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prob1.c

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <errno.h>
#include "prob1.h"

#include "kseq.h"
KSTREAM_INIT(gzFile, gzread, 16384)

#define MC_MAX_EM_ITER 16
#define MC_EM_EPS 1e-4
#define MC_DEF_INDEL 0.15

unsigned char seq_nt4_table[256] = {
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4 /*'-'*/, 4, 4,
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 0, 4, 1,  4, 4, 4, 2,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  3, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 0, 4, 1,  4, 4, 4, 2,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  3, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
      4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4
};

struct __bcf_p1aux_t {
      int n, M, n1, is_indel;
      double *q2p, *pdg; // pdg -> P(D|g)
      double *phi, *phi_indel;
      double *z, *zswap; // aux for afs
      double *z1, *z2, *phi1, *phi2; // only calculated when n1 is set
      double t, t1, t2;
      double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
      const uint8_t *PL; // point to PL
      int PL_len;
};

void bcf_p1_indel_prior(bcf_p1aux_t *ma, double x)
{
      int i;
      for (i = 0; i < ma->M; ++i)
            ma->phi_indel[i] = ma->phi[i] * x;
      ma->phi_indel[ma->M] = 1. - ma->phi[ma->M] * x;
}

static void init_prior(int type, double theta, int M, double *phi)
{
      int i;
      if (type == MC_PTYPE_COND2) {
            for (i = 0; i <= M; ++i)
                  phi[i] = 2. * (i + 1) / (M + 1) / (M + 2);
      } else if (type == MC_PTYPE_FLAT) {
            for (i = 0; i <= M; ++i)
                  phi[i] = 1. / (M + 1);
      } else {
            double sum;
            for (i = 0, sum = 0.; i < M; ++i)
                  sum += (phi[i] = theta / (M - i));
            phi[M] = 1. - sum;
      }
}

void bcf_p1_init_prior(bcf_p1aux_t *ma, int type, double theta)
{
      init_prior(type, theta, ma->M, ma->phi);
      bcf_p1_indel_prior(ma, MC_DEF_INDEL);
}

void bcf_p1_init_subprior(bcf_p1aux_t *ma, int type, double theta)
{
      if (ma->n1 <= 0 || ma->n1 >= ma->M) return;
      init_prior(type, theta, 2*ma->n1, ma->phi1);
      init_prior(type, theta, 2*(ma->n - ma->n1), ma->phi2);
}

int bcf_p1_read_prior(bcf_p1aux_t *ma, const char *fn)
{
      gzFile fp;
      kstring_t s;
      kstream_t *ks;
      long double sum;
      int dret, k;
      memset(&s, 0, sizeof(kstring_t));
      fp = strcmp(fn, "-")? gzopen(fn, "r") : gzdopen(fileno(stdin), "r");
      ks = ks_init(fp);
      memset(ma->phi, 0, sizeof(double) * (ma->M + 1));
      while (ks_getuntil(ks, '\n', &s, &dret) >= 0) {
            if (strstr(s.s, "[afs] ") == s.s) {
                  char *p = s.s + 6;
                  for (k = 0; k <= ma->M; ++k) {
                        int x;
                        double y;
                        x = strtol(p, &p, 10);
                        if (x != k && (errno == EINVAL || errno == ERANGE)) return -1;
                        ++p;
                        y = strtod(p, &p);
                        if (y == 0. && (errno == EINVAL || errno == ERANGE)) return -1;
                        ma->phi[ma->M - k] += y;
                  }
            }
      }
      ks_destroy(ks);
      gzclose(fp);
      free(s.s);
      for (sum = 0., k = 0; k <= ma->M; ++k) sum += ma->phi[k];
      fprintf(stderr, "[prior]");
      for (k = 0; k <= ma->M; ++k) ma->phi[k] /= sum;
      for (k = 0; k <= ma->M; ++k) fprintf(stderr, " %d:%.3lg", k, ma->phi[ma->M - k]);
      fputc('\n', stderr);
      for (sum = 0., k = 1; k < ma->M; ++k) sum += ma->phi[ma->M - k] * (2.* k * (ma->M - k) / ma->M / (ma->M - 1));
      fprintf(stderr, "[%s] heterozygosity=%lf, ", __func__, (double)sum);
      for (sum = 0., k = 1; k <= ma->M; ++k) sum += k * ma->phi[ma->M - k] / ma->M;
      fprintf(stderr, "theta=%lf\n", (double)sum);
      bcf_p1_indel_prior(ma, MC_DEF_INDEL);
      return 0;
}

