modified: src1/input.c

[GalaxyCodeBases.git] / c_cpp / lib / klib / khmm.c

#include <math.h>
#include <stdio.h>
#include <assert.h>
#include <string.h>
#include <stdlib.h>
#include "khmm.h"

// new/delete hmm_par_t

hmm_par_t *hmm_new_par(int m, int n)
{
        hmm_par_t *hp;
        int i;
        assert(m > 0 && n > 0);
        hp = (hmm_par_t*)calloc(1, sizeof(hmm_par_t));
        hp->m = m; hp->n = n;
        hp->a0 = (FLOAT*)calloc(n, sizeof(FLOAT));
        hp->a = (FLOAT**)calloc2(n, n, sizeof(FLOAT));
        hp->e = (FLOAT**)calloc2(m + 1, n, sizeof(FLOAT));
        hp->ae = (FLOAT**)calloc2((m + 1) * n, n, sizeof(FLOAT));
        for (i = 0; i != n; ++i) hp->e[m][i] = 1.0;
        return hp;
}
void hmm_delete_par(hmm_par_t *hp)
{
        int i;
        if (hp == 0) return;
        for (i = 0; i != hp->n; ++i) free(hp->a[i]);
        for (i = 0; i <= hp->m; ++i) free(hp->e[i]);
        for (i = 0; i < (hp->m + 1) * hp->n; ++i) free(hp->ae[i]);
        free(hp->a); free(hp->e); free(hp->a0); free(hp->ae);
        free(hp);
}

// new/delete hmm_data_t

hmm_data_t *hmm_new_data(int L, const char *seq, const hmm_par_t *hp)
{
        hmm_data_t *hd;
        hd = (hmm_data_t*)calloc(1, sizeof(hmm_data_t));
        hd->L = L;
        hd->seq = (char*)malloc(L + 1);
        memcpy(hd->seq + 1, seq, L);
        return hd;
}
void hmm_delete_data(hmm_data_t *hd)
{
        int i;
        if (hd == 0) return;
        for (i = 0; i <= hd->L; ++i) {
                if (hd->f) free(hd->f[i]);
                if (hd->b) free(hd->b[i]);
        }
        free(hd->f); free(hd->b); free(hd->s); free(hd->v); free(hd->p); free(hd->seq);
        free(hd);
}

// new/delete hmm_exp_t

hmm_exp_t *hmm_new_exp(const hmm_par_t *hp)
{
        hmm_exp_t *he;
        assert(hp);
        he = (hmm_exp_t*)calloc(1, sizeof(hmm_exp_t));
        he->m = hp->m; he->n = hp->n;
        he->A0 = (FLOAT*)calloc(hp->n, sizeof(FLOAT));
        he->A = (FLOAT**)calloc2(hp->n, hp->n, sizeof(FLOAT));
        he->E = (FLOAT**)calloc2(hp->m + 1, hp->n, sizeof(FLOAT));
        return he;
}
void hmm_delete_exp(hmm_exp_t *he)
{
        int i;
        if (he == 0) return;
        for (i = 0; i != he->n; ++i) free(he->A[i]);
        for (i = 0; i <= he->m; ++i) free(he->E[i]);
        free(he->A); free(he->E); free(he->A0);
        free(he);
}

// Viterbi algorithm

FLOAT hmm_Viterbi(const hmm_par_t *hp, hmm_data_t *hd)
{
        FLOAT **la, **le, *preV, *curV, max;
        int **Vmax, max_l; // backtrace matrix
        int k, l, b, u;
        
