List objectivex(const arma::mat& transition, NumericVector emissionArray,
const arma::vec& init, IntegerVector obsArray, const arma::imat& ANZ,
IntegerVector emissNZ, const arma::ivec& INZ, const arma::ivec& nSymbols,
const arma::mat& coef, const arma::mat& X, arma::ivec& numberOfStates,
int threads) {
IntegerVector eDims = emissionArray.attr("dim"); //m,p,r
IntegerVector oDims = obsArray.attr("dim"); //k,n,r
arma::cube emission(emissionArray.begin(), eDims[0], eDims[1], eDims[2], false, true);
arma::icube obs(obsArray.begin(), oDims[0], oDims[1], oDims[2], false, true);
arma::icube BNZ(emissNZ.begin(), emission.n_rows, emission.n_cols - 1, emission.n_slices, false, true);
unsigned int q = coef.n_rows;
arma::vec grad(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
arma::fill::zeros);
arma::mat weights = exp(X * coef).t();
if (!weights.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
weights.each_row() /= sum(weights, 0);
arma::mat initk(emission.n_rows, obs.n_slices);
for (unsigned int k = 0; k < obs.n_slices; k++) {
initk.col(k) = init % reparma(weights.col(k), numberOfStates);
}
arma::cube alpha(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
arma::cube beta(emission.n_rows, obs.n_cols, obs.n_slices); //m,n,k
arma::mat scales(obs.n_cols, obs.n_slices); //m,n,k
arma::sp_mat sp_trans(transition);
internalForwardx(sp_trans.t(), emission, initk, obs, alpha, scales, threads);
if (!scales.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
internalBackwardx(sp_trans, emission, obs, beta, scales, threads);
if (!beta.is_finite()) {
grad.fill(-arma::math::inf());
return List::create(Named("objective") = arma::math::inf(), Named("gradient") = wrap(grad));
}
arma::ivec cumsumstate = arma::cumsum(numberOfStates);
arma::mat gradmat(
arma::accu(ANZ) + arma::accu(BNZ) + arma::accu(INZ) + (numberOfStates.n_elem- 1) * q,
obs.n_slices, arma::fill::zeros);
#pragma omp parallel for if(obs.n_slices >= threads) schedule(static) num_threads(threads) \
default(none) shared(q, alpha, beta, scales, gradmat, nSymbols, ANZ, BNZ, INZ, \
numberOfStates, cumsumstate, obs, init, initk, X, weights, transition, emission)
for (int k = 0; k < obs.n_slices; k++) {
int countgrad = 0;
// transitionMatrix
if (arma::accu(ANZ) > 0) {
for (int jj = 0; jj < numberOfStates.n_elem; jj++) {
arma::vec gradArow(numberOfStates(jj));
arma::mat gradA(numberOfStates(jj), numberOfStates(jj));
int ind_jj = cumsumstate(jj) - numberOfStates(jj);
for (int i = 0; i < numberOfStates(jj); i++) {
arma::uvec ind = arma::find(ANZ.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1));
if (ind.n_elem > 0) {
gradArow.zeros();
gradA.eye();
gradA.each_row() -= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1);
gradA.each_col() %= transition.row(ind_jj + i).subvec(ind_jj, cumsumstate(jj) - 1).t();
for (int j = 0; j < numberOfStates(jj); j++) {
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
double tmp = alpha(ind_jj + i, t, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_jj + j, obs(r, t + 1, k), r);
}
gradArow(j) += tmp * beta(ind_jj + j, t + 1, k) / scales(t + 1, k);
}
}
gradArow = gradA * gradArow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradArow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(BNZ) > 0) {
// emissionMatrix
for (unsigned int r = 0; r < obs.n_rows; r++) {
arma::vec gradBrow(nSymbols(r));
arma::mat gradB(nSymbols(r), nSymbols(r));
for (unsigned int i = 0; i < emission.n_rows; i++) {
arma::uvec ind = arma::find(BNZ.slice(r).row(i));
if (ind.n_elem > 0) {
gradBrow.zeros();
gradB.eye();
gradB.each_row() -= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1);
gradB.each_col() %= emission.slice(r).row(i).subvec(0, nSymbols(r) - 1).t();
for (int j = 0; j < nSymbols(r); j++) {
if (obs(r, 0, k) == j) {
double tmp = initk(i, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, 0, k), r2);
}
}
gradBrow(j) += tmp * beta(i, 0, k) / scales(0, k);
}
for (unsigned int t = 0; t < (obs.n_cols - 1); t++) {
if (obs(r, t + 1, k) == j) {
double tmp = beta(i, t + 1, k) / scales(t + 1, k);
for (unsigned int r2 = 0; r2 < obs.n_rows; r2++) {
if (r2 != r) {
tmp *= emission(i, obs(r2, t + 1, k), r2);
}
}
gradBrow(j) += arma::dot(alpha.slice(k).col(t), transition.col(i)) * tmp;
}
}
}
gradBrow = gradB * gradBrow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradBrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
}
if (arma::accu(INZ) > 0) {
for (int i = 0; i < numberOfStates.n_elem; i++) {
int ind_i = cumsumstate(i) - numberOfStates(i);
arma::uvec ind = arma::find(
INZ.subvec(ind_i, cumsumstate(i) - 1));
if (ind.n_elem > 0) {
arma::vec gradIrow(numberOfStates(i), arma::fill::zeros);
for (int j = 0; j < numberOfStates(i); j++) {
double tmp = weights(i, k);
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(ind_i + j, obs(r, 0, k), r);
}
gradIrow(j) += tmp * beta(ind_i + j, 0, k) / scales(0, k);
}
arma::mat gradI(numberOfStates(i), numberOfStates(i), arma::fill::zeros);
gradI.eye();
gradI.each_row() -= init.subvec(ind_i, cumsumstate(i) - 1).t();
gradI.each_col() %= init.subvec(ind_i, cumsumstate(i) - 1);
gradIrow = gradI * gradIrow;
gradmat.col(k).subvec(countgrad, countgrad + ind.n_elem - 1) = gradIrow.rows(ind);
countgrad += ind.n_elem;
}
}
}
for (int jj = 1; jj < numberOfStates.n_elem; jj++) {
int ind_jj = (cumsumstate(jj) - numberOfStates(jj));
for (int j = 0; j < emission.n_rows; j++) {
double tmp = 1.0;
for (unsigned int r = 0; r < obs.n_rows; r++) {
tmp *= emission(j, obs(r, 0, k), r);
}
if ((j >= ind_jj) & (j < cumsumstate(jj))) {
gradmat.col(k).subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) += tmp
* beta(j, 0, k) / scales(0, k) * initk(j, k) * X.row(k).t() * (1.0 - weights(jj, k));
} else {
gradmat.col(k).subvec(countgrad + q * (jj - 1), countgrad + q * jj - 1) -= tmp
* beta(j, 0, k) / scales(0, k) * initk(j, k) * X.row(k).t() * weights(jj, k);
}
}
}
}
return List::create(Named("objective") = -arma::accu(log(scales)),
Named("gradient") = wrap(-sum(gradmat, 1)));
}
