content: import java.io.*;
  import java.lang.*;
  
  public class HmmGlocal
  {
  	private double[] qual2prob;
  	private double cd, ce; // gap open probility [1e-3], gap extension probability [0.1]
  	private int cb; // band width [7]
  
  	public HmmGlocal(final double d, final double e, final int b) {
  		cd = d; ce = e; cb = b;
  		qual2prob = new double[256];
  		for (int i = 0; i < 256; ++i)
  			qual2prob[i] = Math.pow(10, -i/10.);
  	}
  	private static int set_u(final int b, final int i, final int k) {
  		int x = i - b;
  		x = x > 0? x : 0;
  		return (k + 1 - x) * 3;
  	}
  	public int hmm_glocal(final byte[] _ref, final byte[] _query, final byte[] _iqual, int[] state, byte[] q) {
  		int i, k;
  		/*** initialization ***/
  		// change coordinates
  		int l_ref = _ref.length;
  		byte[] ref = new byte[l_ref+1];
  		for (i = 0; i < l_ref; ++i) ref[i+1] = _ref[i]; // FIXME: this is silly...
  		int l_query = _query.length;
  		byte[] query = new byte[l_query+1];
  		double[] qual = new double[l_query+1];
  		for (i = 0; i < l_query; ++i) {
  			query[i+1] = _query[i];
  			qual[i+1] = qual2prob[_iqual[i]];
  		}
  		// set band width
  		int bw2, bw = l_ref > l_query? l_ref : l_query;
  		if (bw > cb) bw = cb;
  		if (bw < Math.abs(l_ref - l_query)) bw = Math.abs(l_ref - l_query);
  		bw2 = bw * 2 + 1;
  		// allocate the forward and backward matrices f[][] and b[][] and the scaling array s[]
  		double[][] f = new double[l_query+1][bw2*3 + 6];
  		double[][] b = new double[l_query+1][bw2*3 + 6];
  		double[] s = new double[l_query+2];
  		// initialize transition probabilities
  		double sM, sI, bM, bI;
  		sM = sI = 1. / (2 * l_query + 2);
  		bM = (1 - cd) / l_query; bI = cd / l_query; // (bM+bI)*l_query==1
  		double[] m = new double[9];
  		m[0*3+0] = (1 - cd - cd) * (1 - sM); m[0*3+1] = m[0*3+2] = cd * (1 - sM);
  		m[1*3+0] = (1 - ce) * (1 - sI); m[1*3+1] = ce * (1 - sI); m[1*3+2] = 0.;
  		m[2*3+0] = 1 - ce; m[2*3+1] = 0.; m[2*3+2] = ce;
  		/*** forward ***/
  		// f[0]
  		f[0][set_u(bw, 0, 0)] = s[0] = 1.;
  		{ // f[1]
  			double[] fi = f[1];
  			double sum;
  			int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1, _beg, _end;
  			for (k = beg, sum = 0.; k <= end; ++k) {
  				int u;
  				double e = (ref[k] > 3 || query[1] > 3)? 1. : ref[k] == query[1]? 1. - qual[1] : qual[1] / 3.;
  				u = set_u(bw, 1, k);
  				fi[u+0] = e * bM; fi[u+1] = .25 * bI;
  				sum += fi[u] + fi[u+1];
  			}
  			// rescale
  			s[1] = sum;
  			_beg = set_u(bw, 1, beg); _end = set_u(bw, 1, end); _end += 2;
  			for (k = _beg; k <= _end; ++k) fi[k] /= sum;
  		}
  		// f[2..l_query]
  		for (i = 2; i <= l_query; ++i) {
  			double[] fi = f[i], fi1 = f[i-1];
  			double sum, qli = qual[i];
  			int beg = 1, end = l_ref, x, _beg, _end;
  			byte qyi = query[i];
  			x = i - bw; beg = beg > x? beg : x; // band start
  			x = i + bw; end = end < x? end : x; // band end
  			for (k = beg, sum = 0.; k <= end; ++k) {
  				int u, v11, v01, v10;
  				double e;
  				e = (ref[k] > 3 || qyi > 3)? 1. : ref[k] == qyi? 1. - qli : qli / 3.;
  				u = set_u(bw, i, k); v11 = set_u(bw, i-1, k-1); v10 = set_u(bw, i-1, k); v01 = set_u(bw, i, k-1);
  				fi[u+0] = e * (m[0] * fi1[v11+0] + m[3] * fi1[v11+1] + m[6] * fi1[v11+2]);
  				fi[u+1] = .25 * (m[1] * fi1[v10+0] + m[4] * fi1[v10+1]);
  				fi[u+2] = m[2] * fi[v01+0] + m[8] * fi[v01+2];
  				sum += fi[u] + fi[u+1] + fi[u+2];
  				//System.out.println("("+i+","+k+";"+u+"): "+fi[u]+","+fi[u+1]+","+fi[u+2]);
  			}
  			// rescale
