// 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)			System.err.print("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+(int)(Math.random()*(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);		System.err.print("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;			}		}		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];			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			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];			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;			}			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;	}		// 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[] label = tmp_label[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+(int)(Math.random()*(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+(int)(Math.random()*(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++)