bcf_p1aux_t *bcf_p1_init(int n)
{
      bcf_p1aux_t *ma;
      int i;
      ma = calloc(1, sizeof(bcf_p1aux_t));
      ma->n1 = -1;
      ma->n = n; ma->M = 2 * n;
      ma->q2p = calloc(256, sizeof(double));
      ma->pdg = calloc(3 * ma->n, sizeof(double));
      ma->phi = calloc(ma->M + 1, sizeof(double));
      ma->phi_indel = calloc(ma->M + 1, sizeof(double));
      ma->phi1 = calloc(ma->M + 1, sizeof(double));
      ma->phi2 = 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->z1 = calloc(ma->M + 1, sizeof(double)); // actually we do not need this large
      ma->z2 = calloc(ma->M + 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 < 256; ++i)
            ma->q2p[i] = pow(10., -i / 10.);
      bcf_p1_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
      return ma;
}

int bcf_p1_set_n1(bcf_p1aux_t *b, int n1)
{
      if (n1 == 0 || n1 >= b->n) return -1;
      b->n1 = n1;
      return 0;
}

void bcf_p1_destroy(bcf_p1aux_t *ma)
{
      if (ma) {
            free(ma->q2p); free(ma->pdg);
            free(ma->phi); free(ma->phi_indel); free(ma->phi1); free(ma->phi2);
            free(ma->z); free(ma->zswap); free(ma->z1); free(ma->z2);
            free(ma->afs); free(ma->afs1);
            free(ma);
      }
}

static int cal_pdg(const bcf1_t *b, bcf_p1aux_t *ma)
{
      int i, j, k;
      long *p, tmp;
      p = alloca(b->n_alleles * sizeof(long));
      memset(p, 0, sizeof(long) * b->n_alleles);
      for (j = 0; j < ma->n; ++j) {
            const uint8_t *pi = ma->PL + j * ma->PL_len;
            double *pdg = ma->pdg + j * 3;
            pdg[0] = ma->q2p[pi[b->n_alleles]]; pdg[1] = ma->q2p[pi[1]]; pdg[2] = ma->q2p[pi[0]];
            for (i = k = 0; i < b->n_alleles; ++i) {
                  p[i] += (int)pi[k];
                  k += b->n_alleles - i;
            }
      }
      for (i = 0; i < b->n_alleles; ++i) p[i] = p[i]<<4 | i;
      for (i = 1; i < b->n_alleles; ++i) // insertion sort
            for (j = i; j > 0 && p[j] < p[j-1]; --j)
                  tmp = p[j], p[j] = p[j-1], p[j-1] = tmp;
      for (i = b->n_alleles - 1; i >= 0; --i)
            if ((p[i]&0xf) == 0) break;
      return i;
}
// f0 is the reference allele frequency
static double mc_freq_iter(double f0, const bcf_p1aux_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 bcf_p1_call_gt(const bcf_p1aux_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)(-4.343 * log(max) + .499);
      if (q > 99) q = 99;
      return q<<2|max_i;
}

