#include <math.h>
#include <stdlib.h>
+#include <stdio.h>
#include "bam_mcns.h"
#define MC_MIN_QUAL 13
+#define MC_AVG_ERR 0.007
#define MC_MAX_SUMQ 3000
#define MC_MAX_SUMQP 1e-300
+#define MC_MAX_EM_ITER 16
+#define MC_EM_EPS 1e-4
struct __mc_aux_t {
- int n, N;
+ int n, M;
int ref, alt;
- double theta;
double *q2p, *pdg; // pdg -> P(D|g)
double *alpha, *beta;
+ double *z, *zswap; // aux for afs
+ double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
int *qsum, *bcnt;
};
-void mc_init_prior(mc_aux_t *ma, double theta)
+void mc_init_prior(mc_aux_t *ma, int type, double theta)
{
- double sum;
int i;
- ma->theta = theta;
- for (i = 0, sum = 0.; i < 2 * ma->n; ++i)
- sum += (ma->alpha[i] = ma->theta / (2 * ma->n - i));
- ma->alpha[2 * ma->n] = 1. - sum;
+ if (type == MC_PTYPE_COND2) {
+ for (i = 0; i <= 2 * ma->n; ++i)
+ ma->alpha[i] = 2. * (i + 1) / (2 * ma->n + 1) / (2 * ma->n + 2);
+ } else {
+ double sum;
+ for (i = 0, sum = 0.; i < 2 * ma->n; ++i)
+ sum += (ma->alpha[i] = theta / (2 * ma->n - i));
+ ma->alpha[2 * ma->n] = 1. - sum;
+ }
}
mc_aux_t *mc_init(int n) // FIXME: assuming diploid
mc_aux_t *ma;
int i;
ma = calloc(1, sizeof(mc_aux_t));
- ma->n = n; ma->N = 2 * n;
+ ma->n = n; ma->M = 2 * n;
ma->q2p = calloc(MC_MAX_SUMQ + 1, sizeof(double));
ma->qsum = calloc(4 * ma->n, sizeof(int));
ma->bcnt = calloc(4 * ma->n, sizeof(int));
ma->pdg = calloc(3 * ma->n, sizeof(double));
ma->alpha = calloc(2 * ma->n + 1, sizeof(double));
ma->beta = calloc((2 * ma->n + 1) * 3, sizeof(double));
+ ma->z = calloc(2 * ma->n + 1, sizeof(double));
+ ma->zswap = calloc(2 * ma->n + 1, sizeof(double));
+ ma->afs = calloc(2 * ma->n + 1, sizeof(double));
+ ma->afs1 = calloc(2 * ma->n + 1, sizeof(double));
for (i = 0; i <= MC_MAX_SUMQ; ++i)
ma->q2p[i] = pow(10., -i / 10.);
- for (i = 0; i <= 2 * ma->n; ++i) {
+ for (i = 0; i <= ma->M; ++i) { // beta[k][g]=P(g|k/M)
double *bi = ma->beta + 3 * i;
- double f = (double)i / (2 * ma->n);
+ double f = (double)i / ma->M;
bi[0] = (1. - f) * (1. - f);
bi[1] = 2 * f * (1. - f);
bi[2] = f * f;
}
- mc_init_prior(ma, 1e-3); // the simplest prior
+ mc_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
return ma;
}
free(ma->qsum); free(ma->bcnt);
free(ma->q2p); free(ma->pdg);
free(ma->alpha); free(ma->beta);
+ free(ma->z); free(ma->zswap);
+ free(ma->afs); free(ma->afs1);
free(ma);
}
}
-static void sum_err(int *n, const bam_pileup1_t **plp, mc_aux_t *ma)
+static int sum_err(int *n, const bam_pileup1_t **plp, mc_aux_t *ma)
{
- int i, j;
+ int i, j, tot = 0;
memset(ma->qsum, 0, sizeof(int) * 4 * ma->n);
memset(ma->bcnt, 0, sizeof(int) * 4 * ma->n);
for (j = 0; j < ma->n; ++j) {
- int tmp, *qsum = ma->qsum + j * 4;
+ int *qsum = ma->qsum + j * 4;
int *bcnt = ma->bcnt + j * 4;
- for (i = tmp = 0; i < n[j]; ++i) {
+ for (i = 0; i < n[j]; ++i) {