        if (hd->v) free(hd->v);
        hd->v = (int*)calloc(hd->L+1, sizeof(int));
        la = (FLOAT**)calloc2(hp->n, hp->n, sizeof(FLOAT));
        le = (FLOAT**)calloc2(hp->m + 1, hp->n, sizeof(FLOAT));
        Vmax = (int**)calloc2(hd->L+1, hp->n, sizeof(int));
        preV = (FLOAT*)malloc(sizeof(FLOAT) * hp->n);
        curV = (FLOAT*)malloc(sizeof(FLOAT) * hp->n);
        for (k = 0; k != hp->n; ++k)
                for (l = 0; l != hp->n; ++l)
                        la[k][l] = log(hp->a[l][k]); // this is not a bug
        for (b = 0; b != hp->m; ++b)
                for (k = 0; k != hp->n; ++k)
                        le[b][k] = log(hp->e[b][k]);
        for (k = 0; k != hp->n; ++k) le[hp->m][k] = 0.0;
        // V_k(1)
        for (k = 0; k != hp->n; ++k) {
                preV[k] = le[(int)hd->seq[1]][k] + log(hp->a0[k]);
                Vmax[1][k] = 0;
        }
        // all the rest
        for (u = 2; u <= hd->L; ++u) {
                FLOAT *tmp, *leu = le[(int)hd->seq[u]];
                for (k = 0; k != hp->n; ++k) {
                        FLOAT *laa = la[k];
                        for (l = 0, max = -HMM_INF, max_l = -1; l != hp->n; ++l) {
                                if (max < preV[l] + laa[l]) {
                                        max = preV[l] + laa[l];
                                        max_l = l;
                                }
                        }
                        assert(max_l >= 0); // cannot be zero
                        curV[k] = leu[k] + max;
                        Vmax[u][k] = max_l;
                }
                tmp = curV; curV = preV; preV = tmp; // swap
        }
        // backtrace
        for (k = 0, max_l = -1, max = -HMM_INF; k != hp->n; ++k) {
                if (max < preV[k]) {
                        max = preV[k]; max_l = k;
                }
        }
        assert(max_l >= 0); // cannot be zero
        hd->v[hd->L] = max_l;
        for (u = hd->L; u >= 1; --u)
                hd->v[u-1] = Vmax[u][hd->v[u]];
        for (k = 0; k != hp->n; ++k) free(la[k]);
        for (b = 0; b < hp->m; ++b) free(le[b]);
        for (u = 0; u <= hd->L; ++u) free(Vmax[u]);
        free(la); free(le); free(Vmax); free(preV); free(curV);
        hd->status |= HMM_VITERBI;
        return max;
}

// forward algorithm

void hmm_forward(const hmm_par_t *hp, hmm_data_t *hd)
{
        FLOAT sum, tmp, **at;
        int u, k, l;
        int n, m, L;
        assert(hp && hd);
        // allocate memory for hd->f and hd->s
        n = hp->n; m = hp->m; L = hd->L;
        if (hd->s) free(hd->s);
        if (hd->f) { 
                for (k = 0; k <= hd->L; ++k) free(hd->f[k]);
                free(hd->f);
        }
        hd->f = (FLOAT**)calloc2(hd->L+1, hp->n, sizeof(FLOAT));
        hd->s = (FLOAT*)calloc(hd->L+1, sizeof(FLOAT));
        hd->status &= ~(unsigned)HMM_FORWARD;
        // at[][] array helps to improve the cache efficiency
        at = (FLOAT**)calloc2(n, n, sizeof(FLOAT));
        // transpose a[][]
        for (k = 0; k != n; ++k)
                for (l = 0; l != n; ++l)
                        at[k][l] = hp->a[l][k];
        // f[0], but it should never be used
        hd->s[0] = 1.0;
        for (k = 0; k != n; ++k) hd->f[0][k] = 0.0;
        // f[1]
        for (k = 0, sum = 0.0; k != n; ++k)
                sum += (hd->f[1][k] = hp->a0[k] * hp->e[(int)hd->seq[1]][k]);
        for (k = 0; k != n; ++k) hd->f[1][k] /= sum;
        hd->s[1] = sum;
        // f[2..hmmL], the core loop
        for (u = 2; u <= L; ++u) {
                FLOAT *fu = hd->f[u], *fu1 = hd->f[u-1], *eu = hp->e[(int)hd->seq[u]];
                for (k = 0, sum = 0.0; k != n; ++k) {
                        FLOAT *aa = at[k];
                        for (l = 0, tmp = 0.0; l != n; ++l) tmp += fu1[l] * aa[l];
                        sum += (fu[k] = eu[k] * tmp);
                }
                for (k = 0; k != n; ++k) fu[k] /= sum;
                hd->s[u] = sum;
        }
        // free at array
        for (k = 0; k != hp->n; ++k) free(at[k]);
        free(at);
        hd->status |= HMM_FORWARD;
}

//  precalculate hp->ae

void hmm_pre_backward(hmm_par_t *hp)
{
        int m, n, b, k, l;
        assert(hp);
        m = hp->m; n = hp->n;
        for (b = 0; b <= m; ++b) {
                for (k = 0; k != n; ++k) {
                        FLOAT *p = hp->ae[b * hp->n + k];
                        for (l = 0; l != n; ++l)
                                p[l] = hp->e[b][l] * hp->a[k][l];
                }
        }
}

