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) { // the best base is not ref
119 if (ref >= 0 && ref <= 3) { // ref is not N
120 if (ma->alt == ref) tmp = ma->ref, ma->ref = ma->alt, ma->alt = tmp; // then switch alt and ref
121 else ma->alt2 = ma->alt, ma->alt = ma->ref, ma->ref = ref; // then set ref as ref
122 } else ma->alt2 = ma->alt, ma->alt = ma->ref, ma->ref = sum[0]&3; // then set the weakest as ref
126 static void cal_pdg(mc_aux_t *ma)
129 for (j = 0; j < ma->n; ++j) {
130 int pi[3], *qsum, *bcnt;
131 double *pdg = ma->pdg + j * 3;
132 qsum = ma->qsum + j * 4;
133 bcnt = ma->bcnt + j * 4;
134 pi[1] = 3 * (bcnt[ma->ref] + bcnt[ma->alt]);
135 pi[0] = qsum[ma->ref];
136 pi[2] = qsum[ma->alt];
137 for (i = 0; i < 3; ++i)
138 pdg[i] = pi[i] > MC_MAX_SUMQ? MC_MAX_SUMQP : ma->q2p[pi[i]];
141 // this calculates the naive allele frequency and Nielsen's frequency
142 static double mc_freq0(const mc_aux_t *ma, double *_f)
145 double f, f_nielsen, w_sum;
147 for (i = cnt = 0, f = f_nielsen = w_sum = 0.; i < ma->n; ++i) {
148 int *bcnt = ma->bcnt + i * 4;
149 int x = bcnt[ma->ref] + bcnt[ma->alt];
153 f += (double)bcnt[ma->ref] / x;
154 p = (bcnt[ma->ref] - MC_AVG_ERR * x) / (1. - 2. * MC_AVG_ERR) / x;
155 w = 2. * x / (1. + x);
162 if (f_nielsen < 0.) f_nielsen = 0.;
163 if (f_nielsen > 1.) f_nielsen = 1.;
168 // f0 is the reference allele frequency
169 static double mc_freq_iter(double f0, const mc_aux_t *ma)
173 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
174 for (i = 0, f = 0.; i < ma->n; ++i) {
176 pdg = ma->pdg + i * 3;
177 f += (pdg[1] * f3[1] + 2. * pdg[2] * f3[2])
178 / (pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2]);
184 static double mc_ref_prob(const mc_aux_t *ma, double *_PD, double *f_exp)
187 long double PD = 0., Pref = 0., Ef = 0.;
188 for (k = 0; k <= ma->M; ++k) {
189 long double x = 1., y = 0.;
190 double *bk = ma->beta + k * 3;
191 for (i = 0; i < ma->n; ++i) {
192 double *pdg = ma->pdg + i * 3;
193 double z = pdg[0] * bk[0] + pdg[1] * bk[1] + pdg[2] * bk[2];
195 y += (pdg[1] * bk[1] + 2. * pdg[2] * bk[2]) / z;
197 PD += x * ma->alpha[k];
198 Ef += x * y * ma->alpha[k];
200 for (k = 0; k <= ma->n * 2; ++k) {
202 for (i = 0; i < ma->n; ++i)
203 x *= ma->pdg[i * 3 + 2] * ma->beta[k * 3 + 2];
204 Pref += x * ma->alpha[k];
206 *f_exp = (double)(Ef / PD / ma->M);
211 int mc_call_gt(const mc_aux_t *ma, double f0, int k)
214 double max, f3[3], *pdg = ma->pdg + k * 3;
216 f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
217 for (i = 0, sum = 0.; i < 3; ++i)
218 sum += (g[i] = pdg[i] * f3[i]);
219 for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
221 if (g[i] > max) max = g[i], max_i = i;
224 if (max < 1e-308) max = 1e-308;
225 q = (int)(-3.434 * log(max) + .499);
229 static void mc_cal_z2(mc_aux_t *ma)
231 double *z[2], *tmp, *pdg;
236 z[0][0] = 1.; z[0][1] = z[0][2] = 0.;
237 for (j = 0; j < ma->n; ++j) {
238 int max = (j + 1) * 2;
240 pdg = ma->pdg + j * 3;
241 p[0] = pdg[0]; p[1] = 2. * pdg[1]; p[2] = pdg[2];
242 z[1][0] = p[0] * z[0][0];
243 z[1][1] = p[0] * z[0][1] + p[1] * z[0][0];
244 for (i = 2; i <= max; ++i)
245 z[1][i] = p[0] * z[0][i] + p[1] * z[0][i-1] + p[2] * z[0][i-2];
246 if (j < ma->n - 1) z[1][max+1] = z[1][max+2] = 0.;
247 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
249 if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (2 * ma->n + 1));