const bam_pileup1_t *p = plp[j] + i;
int q, b;
if (p->is_del || (p->b->core.flag&BAM_FUNMAP)) continue;
if (b > 3) continue; // N
qsum[b] += q;
++bcnt[b];
- ++tmp;
+ ++tot;
}
}
+ return tot;
}
static void set_allele(int ref, mc_aux_t *ma)
pdg[i] = pi[i] > MC_MAX_SUMQ? MC_MAX_SUMQP : ma->q2p[pi[i]];
}
}
-// return the reference allele frequency
-double mc_freq0(int ref, int *n, const bam_pileup1_t **plp, mc_aux_t *ma, int *_ref, int *alt)
+// this calculates the naive allele frequency and Nielsen's frequency
+static double mc_freq0(const mc_aux_t *ma, double *_f)
{
int i, cnt;
- double f;
- sum_err(n, plp, ma);
- set_allele(ref, ma);
- cal_pdg(ma);
- *_ref = ma->ref; *alt = ma->alt;
- for (i = cnt = 0, f = 0.; i < ma->n; ++i) {
+ double f, f_nielsen, w_sum;
+ *_f = -1.;
+ for (i = cnt = 0, f = f_nielsen = w_sum = 0.; i < ma->n; ++i) {
int *bcnt = ma->bcnt + i * 4;
int x = bcnt[ma->ref] + bcnt[ma->alt];
if (x) {
+ double w, p;
++cnt;
f += (double)bcnt[ma->ref] / x;
+ p = (bcnt[ma->ref] - MC_AVG_ERR * x) / (1. - 2. * MC_AVG_ERR) / x;
+ w = 2. * x / (1. + x);
+ w_sum += w;
+ f_nielsen += p * w;
}
}
- return f / cnt;
+ if (cnt) {
+ f_nielsen /= w_sum;
+ if (f_nielsen < 0.) f_nielsen = 0.;
+ if (f_nielsen > 1.) f_nielsen = 1.;
+ *_f = f_nielsen;
+ return f / cnt;
+ } else return -1.;
}
// f0 is the reference allele frequency
-double mc_freq_iter(double f0, mc_aux_t *ma)
+static double mc_freq_iter(double f0, const mc_aux_t *ma)
{
double f, f3[3];
- int i, j;
+ int i;
f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
for (i = 0, f = 0.; i < ma->n; ++i) {
- double up, dn, *pdg;
+ double *pdg;
pdg = ma->pdg + i * 3;
- for (j = 1, up = 0.; j < 3; ++j)
- up += j * pdg[j] * f3[j];
- for (j = 0, dn = 0.; j < 3; ++j)
- dn += pdg[j] * f3[j];
- f += up / dn;
+ f += (pdg[1] * f3[1] + 2. * pdg[2] * f3[2])
+ / (pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2]);
}
f /= ma->n * 2.;
return f;
}
-double mc_ref_prob(mc_aux_t *ma)
+static double mc_ref_prob(const mc_aux_t *ma, double *_PD, double *f_exp)
{
- int k, i, g;
- long double PD = 0., Pref = 0.;
- for (k = 0; k <= ma->n * 2; ++k) {
- long double x = 1.;
+ int k, i;
+ long double PD = 0., Pref = 0., Ef = 0.;
+ for (k = 0; k <= ma->M; ++k) {
+ long double x = 1., y = 0.;
double *bk = ma->beta + k * 3;
for (i = 0; i < ma->n; ++i) {
- double y = 0., *pdg = ma->pdg + i * 3;
- for (g = 0; g < 3; ++g)
- y += pdg[g] * bk[g];
- x *= y;
+ double *pdg = ma->pdg + i * 3;
+ double z = pdg[0] * bk[0] + pdg[1] * bk[1] + pdg[2] * bk[2];
+ x *= z;
+ y += (pdg[1] * bk[1] + 2. * pdg[2] * bk[2]) / z;
}
PD += x * ma->alpha[k];
+ Ef += x * y * ma->alpha[k];
}
for (k = 0; k <= ma->n * 2; ++k) {
long double x = 1.0;
x *= ma->pdg[i * 3 + 2] * ma->beta[k * 3 + 2];
Pref += x * ma->alpha[k];
}
+ *f_exp = (double)(Ef / PD / ma->M);
+ *_PD = PD;
