#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 {

};

void mc_init_prior(mc_aux_t *ma, int type, double theta)

{

int i;

if (type == MC_PTYPE_COND2) {

for (i = 0; i <= 2 * ma->n; ++i)

ma->phi[i] = 2. * (i + 1) / (2 * ma->n + 1) / (2 * ma->n + 2);

} else if (type == MC_PTYPE_FLAT) {

for (i = 0; i <= ma->M; ++i)

ma->phi[i] = 1. / (ma->M + 1);

} else {

double sum;

for (i = 0, sum = 0.; i < 2 * ma->n; ++i)

sum += (ma->phi[i] = theta / (2 * ma->n - i));

ma->phi[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->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->phi = calloc(ma->M + 1, sizeof(double));

ma->CMk = calloc(ma->M + 1, 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 <= ma->M; ++i)

ma->CMk[i] = exp(lgamma(ma->M + 1) - lgamma(i + 1) - lgamma(ma->M - i + 1));

mc_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior

return ma;

}

void mc_destroy(mc_aux_t *ma)

{

if (ma) {

free(ma->qsum); free(ma->bcnt);

free(ma->q2p); free(ma->pdg);

free(ma->phi); free(ma->CMk);

free(ma->z); free(ma->zswap);

free(ma->afs); free(ma->afs1);

free(ma);

}

}

static int sum_err(int *n, const bam_pileup1_t **plp, mc_aux_t *ma)

{

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 *qsum = ma->qsum + j * 4;

int *bcnt = ma->bcnt + j * 4;

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;

q = bam1_qual(p->b)[p->qpos];

if (p->b->core.qual < q) q = p->b->core.qual;

if (q < MC_MIN_QUAL) continue; // small qual

b = bam_nt16_nt4_table[(int)bam1_seqi(bam1_seq(p->b), p->qpos)];

if (b > 3) continue; // N

qsum[b] += q;

++bcnt[b];

++tot;

}

}

return tot;

}

static void set_allele(int ref, mc_aux_t *ma)

{

int i, j, sum[4], tmp;

sum[0] = sum[1] = sum[2] = sum[3] = 0;

for (i = 0; i < ma->n; ++i)

for (j = 0; j < 4; ++j)

sum[j] += ma->qsum[i * 4 + j];

for (j = 0; j < 4; ++j) sum[j] = sum[j]<<2 | j;

for (i = 1; i < 4; ++i) // insertion sort

for (j = i; j > 0 && sum[j] < sum[j-1]; --j)

tmp = sum[j], sum[j] = sum[j-1], sum[j-1] = tmp;

ma->ref = sum[3]&3; ma->alt = sum[2]&3; ma->alt2 = -1;

if (ma->ref != ref) { // the best base is not ref

if (ref >= 0 && ref <= 3) { // ref is not N

if (ma->alt == ref) tmp = ma->ref, ma->ref = ma->alt, ma->alt = tmp; // then switch alt and ref

else ma->alt2 = ma->alt, ma->alt = ma->ref, ma->ref = ref; // then set ref as ref

} else ma->alt2 = ma->alt, ma->alt = ma->ref, ma->ref = sum[0]&3; // then set the weakest as ref

}

}

static void cal_pdg(mc_aux_t *ma)

{

int i, j;

for (j = 0; j < ma->n; ++j) {

int pi[3], *qsum, *bcnt;

double *pdg = ma->pdg + j * 3;

qsum = ma->qsum + j * 4;

bcnt = ma->bcnt + j * 4;

pi[1] = 3 * (bcnt[ma->ref] + bcnt[ma->alt]);

pi[0] = qsum[ma->ref];

pi[2] = qsum[ma->alt];

for (i = 0; i < 3; ++i)

pdg[i] = pi[i] > MC_MAX_SUMQ? MC_MAX_SUMQP : ma->q2p[pi[i]];

}

}

// 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, 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;

}

}

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

static double mc_freq_iter(double f0, const mc_aux_t *ma)

{

double f, f3[3];

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 *pdg;

pdg = ma->pdg + i * 3;

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;

}

int mc_call_gt(const mc_aux_t *ma, double f0, int k)

{

double sum, g[3];

double max, f3[3], *pdg = ma->pdg + k * 3;

int q, i, max_i;

f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;

for (i = 0, sum = 0.; i < 3; ++i)

sum += (g[i] = pdg[i] * f3[i]);

for (i = 0, max = -1., max_i = 0; i < 3; ++i) {

g[i] /= sum;

if (g[i] > max) max = g[i], max_i = i;

}

max = 1. - max;

if (max < 1e-308) max = 1e-308;

q = (int)(-3.434 * log(max) + .499);

if (q > 99) q = 99;

return q<<2|max_i;

}

static void mc_cal_z(mc_aux_t *ma)

{

double *z[2], *tmp, *pdg;

int i, j;

z[0] = ma->z;

z[1] = ma->zswap;

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] = pdg[0]; p[1] = 2. * pdg[1]; p[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.;

// int k; for (k = 0; k <= max; ++k) printf("%d:%.3lg ", k, z[1][k]); putchar('\n');

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));

}

static double mc_add_afs(mc_aux_t *ma)

{

int k;

long double sum = 0.;

memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));

mc_cal_z(ma);

for (k = 0, sum = 0.; k <= ma->M; ++k)

sum += (long double)ma->phi[k] * ma->z[k] / ma->CMk[k];

for (k = 0; k <= ma->M; ++k) {

ma->afs1[k] = ma->phi[k] * ma->z[k] / ma->CMk[k] / sum;

if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return -1.;

}

for (k = 0, sum = 0.; k <= ma->M; ++k) {

ma->afs[k] += ma->afs1[k];

sum += k * ma->afs1[k];

}

return sum / ma->M;

}

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; rst->alt2 = ma->alt2;

// 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) {

rst->f_exp = mc_add_afs(ma);

rst->p_ref = ma->afs1[ma->M];

}

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));

}