#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "bcf.h"
#include "kmin.h"
static double g_q2p[256];
#define ITER_MAX 50
#define ITER_TRY 10
#define EPS 1e-5
extern double kf_gammaq(double, double);
/*
Generic routines
*/
// get the 3 genotype likelihoods
static double *get_pdg3(const bcf1_t *b)
{
double *pdg;
const uint8_t *PL = 0;
int i, PL_len = 0;
// initialize g_q2p if necessary
if (g_q2p[0] == 0.)
for (i = 0; i < 256; ++i)
g_q2p[i] = pow(10., -i / 10.);
// set PL and PL_len
for (i = 0; i < b->n_gi; ++i) {
if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
PL = (const uint8_t*)b->gi[i].data;
PL_len = b->gi[i].len;
break;
}
}
if (i == b->n_gi) return 0; // no PL
// fill pdg
pdg = malloc(3 * b->n_smpl * sizeof(double));
for (i = 0; i < b->n_smpl; ++i) {
const uint8_t *pi = PL + i * PL_len;
double *p = pdg + i * 3;
p[0] = g_q2p[pi[2]]; p[1] = g_q2p[pi[1]]; p[2] = g_q2p[pi[0]];
}
return pdg;
}
// estimate site allele frequency in a very naive and inaccurate way
static double est_freq(int n, const double *pdg)
{
int i, gcnt[3], tmp1;
// get a rough estimate of the genotype frequency
gcnt[0] = gcnt[1] = gcnt[2] = 0;
for (i = 0; i < n; ++i) {
const double *p = pdg + i * 3;
if (p[0] != 1. || p[1] != 1. || p[2] != 1.) {
int which = p[0] > p[1]? 0 : 1;
which = p[which] > p[2]? which : 2;
++gcnt[which];
}
}
tmp1 = gcnt[0] + gcnt[1] + gcnt[2];
return (tmp1 == 0)? -1.0 : (.5 * gcnt[1] + gcnt[2]) / tmp1;
}
/*
Single-locus EM
*/
typedef struct {
int beg, end;
const double *pdg;
} minaux1_t;
static double prob1(double f, void *data)
{
minaux1_t *a = (minaux1_t*)data;
double p = 1., l = 0., f3[3];
int i;
// printf("brent %lg\n", f);
if (f < 0 || f > 1) return 1e300;
f3[0] = (1.-f)*(1.-f); f3[1] = 2.*f*(1.-f); f3[2] = f*f;
for (i = a->beg; i < a->end; ++i) {
const double *pdg = a->pdg + i * 3;
p *= pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2];
if (p < 1e-200) l -= log(p), p = 1.;
}
return l - log(p);
}
// one EM iteration for allele frequency estimate
static double freq_iter(double *f, const double *_pdg, int beg, int end)
{
double f0 = *f, f3[3], err;
int i;
// printf("em %lg\n", *f);
f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
for (i = beg, f0 = 0.; i < end; ++i) {
const double *pdg = _pdg + i * 3;
f0 += (pdg[1] * f3[1] + 2. * pdg[2] * f3[2])
/ (pdg[0] * f3[0] + pdg[1] * f3[1] + pdg[2] * f3[2]);
}
f0 /= (end - beg) * 2;
err = fabs(f0 - *f);
*f = f0;
return err;
}
/* The following function combines EM and Brent's method. When the signal from
* the data is strong, EM is faster but sometimes, EM may converge very slowly.
* When this happens, we switch to Brent's method. The idea is learned from
* Rasmus Nielsen.
