HMM.c

/* The MIT License

   Copyright (c) 2014-2017 Genome Research Ltd.

   Author: Petr Danecek <pd3@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 <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <htslib/hts.h>
#include "HMM.h"

typedef struct
{
    int nstates;            // number of hmm's states
    uint32_t snap_at_pos;   // snapshot at this position, 0 when inactive
    double *vit_prob;       // viterbi probabilities, NULL for uniform probs
    double *fwd_prob;       // transition probabilities
    double *bwd_prob;       // transition probabilities
}
snapshot_t;

struct _hmm_t
{
    int nstates;    // number of states

    double *vprob, *vprob_tmp;  // viterbi probs [nstates]
    uint8_t *vpath;             // viterbi path [nstates*nvpath]
    double *bwd, *bwd_tmp;      // bwd probs [nstates]
    double *fwd;                // fwd probs [nstates*(nfwd+1)]
    int nvpath, nfwd;

    int ntprob_arr;             // number of pre-calculated tprob matrices
    double *curr_tprob, *tmp;   // Temporary arrays; curr_tprob is short lived, valid only for
                                //  one site (that is, one step of Viterbi algorithm)
    double *tprob_arr;          // Array of transition matrices, precalculated to ntprob_arr
                                //  positions. The first matrix is the initial tprob matrix
                                //  set by hmm_init() or hmm_set_tprob()
    set_tprob_f set_tprob;      // Optional user function to set / modify transition probabilities
                                //  at each site (one step of Viterbi algorithm)
    void *set_tprob_data;
    snapshot_t init, state;     // Initial and current state probs. Set state from snapshot if prev_snap_pos!=0 or from init otherwise
    snapshot_t *snapshot;       //  snapshot->snap_at_pos  .. request a snapshot at this position
                                //  hmm->state.snap_at_pos .. the current state comes from snapshot made at this position
};

uint8_t *hmm_get_viterbi_path(hmm_t *hmm) { return hmm->vpath; }
double *hmm_get_tprob(hmm_t *hmm) { return hmm->tprob_arr; }
int hmm_get_nstates(hmm_t *hmm) { return hmm->nstates; }
double *hmm_get_fwd_bwd_prob(hmm_t *hmm) { return hmm->fwd; }

static inline void multiply_matrix(int n, double *a, double *b, double *dst, double *tmp)
{
    double *out = dst;
    if ( a==dst || b==dst )
        out = tmp;

    int i,j,k;
    for (i=0; i<n; i++)
    {
        for (j=0; j<n; j++)
        {
            double val = 0;
            for (k=0; k<n; k++) val += MAT(a,n,i,k)*MAT(b,n,k,j);
            MAT(out,n,i,j) = val;
        }
    }
    if ( out!=dst )
        memcpy(dst,out,sizeof(double)*n*n);
}

void hmm_init_states(hmm_t *hmm, double *probs)
{
    hmm->init.snap_at_pos = hmm->state.snap_at_pos = 0;

    if ( !hmm->init.vit_prob )
        hmm->init.vit_prob = (double*) malloc(sizeof(double)*hmm->nstates);
    if ( !hmm->init.fwd_prob )
        hmm->init.fwd_prob = (double*) malloc(sizeof(double)*hmm->nstates);
    if ( !hmm->init.bwd_prob )
        hmm->init.bwd_prob = (double*) malloc(sizeof(double)*hmm->nstates);

    if ( !hmm->state.vit_prob )
        hmm->state.vit_prob = (double*) malloc(sizeof(double)*hmm->nstates);
    if ( !hmm->state.fwd_prob )
        hmm->state.fwd_prob = (double*) malloc(sizeof(double)*hmm->nstates);
    if ( !hmm->state.bwd_prob )
        hmm->state.bwd_prob = (double*) malloc(sizeof(double)*hmm->nstates);
    
    int i;
    if ( probs )
    {
        memcpy(hmm->init.vit_prob,probs,sizeof(double)*hmm->nstates);
        double sum = 0;
        for (i=0; i<hmm->nstates; i++) sum += hmm->init.vit_prob[i];
        for (i=0; i<hmm->nstates; i++) hmm->init.vit_prob[i] /= sum;
    }
    else
        for (i=0; i<hmm->nstates; i++) hmm->init.vit_prob[i] = 1./hmm->nstates;

