From: Heng Li Date: Tue, 28 Sep 2010 04:06:11 +0000 (+0000) Subject: improve numerical stability X-Git-Url: https://git.donarmstrong.com/?a=commitdiff_plain;ds=sidebyside;h=0f490725235e5f93e60577a6a9fbd40053c8be82;p=samtools.git improve numerical stability --- diff --git a/kaln.c b/kaln.c index bfb011d..b20ae6f 100644 --- a/kaln.c +++ b/kaln.c @@ -377,7 +377,7 @@ uint32_t *ka_global_core(uint8_t *seq1, int len1, uint8_t *seq2, int len2, const #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 = { 0.0001, 0.1, 10 }; /* The profile HMM is: @@ -403,13 +403,11 @@ ka_probpar_t ka_probpar_def = { 0.0001, 0.1, 1 }; int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float *_qual, const ka_probpar_t *c, int *state, uint8_t *q) { - double **f, **b, m[9], f_sink, sI, sM, pf, pb, pD; + double **f, **b, *s, m[9], sI, sM, pb; float *qual; uint8_t *ref, *query; int bw, bw2, i, k, is_diff = 0; - // FIXME: floating point underflow - /*** initialization ***/ ref = _ref - 1; // change to 1-based coordinate query = _query - 1; @@ -423,6 +421,7 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float 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 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); @@ -433,59 +432,72 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float set_u(k, bw, 0, 0); f[0][k] = 1.; { // write D cells - int beg = 1, end = l_ref, x; + int beg = 1, end = l_ref, x, _beg, _end; + double sum; x = 0 - bw; beg = beg > x? beg : x; x = 0 + bw; end = end < x? end : x; - for (k = beg; k <= end; ++k) { + for (k = beg, sum = 0.; 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]; + sum += (f[0][u+2] = m[2] * f[0][v01+0] + m[8] * f[0][v01+2]); } + // rescale to avoid floating point underflow + s[0] = sum; + set_u(_beg, bw, 0, 0); set_u(_end, bw, 0, end); _end += 2; + for (k = _beg; k <= _end; ++k) f[0][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; + double *fi = f[i], *fi1 = f[i-1], sum; + int beg = 0, 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; k <= end; ++k) { + for (k = beg, sum = 0.; k <= end; ++k) { int u, v11, v01, v10; double e; - // FIXME: the following line can be optimized without branching! + // 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; + { // sink (actually f[l_query+1]) + double sum; + for (k = 0, 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; // this P(x) calculated by the forward algorithm /*** backward ***/ - // sink + // 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 = 0; 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; + int beg = 0, end = l_ref, x, _beg, _end; double *bi = b[i], *bi1 = b[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]; @@ -493,11 +505,13 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float bi[u+2] = e * m[6] * bi1[v11+0] + m[8] * bi[v01+2]; // 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; k <= _end; ++k) bi[k] /= s[i]; } set_u(k, bw, 0, 0); - pb = b[0][k]; - pD = (pf + pb) / 2.; - is_diff = fabs(pb/pf - 1.) > 1e-7? 1 : 0; + pb = b[0][k]; // if everything works as is expected, pb==1 + 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.; @@ -511,28 +525,28 @@ int ka_prob_extend(uint8_t *_ref, int l_ref, uint8_t *_query, int l_query, float 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; } - 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); #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, 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); 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!!! + 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); return 0;