prob1.c

/*  prob1.c -- mathematical utility functions.

    Copyright (C) 2010, 2011 Broad Institute.
    Copyright (C) 2012, 2013 Genome Research Ltd.

    Author: Heng Li <lh3@sanger.ac.uk>

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.  */

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

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

#define MC_MAX_EM_ITER 16
#define MC_EM_EPS 1e-5
#define MC_DEF_INDEL 0.15

gzFile bcf_p1_fp_lk;

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);
}


/* Initialise a bcf_p1aux_t */
bcf_p1aux_t *bcf_p1_init(int n_smpl, uint8_t *ploidy)
{
    bcf_p1aux_t *ma;
    int i;
    ma = (bcf_p1aux_t*) calloc(1, sizeof(bcf_p1aux_t));
    ma->n1 = -1;
    ma->n = n_smpl;
    ma->M = 2 * n_smpl;
    if (ploidy) {
        ma->ploidy = (uint8_t*) malloc(n_smpl);
        memcpy(ma->ploidy, ploidy, n_smpl);
        for (i = 0, ma->M = 0; i < n_smpl; ++i) ma->M += ploidy[i];
        if (ma->M == 2 * n_smpl) {
            free(ma->ploidy);
            ma->ploidy = 0;
        }
    }
    ma->q2p = (double*) calloc(256, sizeof(double));
    ma->pdg = (double*) calloc(3 * ma->n, sizeof(double));
    ma->phi = (double*) calloc(ma->M + 1, sizeof(double));
    ma->phi_indel = (double*) calloc(ma->M + 1, sizeof(double));
    ma->phi1 = (double*) calloc(ma->M + 1, sizeof(double));
    ma->phi2 = (double*) calloc(ma->M + 1, sizeof(double));
    ma->z = (double*) calloc(ma->M + 1, sizeof(double));
    ma->zswap = (double*) calloc(ma->M + 1, sizeof(double));
    ma->z1 = (double*) calloc(ma->M + 1, sizeof(double)); // actually we do not need this large
    ma->z2 = (double*) calloc(ma->M + 1, sizeof(double));
    ma->afs = (double*) calloc(ma->M + 1, sizeof(double));
    ma->afs1 = (double*) calloc(ma->M + 1, sizeof(double));
    ma->lf = (double*) calloc(ma->M + 1, sizeof(double));
    for (i = 0; i < 256; ++i)
        ma->q2p[i] = pow(10., -i / 10.);
    for (i = 0; i <= ma->M; ++i) ma->lf[i] = lgamma(i + 1);
    bcf_p1_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
    return ma;
}

int bcf_p1_get_M(bcf_p1aux_t *b) { return b->M; }

int bcf_p1_set_n1(bcf_p1aux_t *b, int n1)
{
    if (n1 == 0 || n1 >= b->n) return -1;
    if (b->M != b->n * 2) {
        fprintf(stderr, "[%s] unable to set `n1' when there are haploid samples.\n", __func__);
        return -1;
    }
    b->n1 = n1;
    return 0;
}

void bcf_p1_destroy(bcf_p1aux_t *ma)
{
    if (ma) {
        int k;
        free(ma->lf);
        if (ma->hg && ma->n1 > 0) {
            for (k = 0; k <= 2*ma->n1; ++k) free(ma->hg[k]);
            free(ma->hg);
        }
        free(ma->ploidy); 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);
    }
}

extern double kf_gammap(double s, double z);
int test16(bcf1_t *b, anno16_t *a);

/* Calculate P(D|g) */
static int cal_pdg(const bcf1_t *b, bcf_p1aux_t *ma)
{
    int i, j;
    long p_a[16], *p=p_a, tmp;
    if (b->n_allele > 16)
        p = (long*) malloc(b->n_allele * sizeof(long));
    memset(p, 0, sizeof(long) * b->n_allele);

