424 lines
11 KiB
C
424 lines
11 KiB
C
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#include <math.h>
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#include <stdio.h>
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#include <assert.h>
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#include <string.h>
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#include <stdlib.h>
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#include "khmm.h"
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// new/delete hmm_par_t
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hmm_par_t *hmm_new_par(int m, int n)
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{
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hmm_par_t *hp;
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int i;
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assert(m > 0 && n > 0);
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hp = (hmm_par_t*)calloc(1, sizeof(hmm_par_t));
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hp->m = m; hp->n = n;
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hp->a0 = (FLOAT*)calloc(n, sizeof(FLOAT));
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hp->a = (FLOAT**)calloc2(n, n, sizeof(FLOAT));
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hp->e = (FLOAT**)calloc2(m + 1, n, sizeof(FLOAT));
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hp->ae = (FLOAT**)calloc2((m + 1) * n, n, sizeof(FLOAT));
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for (i = 0; i != n; ++i) hp->e[m][i] = 1.0;
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return hp;
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}
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void hmm_delete_par(hmm_par_t *hp)
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{
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int i;
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if (hp == 0) return;
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for (i = 0; i != hp->n; ++i) free(hp->a[i]);
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for (i = 0; i <= hp->m; ++i) free(hp->e[i]);
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for (i = 0; i < (hp->m + 1) * hp->n; ++i) free(hp->ae[i]);
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free(hp->a); free(hp->e); free(hp->a0); free(hp->ae);
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free(hp);
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}
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// new/delete hmm_data_t
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hmm_data_t *hmm_new_data(int L, const char *seq, const hmm_par_t *hp)
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{
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hmm_data_t *hd;
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hd = (hmm_data_t*)calloc(1, sizeof(hmm_data_t));
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hd->L = L;
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hd->seq = (char*)malloc(L + 1);
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memcpy(hd->seq + 1, seq, L);
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return hd;
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}
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void hmm_delete_data(hmm_data_t *hd)
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{
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int i;
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if (hd == 0) return;
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for (i = 0; i <= hd->L; ++i) {
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if (hd->f) free(hd->f[i]);
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if (hd->b) free(hd->b[i]);
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}
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free(hd->f); free(hd->b); free(hd->s); free(hd->v); free(hd->p); free(hd->seq);
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free(hd);
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}
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// new/delete hmm_exp_t
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hmm_exp_t *hmm_new_exp(const hmm_par_t *hp)
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{
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hmm_exp_t *he;
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assert(hp);
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he = (hmm_exp_t*)calloc(1, sizeof(hmm_exp_t));
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he->m = hp->m; he->n = hp->n;
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he->A0 = (FLOAT*)calloc(hp->n, sizeof(FLOAT));
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he->A = (FLOAT**)calloc2(hp->n, hp->n, sizeof(FLOAT));
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he->E = (FLOAT**)calloc2(hp->m + 1, hp->n, sizeof(FLOAT));
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return he;
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}
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void hmm_delete_exp(hmm_exp_t *he)
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{
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int i;
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if (he == 0) return;
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for (i = 0; i != he->n; ++i) free(he->A[i]);
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for (i = 0; i <= he->m; ++i) free(he->E[i]);
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free(he->A); free(he->E); free(he->A0);
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free(he);
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}
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// Viterbi algorithm
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FLOAT hmm_Viterbi(const hmm_par_t *hp, hmm_data_t *hd)
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{
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FLOAT **la, **le, *preV, *curV, max;
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int **Vmax, max_l; // backtrace matrix
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int k, l, b, u;
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if (hd->v) free(hd->v);
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hd->v = (int*)calloc(hd->L+1, sizeof(int));
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la = (FLOAT**)calloc2(hp->n, hp->n, sizeof(FLOAT));
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le = (FLOAT**)calloc2(hp->m + 1, hp->n, sizeof(FLOAT));
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Vmax = (int**)calloc2(hd->L+1, hp->n, sizeof(int));
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preV = (FLOAT*)malloc(sizeof(FLOAT) * hp->n);
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curV = (FLOAT*)malloc(sizeof(FLOAT) * hp->n);
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for (k = 0; k != hp->n; ++k)
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for (l = 0; l != hp->n; ++l)
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la[k][l] = log(hp->a[l][k]); // this is not a bug
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for (b = 0; b != hp->m; ++b)
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for (k = 0; k != hp->n; ++k)
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le[b][k] = log(hp->e[b][k]);
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for (k = 0; k != hp->n; ++k) le[hp->m][k] = 0.0;
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// V_k(1)
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for (k = 0; k != hp->n; ++k) {
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preV[k] = le[(int)hd->seq[1]][k] + log(hp->a0[k]);
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Vmax[1][k] = 0;
