7 #define MC_AVG_ERR 0.007
8 #define MC_MAX_SUMQ 3000
9 #define MC_MAX_SUMQP 1e-300
10 #define MC_MAX_EM_ITER 16
11 #define MC_EM_EPS 1e-4
16 double *q2p, *pdg; // pdg -> P(D|g)
18 double *z, *zswap; // aux for afs
19 double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
23 void mc_init_prior(mc_aux_t *ma, int type, double theta)
26 if (type == MC_PTYPE_COND2) {
27 for (i = 0; i <= 2 * ma->n; ++i)
28 ma->alpha[i] = 2. * (i + 1) / (2 * ma->n + 1) / (2 * ma->n + 2);
29 } else if (type == MC_PTYPE_FLAT) {
30 for (i = 0; i <= ma->M; ++i)
31 ma->alpha[i] = 1. / (ma->M + 1);
34 for (i = 0, sum = 0.; i < 2 * ma->n; ++i)
35 sum += (ma->alpha[i] = theta / (2 * ma->n - i));
36 ma->alpha[2 * ma->n] = 1. - sum;
40 mc_aux_t *mc_init(int n) // FIXME: assuming diploid
44 ma = calloc(1, sizeof(mc_aux_t));
45 ma->n = n; ma->M = 2 * n;
46 ma->q2p = calloc(MC_MAX_SUMQ + 1, sizeof(double));
47 ma->qsum = calloc(4 * ma->n, sizeof(int));
48 ma->bcnt = calloc(4 * ma->n, sizeof(int));
49 ma->pdg = calloc(3 * ma->n, sizeof(double));
50 ma->alpha = calloc(2 * ma->n + 1, sizeof(double));
51 ma->beta = calloc((2 * ma->n + 1) * 3, sizeof(double));
52 ma->z = calloc(2 * ma->n + 1, sizeof(double));
53 ma->zswap = calloc(2 * ma->n + 1, sizeof(double));
54 ma->afs = calloc(2 * ma->n + 1, sizeof(double));
55 ma->afs1 = calloc(2 * ma->n + 1, sizeof(double));
56 for (i = 0; i <= MC_MAX_SUMQ; ++i)
57 ma->q2p[i] = pow(10., -i / 10.);
58 for (i = 0; i <= ma->M; ++i) { // beta[k][g]=P(g|k/M)
59 double *bi = ma->beta + 3 * i;
60 double f = (double)i / ma->M;
61 bi[0] = (1. - f) * (1. - f);
62 bi[1] = 2 * f * (1. - f);
65 mc_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
69 void mc_destroy(mc_aux_t *ma)
72 free(ma->qsum); free(ma->bcnt);
73 free(ma->q2p); free(ma->pdg);
74 free(ma->alpha); free(ma->beta);
75 free(ma->z); free(ma->zswap);
76 free(ma->afs); free(ma->afs1);
81 static int sum_err(int *n, const bam_pileup1_t **plp, mc_aux_t *ma)
84 memset(ma->qsum, 0, sizeof(int) * 4 * ma->n);
85 memset(ma->bcnt, 0, sizeof(int) * 4 * ma->n);
86 for (j = 0; j < ma->n; ++j) {
87 int *qsum = ma->qsum + j * 4;
88 int *bcnt = ma->bcnt + j * 4;
89 for (i = 0; i < n[j]; ++i) {
90 const bam_pileup1_t *p = plp[j] + i;
92 if (p->is_del || (p->b->core.flag&BAM_FUNMAP)) continue;
93 q = bam1_qual(p->b)[p->qpos];
94 if (p->b->core.qual < q) q = p->b->core.qual;
95 if (q < MC_MIN_QUAL) continue; // small qual
96 b = bam_nt16_nt4_table[(int)bam1_seqi(bam1_seq(p->b), p->qpos)];
97 if (b > 3) continue; // N
106 static void set_allele(int ref, mc_aux_t *ma)
108 int i, j, sum[4], tmp;
109 sum[0] = sum[1] = sum[2] = sum[3] = 0;
110 for (i = 0; i < ma->n; ++i)
111 for (j = 0; j < 4; ++j)
