}
  
  		// initialize gradient
  		{
  			G = new double[l];
  			G_bar = new double[l];
  			int i;
  			for(i=0;i<l;i++)
  			{
  				G[i] = p[i];
  				G_bar[i] = 0;
  			}
  			for(i=0;i<l;i++)
  				if(!is_lower_bound(i))
  				{
  					float[] Q_i = Q.get_Q(i,l);
  					double alpha_i = alpha[i];
  					int j;
  					for(j=0;j<l;j++)
  						G[j] += alpha_i*Q_i[j];
  					if(is_upper_bound(i))
  						for(j=0;j<l;j++)
  							G_bar[j] += get_C(i) * Q_i[j];
  				}
  		}
  
  		// optimization step
  
  		int iter = 0;
  		int max_iter = Math.max(10000000, l>Integer.MAX_VALUE/100 ? Integer.MAX_VALUE : 100*l);
  		int counter = Math.min(l,1000)+1;
  		int[] working_set = new int[2];
  
  		while(iter < max_iter)
  		{
  			// show progress and do shrinking
  
  			if(--counter == 0)
  			{
  				counter = Math.min(l,1000);
  				if(shrinking!=0) do_shrinking();
  				svm.info(".");
  			}
  
  			if(select_working_set(working_set)!=0)
  			{
  				// reconstruct the whole gradient
  				reconstruct_gradient();
  				// reset active set size and check
  				active_size = l;
  				svm.info("*");
  				if(select_working_set(working_set)!=0)
  					break;
  				else
  					counter = 1;	// do shrinking next iteration
  			}
  
  			int i = working_set[0];
  			int j = working_set[1];
  
  			++iter;
  
  			// update alpha[i] and alpha[j], handle bounds carefully
  
  			float[] Q_i = Q.get_Q(i,active_size);
  			float[] Q_j = Q.get_Q(j,active_size);
  
  			double C_i = get_C(i);
  			double C_j = get_C(j);
  
  			double old_alpha_i = alpha[i];
  			double old_alpha_j = alpha[j];
  
  			if(y[i]!=y[j])
  			{
  				double quad_coef = QD[i]+QD[j]+2*Q_i[j];
  				if (quad_coef <= 0)
  					quad_coef = 1e-12;
  				double delta = (-G[i]-G[j])/quad_coef;
  				double diff = alpha[i] - alpha[j];
  				alpha[i] += delta;
  				alpha[j] += delta;
  
  				if(diff > 0)
  				{
  					if(alpha[j] < 0)
  					{
  						alpha[j] = 0;
  						alpha[i] = diff;
  					}
  				}
  				else
  				{
  					if(alpha[i] < 0)
  					{
  						alpha[i] = 0;
  						alpha[j] = -diff;
  					}
  				}
  				if(diff > C_i - C_j)
  				{
  					if(alpha[i] > C_i)
  					{
  						alpha[i] = C_i;
  						alpha[j] = C_i - diff;
  					}
  				}
  				else
  				{
  					if(alpha[j] > C_j)
  					{
  						alpha[j] = C_j;
  						alpha[i] = C_j + diff;
  					}
  				}
  			}
  			else
  			{
  				double quad_coef = QD[i]+QD[j]-2*Q_i[j];
  				if (quad_coef <= 0)
  					quad_coef = 1e-12;
  				double delta = (G[i]-G[j])/quad_coef;
  				double sum = alpha[i] + alpha[j];
  				alpha[i] -= delta;
  				alpha[j] += delta;
  
  				if(sum > C_i)
  				{
  					if(alpha[i] > C_i)
  					{
  						alpha[i] = C_i;
  						alpha[j] = sum - C_i;
  					}
  				}
  				else
  				{
  					if(alpha[j] < 0)
  					{
  						alpha[j] = 0;
  						alpha[i] = sum;
  					}
  				}
  				if(sum > C_j)
  				{
  					if(alpha[j] > C_j)
  					{
  						alpha[j] = C_j;
  						alpha[i] = sum - C_j;
  					}
  				}
  				else
  				{
  					if(alpha[i] < 0)
  					{
  						alpha[i] = 0;
  						alpha[j] = sum;
  					}
  				}
  			}
  