    // Set P(D|g) for each sample and sum phread likelihoods across all samples to create lk
    for (j = 0; j < ma->n; ++j) {
        // Fetch the PL array for the sample
        const int *pi = ma->PL + j * ma->PL_len;
        // Fetch the P(D|g) array for the sample
        double *pdg = ma->pdg + j * 3;
        pdg[0] = ma->q2p[pi[2]]; pdg[1] = ma->q2p[pi[1]]; pdg[2] = ma->q2p[pi[0]];
        for (i = 0; i < b->n_allele; ++i)
            p[i] += (int)pi[(i+1)*(i+2)/2-1];
    }
    for (i = 0; i < b->n_allele; ++i) p[i] = p[i]<<4 | i;
    for (i = 1; i < b->n_allele; ++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_allele - 1; i >= 0; --i)
        if ((p[i]&0xf) == 0) break;
    if (p != p_a)
        free(p);
    return i;
}


/* f0 is freq of the ref allele */
int bcf_p1_call_gt(const bcf_p1aux_t *ma, double f0, int k, int is_var)
{
    double sum, g[3];
    double max, f3[3], *pdg = ma->pdg + k * 3;
    int q, i, max_i, ploidy;
    /* determine ploidy */
    ploidy = ma->ploidy? ma->ploidy[k] : 2;
    if (ploidy == 2) {
    /* given allele frequency we can determine how many of each
     * genotype we have by HWE p=1-q PP=p^2 PQ&QP=2*p*q QQ=q^2 */
        f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
    } else {
        f3[0] = 1. - f0; f3[1] = 0; f3[2] = f0;
    }
    for (i = 0, sum = 0.; i < 3; ++i)
        sum += (g[i] = pdg[i] * f3[i]);
    /* normalise g and then determine max */
    for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
        g[i] /= sum;
        if (g[i] > max) max = g[i], max_i = i;
    }
    if ( !is_var ) { max_i = 2; max = g[2]; }   // force 0/0 genotype if the site is non-variant
    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;
}

// If likelihoods fall below this they get squashed to 0
#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;
    assert(beg == 0 || ma->M == ma->n*2);
    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.;
    if (ma->M == ma->n * 2) {
        int M = 0;
        for (_j = beg; _j < ma->n; ++_j) {
            int k, j = _j - beg, _min = last_min, _max = last_max, M0;
            double p[3], sum;
            M0 = M; M += 2;
            // Fetch P(D|g) for this sample
            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] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
            if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
            for (k = _min < 2? 2 : _min; k <= _max; ++k)
                z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * 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 / (M * (M - 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 we are not on the last sample
            if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
            if (_j == ma->n1 - 1) { // set pop1; ma->n1==-1 when unset
                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;
        }
        //for (_j = 0; _j < last_min; ++_j) z[0][_j] = 0.; // TODO: are these necessary?
        //for (_j = last_max + 1; _j < ma->M; ++_j) z[0][_j] = 0.;
    } else { // this block is very similar to the block above; these two might be merged in future
        int j, M = 0;
        for (j = 0; j < ma->n; ++j) {
            int k, M0, _min = last_min, _max = last_max;
            double p[3], sum;
            // Fetch P(D|g) for this sample
            pdg = ma->pdg + j * 3;
            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.;
            M0 = M;
            M += ma->ploidy[j];
            if (ma->ploidy[j] == 1) {
                p[0] = pdg[0]; p[1] = pdg[2];
                _max++;
                if (_min == 0) k = 0, z[1][k] = (M0+1-k) * p[0] * z[0][k];
                for (k = _min < 1? 1 : _min; k <= _max; ++k)
                    z[1][k] = (M0+1-k) * p[0] * z[0][k] + k * p[1] * z[0][k-1];
                for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
                ma->t += log(sum / M);
                for (k = _min; k <= _max; ++k) z[1][k] /= sum;
                if (_min >= 1) z[1][_min-1] = 0.;
                // If we are not on the last sample
                if (j < ma->n - 1) z[1][_max+1] = 0.;
            } else if (ma->ploidy[j] == 2) {
                p[0] = pdg[0]; p[1] = 2 * pdg[1]; p[2] = pdg[2];
                _max += 2;
                if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
                if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
                for (k = _min < 2? 2 : _min; k <= _max; ++k)
                    z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * 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 / (M * (M - 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 we are not on the last sample
                if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
            }
            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));
    if (bcf_p1_fp_lk)
        gzwrite(bcf_p1_fp_lk, ma->z, sizeof(double) * (ma->M + 1));
}

static void mc_cal_y(bcf_p1aux_t *ma)
{
    if (ma->n1 > 0 && ma->n1 < ma->n && ma->M == ma->n * 2) { // NB: ma->n1 is ineffective when there are haploid samples
        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);
}

