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+/* The MIT License

+

+   Copyright (c) 2003-2006, 2008-2010, by Heng Li <[email protected]>

+

+   Permission is hereby granted, free of charge, to any person obtaining

+   a copy of this software and associated documentation files (the

+   "Software"), to deal in the Software without restriction, including

+   without limitation the rights to use, copy, modify, merge, publish,

+   distribute, sublicense, and/or sell copies of the Software, and to

+   permit persons to whom the Software is furnished to do so, subject to

+   the following conditions:

+

+   The above copyright notice and this permission notice shall be

+   included in all copies or substantial portions of the Software.

+

+   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

+   EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

+   MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND

+   NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS

+   BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN

+   ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN

+   CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

+   SOFTWARE.

+*/

+

+#include <stdlib.h>

+#include <stdio.h>

+#include <string.h>

+#include <stdint.h>

+#include <math.h>

+#include "kprobaln.h"

+

+/*****************************************

+ * Probabilistic banded glocal alignment *

+ *****************************************/

+

+#define EI .25

+#define EM .33333333333

+

+static float g_qual2prob[256];

+

+#define set_u(u, b, i, k) { int x=(i)-(b); x=x>0?x:0; (u)=((k)-x+1)*3; }

+

+kpa_par_t kpa_par_def = { 0.001, 0.1, 10 };

+kpa_par_t kpa_par_alt = { 0.0001, 0.01, 10 };

+

+/*

+  The topology of the profile HMM:

+

+           /\             /\        /\             /\

+           I[1]           I[k-1]    I[k]           I[L]

+            ^   \      \    ^    \   ^   \      \   ^

+            |    \      \   |     \  |    \      \  |

+    M[0]   M[1] -> ... -> M[k-1] -> M[k] -> ... -> M[L]   M[L+1]

+                \      \/        \/      \/      /

+                 \     /\        /\      /\     /

+                       -> D[k-1] -> D[k] ->

+

+   M[0] points to every {M,I}[k] and every {M,I}[k] points M[L+1].

+

+   On input, _ref is the reference sequence and _query is the query

+   sequence. Both are sequences of 0/1/2/3/4 where 4 stands for an

+   ambiguous residue. iqual is the base quality. c sets the gap open

+   probability, gap extension probability and band width.

+

+   On output, state and q are arrays of length l_query. The higher 30

+   bits give the reference position the query base is matched to and the

+   lower two bits can be 0 (an alignment match) or 1 (an

+   insertion). q[i] gives the phred scaled posterior probability of

+   state[i] being wrong.

+ */

+int kpa_glocal(const uint8_t *_ref, int l_ref, const uint8_t *_query, int l_query, const uint8_t *iqual,

+			   const kpa_par_t *c, int *state, uint8_t *q)

+{

+	double **f, **b = 0, *s, m[9], sI, sM, bI, bM, pb;

+	float *qual, *_qual;

+	const uint8_t *ref, *query;

+	int bw, bw2, i, k, is_diff = 0, is_backward = 1, Pr;

+

+    if ( l_ref<=0 || l_query<=0 ) return 0; // FIXME: this may not be an ideal fix, just prevents sefgault

+

+	/*** initialization ***/

+	is_backward = state && q? 1 : 0;

+	ref = _ref - 1; query = _query - 1; // change to 1-based coordinate

+	bw = l_ref > l_query? l_ref : l_query;

+	if (bw > c->bw) bw = c->bw;

+	if (bw < abs(l_ref - l_query)) bw = abs(l_ref - l_query);

+	bw2 = bw * 2 + 1;

+	// allocate the forward and backward matrices f[][] and b[][] and the scaling array s[]

+	f = calloc(l_query+1, sizeof(void*));

+	if (is_backward) b = calloc(l_query+1, sizeof(void*));

+	for (i = 0; i <= l_query; ++i) {    // FIXME: this will lead in segfault for l_query==0

+		f[i] = calloc(bw2 * 3 + 6, sizeof(double)); // FIXME: this is over-allocated for very short seqs