// backward algorithm

void hmm_backward(const hmm_par_t *hp, hmm_data_t *hd)
{
        FLOAT tmp;
        int k, l, u;
        int m, n, L;
        assert(hp && hd);
        assert(hd->status & HMM_FORWARD);
        // allocate memory for hd->b
        m = hp->m; n = hp->n; L = hd->L;
        if (hd->b) { 
                for (k = 0; k <= hd->L; ++k) free(hd->b[k]);
                free(hd->b);
        }
        hd->status &= ~(unsigned)HMM_BACKWARD;
        hd->b = (FLOAT**)calloc2(L+1, hp->n, sizeof(FLOAT));
        // b[L]
        for (k = 0; k != hp->n; ++k) hd->b[L][k] = 1.0 / hd->s[L];
        // b[1..L-1], the core loop
        for (u = L-1; u >= 1; --u) {
                FLOAT *bu1 = hd->b[u+1], **p = hp->ae + (int)hd->seq[u+1] * n;
                for (k = 0; k != n; ++k) {
                        FLOAT *q = p[k];
                        for (l = 0, tmp = 0.0; l != n; ++l) tmp += q[l] * bu1[l];
                        hd->b[u][k] = tmp / hd->s[u];
                }
        }
        hd->status |= HMM_BACKWARD;
        for (l = 0, tmp = 0.0; l != n; ++l)
                tmp += hp->a0[l] * hd->b[1][l] * hp->e[(int)hd->seq[1]][l];
        if (tmp > 1.0 + 1e-6 || tmp < 1.0 - 1e-6) // in theory, tmp should always equal to 1
                fprintf(stderr, "++ Underflow may have happened (%lg).\n", tmp);
}

// log-likelihood of the observation

FLOAT hmm_lk(const hmm_data_t *hd)
{
    FLOAT sum = 0.0, prod = 1.0;
        int u, L;
        L = hd->L;
        assert(hd->status & HMM_FORWARD);
        for (u = 1; u <= L; ++u) {
                prod *= hd->s[u];
                if (prod < HMM_TINY || prod >= 1.0/HMM_TINY) { // reset
                        sum += log(prod);
                        prod = 1.0;
                }
        }
        sum += log(prod);
        return sum;
}

// posterior decoding

void hmm_post_decode(const hmm_par_t *hp, hmm_data_t *hd)
{
        int u, k;
        assert(hd->status && HMM_BACKWARD);
        if (hd->p) free(hd->p);
        hd->p = (int*)calloc(hd->L + 1, sizeof(int));
        for (u = 1; u <= hd->L; ++u) {
                FLOAT prob, max, *fu = hd->f[u], *bu = hd->b[u], su = hd->s[u];
                int max_k;
                for (k = 0, max = -1.0, max_k = -1; k != hp->n; ++k) {
                        if (max < (prob = fu[k] * bu[k] * su)) {
                                max = prob; max_k = k;
                        }
                }
                assert(max_k >= 0);
                hd->p[u] = max_k;
        }
        hd->status |= HMM_POSTDEC;
}

// posterior probability of states

FLOAT hmm_post_state(const hmm_par_t *hp, const hmm_data_t *hd, int u, FLOAT *prob)
{
        FLOAT sum = 0.0, ss = hd->s[u], *fu = hd->f[u], *bu = hd->b[u];
        int k;
        for (k = 0; k != hp->n; ++k)
                sum += (prob[k] = fu[k] * bu[k] * ss);
        return sum; // in theory, this should always equal to 1.0
}

