/*  errmod.c -- revised MAQ error model.

    Copyright (C) 2010 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 "errmod.h"
#include "htslib/ksort.h"
KSORT_INIT_GENERIC(uint16_t)

/* table of constants generated for given depcorr and eta */
typedef struct __errmod_coef_t {
    double *fk, *beta, *lhet;
} errmod_coef_t;

typedef struct {
    double fsum[16], bsum[16];
    uint32_t c[16];
} call_aux_t;

/* \Gamma(n) = (n-1)! */
#define lfact(n) lgamma(n+1)

/* generates a success * trials table of bionomial probability densities (log transformed) */
static double* logbinomial_table( const int n_size )
{
    /* prob distribution for binom var is p(k) = {n! \over k! (n-k)! } p^k (1-p)^{n-k} */
    /* this calcs p(k) = {log(n!) - log(k!) - log((n-k)!) */
    int k, n;
    double *logbinom = (double*)calloc(n_size * n_size, sizeof(double));
    for (n = 1; n < n_size; ++n) {
        double lfn = lfact(n);
        for (k = 1; k <= n; ++k)
            logbinom[n<<8|k] = lfn - lfact(k) - lfact(n-k);
    }
    return logbinom;
}

static errmod_coef_t *cal_coef(double depcorr, double eta)
{
    int k, n, q;
    long double sum, sum1;
    double *lC;
    errmod_coef_t *ec;

    ec = calloc(1, sizeof(errmod_coef_t));
    // initialize ->fk
    ec->fk = (double*)calloc(256, sizeof(double));
    ec->fk[0] = 1.0;
    for (n = 1; n != 256; ++n)
        ec->fk[n] = pow(1. - depcorr, n) * (1.0 - eta) + eta;
    // initialize ->coef
    ec->beta = (double*)calloc(256 * 256 * 64, sizeof(double));

    lC = logbinomial_table( 256 );

    for (q = 1; q != 64; ++q) {
        double e = pow(10.0, -q/10.0);
        double le = log(e);
        double le1 = log(1.0 - e);
        for (n = 1; n <= 255; ++n) {
            double *beta = ec->beta + (q<<16|n<<8);
            sum1 = sum = 0.0;
            for (k = n; k >= 0; --k, sum1 = sum) {
                sum = sum1 + expl(lC[n<<8|k] + k*le + (n-k)*le1);
                beta[k] = -10. / M_LN10 * logl(sum1 / sum);
            }
        }
    }
    // initialize ->lhet
    ec->lhet = (double*)calloc(256 * 256, sizeof(double));
    for (n = 0; n < 256; ++n)
        for (k = 0; k < 256; ++k)
            ec->lhet[n<<8|k] = lC[n<<8|k] - M_LN2 * n;
    free(lC);
    return ec;
}

/**
 * Create errmod_t object with obj.depcorr set to depcorr and initialise
 */
errmod_t *errmod_init(double depcorr)
{
    errmod_t *em;
    em = (errmod_t*)calloc(1, sizeof(errmod_t));
    em->depcorr = depcorr;
    em->coef = cal_coef(depcorr, 0.03);
    return em;
}

/**
 * Deallocate an errmod_t object
 */
void errmod_destroy(errmod_t *em)
{
    if (em == 0) return;
    free(em->coef->lhet); free(em->coef->fk); free(em->coef->beta);
    free(em->coef); free(em);
}

//
// em: error model to fit to data
// m: number of alleles across all samples
// n: number of bases observed in sample
// bases[i]: bases observed in pileup [6 bit quality|1 bit strand|4 bit base]
// q[i*m+j]: (Output) phred-scaled likelihood of each genotype (i,j)
int errmod_cal(const errmod_t *em, int n, int m, uint16_t *bases, float *q)
{
    // Aux
    // aux.c is total count of each base observed (ignoring strand)
    call_aux_t aux;
    // Loop variables
    int i, j, k;
    // The total count of each base observed per strand
    int w[32];

    memset(q, 0, m * m * sizeof(float)); // initialise q to 0
    if (n == 0) return 0;
    // This section randomly downsamples to 255 depth so as not to go beyond our precalculated matrix
    if (n > 255) { // if we exceed 255 bases observed then shuffle them to sample and only keep the first 255
        ks_shuffle(uint16_t, n, bases);
        n = 255;
    }
    ks_introsort(uint16_t, n, bases);
    /* zero out w and aux */
    memset(w, 0, 32 * sizeof(int));
    memset(&aux, 0, sizeof(call_aux_t));

    for (j = n - 1; j >= 0; --j) { // calculate esum and fsum
        uint16_t b = bases[j];
        /* extract quality and cap at 63 */
        int qual = b>>5 < 4? 4 : b>>5;
        if (qual > 63) qual = 63;
        /* extract base ORed with strand */
        int basestrand = b&0x1f;
        /* extract base */
        int base = b&0xf;
        aux.fsum[base] += em->coef->fk[w[basestrand]];
        aux.bsum[base] += em->coef->fk[w[basestrand]] * em->coef->beta[qual<<16|n<<8|aux.c[base]];
        ++aux.c[base];
        ++w[basestrand];
    }

    // generate likelihood
    for (j = 0; j < m; ++j) {
        float tmp1, tmp3;
        int tmp2;
        // homozygous
        for (k = 0, tmp1 = tmp3 = 0.0, tmp2 = 0; k < m; ++k) {
            if (k == j) continue;
            tmp1 += aux.bsum[k]; tmp2 += aux.c[k]; tmp3 += aux.fsum[k];
        }
        if (tmp2) {
            q[j*m+j] = tmp1;
        }
        // heterozygous
        for (k = j + 1; k < m; ++k) {
            int cjk = aux.c[j] + aux.c[k];
            for (i = 0, tmp2 = 0, tmp1 = tmp3 = 0.0; i < m; ++i) {
                if (i == j || i == k) continue;
                tmp1 += aux.bsum[i]; tmp2 += aux.c[i]; tmp3 += aux.fsum[i];
            }
            if (tmp2) {
                q[j*m+k] = q[k*m+j] = -4.343 * em->coef->lhet[cjk<<8|aux.c[k]] + tmp1;
            } else q[j*m+k] = q[k*m+j] = -4.343 * em->coef->lhet[cjk<<8|aux.c[k]]; // all the bases are either j or k
        }
        /* clamp to greater than 0 */
        for (k = 0; k < m; ++k) if (q[j*m+k] < 0.0) q[j*m+k] = 0.0;
    }

    return 0;
}