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}
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// all the rest
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for (u = 2; u <= hd->L; ++u) {
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FLOAT *tmp, *leu = le[(int)hd->seq[u]];
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for (k = 0; k != hp->n; ++k) {
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FLOAT *laa = la[k];
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for (l = 0, max = -HMM_INF, max_l = -1; l != hp->n; ++l) {
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if (max < preV[l] + laa[l]) {
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max = preV[l] + laa[l];
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max_l = l;
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}
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}
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assert(max_l >= 0); // cannot be zero
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curV[k] = leu[k] + max;
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Vmax[u][k] = max_l;
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}
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tmp = curV; curV = preV; preV = tmp; // swap
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}
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// backtrace
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for (k = 0, max_l = -1, max = -HMM_INF; k != hp->n; ++k) {
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if (max < preV[k]) {
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max = preV[k]; max_l = k;
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}
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}
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assert(max_l >= 0); // cannot be zero
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hd->v[hd->L] = max_l;
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for (u = hd->L; u >= 1; --u)
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hd->v[u-1] = Vmax[u][hd->v[u]];
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for (k = 0; k != hp->n; ++k) free(la[k]);
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for (b = 0; b < hp->m; ++b) free(le[b]);
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for (u = 0; u <= hd->L; ++u) free(Vmax[u]);
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free(la); free(le); free(Vmax); free(preV); free(curV);
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hd->status |= HMM_VITERBI;
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return max;
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}
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// forward algorithm
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void hmm_forward(const hmm_par_t *hp, hmm_data_t *hd)
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{
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FLOAT sum, tmp, **at;
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int u, k, l;
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int n, m, L;
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assert(hp && hd);
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// allocate memory for hd->f and hd->s
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n = hp->n; m = hp->m; L = hd->L;
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if (hd->s) free(hd->s);
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if (hd->f) {
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for (k = 0; k <= hd->L; ++k) free(hd->f[k]);
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free(hd->f);
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}
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hd->f = (FLOAT**)calloc2(hd->L+1, hp->n, sizeof(FLOAT));
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hd->s = (FLOAT*)calloc(hd->L+1, sizeof(FLOAT));
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hd->status &= ~(unsigned)HMM_FORWARD;
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// at[][] array helps to improve the cache efficiency
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at = (FLOAT**)calloc2(n, n, sizeof(FLOAT));
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// transpose a[][]
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for (k = 0; k != n; ++k)
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for (l = 0; l != n; ++l)
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at[k][l] = hp->a[l][k];
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// f[0], but it should never be used
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hd->s[0] = 1.0;
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for (k = 0; k != n; ++k) hd->f[0][k] = 0.0;
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// f[1]
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for (k = 0, sum = 0.0; k != n; ++k)
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sum += (hd->f[1][k] = hp->a0[k] * hp->e[(int)hd->seq[1]][k]);
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for (k = 0; k != n; ++k) hd->f[1][k] /= sum;
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hd->s[1] = sum;
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// f[2..hmmL], the core loop
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for (u = 2; u <= L; ++u) {
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FLOAT *fu = hd->f[u], *fu1 = hd->f[u-1], *eu = hp->e[(int)hd->seq[u]];
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for (k = 0, sum = 0.0; k != n; ++k) {
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FLOAT *aa = at[k];
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for (l = 0, tmp = 0.0; l != n; ++l) tmp += fu1[l] * aa[l];
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sum += (fu[k] = eu[k] * tmp);
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}
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for (k = 0; k != n; ++k) fu[k] /= sum;
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hd->s[u] = sum;
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}
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// free at array
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for (k = 0; k != hp->n; ++k) free(at[k]);
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free(at);
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hd->status |= HMM_FORWARD;
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}
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// precalculate hp->ae
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void hmm_pre_backward(hmm_par_t *hp)
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{
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int m, n, b, k, l;
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assert(hp);
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m = hp->m; n = hp->n;
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for (b = 0; b <= m; ++b) {
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for (k = 0; k != n; ++k) {
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FLOAT *p = hp->ae[b * hp->n + k];
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for (l = 0; l != n; ++l)
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p[l] = hp->e[b][l] * hp->a[k][l];
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}
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}
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}
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// backward algorithm
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void hmm_backward(const hmm_par_t *hp, hmm_data_t *hd)
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{
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FLOAT tmp;
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int k, l, u;