  			// update G
  
  			double delta_alpha_i = alpha[i] - old_alpha_i;
  			double delta_alpha_j = alpha[j] - old_alpha_j;
  
  			for(int k=0;k<active_size;k++)
  			{
  				G[k] += Q_i[k]*delta_alpha_i + Q_j[k]*delta_alpha_j;
  			}
  
  			// update alpha_status and G_bar
  
  			{
  				boolean ui = is_upper_bound(i);
  				boolean uj = is_upper_bound(j);
  				update_alpha_status(i);
  				update_alpha_status(j);
  				int k;
  				if(ui != is_upper_bound(i))
  				{
  					Q_i = Q.get_Q(i,l);
  					if(ui)
  						for(k=0;k<l;k++)
  							G_bar[k] -= C_i * Q_i[k];
  					else
  						for(k=0;k<l;k++)
  							G_bar[k] += C_i * Q_i[k];
  				}
  
  				if(uj != is_upper_bound(j))
  				{
  					Q_j = Q.get_Q(j,l);
  					if(uj)
  						for(k=0;k<l;k++)
  							G_bar[k] -= C_j * Q_j[k];
  					else
  						for(k=0;k<l;k++)
  							G_bar[k] += C_j * Q_j[k];
  				}
  			}
  
  		}
  
  		if(iter >= max_iter)
  		{
  			if(active_size < l)
  			{
  				// reconstruct the whole gradient to calculate objective value
  				reconstruct_gradient();
  				active_size = l;
  				svm.info("*");
  			}
  			System.err.print("\nWARNING: reaching max number of iterations\n");
  			throw new RuntimeException("WARNING: reaching max number of iterations");
  		}
  
  		// calculate rho
  
  		si.rho = calculate_rho();
  
  		// calculate objective value
  		{
  			double v = 0;
  			int i;
  			for(i=0;i<l;i++)
  				v += alpha[i] * (G[i] + p[i]);
  
  			si.obj = v/2;
  		}
  
  		// put back the solution
  		{
  			for(int i=0;i<l;i++)
  				alpha_[active_set[i]] = alpha[i];
  		}
  
  		si.upper_bound_p = Cp;
  		si.upper_bound_n = Cn;
  
  		svm.info("\noptimization finished, #iter = "+iter+"\n");
  	}
  
  	// return 1 if already optimal, return 0 otherwise
  	int select_working_set(int[] working_set)
  	{
  		// return i,j such that
  		// i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
  		// j: mimimizes the decrease of obj value
  		//    (if quadratic coefficeint <= 0, replace it with tau)
  		//    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
  
  		double Gmax = -INF;
  		double Gmax2 = -INF;
  		int Gmax_idx = -1;
  		int Gmin_idx = -1;
  		double obj_diff_min = INF;
  
  		for(int t=0;t<active_size;t++)
  			if(y[t]==+1)
  			{
  				if(!is_upper_bound(t))
  					if(-G[t] >= Gmax)
  					{
  						Gmax = -G[t];
  						Gmax_idx = t;
  					}
  			}
  			else
  			{
  				if(!is_lower_bound(t))
  					if(G[t] >= Gmax)
  					{
  						Gmax = G[t];
  						Gmax_idx = t;
  					}
  			}
  
  		int i = Gmax_idx;
  		float[] Q_i = null;
  		if(i != -1) // null Q_i not accessed: Gmax=-INF if i=-1
  			Q_i = Q.get_Q(i,active_size);
  
  		for(int j=0;j<active_size;j++)
  		{
  			if(y[j]==+1)
  			{
  				if (!is_lower_bound(j))
  				{
  					double grad_diff=Gmax+G[j];
  					if (G[j] >= Gmax2)
  						Gmax2 = G[j];
  					if (grad_diff > 0)
  					{
  						double obj_diff;
  						double quad_coef = QD[i]+QD[j]-2.0*y[i]*Q_i[j];
  						if (quad_coef > 0)
  							obj_diff = -(grad_diff*grad_diff)/quad_coef;
  						else
  							obj_diff = -(grad_diff*grad_diff)/1e-12;
  