+		if (is_backward) b[i] = calloc(bw2 * 3 + 6, sizeof(double));

+	}

+	s = calloc(l_query+2, sizeof(double)); // s[] is the scaling factor to avoid underflow

+	// initialize qual

+	_qual = calloc(l_query, sizeof(float));

+	if (g_qual2prob[0] == 0)

+		for (i = 0; i < 256; ++i)

+			g_qual2prob[i] = pow(10, -i/10.);

+	for (i = 0; i < l_query; ++i) _qual[i] = g_qual2prob[iqual? iqual[i] : 30];

+	qual = _qual - 1;

+	// initialize transition probability

+	sM = sI = 1. / (2 * l_query + 2); // the value here seems not to affect results; FIXME: need proof

+	m[0*3+0] = (1 - c->d - c->d) * (1 - sM); m[0*3+1] = m[0*3+2] = c->d * (1 - sM);

+	m[1*3+0] = (1 - c->e) * (1 - sI); m[1*3+1] = c->e * (1 - sI); m[1*3+2] = 0.;

+	m[2*3+0] = 1 - c->e; m[2*3+1] = 0.; m[2*3+2] = c->e;

+	bM = (1 - c->d) / l_ref; bI = c->d / l_ref; // (bM+bI)*l_ref==1

+	/*** forward ***/

+	// f[0]

+	set_u(k, bw, 0, 0);

+	f[0][k] = s[0] = 1.;

+	{ // f[1]

+		double *fi = f[1], 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] * EM;

+			set_u(u, bw, 1, k);

+			fi[u+0] = e * bM; fi[u+1] = EI * bI;

+			sum += fi[u] + fi[u+1];

+		}

+		// rescale

+		s[1] = sum;

+		set_u(_beg, bw, 1, beg); set_u(_end, 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], sum, qli = qual[i];

+		int beg = 1, end = l_ref, x, _beg, _end;

+		uint8_t 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 * EM;

+			set_u(u, bw, i, k); set_u(v11, bw, i-1, k-1); set_u(v10, bw, i-1, k); set_u(v01, 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] = EI * (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];

+//			fprintf(stderr, "F (%d,%d;%d): %lg,%lg,%lg\n", i, k, u, fi[u], fi[u+1], fi[u+2]); // DEBUG

+		}

+		// rescale

+		s[i] = sum;

+		set_u(_beg, bw, i, beg); set_u(_end, 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(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

+	}

+	{ // compute likelihood

+		double p = 1., Pr1 = 0.;

+		for (i = 0; i <= l_query + 1; ++i) {

+			p *= s[i];

+			if (p < 1e-100) Pr1 += -4.343 * log(p), p = 1.;

+		}

+		Pr1 += -4.343 * log(p * l_ref * l_query);

+		Pr = (int)(Pr1 + .499);

+		if (!is_backward) { // skip backward and MAP

+			for (i = 0; i <= l_query; ++i) free(f[i]);

+			free(f); free(s); free(_qual);

+			return Pr;

+		}

+	}

+	/*** 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;

+		double *bi = b[l_query];

+		set_u(u, bw, l_query, k);

+		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], y = (i > 1), qli1 = qual[i+1];

+		uint8_t 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;

+			set_u(u, bw, i, k); set_u(v11, bw, i+1, k+1); set_u(v10, bw, i+1, k); set_u(v01, bw, i, k+1);

+			e = (k >= l_ref? 0 : (ref[k+1] > 3 || qyi1 > 3)? 1. : ref[k+1] == qyi1? 1. - qli1 : qli1 * EM) * bi1[v11];

+			bi[u+0] = e * m[0] + EI * m[1] * bi1[v10+1] + m[2] * bi[v01+2]; // bi1[v11] has been foled into e.