#define CONTRAST_TINY 1e-30

extern double kf_gammaq(double s, double z); // incomplete gamma function for chi^2 test

static inline double chi2_test(int a, int b, int c, int d)
{
    double x, z;
    x = (double)(a+b) * (c+d) * (b+d) * (a+c);
    if (x == 0.) return 1;
    z = a * d - b * c;
    return kf_gammaq(.5, .5 * z * z * (a+b+c+d) / x);
}

// chi2=(a+b+c+d)(ad-bc)^2/[(a+b)(c+d)(a+c)(b+d)]
static inline double contrast2_aux(const bcf_p1aux_t *p1, double sum, int k1, int k2, double x[3])
{
    double p = p1->phi[k1+k2] * p1->z1[k1] * p1->z2[k2] / sum * p1->hg[k1][k2];
    int n1 = p1->n1, n2 = p1->n - p1->n1;
    if (p < CONTRAST_TINY) return -1;
    if (.5*k1/n1 < .5*k2/n2) x[1] += p;
    else if (.5*k1/n1 > .5*k2/n2) x[2] += p;
    else x[0] += p;
    return p * chi2_test(k1, k2, (n1<<1) - k1, (n2<<1) - k2);
}

static double contrast2(bcf_p1aux_t *p1, double ret[3])
{
    int k, k1, k2, k10, k20, n1, n2;
    double sum;
    // get n1 and n2
    n1 = p1->n1; n2 = p1->n - p1->n1;
    if (n1 <= 0 || n2 <= 0) return 0.;
    if (p1->hg == 0) { // initialize the hypergeometric distribution
        /* NB: the hg matrix may take a lot of memory when there are many samples. There is a way
           to avoid precomputing this matrix, but it is slower and quite intricate. The following
           computation in this block can be accelerated with a similar strategy, but perhaps this
           is not a serious concern for now. */
        double tmp = lgamma(2*(n1+n2)+1) - (lgamma(2*n1+1) + lgamma(2*n2+1));
        p1->hg = (double**) calloc(2*n1+1, sizeof(double*));
        for (k1 = 0; k1 <= 2*n1; ++k1) {
            p1->hg[k1] = (double*)calloc(2*n2+1, sizeof(double));
            for (k2 = 0; k2 <= 2*n2; ++k2)
                p1->hg[k1][k2] = exp(lgamma(k1+k2+1) + lgamma(p1->M-k1-k2+1) - (lgamma(k1+1) + lgamma(k2+1) + lgamma(2*n1-k1+1) + lgamma(2*n2-k2+1) + tmp));
        }
    }
    { // compute
        long double suml = 0;
        for (k = 0; k <= p1->M; ++k) suml += p1->phi[k] * p1->z[k];
        sum = suml;
    }
    { // get the max k1 and k2
        double max;
        int max_k;
        for (k = 0, max = 0, max_k = -1; k <= 2*n1; ++k) {
            double x = p1->phi1[k] * p1->z1[k];
            if (x > max) max = x, max_k = k;
        }
        k10 = max_k;
        for (k = 0, max = 0, max_k = -1; k <= 2*n2; ++k) {
            double x = p1->phi2[k] * p1->z2[k];
            if (x > max) max = x, max_k = k;
        }
        k20 = max_k;
    }
    { // We can do the following with one nested loop, but that is an O(N^2) thing. The following code block is much faster for large N.
        double x[3], y;
        long double z = 0., L[2];
        x[0] = x[1] = x[2] = 0; L[0] = L[1] = 0;
        for (k1 = k10; k1 >= 0; --k1) {
            for (k2 = k20; k2 >= 0; --k2) {
                if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
                else z += y;
            }
            for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
                if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
                else z += y;
            }
        }
        ret[0] = x[0]; ret[1] = x[1]; ret[2] = x[2];
        x[0] = x[1] = x[2] = 0;
        for (k1 = k10 + 1; k1 <= 2*n1; ++k1) {
            for (k2 = k20; k2 >= 0; --k2) {
                if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
                else z += y;
            }
            for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
                if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
                else z += y;
            }
        }
        ret[0] += x[0]; ret[1] += x[1]; ret[2] += x[2];
        if (ret[0] + ret[1] + ret[2] < 0.95) { // in case of bad things happened
            ret[0] = ret[1] = ret[2] = 0; L[0] = L[1] = 0;
            for (k1 = 0, z = 0.; k1 <= 2*n1; ++k1)
                for (k2 = 0; k2 <= 2*n2; ++k2)
                    if ((y = contrast2_aux(p1, sum, k1, k2, ret)) >= 0) z += y;
            if (ret[0] + ret[1] + ret[2] < 0.95) // It seems that this may be caused by floating point errors. I do not really understand why...
                z = 1.0, ret[0] = ret[1] = ret[2] = 1./3;
        }
        return (double)z;
    }
}