*/
static double freqml(double f0, int beg, int end, const double *pdg)
{
int i;
double f;
for (i = 0, f = f0; i < ITER_TRY; ++i)
if (freq_iter(&f, pdg, beg, end) < EPS) break;
if (i == ITER_TRY) { // haven't converged yet; try Brent's method
minaux1_t a;
a.beg = beg; a.end = end; a.pdg = pdg;
kmin_brent(prob1, f0 == f? .5*f0 : f0, f, (void*)&a, EPS, &f);
}
return f;
}
// one EM iteration for genotype frequency estimate
static double g3_iter(double g[3], const double *_pdg, int beg, int end)
{
double err, gg[3];
int i;
gg[0] = gg[1] = gg[2] = 0.;
// printf("%lg,%lg,%lg\n", g[0], g[1], g[2]);
for (i = beg; i < end; ++i) {
double sum, tmp[3];
const double *pdg = _pdg + i * 3;
tmp[0] = pdg[0] * g[0]; tmp[1] = pdg[1] * g[1]; tmp[2] = pdg[2] * g[2];
sum = (tmp[0] + tmp[1] + tmp[2]) * (end - beg);
gg[0] += tmp[0] / sum; gg[1] += tmp[1] / sum; gg[2] += tmp[2] / sum;
}
err = fabs(gg[0] - g[0]) > fabs(gg[1] - g[1])? fabs(gg[0] - g[0]) : fabs(gg[1] - g[1]);
err = err > fabs(gg[2] - g[2])? err : fabs(gg[2] - g[2]);
g[0] = gg[0]; g[1] = gg[1]; g[2] = gg[2];
return err;
}
// perform likelihood ratio test
static double lk_ratio_test(int n, int n1, const double *pdg, double f3[3][3])
{
double r;
int i;
for (i = 0, r = 1.; i < n1; ++i) {
const double *p = pdg + i * 3;
r *= (p[0] * f3[1][0] + p[1] * f3[1][1] + p[2] * f3[1][2])
/ (p[0] * f3[0][0] + p[1] * f3[0][1] + p[2] * f3[0][2]);
}
for (; i < n; ++i) {
const double *p = pdg + i * 3;
r *= (p[0] * f3[2][0] + p[1] * f3[2][1] + p[2] * f3[2][2])
/ (p[0] * f3[0][0] + p[1] * f3[0][1] + p[2] * f3[0][2]);
}
return r;
}
// x[0]: ref frequency
// x[1..3]: alt-alt, alt-ref, ref-ref frequenc
// x[4]: HWE P-value
// x[5..6]: group1 freq, group2 freq
// x[7]: 1-degree P-value
// x[8]: 2-degree P-value
int bcf_em1(const bcf1_t *b, int n1, int flag, double x[10])
{
double *pdg;
int i, n, n2;
if (b->n_alleles < 2) return -1; // one allele only
// initialization
if (n1 < 0 || n1 > b->n_smpl) n1 = 0;
if (flag & 1<<7) flag |= 7<<5; // compute group freq if LRT is required
if (flag & 0xf<<1) flag |= 0xf<<1;
n = b->n_smpl; n2 = n - n1;
pdg = get_pdg3(b);
if (pdg == 0) return -1;
for (i = 0; i < 10; ++i) x[i] = -1.; // set to negative
{
if ((x[0] = est_freq(n, pdg)) < 0.) {
free(pdg);
return -1; // no data
}
x[0] = freqml(x[0], 0, n, pdg);
}
if (flag & (0xf<<1|3<<8)) { // estimate the genotype frequency and test HWE
double *g = x + 1, f3[3], r;
f3[0] = g[0] = (1 - x[0]) * (1 - x[0]);
f3[1] = g[1] = 2 * x[0] * (1 - x[0]);
f3[2] = g[2] = x[0] * x[0];
for (i = 0; i < ITER_MAX; ++i)
if (g3_iter(g, pdg, 0, n) < EPS) break;
// Hardy-Weinberg equilibrium (HWE)
for (i = 0, r = 1.; i < n; ++i) {
double *p = pdg + i * 3;
r *= (p[0] * g[0] + p[1] * g[1] + p[2] * g[2]) / (p[0] * f3[0] + p[1] * f3[1] + p[2] * f3[2]);
}
x[4] = kf_gammaq(.5, log(r));
}
if ((flag & 7<<5) && n1 > 0 && n1 < n) { // group frequency
x[5] = freqml(x[0], 0, n1, pdg);
x[6] = freqml(x[0], n1, n, pdg);
}
if ((flag & 1<<7) && n1 > 0 && n1 < n) { // 1-degree P-value