// expected counts

hmm_exp_t *hmm_expect(const hmm_par_t *hp, const hmm_data_t *hd)
{
        int k, l, u, b, m, n;
        hmm_exp_t *he;
        assert(hd->status & HMM_BACKWARD);
        he = hmm_new_exp(hp);
        // initialization
        m = hp->m; n = hp->n;
        for (k = 0; k != n; ++k)
                for (l = 0; l != n; ++l) he->A[k][l] = HMM_TINY;
        for (b = 0; b <= m; ++b)
                for (l = 0; l != n; ++l) he->E[b][l] = HMM_TINY;
        // calculate A_{kl} and E_k(b), k,l\in[0,n)
        for (u = 1; u < hd->L; ++u) {
                FLOAT *fu = hd->f[u], *bu = hd->b[u], *bu1 = hd->b[u+1], ss = hd->s[u];
                FLOAT *Ec = he->E[(int)hd->seq[u]], **p = hp->ae + (int)hd->seq[u+1] * n;
                for (k = 0; k != n; ++k) {
                        FLOAT *q = p[k], *AA = he->A[k], fuk = fu[k];
                        for (l = 0; l != n; ++l) // this is cache-efficient
                                AA[l] += fuk * q[l] * bu1[l];
                        Ec[k] += fuk * bu[k] * ss;
                }
        }
        // calculate A0_l
        for (l = 0; l != n; ++l)
                he->A0[l] += hp->a0[l] * hp->e[(int)hd->seq[1]][l] * hd->b[1][l];
        return he;
}

FLOAT hmm_Q0(const hmm_par_t *hp, hmm_exp_t *he)
{
        int k, l, b;
        FLOAT sum = 0.0;
        for (k = 0; k != hp->n; ++k) {
                FLOAT tmp;
                for (b = 0, tmp = 0.0; b != hp->m; ++b) tmp += he->E[b][k];
                for (b = 0; b != hp->m; ++b)
                        sum += he->E[b][k] * log(he->E[b][k] / tmp);
        }
        for (k = 0; k != hp->n; ++k) {
                FLOAT tmp, *A = he->A[k];
                for (l = 0, tmp = 0.0; l != hp->n; ++l) tmp += A[l];
                for (l = 0; l != hp->n; ++l) sum += A[l] * log(A[l] / tmp);
        }
        return (he->Q0 = sum);
}

// add he0 to he1

void hmm_add_expect(const hmm_exp_t *he0, hmm_exp_t *he1)
{
        int b, k, l;
        assert(he0->m == he1->m && he0->n == he1->n);
        for (k = 0; k != he1->n; ++k) {
                he1->A0[k] += he0->A0[k];
                for (l = 0; l != he1->n; ++l)
                        he1->A[k][l] += he0->A[k][l];
        }
        for (b = 0; b != he1->m; ++b) {
                for (l = 0; l != he1->n; ++l)
                        he1->E[b][l] += he0->E[b][l];
        }
}

// the EM-Q function

FLOAT hmm_Q(const hmm_par_t *hp, const hmm_exp_t *he)
{
        FLOAT sum = 0.0;
        int bb, k, l;
        for (bb = 0; bb != he->m; ++bb) {
                FLOAT *eb = hp->e[bb], *Eb = he->E[bb];
                for (k = 0; k != hp->n; ++k) {
                        if (eb[k] <= 0.0) return -HMM_INF;
                        sum += Eb[k] * log(eb[k]);
                }
        }
        for (k = 0; k != he->n; ++k) {
                FLOAT *Ak = he->A[k], *ak = hp->a[k];
                for (l = 0; l != he->n; ++l) {
                        if (ak[l] <= 0.0) return -HMM_INF;
                        sum += Ak[l] * log(ak[l]);
                }
        }
        return (sum -= he->Q0);
}

// simulate sequence

char *hmm_simulate(const hmm_par_t *hp, int L)
{
        int i, k, l, b;
        FLOAT x, y, **et;
        char *seq;
        seq = (char*)calloc(L+1, 1);
        // calculate the transpose of hp->e[][]
        et = (FLOAT**)calloc2(hp->n, hp->m, sizeof(FLOAT));
        for (k = 0; k != hp->n; ++k)
                for (b = 0; b != hp->m; ++b)
                        et[k][b] = hp->e[b][k];
        // the initial state, drawn from a0[]
        x = drand48();
        for (k = 0, y = 0.0; k != hp->n; ++k) {
                y += hp->a0[k];
                if (y >= x) break;
        }
        // main loop
        for (i = 0; i != L; ++i) {
                FLOAT *el, *ak = hp->a[k];
                x = drand48();
                for (l = 0, y = 0.0; l != hp->n; ++l) {
                        y += ak[l];
                        if (y >= x) break;
                }
                el = et[l];
                x = drand48();
                for (b = 0, y = 0.0; b != hp->m; ++b) {
                        y += el[b];
                        if (y >= x) break;
                } 
                seq[i] = b;
                k = l;
        }
        for (k = 0; k != hp->n; ++k) free(et[k]);
        free(et);
        return seq;
}