- double **f, **b, *s, m[9], sI, sM, bI, bM, pb;
- float *qual, *_qual;
- const uint8_t *ref, *query;
- int bw, bw2, i, k, is_diff = 0;
-
- /*** initialization ***/
- 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*));
- b = calloc(l_query+1, sizeof(void*));
- for (i = 0; i <= l_query; ++i) {
- f[i] = calloc(bw2 * 3 + 6, sizeof(double)); // FIXME: this is over-allocated for very short seqs
- 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_query; bI = c->d / l_query; // (bM+bI)*l_query==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] / 3.;
- set_u(u, bw, 1, k);
- fi[u+0] = e * bM; fi[u+1] = .25 * 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 / 3.;
- 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] = .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];
-// 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; 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