112 sum[j] += ma->qsum[i * 4 + j];
113 for (j = 0; j < 4; ++j) sum[j] = sum[j]<<2 | j;
114 for (i = 1; i < 4; ++i) // insertion sort
115 for (j = i; j > 0 && sum[j] < sum[j-1]; --j)
116 tmp = sum[j], sum[j] = sum[j-1], sum[j-1] = tmp;
117 ma->ref = sum[3]&3; ma->alt = sum[2]&3; ma->alt2 = -1;
118 if (ma->ref != ref) {
119 if (ma->alt == ref) tmp = ma->ref, ma->ref = ma->alt, ma->alt = tmp;
120 else ma->alt2 = ma->alt, ma->alt = ma->ref, ma->ref = ref;
124 static void cal_pdg(mc_aux_t *ma)
127 for (j = 0; j < ma->n; ++j) {
128 int pi[3], *qsum, *bcnt;
129 double *pdg = ma->pdg + j * 3;
130 qsum = ma->qsum + j * 4;
131 bcnt = ma->bcnt + j * 4;
132 pi[1] = 3 * (bcnt[ma->ref] + bcnt[ma->alt]);
133 pi[0] = qsum[ma->ref];
134 pi[2] = qsum[ma->alt];
135 for (i = 0; i < 3; ++i)
136 pdg[i] = pi[i] > MC_MAX_SUMQ? MC_MAX_SUMQP : ma->q2p[pi[i]];
139 // this calculates the naive allele frequency and Nielsen's frequency
140 static double mc_freq0(const mc_aux_t *ma, double *_f)
143 double f, f_nielsen, w_sum;
145 for (i = cnt = 0, f = f_nielsen = w_sum = 0.; i < ma->n; ++i) {
146 int *bcnt = ma->bcnt + i * 4;
147 int x = bcnt[ma->ref] + bcnt[ma->alt];
151 f += (double)bcnt[ma->ref] / x;
152 p = (bcnt[ma->ref] - MC_AVG_ERR * x) / (1. - 2. * MC_AVG_ERR) / x;
153 w = 2. * x / (1. + x);
160 if (f_nielsen < 0.) f_nielsen = 0.;
161 if (f_nielsen > 1.) f_nielsen = 1.;
166 // f0 is the reference allele frequency
167 static double mc_freq_iter(double f0, const mc_aux_t *ma)
171 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
172 for (i = 0, f = 0.; i < ma->n; ++i) {
174 pdg = ma->pdg + i * 3;
175 f += (pdg[1] * f3[1] + 2. * pdg[2] * f3[2])
176 / (pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2]);
182 static double mc_ref_prob(const mc_aux_t *ma, double *_PD, double *f_exp)
185 long double PD = 0., Pref = 0., Ef = 0.;
186 for (k = 0; k <= ma->M; ++k) {
187 long double x = 1., y = 0.;
188 double *bk = ma->beta + k * 3;
189 for (i = 0; i < ma->n; ++i) {
190 double *pdg = ma->pdg + i * 3;
191 double z = pdg[0] * bk[0] + pdg[1] * bk[1] + pdg[2] * bk[2];
193 y += (pdg[1] * bk[1] + 2. * pdg[2] * bk[2]) / z;
195 PD += x * ma->alpha[k];
196 Ef += x * y * ma->alpha[k];
198 for (k = 0; k <= ma->n * 2; ++k) {
200 for (i = 0; i < ma->n; ++i)
201 x *= ma->pdg[i * 3 + 2] * ma->beta[k * 3 + 2];
202 Pref += x * ma->alpha[k];
204 *f_exp = (double)(Ef / PD / ma->M);
209 int mc_call_gt(const mc_aux_t *ma, double f0, int k)
212 double max, f3[3], *pdg = ma->pdg + k * 3;
214 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
215 for (i = 0, sum = 0.; i < 3; ++i)
216 sum += (g[i] = pdg[i] * f3[i]);
217 for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
219 if (g[i] > max) max = g[i], max_i = i;