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int m, n, L;
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assert(hp && hd);
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assert(hd->status & HMM_FORWARD);
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// allocate memory for hd->b
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m = hp->m; n = hp->n; L = hd->L;
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if (hd->b) {
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for (k = 0; k <= hd->L; ++k) free(hd->b[k]);
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free(hd->b);
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}
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hd->status &= ~(unsigned)HMM_BACKWARD;
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hd->b = (FLOAT**)calloc2(L+1, hp->n, sizeof(FLOAT));
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// b[L]
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for (k = 0; k != hp->n; ++k) hd->b[L][k] = 1.0 / hd->s[L];
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// b[1..L-1], the core loop
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for (u = L-1; u >= 1; --u) {
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FLOAT *bu1 = hd->b[u+1], **p = hp->ae + (int)hd->seq[u+1] * n;
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for (k = 0; k != n; ++k) {
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FLOAT *q = p[k];
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for (l = 0, tmp = 0.0; l != n; ++l) tmp += q[l] * bu1[l];
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hd->b[u][k] = tmp / hd->s[u];
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}
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}
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hd->status |= HMM_BACKWARD;
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for (l = 0, tmp = 0.0; l != n; ++l)
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tmp += hp->a0[l] * hd->b[1][l] * hp->e[(int)hd->seq[1]][l];
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if (tmp > 1.0 + 1e-6 || tmp < 1.0 - 1e-6) // in theory, tmp should always equal to 1
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fprintf(stderr, "++ Underflow may have happened (%lg).\n", tmp);
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}
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// log-likelihood of the observation
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FLOAT hmm_lk(const hmm_data_t *hd)
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{
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FLOAT sum = 0.0, prod = 1.0;
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int u, L;
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L = hd->L;
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assert(hd->status & HMM_FORWARD);
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for (u = 1; u <= L; ++u) {
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prod *= hd->s[u];
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if (prod < HMM_TINY || prod >= 1.0/HMM_TINY) { // reset
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sum += log(prod);
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prod = 1.0;
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}
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}
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sum += log(prod);
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return sum;
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}
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// posterior decoding
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void hmm_post_decode(const hmm_par_t *hp, hmm_data_t *hd)
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{
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int u, k;
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assert(hd->status && HMM_BACKWARD);
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if (hd->p) free(hd->p);
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hd->p = (int*)calloc(hd->L + 1, sizeof(int));
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for (u = 1; u <= hd->L; ++u) {
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FLOAT prob, max, *fu = hd->f[u], *bu = hd->b[u], su = hd->s[u];
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int max_k;
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for (k = 0, max = -1.0, max_k = -1; k != hp->n; ++k) {
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if (max < (prob = fu[k] * bu[k] * su)) {
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max = prob; max_k = k;
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}
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}
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assert(max_k >= 0);
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hd->p[u] = max_k;
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}
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hd->status |= HMM_POSTDEC;
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}
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// posterior probability of states
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FLOAT hmm_post_state(const hmm_par_t *hp, const hmm_data_t *hd, int u, FLOAT *prob)
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{
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FLOAT sum = 0.0, ss = hd->s[u], *fu = hd->f[u], *bu = hd->b[u];
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int k;
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for (k = 0; k != hp->n; ++k)
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sum += (prob[k] = fu[k] * bu[k] * ss);
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return sum; // in theory, this should always equal to 1.0
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}
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// expected counts
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hmm_exp_t *hmm_expect(const hmm_par_t *hp, const hmm_data_t *hd)
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{
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int k, l, u, b, m, n;
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hmm_exp_t *he;
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assert(hd->status & HMM_BACKWARD);
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he = hmm_new_exp(hp);
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// initialization
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m = hp->m; n = hp->n;
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for (k = 0; k != n; ++k)
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for (l = 0; l != n; ++l) he->A[k][l] = HMM_TINY;
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for (b = 0; b <= m; ++b)
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for (l = 0; l != n; ++l) he->E[b][l] = HMM_TINY;
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// calculate A_{kl} and E_k(b), k,l\in[0,n)
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for (u = 1; u < hd->L; ++u) {
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FLOAT *fu = hd->f[u], *bu = hd->b[u], *bu1 = hd->b[u+1], ss = hd->s[u];
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FLOAT *Ec = he->E[(int)hd->seq[u]], **p = hp->ae + (int)hd->seq[u+1] * n;
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for (k = 0; k != n; ++k) {
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FLOAT *q = p[k], *AA = he->A[k], fuk = fu[k];
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for (l = 0; l != n; ++l) // this is cache-efficient
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AA[l] += fuk * q[l] * bu1[l];
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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;
|
||
|
|
}
|