--- /dev/null
+#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;
+}
--- /dev/null
+#ifndef AC_SCHMM_H_
+#define AC_SCHMM_H_
+
+/*
+ * Last Modified: 2008-03-10
+ * Version: 0.1.0-8
+ *
+ * 2008-03-10, 0.1.0-8: make icc report two more "VECTORIZED"
+ * 2008-03-10, 0.1.0-7: accelerate for some CPU
+ * 2008-02-07, 0.1.0-6: simulate sequences
+ * 2008-01-15, 0.1.0-5: goodness of fit
+ * 2007-11-20, 0.1.0-4: add function declaration of hmm_post_decode()
+ * 2007-11-09: fix a memory leak
+ */
+
+#include <stdlib.h>
+
+#define HMM_VERSION "0.1.0-7"
+
+#define HMM_FORWARD 0x02
+#define HMM_BACKWARD 0x04
+#define HMM_VITERBI 0x40
+#define HMM_POSTDEC 0x80
+
+#ifndef FLOAT
+#define FLOAT double
+#endif
+#define HMM_TINY 1e-25
+#define HMM_INF 1e300
+
+typedef struct
+{
+ int m, n; // number of symbols, number of states
+ FLOAT **a, **e; // transition matrix and emitting probilities
+ FLOAT **ae; // auxiliary array for acceleration, should be calculated by hmm_pre_backward()
+ FLOAT *a0; // trasition matrix from the start state
+} hmm_par_t;
+
+typedef struct
+{
+ int L;
+ unsigned status;
+ char *seq;
+ FLOAT **f, **b, *s;
+ int *v; // Viterbi path
+ int *p; // posterior decoding
+} hmm_data_t;
+
+typedef struct
+{
+ int m, n;
+ FLOAT Q0, **A, **E, *A0;
+} hmm_exp_t;
+
+typedef struct
+{
+ int l, *obs;
+ FLOAT *thr;
+} hmm_gof_t;
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+ /* initialize and destroy hmm_par_t */
+ hmm_par_t *hmm_new_par(int m, int n);
+ void hmm_delete_par(hmm_par_t *hp);
+ /* initialize and destroy hmm_data_t */
+ hmm_data_t *hmm_new_data(int L, const char *seq, const hmm_par_t *hp);
+ void hmm_delete_data(hmm_data_t *hd);
+ /* initialize and destroy hmm_exp_t */
+ hmm_exp_t *hmm_new_exp(const hmm_par_t *hp);
+ void hmm_delete_exp(hmm_exp_t *he);
+ /* Viterbi, forward and backward algorithms */
+ FLOAT hmm_Viterbi(const hmm_par_t *hp, hmm_data_t *hd);
+ void hmm_pre_backward(hmm_par_t *hp);
+ void hmm_forward(const hmm_par_t *hp, hmm_data_t *hd);
+ void hmm_backward(const hmm_par_t *hp, hmm_data_t *hd);
+ /* log-likelihood of the observations (natural based) */
+ FLOAT hmm_lk(const hmm_data_t *hd);
+ /* posterior probability at the position on the sequence */
+ FLOAT hmm_post_state(const hmm_par_t *hp, const hmm_data_t *hd, int u, FLOAT *prob);
+ /* posterior decoding */
+ void hmm_post_decode(const hmm_par_t *hp, hmm_data_t *hd);
+ /* expected counts of transitions and emissions */
+ hmm_exp_t *hmm_expect(const hmm_par_t *hp, const hmm_data_t *hd);
+ /* add he0 counts to he1 counts*/
+ void hmm_add_expect(const hmm_exp_t *he0, hmm_exp_t *he1);
+ /* the Q function that should be maximized in EM */
+ FLOAT hmm_Q(const hmm_par_t *hp, const hmm_exp_t *he);
+ FLOAT hmm_Q0(const hmm_par_t *hp, hmm_exp_t *he);
+ /* simulate sequences */
+ char *hmm_simulate(const hmm_par_t *hp, int L);
+#ifdef __cplusplus
+}
+#endif
+
+static inline void **calloc2(int n_row, int n_col, int size)
+{
+ char **p;
+ int k;
+ p = (char**)malloc(sizeof(char*) * n_row);
+ for (k = 0; k != n_row; ++k)
+ p[k] = (char*)calloc(n_col, size);
+ return (void**)p;
+}
+
+#endif
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