#define TINY 1e-20

static void mc_cal_y_core(bcf_p1aux_t *ma, int beg)
{
      double *z[2], *tmp, *pdg;
      int _j, last_min, last_max;
      z[0] = ma->z;
      z[1] = ma->zswap;
      pdg = ma->pdg;
      memset(z[0], 0, sizeof(double) * (ma->M + 1));
      memset(z[1], 0, sizeof(double) * (ma->M + 1));
      z[0][0] = 1.;
      last_min = last_max = 0;
      ma->t = 0.;
      for (_j = beg; _j < ma->n; ++_j) {
            int k, j = _j - beg, _min = last_min, _max = last_max;
            double p[3], sum;
            pdg = ma->pdg + _j * 3;
            p[0] = pdg[0]; p[1] = 2. * pdg[1]; p[2] = pdg[2];
            for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
            for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
            _max += 2;
            if (_min == 0) 
                  k = 0, z[1][k] = (2*j+2-k)*(2*j-k+1) * p[0] * z[0][k];
            if (_min <= 1)
                  k = 1, z[1][k] = (2*j+2-k)*(2*j-k+1) * p[0] * z[0][k] + k*(2*j+2-k) * p[1] * z[0][k-1];
            for (k = _min < 2? 2 : _min; k <= _max; ++k)
                  z[1][k] = (2*j+2-k)*(2*j-k+1) * p[0] * z[0][k]
                        + k*(2*j+2-k) * p[1] * z[0][k-1]
                        + k*(k-1)* p[2] * z[0][k-2];
            for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
            ma->t += log(sum / ((2. * j + 2) * (2. * j + 1)));
            for (k = _min; k <= _max; ++k) z[1][k] /= sum;
            if (_min >= 1) z[1][_min-1] = 0.;
            if (_min >= 2) z[1][_min-2] = 0.;
            if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
            if (_j == ma->n1 - 1) { // set pop1
                  ma->t1 = ma->t;
                  memcpy(ma->z1, z[1], sizeof(double) * (ma->n1 * 2 + 1));
            }
            tmp = z[0]; z[0] = z[1]; z[1] = tmp;
            last_min = _min; last_max = _max;
      }
      if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (ma->M + 1));
}

static void mc_cal_y(bcf_p1aux_t *ma)
{
      if (ma->n1 > 0 && ma->n1 < ma->n) {
            int k;
            long double x;
            memset(ma->z1, 0, sizeof(double) * (2 * ma->n1 + 1));
            memset(ma->z2, 0, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
            ma->t1 = ma->t2 = 0.;
            mc_cal_y_core(ma, ma->n1);
            ma->t2 = ma->t;
            memcpy(ma->z2, ma->z, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
            mc_cal_y_core(ma, 0);
            // rescale z
            x = expl(ma->t - (ma->t1 + ma->t2));
            for (k = 0; k <= ma->M; ++k) ma->z[k] *= x;
      } else mc_cal_y_core(ma, 0);
}

static void contrast(bcf_p1aux_t *ma, double pc[4]) // mc_cal_y() must be called before hand
{
      int k, n1 = ma->n1, n2 = ma->n - ma->n1;
      long double sum1, sum2;
      pc[0] = pc[1] = pc[2] = pc[3] = -1.;
      if (n1 <= 0 || n2 <= 0) return;
      for (k = 0, sum1 = 0.; k <= 2*n1; ++k) sum1 += ma->phi1[k] * ma->z1[k];
      for (k = 0, sum2 = 0.; k <= 2*n2; ++k) sum2 += ma->phi2[k] * ma->z2[k];
      pc[2] = ma->phi1[2*n1] * ma->z1[2*n1] / sum1;
      pc[3] = ma->phi2[2*n2] * ma->z2[2*n2] / sum2;
      for (k = 2; k < 4; ++k) {
            pc[k] = pc[k] > .5? -(-4.343 * log(1. - pc[k] + TINY) + .499) : -4.343 * log(pc[k] + TINY) + .499;
            pc[k] = (int)pc[k];
            if (pc[k] > 99) pc[k] = 99;
            if (pc[k] < -99) pc[k] = -99;
      }
      pc[0] = ma->phi2[2*n2] * ma->z2[2*n2] / sum2 * (1. - ma->phi1[2*n1] * ma->z1[2*n1] / sum1);
      pc[1] = ma->phi1[2*n1] * ma->z1[2*n1] / sum1 * (1. - ma->phi2[2*n2] * ma->z2[2*n2] / sum2);
      pc[0] = pc[0] == 1.? 99 : (int)(-4.343 * log(1. - pc[0]) + .499);
      pc[1] = pc[1] == 1.? 99 : (int)(-4.343 * log(1. - pc[1]) + .499);
}