    memcpy(hmm->init.fwd_prob,hmm->init.vit_prob,sizeof(double)*hmm->nstates);  // these remain unchanged
    memcpy(hmm->init.bwd_prob,hmm->init.vit_prob,sizeof(double)*hmm->nstates);
    memcpy(hmm->state.vit_prob,hmm->init.vit_prob,sizeof(double)*hmm->nstates); // can be changed by snapshotting
    memcpy(hmm->state.fwd_prob,hmm->init.fwd_prob,sizeof(double)*hmm->nstates);
    memcpy(hmm->state.bwd_prob,hmm->init.bwd_prob,sizeof(double)*hmm->nstates);
}
hmm_t *hmm_init(int nstates, double *tprob, int ntprob)
{
    hmm_t *hmm = (hmm_t*) calloc(1,sizeof(hmm_t));
    hmm->nstates = nstates;
    hmm->curr_tprob = (double*) malloc(sizeof(double)*nstates*nstates);
    hmm->tmp = (double*) malloc(sizeof(double)*nstates*nstates);
    hmm_set_tprob(hmm, tprob, ntprob);
    hmm_init_states(hmm, NULL);
    return hmm;
}

void *hmm_snapshot(hmm_t *hmm, void *_snapshot, uint32_t pos)
{
    snapshot_t *snapshot = (snapshot_t*) _snapshot;
    if ( snapshot && snapshot->nstates!=hmm->nstates )
    {
        free(snapshot);
        snapshot = NULL;
    }
    if ( !snapshot )
    {
        // Allocate the snapshot as a single memory block so that it can be
        // free()-ed by the user. So make sure the arrays are aligned..
        size_t str_size = sizeof(snapshot_t);
        size_t dbl_size = sizeof(double);
        size_t pad_size = (dbl_size - str_size % dbl_size) % dbl_size;
        uint8_t *mem = (uint8_t*) malloc(str_size + pad_size + dbl_size*2*hmm->nstates);
        snapshot = (snapshot_t*) mem;
        snapshot->nstates  = hmm->nstates;
        snapshot->vit_prob = (double*) (mem + str_size + pad_size);
        snapshot->fwd_prob = snapshot->vit_prob + hmm->nstates;
    }
    snapshot->snap_at_pos = pos;
    hmm->snapshot = snapshot;
    return snapshot;
}
void hmm_restore(hmm_t *hmm, void *_snapshot)
{
    snapshot_t *snapshot = (snapshot_t*) _snapshot;
    if ( !snapshot || !snapshot->snap_at_pos ) 
    {
        hmm->state.snap_at_pos = 0;
        memcpy(hmm->state.vit_prob,hmm->init.vit_prob,sizeof(double)*hmm->nstates);
        memcpy(hmm->state.fwd_prob,hmm->init.fwd_prob,sizeof(double)*hmm->nstates);
    }
    else
    {
        hmm->state.snap_at_pos = snapshot->snap_at_pos;
        memcpy(hmm->state.vit_prob,snapshot->vit_prob,sizeof(double)*hmm->nstates);
        memcpy(hmm->state.fwd_prob,snapshot->fwd_prob,sizeof(double)*hmm->nstates);
    }
}
void hmm_reset(hmm_t *hmm, void *_snapshot)
{
    snapshot_t *snapshot = (snapshot_t*) _snapshot;
    if ( snapshot ) snapshot->snap_at_pos = 0;
    hmm->state.snap_at_pos = 0;
    memcpy(hmm->state.vit_prob,hmm->init.vit_prob,sizeof(double)*hmm->nstates);
    memcpy(hmm->state.fwd_prob,hmm->init.fwd_prob,sizeof(double)*hmm->nstates);
}

void hmm_set_tprob(hmm_t *hmm, double *tprob, int ntprob)
{
    hmm->ntprob_arr = ntprob;
    if ( ntprob<=0 ) ntprob = 1;

    if ( !hmm->tprob_arr )
        hmm->tprob_arr  = (double*) malloc(sizeof(double)*hmm->nstates*hmm->nstates*ntprob);

    memcpy(hmm->tprob_arr,tprob,sizeof(double)*hmm->nstates*hmm->nstates);

    int i;
    for (i=1; i<ntprob; i++)
        multiply_matrix(hmm->nstates, hmm->tprob_arr, hmm->tprob_arr+(i-1)*hmm->nstates*hmm->nstates, hmm->tprob_arr+i*hmm->nstates*hmm->nstates, hmm->tmp);
}

void hmm_set_tprob_func(hmm_t *hmm, set_tprob_f set_tprob, void *data)
{
    hmm->set_tprob = set_tprob;
    hmm->set_tprob_data = data;
}