  						if (obj_diff <= obj_diff_min)
  						{
  							Gmin_idx=j;
  							obj_diff_min = obj_diff;
  						}
  					}
  				}
  			}
  			else
  			{
  				if (!is_upper_bound(j))
  				{
  					double grad_diff= Gmax-G[j];
  					if (-G[j] >= Gmax2)
  						Gmax2 = -G[j];
  					if (grad_diff > 0)
  					{
  						double obj_diff;
  						double quad_coef = QD[i]+QD[j]+2.0*y[i]*Q_i[j];
  						if (quad_coef > 0)
  							obj_diff = -(grad_diff*grad_diff)/quad_coef;
  						else
  							obj_diff = -(grad_diff*grad_diff)/1e-12;
  
  						if (obj_diff <= obj_diff_min)
  						{
  							Gmin_idx=j;
  							obj_diff_min = obj_diff;
  						}
  					}
  				}
  			}
  		}
  
  		if(Gmax+Gmax2 < eps || Gmin_idx == -1)
  			return 1;
  
  		working_set[0] = Gmax_idx;
  		working_set[1] = Gmin_idx;
  		return 0;
  	}
  
  	private boolean be_shrunk(int i, double Gmax1, double Gmax2)
  	{
  		if(is_upper_bound(i))
  		{
  			if(y[i]==+1)
  				return(-G[i] > Gmax1);
  			else
  				return(-G[i] > Gmax2);
  		}
  		else if(is_lower_bound(i))
  		{
  			if(y[i]==+1)
  				return(G[i] > Gmax2);
  			else
  				return(G[i] > Gmax1);
  		}
  		else
  			return(false);
  	}
  
  	void do_shrinking()
  	{
  		int i;
  		double Gmax1 = -INF;		// max { -y_i * grad(f)_i | i in I_up(\alpha) }
  		double Gmax2 = -INF;		// max { y_i * grad(f)_i | i in I_low(\alpha) }
  
  		// find maximal violating pair first
  		for(i=0;i<active_size;i++)
  		{
  			if(y[i]==+1)
  			{
  				if(!is_upper_bound(i))
  				{
  					if(-G[i] >= Gmax1)
  						Gmax1 = -G[i];
  				}
  				if(!is_lower_bound(i))
  				{
  					if(G[i] >= Gmax2)
  						Gmax2 = G[i];
  				}
  			}
  			else
  			{
  				if(!is_upper_bound(i))
  				{
  					if(-G[i] >= Gmax2)
  						Gmax2 = -G[i];
  				}
  				if(!is_lower_bound(i))
  				{
  					if(G[i] >= Gmax1)
  						Gmax1 = G[i];
  				}
  			}
  		}
  
  		if(unshrink == false && Gmax1 + Gmax2 <= eps*10)
  		{
  			unshrink = true;
  			reconstruct_gradient();
  			active_size = l;
  		}
  
  		for(i=0;i<active_size;i++)
  			if (be_shrunk(i, Gmax1, Gmax2))
  			{
  				active_size--;
  				while (active_size > i)
  				{
  					if (!be_shrunk(active_size, Gmax1, Gmax2))
  					{
  						swap_index(i,active_size);
  						break;
  					}
  					active_size--;
  				}
  			}
  	}
  
  	double calculate_rho()
  	{
  		double r;
  		int nr_free = 0;
  		double ub = INF, lb = -INF, sum_free = 0;
  		for(int i=0;i<active_size;i++)
  		{
  			double yG = y[i]*G[i];
  
  			if(is_lower_bound(i))
  			{
  				if(y[i] > 0)
  					ub = Math.min(ub,yG);
  				else
  					lb = Math.max(lb,yG);
  			}
  			else if(is_upper_bound(i))
  			{
  				if(y[i] < 0)
  					ub = Math.min(ub,yG);
  				else
  					lb = Math.max(lb,yG);
  			}
  			else
  			{
  				++nr_free;
  				sum_free += yG;
  			}
  		}
  
  		if(nr_free>0)
  			r = sum_free/nr_free;
  		else
  			r = (ub+lb)/2;
  
  		return r;
  	}
  
  }
  
  //
  // Solver for nu-svm classification and regression
  //
  // additional constraint: e^T \alpha = constant
  //
  final class Solver_NU extends Solver
  {
  	private SolutionInfo si;
  
  	void Solve(int l, QMatrix Q, double[] p, byte[] y,
  		   double[] alpha, double Cp, double Cn, double eps,
  		   SolutionInfo si, int shrinking)
  	{
  		this.si = si;
  		super.Solve(l,Q,p,y,alpha,Cp,Cn,eps,si,shrinking);
  	}
  
