void mexFunction( int nlhs, mxArray *plhs[] , int nrhs, const mxArray *prhs[] )
{
double *PI , *A, *L ;
double *alpha, *beta, *gamma, *loglik, *xi_summed;
const int *dimsPI , *dimsA , *dimsL ;
int K , N , numdimsPI , numdimsA , numdimsL , filter = 2;
double *scale, *tmp_xi;
/*---------------------------------------------------------------*/
/*---------------------- PARSE INPUT ----------------------------*/
/*---------------------------------------------------------------*/
if( (nrhs < 3) | (nrhs >5))
{
mexErrMsgTxt("3 or 4 input are requiered");
}
PI = mxGetPr(prhs[0]);
numdimsPI = mxGetNumberOfDimensions(prhs[0]);
dimsPI = mxGetDimensions(prhs[0]);
if ( (numdimsPI != 2) | (dimsPI[1] > dimsPI[0]) )
{
mexErrMsgTxt("PI must be (N x 1)");
}
A = mxGetPr(prhs[1]);
numdimsA = mxGetNumberOfDimensions(prhs[1]);
dimsA = mxGetDimensions(prhs[1]);
if ( (numdimsA != 3) | (dimsA[1] != dimsA[0]) )
{
mexErrMsgTxt("A must be (N x N x K-1)");
}
L = mxGetPr(prhs[2]);
numdimsL = mxGetNumberOfDimensions(prhs[2]);
dimsL = mxGetDimensions(prhs[2]);
if ( (numdimsL != 2) | (dimsL[0] != dimsA[0]) )
{
mexErrMsgTxt("L must be (N x K)");
}
N = dimsL[0];
K = dimsL[1];
if (nrhs == 4)
{
filter = (int)mxGetScalar(prhs[3]);
}
/*---------------------------------------------------------------*/
/*---------------------- PARSE OUTPUT ---------------------------*/
/*---------------------------------------------------------------*/
plhs[0] = mxCreateDoubleMatrix(N , K , mxREAL);
alpha = mxGetPr(plhs[0]);
plhs[1] = mxCreateDoubleMatrix(N , K , mxREAL);
gamma = mxGetPr(plhs[1]);
plhs[2] = mxCreateDoubleMatrix(1 , 1 , mxREAL);
loglik = mxGetPr(plhs[2]);
if (filter > 0) { /*calculate beta*/
plhs[3] = mxCreateDoubleMatrix(N , K , mxREAL);
beta = mxGetPr(plhs[3]);
}
if (filter > 1) { /*calculate xi_summed*/
plhs[4] = mxCreateDoubleMatrix(N , N , mxREAL);
xi_summed = mxGetPr(plhs[4]);
}
/*---------------------------------------------------------------*/
/*--------- Internal Tempory vector & matrices ------------------*/
/*---------------------------------------------------------------*/
scale = (double *)mxMalloc(K*sizeof(double));
tmp_xi = (double *)mxMalloc(N*N*sizeof(double));
/*---------------------------------------------------------------*/
/*------------------------ MAIN CALL ----------------------------*/
/*---------------------------------------------------------------*/
ForwardWithScale(N, K, filter, PI, A, L, alpha, gamma, loglik, scale);
if (filter > 0) /*calculate both alpha and beta, but xi_summed is not calculated*/
BackwardWithScale(N, K, PI, A, L, beta);
if (filter == 1) /*calculate gamma with alpha and beta*/
ComputeGamma(N, K, alpha, beta, gamma);
if (filter > 1) /*calculate gamma and xi_summed based on xi*/
ComputeXi(N, K, A, L, alpha, beta, gamma, tmp_xi, xi_summed);
/*---------------------------------------------------------------*/
/*------------------------ FREE MEMORY --------------------------*/
/*---------------------------------------------------------------*/
mxFree(scale);
mxFree(tmp_xi);
}
void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma)
{
int i, j, k;
int t, l = 0;
double probf, probb, val, threshold;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, probprev;
double ratio;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &probf);
BackwardWithScale(phmm, T, O, beta, scale, &probb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
probprev = probf;
do {
/* reestimate frequency of state i in time t=1 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* reestimate transition matrix and symbol prob in
each state */
for (i = 1; i <= phmm->N; i++) {