+			bi[u+1] = e * m[3] + EI * m[4] * bi1[v10+1];

+			bi[u+2] = (e * m[6] + m[8] * bi[v01+2]) * y;

+//			fprintf(stderr, "B (%d,%d;%d): %lg,%lg,%lg\n", i, k, u, bi[u], bi[u+1], bi[u+2]); // DEBUG

+		}

+		// rescale

+		set_u(_beg, bw, i, beg); set_u(_end, bw, i, end); _end += 2;

+		for (k = _beg, y = 1./s[i]; k <= _end; ++k) bi[k] *= y;

+	}

+	{ // 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;

+			double e = (ref[k] > 3 || query[1] > 3)? 1. : ref[k] == query[1]? 1. - qual[1] : qual[1] * EM;

+			set_u(u, bw, 1, k);

+			if (u < 3 || u >= bw2*3+3) continue;

+		    sum += e * b[1][u+0] * bM + EI * b[1][u+1] * bI;

+		}

+		set_u(k, bw, 0, 0);

+		pb = b[0][k] = sum / s[0]; // if everything works as is expected, pb == 1.0

+	}

+	is_diff = fabs(pb - 1.) > 1e-7? 1 : 0;

+	/*** MAP ***/

+	for (i = 1; i <= l_query; ++i) {

+		double sum = 0., *fi = f[i], *bi = b[i], max = 0.;

+		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;

+			double z;

+			set_u(u, bw, i, k);

+			z = fi[u+0] * bi[u+0]; if (z > max) max = z, max_k = (k-1)<<2 | 0; sum += z;

+			z = fi[u+1] * bi[u+1]; if (z > max) max = z, max_k = (k-1)<<2 | 1; sum += z;

+		}

+		max /= sum; sum *= s[i]; // if everything works as is expected, sum == 1.0

+		if (state) state[i-1] = max_k;

+		if (q) k = (int)(-4.343 * log(1. - max) + .499), q[i-1] = k > 100? 99 : k;

+#ifdef _MAIN

+		fprintf(stderr, "(%.10lg,%.10lg) (%d,%d:%c,%c:%d) %lg\n", pb, sum, i-1, max_k>>2,

+				"ACGT"[query[i]], "ACGT"[ref[(max_k>>2)+1]], max_k&3, max); // DEBUG

+#endif

+	}

+	/*** free ***/

+	for (i = 0; i <= l_query; ++i) {

+		free(f[i]); free(b[i]);

+	}

+	free(f); free(b); free(s); free(_qual);

+	return Pr;

+}

+

+#ifdef _MAIN

+#include <unistd.h>

+int main(int argc, char *argv[])

+{

+	uint8_t conv[256], *iqual, *ref, *query;

+	int c, l_ref, l_query, i, q = 30, b = 10, P;

+	while ((c = getopt(argc, argv, "b:q:")) >= 0) {

+		switch (c) {

+		case 'b': b = atoi(optarg); break;

+		case 'q': q = atoi(optarg); break;

+		}

+	}

+	if (optind + 2 > argc) {

+		fprintf(stderr, "Usage: %s [-q %d] [-b %d] <ref> <query>\n", argv[0], q, b); // example: acttc attc

+		return 1;

+	}

+	memset(conv, 4, 256);

+	conv['a'] = conv['A'] = 0; conv['c'] = conv['C'] = 1;

+	conv['g'] = conv['G'] = 2; conv['t'] = conv['T'] = 3;

+	ref = (uint8_t*)argv[optind]; query = (uint8_t*)argv[optind+1];

+	l_ref = strlen((char*)ref); l_query = strlen((char*)query);

+	for (i = 0; i < l_ref; ++i) ref[i] = conv[ref[i]];

+	for (i = 0; i < l_query; ++i) query[i] = conv[query[i]];

+	iqual = malloc(l_query);

+	memset(iqual, q, l_query);

+	kpa_par_def.bw = b;

+	P = kpa_glocal(ref, l_ref, query, l_query, iqual, &kpa_par_alt, 0, 0);

+	fprintf(stderr, "%d\n", P);

+	free(iqual);

+	return 0;

+}

+#endif