  	// return 1 if already optimal, return 0 otherwise
  	int select_working_set(int[] working_set)
  	{
  		// return i,j such that y_i = y_j and
  		// i: maximizes -y_i * grad(f)_i, i in I_up(\alpha)
  		// j: minimizes the decrease of obj value
  		//    (if quadratic coefficeint <= 0, replace it with tau)
  		//    -y_j*grad(f)_j < -y_i*grad(f)_i, j in I_low(\alpha)
  
  		double Gmaxp = -INF;
  		double Gmaxp2 = -INF;
  		int Gmaxp_idx = -1;
  
  		double Gmaxn = -INF;
  		double Gmaxn2 = -INF;
  		int Gmaxn_idx = -1;
  
  		int Gmin_idx = -1;
  		double obj_diff_min = INF;
  
  		for(int t=0;t<active_size;t++)
  			if(y[t]==+1)
  			{
  				if(!is_upper_bound(t))
  					if(-G[t] >= Gmaxp)
  					{
  						Gmaxp = -G[t];
  						Gmaxp_idx = t;
  					}
  			}
  			else
  			{
  				if(!is_lower_bound(t))
  					if(G[t] >= Gmaxn)
  					{
  						Gmaxn = G[t];
  						Gmaxn_idx = t;
  					}
  			}
  
  		int ip = Gmaxp_idx;
  		int in = Gmaxn_idx;
  		float[] Q_ip = null;
  		float[] Q_in = null;
  		if(ip != -1) // null Q_ip not accessed: Gmaxp=-INF if ip=-1
  			Q_ip = Q.get_Q(ip,active_size);
  		if(in != -1)
  			Q_in = Q.get_Q(in,active_size);
  
  		for(int j=0;j<active_size;j++)
  		{
  			if(y[j]==+1)
  			{
  				if (!is_lower_bound(j))
  				{
  					double grad_diff=Gmaxp+G[j];
  					if (G[j] >= Gmaxp2)
  						Gmaxp2 = G[j];
  					if (grad_diff > 0)
  					{
  						double obj_diff;
  						double quad_coef = QD[ip]+QD[j]-2*Q_ip[j];
  						if (quad_coef > 0)
  							obj_diff = -(grad_diff*grad_diff)/quad_coef;
  						else
  							obj_diff = -(grad_diff*grad_diff)/1e-12;
  
  						if (obj_diff <= obj_diff_min)
  						{
  							Gmin_idx=j;
  							obj_diff_min = obj_diff;
  						}
  					}
  				}
  			}
  			else
  			{
  				if (!is_upper_bound(j))
  				{
  					double grad_diff=Gmaxn-G[j];
  					if (-G[j] >= Gmaxn2)
  						Gmaxn2 = -G[j];
  					if (grad_diff > 0)
  					{
  						double obj_diff;
  						double quad_coef = QD[in]+QD[j]-2*Q_in[j];
  						if (quad_coef > 0)
  							obj_diff = -(grad_diff*grad_diff)/quad_coef;
  						else
  							obj_diff = -(grad_diff*grad_diff)/1e-12;
  
  						if (obj_diff <= obj_diff_min)
  						{
  							Gmin_idx=j;
  							obj_diff_min = obj_diff;
  						}
  					}
  				}
  			}
  		}
  
  		if(Math.max(Gmaxp+Gmaxp2,Gmaxn+Gmaxn2) < eps || Gmin_idx == -1)
  			return 1;
  
  		if(y[Gmin_idx] == +1)
  			working_set[0] = Gmaxp_idx;
  		else
  			working_set[0] = Gmaxn_idx;
  		working_set[1] = Gmin_idx;
  
  		return 0;
  	}
  
  	private boolean be_shrunk(int i, double Gmax1, double Gmax2, double Gmax3, double Gmax4)
  	{
  		if(is_upper_bound(i))
  		{
  			if(y[i]==+1)
  				return(-G[i] > Gmax1);
  			else
  				return(-G[i] > Gmax4);
  		}
  		else if(is_lower_bound(i))
  		{
  			if(y[i]==+1)
  				return(G[i] > Gmax2);
  			else
  				return(G[i] > Gmax3);
  		}
  		else
  			return(false);
  	}
  
  	void do_shrinking()
  	{
  		double Gmax1 = -INF;	// max { -y_i * grad(f)_i | y_i = +1, i in I_up(\alpha) }
  		double Gmax2 = -INF;	// max { y_i * grad(f)_i | y_i = +1, i in I_low(\alpha) }
  		double Gmax3 = -INF;	// max { -y_i * grad(f)_i | y_i = -1, i in I_up(\alpha) }
  		double Gmax4 = -INF;	// max { y_i * grad(f)_i | y_i = -1, i in I_low(\alpha) }
  