double f[3], f3[3][3], tmp;
f[0] = x[0]; f[1] = x[5]; f[2] = x[6];
for (i = 0; i < 3; ++i)
f3[i][0] = (1-f[i])*(1-f[i]), f3[i][1] = 2*f[i]*(1-f[i]), f3[i][2] = f[i]*f[i];
tmp = log(lk_ratio_test(n, n1, pdg, f3));
if (tmp < 0) tmp = 0;
x[7] = kf_gammaq(.5, tmp);
}
if ((flag & 3<<8) && n1 > 0 && n1 < n) { // 2-degree P-value
double g[3][3], tmp;
for (i = 0; i < 3; ++i) memcpy(g[i], x + 1, 3 * sizeof(double));
for (i = 0; i < ITER_MAX; ++i)
if (g3_iter(g[1], pdg, 0, n1) < EPS) break;
for (i = 0; i < ITER_MAX; ++i)
if (g3_iter(g[2], pdg, n1, n) < EPS) break;
tmp = log(lk_ratio_test(n, n1, pdg, g));
if (tmp < 0) tmp = 0;
x[8] = kf_gammaq(1., tmp);
}
// free
free(pdg);
return 0;
}
/*
Two-locus EM (LD)
*/
#define _G1(h, k) ((h>>1&1) + (k>>1&1))
#define _G2(h, k) ((h&1) + (k&1))
// 0: the previous site; 1: the current site
static int pair_freq_iter(int n, double *pdg[2], double f[4])
{
double ff[4];
int i, k, h;
// printf("%lf,%lf,%lf,%lf\n", f[0], f[1], f[2], f[3]);
memset(ff, 0, 4 * sizeof(double));
for (i = 0; i < n; ++i) {
double *p[2], sum, tmp;
p[0] = pdg[0] + i * 3; p[1] = pdg[1] + i * 3;
for (k = 0, sum = 0.; k < 4; ++k)
for (h = 0; h < 4; ++h)
sum += f[k] * f[h] * p[0][_G1(k,h)] * p[1][_G2(k,h)];
for (k = 0; k < 4; ++k) {
tmp = f[0] * (p[0][_G1(0,k)] * p[1][_G2(0,k)] + p[0][_G1(k,0)] * p[1][_G2(k,0)])
+ f[1] * (p[0][_G1(1,k)] * p[1][_G2(1,k)] + p[0][_G1(k,1)] * p[1][_G2(k,1)])
+ f[2] * (p[0][_G1(2,k)] * p[1][_G2(2,k)] + p[0][_G1(k,2)] * p[1][_G2(k,2)])
+ f[3] * (p[0][_G1(3,k)] * p[1][_G2(3,k)] + p[0][_G1(k,3)] * p[1][_G2(k,3)]);
ff[k] += f[k] * tmp / sum;
}
}
for (k = 0; k < 4; ++k) f[k] = ff[k] / (2 * n);
return 0;
}
double bcf_pair_freq(const bcf1_t *b0, const bcf1_t *b1, double f[4])
{
const bcf1_t *b[2];
int i, j, n_smpl;
double *pdg[2], flast[4], r, f0[2];
// initialize others
if (b0->n_smpl != b1->n_smpl) return -1; // different number of samples
n_smpl = b0->n_smpl;
b[0] = b0; b[1] = b1;
f[0] = f[1] = f[2] = f[3] = -1.;
if (b[0]->n_alleles < 2 || b[1]->n_alleles < 2) return -1; // one allele only
pdg[0] = get_pdg3(b0); pdg[1] = get_pdg3(b1);
if (pdg[0] == 0 || pdg[1] == 0) {
free(pdg[0]); free(pdg[1]);
return -1;
}
// set the initial value
f0[0] = est_freq(n_smpl, pdg[0]);
f0[1] = est_freq(n_smpl, pdg[1]);
f[0] = (1 - f0[0]) * (1 - f0[1]); f[3] = f0[0] * f0[1];
f[1] = (1 - f0[0]) * f0[1]; f[2] = f0[0] * (1 - f0[1]);
// iteration
for (j = 0; j < ITER_MAX; ++j) {
double eps = 0;
memcpy(flast, f, 4 * sizeof(double));
pair_freq_iter(n_smpl, pdg, f);
for (i = 0; i < 4; ++i) {
double x = fabs(f[i] - flast[i]);
if (x > eps) eps = x;
}
if (eps < EPS) break;
}
// free
free(pdg[0]); free(pdg[1]);
{ // calculate r^2
double p[2], q[2], D;
p[0] = f[0] + f[1]; q[0] = 1 - p[0];
p[1] = f[0] + f[2]; q[1] = 1 - p[1];
D = f[0] * f[3] - f[1] * f[2];
r = sqrt(D * D / (p[0] * p[1] * q[0] * q[1]));
// printf("R(%lf,%lf,%lf,%lf)=%lf\n", f[0], f[1], f[2], f[3], r);
if (isnan(r)) r = -1.;
}
return r;
}