static void _set_tprob(hmm_t *hmm, int pos_diff)
{
    assert( pos_diff>=0 );

    int i, n;

    n = hmm->ntprob_arr ? pos_diff % hmm->ntprob_arr : 0;  // n-th precalculated matrix
    memcpy(hmm->curr_tprob, hmm->tprob_arr+n*hmm->nstates*hmm->nstates, sizeof(*hmm->curr_tprob)*hmm->nstates*hmm->nstates);

    if ( hmm->ntprob_arr > 0  )
    {
        n = pos_diff / hmm->ntprob_arr;  // number of full blocks to jump
        for (i=0; i<n; i++)
            multiply_matrix(hmm->nstates, hmm->tprob_arr+(hmm->ntprob_arr-1)*hmm->nstates*hmm->nstates, hmm->curr_tprob, hmm->curr_tprob, hmm->tmp);
    }
}

void hmm_run_viterbi(hmm_t *hmm, int n, double *eprobs, uint32_t *sites)
{
    // Init arrays when run for the first time
    if ( hmm->nvpath < n )
    {
        hmm->nvpath = n;
        hmm->vpath  = (uint8_t*) realloc(hmm->vpath, sizeof(uint8_t)*hmm->nvpath*hmm->nstates);
    }
    if ( !hmm->vprob )
    {
        hmm->vprob     = (double*) malloc(sizeof(double)*hmm->nstates);
        hmm->vprob_tmp = (double*) malloc(sizeof(double)*hmm->nstates);
    }

    // Init all states with equal likelihood
    int i,j, nstates = hmm->nstates;
    memcpy(hmm->vprob, hmm->state.vit_prob, sizeof(*hmm->state.vit_prob)*nstates);
    uint32_t prev_pos = hmm->state.snap_at_pos ? hmm->state.snap_at_pos : sites[0];

    // Run Viterbi
    for (i=0; i<n; i++)
    {
        uint8_t *vpath = &hmm->vpath[i*nstates];
        double *eprob  = &eprobs[i*nstates];

        int pos_diff = sites[i] == prev_pos ? 0 : sites[i] - prev_pos - 1;
        _set_tprob(hmm, pos_diff);
        if ( hmm->set_tprob ) hmm->set_tprob(hmm, prev_pos, sites[i], hmm->set_tprob_data, hmm->curr_tprob);
        prev_pos = sites[i];

        double vnorm = 0;
        for (j=0; j<nstates; j++)
        {
            double vmax = 0;
            int k, k_vmax = 0;
            for (k=0; k<nstates; k++)
            {
                double pval = hmm->vprob[k] * MAT(hmm->curr_tprob,hmm->nstates,j,k);
                if ( vmax < pval ) { vmax = pval; k_vmax = k; }
            }
            vpath[j] = k_vmax;
            hmm->vprob_tmp[j] = vmax * eprob[j];
            vnorm += hmm->vprob_tmp[j];
        }
        for (j=0; j<nstates; j++) hmm->vprob_tmp[j] /= vnorm;
        double *tmp = hmm->vprob; hmm->vprob = hmm->vprob_tmp; hmm->vprob_tmp = tmp;

        if ( hmm->snapshot && sites[i]==hmm->snapshot->snap_at_pos )
            memcpy(hmm->snapshot->vit_prob, hmm->vprob, sizeof(*hmm->vprob)*nstates);
    }

    // Find the most likely state
    int iptr = 0;
    for (i=1; i<nstates; i++) 
        if ( hmm->vprob[iptr] < hmm->vprob[i] ) iptr = i;

    // Trace back the Viterbi path, we are reusing vpath for storing the states (vpath[i*nstates])
    for (i=n-1; i>=0; i--)
    {
        assert( iptr<nstates && hmm->vpath[i*nstates + iptr]<nstates );
        iptr = hmm->vpath[i*nstates + iptr];
        hmm->vpath[i*nstates] = iptr;     // reusing the array for different purpose here
    }
}

void hmm_run_fwd_bwd(hmm_t *hmm, int n, double *eprobs, uint32_t *sites)
{
    // Init arrays when run for the first time
    if ( hmm->nfwd < n )
    {
        hmm->nfwd = n;
        hmm->fwd  = (double*) realloc(hmm->fwd, sizeof(double)*(hmm->nfwd+1)*hmm->nstates);
    }
    if ( !hmm->bwd )
    {
        hmm->bwd     = (double*) malloc(sizeof(double)*hmm->nstates);
        hmm->bwd_tmp = (double*) malloc(sizeof(double)*hmm->nstates);
    }


    int i,j,k, nstates = hmm->nstates;
    memcpy(hmm->fwd, hmm->state.fwd_prob, sizeof(*hmm->state.fwd_prob)*nstates);
    memcpy(hmm->bwd, hmm->state.bwd_prob, sizeof(*hmm->state.bwd_prob)*nstates);
    uint32_t prev_pos = hmm->state.snap_at_pos ? hmm->state.snap_at_pos : sites[0];