  		// find maximal violating pair first
  		int i;
  		for(i=0;i<active_size;i++)
  		{
  			if(!is_upper_bound(i))
  			{
  				if(y[i]==+1)
  				{
  					if(-G[i] > Gmax1) Gmax1 = -G[i];
  				}
  				else	if(-G[i] > Gmax4) Gmax4 = -G[i];
  			}
  			if(!is_lower_bound(i))
  			{
  				if(y[i]==+1)
  				{
  					if(G[i] > Gmax2) Gmax2 = G[i];
  				}
  				else	if(G[i] > Gmax3) Gmax3 = G[i];
  			}
  		}
  
  		if(unshrink == false && Math.max(Gmax1+Gmax2,Gmax3+Gmax4) <= eps*10)
  		{
  			unshrink = true;
  			reconstruct_gradient();
  			active_size = l;
  		}
  
  		for(i=0;i<active_size;i++)
  			if (be_shrunk(i, Gmax1, Gmax2, Gmax3, Gmax4))
  			{
  				active_size--;
  				while (active_size > i)
  				{
  					if (!be_shrunk(active_size, Gmax1, Gmax2, Gmax3, Gmax4))
  					{
  						swap_index(i,active_size);
  						break;
  					}
  					active_size--;
  				}
  			}
  	}
  
  	double calculate_rho()
  	{
  		int nr_free1 = 0,nr_free2 = 0;
  		double ub1 = INF, ub2 = INF;
  		double lb1 = -INF, lb2 = -INF;
  		double sum_free1 = 0, sum_free2 = 0;
  
  		for(int i=0;i<active_size;i++)
  		{
  			if(y[i]==+1)
  			{
  				if(is_lower_bound(i))
  					ub1 = Math.min(ub1,G[i]);
  				else if(is_upper_bound(i))
  					lb1 = Math.max(lb1,G[i]);
  				else
  				{
  					++nr_free1;
  					sum_free1 += G[i];
  				}
  			}
  			else
  			{
  				if(is_lower_bound(i))
  					ub2 = Math.min(ub2,G[i]);
  				else if(is_upper_bound(i))
  					lb2 = Math.max(lb2,G[i]);
  				else
  				{
  					++nr_free2;
  					sum_free2 += G[i];
  				}
  			}
  		}
  
  		double r1,r2;
  		if(nr_free1 > 0)
  			r1 = sum_free1/nr_free1;
  		else
  			r1 = (ub1+lb1)/2;
  
  		if(nr_free2 > 0)
  			r2 = sum_free2/nr_free2;
  		else
  			r2 = (ub2+lb2)/2;
  
  		si.r = (r1+r2)/2;
  		return (r1-r2)/2;
  	}
  }
  
  //
  // Q matrices for various formulations
  //
  class SVC_Q extends Kernel
  {
  	private final byte[] y;
  	private final Cache cache;
  	private final double[] QD;
  
  	SVC_Q(svm_problem prob, svm_parameter param, byte[] y_)
  	{
  		super(prob.l, prob.x, param);
  		y = (byte[])y_.clone();
  		cache = new Cache(prob.l,(long)(param.cache_size*(1<<20)));
  		QD = new double[prob.l];
  		for(int i=0;i<prob.l;i++)
  			QD[i] = kernel_function(i,i);
  	}
  
  	float[] get_Q(int i, int len)
  	{
  		float[][] data = new float[1][];
  		int start, j;
  		if((start = cache.get_data(i,data,len)) < len)
  		{
  			for(j=start;j<len;j++)
  				data[0][j] = (float)(y[i]*y[j]*kernel_function(i,j));
  		}
  		return data[0];
  	}
  
  	double[] get_QD()
  	{
  		return QD;
  	}
  
  	void swap_index(int i, int j)
  	{
  		cache.swap_index(i,j);
  		super.swap_index(i,j);
  		do {byte tmp=y[i]; y[i]=y[j]; y[j]=tmp;} while(false);
  		do {double tmp=QD[i]; QD[i]=QD[j]; QD[j]=tmp;} while(false);
  	}
  }
  
  class ONE_CLASS_Q extends Kernel
  {
  	private final Cache cache;
  	private final double[] QD;
  