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++) {
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++) {
numeratorB = 0.0;
for (t = 1; t <= T; t++) {
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &probf);
BackwardWithScale(phmm, T, O, beta, scale, &probb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
delta = probf - probprev;
ratio = delta/deltaprev;
probprev = probf;
deltaprev = delta;
l++;
}
while (ratio > DELTA);
printf("num iterations: %d\n", l);
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}
void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma, int *pniter,
double *plogprobinit, double *plogprobfinal)
{
int i, j, k;
int t, l = 0;
double logprobf, logprobb, threshold;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, logprobprev;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
*plogprobinit = logprobf; /* log P(O |intial model) */
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
logprobprev = logprobf;
do {
/* reestimate frequency of state i in time t=1 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* reestimate transition matrix and symbol prob in
each state */
for (i = 1; i <= phmm->N; i++) {
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++) {
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++) {
numeratorB = 0.0;
for (t = 1; t <= T; t++) {
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
/* compute difference between log probability of
two iterations */
delta = logprobf - logprobprev;
logprobprev = logprobf;
l++;
}
while (delta > DELTA); /* if log probability does not
change much, exit */
*pniter = l;
*plogprobfinal = logprobf; /* log P(O|estimated model) */
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}
/******************************************************************************
**函数名称：BaumWelch
**功能：BaumWelch算法
**参数：phmm：HMM模型指针
** T：观察序列长度
** O：观察序列
** alpha，beta，gamma，pniter均为中间变量
** plogprobinit：初始概率
** plogprobfinal: 最终概率
**/
void BaumWelch(HMM *phmm, int T, int *O, double **alpha, double **beta,
double **gamma, int *pniter,
double *plogprobinit, double *plogprobfinal)
{
int i, j, k;
int t, l = 0;
double logprobf, logprobb;
double numeratorA, denominatorA;
double numeratorB, denominatorB;
double ***xi, *scale;
double delta, deltaprev, logprobprev;
deltaprev = 10e-70;
xi = AllocXi(T, phmm->N);
scale = dvector(1, T);
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
*plogprobinit = logprobf; /* log P(O |初始状态) */
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
logprobprev = logprobf;
do {
/* 重新估计 t=1 时，状态为i 的频率 */
for (i = 1; i <= phmm->N; i++)
phmm->pi[i] = .001 + .999*gamma[1][i];
/* 重新估计转移矩阵和观察矩阵 */
for (i = 1; i <= phmm->N; i++)
{
denominatorA = 0.0;
for (t = 1; t <= T - 1; t++)
denominatorA += gamma[t][i];
for (j = 1; j <= phmm->N; j++)
{
numeratorA = 0.0;
for (t = 1; t <= T - 1; t++)
numeratorA += xi[t][i][j];
phmm->A[i][j] = .001 +
.999*numeratorA/denominatorA;
}
denominatorB = denominatorA + gamma[T][i];
for (k = 1; k <= phmm->M; k++)
{
numeratorB = 0.0;
for (t = 1; t <= T; t++)
{
if (O[t] == k)
numeratorB += gamma[t][i];
}
phmm->B[i][k] = .001 +
.999*numeratorB/denominatorB;
}
}
ForwardWithScale(phmm, T, O, alpha, scale, &logprobf);
BackwardWithScale(phmm, T, O, beta, scale, &logprobb);
ComputeGamma(phmm, T, alpha, beta, gamma);
ComputeXi(phmm, T, O, alpha, beta, xi);
/* 计算两次直接的概率差 */
delta = logprobf - logprobprev;
logprobprev = logprobf;
l++;
}
while (delta > DELTA); /* 如果差的不太大，表明收敛，退出 */
*pniter = l;
*plogprobfinal = logprobf; /* log P(O|estimated model) */
FreeXi(xi, T, phmm->N);
free_dvector(scale, 1, T);
}