return Pref / PD;
}
if (q > 99) q = 99;
return q<<2|max_i;
}
+// calculate z_{nr}^{(k)}
+static void mc_cal_z(mc_aux_t *ma, int k)
+{
+ double *z[2], *tmp, *bk, *pdg;
+ int i, j;
+ z[0] = ma->z;
+ z[1] = ma->zswap;
+ bk = ma->beta + k * 3; pdg = ma->pdg;
+ z[0][0] = 1.; z[0][1] = z[0][2] = 0.;
+ for (j = 0; j < ma->n; ++j) {
+ int max = (j + 1) * 2;
+ double p[3];
+ pdg = ma->pdg + j * 3;
+ p[0] = bk[0] * pdg[0]; p[1] = bk[1] * pdg[1]; p[2] = bk[2] * pdg[2];
+ z[1][0] = p[0] * z[0][0];
+ z[1][1] = p[0] * z[0][1] + p[1] * z[0][0];
+ for (i = 2; i <= max; ++i)
+ z[1][i] = p[0] * z[0][i] + p[1] * z[0][i-1] + p[2] * z[0][i-2];
+ if (j < ma->n - 1) z[1][max+1] = z[1][max+2] = 0.;
+ tmp = z[0]; z[0] = z[1]; z[1] = tmp;
+ }
+ if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (2 * ma->n + 1));
+}
+// Warning: this is cubic in ma->n, very sloooooow
+static void mc_add_afs(mc_aux_t *ma, double PD, double *f_map, double *p_map)
+{
+ int k, l;
+ double sum = 0.;
+ memset(ma->afs1, 0, sizeof(double) * (2 * ma->n + 1));
+ for (k = 0; k <= 2 * ma->n; ++k) {
+ mc_cal_z(ma, k);
+ for (l = 0; l <= 2 * ma->n; ++l)
+ ma->afs1[l] += ma->alpha[k] * ma->z[l] / PD;
+ }
+ for (k = 0; k <= 2 * ma->n; ++k) {
+ ma->afs[k] += ma->afs1[k];
+ sum += ma->afs1[k];
+ }
+ {
+ int max_k = 0;
+ double max = -1., e = 0.;
+ for (k = 0; k <= 2 * ma->n; ++k) {
+ if (ma->afs1[k] > max) max = ma->afs1[k], max_k = k;
+ e += k * ma->afs1[k];
+ }
+ *f_map = .5 * max_k / ma->n; *p_map = max; // e should equal mc_rst_t::f_exp
+// printf(" * %.3lg:%.3lg:%.3lg:%.3lg * ", sum, 1.-.5*max_k/ma->n, max, 1.-.5*e/ma->n);
+ }
+}
+
+int mc_cal(int ref, int *n, const bam_pileup1_t **plp, mc_aux_t *ma, mc_rst_t *rst, int level)
+{
+ int i, tot;
+ memset(rst, 0, sizeof(mc_rst_t));
+ rst->f_em = rst->f_exp = -1.; rst->ref = rst->alt = -1;
+ // precalculation
+ tot = sum_err(n, plp, ma);
+ if (tot == 0) return 0; // no good bases
+ set_allele(ref, ma);
+ cal_pdg(ma);
+ // set ref/major allele
+ rst->ref = ma->ref; rst->alt = ma->alt;
+ // calculate naive and Nielsen's freq
+ rst->f_naive = mc_freq0(ma, &rst->f_nielsen);
+ { // calculate f_em
+ double flast = rst->f_naive;
+ for (i = 0; i < MC_MAX_EM_ITER; ++i) {
+ rst->f_em = mc_freq_iter(flast, ma);
+ if (fabs(rst->f_em - flast) < MC_EM_EPS) break;
+ flast = rst->f_em;
+ }
+ }
+ if (level >= 2) // quadratic-time calculations; necessary for genotyping
+ rst->p_ref = mc_ref_prob(ma, &rst->PD, &rst->f_exp);
+ if (level >= 3)
+ mc_add_afs(ma, rst->PD, &rst->f_map, &rst->p_map);
+ return tot;
+}
+
+void mc_dump_afs(mc_aux_t *ma)
+{
+ int k;
+ fprintf(stderr, "[afs]");
+ for (k = 0; k <= ma->M; ++k)
+ fprintf(stderr, " %d:%.3lf", k, ma->afs[ma->M - k]);
+ fprintf(stderr, "\n");
+ memset(ma->afs, 0, sizeof(double) * (ma->M + 1));
+}
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