    // Run fwd 
    for (i=0; i<n; i++)
    {
        double *fwd_prev = &hmm->fwd[i*nstates];
        double *fwd      = &hmm->fwd[(i+1)*nstates];
        double *eprob    = &eprobs[i*nstates];

        int pos_diff = sites[i] == prev_pos ? 0 : sites[i] - prev_pos - 1;

        _set_tprob(hmm, pos_diff);
        if ( hmm->set_tprob ) hmm->set_tprob(hmm, prev_pos, sites[i], hmm->set_tprob_data, hmm->curr_tprob);
        prev_pos = sites[i];

        double norm = 0;
        for (j=0; j<nstates; j++)
        {
            double pval = 0;
            for (k=0; k<nstates; k++)
                pval += fwd_prev[k] * MAT(hmm->curr_tprob,hmm->nstates,j,k);
            fwd[j] = pval * eprob[j];
            norm += fwd[j];
        }
        for (j=0; j<nstates; j++) fwd[j] /= norm;

        if ( hmm->snapshot && sites[i]==hmm->snapshot->snap_at_pos )
            memcpy(hmm->snapshot->fwd_prob, fwd, sizeof(*fwd)*nstates);
    }

    // Run bwd
    double *bwd = hmm->bwd, *bwd_tmp = hmm->bwd_tmp;
    prev_pos = sites[n-1];
    for (i=0; i<n; i++)
    {
        double *fwd   = &hmm->fwd[(n-i)*nstates];
        double *eprob = &eprobs[(n-i-1)*nstates];
        
        int pos_diff = sites[n-i-1] == prev_pos ? 0 : prev_pos - sites[n-i-1] - 1;

        _set_tprob(hmm, pos_diff);
        if ( hmm->set_tprob ) hmm->set_tprob(hmm, sites[n-i-1], prev_pos, hmm->set_tprob_data, hmm->curr_tprob);
        prev_pos = sites[n-i-1];

        double bwd_norm = 0;
        for (j=0; j<nstates; j++)
        {
            double pval = 0;
            for (k=0; k<nstates; k++)
                pval += bwd[k] * eprob[k] * MAT(hmm->curr_tprob,hmm->nstates,k,j);
            bwd_tmp[j] = pval;
            bwd_norm += pval;
        }
        double norm = 0;
        for (j=0; j<nstates; j++)
        {
            bwd_tmp[j] /= bwd_norm;
            fwd[j] *= bwd_tmp[j];   // fwd now stores fwd*bwd
            norm += fwd[j];
        }
        for (j=0; j<nstates; j++) fwd[j] /= norm;
        double *tmp = bwd_tmp; bwd_tmp = bwd; bwd = tmp;
    }
}

double *hmm_run_baum_welch(hmm_t *hmm, int n, double *eprobs, uint32_t *sites)
{
    // Init arrays when run for the first time
    if ( hmm->nfwd < n )
    {
        hmm->nfwd = n;
        hmm->fwd  = (double*) realloc(hmm->fwd, sizeof(double)*(hmm->nfwd+1)*hmm->nstates);
    }
    if ( !hmm->bwd )
    {
        hmm->bwd     = (double*) malloc(sizeof(double)*hmm->nstates);
        hmm->bwd_tmp = (double*) malloc(sizeof(double)*hmm->nstates);
    }

    // Init all states with equal likelihood
    int i,j,k, nstates = hmm->nstates;
    memcpy(hmm->fwd, hmm->state.fwd_prob, sizeof(*hmm->state.fwd_prob)*nstates);
    memcpy(hmm->bwd, hmm->state.bwd_prob, sizeof(*hmm->state.bwd_prob)*nstates);
    uint32_t prev_pos = hmm->state.snap_at_pos ? hmm->state.snap_at_pos : sites[0];

