return cigar;
}
-/***************************
- * Probabilistic extension *
- ***************************/
+/*****************************************
+ * Probabilistic banded glocal alignment *
+ *****************************************/
+
+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; }
-ka_probpar_t ka_probpar_def = { 0.0001, 0.1, 1 };
+ka_probpar_t ka_probpar_def = { 0.001, 0.1, 10 };
/*
- The profile HMM is:
-
- /\ /\ /\ /\ /\
- I[0] I[1] I[k-1] I[k] I[L]
- ^ \ ^ \ \ ^ \ ^ \ \ ^
- | \ | \ \ | \ | \ \ |
- M[0] -> M[1] -> ... -> M[k-1] -> M[k] -> ... -> M[L] M[L+1]
- \ \/ \/ \/ \/ /
- \ /\ /\ /\ /\ /
- D[1] -> -> D[k-1] -> D[k] ->
- \/ \/ \/
-
- Every {M,I}[k], k=0..L connects M[L+1] at the same probability, while
- no D[k], k=1..L-1 connects M[L+1]. This means an alignment can end up
- with M or I but not D.
-
- Deletions are dumb states which do not emit residues. Frankly, I am
- not sure if they are handled properly in the following
- implementation. This is a potential concern to be resolved in future.
+ 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].
*/
-int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float *_qual,
+int ka_prob_glocal(const uint8_t *_ref, int l_ref, const uint8_t *_query, int l_query, const uint8_t *iqual,
const ka_probpar_t *c, int *state, uint8_t *q)
{
- double **f, **b, m[9], f_sink, sI, sM, pf, pb, pD;
- float *qual;
- uint8_t *ref, *query;
+ 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;
- qual = _qual - 1;
- bw = c->bw;
- bw2 = c->bw * 2 + 1;
+ 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));
+ 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));
}
- // initialize m
- sM = sI = 1. / (2 * l_query + 2);
+ 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] = 1.;
- {
- int beg = 1, end = l_ref, x;
- x = 0 - bw; beg = beg > x? beg : x;
- x = 0 + bw; end = end < x? end : x;
- for (k = beg; k <= end; ++k) {
- int u, v01;
- set_u(u, bw, 0, k); set_u(v01, bw, 0, k-1);
- f[0][u+2] = m[2] * f[0][v01+0] + m[8] * f[0][v01+2];
+ 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[1..l_query]; core loop
- for (i = 1; i <= l_query; ++i) {
- double *fi = f[i], *fi1 = f[i-1];
- int beg = 0, end = l_ref, x;
- x = i - bw; beg = beg > x? beg : x;
- x = i + bw; end = end < x? end : x;
- for (k = beg; k <= end; ++k) {
+ // f[2..l_query]
+ for (i = 2; i <= l_query; ++i) {
+ double *fi = f[i], *fi1 = f[i-1], sum;
+ int beg = 1, end = l_ref, x, _beg, _end;
+ 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;
+ // FIXME: the following line can be optimized without branching
e = (ref[k] > 3 || query[i] > 3)? 1. : ref[k] == query[i]? 1. - qual[i] : qual[i] / 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;
}
- // sink
- for (k = 0, f_sink = 0.; k <= l_ref; ++k) {
- int u;
- set_u(u, bw, l_query, k);
- if (u < 3 || u >= bw2*3+3) continue;
- f_sink += f[l_query][u+0] * sM + f[l_query][u+1] * sI;
+ { // 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
}
- pf = f_sink;
/*** backward ***/
- // sink
- for (k = 0; k <= l_ref; ++k) {
+ // 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; bi[u+1] = sI;
+ 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]; core loop
- for (i = l_query - 1; i >= 0; --i) {
- int beg = 0, end = l_ref, x;
- double *bi = b[i], *bi1 = b[i+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);
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;
+ // FIXME: the following can be optimized without branching
e = k >= l_ref? 0 : (ref[k+1] > 3 || query[i+1] > 3)? 1. : ref[k+1] == query[i+1]? 1. - qual[i+1] : qual[i+1] / 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);
bi[u+0] = e * m[0] * bi1[v11+0] + .25 * m[1] * bi1[v10+1] + m[2] * bi[v01+2];
bi[u+1] = e * m[3] * bi1[v11+0] + .25 * m[4] * bi1[v10+1];
- bi[u+2] = e * m[6] * bi1[v11+0] + m[8] * bi[v01+2];
+ // FIXME: I do not know why I need this (i>1) factor, but only with it the result makes sense.
+ bi[u+2] = (e * m[6] * bi1[v11+0] + 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;
+ y = s[i];
+ for (k = _beg; k <= _end; ++k) bi[k] /= y;
}
- set_u(k, bw, 0, 0);
- pb = b[0][k];
- pD = (pf + pb) / 2.;
- is_diff = fabs(pb/pf - 1.) > 1e-7? 1 : 0;
+ { // 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] / 3.;
+ set_u(u, bw, 1, k);
+ if (u < 3 || u >= bw2*3+3) continue;
+ sum += e * b[1][u+0] * bM + .25 * 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 = 0, end = l_ref, x, max_k = -1;
+ 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<<2 | 0; sum += z;
- z = fi[u+1] * bi[u+1]; if (z > max) max = z, max_k = k<<2 | 1; sum += z;
+ 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 /= pD; // if everything works as is expected, sum == 1.0
+ max /= sum; sum *= s[i]; // if everything works as is expected, sum == 1.0
if (state) state[i-1] = max_k;
- if (q) q[i-1] = -4.343 * log(1. - max);
+ if (q) k = -4.343 * log(1. - max), q[i-1] = k > 100? 99 : k;
#ifdef _MAIN
- fprintf(stderr, "[%d,%.10lg,%.10lg],%d,%lg,%d:%d,%lg\n", is_diff, pf, pb, i, sum, max_k>>2, max_k&3, max);
+ fprintf(stderr, "(%.10lg,%.10lg) (%d,%d:%d)~%lg\n", pb, sum, i-1, max_k>>2, 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(f); free(b); free(s); free(_qual);
return 0;
}
#ifdef _MAIN
int main()
{
- int l_ref = 5, l_query = 3;
+ int l_ref = 5, l_query = 4;
uint8_t *ref = (uint8_t*)"\0\1\3\3\1";
-// uint8_t *query = (uint8_t*)"\0\3\3\1";
- uint8_t *query = (uint8_t*)"\1\3\3\1"; // FIXME: the output is not so right given this input!!!
- static float qual[4] = {.01, .01, .01, .01};
- ka_prob_extend(ref, l_ref, query, l_query, qual, &ka_probpar_def, 0, 0);
+ uint8_t *query = (uint8_t*)"\0\3\3\1";
+// uint8_t *query = (uint8_t*)"\1\3\3\1";
+ static uint8_t qual[4] = {20, 20, 20, 20};
+ ka_prob_glocal(ref, l_ref, query, l_query, qual, &ka_probpar_def, 0, 0);
return 0;
}
#endif
projects / samtools.git / blobdiff