static double mc_cal_afs(bcf_p1aux_t *ma)
{
      int k;
      long double sum = 0.;
      double *phi = ma->is_indel? ma->phi_indel : ma->phi;
      memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));
      mc_cal_y(ma);
      for (k = 0, sum = 0.; k <= ma->M; ++k)
            sum += (long double)phi[k] * ma->z[k];
      for (k = 0; k <= ma->M; ++k) {
            ma->afs1[k] = phi[k] * ma->z[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;
}

long double bcf_p1_cal_g3(bcf_p1aux_t *p1a, double g[3])
{
      long double pd = 0., g2[3];
      int i, k;
      memset(g2, 0, sizeof(long double) * 3);
      for (k = 0; k < p1a->M; ++k) {
            double f = (double)k / p1a->M, f3[3], g1[3];
            long double z = 1.;
            g1[0] = g1[1] = g1[2] = 0.;
            f3[0] = (1. - f) * (1. - f); f3[1] = 2. * f * (1. - f); f3[2] = f * f;
            for (i = 0; i < p1a->n; ++i) {
                  double *pdg = p1a->pdg + i * 3;
                  double x = pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2];
                  z *= x;
                  g1[0] += pdg[0] * f3[0] / x;
                  g1[1] += pdg[1] * f3[1] / x;
                  g1[2] += pdg[2] * f3[2] / x;
            }
            pd += p1a->phi[k] * z;
            for (i = 0; i < 3; ++i)
                  g2[i] += p1a->phi[k] * z * g1[i];
      }
      for (i = 0; i < 3; ++i) g[i] = g2[i] / pd;
      return pd;
}

int bcf_p1_cal(bcf1_t *b, bcf_p1aux_t *ma, bcf_p1rst_t *rst)
{
      int i, k;
      long double sum = 0.;
      ma->is_indel = bcf_is_indel(b);
      // set PL and PL_len
      for (i = 0; i < b->n_gi; ++i) {
            if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
                  ma->PL = (uint8_t*)b->gi[i].data;
                  ma->PL_len = b->gi[i].len;
                  break;
            }
      }
      if (b->n_alleles < 2) return -1; // FIXME: find a better solution
      // 
      rst->rank0 = cal_pdg(b, ma);
      rst->f_exp = mc_cal_afs(ma);
      rst->p_ref = ma->afs1[ma->M];
      // calculate f_flat and f_em
      for (k = 0, sum = 0.; k <= ma->M; ++k)
            sum += (long double)ma->z[k];
      rst->f_flat = 0.;
      for (k = 0; k <= ma->M; ++k) {
            double p = ma->z[k] / sum;
            rst->f_flat += k * p;
      }
      rst->f_flat /= ma->M;
      { // calculate f_em
            double flast = rst->f_flat;
            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;
            }
      }
      { // estimate equal-tail credible interval (95% level)
            int l, h;
            double p;
            for (i = 0, p = 0.; i < ma->M; ++i)
                  if (p + ma->afs1[i] > 0.025) break;
                  else p += ma->afs1[i];
            l = i;
            for (i = ma->M-1, p = 0.; i >= 0; --i)
                  if (p + ma->afs1[i] > 0.025) break;
                  else p += ma->afs1[i];
            h = i;
            rst->cil = (double)(ma->M - h) / ma->M; rst->cih = (double)(ma->M - l) / ma->M;
      }
      rst->g[0] = rst->g[1] = rst->g[2] = -1.;
      contrast(ma, rst->pc);
      return 0;
}

void bcf_p1_dump_afs(bcf_p1aux_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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