  			s[i] = sum;
  			_beg = set_u(bw, i, beg); _end = set_u(bw, i, end); _end += 2;
  			for (k = _beg, sum = 1./sum; k <= _end; ++k) fi[k] *= sum;
  		}
  		{ // f[l_query+1]
  			double sum;
  			for (k = 1, sum = 0.; k <= l_ref; ++k) {
  				int u = set_u(bw, l_query, k);
  				if (u < 3 || u >= bw2*3+3) continue;
  				sum += f[l_query][u+0] * sM + f[l_query][u+1] * sI;
  			}
  			s[l_query+1] = sum; // the last scaling factor
  		}
  		/*** backward ***/
  		// b[l_query] (b[l_query+1][0]=1 and thus \tilde{b}[][]=1/s[l_query+1]; this is where s[l_query+1] comes from)
  		for (k = 1; k <= l_ref; ++k) {
  			int u = set_u(bw, l_query, k);
  			double[] bi = b[l_query];
  			if (u < 3 || u >= bw2*3+3) continue;
  			bi[u+0] = sM / s[l_query] / s[l_query+1]; bi[u+1] = sI / s[l_query] / s[l_query+1];
  		}
  		// b[l_query-1..1]
  		for (i = l_query - 1; i >= 1; --i) {
  			int beg = 1, end = l_ref, x, _beg, _end;
  			double[] bi = b[i], bi1 = b[i+1];
  			double y = (i > 1)? 1. : 0., qli1 = qual[i+1];
  			byte qyi1 = query[i+1];
  			x = i - bw; beg = beg > x? beg : x;
  			x = i + bw; end = end < x? end : x;
  			for (k = end; k >= beg; --k) {
  				int u, v11, v01, v10;
  				double e;
  				u = set_u(bw, i, k); v11 = set_u(bw, i+1, k+1); v10 = set_u(bw, i+1, k); v01 = set_u(bw, i, k+1);
  				e = (k >= l_ref? 0 : (ref[k+1] > 3 || qyi1 > 3)? 1. : ref[k+1] == qyi1? 1. - qli1 : qli1 / 3.) * bi1[v11];
  				bi[u+0] = e * m[0] + .25 * m[1] * bi1[v10+1] + m[2] * bi[v01+2]; // bi1[v11] has been foled into e.
  				bi[u+1] = e * m[3] + .25 * m[4] * bi1[v10+1];
  				bi[u+2] = (e * m[6] + m[8] * bi[v01+2]) * y;
  			}
  			// rescale
  			_beg = set_u(bw, i, beg); _end = set_u(bw, i, end); _end += 2;
  			for (k = _beg, y = 1./s[i]; k <= _end; ++k) bi[k] *= y;
  		}
  		double pb;
  		{ // b[0]
  			int beg = 1, end = l_ref < bw + 1? l_ref : bw + 1;
  			double sum = 0.;
  			for (k = end; k >= beg; --k) {
  				int u = set_u(bw, 1, k);
  				double e = (ref[k] > 3 || query[1] > 3)? 1. : ref[k] == query[1]? 1. - qual[1] : qual[1] / 3.;
  				if (u < 3 || u >= bw2*3+3) continue;
  				sum += e * b[1][u+0] * bM + .25 * b[1][u+1] * bI;
  			}
  			pb = b[0][set_u(bw, 0, 0)] = sum / s[0]; // if everything works as is expected, pb == 1.0
  		}
  		int is_diff = Math.abs(pb - 1.) > 1e-7? 1 : 0;
  		/*** MAP ***/
  		for (i = 1; i <= l_query; ++i) {
  			double sum = 0., max = 0.;
  			double[] fi = f[i], bi = b[i];
  			int beg = 1, end = l_ref, x, max_k = -1;
  			x = i - bw; beg = beg > x? beg : x;
  			x = i + bw; end = end < x? end : x;
  			for (k = beg; k <= end; ++k) {
  				int u = set_u(bw, i, k);
  				double z;
  				sum += (z = fi[u+0] * bi[u+0]); if (z > max) { max = z; max_k = (k-1)<<2 | 0; }
  				sum += (z = fi[u+1] * bi[u+1]); if (z > max) { max = z; max_k = (k-1)<<2 | 1; }
  			}
  			max /= sum; sum *= s[i]; // if everything works as is expected, sum == 1.0
  			if (state != null) state[i-1] = max_k;
  			if (q != null) {
  				k = (int)(-4.343 * Math.log(1. - max) + .499);
  				q[i-1] = (byte)(k > 100? 99 : k);
  			}
  			//System.out.println("("+pb+","+sum+")"+" ("+(i-1)+","+(max_k>>2)+","+(max_k&3)+","+max+")");
  		}
  		return 0;
  	}
  
  	public static void main(String[] args) {
  		byte[] ref = {'\0', '\1', '\3', '\3', '\1'};
  		byte[] query = {'\0', '\3', '\3', '\1'};
  		byte[] qual = new byte[4];
  		qual[0] = qual[1] = qual[2] = qual[3] = (byte)20;
  		HmmGlocal hg = new HmmGlocal(1e-3, 0.1, 7);
  		hg.hmm_glocal(ref, query, qual, null, null);
  	}
  }