222 if (max < 1e-308) max = 1e-308;
223 q = (int)(-3.434 * log(max) + .499);
227 // calculate z_{nr}^{(k)}
228 static void mc_cal_z(mc_aux_t *ma, int k)
230 double *z[2], *tmp, *bk, *pdg;
234 bk = ma->beta + k * 3; pdg = ma->pdg;
235 z[0][0] = 1.; z[0][1] = z[0][2] = 0.;
236 for (j = 0; j < ma->n; ++j) {
237 int max = (j + 1) * 2;
239 pdg = ma->pdg + j * 3;
240 p[0] = bk[0] * pdg[0]; p[1] = bk[1] * pdg[1]; p[2] = bk[2] * pdg[2];
241 z[1][0] = p[0] * z[0][0];
242 z[1][1] = p[0] * z[0][1] + p[1] * z[0][0];
243 for (i = 2; i <= max; ++i)
244 z[1][i] = p[0] * z[0][i] + p[1] * z[0][i-1] + p[2] * z[0][i-2];
245 if (j < ma->n - 1) z[1][max+1] = z[1][max+2] = 0.;
246 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
248 if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (2 * ma->n + 1));
250 // Warning: this is cubic in ma->n, very sloooooow
251 static void mc_add_afs(mc_aux_t *ma, double PD, double *f_map, double *p_map)
255 memset(ma->afs1, 0, sizeof(double) * (2 * ma->n + 1));
256 *f_map = *p_map = -1.;
257 for (k = 0; k <= 2 * ma->n; ++k) {
259 for (l = 0; l <= 2 * ma->n; ++l)
260 ma->afs1[l] += ma->alpha[k] * ma->z[l] / PD;
262 for (k = 0; k <= ma->M; ++k)
263 if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return;
264 for (k = 0; k <= 2 * ma->n; ++k) {
265 ma->afs[k] += ma->afs1[k];
270 double max = -1., e = 0.;
271 for (k = 0; k <= 2 * ma->n; ++k) {
272 if (ma->afs1[k] > max) max = ma->afs1[k], max_k = k;
273 e += k * ma->afs1[k];
275 *f_map = .5 * max_k / ma->n; *p_map = max; // e should equal mc_rst_t::f_exp
276 // printf(" * %.3lg:%.3lg:%.3lg:%.3lg * ", sum, 1.-.5*max_k/ma->n, max, 1.-.5*e/ma->n);
280 int mc_cal(int ref, int *n, const bam_pileup1_t **plp, mc_aux_t *ma, mc_rst_t *rst, int level)
283 memset(rst, 0, sizeof(mc_rst_t));
284 rst->f_em = rst->f_exp = -1.; rst->ref = rst->alt = -1;
286 tot = sum_err(n, plp, ma);
287 if (tot == 0) return 0; // no good bases
290 // set ref/major allele
291 rst->ref = ma->ref; rst->alt = ma->alt; rst->alt2 = ma->alt2;
292 // calculate naive and Nielsen's freq
293 rst->f_naive = mc_freq0(ma, &rst->f_nielsen);
295 double flast = rst->f_naive;
296 for (i = 0; i < MC_MAX_EM_ITER; ++i) {
297 rst->f_em = mc_freq_iter(flast, ma);
298 if (fabs(rst->f_em - flast) < MC_EM_EPS) break;
302 if (level >= 2) // quadratic-time calculations; necessary for genotyping
303 rst->p_ref = mc_ref_prob(ma, &rst->PD, &rst->f_exp);
305 mc_add_afs(ma, rst->PD, &rst->f_map, &rst->p_map);
309 void mc_dump_afs(mc_aux_t *ma)
312 fprintf(stderr, "[afs]");
313 for (k = 0; k <= ma->M; ++k)
314 fprintf(stderr, " %d:%.3lf", k, ma->afs[ma->M - k]);
315 fprintf(stderr, "\n");
316 memset(ma->afs, 0, sizeof(double) * (ma->M + 1));