251 static void mc_add_afs2(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.;
258 for (k = 0; k <= ma->M; ++k) {
259 for (l = 0, sum = 0.; l <= ma->M; ++l)
260 sum += ma->alpha[l] * pow((double)l / ma->M, k) * pow(1. - (double)l / ma->M, ma->M - k);
261 ma->afs1[k] = ma->z[k] * sum / PD;
263 for (k = 0; k <= ma->M; ++k)
264 if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return;
265 for (k = 0, sum = 0.; k <= 2 * ma->n; ++k) {
266 ma->afs[k] += ma->afs1[k];
271 double max = -1., e = 0.;
272 for (k = 0; k <= 2 * ma->n; ++k) {
273 if (ma->afs1[k] > max) max = ma->afs1[k], max_k = k;
274 e += k * ma->afs1[k];
276 *f_map = .5 * max_k / ma->n; *p_map = max; // e should equal mc_rst_t::f_exp
277 printf(" * %.3lg:%.3lg:%.3lg:%.3lg * ", sum, 1.-.5*max_k/ma->n, max, 1.-.5*e/ma->n);
280 // calculate z_{nr}^{(k)}
281 static void mc_cal_z(mc_aux_t *ma, int k)
283 double *z[2], *tmp, *bk, *pdg;
287 bk = ma->beta + k * 3; pdg = ma->pdg;
288 z[0][0] = 1.; z[0][1] = z[0][2] = 0.;
289 for (j = 0; j < ma->n; ++j) {
290 int max = (j + 1) * 2;
292 pdg = ma->pdg + j * 3;
293 p[0] = bk[0] * pdg[0]; p[1] = bk[1] * pdg[1]; p[2] = bk[2] * pdg[2];
294 z[1][0] = p[0] * z[0][0];
295 z[1][1] = p[0] * z[0][1] + p[1] * z[0][0];
296 for (i = 2; i <= max; ++i)
297 z[1][i] = p[0] * z[0][i] + p[1] * z[0][i-1] + p[2] * z[0][i-2];
298 if (j < ma->n - 1) z[1][max+1] = z[1][max+2] = 0.;
299 tmp = z[0]; z[0] = z[1]; z[1] = tmp;
301 if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (2 * ma->n + 1));
303 // Warning: this is cubic in ma->n, very sloooooow
304 static void mc_add_afs(mc_aux_t *ma, double PD, double *f_map, double *p_map)
308 memset(ma->afs1, 0, sizeof(double) * (2 * ma->n + 1));
309 *f_map = *p_map = -1.;
310 for (k = 0; k <= 2 * ma->n; ++k) {
312 for (l = 0; l <= 2 * ma->n; ++l)
313 ma->afs1[l] += ma->alpha[k] * ma->z[l] / PD;
315 for (k = 0; k <= ma->M; ++k)
316 if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return;
317 for (k = 0; k <= 2 * ma->n; ++k) {
318 ma->afs[k] += ma->afs1[k];
323 double max = -1., e = 0.;
324 for (k = 0; k <= 2 * ma->n; ++k) {
325 if (ma->afs1[k] > max) max = ma->afs1[k], max_k = k;
326 e += k * ma->afs1[k];
328 *f_map = .5 * max_k / ma->n; *p_map = max; // e should equal mc_rst_t::f_exp
329 printf(" * %.3lg:%.3lg:%.3lg:%.3lg * ", sum, 1.-.5*max_k/ma->n, max, 1.-.5*e/ma->n);
333 int mc_cal(int ref, int *n, const bam_pileup1_t **plp, mc_aux_t *ma, mc_rst_t *rst, int level)
336 memset(rst, 0, sizeof(mc_rst_t));
337 rst->f_em = rst->f_exp = -1.; rst->ref = rst->alt = -1;
339 tot = sum_err(n, plp, ma);
340 if (tot == 0) return 0; // no good bases
343 // set ref/major allele
344 rst->ref = ma->ref; rst->alt = ma->alt; rst->alt2 = ma->alt2;
345 // calculate naive and Nielsen's freq
346 rst->f_naive = mc_freq0(ma, &rst->f_nielsen);
348 double flast = rst->f_naive;
349 for (i = 0; i < MC_MAX_EM_ITER; ++i) {
350 rst->f_em = mc_freq_iter(flast, ma);
351 if (fabs(rst->f_em - flast) < MC_EM_EPS) break;
355 if (level >= 2) // quadratic-time calculations; necessary for genotyping
356 rst->p_ref = mc_ref_prob(ma, &rst->PD, &rst->f_exp);
358 mc_add_afs2(ma, rst->PD, &rst->f_map, &rst->p_map);
359 mc_add_afs(ma, rst->PD, &rst->f_map, &rst->p_map);
364 void mc_dump_afs(mc_aux_t *ma)
367 fprintf(stderr, "[afs]");
368 for (k = 0; k <= ma->M; ++k)
369 fprintf(stderr, " %d:%.3lf", k, ma->afs[ma->M - k]);
370 fprintf(stderr, "\n");
371 memset(ma->afs, 0, sizeof(double) * (ma->M + 1));