    // New transition matrix: temporary values
    double *tmp_xi = (double*) calloc(nstates*nstates,sizeof(double));
    double *tmp_gamma = (double*) calloc(nstates,sizeof(double));
    double *fwd_bwd = (double*) malloc(sizeof(double)*nstates);

    // Run fwd 
    for (i=0; i<n; i++)
    {
        double *fwd_prev = &hmm->fwd[i*nstates];
        double *fwd      = &hmm->fwd[(i+1)*nstates];
        double *eprob    = &eprobs[i*nstates];

        int pos_diff = sites[i] == prev_pos ? 0 : sites[i] - prev_pos - 1;

        _set_tprob(hmm, pos_diff);
        if ( hmm->set_tprob ) hmm->set_tprob(hmm, prev_pos, sites[i], hmm->set_tprob_data, hmm->curr_tprob);
        prev_pos = sites[i];

        double norm = 0;
        for (j=0; j<nstates; j++)
        {
            double pval = 0;
            for (k=0; k<nstates; k++)
                pval += fwd_prev[k] * MAT(hmm->curr_tprob,hmm->nstates,j,k);
            fwd[j] = pval * eprob[j];
            norm += fwd[j];
        }
        for (j=0; j<nstates; j++) fwd[j] /= norm;
    }

    // Run bwd
    double *bwd = hmm->bwd, *bwd_tmp = hmm->bwd_tmp;
    prev_pos = sites[n-1];
    for (i=0; i<n; i++)
    {
        double *fwd   = &hmm->fwd[(n-i)*nstates];
        double *eprob = &eprobs[(n-i-1)*nstates];
        
        int pos_diff = sites[n-i-1] == prev_pos ? 0 : prev_pos - sites[n-i-1] - 1;

        _set_tprob(hmm, pos_diff);
        if ( hmm->set_tprob ) hmm->set_tprob(hmm, sites[n-i-1], prev_pos, hmm->set_tprob_data, hmm->curr_tprob);
        prev_pos = sites[n-i-1];

        double bwd_norm = 0;
        for (j=0; j<nstates; j++)
        {
            double pval = 0;
            for (k=0; k<nstates; k++)
                pval += bwd[k] * eprob[k] * MAT(hmm->curr_tprob,hmm->nstates,k,j);
            bwd_tmp[j] = pval;
            bwd_norm += pval;
        }
        double norm = 0;
        for (j=0; j<nstates; j++)
        {
            bwd_tmp[j] /= bwd_norm;
            fwd_bwd[j] = fwd[j]*bwd_tmp[j];
            norm += fwd_bwd[j];
        }
        for (j=0; j<nstates; j++) 
        {
            fwd_bwd[j] /= norm;
            tmp_gamma[j] += fwd_bwd[j];
        }

        for (j=0; j<nstates; j++)
        {
            for (k=0; k<nstates; k++)
            {
                MAT(tmp_xi,nstates,k,j) += fwd[j]*bwd[k]*MAT(hmm->tprob_arr,hmm->nstates,k,j)*eprob[k] / norm;
            }
        }

        for (j=0; j<nstates; j++) fwd[j] = fwd_bwd[j];    // fwd now stores fwd*bwd

        double *tmp = bwd_tmp; bwd_tmp = bwd; bwd = tmp;
    }
    for (j=0; j<nstates; j++)
    {
        double norm = 0;
        for (k=0; k<nstates; k++)
        {
            MAT(hmm->curr_tprob,nstates,k,j) = MAT(tmp_xi,nstates,k,j) / tmp_gamma[j];
            norm += MAT(hmm->curr_tprob,nstates,k,j);
        }
        for (k=0; k<nstates; k++)
            MAT(hmm->curr_tprob,nstates,k,j) /= norm;
    }
    free(tmp_gamma);
    free(tmp_xi);
    free(fwd_bwd);
    return hmm->curr_tprob;
}

void hmm_destroy(hmm_t *hmm)
{
    free(hmm->init.vit_prob);
    free(hmm->init.fwd_prob);
    free(hmm->init.bwd_prob);
    free(hmm->state.vit_prob);
    free(hmm->state.fwd_prob);
    free(hmm->state.bwd_prob);
    free(hmm->vprob);
    free(hmm->vprob_tmp);
    free(hmm->vpath);
    free(hmm->curr_tprob);
    free(hmm->tmp);
    free(hmm->tprob_arr);
    free(hmm->fwd);
    free(hmm->bwd);
    free(hmm->bwd_tmp);
    free(hmm);
}