static double mc_cal_afs(bcf_p1aux_t *ma, double *p_ref_folded, double *p_var_folded)
{
    int k;
    long double sum = 0., sum2;
    double *phi = ma->is_indel? ma->phi_indel : ma->phi;
    memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));
    mc_cal_y(ma);
    // compute AFS
    // MP15: is this using equation 20 from doi:10.1093/bioinformatics/btr509?
    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.;
    }
    // compute folded variant probability
    for (k = 0, sum = 0.; k <= ma->M; ++k)
        sum += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
    for (k = 1, sum2 = 0.; k < ma->M; ++k)
        sum2 += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
    *p_var_folded = sum2 / sum;
    *p_ref_folded = (phi[k] + phi[ma->M - k]) / 2. * (ma->z[ma->M] + ma->z[0]) / sum;
    // the expected frequency
    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 bcf_p1_cal(call_t *call, bcf1_t *b, int do_contrast, bcf_p1aux_t *ma, bcf_p1rst_t *rst)
{
    int i, k;
    long double sum = 0.;
    ma->is_indel = bcf_is_snp(b) ? 0 : 1;
    rst->perm_rank = -1;

    ma->PL = call->PLs;
    ma->PL_len = call->nPLs / b->n_sample;
    if (b->n_allele < 2) return -1; // FIXME: find a better solution

    rst->rank0 = cal_pdg(b, ma);
    rst->f_exp = mc_cal_afs(ma, &rst->p_ref_folded, &rst->p_var_folded);
    rst->p_ref = ma->afs1[ma->M];
    for (k = 0, sum = 0.; k < ma->M; ++k)
        sum += ma->afs1[k];
    rst->p_var = (double)sum;
    { // compute the allele count
        double max = -1;
        rst->ac = -1;
        for (k = 0; k <= ma->M; ++k)
            if (max < ma->z[k]) max = ma->z[k], rst->ac = k;
        rst->ac = ma->M - rst->ac;
    }
    // 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;
    { // 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, 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;
    }
    if (ma->n1 > 0) { // compute LRT
        double max0, max1, max2;
        for (k = 0, max0 = -1; k <= ma->M; ++k)
            if (max0 < ma->z[k]) max0 = ma->z[k];
        for (k = 0, max1 = -1; k <= ma->n1 * 2; ++k)
            if (max1 < ma->z1[k]) max1 = ma->z1[k];
        for (k = 0, max2 = -1; k <= ma->M - ma->n1 * 2; ++k)
            if (max2 < ma->z2[k]) max2 = ma->z2[k];
        rst->lrt = log(max1 * max2 / max0);
        rst->lrt = rst->lrt < 0? 1 : kf_gammaq(.5, rst->lrt);
    } else rst->lrt = -1.0;
    rst->cmp[0] = rst->cmp[1] = rst->cmp[2] = rst->p_chi2 = -1.0;
    if (do_contrast && rst->p_var > 0.5) // skip contrast2() if the locus is a strong non-variant
        rst->p_chi2 = contrast2(ma, rst->cmp);
    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));
}