  	ONE_CLASS_Q(svm_problem prob, svm_parameter param)
  	{
  		super(prob.l, prob.x, param);
  		cache = new Cache(prob.l,(long)(param.cache_size*(1<<20)));
  		QD = new double[prob.l];
  		for(int i=0;i<prob.l;i++)
  			QD[i] = kernel_function(i,i);
  	}
  
  	float[] get_Q(int i, int len)
  	{
  		float[][] data = new float[1][];
  		int start, j;
  		if((start = cache.get_data(i,data,len)) < len)
  		{
  			for(j=start;j<len;j++)
  				data[0][j] = (float)kernel_function(i,j);
  		}
  		return data[0];
  	}
  
  	double[] get_QD()
  	{
  		return QD;
  	}
  
  	void swap_index(int i, int j)
  	{
  		cache.swap_index(i,j);
  		super.swap_index(i,j);
  		do {double tmp=QD[i]; QD[i]=QD[j]; QD[j]=tmp;} while(false);
  	}
  }
  
  class SVR_Q extends Kernel
  {
  	private final int l;
  	private final Cache cache;
  	private final byte[] sign;
  	private final int[] index;
  	private int next_buffer;
  	private float[][] buffer;
  	private final double[] QD;
  
  	SVR_Q(svm_problem prob, svm_parameter param)
  	{
  		super(prob.l, prob.x, param);
  		l = prob.l;
  		cache = new Cache(l,(long)(param.cache_size*(1<<20)));
  		QD = new double[2*l];
  		sign = new byte[2*l];
  		index = new int[2*l];
  		for(int k=0;k<l;k++)
  		{
  			sign[k] = 1;
  			sign[k+l] = -1;
  			index[k] = k;
  			index[k+l] = k;
  			QD[k] = kernel_function(k,k);
  			QD[k+l] = QD[k];
  		}
  		buffer = new float[2][2*l];
  		next_buffer = 0;
  	}
  
  	void swap_index(int i, int j)
  	{
  		do {byte tmp=sign[i]; sign[i]=sign[j]; sign[j]=tmp;} while(false);
  		do {int tmp=index[i]; index[i]=index[j]; index[j]=tmp;} while(false);
  		do {double tmp=QD[i]; QD[i]=QD[j]; QD[j]=tmp;} while(false);
  	}
  
  	float[] get_Q(int i, int len)
  	{
  		float[][] data = new float[1][];
  		int j, real_i = index[i];
  		if(cache.get_data(real_i,data,l) < l)
  		{
  			for(j=0;j<l;j++)
  				data[0][j] = (float)kernel_function(real_i,j);
  		}
  
  		// reorder and copy
  		float buf[] = buffer[next_buffer];
  		next_buffer = 1 - next_buffer;
  		byte si = sign[i];
  		for(j=0;j<len;j++)
  			buf[j] = (float) si * sign[j] * data[0][index[j]];
  		return buf;
  	}
  
  	double[] get_QD()
  	{
  		return QD;
  	}
  }
  
  public class svm {
  	//
  	// construct and solve various formulations
  	//
  	public static final int LIBSVM_VERSION=323;
  	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 tmp=perm[i]; perm[i]=perm[j]; perm[j]=tmp;} 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 tmp=label[0]; label[0]=label[1]; label[1]=tmp;} while(false);
  			do {int tmp=count[0]; count[0]=count[1]; count[1]=tmp;} 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 tmp=index[start[c]+j]; index[start[c]+j]=index[start[c]+i]; index[start[c]+i]=tmp;} 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 tmp=perm[i]; perm[i]=perm[j]; perm[j]=tmp;} 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++;
  				}
  			if (nr_class == 2)
  			{
  				prob_estimates[0] = pairwise_prob[0][1];
  				prob_estimates[1] = pairwise_prob[1][0];
  			}
  			else
  				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;
  		// parameters for training only won't be assigned, but arrays are assigned as NULL for safety
  		param.nr_weight = 0;
  		param.weight_label = null;
  		param.weight = null;
  
  		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;
  	}
  }
  